ENERGY LABORATORY
INFORMA iON CENTER
Energy Laboratory
in association with
Heat Transfer Laboratory,
Department of Mechanical Engineering
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
IMPROVING HEAT PUMP PERFORMANCE
VIA COMPRESSOR CAPACITY CONTROL ANALYSIS AND TEST,
Volume II:
Appendices
by
Carl C. Hiller
and Leon R. Glicksman
Energy Laboratory Report No. MIT-EL 76-002
Heat Transfer Laboratory Report No. 24525-96, Vol. II
January 1976
I
Energy Laboratory
in association with
Heat Transfer Laboratory,
Department of Mechanical Engineering
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
IMPROVING HEAT PUMP PERFORMANCE
VIA COMPRESSOR CAPACITY CONTROL ANALYSIS AND TEST,
Volume II:
Appendices
by
Carl C. Hiller
and Leon R. Glicksman
Energy Laboratory Report No. MIT-EL 76-002
Heat Transfer Laboratory Report No. 24525-96, Vol. II
January 1976
ii
ii
TABLE OF CONTENTS
PAGE
APPENDIX A
205
THERMOPHYSICAL PROPERTIES OF REFRIGERANTS
APPENDIX
B
CARRIER
APPENDIX
229
0
MODEL 50 DQ SERIES SINGLE PACKAGE HEAT PUMPS
C
238
SAMPLE THERMODYNAMIC CYCLE DATA FROM SYSTEM SIMULATIONS-CONVENTIONAL VS.CAPACITY CONTROLLED HEAT PUMP
APPENDIX
D
245
DETAILS OF SYSTEM FLOW BALANCE MODELING
APPENDIX
E
263
DETAILS OF COMPRESSOR SIMULATION MODEL
APPENDIX
F
317
REFRIGERANT-OIL SOLUBILITY
APPENDIX
G
321
COMPRESSOR DATA
APPENDIX
H
325
PARAMETRIC STUDIES ON CARRIER 06D-537 COMPRESSOR
APPENDIX
I
330
DETAILS OF AIR-COOLED, CROSS-FLOW CONDENSER MODELING
APPENDIX
J
COMPLEMENTS TO HEAT EXCHANGER ANALYSIS
· Overall Surface Efficiency
. Cross-Flow Effectiveness
361
I
iii
PAGE
APPENDIX K
370
HEAT TRANSFER COEFFICIENTS
· Condensation Two-Phase
. Evaporation Two-Phase
· Single! Phase
APPENDIX
L
381
PRESSURE DROP RELATIONS
·
·
·
·
Two Phase
Single Phase in Heat Exchangers
Single Phase Line Pressure Drops
Air Side
APPENDIX M
397
DETAILS OF CROSS-FLOW EVAPORATOR MODELING
APPENDIX N
434
CAPACITY CONTROLLED 50 DQ 016 STUDIES
APPENDIX 0
437
HEAT PUMP PERFORMANCE DATA FOR LOAD LINE "D" STUDIES
APPENDIX P
WEATHER DATA
442
Ii
iv
LIST OF FIGURES
FIGURE
PAGE
A-1
VISCOSITY OF REFRIGERANT 12
208
A-2
THERMAL CONDUCTIVITY OF REFRIGERANT 12
208
A-3
VISCOSITY OF REFRIGERANT 22
209
A-4
THERMAL CONDUCTIVITY OF REFRIGERANT 22
209
A-5
SPECIFIC HEAT AT CONSTANT PRESSURE OF REFRIGERANT 12
210
A-6
SPECIFIC HEAT AT CONSTANT PRESSURE OF REFRIGERANT 22
210
B-1
INDOOR COIL - CARRIER MODEL 50 DQ 016 HEAT PUMP
235
B-2
OUTDOOR COIL - CARRIER MODEL 50 DQ 016 HEAT PUMP
236
B-3
CHARGING CHARTS - CARRIER MODEL 50 DQ 016 HEAT
PUMP DURING HEATING MODE
237
C-1
EXAGGERATED P-h DIAGRAM OF ACTUAL HEAT PUMP CYCLE
243
C-2
CYLINDER P-V DIAGRAMS
244
a.
b.
CONVENTIONAL HEAT PUMP
CAPACITY CONTROLLED HEAT PUMP
D-1
FLOW CHART FOR SYSTEM FLOW BALANCE MODEL
251
E-1
DEFINITION OF COMPRESSOR CAPACITY
289
E-2
FLOW CHART FOR COMPRESSOR MODEL
290
F-1
COMPARISON OF ACTUAL AND PREDICTED REFRIGERANT
12 - OIL SOLUBILITY
320
F-2
COMPARISON OF ACTUAL AND PREDICTED REFRIGERANT
22 - OIL SOLUBILITY
320
I-1
DIMENSIONS FOR FINNED TUBE HEAT EXCHANGER WITH
STAGGERED ROUND TUBES
344
I-2
FLOW CHART FOR GENERAL CONDENSER MODEL -
345
'EXCH'
i
V
FIGURE
PAGE
I-3
FLOW CHART FOR FINNED TUBE CONDENSER MODEL
346
J-1
FINNED SURFACE
361
J-2
ELECTRICAL ANALOGY OF FINNED SURFACE
362
J-3
CROSS-FLOW EFFECTIVENESS, BOTH FLUIDS UNMIXED
367
K-1
HEAT'TRANSFER CORRELATION FOR SINGLE PHASE FLOW
INSIDE CIRCULAR TUBES
376
K-2
AIR SIDE HEAT TRANSFER CORRELATION FOR CROSS-FLOW
OVER BANKS OF FINNED CIRCULAR TUBES
376
L-1-
MOODY FRICTION FACTOR FOR FLOW IN CIRCULAR PIPES
391
L-2
KAYS & LONDON AIR SIDE FRICTION FACTOR CORRELATION
FOR CROSS FLOW OVER BANKS OF FINNED CIRCULAR TUBES
392
L-3
IMPROVED AIR SIDE FRICTION FACTOR CORRELATION FOR
CROSS FLOW OVER BANKS OF FINNED CIRCULAR TUBES,
392
BY HILLER
M-1
FLOW CHART FOR GENERAL EVAPORATOR MODEL 'EVAP'
410
M-2
FLOW CHART FOR FINNED TUBE EVAPORATOR MODEL
413
205
APPENDIX A
THERMOPHYSICAL PROPERTIES
Presented
OF REFRIGERANTS
here are curve fits and computer programs for producing
thermophysical properties of refrigerants 12, 22, and 502 from basic
equations.
Program listings are given at.the end of this section.
Plots of viscosity, thermal conductivity, and specific heat for
refrigerants 12 and 22 are given in Figures
A-1
through A-6 1'o
Curve fits for the above properties in both the liquid and vapor states
are indicated on the
figures.
The following thermodynamic properties subroutines have been
modified from Kartsounes & Erth, 'Computer Calculation of the Thermo-
dynamic Properties of Refrigerants
12,
22 and 502 ' 3 .
The programs
produce values of enthalpy, entropy, specific volume, specific heat,
sonic velocity, pressure, and temperature.
The. Kartsounes & Erth
programs have been checked and were found to be highly accurate, with
the exception of a possible convergence problem near the critical point.
Subroutine TABLES
TABLES is a simple program which, when called upon by the other
thermodynamic properties programs, delivers (into common) the constants
necessary to calculate thermodynamic properties from basic equations.
See comments in the listing for details.
Subroutine TSAT
TSAT is a program which produces the saturation temperature of
206
a refrigerant corresponding to a given saturation pressure.
See
comments in the listing for details.
Subroutine SPVOL
SPVOL is a program which calculates specific volume of the
vapor phase, given temperature and pressure.
See comments in the
listing for details.
Subroutine SATPRP
SATPRP is a program which, given saturation temperature, determines
the corresponding saturation properties:
PSAT -
saturationpressure
VF
-
specific volume of saturated liquid
VG
-
specific volume of saturated vapor
HF
-
enthalpy of saturated liquid
BFG
-
latent enthalpy of vaporization
KG
-
enthalpy of saturated vapor
SF
-
entropy of saturated lquid
SG
-
entropy of saturated vapor
See comments in the listing for
more details.
Subroutine VAPOR
VAPOR is
a program which determines specific volume, enthalpy,
and entropy of superheated vapor, given the temperature and pressure.
See comments in the listing for details.
207
Subroutine SPFHT
SPFffr is a program which, given temperature and pressure,
determines the following:
CV
-
specific heat at constant volume
CP
-
specific heat at constant pressure
GAMMA
-
specific heat ratio CP/CV
SONIC
- sonic velocity
Subroutine TRIAL
TRIAL is a program which, given pressure and one other property
(temperature, specific volume, enthalpy or entropy), determines the
remaining superheated vapor properties.
See comments in the listing
for more details.
REFERENCES
1.
ASHRAE HANDBOOK OF FUNDAMENTALS (New York: American Soco of Heat.,
Refg., & Air-Cond.Eng., Inc., 1972).
2.
THERMOPHYSICAL PROPERTIES OF REFRIGERANTS (New York:
Soc. of Heat, Refg. & Air-Cond. Eng., Inc., 1973)o
3.
Kartsounes, G. T., and Erth, R. A., "Computer Calculation of the
Thermodynamic Properties of Refrigerants 12, 22, and 502", ASHRAE
Transactions, Vol. 77, Part I, 1971.
American
208
Q
* C
.7
.6
.5
Satura
Viscosity
lbm
hr-ft
.4
.3
.2
P=
.1
14.7
U
P
-100
.
-60
-20
20
60
100
Temperature (F)
n
r zi n
_-
I
I
.
140
180
220
260
--
*Ub
FIGURE A-2
OF
THERMAL CONDUCTIVITY
.05
REFRIGERANT 12
I
.04
Thermal
Conduct
Saturated Liquid
(.00012)T+ .048
k
t('F)
.03
Btu
hr-ft-°F
9
.02
.01
Saturated Vaporr F)
k
=
(.0000175)T+ .00435
_
..
_
-
-
O
-100
-60
-20
20
60
Temperature (F)
100
140
-
180
220
260
209
.8
.7
FIGURE A-3
.6
VISCOSITy OF REFRIGERANT 22
.5
Viscosity
Saturated Liquid
ibm
.4
P
hr-ft
=-(5.625xl0
.3
.2
8)
T3
+(1.525xlO
5) T2
-(2.982x10
3
) T
+(.646)
(OF)
Saturated Vapor
tV = (.0000759)T
.1
+ .0272
14.7
psia
o-i
-1(
uv
rl~~n
-Dv
_X~~~~n~_ _
-Zo
20
60
100
Temperature (F)
140
180
220
260
-
^ I
.Vo
fi
Thermal
Conduct.
A-4
.05
.04
-I
JCTIVITY OF
22
r
Saturate
k = (-.
.03
Btu
hr-ft-OF
02
sj
.£
. 01
k
o0
-100
CP
k
_CP
a
-60
-20
20
60
lemperature (F)
100
140
-
180
220
__-- _
2?XI
.v
210
I
.6
Z = saturated liquid
.5
v = saturated vapor
.4
C_
,,
C
p
= (.000482)P + .
,
-
Btu
lbm-°R .3
- .00149
.2
-- (ps a)
,-- (psia)
.1
0
0
100
200
300
Pressure (psia)-
400I
500
600
-
SPECIFIC HEAT AT CONSTANT PRESSURE OF REFRIGERANT 12
FIGURE A-5
.5
2 = saturated lic
v = saturated val
.4
f
C
p
.3
Btu
Ibm-°R .2
(psia)
)P + .2575
.1
sO
0
100
200
300
Pressure (psia) --
400
500
600
SPECIFIC HEAT AT CONSTANT PRESSURE OF REFRIGERANT 22
FIGURE A-6
211
SUeROfTINE TAPeLES(NR IJ
C
C
C
PLFFCSE
TC PRCVIDE
CCRRECT
FCR
VALLES
CONSTANTS
IN
THE
FROPERTIES SPRCGRAMS,
CORRESPONDING
tMERVCCyN'IC
'CR 502)
TC TE CESIRC REFRIGERANT (12,22,
C
C
C
C
C
CF PARAMETERS
CESCRIPTICN
INPLT
C
-
NR
C
NUrBER
REFRtGERANT
(12s22,
OR 502)
CGTFUT
CCNSTANTS HELC IN COMrON
ALL CF T
ThE REFRIGERANT INCICATCR
It
C
C
LOCKS
REAL KLE1eL12F,j
C
C
CF
CESCRIPTICN
CNSTANTS
C
C
VAPCR FRESSLRE
CONSTANTS
CCPM~CN/SAT/AvF,
pvPCVPVPEVPFVP
C
CRITICAL
C
FCINT
C
INITIAL
C
rISCE'LLANCLs
PC,
CCNSTANTS
APFrCxIMATION
CCSTASrTS
Tr PC vC AB
COrrCN/SFPEN,
TC,
PROPERTIES
TR,
A,
VC
B
LE1C
TFR, LE
C
C
ECLATICN
CF STATE CONSTANTS
CCPrCN/STATE/R,
E 1, A2dc,
23
3
C333A
B4, C4J A5, B5,
1C5A6,AE6sC6,KJAI FACFPR
C
C
SPECIFIC
C
ACVBCVCCVPCVECVFCV
C
ENTHALFY
C
VISCELLANECUL
-EAT
ANC
AT CCNSTANT
ENTROPY
OF
VAPOR
CSTANTS
COfrCN/CTi-ER/ACv
LIOE,
SET REFRIGERANT
IIF(NREGI!2)
1i
IF(NR*EGE2)
INCICATOR
I=p
IF(KREC,502) I.3
IF(I*EG,)
L1CE
GC
T
599
."44294
LE10 = 2.32585
GO
TC(l1C;'E3£
C CONSTANTS
2e
VF
eVF w
FCf
3,836
I
REFRIsERANT
17
3436.*6C32
CCNSTANTS
CONSTANTS
12
I
X,
J
CVCCV, CCVECVFCV,
IWRITE
C
VOLLME
X YL10E, J
Y
212
CVP - 12*471522
CVF 4,7344E.3
EVF
FV
TC
a eC
= C oe
a 63
*
PC - 5S6 .'t
VC
A ·
e '
*e87¢
12e.£
312,E
TFF
R
459,7
.C82734
61 = 6,5ic38SE-73
A2
-33.4tS727
B2 = 1.ob430,E3
C2
-56*762767
A3 = 6.E3cS4E-vl 2
3
-1.7561i.E5
C3 = l3i139
A4 a -594b?7tiE.4
e4 swe
C5 w -2*535V7E-e5
At
C6
K
0~,0
=
8.8
5*475
ALPHA
CPR a
ACV a
ECv
CCV =
GCv
a e*
9 45Eme
3.3266EE--,4
8.
-2.41363=F11e7
6,72363E-
1
ECv . f .
FCV
=
X
39.56551
Y
-1,*653794E-2
,£
RETLRN
C CONSTANTS FC RLEFEIGERANT 22
U
AVF *2,S357545
BVF - -3845133152
CVP a -
7861£3i
CVP 21se93sE.e3
EVF = .445747
FVF
.6
TC = 664'
PL
I.1
721.0e6
vC a .~3f25
A '
182g£
213
e a 38ado
TFR a 455.69
R * 124~8
AZ * -4s.53547
E2 - 2*4e7E5c2E-?3
C2
-m44,L66868
A3 a -. i:7464
E3 a 796E78SE-eS
C3 - 1*b,~3763
A4 = 2a.lo+j2.=v3
4 * -3.eQ5723E.e6
C4
L
C
A5 - -3*724C4E25
C5 * -a tE6bl£-e
Ab* 1t:3387E.^
Eb = -17E61.E5
C6 , g.
K * 4.2
ALFhA a 548*2
CPR * Co
.E1283eE-.e2
ACV =
ECV- 2.i545.E.e4
CCV a -6*L'96Ve7F-e8
.,,
ECV
FCV. 27b.341
X
62,4CC9
Y
-4*5335E-e
RETLRfhN
C CONSTANTS FCR REFRInERANT
3
YAVP
= *1 Z 4455
E¥F a "3671,15-3A13
CVF ·
-
,3653;
CVP n -1.746--52F-E3
EVF * *816114
FVF n 654 90
TC - 639O'6
PC
VC
591'g'
.e2Ui-7l
A
117.g
B -
279.i
TFR, 455.67
r
; a*e9bF5
A2
3Z.61334
e2 a £.gC7625E-P3
C2 x -=24.4879
A3
346675.-92
502
21.4
b3 a -867913Et.5
C3 a '33E748
A4
-E, 5765&6E.e4
e4 = 7CE2405SE-o7
2,241237E-.Ec
C4
A5 *a bo. _65E7E-6
85 * =7*S166S~E.C9
C5
-377167cE.
A6
-3
2537
12-
Ev7
e6 . 551;65EZ
C6 = 1°53763ELZq
K
S
4.2
= 6gS .
ALF-A
CPR
ACV
a 7.E-7
= 2U,419E-e
ecv w i95c5t6EZ.e4
*.55e9l
gF't
2E.E1Z61E.11
CCV a
GCV
a
ECv a C.-
FCV, 64.5b511
X
Y a
35.3et
.C7444
RETURN
C
C
C
PRINt ERnCR
N
,' CCEC
NOT
ES5AGE IF
ELAL
12,22,
OR
5e2
999 *RITE(ImITE,12vZ)
leeO FCFr'AT('
RETURN
ENC
***-******ERRCR
IN SLBRCUTINE
*TABLES-')
215
FuNCTICh TSAT(?,pPSAT)
C
C
PLRPCSE
c
C
C
TC EVAL-UATE TE SATURATICN TErPERATURE
CF REFRIGERANT 12#22,
CR 52
GIVEN TE SATLRATICN PESSLRE
C
C
CESCRIPTICN
INPLT
C
C
Nh
a
PSAT a
c
CF FPARAMETERS
REFRTGERANT NLPEER (12E22,
SATLRATION PESSURE
(SIA)
OF 502)
CLTPLT
c
TSAT -
SATrFATICN
C
REtPAeK
C
SLERCLTINE
REAL LE1
TAELES
TErFERATLURE (F)
CALLEC
By
TIS
FUNCTION
C
C
CCKSTANT'S
C
C
'APCR
FRESSL.E
CGNSTANTS
CCPICN/SAT/AVP,
VP CVFjDvP,
EV
FVP
C
C
CRITICAL
C
INITIAL
C
PCINT
PRCFERTIES
APP-RcXIrATION
TC,
CONSTANTS
rISCELLANECLs
CONSTANTS
TFRP
CCPrrCN/SFERE
TrPC,VCJAa,TFRLE1e
VC
PC,
A,
LElO
B
IhITE
C
C
C
OBTAIN VALLES F TE CONSTANTS FOR THE
CESIREC REFkIGEPANT FROM SLERCUTINE
TABLES'
C
CUOrtCNi
(TfHCUG.
CALL TAB.LS(bRT)
C
C
CHECK
PATI
IF(PSAT.*LE.c.)
GO TO 999
C
C
C
CCrPLTE IITIAL
ESTIMATE CF
LINEAR AFFROXI'ATICN
PLCG
AlC/1t(PSAT)
TSAT'
FRCM
TRSA*PLCG
+
ITER .
2
C
C
ITERATE
1
TRC
*
TC WITPTK ,1
ITER - ITER
IF(ITER.GT.
C
USING NhETCN ITERATION
TR
1
3)
GO TO 998
ALCGIZ(AES(FVP
-
TRO))
F-AVF+VP/TRC+CVP*ALCGleTRO)+CVP*TRO+EVP*( (FVP-TC)/
ITROI)C-PLCG
216
FP=-evF/TRG**2+rvP/(LE10*TROI+CVP-EVP*(1./(LE10*TRC)+
1FVP*C/TRC**2)
.TR=TRO-F/FP
IF( ArS(TR-TRC)*rTv.
TSAT=TRTi
RETLRN
) GC TC
R
C
PRINT
C
ERRCR rES9AGE IF
FSAT I
NLPBEF
C
C
TO ZERO
LESS TAN CR ELAL
IS GREATER THAN
OF ITFRATIGNS
598 TSATTRwTFR
REITE(IehITEJ
10,
RETLRN
999 TSAT=o
(IITE,ie )
WRITE
le
FCkATT(lZX'lEHRkR
RETLN
E NC
IN CALLING SBRCUTINE
-TSAT
)
217
FUNCTICN SPVCL(KRTFPPSIA)
C
C
PL;PCS.E
SPECIFIC
VCLUIE
F THE VAPCR
C
TC EVALUATE
C
C
CF REF;IGERAKT 12,22 CR 52
AND TEMPERATURE
GIVEN TE PFSSLRE
rTE
PASE
C
C
C
INPUcT
C .N
-
a
PPSIA-
C
TF
C
C
C
pARAMETERS
CF
CESCRIPTICN
REFRTGERANT
NUMeER
TEtFFRATURE
(F)
OR 502)
(12,22i
PRLSSLRE (PSIA)
CLTrUT
SPFECTFIC VOLUME (Cu FT/LBM)
SPVCL
C
C
C
C
C
RErARKS
FLNCTICNh SBPRCGRAP TSAT CALLED BY THIS FUNCTICN
SLERCLTINE TAELES CALLED BY THIS SBROUTINE
REAL KILEle
CChSTANTS
C
TCP
C
CRITICAL PCINT PROPERTIES
C
C
CCNSTANTS
APFRCXIMATION
INITIAL
TFkR
CCNSTANTS
MISCELLANECLS
VC
PCs
A,
LE:0
B
,eTFRLEle
TrPC vC',AJ
CCr"MCN/SLFER/
C
C
EGLATICN
CF STATE CCNSTANTS
4
EJeEC2A,83,C3A
,AE,
CCCN/STATEG/R
B4C4
A5s
5,
lC5,A6*B6JC6JKsAr PhACFR
I"RITE
x
C
C
C
C6TAIN .VALUES O TE CONSTANTS CCRRESPONDING T
CESIREC EFRIGE';ANT FROM SUBRCUTINE TABLES
C
(TRCLGH
CALL
CCMrChN
TABLESl(NR
T)
C
C
TC
TF'
CCNVERT
TF + TFR
T
AND CFECK
'T'
VALUE
GO TC 995
IF(TLE.a)
C
C
TFSAT'
CALCLLATE
AND
GC TO 999
IF(TF,LT.(TFSAT..e5))
C
PPSIA'
CHiECK
IF(FPSIA'LEe.*et
G
C
C
COMPARE WITH
TFATxTSAT (NRPpSIA)
CALCLLATE
ESe
CONSTANTS
EXP(-K*T/rC)
TO
99S
TFI
TE
218
ESi-PPSIA
ES2 a R*T
ES3=A2+E2*T+C2*rS
ES4WA3*e3*T+C3*SF
ESnA4v;-w4*TC4*FCS
'.wT*C5
ES6-0St-5vT
sc
ES7wmA6*6eTrC6*F
ES3Z"2'
L'3
ES43 . *Et4
*-.5
ESE4=a4
C
ESTIMATE
CCt"FbTE INITIAL
C
V,,-T/FR
CCrPTE
1
*
V2
ITWIN 1.eE-e6
TC
tv'
ITER w ITLR
IF(ITER,GT*£C)
V
IDEAL GAS LAA
e
ITER
C
CF 'V' FROM
IA
BY NEWTCN
ITERATICN
+
nC
TO 998
VN
-
V**E
V3 " V*w3
Vd.
V5
V.21,4
,
V,*
V6 * V..6
Z * ALF-A*(V+El)
IF (ZGT1.5.)
7150te
ErAVEXF (-Z)
GGTC (2ir'3)I
2
FES1ESc/V-ES3/V2-ES4/V3-ES5/V4-ES6/v5-ES7*EMAV
F-.SES£/V+ESS3/v3V4+3/4/+ES/5ES65/V6+ES7*ALPkA*E
r1tAV
GC
3
4
TC
ErAV**E
Er2AV
FESl-ESi/V-E3/V2-ES4/EV3ES
5/V4"ES6/ 5ES7*E2Av/(E
1AV+CFR)
FV=ES2/VE+ES3//V3
3ES43/V4+ES54/V5+ES65/V6+ES7*ALPNA*E
1M2A (EtAV+,*Cc }/
4
AVCPR )**2
EFAV+
VN=VwF/Fv
IF(ABS((VN-V)/V)'GT1oE-06)
GO TG 1
hVN+61
SPVCL
Rf T LN
C
C
C
C
C
958
PRINT
ERRCH eEScAGE IF
TF IS
TF IS
PPSIA
PCRE
*N
SPVCL. =
LESS T~AN OR EQUAL To ZERO CEGREE R
LESS TkAN TFSAT CORRESPCNDING TO PSAT
IS LESs THAN OR EGbAL TC ZERC
ARE NEEDED
T-AN 3e ITERATIONS
+ E1
hRITE(IWRTES )
-
PPSIA
219
RETURN
999 SPVCL'e,
wRITE'(II
S
FC;r'AT('
RETLRN
.hC
TE,.S
****EpRCR
IN CALLING SLEROUTINE -SPVOL-1)
220
SLERCUTINE SATFRP(NRTFJPSATVFJVGjHFJHFG,
HGSFSG)
C
C
CDIPENSICh
ANC TYPE STATEMENTS
CIrEN SICN AL(3) .EL(3')CL(3
REAL jjKKTCTCI
E1iJLIoE
iL (3),EL(3)
C
C
PLRPCSE
C
TC EALUATE
C
CF
C
GIVEN TE
C
C
CESCRIPTICN
IPLT
C
C
N.R
-
TF
a
C
OUTPUT
C
TE
EFkIGEAtT
SATURATION TERMODYNAMIC
PROPERTIES
CR 52
12'P2'
SATLRATION TEMPERATURE
pARAMETERS
CF
REFRFGERANT NUrEER
TEPFPRATURE tF)
(12J22,
OR 502)
FPAT - SATURaTICN PRESSURE (PSIA)
C
vF
C
viG -
C
C
HF
a
w
C
f-FG
-
C
C
SF
SG
a
-
C
REP"AKS
*
SPECTFIC
VCLUrE OF SATLRATED LIQG(CU
SPECIFIC
VCLUrE CF SATURATED VAP.(CU FT/LBM)
FT/LEM)
ENTPfALFY CF SATUAATEL LICUID
(TU/LEM)
LATENT ENTHALPY CF VAPORIZATION
(BTU/LBM)
ENTHALPY OF SATUATE&
ENTRrPY
ENTRCPY
OF SATLRATED
OF SATLRATED
VAPOR (BTU/LB,
)
R)
- R)
(TU/Lbr
(BTU/LSB
LIULID
VAPCR
C
FLNCTiCN
C
C
C
SUERCLTINE TABLES CALLED by THIS SLBROUTINE
FLNCTICN SLEpRGGRA' TSAT AVAILABLE FR CALCULATING
THE SATLRATION TEMPFEATLUE GIVEN THE SATURATICN
C
PRESSLRE
SL~eROGRAM
SPVCL
CALLED
Y THIS
SUBRCUTINE
C
C
CChSTANTS
C
C
VAPCR PRESSURE CONSTANTS
COCPCN/SSAT/AVF,
pVP CVP
vP EVpFVP
C
C
CRITI.CAL PCINT PROPERTIES
C
INITIAL
C
rISCELLANECLs
AFPRFXIrATION
CCrCN/SLPER
C
ECUATICN
CCNSTANTS
TpFPCvCJAT
CF
TATE
PCs
TC,
CONSTANTS
TFR,
A
vC
B (NOT
USED)
LE10
TFRpLE1e
CONSTANTS
CCrrCN/STATEG/R.ei1A2JBZEC~2A3,B3,C3,A4,B4JC4JA5J85
1C5 A6,E6 eC6.KA
PA, CPR
C
C
SPECIFIC
C
ACVBC¥VCCVprCVECVFCV
C
ENTALFY
C
MISCELLANECUc
EAT
ANPC
AT CONSTANT
ENhTRPY
OF
CCNSTANTS
vOCLUME CCNSTANTS
VAPCR
CONSTANTS
L1OE,
J
X,
Y
221
CVECV, FCVJ X YLlEJ
CCMCk/CTrER/ACvBECvccvCC
C
C
CONSTANTS
EENSITY
LIG(LIC
: .0269654.*634409
CATA AL, eL CLCI JEL/34.84,.32.76J35.
6 .2683,-22 *2S256
74892,63.86417,
5
1,53.48437, 834c,36.
J.2 '47329. 48.47901/
26,-7.EC66, -. 6549EC
CBT4IN
CESIREC
(TIfCLGG
C
THE CONSTANTS
OF
VALUES
C
C
EFRIGE;ANT
CCRRESPONDING
TO TE
FRCF, SUeBROTINE TBLES
CMFCN
-
CALL TAILc S(NRhT)
IWRITEt
C
C
TC
CCNVERT 'TF'
T
TF + TFR
IFtT#LE*tZ*)
Te
AND C-ECK
VALUE
GC TO 99S
C
'TCt
IT,
iT,
CGMPARE
C
GC TC 999
IF(TGTTC!
C
C
PSAT,
CALCL.ATE
GC TCI1
1121l)
*S(AVF*pVP/T+CVP*ALGG
PSAT=i
1
GO TC
11
I
(T ) CVP*T)
12
PSATr1., *(AVP+*VP/T.CVP*ALCGIe(T)+CVPsT+EVP.
I
1/T l*ALCG1(FVP-))
(FVP-T)
C
CALCLLATE
C
12
'VG1
vG - SFVCL(NhTFPSAT)
C
CALCLLATE 'VF
C
GC
TC
T
(1*2*2)J
TC-T
I
(+
VFI/(AL(
TCMrT
eL I)*TCT+CL(
(I*/2*
I )TCT**
)DL( I )*TCm
)+LL(I i.*TCMT*2 )
1T* (1/3
GC TO 3
2 TI
1'-T/TC
VFI/(AL(
)+L
I )*TRI**I 1/3.
TRI** (4./3. )
( I ).TrR:+EL(I.)
)+CL(I )*TRI**(2,/3
+DL
C
C
3
31
CALCULAt t 'IFG'
GC TC(31,3232)
Y CLAUSILS
I
FC-t{VGVF ) FSATLEl*
CLAPEYRCN EQUATION
(wBVF/T+CVP/LEl+DVP*T ) J
GC TC 33
32 rFG-t (VCVF) wPSAPLEI1
IE+FVPOALCClIJ (FVW-T/T
I-FG/T
33 SFG
(-BVP/T+CVP/LEI+DVP*T-EVP
} ) ,J
C
C
CALCLATE
t2 Tc
'tG'
ANhD SG'
( L10
222
T3
T**
T4 a T**4
VR
VG-El
.*VR**-.
VRE -
3.'VR*-3
VR34
Vn4 a # . 99$$
KTCTC * h*T/TC
EKTCTC - EXP(-KtCTC)
Z
ALF~A*V$
IF(Z.GT.IlbzV)
E~A¥
7
5e*.
EXF(-Z)
5
FHIACVsT+cCVT2C/2+CCV*T3/3e+cCV*T4/4.-FCV/T
rZ
j*PSAT*vG
i-3pA/VR.+A3/Vkh2A4/VR3+A5/VR4
h4C2/V+/C3/
VRE++C'/ VR3*C5/VR4
Sl1ACV*ALCG T)+PCV*T*CCV*,2/2,+ULV*T3/39-FCV/(2,*T2)
S3rE2/¥R+ 3/VN2,B~/V3BS./VR~
S4
GC
4
I
I..3.Ia+A6/ALP-AmFtAV
S3*S a E6/ALPA *LrAV
GC
5
H 44
TC(6*,S5)
TC
h-Ze/ALFN-A*(EVAV-CPR*ALOG(I.+EMAV/CPR))
$S a
S3+et*Hc
S4 * S4-C6*.
6
mG,-l+-2*i,+J*EKCTC
(1+KTTC TC)*H4+X
S(-S1+'-waS3*.*EKTDTC*K/TC$e4+Y
C
C
CALCLLATE
F
*
'HF'
-FG
AND
SF'
SF a SL-SFQ
RETLRN
C
C
C
9S9
leeO
PRINT ERfCR PrESsAGE IF
TF IS LESS TAN OR EQUAL TC ZERO DEGREE R
TF IS GREATER ThAN TE CRITICAL TEMPERATURE
NHITEIvRhITE, le¢)
FGRAT(t
RETURN
ENC
*****ERRGR IN CALLING SUBROUTINE SATPRP-I)
223
SUERCLTINE SPFfT(NRTFPPSIAPCVCP,GAMASONIC)
C
C
C
PURCSE
TC CALCULATE
SPECIFIC
C
SPECIFIC
C
mEAT
C
REFRICERAi\T 12,22,
EAT
AT CCNSTANT
EAT AT CCNSTANT
ATIC,
NC
SONIC
RESSURE,
VELOCITY
VOLUME,
SPECIFIC
FCR
OR e2
C
C
C
C
C
C
CESCRIPTICN
INFLT
NR
'
TF
-
PPSIA-
CF PARAMETERS
HEFRTGERANT
TEPFRATUE
UreBER (12,22,
(F)
OR 5e2)
PRcS9SRE (PSIA)
C
OLTPFUT
C
CJ
C
CP
C
GArrA-
SFEC;FIC
C
SCNIC-
SCNIr VELCCITy (FPS)
SPECTFIC
-
SrECTFIC
EAT
hE.AT
t.AT
ArT.CCSTANT
AT
OL.
CCONSTANT
(BeU/Lef-R)
PRES.
(BTU/LEM-R)
fATIc
C
C
REPARKS
C
FLNCTICh
SLEPROGRAM SPvCL CALLED By THIS
C
FLNCTICN
SuBpPCGRAr
C
TSAT
CALLED
SBLRGCLTINE TABLES CALLED 8y
REAL
BY THIS
TfIS
SUBROUTINE
SUEROUTINE
SLBROUTINE
K
C
C
CONSTANTS
C
C
CRITICAL
C
C
INITIAL
AFPRrxIPATION
CONSTANTS A,
rISCELLANECUq
CCNSTANTS TFP
LEIC
PCINT
PRGFERTIES
TC,
FC,
vC
(NOT USED)
COPMC,/SUPER/TrC,PVC, A,, TFRLE1,Z
C
C
EELATICN
OF STATE CCNSTANTS
CCPCN/STATEG/R.E1,A2,BC2, A3,3, C3,A4,B4,C4, A5E5
lCSA6,E6 ,C6t KAI FHACPi
C
C
C
C
SPECIFIC
EAT AT CCNSTANT vCLUME CCNSTANTS
ACVPECV,CCVirCVECvFCV
ENTFALFY ANC ENTOPY
OF VAPOR CONSTANTS
X,
C
VISCELLANECUs CONSTANTS
LIOE,
Y
J
COPCh/CTMER/ACVBCV, CCV CCVECVFCVX, Y L1E, J
C
C
C
C
CBTAIN VALUES OF TE CCNSTANTS CORRESPONDING TC TE
CESIFEC REFRIGERANT FOMr SUEROUTINE TABLES
(T-CUG
CrCNh
CALL TABLES(KRrT)
IWRITE
5
C
C
CCNVERT
TFt TC 'TT
T
TF + TFR
AND CECK
VALUE
224
IF(T.LE.Ze)
GC TC 999
C
C
CALCLLATE TFSAT' AN CCMPARE hITk
TFSET
TSAT(Nh.PSIA)
IF(TF*LTTFSAT)
'TF'
GO TO 999
C
C
CHECK
PFSIa,
IF(PPSiA.LE.£.v
C
CALCLLATE
GC TGC 999
'VVAPF
VVAP = SFvCL(hRTFjPPSIA)
C
C
CALCLLATICN
ERIVATIVES
CF
vi s VVAP - cl
V2 s V1*'E
V3
VI*
V4 = V, *4
V5 z V
'
V6 s*
:Pt:
LKT C=EAk(-K*T/TC)
Z
PLFhA*VViP
A
Z2 *,Z
=
IF(ZoGTolt¢.v:)
7 = tS§e,
IF(Z.CT.*15U.&)
iF(Z.GT.I1_es)
Z2
a
15ee
Z3=15Z92
UC TC(ltEs3)iI
1
F2PCva.£,
FCPCT
= 2 e
GC
4
TC
2 FCPVs-ALF;A-LXc-Z)*IA6+E6*T)
FCPCT=6*,EXP ( -Z
,,C
TC
3 FPCVa-(ALFeA*(XP(-Z3)+2**CPR*EXP(-ZP)
)/(EXP(-Z2)+2.
1*CP*EXP(-Z)+CPP.*2)).(A6+B6*T+C6*EKTTC)
FCFCT=IUt-K*Ct*eKTTC/TC)*EXP(.Z2)/(EXP(-Z)+CPR)
4 CFCv=--T/V-I*(A2+82*T++C*EKTTC)/v3-3,*(A3+B3*T+C3*
1EKTTL)/V4-4*(A4+4* T+C4=EKTTC)/Vb-5.*(A5+Bb*T+C5*EKT
2TC)/Vo+FCFCV
POTSR/Vl+(( bC-K*CCEKTTC/TCI/V2+(B3-KC3*EKTTC/TC)/V
1+(B4mK.C4$EKTTC/TC)/V4+B5m-K*C5EKTTC/TC)/Vb+FDPDT
GC TC5t~j,1f).I
5
CCv
c.:
GC TC 1b
le FCCVuC6SLXP(-Z)/ALpHA-(C6*CPR/ALPHA)*ALOG(1.+EXP(.Z)/
1CPP;
C
C
CALCULATE
CV'
15 CV=ACV+tCvT4CC\sT**2C+CV*Te
3 +FCV/,T**2(
185e53***2
l*T*EKTTC/TC*c)*,(C2/VI+C3/(2.*V2)+C4/(3*V3)+C5/(4.V
225
24 )*FCCV)
C
CALCULATE
C
'CFP'
CV-*185lE53*T*CPCT**2/DFOV
CP
C
CALCULATE
C
GAJrA
'GArr'A
CF/Cv
C
CALCULATE
C
SCNIr'
SCNIC.VVAP*SCRT 85 7 *3691*T*DCT**2/Cv-4633.56*CPCV)
RETURN
C
ESSAGE IF
PRINT ERRCR
To ZERO CEGREE R
TF IS LESS TAN ORfiEUAL
TO PSAT
TFSAT CCRRESPCNCINr
TF IS LESS TAN
C
C
C
C
PPSIA
IS LESS
599 WRITE( %ITTEItEC
le20
FCRIAT( '
RETURN
ENC
PPSIA
TfAN OR EQUAL TO ZERO
)
***-*wLRROR
IN CALLING SUBROUTINE -SPFfT-9)
226
SUBROUTINE
VAPCR (R, RTF,PPSIA,
VVAP, HVAP SVAP )
C
C
FLRFPCSE
C
TC EVALUATE TE
C
CF THE SFEREATED
C
C
C
C
THERMCCYNAMIC
APCR
CF
EFIGE;ANT
12J22* CR 52
GIVEN TE
TEMPERATLRE ANC FRESSURE
CESCRIPTICh CF PAAMETERS
INPFLT
C
NR
-
REFRTGERANT
NurBER
C
TF
-
TEOFFATLRE
(F)
PPSIA-
C
C
(12,22t OR 502)
(PSIA)
PA£S~SE
OLTPUT
C
C
C
C
PROPERTIES
PASE
VVAP
HVAF
*
SVAP
RE
SFtCTFIC
vCLUME CF VAPCR (CU FT/LBM)
IENT-ALFY CF VAPOR (TL/LEM)
ENTRrCY OF VAPCR (BTU/LBM
- R
PAHKS
C
FLNCTICCN SL2peF GRAr
C
C
FLNCTICN SLE'rCGRA
TSATr CALLED BY THIS SUBRCOTINE
SLEROLTINE TAEES CALLEC By TIS
SLBROUTINE
SPVCL
CALLED
BY THIS
SUBRCUTINE
REALKKTCTCpi Cile,LiE
c
C
C
C
C
CONSTANTS
CRITICAL
CINT PRCPERTIES
TC,
PC,
INITIAL
AFFRrXI'ATION
CCNSTANTS
A,
rISCELLANECLS
CCNSTANTS
TFRP
LEIC
CCrrCN/SFER/
VC
B (NOT
USEC)
Tr, PC VCj A, 8TFRLE1
C
C
EGLATICN
OF STATE CONSTANTS
CCMCN/STATEC/R
8l, ,A2,8 2, C2 A3, B3C3
iC5,A6E6C6jCA,
44, B4,J C4, A5, E5
PF-A, CFHR
C
SPECIFIC
C
ACVBeCV,CCVrCV,ECVFFC
C
ENThAFY
C
rISCELLANECLS
EAT AT
ACCSTANT
ANC
ENTRCPY
CF
VCLUE
CONSTANTS
VAPCR
C NSTANTS
CCNSTANTS
LIE.
COMCN/OCTt-ER/ACv BCVCCVCCVECV
X,
Y
J
FCV, X y, L10E, j
C
C
CBTAIN
C
CESIREC
C
VALUES
(TI-RCUGH
C
CCRRESPONDING
TABLES
CCMrCN)
CALL TABLESrR,
IWRITE
CONSTANTS
TE
REFRIGERANT FROM SeROUTINE
T)
5
C
C
C
CCKVERT 'TFt
T w TF * TFR
TC
IF(T.LE.e.e)
GC TO 999
CALCLLATE
TFSAT
TFSAT'
T
AND CECK
A
TSAT(NR.PPSIA)
COMPARE
VALUE
WITH
TF'
TO T"E
227
GO TO 999
IF(TF,LT.TFSAT)
C
PPSIAt
CI-ECK
C
GC TC 99
IF(PFS'IA.LE.e.e!
C
CALCLLATE
C
'VvAP,
SFVCL(NR.TFPPSIA)
VVAP
C
CALCLLATE
C
T
T*
T3
T*w
T4
Tw4
VHVAPT ANDC 'SAP
t
VVF-E81
VR
VR2 a 2q* R**E
3VR*-3
VR3
49*.vR**4
VR4
KTCTC = *rT/TC
EKTCTC
txP(-KrTCC
ALF-VAVVAP
Z
V) 7
IFI'ZGT.*1';t
· i5ese
EXF(-Z)
EMAV
/.*+CCV*T33.+CCV*T4/4"FCV/T
I=ACV*T+cV*T
j,*FFbsA*VVAP
2-
h3A2s/VR+A3A/v2+4/VR3*A5/VR4
t4sCp2/¥vC3/VR2.C44/VR3*C5/VR4
;CV-TC^+CCV/CV*33T3/3-FCV/(2
IsulACV*ALLG(TI+
5
=
jrf*ALU
' * T2 )
V )
S3we2/VR+ 3/VR2+84/VR3+6S/VR4
S4
4
a
4
GC TC(6,4p5)uI
1-3 - 3+6/ALF-A*El-AV
S_3.E/ALFAEPAV
S3
GG
6
TC
ali,*/ALFtA*(EIAV=CPR*ALCG(+EMAV/CPR))
5
193
4
S3
h3+A6*z
4 -C6*He
= S3+ae6HZ
$4 * S4-Ce*
6
HYVAF hlHt*~$H3$J*EKTCTC*$1**KTCTC)*w94+X
SVAPS$1 +S2-
*SiJ*EKTDTC*K/TC*S4+Y
RETLRN
C
PRINT ERRCR rESFAGE IF
C
C
C
C
TF IS
TF IS
PPSIA
LESS ThAN OR EGLAL TO ZERO DEGREE R
LESS ThAN TFSAT CORRESPONCING TO PSAT
IS LESS TAN OR EQUAL TO ZERC
S99 iRITE(I WITE lev)
iee
FCF'AT(' **f**.ENROR
RETLRN
ENC
·
PPSIA
IN CALLING SUBRCUTINE *VAPCRU-)
228
SERCLTINE TRIALh(NRTIDTIPNARGTCLVHS,
T)
C
PURPCSE
TC CETERMINE REMAINING SPER-EATEC VAPGR PROPERTIES,
GIVEN TE PRFSSLRE AND CNE OTHER PROPERTY
C
C
C
C
DESCRIPTICN CF pARAMETERS
INPLT
NP
-
REFRTCERANTNBER
TI
-
INITTAL TEMPERATURE GUESS
(12,22,
OR 502)
IF)
CTI
INITTAL STEP SIZE FCR TEMP, ITERATICN
F
N
PRESsLRE (PSIA)
ARGLENT IDICATOR
IF
2, TF
(F)
SECONC KNGN PRCPERTY IS SPECIFIC VCL.
IF N
N
3
T
SECOND KNCfN PkCFERTv IS
IF N
4,
- SECChN KNhCA PCGPERTY IS
ARG T-E cECCNO KNLWN PROPtRTY
TCL CCNVERGENCE TCLLELANCE
ENThALPY
ENTROPY
CLTPLT
V
S
-
SPECIFIC
a
ENTabLPY
-
ENTRrPY
VCLUME
CF VAPOCR (CU FT/LBM)
OF VAPCn
(BTU/LeM)
OF VAPCR (TU/LM-R)
T
TEMFFERATRE
OF VAPOR
REPARKS
T-IS
FROGraM CALLS SROLTINE
TiE CSIREC
T
IF(NU,.E_)
t,T,Pvv
=
VAPHVAPiSVAP)
VVAP
A.NGh VAP
iF(N.*EC.)
AGhN
SVAP
IF((NtNE.E.ANC.I(NNE.3).ANUD(N.NE.4))
IF(CT.LT.e.C)
CTFF
ARG - ARGN
IF(CTGT*c-C)
CTFF
G
2F(CToEC.,**)
ZF(ABS(CFF).LE.TOL)
IF(CIFF)
Tr
2e
CT a DT/B.g
COCTINLE
T -
ARITE('ile)
V
IVAP
v- aa V9aP
GO TC
25
ARGN - ARG
TC 25
GO TC 30
Ee*3egtv
16
S -
DETERMINE
,i4
IF(NEC.E)ARGN
3~
Ic-
VAPOR TO
REFRIGERANT FRGPERTIES
TI
CT
CTI
CO
e I *'
T - T+CT
CALL VAPC(
CE
(F)
CT
N
SVAF
RET L RN
1116 iCRFAT(
END
*****TRIAL
DCES
OT CONVERGE N',I2,'
******')
229
APPENDIX
CARRIER
B
MODEL 50 D Q SERIES SINGLE PACKAGE HEAT PUMPS
(CARRIER CORPORATION, 1972, With Permission)
PHYSICAL DATA
Unit 50 D Q
004
006
008
016
Refrigerant
500
500
22
22
Compressor
Type
Cylinders
06R Hermetic
RPM
3500
3
Type - Drive
06D Semi-Hermetic
4
44
6
1750
1750
1750
Propeller 1 - 18
irect tDri.ve
1 - 24
Outdoor
No. - Dia (in)
Air
Nom CFM
Fans
Motor hp - RPM 1/6 - 1075
1750
1 - 26
2 - 26
3700
5200
10,000
1/3-825
1/2-825
3/4-1140
(3 ph)
Type - Drive
Centrifugal with Scroll - Belt Drive
Indoor
No - Dia (in)
1 - 10
-
Air
Nom CFM
1300
Motor hp - RPM
5
1/3-1725
1 - 12
5
5
2 - ln -
3 - 12
2100
3220
6300
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232
ADDITIONAL DATA ON MODEL 50 D Q 016
Indoor Coil - Plate Fin Type (See Figure B-1)
Fin Pitch
- 14.1 Fins/in
Fin Thickness (6) - .0055 in
Fin Material - Aluminum
Height of Coil (h) - 22.5 in
Width of Coil (L) - 86.5 in
Thickness of Coil (t) - 3.24 in
Number of Tubes in Direction of Air Flow (NT) - 3
Number of Tubes Normal to Air Flow (NP) - 18
Tube Spacing - Equilateral Triangular Pitch
Vertical Tube Spacing (S) = 1.25 in
Horizontal Tube Spacing (w)
Outer Diameter of Tubes (D)
=
1.08 in
- .506 in
Inner Diameter of Tubes (Di ) - .471 in
Number of Flow subsections (NSECT) - 9
233
Outdoor Coil
- Plate Fin Type (See Figure B-2)
Fin Pitch - 15 Fins/in
Fin Thickness 6)
- .0055 in
Fin Material - Aluminum
Height of Coil (h) - 40 in
Width of Coil (L)
- 86.5 in
Thickness of Coil (t)
- 3.24 in
Number of Tubes in Direction of Air Flow (NT)
- 3
Number of Tubes Normal to Air Flow (NP) - 32
Tube Spacing
Vertical
- Equilateral Triangular Pitch
Tube Spacing (S) - 1.25 in
HorizontalTube Spacing(w) - 1.08 in
Outer Diameter of Tubes (Do )
- .506 in
Inner Diameter of Tubes (Di)
- .471 in
Number of Flow subsections (NSECT) - 15
EQUIVALENT LENGTHS OF PIPING AND OTHER COMPONENTS (ON HEATING)
- 130
Liquid Line ()
EQ
Suction Line ( ) - 180
EQ
Discharge Line ()
- 144
EQ
234
Suction and Discharge Risers
Suction Riser
- 1.32 in
Discharge Riser - 1l08
I. D.
in
I. D.
Thermal Expansion Valve, and Distributor Nozzle & Tubes
Thermal Expansion Valve -
ALCO Controls
Type
TNE IOHWIOO With A
4 A Superheat Setting
(i.e., 4
Superheat at 320 F Remote
Bulb Temp.)
Distributor
Nozzle & Tubes - Sporlan Type
1655-15 -
3
- 12-
(See Appendix
Compressor
Chart Data -
See Figure B-3
5
For Performance Data)
Carrier Type 06D-537
(Physical Data Given in Appendix
Charging
D
one
c
)
235
sect - 6 as shown
n
- tube O.1.
N.i
t
t-
- tube
.D.
-
S
2
FIGURE B-1
S
INDOOR COIL - CARRIER
MODEL 50 DQ 016 HEAT PUMP
h
At1
Fli
W W
2
236
N
= 4
sect
as shown
l
D = tube O.D.
Di= tube I.D.
1.
S
S
OUTDOOR COIL - CARRIER
MODEL 50 DQ 016 HEAT PUMP
Ai
FIGURE B-2.
h
Fl(
W
2
W
237 .
65°F
C·
A_
JbU
55°F
43°F
340
I
Outdoor
WetIBulb
320
30"F
300
Gage
Pressure
10
at
280
Discharge
Valve
F
I
I
I
I
I
/
I
I
I
I
260
(psig)
240
220
0
20oF
1/
I
I
I
I
I
I
I
I
I
1/I
I
I
I
_
I
I
I
I
I
200
I
180
_
0
10
20
30
Gage Pressure at
40
50
60
70
Suction Valve (psig)
CHARGING CHARTS - CARRIER MODEL 50 DQ 016
HEAT PUMP DURING HEATING MODE
FIGURE B-3
80
238,
APPENDIX
C
SAMPLE THERIODYNAMIC CYCLE DATA FOR SYSTEM SIMULATIONS CONVENTIONAL
Exaggerated
P-h
VS CAPACITY
and
P-V
CONTROLLED HEAT PUMP
diagrams, showing
details of the
actual thermodynamic heat pump cycle are given in Figures C-1 and
C-2.
Comparing states in the cycle for both conventional and capacity
controlled Carrier Model 50 DQ 016 heat pumps at the following
conditions
Entering Indoor Air
=
Entering Outdoor Air =
700°F
620F db, 85% rel. hum.
We find, from the computer simulations:
CONVENTIONAL
Indoor Air Flow
Outdoor Air Flow
x
Heating Capacity Reduction
CAPACITY
CONTROLLED
(14'BP)
6330 CFM
3165 CFM
10,000 CFM
5200 CFM
0
62%
STATE 1 - Evaporator Exit Saturation
State
T1
39.6°F
44°F
P1
82 psia
89 psia
54°F
59-F
STATE 2 - Evaporator Exit Superheated
Vapor State
T2
P,
-82
psia .
=89 psia
239
PROCESS 2-3 SUCTION LINE
1 psi
A2-3
.1 psi
STATE 3 - Superheated Vapor State Entering
Compressor
P
3
54°F
590°F
81 psia
89 psia
3.9 Btu/lbm
3 Btu/lbm
760°F
750°F
76 0 F
75 0°F
PROCESS 3-4 MOTOR COOLING
Ah3-4
STATE 4 - State of Vapor After Motor
Cooling
T4
PROCESS 4-5
SUCTION-DISCHARGE HEAT TRANSFER
A 4-5
STATE 5 - State of Vapor After Suct-Disc
Heat Transfer
T5
PROCESS 5-6 SUCTION VALVE AND MANIFOLD
AP
3 psi
5-6
3 psi
STATE 6 - State of Gas Entering Cylinder
T6
=76°F
=75 0 F
97F
102°F
COMPRESSOR CYCLINDER PROCESSES
STATE a - State of Re-Expansion
T
a
Gas
240
V
a
D
D
.20
o15
81°F
83°F
STATE b - State at End of Intake and
Mixing with Residual
Tb
V
1.05
.41
D
STATE b - State at End of Expansion
After Cut-Off
Tb
29 psia
STATE c - State At End of Compression
T
C
234°F
216°F
.34
.14
V
VD
P
C
360 psia
286 psia
2340°F
216°F
360 psia
286 psia
25 psi
25 psi
STATE d and 7 - State At End of Discharge
Td and 7
d and 7
PROCESS 7-8 DISCHARGE VALVE AND MANIFOLD
A7-8
STATE 8 - State of Gas Entering Disc.
Manifold
231°F
2120 F
335 psia
261 psia
241.
PROCESS 8-9 SUCTION-DISCHARGE HEAT
TRANSFER
Ah8-9
-= 0
=0
STATE 9 - State of Gas Leaving Compressor
T9
P9
2310°F
212°F
335 psia
261 psia
PROCESS 9-10 DISCHARGE LINE
AP9-10
9-10
.4 psia
<.1 psi
STATE 10 - State Entering Condenser
P1 0
231°F
212°F
335 psia
261 psia
136°F
116°F
STATE 11 - Condenser Inlet Saturation
State
T11
Pll
P1 1
=335 psia
=261 psia
1.7 psia
.3 psia
PROCESS 11-12 FLOW THROUGH CONDENSER
AP11-12
STATE 12 - Condenser Exit Subcooled
Liquid State
121°F
91°F
PROCESS 12-13 LIQUID LINE, TXV,
DISTRIBUTOR
AP12-13
249 psi
172 psi
242
STATE
13 - Evaporator Inlet State
.28
x1 3
T1 3
P13
PROCESS 13-1
FLOW
THROUGH
AP13- 1
.16
400 F
440 F
84.7 psi
89 psi
2.7 psi
.4 psi
EVAPORATOR
NET OUTPUT
Mass Flow
Power Input to Compressor
Heat Rejected in Condenser
2430 lbm/hr
17.6 kw
217,700 Btu/hr
843 lbm/hr
5.6 kw
82,315 Btu/hr
243
p
r
e
s
S
;sion
u
.agrams)
r
e
(P)
4 Cr-harge
Uur~-c--
ansfer
EathalpPY
EAGGERATED
P-h
(11)
HEAT PUM
DIAGRAM OF ACTUAL
FIGURE C-1
CYCLE
244.
t
P
P
V.
min
V
max
V
V
V
max
min
V
_
(a)
(b)
Conventional
Capacity Controlled
CYLINDER P-V DIAGRAMS
FIGURE C-2
245
APPENDIX
DETAILS
OF SYSTEM
D
FLOW BALANCE MODELING,
dimensionsnecessaryfor the system flow balance
Physical
outlined in Figure 2.1-3 are:
or equivalent
model
diameters of flow passages and lengths
lengths of the flow paths, compressor dimensions, and
device
expansion
data.
Information
on required compressor data is
given in section 2.3, and Appendix E.
Pressure drops through piping
and components other than the heat
exchangers and expansion device are found using the equivalent length
method of pressure drop calculation
AP
4 f
L
D
for
incompressible flow:
G
2P g
(psi)
Where:
f
-
Moody friction factor (subprogram 'FRICT', in Appendix
L produces values of Moody friction factor for laminar,
transition, and turbulent flow regimes, and for rough
as well as smooth pipes)
O - Mass flow per unit flow area (lbm/hr-ft2)
p
-
inlet fluid density (lbm/ft3)
equivalent length
s
-
conversion factor (32.2 lbm-ft/lbf sec )
246
Subprogram "DPLINE' , in Appendix L , is used to determine the above
pressure drop.
Values of L/D used in simulating the Carrier model
50 DQ 016 heat pump system are given in Appendix B.
Two-phase pressure drops in the condenser and evaporator are
calculated by subprogram 'PDROP', outlined in Appendix Lo
Subprogram
'PDROP' is capable of determining single phase liquid and vapor
pressure drops in the heat exchangers, as well as two-phase pressure
drops, although as used in the system flow balance model, only the
The two-phase pressure drop
two-phase capability is employed.
correlations are from Lockhart and Martinelli , and are valid for
laminar, transition, and turbulent flow regimes, as are all of the
single phase pressure drop relations.
Expressions describing the distributor nozzle and tubes for the
Carrier model 50 DQ 016 heat pump during the heating mode, developed
by curve fitting published performance data2 , are as follows:
Nozzle:
1.8384
AP
noz
)
3 25.0 (% CAP
noz
(psi)
< 1.2
noz -
%CAP
.954735
AP
noz
%CAP
CAP
noz
noz
= 29.408 (
CAP
noz
)
(psi)
%CAPnoz > 1.2
CAP
CAP
CAP
noz
= (12000) (CORFAC) 10 [ .00511 (Tsat) + .944803]
(Btu/hr)
evap
247
[-.006444 (TROC) + .64441
CORFAC
=
10
TROC < 100OF
110 [-.007133 (TROC) + .71331
CORFAC
CORFAC =
TROC > 100°F
Where:
CAP
CAPNOZ
=
amount of heat transfer in the evaporator (Btu/hr)
=
amount of heat that could be transferred in the
evaporator at the rated pressure drop across the
nozzle (btu/hr)
correction factor for non-standard rating temperature
CORFAC
of incoming refrigerant liquid
%CAP
noz
=
percent of rated capacity
TROC
=
temperature of refrigerant liquid leaving condenser
AP
=
pressure drop through nozzle under the given
noz
conditions
Tubes:
1.81217
APtubes
-
%CPubes
tubes
CAPtubes
(10.0) (%CAPtubes)
(psi)
CAP
CAPtube s
(Nsect) (12000) (CORFAC) 10
(Btu/hr)
(.005291(Tsat ) - .48733]
evap
248
Where:
CAP
= amount of heat that could be transferred in the
tubes
evaporator at the rated pressure drop across the tubes
(btu/hr)
N
sect
%CAP
tubes
= number of tubes or separate flow paths in evaporator
= percent of rated capacity
AP t
tubes
pressure drop through tubes under the given conditions
The expression for the thermal expansion valve coefficient CTXV
for the 50 DQ 016 unit on heating was found to be:
2
CTXV = .002128 (Tsat )
ibm
+ .2491 (Tsat )+
9.455
evap
evap
[bm
b
ft
1bf
(ifn
in
The system flow balance model, as outlined in the flow chart
of Figure D-l, requires that the pressure drop across the expansion
device 'DPACT' be equal to that available across the device, 'DPSYS'.
These quantities are defined as:
DPACT
=
APTX V
+ APnoz
TVDPY
-=
PIEo
POC
DPSYS
POC - PIE
POC
PIC
tubes
where
- APdisc
line
cond - APliq
line
249
+
APevap
PIE
=
PlOE
PIC
=
Pressure at exit from compressor
hAis c
+ AP
suct
line
Pressure drop in discharge line
line
Pressure drop through condenser
APcond
APli q
-
Pressure drop in liquid line
line
P1OE =
Pressure at entrance to compressor
AP
-
Pressure drop in suction line
=
Pressure drop through evaporator
AP
suct
line
evap
Thermodynamic properties required for the system flow balance
model are determined from basic equations, as described in Appendix
A.
To check for liquid line flashing it is necessary to determine
the saturation pressure corresponding to the temperature of the
refrigerant leaving the condenser.
If the drop in pressure in the
liquid line is enough to lower the pressure below the saturation
pressure, then some liquid will flash into vapor.
Finally, to check for adequate oil return in suction and discharge
risers, we must compute the actual vapor velocity in the risers and
compare it to the minimum vapor velocity required for oil entrainment
250
Data on minimum velocity for oil entrainment in suction and discharge
risers, for refrigerant 223, has been curve fit, yielding the
following:
) + .5 log1 0 (DsL) + 34826]
[-.005875 (sat
VSR = (60.0)
10evap
(ft/hr)
[-.00315 (Tsat ) + .5 log1 0 (DDL) + 3.40]
VDR = (60.0)
10
cond
(ft/hr)
Where:
DSL
=
Diameter of suction rister (ft)
DDL
=
Diameter of discharge riser (ft)
VSR
=
Minimum velocity for oil entrainment for refrigerant 22
in suction riser (ft/hr)
VDR
=
Minimum velocity for oil entrainment for refrigerant 22
in discharge riser (ft/hr)
For more information concerning the specifics of the computer
simulation of the system flow balance model, see comments in the
program listing at the end of this section.
REFERENCES
1.
Lockhart, R.W. and Martinelli, R.C., "Proposed Correlation of Data
For Isothermal Two-Phase, Two-Component Flow in Pipes", Chemical
Engineering Process, Vol. 45, No. 1, pg. 39 (1949).
2.
"Refrigerant Distributors", Bulletin 20-10, (Sporlan Valve Company,
St. Louis, Missouri), July 1973.
3.
ASHRAE GUIDE & DATA BOOK, SYSTEMS & EQUIPMENT VOL. (New York:
American Soc. of Heat., Refg., & Air-Cond. Eng., Inc., 1967)
pg. 801-805.
251
FIGURE D-1
FLOW C.ART
FOR SYSTEM FLOW BALANCE MODEL
Start
l~~~
-
i
Define constants
!
·
r
'
Input
,
Physical dimensions, Tsat
__
superheat, subcoo.ln
evas
'
.
_
I
!
Initial guess for Tatcond
Iteration on 7
p
i [ m
·
r--
Iteration on Ttsat
cond
to find balance condition
I
I
'Determifne
I
'Exit
temo.o from-condenser
TROC- sa
- subcoolingR
cofid
Determine
Thermodynamicproperties
,
I
of liquid leaving condenser]
Use subprogram 'COYP' to determine
compressor performance & hence
mass flow rate
252
Determine
Liquid line pressure drop
i~~~
F,
Check for liquid line flashing
3
i
Determine
Saturation thermodynamic
rop. in cond.
F~~~~-
Determine
Pressure drop through condenser,
assuming two-phase flow throughout
It
Determine
Pressure drop in discharge line
Check for adequate oil return
in discharge riser
Determine
Saturation thermodynamic prop. in evar.
Determine
Pressure dropthrough evaporator
assuming two-nhase flow throughout
ii
Determine
Pressure drop in suction line
~~~~~~~~~_
.
1
oil return
Check for adequate
in suction riser
__
b~~~~~~~~1
253
Determine
Pressure drop 'DPACT'through TXV
& distributor
nozzle and tubes,
for the givenmassflow rate
Determine
Available system pressure difference 'DPSYS'
across TXV&distributor
t
I
L·r.i
254
C
FLOC
SYSTEM
PROGRAM
EALANCE
C
C
PLPFCSE
C
TO CETERMINE
C
C
wrICt-
C
CAPACITY
C
eALANCE IN TE
C
C
GIVEN TERMAL EXPANSICN VALVE tEHAVIOR
rCFPRESSOR (EITHER CONVENTIONAL CR
ITh
ANC A GIVLN
A MASS FL3w
PCCUCE
ILL
CCNTiCLLEC)o
SSTEm
EXFLICIT INFLT FPRAMETERS
CLLCC- tIAr;TEmR OF I(GID LINE COMMING FROM
C
CCIL
CLTCrCR
(FT)
C
C
XLEGLC- EGLIVALFNT LENGT
FRCr' CTCOOR CIL
C
CLDLICw
C
OF LIOLIG
2IAvFTEN
CCIL
COF LIGUIC LINE CCMMING
(Lc/D- CIMENSICNLESS)
(FT)
XLEGLIW EtGLIv~AENT LENGTH CF LIGlIC
C
C
C
C
CSL
XLEGSL-
C
CCL
C
XLEGCL-
=
OF
CIAMTER
ELIvALENT
-
(vAPCOR)
LINE
I3CHARGE
cF CISCHARGE
LiGTr
(FT)
LINE
IrENSICNLESS)
C
DCC
-
INSIrE CIAMETER
C
CZCC
-
rFRLCEANT
C
LINE CCMMING
CDirENSICNLESS)
FRCM INCCGO CCIL (L/C
(FT)
(APOF)
iAmrFTlEROF SLCTION LIrE
LINE
CF SCTICN
EGLIvA.ENT LNGT
(L/C - DIMENSINLESS)
(L/C
C
FROM INCOCR
LINE CCMMING
C
C
C
CONDCITIONS
CCNDENSER ANC EVAPORATOR
T-E
IN OUTOOCR
CF TuEES
FLCW
EACH
I
LENiT
COIL (FT)
IN INDOOR COIL
RANCH IN Tt CTCCR
CIAMETER CF TUrES
CIC
FCw
I SIrt
CZIC '
REFRTGERANT FLOW LENGTH IN EACH PARALLEL
C
oC
-
2EPANCH IN T
FC
NwirEm- CF CIFFERENT
(FT)
CCIL
PARALLEL
INCCOR COIL (FT)
CCNFIGURATIONS
FLO
(FT)
TC
6_E STLCIED
C
SATLPATION
CF EvAPORATOR (F)
EIT
TErPeAT
C
TSATE-
C
CTE
-
TrFFmATRE
C
NE
=
NLMwR
C
C
TSATCOTC -
C
NC
C
SLPERi
SLFEEtEAT
C
C
CTRCC-
ENTEciNG TE CCPERFSSCR (F)
GLES FCR AMOUNT F SLbCCOLING OF REFRIGERANT
C
C
NCCRH-
(F)
LEAVTNG CONCENSER
FCR COOLING
INCIrATCR
Is
C
SECT-
TSAT8F-
FOR EVAP.
(F)
EXAmINED
SATURATION TEMF. AT ENTRANCE TC CCNDENSER (F)
TFtrFRATuRE INCRErENT FOR CONDIF)
NLMlF
IF
C
INCREMENT
CF EVAP* TEMPbS
CF CONCENSER
'NCCRH'
IF 'CCRm'
CF
tNMFHi
TEMPS.
F vAPCR LEAVING
I
OR
EXAMINED
EAPORATOR
EATING
AND
MODE
COCLING M:CE
MODE
2
HEATING
F'LCi SECTIONS
ARALLE
A\ INFLT TEMPEATLWRE LSEC TO SPECIFY THE
EXPANSICON
FLC CCEFFICIENT Gf TE TERMAL
VA
Vf- (F)
255
C
C
C
C
C
ICOKTA- CCNTCL
CLTCFF-
INCICATCR
'ICCNTR'
= 1 MEANS CCNVENTIONAL
SYSTEM
'ICCkTR'
2 MEANS CAPACITY
CONTROLLEC
S'STFM
A FPARAMETER USEC T
INDICATE
TE
AOUNT
OF
C
C
C
CAFArITY CONTROL USEC - IT IS CEFINED AS
'CUT-FF'
1oZ
(VCL*CUT - VGL.MI)/VCLIISP.
~hER
VCL.CUT IS THE VLUME SWEPT Y tkE
C
FPSTrN
C
C
VCL,-IN I TE CLEARANCE VCLUME
vCi.rISP, IS TE DISPLACEMENT VOLUME
C
(ALL PFR CYLINCERI
EFCRE
SCTION
TE
VALVE
IS
CLCSED
C
C
C
C
INPLT PARAMETERg IN CCMMCh
NCYL NLFER
CF COMPrESSCR CYLINDCERS
VP
CLEAPANCE
VCLUME RATIC
CEFINED
1f0V w
C
AS
VOL.tIN/VCLCISP,
C
C
vC:
=
ISPi ACEMErT VCLL"E PER CYLINDER
ShEFT
y PISTON) (CL FT)
C
C
SYNC
RFP
a
-
SYNC~RCNCUS MCTCR SPEED
(RPM)
INITtAL
GUESS FCR ACTUAL MCTOR SPEED
C
EFFIS-
ISENTGPIC
C
EXFANSICN
C
PRCCFSSES
C
CF'DI
FRTIONS
E6LIvALENT
CF'S
=
tIvALE.NT
PRESSLRE
VALV
C
FLCW LOSSES
CFFRACSCELAY-
C
C
C
TO ACCOUNT
CYLINDER
AND
FOR VALVE
DYNAMICS
ANC
(PSI)
DELAY
(DEGREES
AFTER
CEAD CENTER)
PEfiCFNT
REPOvEC
OF COMPRESSCR
BY TE
SCTICN
IS LrST
Y CNVECTICN
FT
F.TC
-
(NCT
(NCT
SFDO ERE)
SED
ERE)
C
EAC
-
(NCT
SED
ERE)
C
EAS
-
(NCT
SED
iHERE)
C
C
C
C
C
C
P,.RNLEFFMEPC:VAX.
EAREA-
DYNAMICS
CROCP ACROSS SUCTION
(NCT
SED ERE)
S:CTCN
VALVE CLOSING
BCTTot
FMC'
C
C
C
THE
(RPM)
COMPRESSICN ANC
PRESSURE DROP ACROSS DISCHARGE
C
C
C
F
CF TE
vtAVF
T
ACCOUNT FOR VALVE
FLCW LOSSES
(PSI)
C
C
C
EFFICIENCY
(VCLUmE
OTOR EAT wHICh
IS
GAS (THE REMAINCER
TC TE
AMBIENT)
(NCT
SED
ERE)
MECHANICAL EFICIENCY
CF CCMPRESSOR
t 4AXIMLM POPER CUTPUT OF CCrPrESSCR
OTCR
(Kn)
HENCPERATING
AT MAXIMUM PERMISSIBLE
OvERi CAC
E-lIvALENT
EAT TRANSFER AREA BETwEEN
C
C
C
SLCTTCN AND DISCHARGE MANIFOLDS - THIS IS
USEC TC GIVE A ROUGH APPROXIMATION
OF
It.TERNAL HEAT TRANSFER LCSSESs
IF A
C
PARTTCULAR
COrFRESSOR
ESIGN
SHOUCLD REGIRE
256
C
T-AT IT BE INCLUCE C
C
(TH-E4E
C
C
IS,
HOWEVER,
REPLACEMENT
NC
FOR
THE
ACTLAL CCNCITICNS IN EACH COMPRESSCR)
CCELAY- CISC-ARGE VALVE CLCSING CELAY (EG-EES
AFTER
C
C
TCP
EAC CENTER)
CiL . IRCULATICN RATE (LBM
XCIL -
IL/LaB CF REF.+OIL)
C
C
INPLT
CATA CChSTrNTS
SLPEVV & XINV
C
- CCEFFICIENTS
VISCOSITY
C
X1-Xr4
C
VISCCSITY
EFRIGERAN T
CF
LIbUIC
- CCEFFICIENTS FOR CETEPRYTNINGTE
C1-C3
THERtMAL EXFANSICN
C
C NCTE:
VAPOR
- COEFFICIENTS FOG CETERPINIING
C
C
ETERMINING
FCR
F REFRIGERANT
T-E INFLT CATf CCNSTANTS
AE
FCR
EHAvICR
VALVE
EFRIGERANT
22
NLY
C
C
C
C
CbTPLT
PARAMETEPS
TSATE
ANC TScTC FOH A REFRIGERANT
FLOvN BALANCE
Rxr
EFPTGERANT
MASS FLCO RATE AT BALANCE
C
C
CCNCTTICNS(LeB/HR)
PC
C
C
CCMPRESSCR
TCTAI
-
C
C
(F)
BALANCE
TIC
INPUT
CGOCITICNS
TEMPrRATURE GF REFRIGERANT
"
AT FLOw
PCER
(Kiy)
ENTERING CCNhD(F)
REMARKS
C
C
C
C
THIS FCGiAt
CALLS SERGCTINiE
SATFRPt TO ETERtINE
SATLRATICN PRCPE;TIES CF EFkIGERA\TS
ThIS FCGmAM CALLS SERCLTINE
'CCMP' TO DETERMINE
CCMFRESSC4 FFRFCRPANCE
C
T-IS
C
C
CCp
TN SINGLE PASE
PrESS;E
CCNNECTI\G PThING
C
C
C
PCRCPI TO ETERMINE
T-IS FGOGCAm CALLS SUERCLTINE
FLOO IN THE HEAT ECH.
hCpS IN T-FoASE
FRESSLRE
Ti-IS
CGRAM LSES FNCTICN
SPRCG;AM
'TSAT
TC
C
CETERmiINE
C
GIVEN
CAL&S SUBROUTINE
PkCG.AF'
ATLLATICN
FRESL
'DFLINE'
TO DETERMINE
REGIONS OF
TEMPERATLRES
CORRESPONDING
TO
ES
C
CCPrCN/hCCtPR/NCvL
1SCELAYPTFFiFT-
EFF I
VRVCISYNCRFM
p~TCEADOEASXR
DPD I DPSCPFRAC
COA T IC HIC
H1lCE
ICP
2FiCETICEw,POCvxFPRL,EtREA,CELAYxOIL,EFFME
CATASLFEr'v,XINhv/,*de75s, .*27E/
CATA X
X2, Xr
,Xe/-56Z5EE-08,
1.525E-05,-2,982E-e3i
CATA ClCi2C3/2.128E-'3*,e491,9455/
XCIL
Ci
CiEAY
ELArEA
= e*,
= ~,o
FARNL eC
SYNc
itcosy
257
PCWiAX · 16*89
NR
22
EFFIS
* 94
25
CPCI *
CFS
= 3.Z
CFFRAC
NCYL
RPrF
EAC
= Coe
= 6
17,*e
= ee
AS
r0C*
EFF'E =
*6
FiTC a Coei
SOELAY = V,0
t AC 8, et
) CLLCr, XLEQLO CLLICO XLECL I, CSL, XLEQSL, CCL*
IXLE'CL
RE ( .j6-e ) CC.CZCCCICrZIC
E AC (
4 Z)
CC 13ie
" 1,a
REAC(Ea6
e)
TSATEIOTE,NETSATCICTCPCSUPER
EAC ( i , 6 1 ) TRCr.
eNCCR- ,NSECT
HITE(53,)
) T SATP,ICCNTR,C
CCc,CZUCCIC,ZIC
RI TE t ,
G:) ;LI CC XLELO,
REAC e J 64
%RITE(577C)
TCFF
LLIC, xLEQLI
CS1 ,XLEQSLCCLXLECCL
~ITE(t, -LZ) rTST2P
C
C-"'"-'LCCP
FCR ITERATING ON CNCENSER
TEPPERATURE- -- ----
C
C
ITERATE TC FINC TE CCNiENSER TEiFERATURE WHICH
A YSTEI FLCw ALANCE FOR tmE GIVEN TSATE,
C
GIVES
C
T-ERrAL
EXPANSIrN
TSATC
TATCI
TSATE
TATEI
VALVE eEhAVICH,.
ANC COMPRESSOR
EHAVIOR
C
2se
cc li I
1,20
TSATC
TSATC + CT
CT
WRITiE(6515) TSATE.TSATCPCUTCFF
C
C
PRCVISICh
FOR RhN-TIME
INTERACTIVE
DATA INPUT
C
REAC(6a514 EC-C6 )
C
C
C
C
L
CALCLLATE
TE
GI,ESSEC TEMP
~-EFRIGERANT FCv
tTROC
FOR EXIT TEMP. CF
CCNDENSER (THIS MUST BE CHECKED
trAuAI LY wiTh- TE CUTPUT CF TE CONCENSER PERFORMANCE
FRCGFRA,
)
258
TATC - rTRCC
TRCC
C
C
CETERMINE
PRCFERTIES
CF LICLUI
REFRIGERANT
LEA'VING
CONC
C
CALL SATfip
~FC3
(hJTPRCP
VFVGPH3J.FGJp
GJSFPSG)
IC/VF
xrLL - Xl*TrCC**3 + XM2*tRCC**2
+ X3*TRCC
+ X4
VR -
e5
VC s *egs 22
C
C
CALL SLCLTIEE
C
rERFCANhCE
COPP TO DETERMINE
ANC
EFRIERANT
FLCA
TE
RATE
COMPRESSCR
XMRt
C
CALL CFF(NR,STSTEJTEJNEjTSATC
1CUTCFF
IF(CCR'F.*U1
)
ICONTR,
CTCNCSUPER
C TO 40
IF(NCCRF*Eg2)
C T
5C
C
C
vARIAEBLEq IF OERATING
CEFINE
IN TWE COOLING MODE
C
4e
CERC a CCC
4. *t
xMo/(i5.e*3.14*CERC**2)
GRC
CZTPC
LZCC
CIC
CERLE
4.Z.*XtR/(q.C*3*,4*DERE**2)
GRE
CZTPE
CZIC
CLL a CLLLC
XLECLL
XLECLC
GC
rC
e
c
C
CEFINE
VARIAELEP
CERC
CIC
IF CPERATING
IN THE
EATING
MCDE
C
5e
GRC
.4#£*X /I
CZTPC = CZIC
CCC
CERE
GRE
9q*C*3*14*CERC**2)
4*.Z*XMR/(15.e*3.14*CERE**2)
ZZTPE -
CZCC
CLL
CLLIC
XLECLL
XLEGLI
60
E - 5E'YE
C
C
CETERVINE
LIGUIn
LINE
PRESSURE
CROP 'CPLL'
CALL OPLINE(CLL.XLEQLLEXMFRRO3,XPMUL
C
C
CETERMINE SATURATICK PROPERTIES
(PSI)
DPLL)
CF REFRIGERANT
CALLSATFRP(NRpTSATCPjVFjVVkFsFGpkG, SFSG )
R~CL.- 1£/VF
IN CCNC.
259
Ri"Cv * ,/VV
XMLL
Xrl*TSATr **3 + XM2*TSATC **2 + xM3*TSATC
XF'LV
SLFErV*TsATC
C
CETERVINE
C
C
ASSLtING
T'E TrTA.
+ xr4
+ XINMV
PRESSI RE CRCP I
CGNCENSER 'DELPC'
THAT TE
TC-PPASE
PRESSLRE
C.OCENSER
PRESSLRE
ROP
(PSI)
CROP IS
APPRCX.
C
CALL PCRCFt4,CECE*,GRC*XLViXURRHQOVRRHOLiO,1,et
1CZTPC,(e *, 1*L VVIC.Cs *CELPC|
C
C
C
CETERrINE TE
RISER 'V.RACT'
ATLAL VAPOR VELCCITY
FT/HR)
IN TE
DISCHARGE
C
VCRACT
4k.s4
*/(R1hOV*3j 14*CCL*2 )
C
C
CETERINKE
C
IN T-E CISCARGF'LINE
TE
PESSuRE
'DPODL
DRCP
(PSI)
OF VAPOR
C
CL, E,Xr R R-CV XrU. jDPCL )
CALL CFLINE(CCLXLE
C
C
CETEFiINE
C
EVAPC:RATCR
SATLRATICN
PROPERTIES OF REFRIGERANT
IN TE
C
, fJTSATEsPVFVVihLICHFG
CALL SATPRP(N
t-CL
=
R-CCv
HGSFJSG)
1aXVF
14/Vv
X"L = Xt'l*TSATr**i
·
+ XM3*TSATE
+ X4
XM2*TSATE,*2
Xl.V
XI
XINV
, SLFEMV*TSATE E
( 3'-L iG )/I-FG
C
C
CETERRINE
C
ASSLUPINGTAT
C
THE
TCTAL
CRESS
HE DRCP
TE
I
THE EVAPORATOR
TCPHASE
PRESSURE
EVAPC;ATCR
(PSI)
CELPE'
FRESSRE CRCP IS APPRCX.
aCOP
C
CALL PCRCF(3,CEFEESGREXFUVJXM'ULDRhOvoRHOLIO
1 ZTFE,i:*Z.xlv V, Ze.g,.O
*, CELPEI
11,*
C
C
C
CETERMINE ACTLAL VAPC; VELCCITY
IVSRACT
FT/hRi
VSRACT
a XVR*4e/iR'
IN SUCTION RISER
OV*3½14*DSLi*E)
C
C
CETERMINE PRESS1 RE GRCP OF VAPCR IN SUCTION LINE
C
(FSI)
C
CALL CPLINE(CSL.XLEGSL EXMR,RHUV,XUVDPSL)
CAP
X*(i-1CE,
- -3)
PIE a. PiCE - CE, FE + CPSL
FCC
F IC
+ CELC
-
DFDL - CPLL
'DPSL'
260
T
TAT(,jPCC;
IF( TLE.TRCC)
pITE(5595)
CAPPT a CP/FLC&T{.SECT)
C
C
CETERMINE FRESSi RE CRCP TRCUGI
C
ANC TLeES
C
CISTRIBUTOR NCZZLE
*
') CORFAC=10*0* (- e6444*TRCC *6444)
IF t fCC .LEill
iF ( CC.GT* (l *) CORFAC 10,e=* (-*7133*TPOC+ 7133)
TIE
r TSAT(NF
PTE)
IF(NCCRh,*El)CAFNCZlO*-em*I 4642*TIE+,55162)
IF (CCRk-Ec, ) rAFPNOZ31*,*(,g511*TIE.,944603)*
112kZV*Z*CCNFAC
IF(NCCrM*-.CI
rAPTUBa1fr,.¢(,e5629*TIEa-,S377b)*
IF(NCCk.E&.Z)v rAPTUE le .* (.*e5291*TIE-4.733
yAP
IF(NCG0-'E-.*1)
)*
CAP4.e/9.1
CAR/CLAFCZ
PCAPFN
FCAFT r
CAPPT/CaFTLB
CPNCZ
IF(FCAFtL.E.1.2
IF(FCAN.*CT.*1.2
25.0*PCAPN.*1l8384
c59*.48*FCAPN*.954735
CPNCZ
CPTbeE = 1Z.V*FrAT*1*81217
CFSYS
-
FCC
TE
C
C
TMEiRAL ExPrI.SIrN VALVE
C
C
CETERMINE
C
CONVENTICNAL
T-E FLCG AEA
CCEFFICIENT 'CTXV'
CAPACITY
CCNTRCLLED SYSTEMS
C
FCR EITHER
C
IF(ICOhNTR
C
C
CETER I1E
C1lTSArE**2 + C2*TSATE + C3
= CI*TSATBP**2 + C2*TSATBP +
1 ) CTxV
EGC 2
CTXV
IF( ICGhTR.E
PRESStjRE DRCP TROUGH TXV
C3
CPTXVI(PSI)
C
IF(NCOF'EG..2)
PTXV
(XR/CTXV)**2/RH03
IF(hCCRE(g.1)CFTXV=(XMR-4oe/(9*l178.1))**2*71.236*
C
C
C
CETERMINE TE
ArTLAL
PRESSLRE CROP
HIC4 WCCLC EXIsT wITf
TE
DPACT'
(PSI)
GIVEN FLCW RATE
C
CPACT - CFTXV + CFNOZ + OPTuBE
RITEr5Z-g)
WRITE(5, )
NCr R-,NSECT SUPER, TROCH3
-ir,-lCEPOCPIE
PIC
5TIE
WRITE(5C*-e) CEi PE,CELPCCPTXVLDPNOZCPTUBEDPOLL,
ICFSLJ
FCOL
WRITE(5,30 ) CAPCAPFTICORFACCAPNOZ,CAPTU.-,'OCAPN.PCAPT
WRITE(E,540) TSATtTSATC ,,CPSyS2CPACT,XMR,,-' -',PGW
261
SATEjTSATCCUTOFFpCPSYSDPACT
WRITE(6s515)
-3)
-
X(Hl1C
CAPE
*3)
CAPC X*(-IC
WRITE(5SjEC) CAPECAPC
C
VAPOR VELCCITY
CETERf INE THE MrTNIrUM SUCTICN RISER
RFGUIcEC FOR OIL ETRAINMENT
IVSR, (FT/HR)
C
C
C
VSRrbgoZ+le*O**t-*eW5875*TSATE+95*ALOGI(DLi3486
C
RISER vAPOR VELCCITY
MTNhiUM DISCHARGE
kFGUIREC FOR OIL ENTRAINMENT
CETERViNE TE
'VCR? (FT/HR)
C
C
C
+5*ALCG10(DDL)+34)
VCR60r.*10.,**l.(=-e315*TSATC
VSPVSRACT*VCRHVCRACT*CTXV
WRITE(Sj,575)
C
C
IS INACEQUATE OIL
FSSAGE IF TERE
WRITE hAlKING
C
ETLR.N
IF ( VSRACT *LT VSRP) hRITE(5,65 ) VSRACT, VSR
VCRACT, VDR
IF ( C:RACTLT.VCR ) R I TE 5, 6
)
67
(
5
TE
R
I
IF (TiC.GE .2 C e
C
C
CROP ACROSS THE SYSTEM AT
ACTUAL PRESSURE
CHECK TE
THE AVAILABLE PRESSURE
ITCPACT'
ATE
THE GIVEN FLCW
TO SEE
'UPSYSs
AND EVAPCRATOR
CRCP BETWEEN CCNSENSER
C
IF
C
C
ALANrE
A FLC6
ACTbALLY EXISTS
C
LT.5.eZ)
IF(AES(CFSYS-CFPCT
S0
CT/E.C
CT
GC
T
10
IF(1'TLT*k.;)
TSATC
IF(CT.LT.[io)
CT
ieL CON TIhLE
C-------w-----CCNTjINLE
130
59e
.514
515
52c
ENC
FGORT ( IlT )
'
FCRt'AT(
CT
TSATC
DT/290
ChCENSER TEPPERA TURE LOOPm - - am
' '=
m--
R'
SUPE
NSECTl,J15
I3J
CCRI-''
H30FF1I094 t
TRCr=',FI~o3,
loFlZ3s'
510
CT
TSATC
TSATC
450
T1C
TC leO
G
IF(CT.LT'-.c)
95
GO
IF(CPSYS-CPACT) 95J3g*90
-CT
T
IF(IEG*1)
#MIOE=51FlO.4J
PIC='iFI~3
PoC = l
FCRFT(
HIC"wtFl0.4+#
NArELIST
IhPLT VARIABLES ARE ?', ( TSATETSATCPCUTCFF)
#Fl!,,3, *
TIET*Fe03)
PI=SF10,3J
TSATCtF7,2p'
FCRP'AT('TSATE;,F72.
1, CPSVSu'F7'2,I t PACT=',F7 e 2)
FGCRPAT'
1iF82
2'
'
CELpCn',F8#.p'
CELt`E.l'F8.2l
CFNCZV,Fa.2,
CFSLP'lF.8:,j
'
CPTUBE' , F8 2'
CPCL-'Foa2)
CUTOFF=JF4.2,
CPTXVu'
CPLL = ',
F 8*2p
)
262
JF
CAPPFT'/Fle3,'
,F123
CA'
FCFrAT(r
53g
21,Fls'
PCFT=jFle.4 )
540
XLEL T '
jSL ='sJF15*5
XL.ECrL'eFi'
Fc~r"rTrI '
FC;AT
FCNrAT
575
VSR ='
FT/Hf
1
2'
F T/
FCR; AT
F CR AT
555
FCR AT
62C
FCREGAT ( F15.
FCRr'T('
CLLIC''
155J''
5)
LCL ='
5)
F
VSRACT'fJ12.5J
T/-R
VCRACTu'JE12*.5
FT/HR
CIL
LIE******')
.w,*.,w**.r
ETLRN IN SUCTICN'
VS'sFJS.5,''*******'
VSRrT='rSF155.J
It*ACE(UATE OIL
CISCARULERTELR VORACT',F15.5s
FCF'AT('
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*3
)
*...**u*w*,COMPRESSOR
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120
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11poF IO 4
FCRM:r (F1'o}
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670
pi15
pit
F 1
(8FlS.5)
1,m* RISE
666
2.b,
VCN=.
CPSYS '
C',
CZOCm F15.5 '
R
CTXv ',FA;.' 4
CAPC -',F15
CAFE ',Fi1b.,'
('
CEG, F')
=',Fik.;41'
TSATpf('
(I ****r*F.AS IG OCCURSI LIGLID
)
iI1,FlC'2
(2FIg.CJ 1 I~ 2Fi
61
650
F
TI
XMR.'sF12*4J
'1
3
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CLLCr"-'sF15*5J'
1,F 1.5'
64 0
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567
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t
PCAPN='
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3,
TSATF= ', F1i.
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CAPTUB'ITF124u1
CAPNCZ=1'F124''
***- t
)
)
ETURN I'
VCH='sF1'5,5
ISCHARGE TfYPERATURE'
263
APPENDIX E
DETAILS OF THE COMPRESSOR SIMULATION MODEL
Details of the compressor model discussed in section 2.3 are
given in this section, accompanied by a detailed flow chart and program
listings.
Discussion of the compressor model can be divided into three
major sections:
1.
Cylinder processes, valve, and manifold modeling
2.
Motor
cooling,
friction, and suction-discharge heat
transfer
3.
Cylinder
Oil circulation effect on capacity
Processes, Valve, and Manifold Modeling
Valve dynamics, manifold pressure
pulsations, and cylinder/
manifold interactions have been modeled as equivalent cylinder pressure
overshoots or undershoots, and valve closing delays, as discussed in
section 2.3.
Cylinder processes on each complete compressor stroke
are:
1.
Intake of suction gas and mixing with residual
2.
Compression
3.
Discharge
4.
Re-expansion of residual mass.
Before going into details of the cylinder processes it is necessary
to determine the effect of suction valve closing delay on effective
264
displacement volume, and of discharge valve closing delay on effective
clearance volume:
The expression for cylinder volume as a function of crank angle,
referencing from
cyl
e = 00
at top dead center (TDC) is:
V2
R
R
4
[Rr{1 + R
R
Vmin +
- cos [sin-
r
1
R
(
sin
r
cos e
)1}
r
Where:
R
=
center-to-center length of crankshaft throw
Rr
=
Center-to-center length of connecting rod
=
Clearance Volume
=
Cylinder diameter
V
min
D
Typically,
R
c
<
.25
r
Hence for angles near TDC
(e
0 )
and
BDC (
approximate cylinder volume as:
V
cyl
V
min
+ V
(1 - os e)
D
2
Where:
VD
4
(2 R)
(2 R)
=
displacement volume
displacement volume
= 180 )
we can
265-
.The.effective .displacement volume accounting for.suction valve closing
delay thus becomes:
V
V
= Vcyl
Deff
min
max
eff
or
{1 - cos[ (1 V-
eff
=
VD
8o )
2
Where
e
- Suction valve closing delay. in degrees after bottom dead
.center (ABDC).
V.
M aximum cylinder volume
Then:
V
Dff
- Displacement efficiency -
V
VD
.6
{1 - Cos[ (1
180
m
)
.]}
2
The effective clearance volume accounting for discharge valve closing
delay becomes:
{1 - cos[eD 1801I
Vm
- Vmin
+ VD
2
eff
Where:
D
Discharge valve closing delay in degrees after top dead
center (ATDC)
266
We can now define the following volume ratios:
-
VR
min
VD
VR
eff
VMAX
=
Vmin
VD
eff
VR
qD
Vmin
V
VR
1 +VR
max
eff
V .
VR
V
1+
min
VRMEV
=
eff
{1-cos
efmin
1 +
D
180]
2 VR
Derivation of relations describing the four cylinder processes then
proceeds as follows:
Intake Of Suction Gas And Mixing With Residual
Amam
max
eff
-m
res
Where:
Am
-
Mass pumped per stroke
m
max - Mass in cylinder at maximum effective volume
eff
V
v
max max
eff
Vax
max
= Specific volume of gas in cylinder at maximum effective
volume ft3lbm
volume
(ft3/lbm)
'267
m
' Mass in cylinder at minim:tm effective volume
res
(residual mass)
min res
eff
"1res
res.
Specific volume of gas in cylinder at minimum
-
effective volume (ft3/lbm)
Considering the intake process occuring at constant cylinder pressure,
the first law of thermodynamics gives:
010
· u-WI +
'
h
e.
ff
h +
zm
i
i
f
- Zm
-
u
o
or
mi h i + mo u
WI
- mf Uf
Where:
mi
m
Am Mf-
mo
=- Original mass in cylinder
mf - Final mass in cylinder
hi
-
Enthalpy (Btu/lbm) of incoming suction gas
atP
APs
cyl
suct
P
suct
-P
s
Equivalent cylinder pressure undershoot on intake
uo S Internal energy (Btulbm)
uf
of original mass in cylinder
Internal energy (Btu/lbm) of final mass in cylinder
WI - Work produced by ga(Btu/lbs
on intake
268
Also:
f
P dV
wI
Pcyl
(Va
suct
)
-
eff
Where:
VR
=
Cylinder volume at the end of re-expansion of residual
x
mass.
Equating expressions for work we find after some manipulation:
o=(h
i h-h
)+(VRMEV)(V~RAX
ax
L) (h h
f)(
)(
efft r
Rx
res
i max) (
Equation E-L
Where:
hmax = Enthalpy (Btu/lbm) of gas in cylinder at end of
intake and mixing (at maximum effective volume)
h\
= Enthalpy
(Btu/lbm) of residual mass in cylinder after
re-expansion
To find the state at the end of the intake and mixing process, we
guess T
max
(and hence
E-l is satisfied.
h
max
and Vax
max
)
, and iterate until equation
269
Then
VR
1
W
(VAX
Pcyl
i
e
) (VRMEV)
v
res
suct
1
res )
(VRMAXeff)(VMEV)
(ax)
For the initial calculation we do not know the state of the reexpansion gas.
Hence, on the first calculation we ignore the
effect of mixing and assume that the state at the end of intake
is the same as the state of the incoming suction gas.
Compression
The first law of thermodynamics yields for the compression
'W '
work
, assuming no heat transfer:
Wc. m max (uo -u)f
eff
Then, for isentropic compression:
W
[Umax- cyl ]
max
max
disc
is
effi
Where:
Ucyl = Internal energy (Btu/lbm) of gas in cylinder at the
disc
isc
is
end of compression
270
And, for non-isentropic compression:
.
W
=
(v..)
max
C
v
em
is
qis
eff
non
is
Where
nis - isentropic compression efficiency
The non-isentropic compression end state is found by guessing
T
)
ucyl
cyl
disc
non-is
(and hence
cyl
disc
Evaluating
Wc
(v
)
1
[max
Iax
max
I
cyl
disc
non-is
eff guess
and iterating until
W
W
max
eff
maxf
eff guess
non-is
Compression work can be found later from the expression:
[u
W
C
w--8on
is
-
u
1l
non-is
non-is
_=
[
- (VRMEV) (VRMAXeff)
max ]
Vres
271
Discharge
WD
PdV P
(V
-V
)
Where:
Work required to discharge the gas from the cylinder
WD
s
P
Cylinder pressure at end of compression (constant
during discharge)
disc + APD
APD
- Equivalent cylinder pressure overshoot
Vcy 1 - Cylinder
on discharge
volume at end of compression
disc
And,
since
discharge
is
assumed to take place at constant pressure
there is no change of state of the gas.
residual mass
in
the
cylinder is
the
gas at the end of compression.
Hence:
VD
'-
cyl vcyl
disc
Pcyl
disc
disc
rVres
That is, the state of the
same as the state of the
272
Re-Expansion Of Residual Mass
As for compression, the first law of thermodynamics yields,
assuming no heat transfer:
WRx rres (
-Uf)
and then
WD
UR
[Ures
V 1Vres
) =
is
eff is
Where:
u
- Internal Energy (Btu/lbm) of gas in cylinder at end
xis
is
of re-expansion
Then
(W
(V
)
- is (V
Mae
efnf
)
is
Where:
nqi
=
Isentropic expansion efficiency (assumed same as
isentropic compression efficiency)
The non-isentropic re-expansion end state is
TRx
(and hence
uR.
non-is
) ,
evaluating
found by guessing
273
W
1
rI
.
ess
guess
non-is
res
res
non-is
and iterating until
W
wx
I
W
-u
_(
eff guess
x )
vE
non-is
Re-expansion work can be found later from the expression:
w
ures -
R
(- Am ) non-is s
V
res
x
]
non-is
1
[ -) (VRMAXeff)(VREV)
-1
After completing one full cycle of calculations, an estimate
for the state of the re-expansion gas is
cycle is
available.
The entire
repeated until the correct valves for the re-expansion
state, and for the
end state after intake and mixing are determined.
For more details, see the flow chart in Figure E-2 and comments
in the program listing for subroutine 'COMP'
at the end of this
section.
Motor Cooling, Friction, and Suction-Discharge Heat Transfer
An iterative solution is
amount
required to properly determine the
of heat given to the suction gas by internal friction, motor
waste heat, and suction-discharge heat transfer.
A first guess for
the temperature of the suction gas entering the cylinder is made
274
and, using the results from the cylinder process portion of the
model, the resulting refrigerant mass flow rate and motor power
are calculated.
The amount of waste heat
due to
friction is next calculated, followed by determination of actual
motor speed, motor efficiency, and motor waste heat.
mechanical efficiency
'nmech'
The assumed
of the compressor, accounting for
friction, has been assumed to be 96% in all of the studies done to
Curves showing the assumed variation of motor speed 'RPM'
date.
and motor efficiency
'n
t
motor
with load on the motor are given
in Figures 2.3-4 and 2.3-5 respectively.
The latter curves are
fairly respresentative of squirrel-cage induction motors in the
3 to 10 horsepower range .
Most of the heat generated by friction
and motor inefficiency in hermetic and semi-hermetic compressors is
given to the suction gas.
A small portion, however, is lost to the
ambient by convection and radiation from the compressor shell.
Next, an estimate of heat transfer between suction and discharge gas is made, using an approximate method to be discussed
shortly.
After estimating friction, motor cooling, and heat transfer
effects on the suction gas, a new estimate of the state of the
suction gas entering the cylinder can be made and the entire process
repeated until the correct state of gas entering the cylinder is
found.
The procedure is outlined below, and is also shown on the
flow chart in Figure E-2.
275
*1.
2.
Assume temperature of suction gas entering cylinder
Use cylinder process model to determine total work
'Wt'
input to the gas
, mass pumped per stroke
tot
'Am' , and temperature of discharge gas
3.
Determine work input to compressor
W
Wcomp
4.
-
tot
Btu
mech
lbm
'Tdisc'
'W
comp
Iterate on motor speed
Assume Motor Speed
i
P
- (m)
(Ncyl) (RPM) (Total Mass Flow)
co ' (W
comp
comp
) A
(Power Output of Motor)
Z Load ' Fm~rmax
o
( ax1
max
on
Maximum Power Output of Motor)
Motor
RPM- f (% Load) (See Figure 2.3-4)
Repeat until correct RPM is
5.
found
oto r - f (Z Load) (See Figure 2.3-5 and listing for subroutine 'EFFM' at end of this section)
6.
Determine waste heat
'QMC'
given to suction gas by
friction and motor cooling
W
QHC - (% Motor Cooling)
(Z Motor cooling
-
comp _ w t]
Tmotor
tot
Percent of waste heat which is absorbed
by the suction gas)
276.
7,
Determine temperature of suction gas after absorbing
waste heat
8.
Determining suction-discharge heat transfer 'QHT' as
described shortly
9.
Determine a new guess for the state of the suction gas
entering the cylinder using
h
new
= h
1
+ QMC + QHT
where
h
new
hi
10.
= enthalpy of gas entering cylinder
= enthalpy of gas leaving evaporator
Repeat steps 1-9 until correct amounts of motor cooling
and heat transfer are found
For more information see the flow chart in Figure E-2 and comments
in the program listing for subroutine
COMP' at the end of this
section.
Approximate Suction-Discharge Manifold Heat transfer
As mentioned in section 2.3, some compressor designs have
negligible amounts of suction-discharge heat transfer, while others
have large amounts.
Presented here is a very rough method of estimating
suction-discharge heat transfer, which is designed to permit study
of the variation of suction gas superheat due to heat transfer with
the discharge gas, while pumping across different pressure ratios.
277
Suction-discharge heat transfer is
.
calculated by subrountine 'HEAT'
·so that, if more correct heat.transfer information for a particular
compressor
is
available, subroutine 'HEAT' may be changed without
affecting the remainder of the compressor model.,
The present 'suction-discharge heat transfer model is as
follows:
Let us first assume that the heat transfer occurs across a flat
metal surface of negligible heat transfer resistance.
ot
TC
I
h
Cold
Then
q =U
U=
t ATlm
1
1
hhH
Where:
q
=
Heat transfer rate per manifold
A t
=
Heat transfer area per manifold
U
-
Overall heat transfer coefficienct
h
-
Heat transfer coefficient
278
(TH
-T
in
)- (TH
ATm
(T, - Tc
iin
-T
(THoul t
)
-T
out
Cut
Cin
)
out
)
(Assuming
counter flow)
I]
Cin
Using the following relation for the heat transfer coefficients in the
2
manifolds
Nu = 1.48 Re'63 Pr .6
and assuming
D
: .75 D
eq
suct
eq
disc
= 1.5 PERdisc
disc
PER
We get, after some manipulation:
.63
(EQAREA ) ATlm
(m)
q
F
+ FD
Where:
Nu
=
hDeq
Nusselt number =
k
pV D
Pr
=
k
C
P
P
eQ
Reynolds number =
Re
P
Prantl number
k
Thermal conductivity of fluid
=
Viscosity of fluid
=
Specific heat at constant pressure of fluid
=
Density of Fluid
279
V
Velocity of fluid
=
Equivalent diameter of flow passage
D
=
eq
4Axs
PER
A
-
Cross-sectional or flow area of flow passage
PER
-
Wetted perimeter of flow passage
&
=
Mass flow rate per manifold
xs
(4) (.75)
(1.48)(k) (Pr" )[
D
s
=
D =
EQAREA=
6 3
v.63
Subscript indicating suction gas
Subscript indicating discharge gas
A
ht
(PER37)
s
xss
Note that the equivalent area term 'EQAREA' does not have units of AEA.
The heat transfer between suction and discharge
found by iteration as follows:
1.
Guess
Tdisc
out
2. T
t = T
out
out
in
in
+
(Td
CP
(Tdisc
in
)
dis
out
out
T
gases is then
280
(TD
3.
AT
-T
in
=
~Im
)-
out
(TD
in
in [(Tn out
-(T
in
Ts
-
)
s
out
F )
Sin
Ts
in+
Toout
in
4.
TD
TD
avg
, k, and
Evaluate properties
*
(i)
q -
out
2
pat
.63
6.
+ TD
Tin
2
avg
5.
)
-T
out
TS
avg
an d TD
avg
(EQAREA)
+ F
ATlm
F
a
D
7,
Repeat
1 - 6 until
8.
QHT =
-
q = q
For more information, see comments
in the program listing for subroutine
'HEAT' given at the end of this section.
Oil Circulation Effect on Capacity
The effect of oil circulation on capacity can be determined once
the refrigerant-oil solubility characteristics, as shown in Appendix F,
are known.
is
As illustrated in Figure E-l, the capacity of a compressor
defined as the evaporator capacity
'Qe'
of a refrigeration system:
:(m - h3
Qer
Where:
hl'
h3m
-
Enthalpy of total mixture leaving evaporator.
-
Enthalpy of total mixture entering evaporator
-
Total mixture mass
m
flow rate
281
The enthalpy entering the evaporator can be defined as: (from Cooper 3)
h3- (x) (h3 ) + (1
m
x) (h3.
oil
)
ref
Where:
h3
Enthalpy of pure refrigerant entering evaporator
ref
h3
-
Enthalpy of oil entering evaporator
-
Weight percent of oil circulating in system
oil
x
ibm.oil
(ibm oil + Ibm ref)'
The enthalpy of the total mixture leaving the evaporator can be
'defined as:
hlm - (z)+(I-z)
(hl
z) + (1 z) (h
m
Z
ref
vapor
Where:
Enthalpy of pure refrigerant vapor at
hl
1
ref
vapor
and
T
super
Enthalpy of
hz
Pt
sat
leaving the evaporator
liquid mixture leaving evaporator
at T
super
z
-
Weight percent of liquid leaving evaporator
lbm liquid
lbm total mixture )
282
The enthalpy of. the liquid leaving the evaporator can be defined as:
) + (
= (w) (h1
h
ref
liq
-
)
(hl
oil
Where:
h 1i
oil
h
Enthalpy of oil leaving evaporator at
Enthalpy of refrigerant liquid at
href
liq
w
T
T
super
r
supe !r
leaving
the evaporator
= Weight percent of refrigerant in the liquid leaving
the evaporator
lbm ref liq
(Ibm oil + bm ref liq)
Then, from continuity we find:
x
1 -w
The enthalpy of a typical refrigeration compressor oil, referenced to
a base at -400 F , as are the refrigerants, is:
h
oil
(.403) T + (.00025) T 2 + 15.75
283
Where:
T
h
Temperature (oF)
=
Btu/lbm
oil
The density of a typical refrigeration oil is about:
57.6 lbm/ft3
P o7
The work of compression of the oil
'Wo'
oil
is hence:
AP
oil
Pol
Where
P Psuct
Finally, the total power
ref
disc
''
required by the compressor is
oil
Where:
Pf
' Power required to compress refrigerant
foil~ wx
mref
-
W
-Power
required to compress oil
Total mass flow of pure refrigerant
For more information, see comments in the listings for subroutines 'OIL'
and 'COMP' at the end of this section.
284
Modeling Early Suction-Valve Closing
The early suction-valve cut-off method of compressor capacity
control is modeled using the same model as for a conventional
compressor with two exceptions.
First, the effect
of late suction
valve closing is eliminated when cut-off control is in use.
Second,
there is an expansion of the gas in the cylinder after the suction
valve is closed.
Only one additional input is required to model early suctionvalve cut-off control:
V
V
CUTOFF - 1
cut
m
V
Where:
V
out
CUTOFF
=
Total volume of cylinder when suction valve is closed.
=
Indicates the amount of capacity reduction, but is
not synonomous with
flow reduction
Modifications to the compressor model are as follows:
First let us define the following volume ratio
V
VRCUT=
cut
= 1 - CUTOFF + VR
D
Let us
also define the state in the cylinder at cut-off as the end
state for the intake-mixing-process, and give it the subscript 'CUT'.
We then have, from the first law of thermodynamics on the expansion
of the gas after cut-off:
285
W`x = m (
-
f)
Where:
W
work produced by adiabatic expansion of gas
ex
V
m. m
V
max
max vmax.
=
cut
vcut
---
Then
1 + VR
l+VR
V
max
VRCUT
cut
and
V
max
ex
(u-
vcut
=
m-ax
max
Where
cut = Internal energy of the gas in the cylinder at the
beginning of expansion after cut-off.
IV
= Specific volume of the gas at the beginning of expancut
sion
First, assume isentropic expansion and evaluate:
W
ex
m is
_ ex)
= u
cut
-u
maXis
The non-isentropic work of expansion is then
W
ex
(m -)is
exW
(5_
)is
non-is
Where
is = Isentropic compression and expansion efficiency
286
To find the non-isentropic end state 'max' for expansion of cutoff gas, we guess
Tmax
W
ex
(-))
m
guess
(and hence
umax
) evaluate
nns
=u cut -u max
is
non-is
and iterate until
W
W
ex
m
ex
guess
m
non-is
The non-isentropic work of expansion can be evaluated later from the
expression:
W
(cu
t - uax
ex
=
non-is
[ 1 - (RMAXM)MEV ) ax ]
am
res
Unfortunately,
implementing the expansion of cut-off gas cal-
culation into the simulation program is not as simple as presented
above.
The superheat of the suction gas is always great enough to
prevent expansion of the suction gas into the saturation region,
because of motor cooling, internal heat-transfer, and mixing with
residual gas.
However, during the first few iterations on the effect
of motor cooling, mixing, and the like, the superheat has not been
added in, and expansion of the cut-off gas does go into the saturation
region.
To prevent an abundance of error messages and possibly
fatal errors (which would terminate the calculation), expansion into
287
the saturation region has been accounted for.
The relations describing expansion into the saturation region
are as follows:
Isentropic expansion:
S
cut
-S
max
Guess various
and evaluate
sat
Quality
-
vf)
and
Quality
-
cut'
S
f
Sf
-S
Sg
Where
r -
Specific volume
S
-
Entropy
f
-
Subscript indicating saturated liquid
g
-
Subscript indicating saturated vapor
Quality < 1
If the two qualities are contradictory, i.e.
and
Quality
> 1, then the isentropic expansion is not into the saturation
region.
If, however, the two qualities can be made equal at some
Tsa t ,
the expansion was into the saturation region.
Evaluate:
ax
max
non-is
- n
cut
cut
is
cut
-h
maxis
+P
mais
max
288
T
and repeat the iteration of
Guess
T
u
u
>
max
non-is
for the non-isentropic expansion:
sat
Evaluate
If
sat
-
= h
g
g
- P
sat
V
g
, then the non-isentropic expansion is not into
u
g
the saturation region.
If, however, the internal energy
'umix '
at
the guessed saturated mixture can be made equal to u
max
Tsat
some
of
non-is
then the expansion went into the saturation region.
W
As before, the work of expansion
ex
ex , can be evaluated later.
For more details see the program flow chart in Figure E-2 and comments
in the program listing for subroutine 'COMP' at the end of this
section.
References
1.
Handbook of Air Conditioning System Design (New York: McGrawHill Inc., 1965) pg. 8-21.
2.
Hughes, J.M., Qvale, E.B., Pearson, J.T., "Experimental Investigation
of Some Thermodynamic Aspects of Refrigerating Compressors",
Proceedings of the 1972 Purdue Compressor Technology Conference
(Purdue Research Foundation, 1972) pg. 516-520.
3.
Cooper, K. W., and Mount, A. G., "Oil Circulation - Its Effects
on Compressor Capacity, Theory and Experiment", Proceedings of the
1972 Purdue Compressor Technology Conference (Purdue Research
Foundation, 1972) pg. 52-59.
289
3
2
P
r
e
S
u
r
e
(P)
Compressor Capacity Defined As:
-
(h - h 4 )
Where:
m = Refrigerant Mass Flow Rate
Enthalpy (h)-
-
COMPRESSOR CAPACITY DEFINITION
FIGURE E-1
290
FIGURE E-2
FLOW CHART FOR COMPRESSOR MODEL
,art
Ir
Define Constants
1
L
,
1l
Yes
Caoacit
Control
No
:)
7~E
-
=
Ir
L------Define
Volume Ratios,
Including Cut-off
Volume Ratio
Fffect of
Suction Valve
Closln
Delav
.=
i
4,
!
Define
Volume Ratios
-
l
r
Effect of
Discharge Valve
Closing Delay
Define
Effective Clearance
Volume
,
_
Repetitive Loop
K
To Vary
Condensing Temperature
N>-
_'1
'F~~~~~~~~~~~~~~~~~~~~
I
Repetitive Loop
Ir- -
-
-
To Vary
Evaporating Temnerature
I
4?
291
Add Superheat
I
From Evaporator
T - Tsat + Super
w
Approx. Discharge
Valve Dynamics
Using Pressure Overshoot
i.e. Pcy - Psatc + Pdisc.
_
_
_
_
_
7
.
Approx.
Suction
Valve Dynamics
Using Pressure Undershoot
i.e. Pcy] - Psate - APsuct.
--
-
--
r
I1
Define
Initial
Guess
For Suction Gas State
Entering Cylinder
Iterate on Motor Cooling
and Internal
,
Heat Trans.
_
-
,
I
Define
Suction Gas State Entering
Cyl. AfterMotor Cooling &
Internal
eat Trans.
I
!
j
Iterate on State at End of
Suction Stroke due to Mixing
Suction Gas With Residual Gas
r _<
I--
1
-
I
=
Yes
F
I
Capacity
Control
?
No
292
1_
Expansion of Gas
After Cut-off
Set States
At BDC Equal
to States
at
Suction Valve Closing
,
.
,
,
Check For
Isentropic Expansion
Into Saturation Region
_
Calc. Isen.
Expansion in
Vapor Region
No
_
_
Yes
r
Non-isen
4'
l
No Calc.
Check For
Non-isentropic Expansion
Into Saturation Region
.
_
,
Expansion in
Vapor Region
o-ise
M~al.
L
.L
I···.v
Yes
I
.
Define
State at BDC
!
I
r
4'7 __
Iz r
·
IIsentropic
_
_
Compression
Ia
__
r
!
_
Non-isentropic Compression
I
·
!
Define
State at End of Compression
i
I_
_
7
Discharge
At Constant Pressure
.
!!
·
,~~~
l
293
Define
State of Residual Mass
At End of Discharge
Isentropic Re-expansion
of Residual B1ass
Non-isentrovic Re-expansion
of Residual Mass
I
I
Define
State at End of Re-expansion
Mixing .of Residual Mass
With Suction as
Define
State at End of Suction
Stroke, Accounting for Mixing
q
A
/;E2
T
~L_~
F
~Iteration
i ion
P¢ing
I
2a
7
r
r
Determine Refrigerant
Flow
Based on First Guess
For Motor Speed
iii~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
r
294
-
Iterate
-<
-
I
I
To Find Actual
\ Motor Speed
_
I
_
I
I
Determine Power
& Percent
Load on Motor,
Accounting for Friction
I
l
Losses
I
_
I
ompressor
in
_
Determine Actual
Motor Speed
I
i-
I_
_
P
I
Determine Actual
Refrigerant Flow Rate
I
I
L-
I
I/
End
4
f Iteration
-
on Motor
Speed
IF
·
Determine Motor Efficiency
As A Function of Load
.
Ir
!,
_
I
Determine Motor Cooling &
Effect on Suction as
_
-
·
Between
.~~~~~~~~~~~~~i
-
Account for Heat Transfer
Suction and Discharge Manifolds
I
.
M
.~~~h
295
Define
New Estimate of State
of Suction Gas Entering
Cyl.H1 - HII + OMC+ OHT
End
Iteration
on Motor
Cooling
4
+
-
r
Estimate Steady Flow
Pressure Drop Through Valves
(For Reference Only)
r
I1
Determine Oil-Refrigerant
Solubility at Evaporator Exit
i~~~~~~-
I
I~ll
I
I
I9
i
Determine Effect of Oil Circulation
on Evap. Exit Enthalpy & Net Capacity
__
Power Required
Determine Total qIre
s
Determine Discharge Vapor Temp.,
Affected by Suct.-Disc. Peat Trans.
_,!
+
L_
/
_
E_
End
Nvap. Temp.
Repetitive
Loop
296
.
--
_J
297
SUERCLTINE CCrtPFNRTSATEICTEJNEP TSATCI DTC,NC, SUPER,
ICCNTRCLTOFF)
C
C
C'
C
C
.C
C
C
'C
C
C
C
C
PURFPCSE
TC SIPLLATE kERPETICALLY SEALED REFRIGERATION
CCrPRESSORS
ThIS FCGRAl
PREDICTS SLCH THINGS AS MASS FLOW
RATEJ CISC-A:GE
TEMPERATURE, PC*ER CONSUMPTIONs
ANC CEfTAIN.t.NVESIRABLE
OPERATING CONDITICONS SUCH
AS IC.ELATF
CTON CCLINGJ
EXCESSIVE CiSCHARGE
T'EMPERATLREFxCESSIVmE FC.ER CONSUMrPTION, AN: LC~
r'CTCR EFFI.INtCy
NOTE:
TrIS PCRA'
CAN SIMLLATE EITHER CONVENTIONAL
CCrFiCSRSG
~, vARIAdLE CAPACITY CMPRESSCORS
tACrIEVE
cYtARLY
SUCTIGN VALVE CLOSING)
C
C
C
C
c
C
C
GENERAL CtSCkIPTICN
l'E CCPmRSSr
ScTECKE IS
SEPAiATEC
SEPArATE
-RC£ESSES: NE-EXPANSICN
INTAKE OF SLrTICN GAS AND MIXING
INTO
FOUR
O
FIVE
F ESIDUAL
ASS,
ITH RESIt;UALp
c
C
c
EXPANSION
c
VALVE CLCSING (CKLY UN CAPACITY CTOL
CASiS)
CCrFRESSICN
CF GAS IN CYLINCck TC ~-I3H PESSLRE
CISCiARGE CF GAS IN CYLINDER
T CCNSTANT FnESSURE
C
cC
CF GAS IN CYLINDER
AFTER
EXPLICIT
INPUT PARAMETERS
KR
*
NLteR
CF REFRIGERANT
TSATE-
SATURATIGN
GR IF
(12*22,
TEMPERATURE
SCTICN
EARLY
OR b2)}
AT EXIT
NE
a
a
TSATC-
EXCESSIVE*
TO TrE
ENTE;ING
TE
CC-ePESSCR
(;
TE PFRATLRE INCREMENT FOR EVAP.
NULtV-R CF EVAP. TEMPS,
EXAMINED
PES.
(F)
SATLRATIGN TEePIN
CCNDENSER (F), OR,
IF' TSCHARGL LINE PRESSURE DOP IS EXCESSIVE,
SAT.
EXIT
TEPP CORRESPGNCING
CF COMPRESSOR
CTC
-
TEFRATURE
NC
'
NLMEF
S:PER-
OF EVAPORATOR
LINE PRESSURE DROP I
SATURATION TEMP.CORRESPCNCING
CTE
SCTICN
T
PRESSURE
AT
INCREMENT FOR COND.(F)
CF CONDENSER
TEMPS.
ExAMINED
SLFPEREAT CF VAPFG ENTERING THE COMPRESSOR
AeCVF TE SATURATIch TEMP. AT THE ENTERING
PRESSURE (F)
ICCNTR- CCNT4CL INICATCR
'ICCNTR
I MEANS CCNVENTIONAL COMPRESSOR
'ICCNTR - 2 rMEANS CAPACITY CONTROLLED
CCIFESS'GR
CUTCFFe
A FAPAMETER
USED
TO INDICATE
CAPACITY CCNTRCL USED -
tCLTOFFF'
1.e -
IT
(VCLCUT
THE ACUNT
IS
DEFINED
OF
AS
VOL.MIN)/vCLGDISP.
298
C
C
vWERF VCLCUT IS TE VCLUME SWEPT BY THE
PISTcN BEFCRE TE SUCTION ALVE IS CLOSED
C
VCLrmIN
C
vC.rISP,
C
(ALL FER CYLINDE.R)
C
INPLT PARAPMTERc
C
NCYL
C
VR
IS THE
IS TE
CF
CLEArANCE
'V'
C
VCLUME
ISPLACErENT VCLUVE
FRCM CCrrCN
NLtrBF
a
CLEARANCE
COMPRESSOR
VCLUrE
CYLINCERS
RATIC,
CEFINED
C
VC
C
C
C
SYNC RPM -
SvcFT
Y PSTCN)
(CU FT)
SY~NCcRGNO6S CTCR SPEED (RPM)
iNITTAL GUESS F
ACTUAL MCTOR
C
EFFIS-
INTrkCPIC
a
C
C
-
VaLVF
CPS
VtVF
FLCw
C
CPFRAC-
C
SCELAY-
C
C
C
C
C
C
C
TC ACCOUNT
P-T
PHTC
EAD
EAS
SPEEDC (PM)
COMPRESSION AND
CF THE CYLINDER
FOR
VALVE
'
*
C
C
C
FCWPAX-
C
PRhL-
C
EGAREA.
VALVE
AND
DYNAMICS
CRCP ACROSS
TC ACCOUNT FOR
LOSSES
(I)
SUCTICN
DYNAMICS
ANC
(NCT .LSEC EkE)
VALVE CLOSING
SLCTTCN
BCTTrr
FrC
FORTIChS
FLCh LOSSES (PI)
- EgIIvALENT PRESSURE
C
C
C
EFFICIENCY CF TE
EPRI
E>-IvALENT
PRESSLRE CRCP ACROSS DISCHAFGE
C
C
C
C!iPLACEMEtT VCLUME PER CYLINDER (VOLUrE
ELxFAKICN
PZCSSES
C
AS
OLMIN/VGLCISP,
CELAY
(DEGREES
AFTER
CEAG CENTER)
FERCFNT OF COMPRESSCR
RErOvED
Y ThE SCTION
IS LCET 6Y CNVECTICN
(NCt SED ERE}
(NCT SED EcE)
(NCT SED rEE)
(NCT USED
EERE)
OTCR HEAT WHICH IS
GAS (THE WEMAINCER
TO TE AMBIENT)
tVx iuf
PCiEk
CUTPUT CF COPRESSOR
MCTCR
(K')
e.hEN CPERATING AT MAxIMUM PERMISSIBLE
CVERi CA
NT
ct
$E
HERE
E4LIVALENT
EAT TRANSFER AREA
ETWEEN
ANC DISCHARGE MANIFOLDS
(FT***37)
C
SLCTTCN
C
-
C
C
CF INTERNAL
EAT TRANSFER LOSSESJ IF A
FARTTCULAR COFPRESSCR CESI3N SCULD
REQXIRE
C
THAT
C
(T-ERE
C
C
THiS
SEC T
IS
IT
GIVE
A RUSH
APPROXIMATION
E ICLLCEC
ISP HCOEVER,
NC REPLACEMENT
FR
THE
ACTUAL CCNCITICNS IN EACH COMPRESSGR)
CCELAY- DISCHARGE VALVE CLOSING CELA (GREES
C
AFTE;
TCP CEAD CNTER)
C
xCIL
GIL rIRCuLATIcN
C
EFFME-
MECHANICAL
RATE (LBM CIL/LBM OF
EFFICIENCY
OF
CCMPRESSOR
EF*+OIL)
299
C
CATA CCNStANTS
INPLT
C
NREF
C
SLPEMV &
-
REFRTGERANT
NUMBER (USUALLY
INhV - CCEFFICIENTS FCR
C
VISCCSITY
C
THERMAL
C
.
C
C
CPRV1
AS
NR)
VAPOf
F REFRIGERANT
SLPEKV & XIKKV - CCEFFICIENTS
C
SAME
CETERMINING
ETEMrINING
FR
CCNiLCCTIVlTY
OF
LFRIGERANT
VAPOR
CCEFFICIENTS
FOR CETEAINING
SFECIFIC
&.EAT AT CONS. PRES.
a CRvP
C
CF
VAFCR
C
C
C
OUTPFT PRAMETEPS
TIC
a
TErP.CF
C
fC
C
C
C
x~*R P
* a
E
-
J
a
REFRIGERANT LEAVING COMP.(F)
ENT-LPY
CF
EFRG.LEAVING
COMP. (BTU/LEr)
rASS FLCu RATE CF
EFRG.LEAVING CCP,(LeM/HR)
FCwEp INPLT
Kw) REGUIREC EYCOMPESSCk
MTOR
CCCLTNG CAPACITY OF CCPRESOSOR (:/R)
C
C
eASEr
LCSSS
C
EFFECT
C
ZERO SCCGLING
ON I-IG - U LC,
CF
AND NO PRESSURE
SICE,
ITi- THE
IL CIRCULATION
INCLUDED
C
C
C
REP AKS
tIoIs
FCGRAM
CALLS S;EHCUTINE
TIAL
TO CETEkMINE
C
C
C
C
VAPCR PROPERTIES
rMUST BE FCUD
PUICH
BY ITERATION
TI-IS
FCG;AM
CALLS SRCUTINE
VAPCR TO DETERMINE
VAPCR PRCERrT!ES
TI-Is
FCGAVf
LES
FUNCTION
SUBPROGRAMTSAT TC
C
CETERPlINE
C
TC
C
C
C
C
C
A?;LRATICN TEMtERATuttES CORRESPONDCING
ihESuRES
Ti-IS FRCGAM CALLS SBRCUTINE
SATP;P TO DETERMINE
SATLRArTICN STATE PRCGFETIES
TI-IS FCGAAM
LSES SL 6RCLTINE CIL TC DETERMINE THE
REFR ICrANT-rILL
SOLUcILITY
kE±AVIC'
Tt-IS FCGRAt
LSES FuNCTICN SLPRCG.AM
EFFM TO
C
C
CETER"INE
CF LCAC
C
T-IS
C
SLCTIChN-ISCtikGE
C
C
NOTE:
GIVENh
CCrO-FESSCR
FG-RAM
CTCR EFFICIENCY
LSES SuRCUTINE
rEAT
AS A FNCTICN
TO DETERMINE
hEAT TRAkSFrR
INPlT
CATA rCNSTANTS FCR VAPOR VISCOSITY,
ETC. ARE
FCR REFRIGERANT 2
CNLYD AND SBRCUTINE CIL,
FCR
C
C'ETERFINING
C
REFRIE
EFRIGERANT-OIL
ANTs 12.
SLUBILITYIS
FOR
AND 22 ONLY
C
CCMPCIN/CCP/N CCLVR
VOSYNCRPM
EFF I S, DP I CPS, CPFRAC,
iSCELALYpr,
PC~lkTT T p TD*EAC EASz
T XVR~ FPO;Q IC h I CJ p 1 CE; P I CJ
2P1CEjiTICElC
P MAN PwRNL EAE
A, D-LA Y XCIL. EFPF'E
CATA hREF sS.FEtvXINMVlSLFEKbVsXIKV/22
CATACPFv CV/;:C.e3
F.3
hRITEI15,6&cZ)
19 I4/
EF;SLtFFVLACFOIPSCPPFkAC
*,.0~
75.3
272
300
*R ITE (
CyL, VRjVCRFPSUPER
6t)
RITE(57vo)
EArEASPkTEFFCGPHTTCDPMC
ITE(5je32) SYNCPOWPAXPv*NLCCELAYSCELAY
ARITE(b,7Z) ICrNTRjCUTCFF
'RACT
v,
IF( ICChT,
EG.2)
CC
1
TC
C
C
CCMFRESSOR
CCNVENTIChAL
c
C
C
'EFFD'
CALCLLATE TE
CSPLACEMENT EFFICIENCY
VALVE
CLCSINC rELAY OF TE SUCTIN
eY TE
C
C
(NCTE TAT
TI-IS EFFECT
IT)- EARLY SUCTICN
S NCT PRESENT)
VALVE
AS AFFECTED
CTOFF
CCNTRCL,
C
EFFC
(i'eC-CCS(.14155*(t1eg-SELAY/18J)))/2*e
C
C
CALCLLATi
TE
EFFECTIVE
vRf
CLEARANCE VOLUME RATIO
C
VR
VR/EFFD
C
C
CALCULATE TE
EFFECTIVE
AXOVOLUPE RATIO
'VRMAX',
C
CEFINEC AS 'VRMAX'tVOL@MIN/VOLMAX,(EFFECTIVE
VOLUMES)
C
VRMAX
·
+
VR/( 1.
R)
C
C
CALCLLATE EFFECTIVE
CISPLACEMENT
VCLUrE
C
EFFC*VC
VC
GC TC
C
C
CAPACITY
CCNTRCI LEC CCMPRESSCR
C
C
CALCLLATE TE
C
#VRtrAX
=
rXVOLLME
VCLM!hN/VOLMAX
ATIC
,VRMAX, DEFINED
(ACTUAL
AS
VCLUMES)
C
1
VRMAX
a
vR/(.Z+VR)
C
CALCLLATE
C
C
AS tVRCUTO
VCi .CF CYLWHIEN
VCL.CISP.
(ACTUAL VOLUMES)
c
VRCUT2
TSATC
=
TE
VLU-E
RATIO CF CLTOFF
sUCTICN
CONTROLCEFINED
VALVE
IS
CLOSED/
1.e-CLT-FF + VR
T
SATCI
-C
C
CALCULATE VOLr;F
C
C
aS
C
RATIO AT
AFFLCTEC
Y TE
·
EFFECTIVE
'VRMEV'
IN.EFFECTIvE
CLCSING CELAY OF TE
MINIPUM VL./ACTUAL
VOLUmE
VRMEV',
DISCHIARiE
VALVE
MINIMUM sVL.
301
C
c
LCCP FCR VARYING CONCENSER SATLRAATION TEMP
CC 45e III - iNC
TSATC
TSA.TC
+
TC
C
C
CETERMINE SATLRATICN
PROPERTIES AT
TSATC'
C
CALL SATFRP ( NF, TSATCPSATC,
VF, VG, HSATLC
HFG, HG, SF, SG )
C
C
LCCP
FCR
ARYINh
EVAPCRATCR
SATLRATION
TEMP.
C
TSATE a TSATEI
CC 35e
.wJ
CFCV
,FSW S
.
ihNE
eo'
Z
TSATE
TSATE
+ CTE
C
C
CETERHINE SATURATICN PROPERTIES
AT
TSATE'
C
CALL SATFP
(NR
T1
TSATL +
T1CE
T1
TSATEPiEsVF
VG,-F,
FG, HG, SF, SG)
SLpER
C
C
CETERMINE REFRIc(ERANTPRCOPERTIES ENTERING COMPRESSCR
C
CALL VAPCR (NR TI CLFiCEvEvAPCE
CE SVAP
C
C
LCCP FCR
C
CRCR
TUCYING TE
CCEL FCH
tE
EFFECT CF THE EUIVALENT
CISCHAGE
VALVE
(NCT
IN
PRESSURE
USE r-E4E)
C
CFC rn CPCI
CFCn
CFcI
CC 2
IFDwl,2v
C
C
CETERMINE THE ACTUAL CYL.PRES.AT
CISCHARGE
P21 (PSIA)
C
P2 a PSATC + CPr + DPCV
C
C
c
iCETERMINE ACTLAi CYL.PRES.CN SCTICN
F;1
F1CE
-
STHOKE'P1I
(PSIA)
PS
C
C
C
C
rtAKE AN INITIAL
GLESS FOR THE
CTUAL TEMPERATURE
OF
Tt-E
AFOR ENTEZTNG THE CYL.CN SUCTIGON STROKE,
AS
AFFECTEC
Y CToR COGLING
'Ti = TCE
+ 2
(F)
C
TI = T1CE + 2c
CALL
VAFCR
F1
FIi-
S
DTiAVG
N,
T1
CDPv
c e .
1 II,VlHIS1
)
302
C
C -----ITERATE CN rCTrR COCLING AND INTERNAL HEAT TRANSFER--PFREV
11
C
C
SET TE
C
TCLLERANCE 't-TCi , tBT/LB ')
ETTALFy
AND INTERNAL ENERGY CONVERGENCE
C
'TCL
CC 12
1
K
. ,2e
,rEF = Ek
VREF
=
TI1
.
T1 + 3.
C
C
LSE TE
C
TC
GENERAL PFCPEkTY CONVERGENCE SUBROUTINE
CETErINhE
VApCR
PRCPLRTIES
CALL TRIAL ( N, TT1-3.,Pl,
GIVEN
3HHTOL,
H,
AN
TRIAL,
P
VH SS; T
C
C
SET
C
C
SLCTICN VALVE C CSING (CUT-CFFI VCUT
HCLT (eTL/Lt,,
SCUT (BTU/LM-R),TCUT
INITIAL
vcUT
VCUT
VALiES
FOR VAFCR PROPERTIES
AT EAkLY
CU FT/Le
(F)
),
V
K
tCLT =
!'
SCLT
= SS
TCLT
=
T
C
Cwmmw-w-IELkMCCYNAMIC
STATE EALANCE AND
IXING----------
C
C
C
ITERATE C A TFRMCCYNAMIC
CF TE SLCTICh
TRCKE
c
STATE
ALANCE
AT TE
END
J = 1, E
CC lge
IF(iCChT*.EG*2)
GC
TO
3
C
C
C
IF 'ICCht,
ANC STATES
C
CEAD CENTER - SKIP EXPANSICN OF SUCTICN GAS SECTICN
1
kE ARE STUDYING
A CONVENTIONAL
CP.
AT C:T-CFF
ARE SAME AS STATES
AT b0TTCM
=
C
VVAX
rM'AX =
SMAX
VCLT
CLT
FCL
a *,e
WEXCLT
GC TC
4
C
C-----EFFECT
CF EXFANSICN CF SLCTION GAS AFTER CUT-OFF----WM
C
C
DETERMINE SPECIFIC
VOLUtE CF VAPCR AT BOTTOM
CEAD CENTER
303
C
(eCC)
C
'VrAX',
3 'AX
CONSERVATICON
USING
GF
MASS
VCLTS(lc,+VRI/vRCUT
C
C
LSE
ICEAL
P
I*VCLT/\vrPA
GAS LAB TO CBTAIN
FIRST
GUESS
FOR END PRESSURE
C'
C
C
CHECK FCR ISENTRCPIC
EXPANSION
INTO SATURATION REGION
C
NCLT = 3
T = TSAT(hR,P)
+ 3e.e
CT = le1,.
CC 2!5e I = 1,3e
T
r + CT
CALL SAT
P(NRsTjPVFpVGFNFG,t-GSFSG)
h
CLAL.S= (SCUT(V~'AA
CLiALV =
iF((GLAL'*GT1a,)
S'F)/SG-SF)
- VFi/( VG - VF)
ANC* (CUALV°GT*1.*))
GO TO 25e
C
C
C
EXFAISICh
CALITIES
C
vAPC; REGICh ICFNTRCPIC EXPANSION AT STEP 272
IS NhC ILTC SATLRATION REGICN IF ThE INCICATED
'GLALS' ANC 'GUALV' ARE CONTRADICTCRYGO TO
C
IF(((;UAL.C*GT*I,*)JANC*(ULV*LT1*0e))
IF(AP!S((;LALS-LALV)*LEEI1)
LAL ) 25eZ26Zj24e
IF((;lALS 240
Tr
T
cT
25¢
GO TO 270
GO TC 260
CT
CT/2.e
CCKT.INLE
R ITE (5,
)
GC TC lelk
260h
;LALSO*F
rAx
AX
SrAX
= SCLT
TrA
=
FFAX
=
+
F
T
LrXsI-CLT-P*VCiT*144.0/778OEFFIS*( HCUT-MAX(P
lVCLTT.IPr'A*VMAX
)144,0/778e)
C
C
IF
C
REGIJC, ThEN CFCK
C
C
GCES INTC THE STURATION
ThE ISENTRHFIC FXPANSICN
T
ITRCPIC
CT a
EXPANSICNh
ENT INTO
TO SEE IF TE
REGION,
THE SATURATION
NON-ISENTROPIC EXPANSION
BASEC ON RESULTS
Ev
Tr
-
CT
CG
!eg I =t i3e
T
'r
+
CT
CALL STFRP(
CGPALV= (VAX
TP,VFVG-FHFNFGh-GSFSG)
-
VF /(VG - VF)
FROM
304
G Tr 28z
IF( 'LALVGT*,
G F*VG*144,e/778*W
LG
C
TE
ENERGIES
C
IF
C
C
ARE CCGhTRACICTOpYs
ATTICN
INTC TE
ITERFNAL
'AX'
AtD
'L'
(BTU/LB
EXPANSION
THEN NCN-ISENTRCPIC
EGICN - GO TO STEP 275
IS NCT
C
C TO 275
IF(UrAXGE.UG)
I
=
+
GUALYV.FG
U *
F
- FvMaX1i44.e/77.*e
IF(A2S(tbrx-L)
IFC'AX
280
cE.-TCL)
rT =
-
GC TO 295
25,299f
2E
U)
CT
CT = CT/E.,
2ce
CCKTINLE
I T E (~
CC TC iCt.
255
1Z)
SSAX = cLALV.(,r-SF)
.R ITE (
/ ) G bLVT
GC
TC
+ SF
P
1C
C
EPANSICN
NCrhSATUATEC
C
SECTIcN
c
270
F
PVCLT/V"AX
PRES RE
ITERATE
C
CC
ECG STATE AT
C
C
CP
-
PF -P
TO FINC
ISENTROPIC
EXPANSICN
.a
CF
OC 6 I
lshCLT
F = P +
r
T s TSAT(NRPF)
TSTART - T - 5,e
CALL SATFRF
IF
N~,
v!,AX. . T.VC)
'T,
PsATV VVG,
eC
HF, HPFGG,G, SF, SG )
TO 5
C
C
USE T-E GENERhALFRCPERTY CCNvERGENCE
C
TC
CETERE'INE
AFCR
GIVEN
PFRGPERTIES
C
GO
t;
TO
IF(CCLT-ES) 6o7,5
P ,
P-CP
CF = CP/2 0
6
CCNTINLE
*iRTE (5 73
R IrE (5
R ITE (
)
42 ) V a Xp SC'UT P VG* Vj SS
71
IFCP,C. K
, ITE ( t 7?:2)
J I
AND
V
.eColsVVSST)
CALL TRIAL(N,TsTTARTt,5:,P,2,vrAX
IF(AES(SCLT-3S).LEC¢005!)
SUBROUTINE
P
7
'TRIAL'
305
GC
7
TC
1gC
iNMAX s
H
S~AX - S'
TrA
= r
Pr'AX - F
L'AX
MCcTPl*vCUT*144½e/778.i-EFFI*(HCUT-W'MAX-
I(P1 VCLT-FMAX*VhAX
I1,44-e/778. )
275
F*VCT/VAx
;.
P
C
C
ITERATE CN PREScLRE TC FIND NON-ISENTROPIC EXPANSICN
STATE AT
C,
USING RESLLTS
FROM THE ISENTHRPIC
C
ENC
C
EXPANSIC
CASE
C
CP
=
F = F: -
F,
CF
= 1,NCLT
CC
F
F
T
TSAT(NR,P)
+
CF
rsTaT
A
T - 5
CALL SATF kP (NfiRT PSAT VF VGG HF, -FG, IG, SF, SG)
IF(Vt'AX.LT.VG) rC TO 8
TC CETEFINE
VApCR PRCPERTIES GIVEN P AND V
C
CALL TRIAL(NRTsTART,5.,P,2,sV'AX,
.eC1,VSST
F*V"144,./778.*
-
IF(A2S(Lj'AX-L.)sI
IF ( L'AX-L
P )
8
P
=
)
GC TO 11
E.TOL)
lg.
FL~P
CP s C1/2*9
S
CChrINhLE
I TE
X
LA
X
U
P
VG
ITE((5,71 ) ICPCK.J I
GC
TC:
CLk.
~R
iTE(5,76)
Tp,FISSV
SrAX
SE
CEFIhE
t.-'aXt
'TIX'
STTE PRCFERTIES AT eDc (AXIMuM
VOLUME.)
(eTU/LEV)s
fVVMAX' (CU FT/LEM)i,
SMAX' (BTU/LB'-R)
r
X
TtFAX
I
C
C
C
C
(F)p
'FMAX'
(PSIA)
C
10
T
C
C----ENC
CF EXPANSTCN
OF SUCTICN
GAS AFTER
CUT-OFF------
C
C
C
CETERMINE STATE PRCFERTIES IN CYLINCEq AFTER COMPFESSIOCN
ASSLINhG ISENTRnPIC CCMPRESSICN
306
C
4
CALL TRIAL(NlrTSATCE~2~P2p4tSMAXpsOeZ5VtHSSJT)
V/
*
V
SE = SS
_ T
T2
c
C
(BTU/LBM)
WC
ORK
CCPRESSIGN
NN-IFENTRCPIC
CALCULATE
C
WCt( -MAX-H2+ (F2*V2WPrAX*VAX )144e/78
EFFIS*
)/(778
1(1,oVEVAX*V'AXvRptEV/VcE)
c
IN CYLINCER
AT END
CF
C
CETEnrINL
C
C
CCPRESSC1N FCi NCk-ISENTROPIC CCMPRESSION; BASED ON
RESLTS FCM ISFNTROPIC CCrPPESSIUN CASE
STATE
FRCPERTIES
C
T * T2
CT - 5og
I = lJ3
+ CT
Cc 28
T * T
CALL VAFCF(NP, t PF2VVAPsIVAPSVAP
Z=(W{AX-~VAP+(FP*VVAP-PMAX*VAX½*144*/778.g)/{[1.
1VNMAX*VrAX*VkREv/VvAP)
IF(AS(Z-hC).LE.-TCL)
15
GO TC 25
E~E;slb
;F(c-Z)
T-CT
T
LT - CT/co
2e
CCNTINLE
WRITE(ps4e)1
C
C
CEFINE ACTUAL STATE PROPERTIES AT END OF COMPRESSION
C
FCRTICh
CF STRCKE
C
E5
2
FVAF
=
vvAF
VE2
Sc - SVAr
S2
= SVT
T
C
C
CETERMINE WCOK REGUIRED FCR DISCHARGE PORTICN OF STROKE
C
*'C
IS
(ICH
SSUrE: TO OCCUR AT CONSTANT
PRESSuRE)
C
WC -
F2*V2*144,Z/779*0
C
CEFINE
C
DISCI-ARGE
STATE
hRES = ~
FRES
SE
TRES
T2
PRnFERTIES
STRCKF
CF RESIDLAL
MASS AT END OF
307
C
USE THE GENERAL FRCPERTY CONVERGENCE SUBROUTINE
C
C
TC CETERINE
ST-ATE PRCPERTIES AT END CF TE RE-EXPANSICN
FCRTIGN CF SThCKE, GIVEN P AND S AND ASSUMING
C
ISENTRCPIC RE-EXPANSICN
TRIAL,
c
P1,,SRES
CALL TRIAL(NNrT1,1e,
VRX
.
*ee5,,
H,SS,T)
V
TRX
T.
C
C
CALCtLATE TE
C
NON-ISENTROPIC WGRKDONE BY RE-EXPANSICN
hWXaEFFIS*
(HRES.HRX(P2*VFES-PI*VRX
)*144/778 )/
1 (VRES/ ( VtAX*VfRFX*,VFiREV)-1.()
C
C
C
ITERATE TC FINC T'E ACTUAL STATE PROPERTIES
CF NCN-ISENTkCPTC
RE-EXPANSION
AT TE
END
C
T -
CT
tRX
1lg
=
CC 35 It
T
lF *
=
1,31'
CT
CALL VAFCR(NRT, P 1 VVAPAP,
sAP)
Z=( ES-va
( AP t PP*VpES-Pl*VVAP
)144e/7780
1 (Vf
A X * vf i
A)(*VR'I
V
IF(AES(ZLo.RX).LFI.HTOL)
J
-5
iF(ZiWRX
T
1*Cr
)/( VRES/
-1
GO TO 4E
3,4e,35
T =
CT/
cT
- Tr,/
*,e
CCNTINLE
,.R ITE. ( 5, 4 1e
C
C
CEFIh,E
C
RE-EXPANS
STATE PRrPERTIES
IN CYLINCER
AFTER NON-ISENTROPIC
ION
C
40
VRX
HRX
= VVAF
= t-V F
SX
5:
SVAF
T X
=
T
C
C
ACCCLNT FR
S:UCTIC GAS
C
CF CLT-UFF
IXTNG F THE RESIDUAL GAS AND THE INCCMMING
TC FINC TE ACTUAL STATE AT THE BEGINNING
C
T
CT
CC 5
T
CALL
rTi
5e
I
r +
T
1, 3C
CT
VAFCR (NR ,T.Fl
VVAP.HVAP SVAP)
308
I)/VPFS
IF( CCNTNEE )Zak.HVAP+V,AX*VVAP*VEV*( HFiX-=
P * ( N X H1
)
EG*2)7=l-HVAP+VR*VRFV/VRCL;T/VVA
,
IF(ICCTF;
1/vPE$
5
GG TO
iFAtnS(Z),LE-TrL)
IF(Z) 45i55,ZD
45
,7
T-CT
CT = T/LC
5i
CChT;IhNE
-5
WRITE (5,;32
HCLT ='
,LT
V
=
s 5vAP
SCUT
TCLT
T
=
I,REF
*CLT
=
¥VILT
Vt tEF
180
TCL)*ANC(IABS(VCUT-VREF)*LEo
CuT-RrF)LEE
C TC 112
IF ((AS(
1-05 )
CCNTIN LE
C
C-----ENC
F Ti-EfCCN'AIC
STATE BALANCE AND MIXING -i.---
C
4,
,.RIT E ( 5
)
C
CALCLLATE WCK FPCCUCED CN VAPCR INTAKE 'WI' (TU/ Lb ),
WCRK PCCLCEC e8 EXFANSIC\ OF GS AFTER CUT-OFF ' EXCUT
ANC vASS FPLtPEC PER STRC<E 'XMFLC>' (LEv/STROKE)
(ETL/LEr
C
C
C
C
Jig
e/ ( VrAX*VREv ) -VPX/VRES)*
IF( ICCNTF9h.Eo).I=P1* (1
iVRES j4,C/(7778 .*(VkS/(VRrAX*VrcLV*vMAX)-1.V))
,.i;=F,EG,2)
IF(ICChT
1VRES*1441 /(778,.
/(vR-\L
(VCLT
AX VR~E'*'
(
VlRES/
IF( ICChThT.E,)EAcUT= (CHLT-t1A^A1*144*0'/77v.-~;/ I,k,.VrfAX*vFEV.Vr'AX/V
14e
iCCUr\T
i
ICCLT
iCLhT+*
T*
IFlCCLhT
i)
GC TO
AX)=*.i
-) )
P*VCUT-rAX*VVAX)
ES )
AXV'Sv*vLAX)i )-1 ./VPES
(I1
*C/(
= vfVkFVV*
XrFLC
>EV)'-VRA/VRFLS)*
15
c
WTCT
C
C
A2S(oC+Wr+WRX+WI+WEXCUT)
CALCLLATE
XVR
TCTAL
i4EFRIGERANT
FLOi
RATE
'XtRt
(LBM/IR)
XFLOCoFF-efg*FLCAT(NCYL)
C
ThE
C
CETEFrINE
C
CCrPfESSCR
C
EFFICIENCY CF CRESSCF
C
C
C
T,-ECCrFtELSCR ,)
C
,ACCPF',
TENM IKNc tPtwE;1,
ACTLAL
WCRK INPUT
ACCCbUTING FCP
(cTL/LB),
T
ACTUAL
TO TE
ECHANICAL
PChER RtQUIRED
TC RLN
ANC TEN CETErINE 'PP', TE
FERCENT LCAL CN THE MCTR,
ANC ITERATE ON MCTCR SPEEC
)
309
TCT/EFFrrE
WCCrPF
XR.*WCCP*.0gE2928
POCER
FP . PChER/PCON.'x
IF((ICCNIF* EC,*EAND(PPLE..*))
*4
PF
RPPNrSYNC (. 1i/4*PP**4-.Z6395s*PP**3+0193e*PF**2
lslc99*PF+9c54)
a
) GO TO 160
F'r-i
kFVh.IoLTt(~Il*'SYICI
IF(AS$(FRPr
fi R
N
GO TC 14t
15
C
",RTE(S,31V)F, FPpRP.N
CETERrINE
EFFICIENCY' .EFFMCI
rCTCR
AS A FUNCTION
CF LOAD
C
160
EFFMC = EFFM(FP)
oACT
wCC,'P/EFr'C
c
WRITE(5
)
C, C,wRX, ,IWEXCUT, WACT
^RITE(bEt2)
EFrvC, P.PF
ACCCLNT
CTCR
C
C
FCR
COCLING
ANC INTERNAL
HEAT
TRANSFER
C
C
CETERMINE
C
GAS
Y
AMCUNT GF
TE
rCTOR
EAT tGMC'
GIvEN TO TfE SUCTION
CCCLING
C
r.C
a
PCw(,wACT.TCT)
a
-l"C
CE
+ G,--C
TRIAL 3g
IF(HFICeCT,.)
IF0-iICLT*- ) rTRIAL -3.
C
TTHE ENEAL
C
LSE
C
TC
C
SUCTICN
CETER~fIN
A
AS
FRCPERTY
.EoN
ALUE
ENTERING
TE
CCNVERGENCE SUBROUTINE
FOR
TE
TEMPERATURE
USING
CYLINDER,
P
CF
TRIAL'
TE
AND
c
CALL TRIAL(NERTi
Tl
,TRItALPPiI'3,IltCvTCLVPsHSST)
-:= T1
C
C
CALCILATE
ESTIIATE
C
REFRInERANT
PRGFERTIES,
EAT TRANSFER
CF T'-E
AND
THEN
UQHT' BETWEEN
MAKE
A ROUGk
SUCTICN
CDISC!-ARGE'AN IFrLCc
C
e
GC-TO 162
IF(E(AREA*LE,.1e)
ChT -
IF(E(;AREA.LE .1)
XMFC- X/FLCa-(NYL)
CFS ,
CFC s
CPFR1i*F-
CPRV2
.
CPRV2
iCFiV*iF
CALL I-EAT t CPr CPCrSLPEMV#XINMvSLPEKVXINKV,
icGARE-AJ tFPC,-T,
Ti
162
TCISCC, TSLCTC.)
TSUCTO
-l = -lVC
i CTr+
IF(AeS(I-ft-HREViLE.PTOL)
GC TO
80
TRES, Tl,
ANC
310
C
kCFERTY
ENERAL
CCNVERGENCE
SUBRCUTIPE
C
;SE
C
C
TC CETERPINE
ENTERING TE
A NEW GESS FCR PRCFERTiES
P AND
CYLINCER, GIvE
CALL TRI4L(
T1 ,3.,P1
FII,3,isHTCL, VsSS, T )
TE
C
vl
a
51
= SS
T
=
V
T
TI# CTiAVGGHTA
1
T
WRITE(SECiN)
lee
OF TE
T I AL
REFR I G
Cs, EGAREA
CCNTINLE
C
C------.-ENC
CTCN CCrLING AND INTERNAL
HEAT
TRANSFER-----.
C
FRITE(S5,c
4)
Ic
IF(AS(CLCFC-UPCF) LE*5k
U)
82Z
LiC.NTINLE
21e
WRI TE({,J c
CFCV = 'I
)
AiJ _
- 1 )
(bs,723)
i _
R ITE
WRiITE
TC
21E
)
CrSV = L'
ITE
CC
ICpLsK,J
T2, P2j V2s
2c,
s-VAP, ScE SVAP
(5,5E7 ) CFr, CPCF,CHF AC, XI
( ,e
) CFPr v ,PS
C
RATE CN
C
CET EPIr,
C
CC~P
THI
E EF FECT CF CIL CIRCLLATICN
PECk
EF,
,i, CE
C
CALCLLATE
TrE
C
ITH TE GAS 'CIL' (BTU/LM),p;ND THE TCTAL
C
PLPEC
(KA)
EGCIREELNT FO,'
CCMFRESSCG PCAE;
C
cIRK NECESSARY
C
#GIL
FCW
TO
COMFRESS
THE CIL BEING
.1
= (FSATL-Pi c *449Z/(778**57v6)
= XMr*(wACT
+ xCIL*WCIL/(C1-XOL)
)**C02928
C
C
C
FINALLY, CETErhTNE
CF TE RtRICENNT,
C
EFFECT FCSSIEE
THE EFFECT CF THE CIL ON TE ETHALPY
ADU FInD THE NET EFRIGERATION
'
(Tu/
I
C
CALL CIL(NRsF1CrFTIGLEXCILs,1CCEsHIM)
H30IL= .4'3TEaTC+ .IE,25*TSATC**2
-_Eh= XCIL*_CI,
E
C
C
X/(lo
+ (GjL*-XCIL)*HSAT
- XGIL).thlr-043r)
PRINT RESLLTS
C
mIT E(
5p
i E10
XC T L
WHHI-31"
ARITEEti67O) XrP, GEJFUW
C
LC
'
15.75
311
COMPRESSCR
TEMPERATURE FROM TE
C
CETERINI
THE ExIT
C
AFFECTEC
BY INTrNAL
AS
TRANSFER
EAT
C
-
c-RES = MhES
G-T
TRES + 2e
TI.
CALL TRIAL(NRTTr"2,gePSATC's3,RES,'lejVHSST)
T
T-IC
hIC
=
FES
FSATC
PIC
IF (TIC.CGE.2.e,
)
mRITE( 54
WRITE(5,3e2)
EIrTE(S5,2) TSATETSATCsPSATCTICJHICHlOEwACT
CChTINLE
CChTIhLE
350
4ee
31
3 X,
FCkPAT()t~?TmtjF6.1,3X IP2t9,F6*2,3X,V2=I,F6o4,
IsF6923Xs'S2"tF694,3XJ
ltih2,',Fbp2,3X, HVAP
',6.)
2' SVAF
TEMPERATUREEXCESSiVE***')
FCARrAT(I *,*****CISCHeRGE
392
31Z
ON tOTCk SPEEC DOES NOCT
.****IERATICN
FCrAT(
PMN,=1El25 · 1
' t RPM'1JEl251
1,ssCCNVEKGEFF-,EI25p
LBM CIL/LBt' MIX
XCIL.p'sFI,5#'
3E2 FCfirAT(I
HIr=1,F7.2,
REFL
+
CIL
Ler kEFL/Lpf'
1'
BTL/LOMI M 'IX')
H3.-,,.F7.2,'
IX
2., '
I
410
Jt
5iZ4
NOT'
CONVEkGE**,*'*$)
FCRfAT('w,**.,*
* ITERATICN CN MOTOR COOLING EFFECT'
E
H
I
FCkiAT(7Fo1,2)
560
FCRMAT(' w**aITERATICN
57e
FCRMAT(t CPC',F1e.*4'
1sF1Z.5#,
v
**
******')
TIC'
PSATC
TSATC
TSATE
FCFvAT('f ',
DOES NOT CONVERGE
ON STATES
i FrCES NOT CCNVERGE
ON ST.TL
los'
550
DOES NUT'
-MAX AND VMAX COES
L
***rArcTU
FCRMfAT(****..ITERATILN
1,it
54
CF RESIDUAL
ws,RF-EXPANSICN
C *W*L,.U*$*** )
CChVEA(E
FCrP'AT(t
list
440
CCNVEhGE*w ^*.'*s')
FCEt'AT('
list
430
COMPRESSION DOES NOT'
FCRVAT(I ****wNCN.ISENTRCPIC
4g
W='Fb6,4
BTU/Lt M'
I)
ON CPO DOES NCT CONVERGE*****')
DPDp='rFle4s
DOPFRAC='
XMF=' ,F 155*5)
62Ek FGHAT( te t'FFSaF10E2,5X,'EFFXME=tJF10*2
CPFRAC='sF105)
t
~UFS'F109,j
.FIe2ESbX
63
FOR'A T (5X,
v ;YN('=IF1.2s
'
RPM
[CELAYm',F0,5p
IP";NLv'.,F10,_
DPCI'I
POWMAX=,F1i0.5t
650 FCrAT( '1,X ,NCYLfI2sI,5X IVR'pJF1v35X
670
6S9
K
DEGEES SDELAY'
VD=
Fi)
tSL;PEfJFl-2}
,,XXfl'P1FO1,2p5X
'
tCl.FT
IJF1V..4
rp5Xs pGE"iF15'2
FCCs'T(1ei, %gXs,XtR-~Fl5.2 ' LE8/HR
FCir-T
ti
(
t
7eO FCR*T(I
x,
CPC
,,FwF14'
ELAC=
' F'
*4 Sx
SGIN
CPSV , F 1¢ 4 )
EAS=vpF'ij4p, SGI Ns '
312
EFFCntFI1e.4
FTtiFlv#4,
ltJ'
FC-',F14j
2'
72e
FCRIAT(' **--****ITERATICN
ssi**'')
Pu
1,, t CChvyFGE
73 e FCRPAT( ' **--=iSENTRCPIC
731
FC
S
C
'
CISCHARGE CCES NOT'
CT CONVERGEC'
CTCFF
J='JI1,
'
uF'. Iv1J '
lATt'
i
PkTC='PFif4,#
I ='
1, I12)
THIS FAILURE TO CCNVEFGE
FCr'AT('
732
IS NCN-CRITICAL'
i,' LtLEiS T-E vLUES OF ICiC,KKANC J AE THE SAE AS'
2j ' T-E F INAL VALLES' )
733
FGRCAT('
74?
FCMAT('
7EO
ip f*
FCPflTATi
7e
FCFT
770
F#CR'MT(,
1'
ICCZ,=',IIet
FINAL
NOT CONvEGEC'
CTGFF
**,r****NCN-IsSENTfiCPIC
*
Tk='tfII#I'
CF)
C =' J,;
Fi
iT
pZ4, j
cT=
:'=*Fle W'
F lg,4'
V' *
CUTOFF='rl5,5)
'
SCLT,'rFl{*,)
78
FINAL
FINAL K=',I1v,'
SCUTs '
F It,
ssi
i4s
:'F 1
,4,
TI'
5'MAX=fPFb.5,1 VMAX='rF6.4P
FCrs-,ATk' IYA'.,'*~'
'
1' tMX- t F8 c ' Pf'X 'IF8,4
I' EXCUT='Fi,
4, t U'AX='
VCLT.'Fl*4,' CLT-,F].4. SCT='FI.4j
870
I'TCT=',F1L~4.,' ,rNF=';FIt2
FC~RtT'
125
8_Z
FORr 'i.T
FCe '
1 X 1I' FS;
w>1t *
I
.ACT=,F1C4
I
A XCLT= ,Flg,~
I =''j F o
RpM=,F1.2,' P
FCr'Tx
LFF r ='F7.3,'
FCR T( '
TlIu,/F72,
F
Tr=',F7.2
' F
IF7,J ' F j-T 'FS.3, *
2'
84e
V"AXa';F-1
T=';F.Ejc2 ' ,o.
U' V=='
VMAX=t ;F& *4+
StrJXc'lf895J
MAX=', Fr 4,
e' TAX:',
I
VSEF=',F1U'4=
,F
10,
P=':I;F1
'F'.4,
,11pE4)
W
TsF-2,'
'.,
' SS'',FC.5w5'
1FC1r'4T('
82Z
;'
tGC; E A
LATU/LE
T/LBt
)
'. F7.3)
LTIAVG ='
Gr'C=Fb .3;
FT/FT,**631,
'84,'
FCRrAT (bl4*.)
685¢
FCRTAT('
1i t FAIL
86
ww
'w5w*,-NC-.-ISENTRGPICCUT-OFF SATURATICN'
FC^RAT('
' )
FAILS TC CNVEr(iEww****
1 9ESEA;RC1
876e
FCRItAT(
875
FCRrAT( '
876
1g6?6
IPP
L
'
='IFj
.be
b'
5
T
SATURATION SEARCH'
'F1r'5.
PFCFFN;TIS AT ENC CF CLT-CF
Ts f o -
FCRVAT(
ENC
*****ISENTRCPC
CUT-CFF
T CCrt'ERGE=w*ws**S'*)
Ss J
XjSF1.S)
)
'
P
STRCKE'
';F1.0b)
313"
SUBRCUTINE OIL (NR,pTjXH1CEWp')
C
C
FURPCSE
C
TC CALCULATE TE
C
IIXTLUES FCR REFRIGERANTS
ETHALPY
OF REFRIGERANT-OIL
12, AND 22
C
C
GESCRIPTICN
CF PARAMETERS
C
INiPLT
C
N'
REFRTCERANT
C
P
PhESSLkE
c
T
C
C
C
C
C
C
X
NUMBER
(12,
OR 22)
(PSIA)
TEFFRATURE
CF
MIXTURE
(F)
,EIGNT PERCENT CF
IL IN THE TOTAL MIXTURE
ENTTALFY CF URE REFRIGERANT VAPCR (BTU/LSM)
At EAPORATC
EXIT TEMP* AND PRES,
-
1GOE OL TFUT
a
v EIG'-T PERCENT
ThE I I,.PASL
.
C
I,
C
LEAVTNG T
a
C
ETHaLFY
CF REFkIGERANT
EFRIGcRANT4CIL
EVAtzORaTOR
(TU/LSr)
MIXTit!E LAVING
C
C
CF TTAL
TIE
LEFT IN
MIX TURE
REFRIGERANT-OIL
VAPGRATOR
ErREIARKS
SLBRCLTINE
C
C
IF(NR.EC.~2)
e
R I TE ( I
CC
C
Z
C
C
T
REFRIGERANT
Gn TC 15
12)
ITE
TC
ThE
I1
)
20¢
a l(ALCG1~(F)e,293+2136ei/TR)/(1696/TR-4448))
1'*(=2 )
GC
15
IS CALLED TC PRCVIDE SATUNATICN
CF
IF(hRE6
e
STPRP
STATE PRCPERrTIS
IWRITE
5
TR = T + 46e*e
T
.EZ
FK
P*o,7e31
Wa
(ALCGlkF(PKi=5.E57+117767/TK)/(98.753/TK
TKa 5.C*(T2.0)/9.e
1) ** ("2,e)
IF(,GE.L.0)}
Z IS TE
iGCNT
PC'LN; CF TCTAL
+ 273.16
-. 558)
,9999
CF OIL ANC REFRIGERANT LIGbID
PER
IXTURE LEAVING TE EVAPORATCR
-CIL = 4+:3*T +_ e25*T**2
CALL SATFhF(Ih'TJPSAT
+ 15,75
VFvG~HLIG,,HFGPHGSFSG)
"Z (1,'-)'fCTL + *I.
r1l0
24
a ZHZ + (c'-Z)*HiCE
FCREAT(
*ws,.ELkERCR
I
RET.;.N
SUBROUTINE
OIL *******'
)
314
FUNCTICN EFFl(Pp)
C
C
PURPCSE
rc ESTIMATE
PERCENT OF
C
C
C
CTCR
IhCCTIONh
C
C
EFFICIENCY
AXIrUM
S
A FUNCTICO
LOAF FCR SCUIREL
CAGE
CTCRS
CESCRIPTICN CF PARAMETERS
C
INLcT
C
C
CLTFUT
*
V .e
IF(PP.OT 1 *
F P fLT
IF (PP LT
T
C
)
5e
PP
) * ITF ( I WiITE, j1)
) kITE (I W ITE 1i1 ) PP
)
FF
= 6. 65*Pp
1.3PP + 555
; FFIr
:F (P.CT 'IM)
. Ze
3
Og)
FFFM
;FFr
',2CCQ
iF(PFRCT..4C2)
1F'FPrCGT..6i2)
IF(PP.GT.8)
5e
EF;'
.J TL,1 122
RETLN
lee
11e
120
FOCirAT(' ***mTCR
FCfirAT(r **
*375wPP+ *,74
85
'=
.1*PP +95
+ 17
a -. 25PP
PP
PWEtR EXCESSIVE PP=,E125'****')
rTCR PChER TO LCW-
1, '' PP =TE;L2 5
w-*=c'rTCR
FC~rAT(
ENC
tPP,
5
P P LTT
RE T L R N
6R fE(
AXIMUM PCGER
CF
PCTCR EFFICIENCY 'EFFr'
IORITE
IF
PERCpNT
-
rTOR
IEFFICIENTT'
$''***')
PCAER IS NEGATI VE PP='E12.b
'**'
)
315
SUERCUTINE HEAT(.CPS,CPD,SLPEMV,XINMVJSLPEKVJ XINKV
ITCISCCI TSUCTIUIFAREAsXMPCQHTTCISCCITSUCTO)
C
C
PFRPCSE
C
C
MANIFOLD HEAT TRANSFER
TC ESTIMATE SLCTION-CISCHARGE
CGFPRFSSCR
iN T
C
C
ARAVETEkS
CESCRIPTICN CF
INTS
CFS
C
C
C
C
EAT AT CCNSTANT PRESSURE CF THE
GAS IN TE SUCTICN MANIFOLD (TU/LLw-R)
SPECIFIC EAT AT CCNSTA.>T RESSLRE CF
-SECIFIC
-
GAS IN THE CISCIAriGE
SLPEM' V & XINMV
CCEFFICIENTS
C
C
C
SLPEK.\V & X INV
MANIFOLD
FOR VISCOSITY
VAPC.R
CCEFFICIENTS
-
CCNDUCTIVITY
C
C
TSLCCT
C
TCICC I-
IA-
C
C
OF GAS ENTEfING
CYLINDER
C
C
FCR TEFrAL
CF VAPOR
SCT.
TEFP. CF GAS ENTERING DISC.
Ei-LIVALENT
ANIFCOL
(F)
ANIFLGC (F)
HEAT TRANSFER -
AREA FR
CF
SEE
GF AREA)
UNITS
FOR UNITS (OT
ExPLANATION
MASS FLCW RATE CF REFRICERANT PER
xrvFC
C
TFbP.
(T/Li-mRK)
(LbM/HR)
OUTPUTS
C
TSUCT( G-
C
CHT
C
TEIP,
OF GAS LEAVING
SCT
MANIFOCLDC (F)
GAS LEAVING DISC. MANIFCLD (F)
TFF*OF
ANIFOLD HEAT TRANSFER
SbCTIN-DCISChARGE
(PTU/LBe)
C
5
IWRITE
TCISCI - 2,
T-
5
CT
C
CF GAS LEAVING
C
ITERATE
C
ThE CCRRECT HEAT TRANSFER
CC 52 I a 132
RATE
CISC. MANIFCLD
I- FOLND
CT
T
T
Ch TEMP.
TSLCTO - TSUCTI + (TGISCI-T)3CPC/CPS
CTA = TCISCI - TSLCTC
CTe
CTLr
=
T
=
- TSUCTT
(CTA-CTe)/ALOG(DTA/CTb)
TSAVG .= (TSUCTI + TSUCTO)/,o
TCAVG (TCISCI * T)/2.
C
C
C
C
C
EVALLATE REFRICFRANT
XMUS
XMLC
PROPERTIES
VISCCSITY
(LPM/(R-FT)
XKS & XKC - TERMA. CONCUCTIVITY (TU/HR-FT-F)
pRANCTL NtrBER
PRC & PRS
.XMLS = LPErv*TsAVG + xINrV
XVLC
SLFEMV*TcAVC
* XINrv
UNTIL
316
SLFEKV*TSAVG +XINKV
XKS
XKC = SLFEKV*TC4VG
+ XINKV
XStCFPS/yKS
PRS
*63)
FST=4 ./(
o.XKsFRS*I.6*(A./XPUS)
F'CT=3./(.s 48XKE*RC**e6*(6/XUC)**63)
- T)
X)FC*CLui Tr;CI
Xt°PC*w6*E(-ACTLY/(FST+FCT)
G
GS
).LE,(.
IFA(S(CQS
Ie=))
GC
TC 62
IF(((CG-C).uL*2.).ANh.(I.EG.1)) CT
C
lF(CTocTis)
42T
IF(C-CS) 4CALt}4
=' T + CT
5E
CT = C T/
CCNTINLE
35
GC
TC
a
T
*
-DT
35
Z
/XYPC
60
CGT
TCISCO
T
!¢
RETbLN
FCNrAT(t
*****SjtEROUTINE
EAT CCES NCT CONVERGE****')
317
APPENDIX
F
REFRIGERANT - OIL SOLUBILITY
Solubility of oil-refrigerant mixtures has been discussed by
Bambach,
Spauschus
, and Cooper3
Many refrigerant-oil mixtures,
such as R12 and R22 are miscible over the entire range of concentrations from
0 to 100%.
BambachI has found that the solubility of R12-
oil mixtures may be described by the following expressions:
-1/2
(A) Log,, ()
-J.U
-
(-1A2
(1177.67[5.0057- .550 w
-
T
T'
)
98.753w
J.
oC
2
(B)
Log1 0 (P) = [ (A) ] -
.002338
(-
.6) - .000075](T-
273.16)
Where:
P = pressure (kg/cm2)
T = temperature (OK)
w '=
bm refrigerant/lbm liquid mixture
Refrigerant 22 behaves slightly differently than refrigerant 12 in
that refrigerant 12-oil mixtures remain a single phase throughout the
entire range 0 to 100% concentration.
R22-oil mixtures, however,
separate into two distinct liquid phases above certain concentration
limits.
One phase is oil-rich, while the other phase is refrigerant-
rich.
We are concerned here with the amount of liquid refrigerant left
in the oil at the exit from the evaporator, and the fact that it
in two phases is
of secondary importance.
is
For this reason, it has
T >
C
318
been assumed that an expression similar to the one described by
Bambach for R12 also holds for R22.
(C)
Logl
0
(P)
=
-1/2
a-
bw
That is:
[C + dw-1/ 2
C
dT
The necessary constants have been determined to be as follows:
a = 6.293
b =
.4448
c = 2136.0
d = -169.6
Where
P
= pressure
(psia)
T = Temperature (R)
For simplicity we shall assume, even for R12, that the solubility may
be described by a single expression of the form of equations (A) or
(C).
Comparisons of predicted results with actual solubility curves
are given in Figures
F-1
and F-2
.
Expressions (A) and (C) may
be rearranged to solve explicitly for an expression of
function of
V
P
and
T
=
for R22
m
P
psia
T
R
w
as a
319
-2
[Loglo (P) - 5.0057 + 1177 67
9 753 -T.55_
T
W-=
for R12
k
P=-
T
OK
References
1.
Bambach, G., "Das Verhalten Von Mineralol -F12-Gemischen
in Kaltmaschinen", C.F. Huller, Karlsruhe, 1955.
2.
Spauschus, "Vapor Pressures, Volumes, & Miscibility Limits of
R22 Oil Solutions", ASHRAE JOURNAL, Dec. '64, pg. 65 and also
ASHRAE TRANSACTIONS, Vol. 70, 1964.
3.
Cooper, K. W., and Mount, A. G., "Oil Circulation - Its Effect
on Compressor Capacity, Theory and Experiment", 1972 Purdue
Compressor
Technology Conference Proceedings (Purdue Research
Foundation, 1972.)
4.
ASHRAE GUIDE & DATA BOOK, Systems & Equipment (New York:
American Soc. of Heat, Refg., & Air Cond. Eng., Inc., 1967)
pg. 265-285.
320
P
r
e
s
s
u
r
e
(psia)
0
10
20
30
40
50
60
70
80
Weight Percent Of Refrigerant In Mixture
90
__
100
90
100
FIGURE F-1
P
r
e
S
s
u
r
e
(psia)
0
10
20
30
40
50
60
70
80
Weight Percent of Refrigerant in Mixture--
FIGURE F-2
321.
APPENDIX G
COMPRESSOR DATA
Carrier 06D-824 Compressor
The 06D-824 is a relatively large, semi-hermetic refrigeration
)
compressor, having a surface to volume ratio
per cylinder.
of about 276
(in)-
1
The difference between a semi-hermetic and a welded
hermetic compressor is that a semi-hermetic unit is bolted together,
and can be disassembled for servicing.
A welded hermetic, as most
smaller refrigeration compressors are, cannot be serviced, but
rather is replaced if failure should occur.
Information concerning
this nominal 9 ton compressor has been provided by Carlyle
Compressor
Company, a Division of Carrier Corporation.
Data for use in the compressor simulation was as follows:
Synchronous Motor Speed = 1800 RPM
Initial Guess for Actual Motor Speed
=
1750 RPM
Refrigerant = 22
Displacement Volume (VD )
Clearance Volume Ratio V
=
min
3
2.273 x 10-3 ft
/V
D
=
VR = .05
Number of Cylinders = 6
Superheat Base for Capacity Rating
=
15°F
Subcooling Base for Capacity Rating = OOF
Ti
~is
= 94%
n
= 96%
% Motor Coolingech
% Motor Cooling = 85%
322
APD
= 25 psi
APS =
5 psi
e
=0
AT
--
AT
0
=
O
suct-dise
H.T.
% Oil Circulation = 0
Maximum Power Output of Compressor Motor = 11.64 kw
Carrier 06D-537 Compressor
The 06D-537 is a large, semi-hermetic refrigeration compressor,
having a surface to volume ratio of about 2.49 (in)
per cylinder.
It should be noted that this nominal 14 ton compressor is a larger
version of the 06D-824 compressor, having the same bore, but a
longer stroke.
The 06D-537 compressor is used in the Carrier Model
50 D Q 016 Heat Pump.
Data for use in the compressor simulation was as follows:
Synchronous Motor Speed
= 1800 RPM
Initial Guess for Actual Motor Speed = 1750 RPM
Refrigerant
= 22
Displacement Volume (V
D ) = 3.522 x 10
Clearance Volume Ratio
Number of Cylinders
Vmi/VD
VR
ft
.05
6
Superheat Base for Capacity Rating = 150 F
323
0°F
Subcooling Base for Capacity Rating.
nis
= 94%
nec= 96X%
Z Motor Cooling = 85%
AP
D
- 25 psi
aPS
= 3 psi.
BD=
0
s
AT
suct-disc
=
0
H.T
x Oil Circulation
-
0
Maximum Power Output of CompressorMotor = 16.89 kw
3-Ton Welded Hermetic Compressor
The manufacturer of this compressor wished to remain unidentified,
but has provided the necessary technical information on this nominal
3 ton refrigeration compressor having an (-)
of about 3.44 (in)
Data for use in the compressor simulation was as follows:
Synchronous Motor Speed
3600 RPM
Initial Guess for Actual Motor Speed
Refrigerant = 22
VD = 1.15 x 10 -3 ft3
VR - .062
Number of Cylinders = 2
-
3500 RPM
324
Superheat Base for Capacity Rating = 200F
Subcooling Base for Capacity Rating = OOF
is
=90%
is
=ech
96%
m
% Motor Cooling = 85%
APD
= 25 psi
AP S
=
eD
= 10
ATDC
eS
=15
ABDC
AT
5 psi
suct-Disc
= 500 F
H.T. @T
= 10F
evap
,
sat
T
= 1200 F
cond
sat
% Oil Circulation = 5%
Max. Power Output of Compressor Motor = 3.
kw
325.
APPENDIX
PARAMETRIC STUDIES
ON CARRIER
EFFECT OF VARYING
e
APD I 10 psi
Tsat -T sat
evap
APs
- O
Change in
COMPRESSOR
lmech
7. Oil
.96.
ATsuct = 0
O
%-Motor = .85
cooling
Change in
Power
Flow or
Capacity
cond
06D-537
FROM 1 PSI TO 5 PSI WITH:
rls 94
-O
D
H
Change in Overall
Compressor Efficiency
(%)
(%)
(Z)
50 -- 145
50 - 120
50 - 80
·I
-
-
-5.0
-5.8
-1.7
-1.6
-4.7
+206
20 - 145
-9.3
-20- 120
-9.1
-8.3
20 - 80
-10 - 120
-10 -
-4.8
.
-19.9*
-17.5*
80
* - Due Mostly to
i i~~~
i
Tsat
= 1 psi
D
-0
-
is
- 145
50
- 120
50
20
- 80
- 145
20
- 120
20
-
-10
-10
-5
-11.5
-6.4
-6
-8
FROM 10 PSI
80
- 120
- 80
* - DueHostly to
~mech
Z Oil
.94
Change in Flow
or Capacity
.
50
-4
-. 9
8
cond
evap
-
|
-3
-3.8
8 =0
T
-5
-
-
Density Changeof Suction Gas at Low.Pressure
EFFECT OF VARYING APD
AP
-2
-2
Change in
Power
(%)
(%)
-1.8
-2.9
-1.3
-2.1
-2.1
-1.9
-3.8
-3.6
+3.7
+5.3
=
to
30 PSI WITH:
.96
ATs
suct
O
% Motor
=0
= .85
cooling
Change in Overall
Compressor Efficiency
(%)
-2
-5
+19.9*
-12
+1.4
+3.2
+9.3*
+.9
-3
-3
-7
-3
+4.7
-6
Increase in CompressionWorkAt low Pressure Ratio
326
EFFECT OF VARYING es FROM 00 ABDC TO 200 ABDC WITH:
T
sat
evap
AP
= 1 psi
eD = 0
n
APD
D
= 10 psi
Tis=
% Oil = 0
-
T
-
145
120
80
145
120
80
-
120
-4.1
-
80
-3.8
--
50
50
50
20
20
20
-10
-10
.-
APD
T
=10
T
sat
cond
sat
evap
20
20
20
-
145
120
80
145
120
80
-10
-
120
-10
-
80
50
50
50
(z)
-3°2
-3.9
-3.4
-3,2
-306
0
-302
0
-3.8
-3.0
-1
eD
-3.9
I
0
0
0
00 ATDC TO 10 ° ATOC WITH:
=0
nmech
96
% Oil = 0
Tis=
.94
:is
AT
suct
=0
% Motor =85
Cooling
Change in Flow
or Capacity
-2.8
-2.0
-1.2
-5.4
-3.9
-2.1
-8.1
-4.6
0
0
-306
FROM
(z)
-
Change in Overall
Compressor
Efficiency
-2.7
-3.0
-3.1
-3.7
psi
psi
% Motor = .85
cooling
Change in
Power
(%)
--
EFFECT OF VARYING
aPs = 1
.94
Change in Flow
Or Capacity
sat
cond
------
AT
= 0
mech - .96
suct
--
Change in Change in Overall
Power
Compressor
Efficiency
(z)
-2.8
-2.1
-1.2
0
-4.5
-1
-2.6
-1.8
-5.8
-2.7
0
0
0
0
-1
-2
327
nis
EFFECTS OF VARYING
FROM 94% TO 98% WITH:
_
AP
S
Tt
=
1 psi
-
1.0psi
-
evap
T
sat
cond
__
e
- o
eD
O
mech
96
% Oil
0
AT
% Motor
or Capacity
(Z)
Power
(%)
Change in Overall
Compressor
Efficiency (%)
50
50
50
-
145
120
80
+1.3
+.6
+.1
-7.1
-6.3
-4.8
+6
+5
+4
20
20
-
145
120
+1.5
+1.0
-7.9
-6.7
+6
+6
20
-
80
+.3
-5.3
+4
-10
-
120
+1.9
-8.9
+8
-10
-
80
+.3
-5.5
+4
APs
AP
D
. psi
s -=0
- 10 psi
Tsat
evap
Tsa
cond
mech
0
D
50
-
145
50
-
120
.50
-
20
-
80
145
20
-
120
20 -10 -10 -
80
120
80
FROM 94% TO 98% WITH:
Tis
.94
% Oil -=0
Change in Flow Change in
or Capacity
Power
(z)
+1.7
+1.3
+.4
+2.2
+1.6
+ .9
.
+2.4
+1.4
.85
cooling
Change in Flow Changein
EFFECTS OF VARYING
O0
suct
(%)
-4.8
-4.6
-3.9
-4.0
-4.3
-4.2
-4.1
-3.7
AT
=0
% Motor = .85
cooling
Change in Overall
Efficiency
(z)
+4
+5
+3
+4
+4
+4
+4
+3
---
328
EFFECTS OF VARYING % MOTOR COOLING FROM 80% TO 100% WITH:
AP
1 psi
s
APD
T
sat
evap
= 10 psi
-
T
sat
cond
e
s
=0
ni
= .94
0D= 0
qmech =
Change in Flow
Or Capacity
Change in
Power
(Z)
(z)
96
% Oil = 0
AT
= 0
suct
Change in Overall
Compressor Efficiency
(%)
-.2
-1
-1
0
-1.7
0
-1
-1.1
-.8
+.1
+0o
0
0
-1.7
-.9
-.3
+.1
-1
-1
50
50
50
-
145
120
80
-1.5
-.8
-.3
20
-
145
20
20
-
120
80
-10
-10
-
120
80
+ .3
.3
EFFECTS OF VARYING % OIL CIRCULATION FROM 0% TO 10% BY WEIGHT
AP
= 1 psi
APD = 10 psi
T
sat
-
evap
T
sat
cond
s
= 0
D
= 0
Change in *
Capacity
()
= .94
=
96
Change in *
Power
(z)
% Motor
Change in Overall
Compressor Efficiency
(x)
-
145
120
80
-13.3
-9.6
-5.5
+.4
+.4
+3
0
0
0
20
20
-
145
120
-15.2
-11.1
+.4
+.3
0
0
20
-
80
-6.6
+.2
0
-10
-10
-
120
80
0
0
*
Oil Circulation Affects Evaporator Capacity, But
On Flow or Power
= .85
ATsuct =0
50
50
50
-12.2
-7.5
Cooling
as Little Effect
329
EFFECT OF INCREASING SUCTION GAS SUPERHEAT BY 300F
ABOVE THAT DUE TO MOTOR COOLING AND OTHER EFFECTS WITH:
1 psi
AP8
APD=10 psi
Tsat
- Tsat
evap
cond
8
is -94
.=
'D
0
120
-10 -
80
sat
evap
96
Change in Flow Change in
Or Capacity
Power
. ()
-10 -
nmech
-6.9
-6.6
z Oil - 0
%XMotor
Cooling
.85
Change in Overall
·Compressor Efficiency
(Z)
(%)
-. 5
-4
-5
0
-
> OOF
Amount of suction gas superheat due to suction-discharge heat transfer
is considerably less than that at the low suction-high discharge
pressure (high pressure ratio) condition given above.
330
APPENDIX
I
DETAILS OF AIR-COOLED, CROSS-FLOW CONDENSER MODELING
Details of the general air-cooled, cross-flow condenser model,
'EXCH', and of the special case, finned tube condenser model, are
given in this section, followed by computer program listings for
each.
General Model 'EXCH'
The effectiveness-NTU method of heat transfer analysis is
described below:
qactual
a4
poin
4jCain
max possible
C
(T
4
(Tin ~ -T~ out
(T
(
in
in
Tc
in
~ c (T
out
C
(T
min
H
in
Where:
4 = Heat transfer rate
£ = Effectiveness
CH = (
C)
of the hotter fluid
CC = (
Cp) of the colder fluid
= Mass flow rate
Cp = Specific heat at constant pressure
Cmi n = the smaller of
TH
CH
and CC
= entering temperature of the hotter fluid
in
= exit temperature of the hotter fluid
TH
out
T
-
T
in
)
c
in
331
TC
entering temperature of the colder fluid
TC uX
out
exit temperature of the colder fluid
-.
-Cin
In general, effectiveness can be expressed by a relation of the
form:
c in
-f
,NTU)
max
Where:
Cms
- The larger of
CH
and
C¢
AU
NTU
min
AU
Overall conductance for heat transfer
=
A general expression for overall conductance, allowing for the
possibility of an extended surface on the coolant side can be
developed as follows:
di
coolan
separating wall
conden
medium
P.-
side
dQ -UdA AT - V dA (TR -
1
Ud
rn
o
1
h
+
dA
c
i
.
Tc)
1
hdAH
T
assuming resistance of
material separating
fluids is negligible
332
Where:
=
overall surface efficiency of extended surfaces,
including contact resistance, as described in
Appendix J.
d4
=
local heat transfer (Btu/hr)
= unit heat transfer area on coolant side (ft2 )
cH.T.
dA
unit heat transfer area on condensing medium side (ft2
dA.uT.
)
.T.
hC -
heat transfer coefficient on coolant side (Btu/hr-ft2-°F)
1
hC
1
hfluid
hH E
scale
heat transfer coefficient on condensing medium side
(Btu/hr-ft2-opF)
1
1
hH
1
hfluid
hscale
The general expression for NTU is hence:
NTU =
C
1
no hc dA h
min
dAT
or
NTU=
C
+
[]
o
where:
ae-
c
c
heat transfer area on coolant side/total heat exchanger
c
volume (l/ft)
333
heat transfer area on condensing medium side/total
heat exchanger volume (l/ft)
Cmin
(di Cp)mi
=
n
The procedure for determining desuperheating, condensing, and
subcooling region performance, as shown in the flow diagram in
Figure I-2, is as follows:
Determine
NTUtp
AOM
=
NTU
htp
dA
Where:
HHT
AOM
dit
c
'tp' = subscript indicating two-phase region
Cp
=
specific heat at constant pressure for the colder
fluid
d ic = local flow rate of coolant (LBM/HR)
Then:
-NTLT
tp
= 1 -e
tp
Next, determine the bulk superheated vapor temperature 'Tds
at the end of the desuperheating region when condensation begins.
d4 = hHv
dA
(Td
- T
ll)
334
also
dq4= UdA(Tds
Tc
)
in
Where:
hH
=
single phase vapor (superheated vapor) heat transfer
v2
coefficient on condensing medium side (Btu/hr-ft2- F)
Twall
= saturation temperature of the condensing
- TH
sat
medium (F)
TI
=
*in
entering temperature of the coolant (F)
Equating the two expressions for
T -(Tds
Hsat)
=
d
we get:
%
a1C
hdhin
(Tds
- T
OHHT
)
-in]
v
rearranging we find:
[(TH
ds
sat
) (RES) - Tc
(RES - 1]
Where:
RES -
+
a
c
h
h
Tl
C CO o
Now the driving enthaply differential for heat transfer in the twophase region
hfg I'[fg
h fg"
fg
can be determined:
PH
H,
-sat )
(Tds TH
(
- X3)
335
Where:
h
latent heat of vaporization of the condensing
fg
medium (Btu/lbm)
Cp
=
specific heat at constant volume of superheated
vapor on condensing medium side (Btu/lbm-°R)
X3
=
exit quality of condensing medium, if we choose
to study cases of incomplete condensation.
Next, we use the definition of effectiveness to determine the
amount of coolant passing over the two-phase region of the heat
exchanger:
(& )
Ctp
(hf")
(CEtp)
Ptp (Cp)
Pc
(THsa
t Tcin)
sat
cin
Where:
= total flow rate of condensing medium (lbm/hr)
The fraction of the heat exchanger 'F
tp
'
which is used for the two-
phase region is hence:
mc
F
=
tp
Where
t
m
= total coolant flow rate (lbm/hr)
Now we seek to determine the fraction of heat exchanger
which is required for desuperheating.
required, as follows:
'F' ,
An iterative procedure is
336
-
Guess F
m
=
(F) (c)
=
(&c ) (C )
sp
C
Cp
sp
CH
sp
sp
=
sp
(Cp
)
vv
=
C .
min
C
(H)
c
Smaller of
=
max
Larger of
C
c
and
sp
1
CH
sp
and C H
sp
sp
[ nOaHah
+
ac hc
1
SPy
(F) (AH )
U_
tot
Cc
ht
1
(Rto t ) (Cmin )
tot
mmn
C .
=
XE
f
(T
-I
CHHin
*
rxF
, NTU)
min
max
=
C
(T
min
Hin
*
-If c,
- ,,,xF
XiF
Tds)
-T
)
Cin
. reneat
Where:
t
Csp
=
flow rate of coolant
region (lbm/hr)
assin
over the desterheatinv
337
T
-
temperature of superheated vapor entering condenser
"in
(°F)
R
tot
=
overall resistance to heat transfer in the desuperheating region
M cross-flow effectiveness as determined from the proper
eXP
expression or chart.
(See Appendix J
for cross-flow
effectiveness, both fluids unmixed)
*
=
effectiveness as determined from the definition of
effectiveness
$Aa
=
total condensing side heat transfer area (ft2 )
'sp'
-
subscript indicating single phase vapor region
F
1 -F-F
Ht'
Then:
sc
tp
Where:
'sc'
If
F
sc
<
-.
=
subscript indicating subcooled liquid region
O , then there was incomplete condensation in the two-
phase region.
In the present model, calculations are terminated
if incomplete condensation occurs.
only slight modifications,
of incomplete condensation.
on
X 3 , the exit quality.
It is possible, however, with
to use the present model for the case
This is done merely by iterating
338
If
F
sc
0 , determine exit temperature of the subcooled liquid:
>
CH
sc
Cc
)
=
(H)
=
(Fsc) (C)
=
smaller of
(Cp
)
(C
SC
C
mln
CH
and
3C
larger of
=
C
max
CH
SC
and
SC
+
R
tot
U
-
SC
Cmin
max
=
SC
(t)
, NTU)
max
SC
= TH
out
1
C
(Fsc)
(E:XF
TH
h
1
(Rto
)(Cmi
tott
inn )
_
.'TV
XF
CC
S¢
a
0C
14
CC
) (Cmin)
CH
sat
(TH
-T
sat
)
in
SC
Where:
=
temperature of subcooled liquid leaving condenser
out
(°F)
C
=
specific heat at constant pressure of subcooled
liquid (Btu/lbm-°R)
9.liquid
(Btu/bm- R)
339'
Finally, we can determine heat transfer rates and exit coolant
temperatures for each region.
C= C
(TH
sc
=Qp
I
Qsp
tH
(Btu/hr)
sat
out
hfg"
CH
(Btu/hr)
(T
sp
T ds)
(Btu/hr)
in
Qtot=
QC
+ Qp
+ QP
tot
sc
tp
sp
T
(Btu/hr)
+ T
CDout
sp
Coutt
cc
sp
(hc
(oF)
Cin
)(Cp
Cin
QS
T +T(F)
T
+ T
Cout
SC
CC
(°F)
Ci
SC
Qtot
Clout
()
(F)
(Cpc
Cin
avg
For more information, see comments in the program listing for subroutine 'EXCH' at the end of this section.
Modeling a Finned Tube Condenser
The geometry factors necessary for use of general model 'EXCH'
are:
aH ' ac
,
AOM , A
, AC
AC
,
tube condenser case, shown in Figure
, and FAR.
-1, the above geometry factors
are developed as follows:
h = (NP - 1) s + 2 (2)
it = (NT - 1) w + 2 (2)
(NP) (s)
=
For the finned
(NT) (w)
340
A
Cflow
= A . --NP ( - D)
IOw
A
Frontal
a
c
=Ai
air
L [1 -(6) (FP)]
= (h) (L) = (NP) (s) (L)
frontal
= a.
air
Ar
ir
dA.
irw
A .
dA.
air
air
frontal
frontal
-D
"A
= S
=
[1 - 6 (FP)
D 2
A
Cheat
A
air
heat
trans
= (NP)(NT)(L) {[(s)(w) -
trans
](2)(FP) +[1-(FP)(6)](Tr )}
0
= (h) (L) (t) = (NP) ()
Volume
4
(L) (NT) (w)
of heat
exchanger
D2
airht
c
volume
(S) (w)
2
ITD
air
=
ht fins
only
1
(2) (FP) [(5)(w) -4
(2) (FP) [(s)(w) -
0
j
+
[1-
(FP) (6)1 (
D )
341
2r
D
Afins
(2) (FP)
ht
ht
FAR
£(2)
[(s)4
(~)
)
{ (2) (FP) [(s) (w) -
total
-X
4
r D
Aair ht
AHh
(s)(w) -
cond. ht ' (
NT) ()
(Di ) (L)
]
L
-
] + [1 - (FP)(6) ](
(NP)
inside
olume
(s)(w)Di
volume
(s) ()
i
4
flow
dAht
AOM -
(NT) ()
dC
(Di)
=
(NP) (dL)
dA
C
(pair) (CFair)( Iaow
air
But
G
air
=
air
Aair
A
air
(NP) (s - Do)[l - 6 (FP)]L
flo
A
(NP) (s - Do) [I - 6(FP)]L
A
(NP) (s)
air
fromltal
Hence
(NT) ()
,Am
(Di)
(NP) (dL)
as
cA
A
dL) (~P)() ()
--
(L)
D )}
342
(NT) ()
(Di )
(GA ) ()
(s)
Having determined the geometry factors, the procedures for
determining total performance, as outlined in the flow chart of
Figure 1-3, is as follows:
Split the condenser up into equivalent sub-circuits.
c
c
N
sect
AH
sect
A
ht
Hht
Nsect
Where:
N
sect
= Number of parallel flow sub-circuits in the heat
exchanger
Then:
Using thermodynamic properties corresponding to the states of
interest, determine the heat transfer coefficients as described
in Appendix K.
Next, use general condenser model 'EXCH' to determine
performance, for the given geometry factors, temperatures, and
flow rates.
343'
And, using results from 'EXCH',
Determine the length of the desuperheating, two-phase, and
subcooling regions:
(FP) (Ait)
(ft) (two-phase)
Di)
DZTP
)
(F) (At
DZV
(ft) (desuperheating)
(R D)
=
DSL
DSL
(AIh )
t
)
(Fs)
(ft) (subcooling)
(r Di)
Where:
Di
inside diameter of tubes in heat exchanger
-
Determine total pressure drop 'PD'
as described in Appendix L.
Convert results back to total flow notation
mc
-&
mc
Qtot
c
(N
sect
Qtot
)
sect)
Finally, using the value of total pressure drop through the coil,
determine the saturation temperature of the condensing medium leaving
the condenser.
If the drop in condensing temperature is greater
than 2 F, repeat the analysis using
T satin
sat
avg
satout
2
For more information, see comments in the program listing for the finned
tube condenser simulation at the end of this section.
344
ATR
6
I
FLOW
,0W
I
Flow
Sub-circuit
N
-<
D
o
-
_
-i
sect
~
= 4
as
shown
tV
tt
-
--
N
N<
i
S
2
FIGURE
I-1
DIMENSIONS FOR FTYED
S
TUREF
HEAT EXCHANGER WITR STAGGFRED)
ROUIDM TURFS
AI
h
FL
W
- W
345
FIGURE 1-2
FLOW CHART FOR GENERAL CONDENSER MODEL -
'EXCH'
art
Input
Geometry factors, heat trans. coeff.,
flow rates, temps., thermodynamic prop.
,
&
Determine
NTU & effectiveness in two-phase region
Determine
Bulk vapor temp. at end
of desuperheating region
,~~~~~
Iterate using NTU method,
to find fraction of heat exch.
used for desuperheatinR
Determine
Two-phase fraction of heat exch.
.
I1
.
.
"
No
-.
"
sd condensation compiete-!
Yes
F_ _
4'
Determine
Heat trans. in subcooling region
using NTU method
I
Determine
Total heat trans. & exit states
L.
346
FIGURE 1-3
FLOW CHART FOR FINNED
TUBE CONDENSER MODEL
Define
Constants for thermodvnamic properties
and heat transfer coef.
r
-
-
I
Reoetitive loop
For changing input data
__
>
Input
Tair
,TH
irin
CFM ir T
,
satM
, DDimensions
in
Calculate geometr
factors
Repetitive loop
Forvarving
Tir
Convert to parallel-flow
sub-circuit notation & analyse
only one of the circuits
I1r
Calculate hai r
Determine
Overall surface efficiency
-
-
-
347
-
-
r
Repetitive loop
For varying refrigerant flow rate
Determine
Saturation properties of refrigerant 1l-
I
Determine
Condensation two-phase heat trans. coef.
I
Determine
Single phase liquid
heat trans. coef.
I
Determine
I
I
Determine
Single phase vapor heat trans. coef.
Use general model 'EXCH'
to determine heat trans. performance
(See flow chart for 'EXCH')
--I
_
_
I
_
I
Determine
Pressure drop through heat exchanger
Is drop in
sat
through coil
Yes
sat
H saT t '
t
ave
avg
I
ou
2
348
I
L
---
_I
349
SUBRCUTI% E EXCHkO'ACrrALFARALFAATHTCHFG)
C
C
PLRPCSE
C
C
C
C
C
TC ETERMINE TE HEAT TRANSFER AND RESULTING
TErFERATbHES IN TE CCOCENSERI GIVEN ALL OF TE
NECESSARY CCFFFICIENTS AND CThER CETAILS
CF PArAMETERS
CESCRIFTICN
C
C
INPiLTS
MEAT
C
EACHANGER
-
ACP
GEOrETRY
APEP/LNIT
C
C
C
ALFA
C
-
C
C
C
C
-
HEAT TRANSFER
FLCW RATE
AIR
(SG FT-hR/Ler
DRy AIP)
Aj FkA REFRIGERANT (REFRIGERANT
FAT
TRANSFER
AREA/TOTAL
ALFAA -
EXCHAN'I-k/FTl
AL.FHA AIR (AIR
ARHT
TPTAL
TOTAL
-
SIDE
NLIT REFRIGERANT
sILE
VCLUME CF
kLFG6
SIDE
SIDE
VOLOE
CF
EAT
EAT TRANSFER AEA/
EAT EXCHANGER-1/FT)
HEAT TANS*
AREA (SQ
FT)
C
C
HEAT
C
HA
-
ATR SIE
EAT TRANSCCEe(B6TU/HR-SG
C
I-RTF
-
RFF
TC-FHASE
C
C
hRSFV -
TRANSFER
C
hRSFL -
C
C
CEFFICIENTS
SICE
REFRIGERANT
COEF.,
(adTU/e-SQ
FT-F)
pRCPERTIES
C
TRI
-
TFrFP
C
C
C
TH
-
SATLRATiO CCNDENSING TEP
GOFREFG,
LATENT ENTeALPY CF VAPOIZATION
TrE
EFNIGEHANT (BTL/Lb')
SPECIFIC
EAT Ar CCNSTANT PRESSURE
C
C
C
*
HFG
CFRV
CF REFGO
CF TfE
SPECIFIC
ENTERING
CONDENSER
EFRIGERANT
VAPCO (TU/LEM-R)
hEAT AT CCNSTANT PRESSURE
CPRL
-
C
X3
-
ExIT
C
x
-
rASS FLCO RTE
C
FT-F)
TRANS.
CrEF. (eT/hR-S
FT-F)
RFF* SICE SINGLE PASE vAPOR HEAT
TRANS COEF. (eTU/hR-SQ FT-F)
RFF SE
SINGLE FPrASE LIOUID HEAT
TRANS,
C
EAT
THE EEFRISEAANT
UALITY
LIULID
FROr
OF
TE
(F)
(F)
CF
(BTU/Le-R)
CCNDENSER
EFRI(ERANT (LBM/FR)
C
C
C
AIR PRCPERTIFS
CPA
C
C
C
TC
xrA
-
SPECIFIC
HEAT AT CONSTANT
TiE AIR
BTL/LeM~-)
TFP
MaS
PRESSURE
OF AIR ENTERING CCNDENSER (F)
FLCW RATE OF AIR (LBM/HR)
C
C
CTHER
INFPTS
C
r
-
AN INDICATOR
(NOT
SED
ERE)
CF
350
SEFFX
C
SURFACE
CF FINNEC
EFFICIENCY
-
SitRFACE
-
STNGLE PHASE VAPOR FRACTION
HFAT EXCHANGER SURFACE
-
TC-PHASE
C
C
C
C
CLTPLTS
F
FTF
C
C
FRACTICN GF TCTAL HEAT
ExCHANGER SLRFACE
FSC
C
C
C
C
C
C
C
;SP
-
ExCtANGEN SRFACE
HFAT TRANSFER RATE IN SINGLE PHASE
GTF
-
GSC
-
TACSF
-
C
C
C
TACTF
-
C
TACSC
-
TAC
-
TRC
-
C
(TU/HR)
TO-PHASE
RATE IN
RwGICN (ETU/iN)
HFAT TRANSFEn RATE IN SBCOCLING
REGICN (BTu/.PR)
F SINGLE PASE
ATk TEMFERATLRE CUT
VaPOR RICN
AI
TErFEkATLRE
(F)
RFICN
F)
CT
F
TWCO-PHASE
CF SUBCOCLING
CT
TEMPERATLRE
ATh
(F)
IXEC
AvERAGEP
TE
C
EGICN
FPAT TANSFER
RFcICN
C
C
HEAT
Si,CCCiLING
PFCKR
C
OF TOTAL
FRaCTICN
-
C
C
C
OF TCTAL
CCNCENSER
TFfPOF
AIR
TEMPERATURE
LEAVING
(F)
REFRIGERANT LEAVING HEAT EXCH,(F)
REMhARKS
C
SLBRCLTINE
ExF
IS
CALLEO
By
THIS
PROGRAM TO
C
c
C
CETEFRIINE TF EFFECTIVENESs IN CROSSFLOW
METHOC
(THIS PFRGArA USES TE EFFFCTIVENESSNTU
EAT TRANSFER PERFCRIANCE)
FCR CALCULATTNG
C
CCrrChN CFaIHA SFFxRSPVFrSPhRSpLCPRL,
IX3
TI,
TP
1TACiTrC, AHT
CISP
F FTPFTPIPFS
GTP,
CPRVXMRtMA
SCP TAOSP, TACTP, TAOSC,
c
C
CETERVIrE
NrT ANC EFFECTIVENESS
FOR TO-PHASE
RGICN
C
XNTUTF=AC/(CFA*(ALFAR/(SEFFX*HA*ALFAA)+1,0/HRTP))
ETF a 1i9 - EXFt-XNTUTP)
RES = 1
+
RSpV*ALFAR/(HA*ALFAA*SEFFX)
C
TE
REFGTFP.f'TRVDS'
C
FIhC
C
CESQPEkHEATIN
C
(F)
AT THE END OF THE
SINGLE PHASE VAPOR REGION
C
TRVCS
(T=REES
IF(TRVCS*GEoTRI
C
C
TC)/tRES-lgc!
TRVDS TRI
FG CrLBLE PRIME
CALCULATE
CRIVING ENTHALFy DIFFEREnCE
HFGDPf'
THE EFFECTIVE
REGICN
IN THE TC-PHASE
351
FFGD'P
(FG
XMATrP
+
PRV*(TRVCS - TH))*(.*-X3)
XR*HFGnF/(ETP*CPA*(TH.TC))
a
kRIrTE(5
57Z)
XNTUTPETP*T RVDSjiF GCP,XATP
F = 2.g
CA
CR
'i 1.e
=' 1.e
IFASTHvCS-TFRT)LE,20)
IF(X3.GT.ge*)
G
TO
GO TO 60
1e0
PS ias co
P'R
N
PS
a'
C
ITEitATE
C
C
C
C
TC FIND
TE
SLFACE
LSED FCR TE
VAPCR REGICN
FRACTION
F TOTAL
CESUPERHEATING
HEAT
EXCHANGER
OR SINGLE
PHASE
C
CF
5
S
"'sg
CC 51 Islip.I5
F
F + CF
XPASF = XA
CA
XASF-CPA
CRfi
X*CFiV
RTCT
(IPAFAR/(.EFFX*AA.ALFAA
CALL ExF(TCTCACRP,ClINjEXFR'
+ 1.*0/RSPV)/(F*AR-T)
EXFuCH*(TRI-TRVCS )/( CMIINS
TRTI-TC)
RIFrE, si ) FxrA AirrT XrASP
RITrE(5, ')
CA,CRpCrIN
aRIZTE(5,*t35) EXr,EXFSPRPS
IF(ABS(EXFR-EXFs),LE.(,O3EXFR)
IF(.,EG.1)
15
GC T
IF(tPFHsPEl/tEXFR-EXFS,) 615,15
IF((iAEqSiFk-PFS.l T,4S(EXFk-EXFS)IIANk(IvEQ*?)GO
.F(AES(Fr-PS),LTAS(EXFR-EXFS))
GO
12
l:C
F
2i
F -
,*CF
[F =- CF/.e
I = 1
Na
+ 1
IF(h.GT.
GC
TC
FR
PS
s-e
CCKTINLE
TC
2i
GeC a e .
CAScC
=
TACSC
TRC a
C
GC TC 55
,i EXFR
EXFC
O*RITE
(5, 5e)
GC
69
C)
5
20
5
GO TC 60
2e
'e
5e0se
eoie-o.e
F
GO rT
55
TO 12
352
CALCLLATE THE TC-FHASE
CF TCTAL EAT ECANGER
C
C
C
C
AND SBCCCLING
SLRFACE
FRACTICNS
IF TE SLECCCLING FRACTICN IS LESS TAN ZERO
PRINT
AN ERC~
ESSAGE ECALSE CCNCENSATION IS INCOMPLETE
C
C
lee
FTP
XP/XrA
FSC = 1.C-F-FTF
oRITE (5t5Z)
!F(FSC)
105 ~IT(
C
i10
FTPFPSC
15
lEVZ,
.1l
j,5-
T
beC
IF(X3.GT*t*k
CrSC
TG 12i
G
Xrh,*CFL
CASC = FSC*XA*rPA
(ALFAR/( EFFX0*A*ALFAA) +
CALL EXFS
tTCTpCASCCRSC*C~'INEXFR)
.e/HRSPL)/(FSC*ARHT)
RTCT
C
CALCLATL
C
HEAT
TANSFER
ANC TEMPERATURES
RATES
C
-
XF.*CMIN*(TH-TC)/CRSC
TRC
T
GEC
CRSC*(T7-TRC)
WITE (5, 6 i)
CACCASCEXFRTRCpSC
Ck*(TRI-TRVCS)
FtCP
xKr-
a
GTF
TACSF
=
S'P/CA
TC
TACTF = TP/(XrFTFPCPA)
TACSC = DGC/LCSr * TC
TAC
k
I TE
(GiC + 6Sp (
,
(5, ,tt
TA-SF, TACOTP TACSCj TAC
r c EiFXP CPA
LF A'ALFAA
-A
, hSPV , SFPL,HRTP
(
F,
ie
.RITE(5,
Tt
wA
2
2~5
TITE
(5
W
N I T E (5
I
b5g
52-0
535
57~
TC
TF~, FSC
,:/
X
A
X4j
X3J
AR HT
TR
U R ti
N
FCR~MAT('W',
1., ,'
52e
+
Sp, TPo CSC
T ; 5PF, TACTt , TA SC, TA0, TRC
i CFRLCPRV, TH, TC,pFG
RITE(tLb ) XP,
iA
TP)/(XMA*CPA)
CFSp GTP
WkITE
(5
W AITE(b,
2
IT
+ TC
CCE
FCRMAT('
X,*ITERATION
hNUTCNVERGE
tCA=
t,1PX,
F ,;;-w5Xs
EXFRu',F4e2,5X
CF7,AT(clS' 'bX',b,'XNTX
1JF7
FRACTION
OF HE.t
)
',10,'F',F5*3,;XsXMA'Fi.4s5X,'ARhTn'
lFour4k)S
'b5·l)
F T
' il;Xl
FCR"AT(
Gh vPCR
M'12
F
CRa
J
Flc
4s5XJ, CMIN=
,IEXFS=',F42,5X
IPR=
X,'ETP
TfRVDSn '
J C Q F>JF=
*X3
4s5X
F
ATP
T4'F=21X'
04 )
353
590
FCRP AT(
555
FCFI'AT(
6eO
FCRMAT(
l*F4 *2;5
610
615
FC-FrAT(
FCRr-T(
t tl,2X'FTP=t,F4'2,5X,
665
IFSCtjF4.2)
***.I**NCCMPLETE CCNCENSATION**L*' )
ixCASC',FI0e4,bXj tEXFR"t
I ,X,Xi'SSCayFl~e4sX
'
=
X, TkC IFe4j5XJ';SC='.FlCg4)
jlg2X,'gSP=I/F'epbX'GTP='tFF10'~4
IleX,*TA CSP. 1,F I .4,5X, 'TAOTP
= ',F10.4J5X,
lTACSC=
6.5
6e6
e',
FC~AT(
FCRrAT{(
FC~r'AT(
)
Fr:e,.s;x, TACa',F1FCO4
3)
* ,XleXr;r=,I2bEXs'SEFFX-',F4.2,25X,'CPA=IF5
,FS3S5X
aL.FAl
'
t, ;[XJP
I ',1,iAu
I.rtFFLuI
.4,5X.
I, FSK
F,,FuXIHTbTP
Fl,4FT.
I ALFAA'I,F*.)
hFI4SPVuiF1.4,bXi
J
6/¢ FCFRrT(
ICPRL=IJFS93JbXS'LPRValJF8*3J5XJ
iJ
1,F792P5 X I TC-r' PP72,jX* 'HFGI ,F b* ½ )
6bo
6t
FC irAT(
'Af4F.Tl,
.4).
1,F4*2 15 iX* X3 wop4#2*bXJ
(
FCRrATI IlicX OFFtPF6o3,bxJ FTPzlpFe3*5X, IFSC=IF6o3)
1t'SC=',
710
'Tra
FC;rAT(
1 '-TACSC
ENC
I *; ;X *,SSP-oFleo*5bX fTP-,Folo4,5XP
F
,;eXX,,.TACSP=IF7.2,SX,
I ,F7
,'; x~TAC;'= F7.2,bX
ITAOTP=',F7F72J5XI
' TR=oI F7 ' 2 )
354
C
CCNCENSER
FRCGRAt
SII'LATICN
C
C
C
CCrPLTING CCNCENSER FERFC-MANCE
TYPE
PLATE-FIN* CRCSSFLO
FPRc-RAr FR
AIR CCCLE
C
C
CATA FCr
INFLT
C
STTi
T A II
FULLY BELCA)
CARC READCER (DESCRIBEC
NT,NSECTP -CONT.
Nh
RLN CEACEr', CELTAFP, XKFAAFCA,
CTA,
TEPrs
TSAXR
I, XtRI,
NX
M
R
I
T
c
C
CLTFLT
C
C
GC
TAC
'
-
R~TE (TU/HR)
TCIAL -EAT TANSFE
AVERAGE AIR TErFERATLRE LEAVING ChD.
C
TRC
-
TEtFFATURE
C
c
R
C
ENTMALPY OF
(F)
CCNC.
LEAVING
CF REFkIGELANT
(F)
LEAVING CCND(8TU/LBM)
EFRI6ERANT
RErARKS
TO DETERMINE
C
Tf-IS
C
SINGLE PASE
C
THIS FukAV
C
C
SLRFACE EFFIcIE\CY
CALLS
Ti-ISiFC3.A
C
SATLRATIC TCyO~YNAIC
C
C
CHTC TO DETERMINE
CALLS SLCLTINe_
T1-S FCG.Ar
COEFFICIENT
T-E CCNCcESATtIC T6C-PthASE iEAT TANSFER
RC6Ar'
CALLS SRCuTINE
SPHTC
EAT TkANSFER CGEFFICIENTS
ETERMiNE
SEFF To
CALLS SCTTNE
OF F INEDC 5RFACE
SE.uE-nC.T.INESATP;P
TO DETERMINE
PPEtTi-5
C
FGR FC;CE
C
Tr-IS rFeCShkF
C
To-ERFCLYNA~PIC FFERTIES
C
\# LF(VAPC_
C
C
C
C
c
T-ITE FCGSRAF CALLS SbBCLbTINt ExCm TO DETERMINE
HEAT TANSe
T-E CEHA L -EArTEXChANGER PFGRCMANCE,
TC.
TFERiATUkES
AI
RATES,
PLRCP TO ETE~RINE
FCM-UAr CALCLSSfGtC;TINE
Ti-IcST
IN THE CIL
PF-,ESSLtE FCP CF kEFEIGEriAtT FCPING
C
T-!S
C
C
DETERmINE ScATLMATIC
TC GIvi\ FkEswRES
FkGTAi$
CrN\vECTIIrCCNDEN6ATIGN ISICE
CALLS
CALLS
S'CLTTINE
TO
OF SLFE-EATED
FuNCTICN
TEE
ETERI>E.E
EFrIGERANT
FPRtCG6RAMTSAT
TEcPFERATES
COrcCN CFAhA, SFFFXhRVRL*CFRL,
1TRIjtTFFFT
vAPC
TC
CCRESFCNCiNG
CPRV XMR,XMA,X3J
FSCgSFGTPiGsCTAOSPTAOTrTAOSCJTAO,
2TRC,AN-T
C . ---. ..°-m'U '--- INPUT
CATA
CONSTANTS
......--...
C
C AIR
C
FRCFERTIE5
A
- fRANCTL
C
XVLA
-
vISCCSITY
CF AIR (LBV/1R-FT)
C
RAL
GAS CCNSTANT
PA
-
LNIVERSAL
C
NLhBER
ATrCSFERIC
F AIR
FCR AIR
PRESSLRE (PSIA)
(FT-LBF/L6M-R)
355'
EAT aT CONST.PRES.CF
SPECIFIC
CFPA
C
AIR
(BTU/LBM-R)
e43,5334# 14.7/
CATA PRAXMUAPJrALPA/.714
*.24
CPA
C
C REFR'IGERANT FROPERTY VARIATION CCEFFICIENtTS
OR 502)
,- NLMEER CF REFRiGERANT (12,2,
C
Jo
C
C
NREF
SLPEMV
hUMERR
XINMV
CF REFRIGERANT
,
COEFFICIENTS
C
SLPEKV
xINKv
-
SAPE
(USUALLY
FCR VISCOSITY
CONDUCTIVITY
-
FR TERMAL
CF LI.UID
FOR VISCOSITY
'
CCEFF:C:ENTS
FOR
SLFEKL & XIN<KL -
C
CP1
C
VAPOR
F
CCEFFICIENTS
CCNDhCTlVITY
CCEFFICIENTS
C
C
C
X!i a X4
THERMAL
COEFFICIENTS FR
C
C
CONST,
AT
AS NR)
CF VAPCR
SPECIFIC
CF
PREE,
OF LI.Q,
HEAT
LIQUID
Kri , 2E
XINKV SLPEKL XINIKL
RtFSLPEpVvXINMVSLPEKV,
DATA
1/22,
2
etV759
le-,Z159,.o629-9/
;,-,482
CATAX1J XK2xr 3,X4/-5.bE5-8s
.525L-5,"2.981EE-3J
1 64! /
CATA CFiJCP2/,cqE-04s*2575/
C ****,CT: - THE ACVF
C
AEL
C AIR
C
C
IF
SIDE
TEY
CF
SAME
TFE
=
CIA-C6A
S
ISAME
FOR BGTH EVAP,&COND.
TYPt.)
FCR EXPRESSING THE
AIR SICE HEAT TRANSFER CCEFFICIENT
XLLA
-
REYNOLDS
LOWLN
FLO
C
C
C
UNLY
COEFFICIENTS
C
C
22
CHARATERISTIC
FLCA
ARE
REFRIGERANT pROFERTY COEFFICIENTS
EFHRIiERANT
FCR
AIR
C
NtMBER
LIMIT
FOR LAMINAR
SICE
LPPER RtYNCLCS NMBER LIMIT FOR TURBULENT
FLOt C AIR SIDE
CATA ClA, C2A, C A,C4APC5ApC6A XLLAULA
ULA
-
C
C REFRIGERANT
'C EVAP,& CCNhC
C
C
C
CFiR-,C6R
C
XLLR
-
-
FOR
BCTH
THE
FCR ExPRESSING
CCEFFICIENTS
EAT
REFRIGERANT SIDE SINGLE PASE
TRANSFER CEFFICIENTS
LOWER REYrCLCS
FLC'
C
C
C
(SAME
ICE FLCk CARACTERISTICS
ARE CF SAME TYPE)
IF TEy
NMEER
CN REFRIGERANT
LIMIT
SIDE
FOR
(SINGLE
LAMINAR
PHASE)
,PPER REYNOLCS NLMBER LIMIT FCR TURBULNT
FLG, CN REFRIGERANT SIDE (SI\GLE PASE)
CATA C1R C2R, C3R C#R C5R C6R XLLR ULR
ULR
-
=- zZ667, *97, 24k' *3500./
1/l, 1,64P 782,4*eg54, · · 49SE5.
C
C
C
*-m-nam-iENC
CF
INPUT CATA CONSTANTS ---------
356
C
C
CLTLE LCCP FCR rLLTIPLE RLNS WHILE VARYING
EXC-ANGE CHARArCTERISTICS
EAT
c
NRLN
REAL (S 5)
I lRUN
IN
5
CC
C
C
m---
mw----mm.-EAT
C
C
CEA
CER
-
CUTSICF CIAIETER CF TUeES (FT)
(FT)
INSICE CIArETER CF TBES
C
CELTA
-
F IN
C
FP
-
C
C
XKF
AAF
-
.-
IN PITCH (FINS/FT)
THEF9'A CCNZLCTIvITY CF FINS (TU/HR-FT-F)
E4T ExCrANGER FRONTAL AREA (S6 FT)
C
C
CA
i\T
-
FLCe RATE (CL FT/toIN )
AI
IN DIRLCTICN
CF T-ES
~NrER
C
C
C
c
C
C
NSECT
-CCNT ST
vT
SIGA
\L7,2ER CF fPAALLtEL CRCwITS
CCNTACT RESISTANCE BErTEEN
(aTL/1-R-SG FT-F)
VERTICAL SPACING CF TUBE PASSES (FT)
AIR FLC
IN DIRCF
- SPACING CF TLBE RCS
AREA)
SIGMA Alk (AIK FLCA AEA/FRCTAL
-
C
ATeC
-
C
C
FTEC
ALFAA -
(FT)
CF TE
CUTTER PERIrETER
ALPHA aIR (AIR SICE EAT TRANSFER AREA/TCTAL
ARFT P
ALFAR -
FLC; AREA INSIDE TUBES (SC FT)
CROSS-sECTiONAL
(FT)
OF TES
INSICE FEPIrETER
SIDE HEAT
ALPHA EFRIGERANT (REFIlCERANT
TTCKNESS
(FT)
CkUSS-.LCTICNAL.
C
C
C
C
EXCHANGER CARACTERISTICS-------
CF
CLLE
HEAT
TRANS,AREA/TCTAL
C
IF FLCw
IN HEAT EXCHANGEP
FINS AND TUBES
AREA CCCUPIEC
CF
BY TUBE
(FT)
(SG
FT)
1/FT)
EXCPAGE~R
VOLUME CF HEAT
EXCHANGEA-1/FT)
FIN r-EAT TRANSAREA/TCTAL
H.T. AEA
-
ATIC
C
FAR
LF
-
LENGTH
C
C
AR-T
CAR
-
TCTAL REFG.SIDE EAT TRANS. AREA/NSECT (SC FT)
kATIC . FIN EAT TRANS.AREA/CGNTACT REA
C
C
C
CF FINS
(FT)
NT FCOR CCNTACT
TC ACC
ANC TUBES
FIN!
ESISTANCE
BETWEEN
aCECE LTAFPXKFAAFs(JANTNSECT
REC(86( ) CEE
REAC(S,611 )
ICGA =
CCNT
ST.r, T
(ST-GE'A)*(le-CELTA*FP)/ST
ATEC
= 34*ILEAw2/4*Z
FTEC
=
ARFT
=
EA
*;'1*C
ALFAA=(·:* ( ST*T-ATEC )*FF +(1DELTA*FP)*PTBO)/(ST*WT)
F
at
,1
=14.
ER,.-2/4*0
.- i4*LvER
ALFAR =
F AR=E*F
*.4*CER/(ST*mT)
P- S T*wT-ATBC) / ( 2*FP*(
ST*WT-ATBO ) PTBO*
1(1 .- FF*LLTA))
XLF
ARHT
= ST/cesC
FC;AT(NTi)*3.14*DER*AAF/(ST*FLOT(NSECT))
357'
CAR
2're* ST*ihT.3.14*CEA*2/4.0
kR ITIE( 5sp
)
WRITIE (5 E C ) CEA, CERD DELTA
kWRITE(5p,t
)
)/(314*DEA*CELTA)
FPs XKF , AAF tA; ARHT, NT, NSECT
CCNT,STpr.T
C
C
CF
m.m"--=-END
EAT EXCHANGER CHARACTERISTICS=---
----
C
C
INITIAL
VALUES FOR AIR AC
REFRIGERANT
FLOW CONDITIONS
C
C
TAII
-
AIR
TEFERATRE
C
CTA
-
AiRF
TEwPoINCkEMENT
C
NTEFP -
rIueER
C
C
C
C
C
TSA
=
CXIVRI
xrRI
NXPR THI
-
fEFRIGERANT
ATUtATIoN TEMP. (F)
EFRIGFANT
FLO
RATE INCREMENT
LBM/HR)
I-NITIA
TCTAL EFRIGFRANT FLOW RATE (LBM/HR)
hMEER CF EFRIGERANT FLOw RATES EXA'INEC
TEMF.OF REFRIGERANT vAPOR ENTERING CCN.
(F)
CF AI
ENTERING
CONDENSER (F)
(F)
TEMPS, EXAMINED
C
kEAC(t861£)
TTl'TANTEPTSA
vA
CA*6e9/iSTGAAAF}
LCCP
FCR
CXMRI,XMRINXMRpTRI
C
C
VARYING
AIR
TEMPERATURE
ENTERING
CONDCENSER
C
TAI
CC 4
TAII
I'llNTEFp
WtRITE(5,E4e)
TAI ·
TAI +CTA
+ 46e.e))
GA - VA*PFm144,/IRAUl(TAI
C
AC
C
AIR
FLCW
ACF
a
d-
LNIT
RFFRIGERANT
ATE
(c
SICE
FT-HR/LeM
HEAT TRANSFER AREA/
UNIT
CRY AIR)
FLCAT(NT)*P/(ST.GA*SIGA)
C
C
SUECIvICE
C
LIKE
A SEFARATE
C
FLCo
AT
FLCh
TE
INTC PARALLEL
IRCUITS
EAT EXCHANGER
AND TREAT EACH
CONVERT
BACK T
TOTAL
END
C
XMA
64*GA*PA*1440ie/(RAL*(TAI
+ 460
) *FLOAT(NSECT))
C
C
CETERFINE AIR SCE
HEAT TRANS,CGEFwNA'(BTTU/HR-SG
C
CALL ST
C CEAPr.AClAC2A
C3A,
CAC4AC5AC6AXLLAULA,
IXrtA,CPAsFRA,REAJHA)
C
C
CETERfrIE
CERAIL
SURFACE EFFICIENTCY
SEFFX'
C
CALL SEFF(XKF,CELTAoHAPXLFFARCARHCCNTSEFFX)
ICNT
C
LCCP
FCR
VARYING
REFRIGERANT
FLOW RATE
FTF)
358
C
xrR
xr'RI/FLCAT r
=
CXrF R
CC
C
SECT)
Cxl'RI/FLrATlNSECT)
p"
K( ljhX
WRITE(5t4C)
XMS
r X
+
K
CETER'INh
SATLKRTICN
~XXm
PROPERTIES
CF REFRIGERANT
C
CE
CALL
F-Cv
STFRP(
N, TSA
PSATVFVGPH"SATL,-FGHSATVSFSG)
= 1 '/VG
'-CL = 1'2/'VF
lF(ICtT.E
*) I
F
= PSAT
XLL = Xtt*TSA.*3 + X2*TSA **2 + XM3*TSA + XM4
CP2
* XINKL
C'I=
CFIPFSAT
XKR6 * S6LF-L*TcX, L;V
S
+ XINhV
L.PEV*TTA
= XL-CFRL/XKRL
FI
GR a
XFF</ATF T
C
C
CETER'iNE
C
(
CChCENSATION TwCPHASE
EAT TRANS.CCEF*'I.TP'
~t(fT/Ik-S(
FT-F)
C
CALL C-TC(rCER,GX3,PRRL,XKRL,XrLRV,X'ULROL,RHCVHTP)
C
C
C
CETERFIhE
SIhNGLF PHASE LIGIC
'.Lt
(ETL/h-'S,
FT-F)
EAT TRANSFER CCEF.
C
CALL SP-TC(CE ~CRisCltC2RRC3R,C4REC5RsC6RXLL/uLFs
1XrtLLCFRL, PNk .REL,RL )
C
C
CETERr"INE SINGLF
PASE
APCE pROPERTIES
C
CALL
VAPFCR(Nh
TRIpP2*V21I2IIS2I)
XILRV = SLPErVf(TSA
+ TRI)/2.g
* XINMV
= SLPFEKV*(TSA
+ TRI)/2.c
= (2I-I-STV)/(TRI-TSA
}
= XrRVCFPV/XKRV
XKR'
CPRV
PkR
C
CETERhINE
C
t'RVI
SINhLF
PASE
(ETL/HR-SC
FT-F)
AFOR
XINKv
EAT TRANSFER CCEF,
C
CALL S-TC
{(CER
NC1R,CCRC3RC4RC5,
C6R XLLRULRi
RV)
XLvCPRvPvL,
R,RER,
C
C
LSE
C
TRANSFER FERFCR,ANCE AND RETURN
SUERCLTINE
C
CCt'CN
FXCi
TC DETERMINE
CONDCENSER EAT
LL RESULTS THROUGH
359
CALL EXC (4 ,ACM jALFARALFA,
CZ TP
FTP.*AR
T
TSA, TAI,FG
)
P
CZV
CZL
F*ARHT/F
FSC*AR~-T/p
XIC..
1 .i
E
5,ZE'i6
C
C
LSE SUERCLTINE
PCRCP TC DETERMINE
PRESSURE
REFRIGERANhT TRcLG.
CCNCENSER
PC'
(I)
DROP OF
C
CALL FCRCF(4,CE~,JEGRzXURVXMLLJRHCVRkOL,RERV,
IRLRLCZTF, X3,x IrJ V2ICZVCZLpC )
GC *GP
:
+ CTF
'XF;
=
'SC
.+
XMA * XIA=FLCAT(t
SECT)
(NSECT)
X'R~FLCAT
C
C
C
CNVERT EACK TC TOTAL FLOo
ANC PRINT RESLTS
cC .
AND OVERALL
PERFORMANCE
CC*FLOATiNSECT)
WRITE(5,t25)
WRITE(S,520)
TATTSA ,XPRTRI
WRITE
(5,5)
RITE (5,3
) XMA
,2IV2
V 2IS2I,
,
j
WRITE(5,bte) ( A, EA,E
-a SEFFX
CC
W I TE(5 ,
) . tREVp.RV
E
.RE (5, t65 )
PE;L
iP
RL HTP
:ITE(5, ;
EITE(5,e )
kRITE(5,eL
CALL
SAT FP(NHr.,ITr,P,vF,
WRITE (5, '
X
IF(I
C
I) Tcr,
vGP, ihOpFG,
G, SF, SG)
TRO,ARHTPsRO
· Xt'A/FLCATcNSECT)
XVA
C
C
C
) FFTPoFSC
GSPu TPo %SC
) TAPrSF,TACTPsTAOSC
=F'
3 Xr'/FLCaTrk;,CT}
CNT*NhE1)
GC To ;i5
ClEC:
CRCP IN SATURATICN
TEMPERATURE
CUE TO PRESSURE
CRCFP IN CCIL - TF THE CRCP IN SATLRATION
TEMPERATURE
IS GREATE
Th-A
2 CEGREES F ,
REPEAT ALL CALCULATICNS,
USI.G
AN AVERAGF VALLL
OF SATuRATION
C
FCLT
, PEAT + Pr
TSATC
: TSAT(NRPGUT)
WR I TE (, E
) FCi T,TSATO
IF (TSA
-TSAT ).LE.ZG
) GC TO 2ee
TSA ICNl'
(TSA
= E'
GO TC 2g
+ TSATO)/2e
TEMPERATURE
360
195
ICKT
2eO
1
CCNTINLE
CCNTI N.E
4Vt
5~e
CChTIt\E
, F 12.6,214 )
I-CCI\,T-',FI
FCkMAT(
FCRVAT
5T1
t
CE
,'
FC~F~T(,
1,
iV
( Sf.FT)
FC;T(,
NT
(F)
TSAT (F)
(LBr/R)
21
trTL/LM-)
F C ,, AT
ii
FC% ^T (I 1
XMR (LBI-/HR)
(ibTU/L(M)
PC (PSIA)
)
TRI
v2I
Q
OC
(F)')
(CU-FFT/
BTU/H)')
).
21FC
F.C'
FCUTs',F1e.5J'
TA
.2 rt t
FCE~rtT(
iCFA~T(, I ' ,5x,'', ;A=F1Ve2
'- :',F1e2,
~65
FP'
QA(CUFrT/IN
'F
FCR;AT(
660
AAF (SGFT)
(FT)
NSECT,)
,eFiS.,4)
X,
CELTA
(FT)
4 )
1,
al
FCrOAT(i
WT-1iF1,5)
STmfpF1je95,
CER
S/ FT)XKILETUL/IRFT)
4F
5c
C3,
(FT)
(FIN
F C2,,'
a T
siJ,
521
611
r-, E v
- TSAtO
= E.*TSA
TSA
FCR'AT ( ' Vp
' J 5XJ r;= 3 =F
V7
,J5X, REA-'
LE/R-S-FT
,
)
(BTU/RSC. FT-R)t)
,1:X,
P-fJ-SG
;FT)I
(TU/i-R-$G
FT-R)',
SX, SEFFX=,
iF1F2.,PXS',l~;=,F7.I.,
FCHDaTi'g
TSATCG',F82)
(LE/
5XJ
'iRL',F71,
L=/8,5x
·
~#lH-i~r-',F7,j.''
( T/HM -S
(Tl;/
FT-R)')
87e0
b6e
FCkATI', ',1T.X I,,
F
Fb*4X'FTFI,',F64,5XT'FSC=,b4)
FCRtAT(l
Ii
l tFSFu'IF1
2,
( bTU/H ) I5XP I TP'
8 15
FC
1'
T
':x
(F)'.,bX
TACSF-',p7s2j,
'TACSa',F7
~Sg FOC(Rt),',AX
TT
11 ( )
2
(F)¼,bX,'TACTP n',VF7.2
(F)')
S'tF,),SX'TRO=,1F7*,
X,'AIiT='F
.,' 4+.(ASFT
(dTU/Lt"'
ENC
.,
ACzF71
)
RLERV
l-TO=',F1F
361
APPENDIX J
COMPLEMENTS TO HEAT EXCHANGER ANALYSIS
Presented here are derivations of an expression describing overall surface efficiency of finned circular tubes, including contact
resistance between fins and tubes, and of a closed-form expression
for cross-flow effectiveness, both fluids unmixed, when using the
effectiveness-NTU method of heat exchanger design.
Program listings
are included.
Overall Surface Efficiency
Figure J-1
gives a drawing of a typical finned tube heat
exchanger, while Figure J-2
shows an electrical analogy to the heat
flow of such a configuration.
.
.
I
U
r~-
i
Refrigerant
_-
-b
fin
S
i!
I
J
i iii
FINNED SURFACE
FIGURE J-1
362
Unfinned Tube
Heat Transfer
Resistanc
AVA
AAV V
J
q
--air
Temp T__
Tube
refrig
Bulk
w
Wall
Refrig.
Side
'/VAVIA
esstance AVAVA
D;
_
I
v
__
Fin
Resistance
Contact
Resistance
ELECTRICAL ANALOGYOF FINNED SURFACE
FIGURE
.- 2
-+
From the electrical analog, we see that
R
total
= Rrefrig +
ref rig
1
1
1
R
(contact
unfinned
finned
We know hovrever, that
q
AT
..
' '
R
I
V
-
'
V = IR
hdA AT
=
q
'
1
hdA
negligible
1
Rrefrig
+ Resifn ce of
refrig dAinside tubes
1
Runfinned
hair Aunfinned tubes
1
contact
contact dAcontact
tuhtpt,,I t
363
h
R
fin heat transfer
air
fin =nfin
As discussed in Kreith, Principles of Heat Transfer 1 , and Rohsenow
& Choi, Heat, Mass, and Momentum Transfer , fin efficiency
fin
for plate fins can be expressed as:
Tanh (m )
1 fin
m
whair
fin
where
f in
kf n
fin
Thermal Conductivity of Fin Material
8fi n
Fin Thickness'
h
air
-.
-
Air Side Heat Transfer Coefficient
= Effective Fin Length
" Tube Spacing/2
£
= S12
As discussed in Rohsenow & Choi
o
pg. 307, overall surface efficiency
,
is definedas
dcq
=
dAto
no
where
Ato t
=
hai
t
r
(Tair
wall
Total Air Side Heat Transfer Area
Hence, for the present case, we have
(hA)
equivalent
o
A
tot
h
air
Anfinned
+ Afinned
364
dA
To
h
tot
o
=
h
I
contact + Rfined
air
1
+
dA
air
1
(R
+
LRunfinned(
unfinned
1
h
cont
dA
r
cont
h
fin
air
dAtot hair
air
dA
'° = d+unfinned
h
tot
dA
air
tot
cont
dAcont
1
dA
tot
nfin
or similarly
o
=
dAfinned +
t
1
tot
finned
dAto
dAtot
Io dAtot
o= 1
A
1
finned
f-
tcnt hcont
Using
, we find
this expression for
R
tot
R
=R
refrig
=h
+
1
dA
tothair
~odtot
air
1
+
1
ref
inside
tubes
o
(Tair -Trefrig
bulk )
and
dq =
R
tot
dAtot hair
fi
in
dA
fin
365
Subroutine SEFF, when given-the necessary inputs, produces a value
for overall surface efficiency, using the expression for fin efficinecy
and the latter expression for overall surface efficiency.
For further
details, see comments in the program listing at the end of this section.
Cross-Flow Effectiveness
The analytical expressions for cross-flow effectiveness with both
fluids unmixed are not in closed form, and are hence, normally presented
A correction factor to
in graphical form as in Kays & London
counterflow effectiveness has been empirically determined which, as
approximates the actual cross-flow effectiveness
shown in Figure J-3,
within about 3% over the entire range. .The resulting expression is:
counter flow
XF
=
[1 +
C
min
Cmax
0
Cmin'
.047)C)
NTU
C
max
where:
NTU
cf
min
1 +NTU
(counter flow)
for
max
Ci
Cf
C1
C
1 mi
1- (Cmin e-NTU(1max
max
< 1
For
<
max
366
cf
= counter flow
C
=
C
= Heat Capacity
Rate
p
C .
man = Smaller of the Two Heat Capacity Rates
C
= Larger of the Two Heat Capacity Rates
max
NTU =
AU
(Dimensionless)
Cmin
= R
AU
= Overall Conductance
tot
Subroutine EXF uses the above expressions to evaluate cross-flow
effectiveness for given operating conditions.
See comments in the
program listing at the end of this section for more details.
REFERENCES
1.
Kreith, Frank, Principles of Heat Transfer (2nd ed.; Scranton,
Penn.:
2.
Textbook
Co., 1969)
pgo 62.
Rohsenow, Warren M. and Choi, Harry Y., Heat, Mass, and Momentum
Transfer (Englewood Cliffs, New Jersey: Prentice-Hall, Inco, 1961),
pg. 109,
3.
International
307.
Kays, W. M. and London, A. L., Compact Heat Exchangers (Palo Alto,
California: The National Press, 1955) pg. 27, 33.
367
1.0
I
.8
EXF
.6
alues
Cross-Flow
Effectiveness
at ion
.4
'IXED
.2
0
C)
1
2
3
NTU
FIGURE J-3
4
5
6
368
SLERCLTINE SEFF {)
X GELTAo-AsXLjFAiCAHC
C
C
)
TSEF
FLfFCSE
C
TC CETERrINE TE
C
C
FCR A FINNtC ELcFACE E
ACCOUNTING FCR CONkTCT
RESISTANCE EETNEEN FINS AND EASE
SRFACE
EFFICIENCY
C
C
CESC;IFTICN CF PAFAvETESc
INFLT
xK
C
a
CELTAC
C
w-
C
C
C
C
c
FIN TIC.c.SS
(FT)
ExTEHNiA,
TNSCCEF
-EAT
CF
FIN
(8TL/R-FT
F)
FT-F)
(ETTL/-SC
_r rIN (FT)
-* k.TIC - I\
EAT TANSA;F4/TCT.
FAR
CAR -
RATIC
TC ACCCLNT
C
CCNDCTIVITY
LchGt
XL
C
C
T-Efrt4L
ANC
.T.
FIx rEAT TNSA'E/CCTACT
FCR CZNTACrT ESISTANCE
rET^EEN
FINS
EASE
I-CChT
CLTFrT
CCTC1-T iESIbTANCE ( TL/r--SG FT-F)
CVERALL
SEFFR
SULFACE
EFF IC i ENC Y
C
C
FIN
EFFICIENCY
xrt z SQT ( 2er AI (XK*(LTA)
FINEF
! XL))
C
(EXF(X*XL)-EXPF(-X*XL))/((EXFIX.l*XL)+EXF(-XM
X*'XL
)
EFFICIENCY
SEFFaIl *,-FA*(1,G-leIW/(CARO-A/MCCNT+,//l
SURFACE
RETURN
END
aARt
AEA
FINE ))
369
SeRCtTINE EXF( TCT,CACRjCtINEXFR)
C
C
C
C
P. RPICSE
OF
EFFECTIvESESS
TC CETERMIN E TE
ExCAANGER tSTNG THE EFFECTIVEhESS-NTU
A
CROSS FLOw
METHOD
EAT
C
CF pARAMETERS
CESCRIFTICN
INPI.T
RTGT '
C
C
C
RESISTANCE
TCTAi
ToG EAT
C
BEThEEN
FLLIrS
((4HR-F)/BTU)
C
CA
TCTAI'
EAT CAPACITY
TCTAi
EAT
"
CI
CUTPILT
C IhI
C
C
C
C
'
THE
ExFR
CAPACITY
;CsALLER
A (TU/R)
FLUID
CR
CF CCSS
EFFErTIVENESS
-
F FLUID
CF
CA ANG
CF
FLOy
R
(TU/R)
(TU/R)
FLOA
HEAT
EXCHANGER
C
DETE4RMINE
C
CMIN
ANC
NTrU
IFICJ/CACLT.Ccc5c
GCG TO 5
IF(CA/CR.LT,.oC
) G'TC 1e
CVIN
CA
CrAX
CH
XNTL a 1i*/i(CFrIRTOT)
5
ECF
XpT,/(i
CC
2
TC
CH
CrI
C'AX
GCO TIC
10
15
CA
1-
CrIN
CA
CFrAX
CR
XNTL ,
1ik/(C{IN*RTOT)
EVALI.ATE
C
e * XTU)
ECF
.1*EXF(XhNTL*(i
APPLY
C
TC CeTAIN CHCSS
EXFrk ECF/((i
CCRECTICN
FACTCR
ENC
TC COUNTER
FLOW EFFECTIVENESS
FLCo EFFECTIVENESS
47*CMIN/CMAX)*XNTUL*
+
l(*e36*CINh/CrAX,)
RETLkN
)/(1le.-CMIIN/C-AX
2 - CIN/CMAX )i
C
E
FLCW EFFECTIVENESS
CCLNTER
(i Z-EXF(,xNTU*(1e-CrIN/CAX)
370
APPENDL
K
HEAT TRANSFER COEFFICIENTS
This section outlines the basis for all heat transfer coefficients
used in the present study.
Briefly, these are:
Condensation (two-
phase) heat transfer coefficient, evaporation (two-phase) heat transfer
coefficient, and single phase refrigerant and air side heat transfer
coefficients.
The three subroutines used for computing these coeffi-
cients are described, and listings are included at the end of the
discussion.
Condensation Heat Transfer Coefficient
Condensation of R-12 and R-22
in forced convection was studied
by Traviss, Baron, and Rohsenow
using the Lockhart-Martinelli two-phase
flow pressure drop correlation.
(See Appendix L ).
The following
relations are found from a quite general derivation, and are hence
believed applicable to condensation of other fluids.
The local heat transfer coefficient h
z
is correlated within
+ 15% by
Nu F
.1 < F (Xtt) < 1
ett
9
(X)
PrRe 9
tt
Nu F
1 < F (Xtt) < 15
where
z2
PrtRe9
=
[F(Xt)]
371
tt
+ 2.85 X
tt
F(X tt)
o15 [Xtt 1
1
tt-. 476]
.5
.1
1
Xtt
x
*9' P
*
V
F2 = .707 Pr
Re9 < 50
Re'5
2,2.
2
50 < ReL < 1125
F2 = 5 Pr
+ 5
n [1 + Pr(.09636
Re
> 1125
F2 = 5 Pr
+ 5
n(1 + 5 Pr)
Re
-:
R'
X
5
Re
+ 2.5
- 1)]
n(.00313 Re
G (1-X)D
uR
Local Quality
The length of tube
Az
required to change the quality
Ax
from
an energy balance is
G h
DAx
az =Az4hfg
z
AT
Using this expression, the length of tube
from
xi
at inlet to
xe
z
to change the quality
at exit may be found by dividing the
However, for cases
calculation into steps of
Ax = .05 or .10.
of approximately constant
AT , as in muny air-cooled condensers, the
above expressions may be combined and integrated to yield an expression
for the overall average heat transfer coefficient1 :
81 2)
372
1
h
avg
Xi
(X 1
(x
1
-x)
e
e
dx
h
z
As can be seen, this expression is a function only of quality.
The
average heat transfer coefficient may thus be obtained by dividing
Ax = .05 or .10, and performing a
the calculation into septs of
simple step-wise-constant integration.
Subroutine CHTC has been
programmed to do such an integration and return a value of the average
See
condensation heat transfer coefficient, independent of length.
comments in the program listing at the end of this section for more
details.
Evaporation Heat Transfer Coefficient
A good discussion of two-phase boiling and evaporation is
given in Tong, Boiling Heat Transfer and Two-Phase Flow .
An expression
for the average evaporation two-phase heat transfer coefficient from
entering quality
xi
to exit quality
x e , assuming constant
AT between
tube wall and fluid is as follows.
kg
h
= (.023)(.325)(2.50)
avgD
D.2~
8
(-)
.
4
()v P
.075
(1xe xi)
- v
(Xe - xi)
(xe.325 -
.x 325)
The length of the evaporating region can then be found from an energy
balance yielding:
373
hf
tot
where
P
AT
Ph avg xe- xi)
avg
is perimeter of flow passage.
Subroutine EHTC uses the
above expression to compute the average two-phase evaporation heat
transfer coefficient.
See comments in the program listing at the
end of this section for more details.
Single Phase Heat Transfer Coefficients
3
Kays & London, Compact Heat Exchangers presents. heat transfer
information on a number of different heat exchanger configurations.
The correlations used in the present work for single phase refrigerantside coefficients are developed from data on flow inside circular tubes,
shown in [Figure K-ll.
(Kays & London type ST-1).
Kays & London
suggest that for air-side coefficients, better correlation of data
is achieved using outside tube diameter, rather than the equivalent
diameter as is
used in their book.
For this reason, the Kays & London
data has been replotted, correlated on the basis of tube outside diameter,
for heat exchangers with round tubes in cross-flow.
The results are
shown in [Figure K-2 ].
The heat transfer coefficients obtained from the above correlations
can be modeled in general form by the following expression:
374
2/3
S Pr
T
= A Re
B
Where:
GD
S
ST-=
D
ReRe
GC
P
We find from [Figures
K-1
o
= Tube Outside Diameter
and K-2 I
Refrigerant-side
Laminar flow
2/3
Re < 3500
- 78992
1.10647 Re °
ST Pr
=
ST Pr
= 3.5194 x 10
Transition flow
3500 < Re < 6000
Re
Turbulent flow
Re > 6000
ST
.Pr213 = .01080
Re 13750
Air-side
All flow regimes
ST Pr2/3 = .2243 Re
Subroutine SPHTC
38 5
is structured to accept values of the constants
in the various flow regimes and to produce a value for a single phase
heat transfer coefficient based on the computed Reynolds number.
inputs for this program are structured as follows:
Laminar flow
Re < XLL
ST Pr
2/3
C1 Re
22
Transition flow
XLL < Re < UL
S
T
Pr2/3 -c
C4
3
Re
The
375
Turbulent flow
Re'>
For
UL
S
Pr
2/3.
cC
Re 6
more information, see comments in the program listing.
REFRENCES
1.
Traviss, D. P., Baron, A. G., and Rohsenow, W.M., "Forced Convection
·Condensation Inside Tubes", Report No. 72591-74; Heat Transfer
Laboratory, Massachusetts Institute of Technology, Cambridge,
Mass. (ASHRAE Contract No. RP63).
2.
Tong, L.S.,
Boiling Heat Transfer
And Two-Phase Flow (New York:
John Wiley & Sons, Inc., 1965) CPT 5.
3.
Kays, W. M. and London, A.L., Compact Heat Exchangers,
California: The National Press, 1955).
(Palo Alto,
376
,,-2
lU
St
-. 1375
St Pr2
/3
Re
St Pr
= GD
(3.5194)
2/3
= (3.5194)Re
1=038
1P
10
Re -
FIGURE K-1
-1
10
1
AIR SIDE HEAT TRANSFER CORRELATION
CROSS FLOW OVER BANKS OF FINNED
FOR
CIRCULAR TUBES
St Pr 2 / 3
10- 2
Re
1
I
%
~
·
. ·
.
J,
.
I
. m
102
104
Re
-
FIGURE K-2
.
. . .. ..I
105
377
StERCUTIE
CHTC(CEG, XEPRL
iRHOVHAVG)
XKL XMLV XMUL RHOL
C
C
C
PLRPCSE
TC CETERMIKE TE
FCRCEC CONVECTICON CONDENSATION
TGC-PhASE
EAT TRANS. CCEF. FCR FLCW IN
(eASEC CN CCRRELATIONS BY TRAVIS)
C
C
TUBES
C
C
CF PARAMETERS
CESCRIFTICNS
C
C
C
CE
C
C
XE
"
a
ECLIvALENT
MASS FLCW
DIAfETER
PER LNIT
OF FLOw PASSAGE (FT)
AREA (LBM/HR-SC
FT)
a
EXIT CUALITY
FRL
PRANrTL
NUrBER GF TE
LIGUID
XKL
a
TI-ERiA.
CCNC.
P.PASE(BTU/HR-FT-F)
C
-
VISCrSITY
CF VAPOR PHASE
C
C
a
VISCnSITY
CF LI*.
C
.. CL
OCtESTTY OF LIC.
a
C
C
C
DENSTTY
LG.
CF
PHASE
(LBM/HR-FT)
pHASE (L2M/H'-FT)
PHASE (LE4/CU
OF VAPCR PHASE
(LB'/CU
FT)
FT)
CL TP T
H.AVG
C
E AT
AvERAGE CCNCENSATICN TO-PHASE
(8TL/H-SbG
FT-F)
TRANSFEQ CCEF,
C
C
INITIAL CCKCITIrNS
HP - 5eee.e
hIINT
2.0
C
c
INTEGcRATE FRCr
cLLITY
EGQALS
TC GUAL I TY EQUALS XE
1. g
x
CX
OCte
..5
I=1,2¢
X *, XCX
IF(X*LE.XE)
XTT
C6C C iS
(XPtL/XMLv)**.l*(RHCV/RHCL)**.b((1.oe-X)/X)**.
FXTT .15*(1.e/XTT + 285*XTT**(-.476))
REL
GCtE*(1eX)/XLL
IF(RELLT.5.¢C)
F2 a *707*PRL*REL-ws5
IF((RELoCE5~C.),AND.(REL.LEl1cI25.)
1C*ALCG(l'k+PRL*t
lb36*REL=**.585-1. ))
IF(;ELGT.1jE5,v)
5
F2
1PRL)+2.5ALOG( .e'313REL*812)
IF(FXTT.LE1j
T
rC
F590*PRL + 5 i
PRL + b.*aALOG(1.0 + 50*
I
9
C
C
EVALLATICN
OF LCAL
IF(FXTT.L1T.*g)
IFIFxTT.GE.1lb.e
*1
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381
APPENDIX L
PRESSURE DROP RELATIONS
Discussed in this section are refrigerant two-phase and single
phase pressure drops in the heat exchangers, single phase pressure
drops in connecting piping, and heat exchanger air-side pressure
drop.
Derivations and program listings are included.
Two-Phase Pressure Drops
As described in Travissl and Tong 2 , the method of Lockhart
3
and
Martinelli 3 can be used to express the.total two-phase pressure drop
in either evaporation or condensation in the following manner:
dP
dz
dP
dz f
dP
dz
g
f
dP
dzm
dP
(dP)
is the component due to gravity and static head
g
dP
(dPz
the component due to momentum change
2
is
m
(09)
I)
f
o
v
(I1 + 2.85 (Xtt 523)]
v
subscript v for vapor
V
subscript
for liquid
382
x = Quality
11
Xtt=
D = Tube Equivalent Diameter
o1
ol
p .5
(-)
(1-)
.9
)
(x
G2
1
P
dP
go
dzg
2
D
[ (-.- ) - B a]
Pv
r
G2
F
r
2_=
v
a D
B
-PQ,
Pv
Pv
a = Axial acceleration due to external force i.e.
1
%
Gravity
2 /3
x )Pv
p9
G2
dP
-)
dzm9=
_
Pv
pv2 /3
p 1/3
(-z) [2x + (1 - 2x)(-)
+ (1 - 2x) (-)
Q
Pv
- 2 (1- x)(-)]
Pt
Now, using a given or assumed quality vs length profile (usually assumed
linear), the calculations can be separated into steps of
and the results summed to give the total pressure drop.
we may integrate the expressions as follows:
Rearrange to obtain
Ax
.05 or .01
Alternatively
383
dP
df
- (.09)
lpv.
G 1
- 8
1.2 )
DPp-/\
go
dP
(dj)
g
x1.8
P
go
PV
(.9) (.523}2
x
PR,
Pv )
(P,
a
+ 2.85()
1 - x
.5].523
.1
Pv
+ (
PV)
-X x)
dP
m
2
Pv
1/3
[2
2/3
+ (-2x)(-~
PQ
go
dx
Pv
(1 - 2 x) (-)
P.
d
Let us integrate to find the pressure drop due to momentum change
Pf
fP
Xf
fxi
dP = m
i
G2
(Pf - Pi)m
-G[
2
1/3
x2
Pv go
(Pf
i)
+ Pv
(p)
2
CG
m
Pv
2/3
( x - 2)
Xf
2
P
2
v
P
(x
xi
p 1/3
goPR
v0~~(~l
Pv
PR
PR
Pv
_I
Pt
1/3
Pv
2/3
Pv
{[1 +P
(
2
).
I (xf - xi 2)
2/3
-
Pv
()
Pt
]
(xf -
xi)}
384
Next consider the friction term,
Assume that quality varies linearly with length.
x = C1 dz + B
dx = C
dz
Xf
Pf
Pi
d Pf = -X.
.47 2
1-x
x.
1
1.8
-x)
C2 I1+ C3
where
(.09)
G
v
C2 2
C1 go Pv
12
.262
.0523
Pv
C
-
CvV
Xf
(Pf-
) =-f
f
(-)
Pt
2.85 (-)
3
.47
1 - X
C2 I1
+ 2 ( x )--
I
Xf
2.8
x
2
2.8
1 - x
+ c23 (---)
x
X.
.47
(1- x)
-2 C 2 C3
1
x
9 x41.8
x
1.33
dx
i
.94
.86
x
+mx + m (m-
0 <x<
dx
Xi
Using the binomial expansion
(1+x)m =
dx
1) x
2
+ m (m - 1) (m - 2) x3
-
3.1
1
We may evaluate the last two terms above.
Consider first:
*
v
*O
385
f (1 -
.47 133
x
dx =
x)
1.33
x
I -.
f(1x)
2
47
+ .
o..]dx
dx =
3.33
- .47 x
3.33
2.33
6
1.33
x
2.33t'
x
(.47) (-°53) (-1.53) x 3
47x + (.47) (-.53) x2
[1 -
(.47) (.53)
(2) (4.33)
5.33
(47) (.53)(1o53)x
X
+
(6) (5.33)
Now calculate the ratio of the first and second terms, the second and
third terms, and the third and first terms
3.33
.47
R2-1
x
x
.33
=
.329 x
2.33
4.33
-
R32
(.47) (.53)
(2) (4.33)
x
= .204 x
=
(3.33)X3.33
.2
(.204) (.329) x
13-1
Since 0 < x
2
= .0672 x
1
We see that:we may truncate after the first 3 terms to get
rf
jJ
xi
.47
(1 - x)
1.53
x
dx
=
Xf
.47 x
2.33
3.33
(.47) (.53)
(2) (4.33)
x2} x2.331
Xi
Xf
i
386
Performing a similar expansion on the second integral and truncating
after the second term we find
xf
.94
(1 -
94
.86
x)
86 Xf
1.86-
2.86
}
x
xi
If we neglect the gravity or external acceleration force term,
dP
= 0 , we arrive
(dz)
expression
at the following
g
(Pf
- Pi)
= (Pf-Pi)
+ (Pf-Pi)
total
a
f
-G
(Pf - Pi ) m = Pv go
P
Pv
{[
Pv)
+ (-)
p
1/3
v
- [2 (-) _(-)
Pt
-JP2,f
Pi.
Pt
Pv
2/3
1/3
- Pi)
f
Pv
(-)
1.86
[.538 - .329 x] x
E
.262
P-
2.85 (---)
PI
.2 1.8
(.09) Uv
G
2-
1.2
C1 g
C1 -
P
D
(zf-zi)
Xf
} i
.0523
C3
2
2.33
)
I (Xf - Xi)}
+ 2 C3[.429 - .141 x - .0288 x ] x
= -C2 {.357 x
+c3
2
2/3
-
2.8
(P
2
I (xf - xi
i
387
The above expressions for total two-phase pressure drop, along with
expressions for single phase region pressure drop, are used in subroutine PDROP to determine total pressure drop in the evaporator and
condenser.
See comments in the program listing at the end of this
section for more details.
Single Phase Pressure Drops in Heat Exchangers
Derivation of the vapor region pressure drop in the heat
exchangers, accounting for density change, is as follows:
0
Pi - Pf
G2
1
a
Pf
I_
Pf
1
1
L
PiD
+
G2
2 m + gp
f
- hi)
i
)
Pi
2
Pm
a
1
p
2
(Pi
Pf)
vapor
[
'=GG2 [(,f
-)+f- i ) + fL(+D- (Vf+Y~
V)
where
f = Moody Friction Factor
The expression of the liquid phase pressure drop in the heat exchangers
is the normal incompressible flow relation
AP
4 f
D
Where
f
G2
L
2
pY
Moody Friction Factor.
388'
See comments in the PDROP program listing at the end of this section
for more details.
Single Phase Line Pressure Drops
The equivalent length method is used to account for pressure
drop in the connecting piping.
The standard incompressible flow
relation is used except that an estimated equivalent value of
L/D
is used, instead of the actual L and D.
L G2
AP = 4 f
Where
(§)
2 P
f = Moody friction factor.
Subroutine DPLINE is used to calculate pressure drops in this manner,
For more details, see comments in the program listing at the end of
this section.
Note that the programs previously described used subroutine
FRICT to estimate the Moody friction factor.
This subroutine accepts,
among other inputs, a value for the tube wall surface roughness,
and it can reproduce the entire Moody friction factor plot as shown
in Figure L-1
4
.
This has been used instead of the standard laminar
and turbulent limits for smooth pipe because in some applications, the
connecting piping can be far from smooth.
See comments in the
FRICT program listing at the end of this section for more details.
Air-Side Pressure Drops
Kays & London suggest in, Compact Heat Exchangers5, that for
389
air-side coefficients, better correlation of data is achieved using
outside tube diameter, rather than the equivalent.diameter as is used
in their book.
For this reason, the Kays & London data for tubes with
plate fins has been replotted, correlated on the basis of tube outside
diameter, for heat exchangers with round tubes in cross-flow.
in Figure L -2
As seen
there is generally poor correlation between different
heat exchangers for the friction factor.
The author has developed
a.new method of correlation which accounts for
frontal area.
a
air flow area/total
As can be seen in Figure L-3-, accounting for this
effect in the indicated manner produces excellent correlation between
different heat exchangers.
a
The resulting expression is
-.108
=
fair
air
.367
Re
and the total air side pressure drop expression becomes:
t
air
air
i
4 a
air
2
_
2 Pair
go
Where:
a
=
Air Flow Area
Total Frontal Area
See Discussion
Total Air-Side Heat Transfer Area
Total Heat Exchanger Volume
air
and Condenser
t
-
Total Thickness of Heat Exchanger
390
Re =
D
GD
G
= Tube Outside Diameter
These relations can be used to estimate the magnitude of air-side
flow losses through the coils.
References
1.
Traviss, D.P., Baron, A.E., and Rohsenow, W M., "Forced
Convection Condensation Inside Tubes", Report No. 72591-74;
Heat Transfer Laboratory, Massachusetts Institute of Technology,
Cambridge, Mass. (ASHRAE Contract No. RP63),
2.
Tong, L. S., Boiling Heat Transfer And Two-Phase Flow (New York:
John Wiley & Sons, Inc., 1965) Cpt. 4.
3.
Lockhart, R. W. and Martinelli, R.C., "Proposed Correlation of
Data for Isothermal Two-Phase, Two-Component Flow in Pipes",
Chemical Engineering Progress, Vol. 45, No. 1, pg. 39 (1949).
4.
Miller, D. S., Internal Flow: A Guide To Losses In Pipe And Duct
Systems, (Cranfield, Belford, England: The British Hydromechanics
Research Assoc., 1971).
5,
Kays, W. M. and London, A. L., Compact Heat Exchangers (Palo Alto,
California: The National Press, 1955).
391
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392
-1
10
KAYS & LONDON AIR SIDE FRICTION FACTOR
CORRELATION FOR CROSS FLOW OVER BANKS
-.T
--
l-tan
A·
n
t
f
.
Friction
Factor
- 2
no
__
1
22
I
q
10
.· 1
·
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·
I
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1. I··II
103
.....
i
.
·
.
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I·L1--
.
I
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Reynolds
10 5
Re
Number
FIGURE L-2
100
IMPROVED AIR SIDE FRICTION FACTOR CORRELATION
FOR CROSS FLOW OVER BANKS OF FINNED CIRCULAR
TUBES - BY HILLER
Best Fit
fa
_a
, ,._
-.108
I
IJ
10-i
=
IUDe
·
-
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·
·
· ·
·
·
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·
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Re
Reynolds Number
FIGURE L-3
I
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393
SUERCULTINE PCRCp(NCEG,XUVJXMULjRHCVRHOLREVREL
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INITAL QUALITY
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LCNiGTh CF TwO-FHASE
F INA
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VAPCR PHASE
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FHASE VAPCR REGION (FT)
PASE
LIG
REGION (FT)
PhES.CDCP IN SINGLE FPASE VAPOR EGION (PSI)
P$c. CROP IN SINGLE PHASE LI.
REGION (PSI)
FEiS..CRCP IN TC-PHASE
REGION
TCTAI PRESSUkE ChOP (SI)
CALTICNh
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FTI
PHASE
RELION
REGION
CLeOF
C SINGLE
CF S:NGLE
FT)
(LBY'/Cu
(LBE/CU
REYNrLDS
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(FT)
(FT)
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AND TWO-PHASE
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CESCRIPTICN
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CTH SINGLE
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(PSI)
wATC~ SIGN CONVENTICh **.***=**
REPARKS
C
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THIS FRCGRAM CALLS SUBRCUTINE FRICT, OR
CETERFIINt TE GENERAL OOCY FRICTION FACTOR
C
FCR SINGLE
FPASE FLOW IN TES
C
C
rO'CENTLr' CCFPCNFNT
OF TO-PhASE
PRES,
DROP
CPr
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1
V/RHCL
-(RHOV/RHOL)**.333
1'(CV/C\L/RCLC)*w.A676)-XF-XI)*2.g*RHCV/RbOL.(RHCV/
2RCL)**.3333-(RrVHf/RHOL)*,.667))G**2/(ROV*32.2*
Cl a (XF'XIj/CZTr
CE
=
C3 =
ixr'UV.*.2*G**I.d/(ClRHOV*D**1.2*32.2*3b~.0O
.(XL/XIM
UV) .* .*023* C RO V/RHCL) * .26
C
C
FRICTICN
CFCNhNT
OF TWO-PHASE PRES,
FPF C2( .357*(tF**2.8-XI**28)+20*C3*(
DROP
.429*(XF**2.33
394
1-XI**2 .32 )-.*14 1* ( XF**3, 33-XI**33
) -,287*(
XF4.
33
2'XI**4_.3))+C3*w2*(*538*(XF**1.86-XI**1b6)-.329*(XF
3**2.86-XI**2.86 ))
C
C
TCTAL TC-PASE
CPTP
= CFM
PkESSURE CROP
CPP
CALL FRICT(RfEVCDFFV)
3)) GO TO 2e
IF (.EC.)).C..EC.
C
CCNCENSE
CFVG*2(
SCLF
1
/R
PASE
Cv.VVF,
PRESSURE
COPS
V*CZV (1 */RCV+VV)
/D) /
CALLFICT hLL,p,C,FFL)
CFL = 2 -iFFLC7L'*G-2/(CEOhL*32*2*36000**2*144*0)
CC
TC
~4
C
EVAFCRA1rC
C
2
13292CJ
CP'
C
4?
SINGI E PHASE PkESSURE
CPFV=G**j*
(V1
CROPS
7/k-UV+;FF vw-ZvIvv*./+/RI-OV)/)/
vtlc*2*144 e;
a Voe
TOTAL PRESSukE
rHGCP
PC t -(LFTP + C
+
PL)
ARITE(S-~VO)CZvCZL,CZTP,CPVCPLDPTP
5V
RET'RN
FCR;AT('
~
CZV,.F10.½4,'
DZLufF0.4,'DZTPf,F1j.e,4
.395
SLeRCLTINE CPLINE (CXLE,E,
XM'R,RFCjXML.,CPLNE)
C
C
FLRCSE
C
TC CETERftINE
SINGLE
PASE
FFESSURE
CROPS.
C
C
C
CESCRIFTICK
C
C
C
Xi.EG
C
E
C
CC
C
Xli'R -
C
C
C
C
=
a
xlyv
*
ECLIVALENT
CIAPETER
EaLIVALENT
LEhCTi- (L/C
SLFACE
RCLS'>c-5
CF FLCA PASSC-E
(FT)
CN CIt'ExSICNAL)
CF FLCVb PASSAGE (FT)
'raS FLC, RATE (LEY/l- )
CE=SITY
F FL'.IC (L/CU
FT)
vIECCEITY CF FLLIC (L.ct/-R-FT)
CLTi;UT
C
C
CF PARArETERS
IIFL,T
CLF.hEw
SINGLE
FASE
FrESSAc_
RCP
(PFSI)
REARKS
TI-S FCG~Ar
CALLS S;CLTINE
FHICT FCR
CETEPIINING
TE GENcRAL rCCCY iRICTION FACTCR
FCR SINCLE F-ASE FLC
I
TLES
RE - 4.e*XrlR/(3,14*C*X.)
CALL FRICT (EE,CFF)
CFLNE
**FF*XLLG(4*e*XtR/(
I(EA*RC"E,A262g
*,e*1,eg)
RTLRLi
ENC
3(3"14*C*)
)**2/
396
SUeRCCTIE FRICr (REEsDIpFF)
C
C
C
FURPCSE
TC CETERP INE ThE GENERAL MCCCY FRICTION
IN TUBES
FLC
'FCR SINGLE PASE
C
C
CESCRIPT ICN CF PARAMETERS
C
FACTOR
INPLT
C
C
CI
-
REYNCLOS NiMBER
SLRFACE RC GHNESS OF FLOw PASSAGE (FT)
ECLIvALENT CIANETER CF FLOn PASSAGE (FT)
CLTPLT
FF
a
MCCCv FRICTION
E
C
C
C
C
FACToR
C
LAtINAR FLCA RErIME
C
.ee)
IF(E,.LE,23
IF(RE.LE*23V9,0
FF
= 16.'/RE
GC
TC 3C
C
C
FF
ANC TPULENT
ICN
TRASIT
C
FLCO REGIMES
CI
,iE(2
s
'*egg
CF
CC 2e I = 1J¢
FF + CF
FF
Fr
IF(FFLE'eZ)
. et1
-. *ALOCle251/E
A
L u lo,/gRT(U4*FF)
IF(AeS(AE).LE*t,Z1*Eb))
/(RE*SCRT(
4
*FF )) +.F-/(3r7*C))
CC To
iF(A=E) i,j3Cp2C
FF
= CF/iO
1S
F
CF
EO
CONTINUE
eRITE
31
1gZ
(5
iL
Cf-
)
RETURN
FCRMAT(i
s**s*FRICTION
FACTOR FAILS
TC CONVERGE****?*
)
397
APPENDIX M
DETAILS OF CROSS-FLOW EVAPORATOR MODELING
Details of the general air-conditioning or heat pump type
cross-flow evaporator model
EVAP', and of the special case, finned
tube evaporator model, are given in this section, followed by
computer program listings for each.
General Model 'EVAP'
The effectiveness - NTU method of heat exchanger analysis is
applicable in the single phase region of the evaporator, or for the
entire evaporator if no moisture removal occurs.
The analysis is
exactly the same as for the general condenser model 'EXCH'
Appendix I, except that in the evaporator, the air is
of
the hotter
fluid instead of the colder fluid.
In the event of moisture removal, which is determined automatically
by the model, a modified version of the effective surface temperature
approach discussed by McElgin and Wiley I is used.
It is assumed that
all moisture removal, if it occurs, takes place only in the two-phase
region.
The effective surface temperature approach assumes that the
air side heat transfer coefficient is unaffected by the presence of
water on the surface of the coil, and uses a heat transfer-mass transfer
analogy to determine the amount of moisture removed.
A total driving
enthalpy difference between bulk air and effective surface conditions,
accounting for enthalpy of the moisture in the air, is used to determine
398
the heat transfer rate.
Full psychrometric chart data is used in
the modified method presented here, as opposed to the approximate
method used by McElgin and Wiley, which linearized local sections
of the psychrometric charts.
Subroutine 'XMOIST', as listed at the
end of this section, is a program which produces psychrometric
chart data in the range -30
< 1000F.
wet bulb -
T
The procedure for determining sensible and latent heat transfer
characteristics, and fractions of coil used for evaporating and
superheating, as shown in the flow diagram in Figure MI-1, is as
follows:
Determine the representative coil characteristic 'COIL' using
the representative surface temperature technique.
The heat transfer through the coil surface can be modeled by the
following two analogous electrical circuits:
ase surface
T
air
hair
Tref .
R
fins
R
contact
and
air
Rumped
air
hair
refg.
t
TES
(Effective Surface TemD.)
399
Now, since it is assumed that the presence of water droplets
on the coil surface does not affect the resistance to heat transfer
, the total resistance to heat transfer:
we can define 'Rto'
R
Rt~ttot1
C
dAR
tot
1
h
air
+
1
R
also
R
=
tot
h
a dA
aht
umped
lumped
where:
no
=
Overall surface efficiency, allowing for an extended
surface on the air side, and including contact
resistance, as described in Appendix J.
h
a
=
a
aR
Heat transfer coefficienct (Btu/hr-ft2-°F)
:= Air side heat transfer area/total heat exchanger volume
=
Refrigerant side heat transfer area/total heat exchanger
volume
dA\
(f)
= Unit Heat transfer area on refrigerant side
ht
dA
,= Unit heat transfer area on air side
aht
a
=
Subscript indicating air side
R
=
Subscript indicating refrigerant side
ft
400
Hence:
1
lumped=Rtot
h
a
dA
aht
Then the total heat 'dq' lost by the air in passing over an element
of wetted area
dq
dA
is:
w
h
a
dA
(i - i )
Cpw
w
Where
i
=
Bulk enthalpy of the air (including moisture)
(Btu/lbm dry air)
is =
Enthalpy of the air at the surface of the coil
(Btu/lbm dry air)
Cpw=
Moist air specific heat (Btu/lbm dry air -OR)
Similarly
dq
1Rlumped
dAv (TES - TR)
Equating we find:
COIL -
- (TES -
(i-i)
)
S
Where
Cpw
ha
lumped
CPw
can be approximated by the normal dry air specific heat
over our range of interest,
Cpw = Cpa - .24 (Btu/lbm
dry air -OR)
providing we use wet bulk temperatures when computing enthalpy change
of the air.
401
Next determine the amount of heat
'Q
transferred in the twotp
phase region, assuming complete evaporation
Qtp
=
(1 - X4 ) hfg
(Btu/hr)
where
hfg
=
Latent heat of vaporization (tu/lbm)
X4
=
Quality of mixture entering evaporator
E
=
Mass flow rate of refrigerant (lbm/hr)
Then, using subroutine
'XKOIST'
for psychrometric chart data,
determine the dew point temperature of the entering air.
Determine the bulk air dry bulb temperature when the surface
temperature 'Twa'
wall
drops below the dew point,
a
wa
ab
h
}
a
{T
{a
[_+
n
-
R+
a
a
hR
T
Rsat
h
a
h
tP
-l}
Where subscripts mean:
db
sat
Dry bulb
-
tp
MR
Saturation condition
Two-phase region
= moisture removal
Determine
NTU and effectiveness in two-phase region, assuming
no moisture removal.
402
NTU
AOM
tp
Cp
[
+
-NTU
1- e
tp
]
tp
Where:
dt
AOM
d
a
Local flow rate of air (lbm/hr)
a
a
Using the above effectiveness, determine exit air dry bulb temperature,
assuming no moisture removal.
T
=
T
ain
aouttp
If
T
<out TbMR
-
tP
(Ta
- T
ib
)
sat
, then moisture removal occurs, hence
do moisture
tp
removal analysis.
F
,
tp
If moisture removal did not occur:
Q-
tp
Ia c
tp
Cp a (T a
)
ti n
TRsat
where:
=
Two-phase fraction of total heat exchanger surface
and go to the superheatin. reoion aalvais
403
Moisture Removal
If T
, then moisture removal begins on the leading
< Tdb
ainab
dMR
edge of the coil hence find the effective surface temperature at the
This is an iterative process
leading edge.
-
m
£Yi_
'ES
-I uess
Find
iES
+ (in - S) (COIL)
-. IJ
If
TES *
TES
> T b
T
, find fraction of thickness of coil 'FSENS
ain
dS0
which is used only for sensible heat transfer.
-T
(Ta
aa
=
FSENS
a
a
no
I-
7J
aR hR
Ca Voa
sat
indb
.L
I(Tdb
tr
dbMR
)
R
- TR
)
'sat
a
A, Ch
a
where
t
a
= Total refrigerant side heat transfer area (ft2
=
Mass
flow rate of air (lbm/hr)
)
404
The fraction of coil thickness 'FMOIST '
used for mositure removal is
thus
FMOIST
1-FSENS.
Next, deivide the moisture removal fraction
FMOIST
into two equal
parts and analyze the moisture removal in two steps,
Iterate to find
i2
and
TES
, the bulk air enthalpy and
effective surface temperature at the end of the first moisture
removal section.
L s
-uess
and rnd Ta
l
wall
ES 2
data
(T
i 2 =iwall 22 +
aa
2
wall2
from psychrometric
-T
ES I
a
-
i2 =
(COIL) (12)
(Cp2) in
}
-
I- 4*
z2
2
t
2
Repeat the above for the second moisture removal section.
Then,
determine exit air wet bulb temperature and the fraction of the
total heat exchanger surface occupied by the two-phase region,
Q
tp
a (in
a
in
i
)
out
405
and complete the moisture removal section by finding the exit air
dry bulb temperature, and the total amount of water removal from
the air
HO
(Wa
2
in
~
a
out
(t)-a
where
w
-
Rate of moisture removal (lbm/hr)
=.
Entering moisture content of air (ibm water/lbm.
in
dry air)
w
=
Exit moisture content of air (bm
water/ibm dry air)
aout
Superheating Region
If
F
1 , then evaporation is incomplete, and there is
>
no superheating region.
In the present model, if such is the case,
calculations are terminated.
The case of incomplete condensation
could easily be handled, however, merely by iterating on exit
quality.
If
Ftp
< 1 , then the superheating fraction 'Fs'
of total
heat exchanger surface is:
F
s
= 1 - F
tp
and we can determine exit refrigerant temperature and heat transfer
in the single phase region:
406
ma
a
(Fs
S
a
a
a
) (Cp )
=(A
RCR
a
RV
Rs
Cmax
CR
and
C
= smaller of
min
C
s
as
and
larger of C
CR
S
S
I
aR
Ta
h
hR
a
£no0a
(Fs(F)
) (
R
tot
=
NTU
Rs
ht
(Rtot ) (Cmi)
Ns
Cmin
f
CXF
s
NTU)
max
)minT )
T =T+(F
R
R
QSP
s
sat
out
CR
=
s
(TR
out
(CR
TR
sat
a
in
RS
Rt
sat
)
Where
0
T
=
out
Temperature of superheated vapor leaving evap. ( F)
40.7
-
Cp.
Specific heat at constant pressure of superheated
vapor (Btu/lbm.-OR)
s
XF
=
Superheated region
-
cross-flow
sp
single phase
For more information, see.comments in the program listing for subroutine 'EVAP' at the end of this section.
Modeling a Finned Tube Evaporator
The geometry factors necessary for use of general model
EVAP'
are the same as those required in the general condenser model 'EXCH',
discussed in section 2.3 and Appendix I, and will not be repeated
here.
Having determined the geometry factors, the procedure for
determining total evaporator performance, as outlined in the flow
chart of Figure M-2, is as follows:
Split the evaporator up into equivalent sub-circuits
a
sect
N
sect
mR
Aht
t
sect
408
Where:
N.
sect
=
Number of parallel flow sub-circuits in the heat
exchanger
Then:
Using thermodynamic properties corresponding to the states of
interest, determine the heat transfer coefficients as described
in Appendix K.
Next, use general evaporator model 'EVAP' to determine performance,
for the given geometry factors, temperature, and flow rates.
Using the results from 'EVAP',
determine the length of the
two-phase and- superheating regions:
DZTP
=
(F)
'I
(Fs ) (
DZV
t
(
Di
t)
Di
=
Di
Where:
Di
= Inside diameter of tubes in the heat exchanger
And then determine the total pressure drop 'PD' as described in
Appendix L.
Convert results back to total flow notation:
ma =
(a)
()
Qtot
(Nsect)
(Nsect)
(tot)
(Hsect)
409
Finally, using the value of total pressure drop through the
coil, determine the drop in saturation temperature through the
coil corresponding to the pressure drop.
If the drop is greater
than 20 F, repeat the analysis using
(TR
T
sat
avg
~=
+R
)
~Usat
RaE
t
2
For more information, see comments in the program listing for the
finned tube evaporator simulation at the end of this section.
REFERENCES
1. McElgin, J., and Wiley, D.C., "Calculation of Coil Surface Areas
for Air Cooling and Dehumidification", Heating, Piping, & Air
Conditioning, (March, 1940) pg. 195-201.
410
FIGURE M-1
FLOW CHART FOR GENERAL EVAPORATOR MODEL 'EVAP'
Start
Input
Geometry factors, heat trans. coef., flow rates,
temps., humidity, thermodynamic prop.
Determine
Coil characteristic
Determine
Two-nhase heat trans.
assuming complete evan.
Determine
Bulk air dry bulb tempn.when
moisture removal would bee'in
Determine
NTU & effectiveness in two-phase region
assuming no moisture removal
Determine
Exit air dry bulb temp. from two-phase region,
assuminp no moisture removal
I
-
--
-
Ir
!
-
Is the exit air dry bulb temp.
less than that at which
moisture removal would bevin ?
No
_I
L
Yes
Determine
Two-phase fraction
of heat exch.
411
I
4
. Yes
I
I.
Is inlet air dry bulb temo.
less than that at which
moisture
removal would hegin ?
)
No
Iterate to find
wall temp. at which
moisture removal begins
on the leadin etle
of the heat exch.
'~
L
II
i
i
Determine
Fraction of thickness of coil uhich
is, used on1v for sensible heat transfer
(in two-phase reron)
Determine
fraction of thickness of coil used
for moisture 'removal
(in two-phase rezinn)
Divide moisture removal reion
into two eual
arts
I
Iterate to find exit air enthalpv and wall
temp. at end of first
moisture removal repion
Iterate to find exit air enthalv and wall
temp. at end of-second moisture removal repion
Iterate to find exit air wet bulb tem
io
Determine
Two-phasefraction of heat exch.
I
412
I
Iterate to find exit air drv bulb
temp. & amount of moisture removed
-
'T,'
.ss
I
. No
IS evaporation commlete
Yes
F
Superheatin
Determine
fraction of heat exch.
Determine
Heat transfer & exit vanor temp.
in superheating region
using 'TU method
Determine
Total heat transfer
End
413
FIGURE M-2
FLOW CHART FOR FINNED -TUBE EVAPORATOR MODEL
I
.B
{
De-fine
Constants
l
for thermodvnamic properties
and heat transfer coef.
.
Repettive
For changing
loop
nnut data
I
-
-
-
r
I
I
I
I
414
Convert to parallel - flow
sub-circuit notation & analyse
only one of the circuits
:
I
-
I
X
Repetitive
loo\
for varving refrigerant flow rate
I
I
. ~~~~
Determine
Saturation properties of refrigerant
I
I
I
I
Determine
Single phase vapor heat trans. coef.
Determine
Evaporation
two-phase
heat trans.
F
i
I
]
I
I
I
coef.
.
Use general model 'EVAP'
to determine heat trans. performance
(see flow chart for 'VAP' )
Determine
Pressure drop through heat exchanger
-~~~~~~
I
i! ,i
I
I
tnrougn col
Yes
L
_
_
_
_4
:
J
I
_
I
415
Convert back to
total flow notation
~~~-_
-I-I
I
L
-- -
I
- _- _ _ _j~~~
416
C
EVAPCRATCR
SIMULATICN PCGRAM
C
C
FPRcGAr FCR CCMFLTING EVAPCRATCR PERFCRMANCE, ICLLCING
C
PCISTUE
EMCVAi,
FR
AIR
IN CRCSS FLW', PLATE-FIN
TYPE
C
C
INFLT
C
CARC REACER (CESCRIBEC FULLY
hNRLN
CEA, DE, CELTAFPjXKFJ
S Tsr
CTWEi
C
C
C
ATA FC'
ELCA)
AAF CA NTj ,SECT, -C3NT,
. XM I, NXMRP , T
IJ
AI I,JTATEPs xR TSA,
TiBR I, ThCiC
CLTFLT
CTGT ~LAT -
C
C
C
TCTAi
EAT TRANSFER
ATE (PTU/HR)
LATENT EAT REMCVAL RATE (Tu/hR)
AIR rRY BLLE TEMP. (F)
LEAvING
EVAP.
AIK .ET BULE TEri- (F) LEAvING EVAP.
T-83
TE3
C
C
-
TELF.CF
TRC -
EFRIGERANT VAPOR LEAVING EVAPI(F)
C
C
C
REMRaKS
Ti-IS
C
kCUHAM CALLS
SINGLE FSE
C
T-IS PFC-kAM CALLS SLfGLTINE
EFFIrIE\CY CF FIXNEC
C
SPhTC
SUBROLTINE
TO
CETERMINE
-EAT TRANSFER CCEFFICIENTS
SLRFACE
FCGMAM
SEFF
TO
ETERMINE
SLRACE
C
T>I
C
C
C
SATLRATI;\ TERZCUYNArIC
RCPERTIEL
TiIS FOGGA
CALS
S rOTINE
EHTC TO DETEkmINE
1rE EvAPCM'ATTCN TC-PFASE
EAT TA,\SFF
COEFFICIENT
C
FCR
C
C
TliS F OunAtl CALLS SUaRC.TINL VAPCk TO DETER1iNE
REFRIGERANT
TrEkhrtCYNAtIC PROPERTIES OF SPEREEATE)
C
¥VAPC
C
C
TiIS FCGRAth
F,,iESSLE Cp
CALLS SBOLTINE
COF EFIGEAANtT
C
T--IS FACGAR
CALLS
C
DETEFrINE
FCrCEcF
C
TC
C
TI5
IVN
CALLS SUECLTT\NE SATPrP TO DETERMINE
CrN'ECTICN
ATLATICN
EvAPCRATIC
FNCTICN
iNSIDE
PCG
FLCI\G
TO CETERMINE
I THE COIL
SuEPiOCRAM
TSAT
TO
TEMPERATURES CRESPCNCIN
FtHEsSRES
FG;A
CALLS SUBROLTINE EAF
TO DETERMINE
C
C
C
ThE CVERALL
EAT EXChANGER PERFORmfNCE,
RATES, AI
TFrFERATURES*
ETC.
ALL TEF~LhEATwkE
ARE IN DEGREES F
C
ALL iEAT TA,\XSFR
C
ALL
AS5
TUBES
FLC~;
RATES AE
RTES
CCYtrCN CFPAhAS.
ARE I
FFXI-RVCt-RV,
IN
HEAT
TkANSFER
TU/H
L/i-
XPM~,XMA X4HTP·FFTPQSP,
C
C
=*'''-....."---
INPUT DATA CONSTANTS ............
C
C AIR FkCFEkTIES
C
i-NA
w
FlRAKCTI
NhcuER
OF
AIR
417
F AIR (LB/H-FT)
GAS CChSTANT FR
C
XPLA
C
RAu
*
V-ISCCSrTY
LNIvERsAL
C
PA
-
ATtCSFERIC
C
CPA
-
SPECIFTC
AIR
PRESSURE (PSIA)
(FT-LEF/LEM-R)
(BTU/LBMR)
AIR
EAT AT CCNSTFRESCF
CATA PRA*AMfUA-iA/.714' *043J53.34/
PA
14.7
s
*24
CPA
C
-
NtR
NREF
C
C
& x,,MV
SLPEV
SLFEKV & x.VM
-
C
SL..FE.L 8 XNAL'
-
SLPCPV & XINCPV
-
COEFFICIENTS
COEFFICIENTS
FCORvSCOSITY
FCR THERMAL
CCONDUCTIVITY
CF
COEFFICIENTS
CONDUCTVITY
CCEFFICILNTS
FOR TERMAL
CF LI;UID
PCk SECIFIC
AT
C
C
XMI
a
Cz2
a
VISCCSITIES Ih I Er/(HR-FT)
C
SFECIFIC
Tf-ERAL CCNCLCTTvITIES
OF LIGQ
HEAT
ETU/(Hi-FT-F)
I
-EATS Tn PTU/(LBI-R)
22
DATA cLFCFv,iNCFV/.eC433J'1394/
1 646/
7 5
2,cE-04,925
2*982E-03i
i *525-5t
DATAXlrXM2,X3,4/-56c5L5-Os
CATA CPr1CP/
XINK<L
XINtVp SLFEKV, xIN'KV, SLPEL,
CATA NREFSLPEv
/
ARE FOR
JACVF REFRIGERANT COEFFICIENTS
C****wtNCTE - T-E
C
HEAT
VISCOSITY
FCR SPECIFIC
CCEFFiCILNTS
OF LIGUID
PREoS
AT CNST,
C
n
FOR
CCOEFFICIENTS
Crtl
APCR
vAPOR
CF
CNST,RES,
CF
VAPOR
Xt4
C
C
C
OR 502)
(12,22s
(USUALLY SAME AS NF)
KNMUER CF REFRIGERANT
ER CF REFRIGERANT
m
C
C
C
C
C
COEFFICIENTS
VARIATION
C REFRIGERANT PCPERTy
NLY
E
REFRIGERANT
C
C AIR
SICE
C
CA-C6
FLC,
(SAME
ChARArTERISTICS
FOR
BOTH EVAP*&CONCO
C IF T-FEy ARE CF TEE SAME TYPE)
-
C
C
C
C
XLLA
-
LLA
-
AIR SICE HEAT TRANSFER COEFFICIENT
FOR
LCwEN REYNOLDS NbMBER LIMIT
FLCA CN AIR SILE
LPFPER REYNOLCS NLMBER LIMIT
FLC-
C
CCEFFICIENTS FCR ExPRESSING ThE
CATA CIA2EAj
LAMINAR
FOR TURBULENT
CN AIR SIDE
C3A
1/,2aE3-,.' 5r4 o,:J
C4AJC5AC6A
385,
XLLA
ULA
*C3r , E, l0g00 2-g00*0/
C.
SLDE
C REFRIGERANT
C EVAP.& CChNC IF
C
C
C1R-C6R
(SAME
FLCr, CHARACTERISTICS
E¥ ARE CF SA;E TYFE)
COEFFICIENTS FR
REFRIGERANT
bICL
FOR
BOTH
ExPRESSING THE
SINGLE
PHASE MEAT
418
TRANSFER CCEFFICIEINTS
FOR LAMINAR
LIPIT
EYNOLCS NBER
C
C
XLLR
-
LOwER
C
C
LL R
-
SIDCE (SI'GLE
C. REFRIGERANT
FL~C
KFS
LIMIT
NUrEk
FEYNCh;GS
PFER
CAT
C'
EFRIGERANT
C
FLG
C
SIDE
PASE)
LENT
Tl R
(SINGLE
PASE)
C2~' C_;J C4RA CS5RCRJXLLkJULN
824j,*C Z54
1/1*164-'7,7
49585-Jp
667=,-*837,24'0003500*/
C
C
-"w.----=ENC
INPUT CATA CCNSTANTS
C
----
,----
C
C
C
CUTER LCCF FCR fLLTIPLE RLNS WHILE VAcYING
EXC-ANGEi CrAKPrTEISbTICS
HEAT
C
c
FEAC(8 5')
CG
cZ
IN
ntN
=
j,\W4N
EXCHANGER
...w-----E.AT .--.
C
CARACTERISTICS-------
C
C
C
C
C
C
C
C
CEA
CER
CELTA FP
(FT)
CUTSiCF DIAMETER CF TES
(FT)
Tf!BES
CF
IamETER
IhNICE
FIN T TCKrESS (FT)
XKF
(BTU/hR-FT-F)
F FINS
CNULCTIvITY
THERA
FNChTAL AREA (SC FT)
EAT EyCr-ANGE
RATE (CL FT/,MI.)
Lr
AIR
AAF
CA
C
C
C
C
NSECT
CCT
C
C
ST
mT
C
C
SIGA
ATEC
-
FIN FITCH (FINS/FT)
-
'L'PE C TUeES I DIRECTICk OF AIR FLOW
LT
NLECR CF PARALLEL CTRCLITS IN HEAT EXChANGER
ESISTANCE aFTvtEEN FINS AND TUBES
CCNIACT
FT )
(TL/ H9
-
VErTICi
$PACINh.
SPACING
F TLi3E
(FT)
CF TUBE PASSES
AIR FLON
IN CIR.CF
CS
(FT)
-
CIG'A AIR (AIk FLC AREA/FRCNTAL AREA)
ARE OCCCUPIEC Y TUBE (S;
CRUSs-ECTICChAL
OF TLSE
PERIMETER
FT)
(FT)
C
FTEC
-
CuTTER
C
C
C
ALFAA
-
AREA/TCTAL
IR (AIR SICE -EAT TRASFER
ALPf.A
-I/FT)
EXCtANGER
HEAT
vCLLPE CF
TUBES (SG FT)
AL FLOW AREA I.SIDE
CrOSS-,ECTIOt
C
C
C
C
C
C
C
ARFT
F
ALFAP FAR
XLF
ARHT
CAR
C
C
REAC(Fs
-
INSICE
PERImETER CF TUES
(F.r)
EAT
SICE
EFRIGERANT (EFRIGERANT
EXCHANGLR-I/FT)
HEAT
vCLUrE CF
TRANS.*AEA/TCTAL
mHT. AREA
- FIN tEAT TRANSeAREA/TOTAL
EATIC
ALFPA
LENCTH
TCTAL
ATIC .
CF FINS
EFG.SICL
FIN
(FT)
NEAT TRANS.
AREA/NSECT
-EAT TRANSArEA/CONTACT
CCONTACT RESISTANCE
TC ACC(cLNT FR
FINS ANC TUBES
C EA.CERCELTAAFPXKFSAAFPANTNSECT
6)
REAC(8,611)
CCPT, STT
(SG
AREA
BETWEEN
FT)
419-
SIGA
EA)(1;-iELTA*FP)/ST
(ST-
ATEC
= 3=14*CEA*2/4'g
PTC
= 32 1.4*IE
+l(1 C-ELTA*FP)PT-O)//ST*T)
ALFAAZ=(.c(T*T-ATBC)*FF
34wCER*S2/4.,
ARFT
F a= 3.14WCLk
a
ALFAR
T)
.14*CER/(ST
FAR =uC*F
F
) / (2 *FP*
T-ATC
ST
(ST *TATB
)
+PTEC
I(1.6-FF-LTL)T
XLF = ST/c.C
F
ARkIF'
. 14*CER*AAF/(ST*F.LC
LA.T( t
(
CAir-eT-TmlT14*OEA**2/4'+
T(NSECT))
t/(3914*CEA*CELTA)
WRITE(5p51V)
CEACELER CELT AP FP
~RITE(5 J -L
CCNT,STJ rT
RIXTE (5 - 1)
AIF) GA ARHTJ NTJNSECT
XKF, A
C
C
CF ,kEATEXC'PANGER CtARACTERISTICS
w--w--ENC
"
'°
= ' ' '
C
FCR AIR
FLOW CCNhITIONS
REfRIGERANT
C
INITIAL
ALUES
C
C
ral
C
CTA
AIR CRY
AIR CRy
C
C
NTEVF -
hLtEER
TSA
C
CXMRI -
C
C
C
(F)
EFFIGFiRANT SATURATI-N TrP.
FLG' RAATEINCRE-ENT (LBV/HR)
;ERIGFRAT
FLCv RATE (LEM/HR)
TCTAL REFIGERANT
INITIAl
NXR
a
xrk I
ANC
ENTERING EVAPORATCR (F)
ULB TErF.
*P. INCREMrENT (F)
L T
CF AIR
vRYELUL
NLMBER CF REFRIGERANT FCv
a
LxA1INED
TEM'P,
SATES EXAMINEC
ENT-ALPY CF EFRIGERANT ENTERING EVAP.(BTU/LkM)
VAP. (F)
LLB TEMP, ENTEtING
ET
AIR
INCREMENT (F)
ET EUL TF.
AIR
EXAMINEC
NUMEER CF wET ULe TFrERATuMES
-UlFICITYCF AIR ENTERING EVAPORATOR
RELATIvE
C
C
C
C
FI
C
C
INCIC IF
IhNCIC'
C
iF
'INCIC'
iNFLT TNCICATCK
TCeB
ECLALS
1s
INPUTS
ARE
ELALS
2
INPuTS
ARE TCB,
,ND
ND
TwB
h
C
REAC(8P,61e) TAITCTANTEMPTSA
CXMRI,XMRINXMRJRi-4
iNDIC
REAt()62Z ) TET IyCTWEIJNTW6BjR~I1
C
C
C
LCCP FCR
VARYING AIR i&ET BULB TEP.
ETERING
EVAF.
ENTERING
EVAP.
= TeII
TreI
CC t
I
. 1-*
TWE
%RITE.,54,) Ihp
Tkea - T*EI
+ CEI
C
C
LCCP FCR VARYING AIR CRY BULB TEIP.
C
TA!
a
TAIl
420
CC
4e
IJNTEM
~RITE(554e)
TA I
TAI
kRYrE[(
eJ
p
I
+CTA
6)
TAtOCA
C
C
FR
FKCVISIC\
R-TIME
INTERACTIVE
CATA INPUT
~EAC(6&b5,ECHC.e)
,e7C)
hkITE(
4VA= GcAW6:L
TA T GA
/(c TGA*AAF)
VA*F;A*144*c/(FAU*(TAI + 46('0))
GA
AC
FLCT, t
,/(
ST*GA*SIGA
C
C
C
SLEUIVILt
LIKE A
C
FLCA
FLC
TN
TC PARALLEL
CIRCUITS
AND TREAT EACH
E;ARATE
EAT ExLHANGER - CCNvERT BACK TO TOTAL
AT
t-EE
EN
XtrA=6ggmPA*,A*144*C/(RAbFLCAT(NSSECT)*(TA.I+46ee))
C
C
CETERINE
AIR STCL
EAT TANS,COEF,'.A'(BTU/HR-SG
FTF)
C
CALL SFPTC(IEA;,ACA,
lXA,
CPAA FRA,
EA
C2AC3A,C4ACSA, C6AXLLAULAp
-A
C
C
CETER"INE CVErAPIL SURFACE EFFICIENTCY
SEFFXI
C
CALL SEFFXKFCCF~TAAXLF
FAR CAR~CCNT
SEFFX)
1
ICNT
=
LCCF
FCR
C
C
VARYIN
REFRIGERANT
FLOW RATE
C
XVR a
XRI/FLCAT(NSECT)
CxrR = CXRI/FLrATINsECT)
CC
2e
Kil,pNX
sfITE(
XR
L40 ) K
Xtn + LUX
UlETERMINE SATLNATICN FROPERTIES
C
F REFRIGERANT
C
20
CALL
RS-Cv
RHCL
SATFRP(NTSAjFSATVF,VG,HSATL,HFGHSATVSF,SG)
= lo/VG
/F
CFRL = CF1*PSAT
+ CP2
X-LL = X!'1*TSA**
3
XKIkL = SFUKL*TcA
+
M2*TSA**2 + XM3*TSA + X#
+ XINKL
XKGV = SLFEKv*TCA
XINKV
X'fLRV
;LP
'ST~A
+ XINrV
F
. = XLFLCFR
/XKKL
CPR
= SFCFYvFqAT
+ XNCFV
421
PRRV * XtLVsCFRV/XKRV
XR/ARFT
GR
C
C
C
PHASE VAFCR N-EAT TRANSFER CCEF
FT-F)
DETERMINE SINCLF
tRRVI (ETL/HR'S
C
ClRsC2R
CALL SPTC (CER,,R,
iXrU FVCFi v , PRV, .RV, -RV)
C6Rs XLLR, ULR
SATI )/I-FG
-
(4
X4
C3R, C4RC5R,
X4
WRITE(j,7:e)
IF(x4.LTe..)
C
C
C
CETERt:INE
(BTtU/HR-S
C
CALL E-TC (UER
CX4,
0PRRL,
COEF.tHTP'
EAT TRANS.
LVAFCRATION TvC-PHASE
FT-Ft
XKRL, XFURV, XMUL, RHOL
IRICVJTF}
HEAT
EVAPCRATOR
TO DETERMINE
FVAP
SERCLTINE
C
;SE
C
ETuPN ALL RESULTS
TRANSF'.R FEkFCRr'ANCE AND
A HFG )
AIJ
CALl. EVAF ( AOrs ALFA, ALFAA, TS,
TROUGH
C
TC TOTAL
FLCW RATE
C
RETURN
C
PRINT CEHALL RULTS
REPRESENTATION
AND
C
( NSEC
GTCTSFLCT
(NcEC)
XMAXMA*FLCAT
XR=XX
) * (GSF+TP
)
FLCAT(NSCFCTt1*XrHe*lj57*e
¢LAT
R
}
*FLC A T N cECT
WRI7E(.,1Z ) GTT,xtRX)WA,CLAT
I'rE. (,.65
)K SFFFX,NTP,STCPA,GA
kRITE(,,?)
kRI'rE(,.,,w )
tNVV HTP
R0,T,4,X4
FTFAR-T/F
CZTP
CZV
cIrnA,ALFARALFAA
6e5 ) HA . -V,
WRITE (.,
F-T/F
e*
CZL
E " 5.eE-'
6
C
C
C
USE SUeHCLJTINE PCROP TO DETERMINE
kREFRIGERANT
TRnLGH
EvAPORATOR
'PD
PRESSURE
DRCP OF
(PSI)
C
CALL PCRCF ( 3, DEn
1RERLCZTF, .CX4
WRITE (,I
E, GR, XMuRV XMULJ RHOV RHOL, RERV,
VG,DZV,CZL,P )
53 5 )
ARITE(,53 3 ) X APC TOT
5e) G, EAHA,SEFFX
ITE (,
WKITE(,Et6)
XVA-
GR.RERVWHRV
X,/FLCAT LSECT)
X`RwXMR/FLCAT
IF(ICNThN[.1)
(NhECT)
Cc TC 155
CCVMON
'422
C
CHECK CRCF IN SATURATION TEtPERATRFE CUE T PRESSLRE
C;CF IN CCIL
TF TE CRCF IN SATURATION TE-PERATLRE
C
C
IS GREATE
TfA_ 2 CEGREES F - RPEAT
USI\G AN AVERAGC VLUE
F SATuRATION
4-
C
ALL CALCILATICNS,
TEMPERATLRE
C
PCLT = PEAT
Fr
TSATC z= TST(NR,FCT)
,R I TE (s 8E
FC iT, TSATO
If(ABS(TSA -TSATC).LE.2e)
tSA
= (SA
+
TSATC)/20
TSA
29.,*TSA
- TSATO
IChT
1
ICNT
2
GC TC
155
C
2EG
CCNTINLE
4?(
CCNThINLE
41Z
CCNTINLE
5ae
CCNT!N
t
5b
FCRt'AT('',8F12.6,2I4)
5bl FCArT( '
510
5_
~5
GO TO 20
iCNT"', Fl3,p'
'
FCRrArT('',
CEA
CER (FT)
1,,
(FINS/FT)XK-(ETU/hRFT)
2,'
ARI-T (SGFT)
5.4)
FCRrfiT 't3F
FCri'ATT( 'Z','
xfa
54
bSg
FCR'AT( i4
FFRr T(I1 )
6i:0
FCRfAT(7F2E.*6,2Tl)
6h
FCF'AT(EF14.,
611
FC;YAT(3i
5
ST=t',F1.*5,'
(FT)
NT
CELTA
WT='F1e.5)
(FT)
FP
AF (SGFT) QA(CUFT/MI
I) '
NSECT,)
(LBM/HR)
PC
I1 C,e3Fle.4, I
(PSIA)
GE (E TU/HR) )
F1!i4)
)
6a0 FCRr'AT%2K2Fi.EI1~pF10'5Alie)
6f FCRM T(' 'A iX ,K=~, I2S5XY 'SEFFX=',F4*2tX, s
'NT= t t
15X,fPt='F-.3jX, S=',F6,3/5X, CP=',F5.3,5X, ~A .
66e
FCRtrAT( ''lCXSIGA=',F8,35xp
1 ALFAA-=
66
FCRrPATt
,FS.
I2,
,ALFAP='sF8*.35X
)
,:FX.9FA=flF0I~4fXX
'TSPm',JFl~e4,5XJ
p
IXtF~F1E9='a(~fl4,'R)s,1.
67Gb
675
7£~
61Z
FC rAT(
TI
=',F7.2'l
A
',F1e*2)
NArELIST f iNPJT VIABLES
ARE ?', ( TAI,(A,J)
FCh',AT('
=*rw *X4 IS NEGATIVE - X',F1C.5***S****I)
FCrAT(
(;TT= ',F 15 4J I
A R='JFl~',
*
xrIA='
L ,A
8E3
FClAT(,
F 15,
4) I
PCILT' ,FlCg5,
e5P'5
_F C
IZ
rcT
''rA 'F1*.2'
X,*H.Ainl,Fj1.2,
-
X4 'F1i0.5)
TSTO=', F *2)
(LEM/hR-S;-FT) I5XtREA='
(ETU/j.4R"SC
FT R)'J
XpIlSLFFX
=
423
86e
FCtAT(' '
lsF'
E N U:
e,
lX,
fi3'
t R
FF
3
t(Le/R-SFT
*:2J5~X;)
'hFRV* F7.*T1 (BTU/HR-SGFT-R)')
) , 5X, RE
424
SLepCUTINE
EVAPF ACrALFARALFAApTSAT
C
PLPPCSE
C
TC
ETERMIhE
C
ANC
RESlLTINh
-EAT TANSFER,
IN ThE EVAPFCATCF,
C
CCEFFICIENTS
C
ANC
ALFAr
*-
ETAILS
ALP~A
E2RIGERANT (EFmIGERANT
ALFAA -
Ai rr
AI
TTr.
vC.U'E
kt;G
iAIR
Ai-T
-
T:T'-
C
AC
-
Lx,\T KrEIUEkAT
C
AnEA/UNIT
C
(sC
FEAT TANSFEi
-A
hTP
-
-
C
C
C
SILF
AIR
FT-r/Lt'
-
E.CHANGEk
EAT
EAT T-ANS,
SIE
Z;Y
EAT
AEA/
1/FT)
AcEA (Sr
FT)
-EAT TRANSFER
RATE
FLCA
AiR)
CCEF;ICIEKTS
ATR SIc
RF
SE
hELAT TASCCCEF.(bTU/H-S(
TAC-P-ASE
EAT TRANS.
CrEF, (TU/R-S;
RfV
SICE
VOLUME OF
IDE HEAT TASFER
F
C
C
i:- NECESSARY
GIvEN ALL CF
OTrER
ECOvAL,
UMIDITIES
i-RAT TRANSFE
AREA/TOTAL
ExCANG3E
- 1/FT)
C
C
C
CIST0uE
A
CESCkIPTCN
CF FAHAMETEkS
INfPTS
P-EAT ExCrAGCFk
GtOM-ETRY
C
C
C
T'-ES
TEMPEt
C
C
C
C
IpJ.FG)
FT-F)
T-F )
kF'*
SIZ£ SINGLE PeASE
T ANSCCEF
(L/r'wST
vAPOR HEAT
F TF)
C
C
C
C
C
RERIGCERANT pkCFERTIES
TEA
RF NIGERAiT SAT,,RATIOhN TEP.
(F)
HFG
LATENT ENTHALFY CF VAPFOIZATION CF
THE EFRIERhANT (TU/LE')
C
X4
-
ETERIiNG
C
Xf
-
C
C
CFRV
-
MASS FLCW RATE CF EFRI(ERANT
(Lem/kR)
SECIFIC
EAT AT CNSTANT
PESS-RE
C
C
CF
TE
REFRIGFRANT
VAPOC (TU/L6M-R)
HEAT AT CCNSTANT
PRESSiRE
CF
IR f(TL/LbM-R)
LCW RATE CF AIR
(LBM/HR)
C
XMA
C
C
C
C
C
C
TAI
CY
ULB TErFCF
AIR ETEktNING EiVAP (F)
TAEI
;T EUi.E TEMPFCF AIR ENTERING EAP,
(F)
kRI
RFLATIVE HUMICITY CF AIR ENTERIrG
VAP,
INCIC I1xFT IICATCR
IF 'INuIC
ELALS
1 INPuTS ARE TAI, AND Ti'BI
IF
INCIC'
ELALS
2i INPUTS ARE TAI! AND RHi
C
PA
C
CTHER
C
C
-
-
ATCSPHPERIC PESSURE
(PSIA)
NPFLTS
SEFFX CLTFTS
PASS
CF TE
EFRIGRANT
TE
AIR PRCPERTIFS
CFA
SFECIFIC
C
UALTy
SI RFACE EFFICIENCY
CF FINNED SURFACE
425
C
C
C
F
-
FTP
-
C
STNGLE PASE
VAPCR FRACTION
HFAT EXCHANGER SURFACE
TWC-PHASE FACTICh
OF TCTAL
ExChANgER ScRFACE
C
GSP
C
C
GTP
-
kFAT TRANSFER
-
VAPOR REGIG
(TU/HR)
HFAT TRANSFER RATE IN
C
AFGICN
OF TCTAL
HEAT
ATE IN SINGLE
PHASE
TwO-PHASE
(ETU/o-R)
C
C
TRO
XrMH2
C
TACSF -
C
ExIT- AIR TVFPFRCM SINGLE PASE
TACTF -
ExIT
C
C
TiBN
-
-
C
TCB_
-
C
C
AIR CRY
JLE
TErP.
ExrT
OCCLRS
REGICN (F)
MOISTURE
F)
.RHY ULB TEMP.LEAVING
AIR
AsSLUING
(F)
(LEM/HR)
ASSUMING
Nr MCISTURE
REMOVAL GCCRPS (F)
wFT eUL2 TEFP
LEAVING
EVAP.
IF
RFC'OVAL
C
C
TrP.OF
REFRIGERANT
LEAVING EVAP,
RAtE CF MOISTURE REMOVAL FROM AIR
MOISTURE
EVAP.,
REMOVAL OCCURS
(F)
REMARKS
THIS FROGRAr CALLS SUBRCUTINE XMCIST TO DETERMINE
FMICITY
C
THE
C
C
CF TE
EVAFCRATCR
T~IS PRCGPAM CALLS
C
C
C
T~E EFFECTIVFNrESS IN CRCSS FLCW
(THIS FROGHRA USES THE EFFECTIVENESS-NTU
METHOC
CF CALCULATING EAT TRANSFER FERFORMANCE IF NC
C CISTLiE REMOVAL CCCURi ANDCIN THE SINGLE PHASE
C
VAPCR
CCPFrC
ANO DEHLMIOIFICATICN
SCUTTNE
EXF
EHAVIOR
TO DETERMINE
EGICN.
CF
HA
s
FFX
HRV
CPRV
1CTFTACSFT~CTAF,
TC#ARHTXr~2
XMfR XMA
X4
HTP
FFTP,
QSP
TSW6BI~RIINDICPAsa
c
C
CETERINE
TE
FFRESENTATIVE COIL CHARACTERISTIC
'COIL'
C
CCIL=HA*(ALFAA/(HTPWALFAR)+1
./SEFFX*HA)-1.~/HA)/CPA
CTP
XRfi*(l
X4)*-FQ
C
C
C
CETER:INE
BULK
CEHIIIFICATICK
AIR
RY BULB TMrP.TADHI
CR MOISTLRE REMOVAL
CALL XCIST(TAI.TEIRHI,
wHEN
EGINS
INCIcjPApHAIRIWSATIWAIRIp
1TWALLI)
WRiITE(w,*715)TAI.ThBeIRHIINCICMAIRIiSATIWAIRIRTWALLI
'TACHIa(HA*TWALLTu(I,/{SEFFX=HA)+ALFAA/(HTP*ALFAR))
ITSAI)/(Atr*,/iSEFFX*HA)+ALFAA/(HTP*ALFFAR))-1.C)
C
C
CETER.INE
TRANSFEk
C
REMCVAL
NTL AND EFFECTIVENESS
FCR SENSIBLE
HEAT
IN T E TGC-PHASE REGICN,
ASSU.MING NO MOISTURE
CCCURS
XNTLTP-ACr/(CFPA(ALFAk/(SEFFX*HA*ALFAA)+1.O/HTP))
426
ETP-2,*-EP( -XNTTP)
xMATP=GTP/(ETPrFA(TAI-TSA))
FTPXMATF/XMA
,.RITE(,71e; FTP
IF(FTP.GTs.j.
C
CETERiNE TE EXIT AIR TEFMP'TAOTP' FROM TE
EcGICN, ASSbFING hC MCISTURE REMCVAL CCCURS
C
C
TO-PHASE
C
TACTP=TAI-TP /( xIATPwCPA)
WRITE(~,7g)
TArPI,TACTP
C
C
C-ECK TC SE
C
IF
C
TOAN TACTFI
IF
CISTLRE REMOVAL ACTUALLY CCCLRS
REMrVAL DOES NCT
rMISTLUE
THEN SKIP
TE
CCUR
CISTURE
I*E.
TAlHI
REMOVAL
IS LESS
SECTION
C
IF(TAD-I.LT.*TACTP) TD63-TAOTP
GC TO 140
IF(TACHI.LT.TACTP)
C
w---------w
C w
-1-iC ISTURE
SECTICNi.----ii-------.
REMOVAL
C
NCTE: IT IS ASSIirED TAT rCISTURE RECVAL
REGICN OF THE CCIL
IN TE TC-Pf-AE
C
C
ONLY OCCURS
C
IS GREATER TAN
TE
C
IF TACI
C
C
TE1FFERATLKE TAT', THEN CISTuRE HEMCVAL EGINS AT TE
LEACING ECGE CF THE CCIL - ENCE SIP TO STEP 36
INITIAL
RY BULB
C
GC TC
IF(TACHI.GT.TAI;
36
C
C
CETERMINE TE
C
THE COIL SUNFACF
FRACTION 'FSENS, OF TE
C
HEAT TRAhSFER
~wICH IS
LEADING EDGE OF
SED ONLY FCR SENSIBLE
C
FSENS=XJA*CPA*(Ioe/(SEFFX*-A)+ALFAA/(-TP*ALFAR))*
1ALCG((TAI-TSA)/(T-AHI-TSA))/(RhrT*ALFAA/ALFAR)
IF((FSES.GT.l.).CCR.4FSENhSLT.*Zo))~IlE(JJ720)
FSENS
CO
TC
37
C
ITERATE
C
ICISTLRE
TC FINhC THE CCRRECT
EMCVA
WALL TEMP.'TwALLI '
BEGINS ON LEADING EDGE
F COIL
C
26
T
CT
=
TSA
l e
CC 3
L
1,i
T - T + Ct
CALL Xr'CIST(TT.RHpIFAHWALLIWWALLIWAIRTWALLI)
TS
TEA
+ (-ATRI
WRITE(~,716)
-
WALLI)*CCIL
TALLIPWWALLIPWAIRTWALLIpTS
IF(ABS(T-TS),LE..1)
GC T
35
T WHICH
427
3ep32,55
IF(T-TS)
25
T *: T-CT
CT at CT/r.e
30
CONTINLhE
35
WR TE(
TrALLI
5
T
FSEKS t0
TAI
TAC-I
37
7 17
CPA*(TAI-TADHI)
-AIRf
= HAIRI -
SPLIT
MOISTURE RErCVAL
i . -FsENS
FrCIST
ORITE(,.,,7i6) CTpPXrAsXMRFSENsFFCISTHAIRlFTP
C
C
REGION INTO 2 PARTS
C
C
ITERATE
C
EXIT
TC CETERrINE
t
C
WALL. TEfF.'TAL
C
RErCVAL REGICh
2'
AIR ENTHALPY
END OF
AT TE
HAIk2',
THE FIRST
AND
CISTUkE
C
R I TE (,j 73e)
T
CT
TSA
1.e
1s 3
CC 5b
L
T a
+ CT
T
CALL XrCIST ( TT ,R-
HAIR2 I"hALL:2
i-AIR2S=
(
735)
T
IT,
RH
iWALL2
45
Ed
WWALL2
A IR2
TWALLE2
5ebe6ej45
T = T - CT
CT ; CT/Eoi
CCNTINLE
WRITE (,j
60
(TwALLI
LITSA)/(TALLTSA)
GO TO 60
IF(AES(HAIR--"ATRi2S)L.E.e5)
IF(-Al2-HAIh2S)
)C
WWALL2,WAIR2,TvALL2)
AI1HFtCIST/2.*ARHT*ALAA/A/ALFAR*A*
i-ThALL)/(COILrAALCG(TAL
ARIXTE(,
(
1PAl,-ALLPl
(T-TSA )/CCIL
TwIL2
746)
T
TC CETEprINE
C
ITERATE
C
hALL TErF.'TAL-.3
C
REr;VAL
EXIT
IR ENTHiALPY
AT THE END OF TE
HAIR3,
AhND
SECOtC MOISTLRE
KEGIGO
C
T
CT
TSA
in
e
1,3f
CC 90 L
T a T + CT
,ALL3WWhALL3WAIR3T~ALL3)
CALL XrCIST(T, TRH,1PA
TSA )/COIL
HAIR3 HALL3 + (T
428
"AIRB2wFIST//2. ?*AT*ALFA
S
-AI
ALFAAALR*HA*(TALL2
.ALL3-TSA)}
1-TWALL_3)/(CUILxM~'A*ALCG( (TtALL2-TSA)/(T
2*CP )
(
W I
HhKALL3, WWALL3pAIR3T ALL3
T rTj
7 35)
1HA I k3, -A IR35
IF(AES(RI3-I-ATR3S),LE,,Z5) GO TO 10
j
IF ( a IR3 IRs ) 9WlE Z
8
T =8 T
Se
CT = DT/2,
CCKNINLE
t
IkV
RI T
CT
w
7 C' )
.,
TiALL3
T
C
C
ITERATE TC
C
THE EVAPCnATCR
ETERMINE THE
ET BULB
TEMP.'TWB3'
LEAV ING
C
T
TSA
CT
1V5
CC
T
T
L
+
1,30
CT
AIRTWALL )
,1 PA 4A IR3S ,SAT3,.
CALL XC IST(T, T,
763) TrTp. -AIR3,HAIR3SWSAT3,
WRITE(,
AIR
GC TO 1C6
IF (kAIR3E-HAIF3,
Ie4
1Q5
T
le15,b 1e4
T
T
CT a*;T/E
CCNhTINE
90
WRITE(,7T4)
ie6
C
C
C
C
T
TiO3
DETERMINE THE FRACTION
WHICH
IS
IN
TC.PFASE
'FTP'
FLCG
CF THE
EAT
EXCHANGER
FTP=CTP/(XMA*(HAII-HAIR3))
e) TAr.3,FTP
77
WRITE(,
IF((1.e-FTP).LT..*y)
GO TC 19e
C
ITERATE TC DETERMiNE TE
C
C
THE AIR
C
LEAvING TE
'xMfHC'
A'CGNT CF WATER REMOVED FROM
AND THE FINAL CRY BULB TEMP
'TTCB3'
EVAPCRATCR
C
Twe3
= *5e
L
iEC
T
CT
CC
T
=
T
+
a 1
e
CT
CALL X'CGIST ( T, T3,,RH3,
Xr¼-2 = (AIRI.h
AIR3)*FTP*XMA
"AIR3S=.E4*(T"-3p.*)
ANITE (
WAIR3 TWALL)
1,PAHAIRWSAT
*AIR3*( 160#
775 ) T. CTJ Tw3RH3 I-AIRHAIR3S,
+
4.4*'T)
HAIR3, WAI3
XMi20, WSAT,T
429
IF(AeS(-AIR35--AIR3').LE.-5) GC TOG 13
11t 13C, 12¢
IF (I.IR-3S-AIR3
11
T
CT
T -
*
CT == CiT/f-
12e
CCTrINELE
7bZ )
iRITE(,
120
T
TCE3
C
"-------
C ---
CF
ENC
CISTURE
REMCVAL
SECTION
-'-
'''''
C
FRACTTCN
CF
EAT EXC-ANGER
'F' USED FOR
C
CETERVINE
C
SIN(LE PFASE VApCR (SLFERfEATING) REGION
C
14
FTF
1.g
F
TCp ,F
WRTE(,,J7S)
C
C
IF 'F' I
C
PENCEp
AN
PINT
C
CCCLNS
EVAPORATION
MESSAGE
EROR
19(I,145* 1
IF(F)
145
lse
LESS T-AN ZE'RO, ICGOPLETE
1
F
XrASF
F*X!A
C
LSE TE
EFFLCTIvENFSS-NTU
C
TRANSFER iN TE
C
REGICN
C
SINGLE PASE
ETFCD TO DETERMINE
EAT
vAPOR (SLPERHEATING)
C
XrASF*CPA
CA
CR
I X*CFRV
HT)
(ALFAP/(cEFFX*.A*ALFAA)+I1.e/RV)/(F'AR
FR )
RTCT
TCT/CAJ, CRCIIN,CX
CALLi EXF(
C
ANC FINT
CALCLLATE
CF
ANC TLPEHAT%,REC
C
C
C
RATES
EAT TRANSFER
T-E
INTEREST
,
~RITE
= TSA +EXFRCMTN=(TAI-TSA
)
C*(TkC-TSA
GSF
TRC
hWITE (,6 2)
kRITE(tv,65)
FTF ,XMASP
,T
T
CA,CR,EXFR
)/CR
QSP
TACSP a TAI-;-P/CA
WkITE(w,e4)
(
WT(
75
ct, .c.
CSp,, CGTP
)
TAy,TWITDB3,T8e3,TSA
,TRO,TAOTP
RET U N
150
,,
i, TE(
40 ) FTp
RET. 11FN
635
FCRiMAT('
Fl iZ s 4
,LAX'KFTPatF42t,5X
,FR=tF4.2,5X,
XMASP=
1
635 FCR"AT(' ',5X, r a ,F1Ce45X;CR s'F1J4,X 'EXFR'
430
TRC= ',Fle
lF4*2)EXJ
.
,5X, 'GSPn.'sFl.4)
F0
I *4bX' JCTP',F*4)
640 FCRAT( t'I,XXpGSP=s
TAOTP=',F1C.2)
TA rTs',lF1.2, '
w***FTp S LARGER TAN 1 FTP=',F1.z5,'t***')
705
FCRAT (
71C
715
FCMAT(,
FC.RMAT(3F1C.4,
717
FCerAT(f
716
FCfrAT(I
730
FCRIAT(
760
76e
763
764
77
775
78
C
**s.*.**
T
FCRtAT(
oAI2
HIWALL2
Rh
TWALL2
HAIR2
HAIR2S5)
)
9F
.********FIkSTMCISTURL REMOVAL REGION ITEPR
FCRMAT(I
CCES NcT CONVEkGE**-w****** ** ')
1),'ATICN
T
FCRFAT('
IJ
WATP3
'WALL_
CT
RH
TWALL3
-AIR3
HWALL3
HAIR3S')
MCISTURE REMCvAL REGION ITERA'
FCRMAT(' *******SFCCND
' * * ')
*
CCES NCT CCNV.ERGE**
IPA'TICh
FCGRAT(6Fl5D)
FCrTAT(I t**.**,***ITERATION
1,, CCVERGE *=,****"w)
FCRrAT('
FCRAT ( 4F,
c
FCRrAT(
TBu ',F72s'
s 71
ON Tb63 DOCESNOT
' 5)
m ', F I V
FTP
s,)
***w*,=*.*EXIT
FCRrAT(I
CRY BULB
TwBI
Tai
FCRrAT('
TACTp')
ljso~T~kC
FCkMAT(7Fe*2)
8tIIit
FGRrAT(f **-**INCUPLETE
ENC
TEMP DOES NOT
F='iF10*5)
TCP3=',F82,J
755
84e
EMOVAL'
IN ERROCR FSENS='sFleeb*'****')
DT
RC*1$**'
1p,'CChNVEcE
75'
EAT
SENSIBLE
IS
****FsEhS
Is,')dALLC
74Z
,4F12*5)
ITEkATIUN CCES NCT CONVERGE******w*'*)
lst
720
7 5
Ii
FCtAT(7F15.,)
TC83
TWB3
TSAT
EVAPORATIONFTP-',Fl1e.5'**)
431.
SLUERCuTINEXrCIsT(TCBTWElR, INICPATMpHAIRp,SATi
IhA.[,:t Th A L L)
C
C
F L RPCSE
SATURATION MCISTURE
ENTHALPY,
TE
TC CETERINE
C
CISTURE CCNTENT OF
CIST AIR,
C
CCNTENT
C
C
C
C
AxC AL-C, Tr NECESSARY WAiL TEMPERATURE TC INCUCE
TEMPERATURE A;C
bLa
GIVEN C
rCISTULE RErnALs
CR RELATIVE kU'*IDITY
,oET E2,L- TEI'PL-TLRF
EITtEi
EPPODUCES
PF(CGRAM'ESSE;TIALY
T
(NCTE
C
PSYCr-CrETRIr
C
INLT
TCE
C
-
CAAT
iRY
LLe TE;'PERAT'PE I(F)
~,ET
TAE
C
INLIC-
C
IF
TPERAT,"E
LL-
(F)
H'.ICiTY
INCICATZC
ELAT IvE
-
C
CiATA)
CF PA
rArETERS
CESCRIFTICN
C
C
ACTUAL
A
INPLT
i
'IiCIC
INPLTS
TCeH
ARE
C
IF 'INCIC' - 2s INPUTS ARE TE,
C
PAT/' w
C
C
C
CITFUTS
HtAIR
ovSA T
C
C
C
C
*AIR
C
TWALL"
BTU/LBM CRY AIR)
AIR
CRY AIR)
ATER/LBM
(LL.
ENTOALPY CF MCIST
HUICITy
SATLPA;TION
ULE TE 'p .
ET
TC TE EXISTING
CCR.FSPCNING
uM ICITY (L-r' ATER/L.CM ORY Al')
ACTUAL
ULE TELP.,
IVE\ DY
T TE
fCCRRSPFCNING
TP.
B-L
ET
Gr
PRES., AN~ REL.oL-MIjITY
CCkRF-PCNING
T
C
fCINT
CEDEW
C
SATLFATIC
C
TC T-E
TECPERATiRE
L(.VE\ TBPATM,
(F)
AND
rr
E
I
I
1
IFtIICIChNE,1)
r
T
C TO 30
Te
C
CETERFINING
C
CF
0
TwB
ANS RH
(PSIA)
ATrC;tP-ERIC PESSv;RE
C
K
ANC
PARTIAL. PRESSURE
SATri;ATIGN
AT TE
WATER VAPCR
GIVEN
IF(ToLE*1e,)
FS=os',77*T
IF(TGT,ee)
FS.= 1l24*
IFt(TGTliCI)
TFrPERATu.E
,185
* .185
+
Fcn.'0196*T + Vk113
IF(TGT.,2w:,) FPc=3317"T
.129
-
iF(T.GT4.:o9)
FPc= 4k50"4T - ,1394
'F(fTGT,Z/)
F~r = ,;g7015TT
IF(TeGTebZo)
P.s a
IF(TGT,/,0)
:F(T(jTetzz)
i
*')
TGT.S
k6lb8ST
-
E1284
' *3b45
a * c143=T - *b4 35
* Z1313*T ' "i-E35
i ,bb56b
PS a .9051*T
P
P
'PS'
(PSIA)
432
h
1 .*18.~4*E1*PS/(28.c67*(PATMT-PS))
=
IF(K.tE.e ) GC
IF(ICICI.C.E)
;F(I.E
I
Tr E
rC
O 40
GCCT
.)
20
2
6SAT
=
hAI
=
-s.Mi?236*(TOB
;T
T)
2E4*(T"E.32.2) + WSAT*(le609 +
F=FATr/( 19VO4*lRYl/(289967*6AIR}+1,0
-AI
=
T
444*Te)
TCE
CC
TC
1V
C
FIDINrG T E CCRRESPCNCING RELATIVE HUMIDITYP
C
GIVEN
C
20
R
CC
30
T
=
CC
40
F
T-E nET E LE TEMPERATURE
= P/FpS
TC
i
Tce
TC
1I
n r.
=
^AI
C
*v*(FPFt1-PS)/(PATM-P)
a
FIhCItG
C
GIVEN
CT
CC
;5
T E
1C
- ,-*
S(E;Aik).LE
h0 = ~
IF(VS-h
T
CT
70
IR )
236*(TCDbT)
oC~5)
..
GO TC 8
:2 qZ 7 7 C
T-CT
= CT/c*.
CCNTILE
RTE
80
UMICITY
T+CT
TC
IF(
60
ELLATTVE
-1 Z
7
K,3o
T
CC
TAP
(5
=
i~£)
T
vSAIT
wS
FAIR
=,4*(TvB-32,)
INI;.
I G
C
CETEf
C
CCfiEsPFChNING
C
TEthAT
Se
ET 8ULB TEMPERATURE,
Tl-E CCRpESPCNCING
C
IF(
T hE
:,
+ WSAT*I1C60,9 +
SATURATION
CR CEh POINT
LE.* 1,5 ) T
=LL(P-.1~
8)/,
777
(P-.01Z)/.5/
TA .=(P *.* 13)/.*
1A24
j 9b
)TAL=(P+*i129)/*Z0317
C)
,
TAL=pf(Pfs*1394/*05641
17c
IF(PCGT,. *51
iF(PGT,,Se3i
TEMP.
tTwALL'
Tr TE GIVEN PRFSSURE, CRY BULL
PNr RELATIVE HmICITY C WET ULB TEMP.
ThAAL
IF(r .T
444*TkB
- )I
TALL=(P*345
/o'6E
TkALi
T
s (Pr.6b45)/?1438
433
ee
IF(P.GT
bebc)
FC-HrAT('
RET RN
,*$**
ThALL
(P+135)/
TAALL = (P+l16ee)/
TTERATICN
iN
XMCIT
e01913
CErS
SNT CCNVENGE')
434
APPENDIX N
CAPACITY CONTROLLED 50 DQ 016 STUDIES
Condenser
Evaporator
Entering Air
6330 CFM ,
10000 CFM ,
70°F
Entering Air 85% R.H.
PIF = 9425 Btu/hr
POF = 5300 Btu/hr
Q HP (1000's of Btu/hr)
OUTDOOR
AIR TEMP
0
CONV
53 BP
0
37 BP
0
10 BP
COP
CONV
(OF db)
218
57.5
52.5
205
7.5
2.5
-2.5
530 BP
370 BP
10°BP
3.95
3.73
4.50
4.25
4.05
3.85
3.67
3.48
4.93
4.68
4.43
4.25
4.05
3.87
3.67
3.52
3.35
3.22
3.10
-
62.5
47.5
42.5
37.5
32.5
27.5
22.5
17.5
12.5
No Fans
195
196
192
180
168
155
144
132
119
108
95.6
83.1
71.1
144
145
146
148
152
153
72
74
75
77
78
81
82
84
85
86
88
0
3.62
3.60
3.56
3.53
3.49
3.45
3.41
3.36
3.30
3.20
3.10
2.90
2.65
1.0
+
COP OUTDOOR FANS
OUTDOOR
COP BOTH FANS
AIR TEMP
(°F)
62.5
57.5
52.5
47.5
42.5
37.5
32.5
27.5
22.5
17.5
12.5
7.5
2.5
-2.5
CONV
3.28
3.25
3.20
3.18
3.14
3.08
3.03
2.95
2.88
2.78
2.63
2.43
2.16
1.0
+·
* QP
53°BP
3.56
3.37
370 BP
3.85
3.68
3.54
3.38
3.25
3.11
10°BP
3.67
3.55
3.42
3.30
3.20
3.08
2.98
2.87
2.80
2.70
2.60
CONV
3.01
2.97
2.93
2.87
2.80
2.77
2.67
2.60
2.52
2.42
2.30
2.15
1.93
530 BP
3.15
3.05
1o0
+.
- Does Not Contain Indoor Fan Motor Heat
37°BP
3.30
3.18
3.06
2.95
2.85
2.77
100 BP
2.82
2.77
2.72
2.67
2.62
2.55
2.48
2.43
2.37
2.33
2.26
435
T
Air Cond.
= 4500 CFM
Air Evap.
7500 CFM
Q HP
OUTnOOR
AIR TEMP
Air Cond.
-
= 85%
(1000's Of Btu/hr)
COT. 300 BP 200 BP
(°F)
R.H.
= 70°F
-
CON V
|
62.5
57.5
52.5
47.5
42.5
37.5
32.5
27.5
22.5
17.5
12.5
2010
7.5
81
71
2.85
2.65
0
1.0
191
179
169
158
147
135
125
114
103
100
102
72
103
126
104
105
106
107
75
76
78
80
82
83
84
86
88
127
128
130
108
108.5
92
2.5
-2.5
3.30
3.30
3.29
3.26
3.23
74
3821
3.18
3,13
3,10
3.05
2.97
POF
=
2650 Btu/hr
-
300 BP
200 BP
100BP
4.30
4,12
3.93
3.75
3.57
3.40
3.24
4.53
4.32
4.12
3.92
3.75
3.56
3.40
3.24
3.12
4.67
4.45
4.25
4.05
3.85
3.67
3.50
3.36
3.25
3.15
3.02
-
+
4+
OUTDOOR
AIR TEMP
CONV
(°F)
-
-
= 6919 Btu/hr
COP No Fans
10BP
120
122
124
PIF
COP OUTDOOR FAN
300 BP 200 BP
10°BP
CONV
30°BP
2.98
2.95
2.93
2.89
2.86
2.80
2.75
2.69
3.40
3.28
3.17
3.05
2.95
2.85
2.77
COP BOTH FANS
200 BP
10°BP
-
62.5
57.5
52.5
47.5
42.5
37.5
32.5
27.5
22.5
17.5
12.5
7.5
2.5
-2.5
3.24
3.20
3.17
3.15
3.11
3.06
3.00
2.95
2.87
2.83
2.75
2.65
2.53
1.0
3.96
3.80
3.62
3.45
3.30
3.15
3.04
4.08
3.90
3.73
3.57
3.42
3.27
3.12
3.00
2.87
4.00
3.83
3.68
3.55
3.41
3.27
3.16
3.05
2.95
2.85
2.75
2.65
2.55
2.45
2.30
2.15
1.0
4
*
Q HP - Does
Not Contain Indoor Fan Motor Heat
3.40
3.28
3.17
3.05
2.95
2.85
2.77
2.69
2.65
3.15
3.09
3.01
2.95
2.87
2.80
2.72
2.65
2063
2.50
2.44
436
T
Air Cond. = 3165
Air Cond
= 5200
Air Evap
= 700 F
R.H. = 85%
3535
POF
OF = 1818
Q HP (1000's Btu/hr)
OUTDOOR
=
PF
COP No Fans
AIR TEMP
(°F)
4CONV
23°BP
14°BP
184
176
167
158
148
139
128
120
110
101
90
83
101
102
103
104
105
106
108
110
82
83
i-
62.5
57.5
52.5
47.5
42.5
37.5
32.5
27.5
22.5
12.5
7.5
2.5
-2.5
+
84
85
87
88
89
90
91
92
72
0
23°BP
14°BP
2,89
4006
3°88
4035
3.70
3098
3.56
3.40
3.25
3.12
2.97
3.80
3.62
CONV
23°BP
CONV
230 BP
.
2.80
2.80
2.80
2.80
2.80
3.87
3.68
3.95
2.75
3.47
3.78
2.75
3.52
3.37
3.63
3.47
2.75
3.20
2.80·
3.07
3.35
3.20
2.80
2.80
2.77
2.72
2.65
2.56
2.38
1.0
2.92
2.83
3.35
3.21
3.10
2.97
2.85
2.75
2.70
2.95
2.85
2.77
2.75
2.75
2.73
2.70
2.67
2.63
2.58
2.52
2.45
2.33
1.0
+
*
3045
3.30
3.15
COP BOTH FANS
14 0 BP
3.07
4.17
3.03
2.90
COP OUTDOOR FAN
OUTDOOR
AIR TEMP
62.5
57.5
52.5
47.5
42.5
37.5
32.5
27.5
22.5
17.5
12.5
7.5
2.5
-2.5
CONV
2.89
2.89
2,89
2.89
2,89
2.89
2.89
2.89
2.88
2.82
2.74
2.64
1.0
+,
17.5
(0 F)
-
Q HP - Does Not Contain Indoor Fan Motor Heat
14 0 BP
3.50
3,38
3.27
3.15
3005
2.92
2.82
2.75
2.65
2.60
437
T
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44:2
APPENDIX P
WEATHER DATA.
Hours Spent in 5°F Temperature Bands - 10 Year Average'
TEMP
SAN FRANCISCO -CHARLESTON
(oF)
(HOURS)
·
(HOURS)
NEW YORK-
(HOrS)
·
BOSTON
OMAHA
(HOURS)
(HOURS)
105-109
JO
100-104
+
·95-99
90-94
1
5
85-89
15
80-84
40
1
20
137
425
724
75-79
70-74
65-69
60-64
55-59
50-54
45-49
40-44
35-39
99
285
665
1264
2341
2341
1153
·449
99.
30-34
10
651
576
434
321
192
25-29
5
5-9
0-4
-1-
96
265
604
926
877
127;
288
754
745
804
606
781
558
722
766
757
539
543
838
858
603
330
188
96
26
10
+
828
I
848
I674
543
655
663
I429
511
256
151
74
35
390
287
189
135
4
93
186
1
9
40
1
15
119
62
+
3
31
.796
79
27
20-24
15-19
10-14
1
13
44
149
52
787
-5
-6 - -10
-11 - -15
245- - 445
433
610
I676
726
819
7.21
I
-16 - -20
-21 - -25
621'
690
695
602
538
482
500
560
632
609
514 .
383
311
246
4
2
-
Total Hours 8767
+ Indicates
Series
8
54
147
295
468
10
-26 - -30
-31 - -35
U.S. Dept.
1
(HOURS)
+
10
39
28
1143.
1267.
'1090
889.
MINNEAPOLIS
8768
8768
·
8766
8767
8769
0 < t < .5 Hours
of Commerce Weather Bureaus
No. 82, Decennial
Observations.
Climatography of the U.S.-
Census of U. S. Climate,Summary of Hourly