Heat transfer characteristics of small configuration hot-wires in low Reynolds number subsonic and
supersonic air flows
by Peter Sean Hertel
A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in
Mechanical Engineering
Montana State University
© Copyright by Peter Sean Hertel (1985)
Abstract:
Heat loss measurements from 20 gin. and 50 gin. hot-wires with aspect ratios between 95 and 420 were
obtained in air flows in the range 0<3.0 and 0.1 < 10. Measurements in compressible flows were
obtained in the throat region and test section of the Montana State University Supersonic Wind Tunnel.
An alternative theory suggested by Demetriades is used for determination of the Nusselt number and
recovery temperature of the hot-wire. The heat loss measurements were corrected for conductive end
losses to the hot-wire supports and compared to the correlations of Dewey and Collis and Williams.
The results indicate that flow conditions in the vicinity of lower aspect ratio wires are altered so that
heat loss from the wire may not be correctly determined from theory. High aspect ratio hot-wires
converge toward Dewey's correlation for M>2; however, similar hot-wires may behave differently and
individual flow calibration for each wire is necessary for quantitative flow measurements. Nusseit
number measurements in low velocity flow fall below the correlation of Collis and Williams by 5 to 20
percent. Recovery temperature measurements in M=3 flows vary considerably (30 %) for probes under
similar flow conditions and show no distinct dependence on either SI/d or Kn. Recovery temperatures
of the hot-wires in low velocity flows indicated the stagnation temperature w ithin 2 .5 %. HEAT TRANSFER CHARACTERISTICS OF SMALL CONFIGURATION HOT-WIRES
IN LOW REYNOLDS NUMBER SUBSONIC AND SUPERSONIC AIR FLOWS
by
Peter Se an Hertel
A thesis submitted in partial fulfillment
of the requirements for the degree
of
Master of Science
in
Mechanical Engineering
MONTANA STATE UNIVERSITY
Bozeman, Montana
March 1985
APPROVAL
of a thesis submitted by
Peter Sean Hertel
This t h e s i s has b e e n read by each m e m b e r of the thesis c o m m i t t e e
and has been found to be satisfactory regarding content, English usage,
format, citations, b i b l i o g r a p h i c style, and consistency, and is ready
for submission to the College of Graduate Studies.
Chairperson, Graduate Committee
Date
Approved for the Major Department
2 - 2 7 - (Pd'
Da te
Head, Major Department
Approved for the College of Graduate Studies
Date
Graduate Dean
STATEMENT OF PERMISSION TO USE
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requirements for
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thesis
in
partial
fulfillment
a master's degree at Montana State University,
of
the
I agree
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Library.
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quotations
special permission,
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thesis
are
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A ny copying or use of the
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my written permission.
/5J
Date
O
V
O
ACKNOWLEDGEMENT
O
The author is indebted to the following for
their contributions to
this investigation.
His
advisor.
Dr.
Anthony
D e m e t r i ade s,
for
his
able
guidance
O
throughout the investigation.
G l e n n M c C u l l o u g h and J o h n R o m p e l
for their technical assistance
with the laboratory equipment. ■
Pat V o w e l l
O
and G o r d o n W i l l i a m s o n of the m a c h i n e
shop for their
assistance with fabrication of equipment used in this investigation.
Drs.
Ron Mussulman and Harry Townes for their support as committe
O
members.
The
Department
of
Mechanical
Engineering
and
the
Engineering
Experimental Station for financial assistance.
Special
thanks
to
family
and
friends
O
for
their
support
and
encouragement throughout the course of this graduate program.
O
O
O
TABLE OF CONTENTS
page
LIST OF F I G U R E S ..................................................... viii
NOMENCLATURE ............................................................
A B S T R A C T ............................... ...................... ..
%
xiii
1.
I N T R O D U C T I O N ..............................................
2.
THEORETICAL R E V I E W ...............................................
Incompressible Flows
.............................................
Compressible F l o w s ......................
Free— Molecule Theory
............................................
End loss c o r r e c t i o n ........................... ■.................. 17
Recovery temperature
.............................................
7
7
10
H
14
21
3.
EXPERIMENTAL APPARATUS AND P R O C E D U R E ...............................22
Hot-Wire Probes ...................................................
22
Supersonic Wind Tunnel ...........................................
24
Low Velocity T u n n e l ............
27
Flow Measurement Apparatus
......................................
28
Calibration O v e n ..............................
30
Data A c q u i s i t i o n .................................................... 32
Experimental Procedure ..............
34
4.
R E S U L T S ............................................................... 40
G e n e r a l ......................................
40
Nusselt N u m b e r
.................................................
40
End Loss C o r r e c t i o n ..................................................52
Recovery Temperature
.............................................
52
5.
C O N C L U S I O N .......................................................... 64
A P P E N D I C E S .......................................................... 66
APPENDIX A - OVEN CALIBRATION DATA REDUCTION C O D E ................ 67
APPENDIX B - FLOT CALIBRATION DATA REDUCTION CODE:
INCOMPRESSIBLE F L O W .................................. 70
APPENDIX C - FLOW CALIBRATION DATA REDUCTIOSf CODE:
COMPRESSIBLE F L O W S ..................................... 73
APPENDIX D - HOT-WIRE R E S ISTANCE-TEMPERATURE COEFFICIENTS .
77
O
vii
O
TABLE OF CONTENTS— Continued
APPENDIX E - FLOW CALIBRATION RESULTS
79
REFERENCES CITED ....................
96
O
O
O
O
O
O
O
O
O-
viii
O
L IST O F FIGURES
Page
O
1.
2.
Correlation of end loss corrected hot-wire characteristics
( r e p r o d u c e d f r o m { 3 } ) ......................
3
End loss corrected heat transfer data, MSU/SWT catalog data
(M>3.0) .............................................................
5
O
3.
Hot-wire characteristic data,
from {15] )
incompressible flow (reproduced
12
4.
Hot-wire characteristics,
supersonic flow ......................
13
5.
Hot-wire characteristics,
subsonic flow (reproduced from {15}).
15
6.
Normalized recovery factor data
7.
Hot-wire probe c o n f i g u r a t i o n ......... '.......................... 23
8.
Photographs of hot-wire element .................................
9.
Major components of M S U / SWT (reproduced from {25} ) ................. 25
10.
Test area of M S U / SWT (reproduced from { 2 5 } ) .......................25
11.
Variation of M with axial location in MSU/SWt n o z z l e ............ 26
12.
Low velocity tunnel ( L V T ) ........................................... 27
13.
Probe configuration, M S U /SWT (M=3).
14.
Probe configuration,
M S U /SWT ( .18<M<2.2)........................... 29
15.
Probe configuration,
LVT (M=O)...................................... 30
16.
Oven calibration equipment........... ' ........................... 31
17.
Data acquisition equipment diagram
18.
Oven calibration overheat traverse data ........................
19.
Resistance-temperature correlation obtained from intercept
data (R(W=O)) of figure 1 8 ........................................ 36
20.
Typical
(reproduced from {3})
.........
.............................
.............................
O
21
23
O
O
28
33
O
O
35
O
flow calibration overheat traverse data ...........
38
O
O
ix
LIST OF FIGURES— Continued
21.
End loss corrected
22.
End loss corrected heat transfer data; MSU/SWT catalog
data; M= 3, d=20 g i n .................... .......................... 43
Q.
heat transfer data; M= 3', d=20 jiin.............. 42
O
23.
End loss corrected
heat transfer data; Jfc=3, d=50 (iin.............. 44
24.
Support prong proximity effect on Nusselt number
(normalized with Dewey's correlation) ..........................
47
25.
End loss corrected
heat transfer data; .2<M<1, d=20 pin . . . .
48
26.
End loss corrected
heat transfer data; Probe 2 9/8 . ............
49
27.
End loss corrected
heat transfer data*;. M=O, d=20 pin...............50
28.
End loss corrected heat transfer data; Jfc=O, d=50 pin........... 51
29.
Summary of heat transfer d a t a ................................... 53
30.
Theoretical
end loss correction correlation ....................
31.
Typical end
loss
correction data; M = 3 ,
d=20 p i n ................... 55
32.
Typical -end loss
correction data; Jf=3,
d=50pin . . . . . . . .
33.
Typical end
loss
correction data; M =O,
d=20 p i n ................... 57
34.
Typical end
loss
correction data; Jfc=O,
d=50.p i n ................... 58
35.
Recovery temperature
data; M = 3 , d=20
pi n ..............
36.
Recovery temperature
data; Jfc=3 > d=50
p in........................... 61
37.
Recovery temperature
data; Jfc=O, d=50 p i n ........................... 62
38.
Recovery temperature
data; Jfc=O, d=20 pin. ................
O
O
54
O
56
O
60
O
63
O
O
O
O
X
O
NOMENCLATURE
SvmboI
Description
CD
Drag coefficient
d, D
Wire diameter
f (S 1 ), g(s-i )
Functions of molecular speed ratio S 1
CD
O
Gr
■■ Grashoff Number
h
Heat transfer coefficient
i
Current
k
Thermal conductivity
(amps)
Q
kb
Boltzmann constant,
5.66 X 10 ^
ft-IbsZ0F per molecule
Kn
Knudsen number
I,L
Wire length
LVT
Low velocity tunnel
M
Mach number
MSU
Montana State University
Nu
Nusselt number
Num
Measured Nusselt number (not corrected for end loss)
P
Static pressure
Pd
Dynamic pressure
Pe'
Peclet' number
Po
Stagnation pressure
P o2
Pitot pressure
Pr
Prandlt number
Ic
Convective heat transfer
O
O
O
(yPM^/2)
O
O
O
O
xi
NOMENCLATURE— Continued
SvmboI
Descrintion
R
Wire resistance
Re
Reynolds number
sI
Molecular speed ratio
S
Dimensionless end loss parameter
SWT
Supersonic wind tunnel
T
Temperature
W
Power
^
„
O
Uy H
M)
^
(Watts)
O
a
Thermal accomodation coefficient
ar ■
Temperature-resistance coefficient
Y
Ratio of specific heats
O
Te
Euler's constant
n
Recovery factor
(.577) '
(Ta^ ZT0 )
Experimental continuum recovery factor
O
Rf
Theoretical free-molecule recovery factor
X
Measured wire recovery factor
R
Nondimensional recovery factor
O
crYP
Yield stress of hot-wire material
r
Dimensionless overheat temperature
%
Nusselt number end loss correction factor
( >a
air property
< >aw
evaluated at equilibrium temperature- (i= 0)
( )m
measured value
( >x
evaluated at arbitrary reference
(T-Taw)/Taw
Q
!
O
temperature
O
O
xii
O
NOMENGLATO RE— Continued
Symbol
Description
( )o
evaluated at stagnation conditions
O
evaluated at conditions behind a normal
( )
free stream property
( )
pertaining .to the hot-wire supports
shock
O
O
O
O
O
O
O
O
I
ABSTRACT
Heat loss m e a s u r e m e n t s f r o m 20 jiin. and 50 gin. h o t - w i r e s w i t h
aspect ratios between 95 and 420 were obtained in air flows in the range
0<M <3.0 and 0.1 <Re< 10. Measurements in compressible flows were obtained
in the throat r e g i o n and test s e c t i o n of the M o n t a n a State U n i v e r s i t y
Supersonic W i n d Tunnel.
An alternative theory suggested by Demetriades
is used for determination of the Nusselt number and recovery temperature
of the ho t - w i r e .
The h e a t loss m e a s u r e m e n t s w e r e c o r r e c t e d for
c o n ductive e n d l o s s e s to the h o t - w i r e s u p p o r t s and c o m p a r e d to the
c o r r e l a t i o n s of D e w e y and C o l l i s and W i l l i a m s .
The re s u l t s indicate
that flow c o n d i t i o n s in the v i c i n i t y of l o w e r aspect ratio w i r e s are
altered so that heat loss from the wire may not be correctly determined
f r o m theory.
H i g h aspe c t ratio h o t - w i r e s converge t o w a r d Dewey's
correlation for M>2; however, similar hot-wires may behave differently
and i n d i v i d u a l flow c a l i b r a t i o n for e a c h w i r e is n e c e s s a r y for
quantitative flow measurements.
N u s s e l t n u m b e r m e a s u r e m e n t s in low
velocity flow fall below the correlation of Collis and Williams by 5 to
20 percent.
R e c o v e r y t e m p e r a t u r e m e a s u r e m e n t s in M= 3 fl o w s vary
considerably (30 %) for probes under similar flow conditions and show no
distinct dependence on either H d or Kn.
Recovery temperatures of the
hot-wires in low velocity f l o w s i n d i c a t e d the s t a g n a t i o n t e m p e r a t u r e
w ithin 2 .5 %.
O
I
O
CHAPTER I
INTRODUCTION
O
Hot-wire
anemometers have
determination
of
flow
measuring turbulence.
h e a t-loss
from
the
become
properties
an
and
important
are
especially
This a pplication u t i l i z e s
hot-wire
and
the
mean
instrument
for
the
suitable
for
the r e l a t i o n b e t w e e n
properties
of
flow
O
and
therefore requires the measurement of the Nusselt number, Nu.
In general,
in a
transverse
the Nusselt number dependence
flow
may
be
expressed
for an infinite cylinder
in
terms
of
O
dimensionless
parameters as
Nu=NuCRe, M, Pr, Gr, t w )
(I)
w h e r e Re, M, Pr, and Gr are the R e y n o l d s n u m b e r ,
number,
and G r a s h o f f n u m b e r and T w = ( T w - T a w ) / T aw
loading.
has prevented
the establishment
loading.
of a universal
special a p p l i c a t i o n s (I) m a y be simplified.
the
P randlt
is the t e m p e r a t u r e
Equation (I) neglects radiation effects which have been
to be negligible up to high temperature
flows
M a c h number,
dependence
(Pr=Constant).
overheat (Tw=O),
Further,
of
Nu
on
Prandlt
shown
O
The complexity of (I)
relation,
however,
for
For m e a s u r e m e n t s in air
number
may
be
O
eliminated
if we consider only forced convection for zero
O
equation (I) may be expressed as
N u = N u (Re, M)
In actual a p p l i c a t i o n s ,
O
(2)
the l e n g t h of the h o t - w i r e m u s t be r e s t r i c t e d
for greater resolution and
to prevent
wire breakage.
the infinite wire solution is no longer valid.
For
these
wires,
For a finite hot-wire,
O
a
O
O
2
percentage
of heat, is lost by
axial
conduction to the supports and the
Nusselt number is dependent on an additional parameter,
O
S, such that
(3)
N u ffl= N u (Re, M, S)
O
where
The s t a ndard p r a c t i c e is to e v a l u a t e the N u s s e l t n u m b e r a s s u m i n g all
heat
transfer
from
the
hot-wire
to
be
conv e c t i v e
and
applying
a
O
correction factor,
a
measured
i|^(S),
to account for the losses by conduction:
Thus
Nusselt number is evaluated from
(4)
^nkaNumAT=I2Rw
O
and N u m (Re, M, S) is then c o r r e c t e d to o b t a i n the actual N u s s e l t n u m b e r
Nu(Re, M, S=ro) from
N u (Re, M, S=m )= I^(S)Num (Re7M jS)
(5)
O
The
ea r l y
work
of
Betchov
Kovasznay and T o r mark (2), Dew ey
{I }
and
more
{3}, and Behrens
recently
studies
by
(4) addressed the heat
transfer f r o m fin i t e w i r e s u s i n g the above procedure.
The heat loss
O
correlation presented by Dewey for the special case
N u 0=N u q (Re 0,M, S=°=,r=0)
(6)
where the subscript " o'.1, refers to the evaluation of the air properties |i
O
and k at the s t a g n a t i o n t e m p e r a t u r e , w a s d e t e r m i n e d u t i l i z i n g (4) and
(5) and remains
the
state-of-the-art
for low Reynolds number air flows.
Dewey's correlation,
s h o w n in f i g u r e I, is b a s e d on his m e a s u r e m e n t s
from 100 pin.
mm) hot-wires
O
and M c C l e l l a n
(.00254
{5},
C y b ulski
and
on supplemental
and B a l d w i n
others,
and the theory of Stalder,
Roshko
{§}.
Goodwin,
[6],
data of Laufer
Vrebalovich
and Creager
{7),
and
{8} and Cole and
O
An
outstanding
feature
of
Dewey's
correlation
is
an
O
IO
Z
__
—
—
Z
'
Z
o
D
2
Z
ZZ Z
0
/
z z
OJ
I/
/
x
Z
/
/ Z
/
'
Z
Z ------
/
Z
Zzz
Z
—
4r
a
nr.?j q .
rn i r
P HQM Uf n
FREE M O L E C U L E S O L U T IO N
S T A L O E R ,G O O D W IN , 3 C R E A G E R
_
/
//Z
.01
100
01.
Figure I.
A
'
/
Z
/
/
/
/%
ZZ
"
/
Z
Z
Zz
ZZ
V
Correlation of end loss corrected ho t - w i r e c haracteristics
(reproduced from {3} ).
O
4
independence of N u 0 on M for M>2.0.
For actual applications,
O
it is desireable to utilize the above heat
transfer correlation to predict properties
known,
the f l o w R e y n o l d s N u m b e r m a y t h e n be p r e d i c t e d using Dewey's
correlation.
required for
(note
that additional measurements
hot-wires
of relatively
associated with
limited
to
O
of flow properties are
the determination of the mean velocity.)
Figure I is in some ways restrictive
control
If (5) and (6) are
of flow.
larger
large diameter
smaller
aspect
in that (I) the data are from
O
alleviating problems of quality
configuration probes, . (2) the data are
r a tios
where
the
correction
^(S)
was
O
r e l a t i v e l y small, and (3) there is i n s u f f i c i e n t data to guarantee the
correlation over
the
entire range
of R c q and M.
Therefore,
additional
data are n e e d e d for s m a l l e r d i a m e t e r w i r e s of a w i d e range of aspect
O
ratios in low Reynolds number flows in the range M < 3 .
Finite hot-wire data (Nuffl(Re 0,M>3 .0, S)) o b t a i n e d f r o m a n u m b e r
sources
and
c o m p i l e d by D e m e t r i a d e s
M S U / SWT Catalog data) were
corrected using
Dewey's c o r r e l a t i o n for M > 2.0.
from
the
data
of
measurements were
Dewey's
not
{10}
(hereafter r e f e r r e d to as
(5) in an attempt
correlation
the focus
and aspect ratio.
of
in
that
(I)
conclusion that
(5)
additional
as
the
proper
heat
loss
that
O
of
Figure 2 shows that a fit of these
for Re 0<1.5
such
the
and (2 ) the h o t - w i r e s w e r e
correlation is non-existant
overlooked
to verify
i n v e s t i g a t i o n and the data w e r e
data to Dewey's
is invalid or
O
These data, s h o w n in figure 2, differ
o b t a i n e d u n d e r m o r e severe conditions,
smaller diameter
of
some
measurement
of
leading
to
O
the
factor has been
N u q (Re 0,M, S ) or
the
O
aerodynamics of the miniature probe configurations of the hot-wires used
O
Figure 2.
End loss corrected heat transfer data; MSU/SWT catalog data (M>3)
Q
6
O
in {10}.
C o n s i d e r i n g the p r e c e d i n g discussion,
fluid properties
from
of finite h o t - w i r e s
the heat
of the
transfer
the p r o b l e m of p r e d i c t i n g
Nu 0 CRe0,M,S),
characteristics,
u s e d in {10 } is r el event for actual
type
O
a p p l i c a t i o n s in steady and u n s t e a d y flows but has not yet b e e n fully
examined.
This -investigation,
conducted at the Montana State University
Supersonic Wind Tunnel Laboratory,
was undertaken to provide additional
heat loss data for
smaller diameter hot-wires over a wide
for
numbers
low
Reynolds
alternative
technique
for
in
the
the actual
range
0<M<3
and
to
O
range of &/d
p r esent
an
measurement of the Nusselt number
O
and recovery temperature.
O
O
O
O
O
O
O
7
O
CHAPTER 2
THEORETICAL REVIEW
O
Thi s
investigation
is
concerned
characteristics of fine wires and,
the Nusselt
number
with
therefore,
and recovery temperature
th:e
heat
transfer
requires the evaluation of
of the hot wire.
Assuming
O
n e g l i g i b l e h e a t loss by r a d i a t i o n and na t u r a l convection, the Nu s s e l t
number may be expressed as
Nu=NuCRe, M, S,-c)
(7)
Flow measurement based on the characteristics of an unheated wire
further
simplifies
the
correlation
as
does
theoretically eliminates the dependence on S.
figure I in actual
applications,
the
Thus,
use
of
(5)
O
(t = 0)
which
in order to utilize
O
the c o r r e c t i o n factor 1I^(S) must be
accurately predicted.
Consider the
lumped
evaluation of the heat loss from the hot-wire
O
(8 )
I2Rw = TrLlcaNu0AT - jrd2kv.7dT '
x=L/ 2
where
AT=Tw- T aw-
Equation
(8) m a y
be
simplified
using
a
rough
O
approximation of dT/dx=-(Tw - T a w )/(&/2) where
assumed
equal
to
the
equilibrium
the support temperature
tem p e r a t u r e .
This
is
a
is
valid
assumption considering the relative size of the supports with respect to
O
the hot-wire.
Equation (8) then reduces
to '
I2R=L 7IkaNum AT
(9)
Num= Nu 0 (1+1/S2 )
where
O
Although
the
above
analy s i s
provides
only
a poor
estimate
of
the
O
O
8
magnitude
of
conductive
losses,
justification for
equation (4) (i.e.
conduction losses
using
the p a r a m e t e r
it
is
useful
measurement
a single convective
S on w h i c h .the
correction
in that
of both
it prov i d e s
O
convection and
type relation) and presents
factor
is
dependent.
O
Axial conduct ion and the end loss c o r r e c t i o n factor are a d d r e s s e d in
more detail later in this chapter.
The mechanisms of energy transfer between the hot-wire and the gas
v a r y dep e n d i n g o n the p h y s i c al
characteristics
generally separated according to the continuum,
O
of the fluid and are
slip,
and free-molecule
flow regions.
O
In c o n t i n u u m
flow
the heat
transfer
is,
for
the most part,
a
f u n c t i o n of the R e y n o l d s n u m b e r ( i n d i c a t i n g v i s c o u s effects) and the
M a c h n u m b e r ( i n d i c a t i n g e f f e c t s due to compr e s s i b i l i t y ) .
transfer of e n e r g y is r e l a t e d to the drag on the w i r e
viscosity and the conversion of kinetic energy
Thus,
the
surface due to
into thermal
energy.
At
l o w v e l o c i t i e s ( i n c o m p r e s s i b l e flow) the e n e r g y a s s o c i a t e d w i t h the
velocity
is
compressible
less
influential.
effects b e c o m e m o r e
dependence is evident.
the flow fie l d
Depending
At M= I, a bow
in the v i c i n i t y
on the
strength
incompressible
the
velocity
increases,
d o m i n a n t and a large
shock,
again becomes
we
expect
the
and
the h o t - w i r e
to
the
r e c overy
the
of
the
cylinder
O
attain a temperature equal
to the static t e m p e r a t u r e of the fluid w h i l e at h i g h v e l o c i t i e s
temperature
O
subsonic.
A n u n h e a t e d cylinder p l a c e d in a l o w
continuum flow will
O
Mach number
shock forms ahead of the wire,
of the w i r e
of this
beh a v e as in the s u b s o n i c case.
velocity
As
O
will
approach
or
equal
O
stagnation temperature of the flow.
O
O
9
For- smaller diameter wires
and low density (rarefied)
flow field in the vicinity of the wire no longer behaves
and the
thermal
behavior
structure of the fluid.
by the Knudsen number;
of the hot-wire
O
as a continuum
The approach to free-molecule flow is indicated
O
the ratio of the m e a n free molecular path of the
(Kn=X/d).
molecule
et al. to exist
flow has been shown by
Stalder
Fully developed free
energy transferred between the hot-wire and the fluid is
cylinder.
the
is dependent on the molecular
fluid molecules to the cylinder diameter
molecular
gasses,
at Kn=2.0.
The
O
in the form of
energy i n c ident to and r e - e m i t t e d f r o m the surface of the
In f r e e - m o l e c u l e flow,
the
Reynolds
number
dependency
O
reflects density effects rather than viscosity effects of continuum flow
while the Mach number reflects effects due to free steam velocity rather
than c o m p r e s s i b i l i t y effects.
E x p e r i m e n t a l evidence and theory have
O
shown that the recovery temperature of an unheated wire in free-molecule
flow will
exceed the stagnation temperature of the wire.
h o t - w i r e b e h a v i o r in f r e e - m o l e c u l e f l o w
The theory of
is a d d r e s s e d later in this
O
chapter.
Most
supersonic
the slip f l o w region,
molecule flow.
and compressible
In this region,
at the surface of the hot-wire.
behavior.
so
that a non-zero velocity occurs
In slip flow,
transfer behavior
the fluid retains some of
the m a g n i t u d e
O
also e x h i b i t i n g f r e e - m o l e c u l a r
of
the hot-wire in the slip flow
region will therefore show dependencies both on Mach number and Reynolds
number,
Q
the boundary layer associated with fully
characteristics while
The heat
data falls in
that is, the r e g i o n b e t w e e n c o n t i n u u m and free-
developed continuum flow is altered
its c o n t i n u u m
subsonic hot-wire
O
of w h i c h are d e p e n d e n t on the m a g n i t u d e of the
O
O
10
O
Knudsen number.
E v a l u a t i o n of (4) is n o n - r e s t r i c t i v e as to the type of flow (i.e.
continuum,
slip,
free-molecule,
as long as
the heat
transfer
compressible,
coefficient
is the c o n v e c t i v e h e a t transfer.
or incompressible
flows)
is defined by qc=hAT where q c
O
The v a l u e of h, h o w e v e r , is h e a v i l y
dependent on the flow parameters Re, M, and Kn.
O
Incompressible Flows
The
heat
transfer
from
cylinders
in low
velocity
air flow is w e l l r e p r e s e n t e d at. h i g h Re (see M c A d a m s
incompressible
{11}),
however,
O
hot-wire
data
at
low
Re
(Re <10)
h as
been
obtained
only
by
few
investigations.
There is some disagreement among researchers as to what conditions
O
the R e y n o l d s n u m b e r and N u s s e l t n u m b e r should be evaluated.
The m o s t
common
thermal
practice
conductivity
at
is
the
to
evaluate
free
stream
the
air
viscosity
temperature
or
the
and
mean
(film)
O
temperature b e t ween the
wire,
free stream
and the hat-wire.
For an unheated
the film temperature is equal to the free stream temperature.
One
of
the
first
and
most
widely
applied
relations
used
in
O
incompressible hot-wire
anemometry was
developed by King
{12}.
King's
law,
Nu=O.318 + 0.690(Re)1/2
(9)
O
was
determined
theoretically
assuming
two-dimensional
inviscid
i n c o m p r e s s i b l e f l o w and c o n s t a n t heat flux over the boundary.
King's
relation has been used by many in slightly modified forms retaining
the
O
square-root
dependence
on Reynolds number with empirically determined
O
O
11
constants.
O
Cole and Roshko obtained the relation
2 / Nu= Jln(SZPef)- Y e
bas e d on the O s e e n v i s c o u s
(Ye = E u l e r fS
flow
c o n s t a n t = 0.577).
P e 1= R e 'Pr
(10)
theo r y v a l i d for the
Hilpert
{13}
limit
investigated
as Re-O
the
heat
O
transfer from fine wires in the Reynolds number range from 2.6 to 3x10^.
Hilpert's data
in the
range
of Reynolds numbers between 2.6 and 4.0 may
O
be expressed as
Nu=.891 [Re (Tw Z T 00)174]'330
where
the
conductivity
temperature.
and
viscosity
are
(U)
evaluated
Measurements in low Reynolds number
by Collis and Williams
Nu=
at
the
film
incompressible flows
O
{14} were best expressed by the relation:
T w + T4
-17 [ .2 4 +. 5 6 R e ,4 5 ]
.1<Re <44
(12)
O
Again,
the f l u i d p r o p e r t i e s w e r e e v a l u a t e d at the f i l m temperature.
Baldwin, S a n d b o r n, and L a u r e n c e
and R o s h k o , H i l pert,
{15} have s u m m a r i z e d the data of Cole
Collis and W i l l i a m s ,
and others in the R e y n o l d s
O
n u m b e r range b e t w e e n .01 and IxlO^.
Dewey's correlation for M=O
This
summary
is c o m p a r e d w i t h
in figure 3.
Compressible FlOw
O
A considerable volume
of r e s e a r c h in the 1950's and 196 0's w a s
directed toward hot-wire behavior in compressible flows.
in supe r s o n i c
f l o w s at h i g h e r R e y n o l d s n u m b e r s
{16}, Laufer and McClellan,
of
Investigations
(Re>20) by K o v a s z n a y
and Spahgenberg {17} have shown a dependence
the Nusselt number on the square-root of the Reynolds
number
as was
seen in the incompressible flows.
Kovasznay's data in the range of Mach
numbers
showed
from
1.15
to 2.05
O
also
that
for
small
O
temperature
O
12
-!Ifc^n I
S s ld S t i A i r *
I C T E t if
i
D
%
IfflH
5
IO
Reynolds number, Re
Figure 3.
Heat loss characteristics;
(reproduced from {15}.
differences
between
the
incompressible air flow
hot-wire
i n d e p e n d e n t l y of the M a c h number.
and
air,
the
hot-wire
b ehaves
This M a c h n u m b e r ind e p e n d e n c e for
supersonic flows has been varified many times and is generally accepted
for
Mach
numbers
s u p ersonic
data
Lowell {19},
g r e ater
than
of K o v a s z n a y
2.
Baldwin
and T o r m ark,
Sandborn and Domitz
{20},
et
a I.
Winovich
summarized
and Stine
Laufer and McClellan,
the
{18},
Stalder et
al., W e l t m a n n and Kuhns {21}, and W o n g {22} for air f l o w s in the range
of Mach numbers from 1.155 to 6.083.
shown in figure 4.
agreement
A portion of the data for Re<10 is
Data obtained by Dewey in air at M= 5 .8 was in close
to the data
of L a u f e r
and M c C l e l l a n and is also
shown
in
figure 4.
As w i t h the i n c o m p r e s s i b l e case,
of
the
flow
researchers.
properties
in
the choices for the e v a l u a t i o n
compressible
flow
vary
widely
amo n g
In addition to evaluation of properties at the free stream
13
c o n d i t i o n s or f i l m
t e m p e r a t ure,
p and k m a y also be e v a l u a t e d at the
stagnation temperature or, in the case of supersonic flow, at conditions
behind
the
shock.
As w i t h
the m o r e
recent
investigations,
in this
study, p and k were evaluated at the stagnation conditions.
The
MSU/ SWT
discussion.
Catalog
The
consequence
the
shown
in
figure
These data were collected under
distinguishing them
1.
data
data
of
data w e r e
from
were
merit
the f o l l o w i n g
further
cond i t i o n s
the data presented above.
not
turbulence,
obtained
2
the
focus
boundary
under
of
layer,
conditions
investigation
and wake
more
but
studies.
severe
were
As
a
such,
than n o r m a l l y
encountered in hot-wire heat transfer studies.
2.
20
pin.
M o s t of the data w e r e f r o m h o t - w i r e s of 10 pin. (.000254 mm),
(.000508
mm),
and
50 pin.
ratios m u c h lower than encountered in
Figure 4.
Hot-wire characteristics;
(.0 012 7 mm)
diameter
previous hot-wire
supersonic flow.
with
aspect
investigations
O
14
(£/d
as
I ow
as
120).
Some
sc a t t e r
is
expected
for
these
sm a l l e r
O
configuration probes because of f a b r i c a t i o n d i f f i c u l t i e s r e s u l t i n g in
poor quality control.
data for
included in his
is evident
(Re 0 >1 .5)
larger hot-wires
Dewey's correlation.
with
This scatter
show
in figure 2 in which the
less
scatter
and a p p r o a c h
Data collected by Dewey for 50 pin. hot-wires
correlation)
were
also
(not
scattered and in poor agreement
O
the 100 pin. hot-wire data shown in figure I.
3.
losses
The s m a l l
than
for
wires
asp ect
ratios result
of previous
in greater
investigations,
thus
con d u c t i v e heat
resulting
in
O
larger errors associated w i t h (5).
Subsonic compressible
Baldwin, Baldwin
and L a u r e n c e
{23},
flows have been investigated by Cybulski and
Spangenberg, and Vrebalovich.
(figure I) however
similar
the values
to
the
low
Re
relations
Sandborn,
The data of
O
presented by Dewey
of N u q in figure 5 are considerably lower
than the data by V r e b a l o v i c h (Dewey's
figure I.
Baldwin,
s h o w n in figure 5.
s u g g e s t e d the r e l a t i o n s
figure 5 is qualitatively
O
c o r r e l a t i o n for M< I) s h o w n in
O
This discrepancy and the limited amount of available data in
compressible
research in this area.
subsonic
flows
suggests
the
need
for
further
Measurements in subsonic compressible flows were
O
made in this investigation and will be discussed in chapter 4.
Free-Molecule Theory
O
Stalder et al. have t h e o r e t i c a l l y d e t e r m i n e d the N u s s e l t n u m b e r
and recovery temperature
flow.
relationships
for a hot-wire
in free-molecule
The infinite wire Nusselt number may be expressed as
O
Nun _
( y — I ) U R e n Pr
2(n)3/%
g ( s -, )
si
(13)
O
Cv
Rer
Figure 5.
Hot-wire characteristics;
subsonic flow
(reproduced from {5}).
and the. recovery factor as
=
where
a
is
the
thermal
speed ratio (s^=
(14)
f (s I )
sTip
^aJiC =
O
accomodation
coefficient,
s^
is the molecular
M) and f(s^) and gts^) are functions dependent only
on s^ and the n u m b e r
of e x c i t e d d egrees
of f r e e d o m
of the
gas.
The
thermal accomodation coefficient is an indication of the efficiency with
which energy is exchanged between
impinging
above
air
stream
relation
radiation.
molecules
applies
Equations
to
the
solid hot-wire
surface
and
and is determined experimentalIy.
infinite
(13) and
unheated
(14) were
wires
and
f o r m u l a t e d by
the
The
excludes
equating the
jo u l e h e a t i n g (i^R) to the m o l e c u l a r e n e r g y (both t r a n s l a t i o n a l
and
r o t ational
the
surface
for
a diatomic
of the
gas)
inci d e n t
on and re— e m i t t e d f r o m
cylinder using a simpli f i e d kinetic
classical M a x w e l l i a n v e l o c i t y d i s tribution.
theory a s s u m i n g
A d e t a i l e d anal y s i s and
t a b u l a t e d v a l u e s of s^, f(sq) and g(s]_) m a y be f o u n d in r e f e r e n c e
Equation (13)
is shown in figure I.
As was
wire
indicated earlier,
immersed
temperature.
magnitudes
{ 8}.
in
a free-molecule
Stalder
of
the recovery
flow
temperature of a unheated
exceeds
the
stagnation
et al. explained this phenomenon by comparing the
incident
and
re-emitted
molecular
energies.
The
translational component of the incident molecular energy is the total of
the free
stream
translational
kinetic
molecular
energy
superimposed
kinetic
energy.
on
The
the r a n d o m
incident
thermal
energy
per
molecule has a value ranging from 2k^T to 5/2k^T (depending on the speed
and
orientation
of
the
flow)
as
opposed
to
a value
of
3/2k^T
per
O
17
molecule
for
continuum
flow.
Similarly,
the energy
of the re-emitted
O
stream is Zk^Taw for free-molecule flow and 5/Zk^Taw for continuum flow.
Thus, under steady state conditions,
energy incident in each case,
if the re-emitted energy equals the
the temperature of the body,
T a w , must be
O
higher in the case of free-molecule flow.
As in the c o n t i n u u m f l o w case,
ratio are nearly
independent
the N u s s e l t n u m b e r and r e c o v e r y
of Mach number for M>Z.O.
This effect can
O
be seen in f i g u r e I.
End Loss Correction
O
If the t e r m for axial
c o n d u c t i o n is included,
the steady state
heat equation for the hot-wire is:
+
H k aN u 0 A T
4
dxz
(15)
i2-|»
&
O
The average w i r e r e s i s t a n c e is d e t e r m i n e d by c a l i b r a t i o n and m a y be
expressed as a linear function of temperature as
Rw= R r [l+ar (Tw- T r )]
where Rr is
the resistance
(usually O 0C).
The
at
solution to
some
(16)
arbitrary reference
(15),
temperature
Tr
expressed in terms of the average
wire temperature is:
O
rm=c+frc_c^t a n h ■ p
b
b
p
where
In a similar manner,
O
b= Nu0 -JLJLnfLr
P=ZbTa
C=
. i ^r
[!+ U r
(17)
O
(Taw-Tr)]
equation (4) can be nondimensionaliz ed to obtain:
Num (Tw~T aw)=c+ZTw
(18)
O
where
Z I^RrUx.
K-Jika
O
O
Substituting
(18)
into (5),
the Nusselt number correction factor becomes:
=Nti0 (Trw-1E aw)
^
The
n o n d i m e n s ional
substituting
recovery
(19)
temperature,
T a w , may
be
obtained
by
i=0 into (17) to obtain:
-CgtanhS
(20 )
Then equation (19) b e c o m e s :
C
F o r the
limiting
case
(t 0- c ) t a nh P - t _ t anh
b
3
t
“c + ' ( T 0 - c ) t a nh P
b
b
P
_
c +
„b
Nu0
+
of
Z
i-^0 ,
equation
(21 ) m a y
be
S
(21)
simplified
and
linearized in iz to obtain:
(22 )
tanh S
IfJN=1The above a n a l y s i s w a s fir s t p r e s e n t e d by Dewey.
Nusselt Number Measurements
Consider now the actual measurement of Num
in (4). Using (16),
the
temperature difference in (4) m ay be expressed as:
Tww >Ta0w
(23)
Rw~R aw
Jirar
The heat loss equation for the infinite wire becomes:
I Nu
The
usual
linearizing
technique
used
in
=
many
(24) in the limit as i-*0.
earlier
investigations
involves
Then:
j CarR 1) Iim _i^
R„
_________
i-0
(24)
( Rr1^r \
„
Q r-RrR
nw
—Etr
R rR nw
( K m - R aw) " ( d R w / d i Z ) i =0
(25)
Q
O
19
Substituting,
we
O
then obtain:
Nu.
hawRr
(26)
(dRwZdi2)i=O
'm
In order to determine the Nusselt number in this manner,
measurements of
Q
R w are n e c e s s a r y at v e r y low v a l u e s of i.
A c c u r a t e m e a s u r e m e n t s of i
and R w at small, i are difficult and invite error.
Demetriades
{24) suggests an alternative procedure that eliminates
O
the need to r e s t r i c t m e a s u r e m e n t s
of N u m at l ow v a l u e s
of current.
Equation (24) may be writ t e n as:
R -R 1 + J L
"
i2b
, I 2h=JLiaSlaL
”
-,R 1
V=I2IL
1
(27)
O
.
A linear fit of R vs. W m a y t h e r e f o r e be u s e d to obta i n R aw and N u m if
kNu is assumed
constant.
This method
that (27) is ex a c t and the range
temperature of the wire.
the actual
offers
an advantage
over (26)
in
of i is l i m i t e d only by the m e l t i n g
O
Since k is a function of temperature, however,
r e l a t i o n b e t w e e n R and W
shou l d not be linear.
However,
Demetriades points out that the dependence of kNu on temperature must be
O
weak for the following reasons.
(a) Conduction, k, is
not a strong
function of T.
O
(b) The temperature controlling k is only partially
d u e to
the w i r e t e m p e r a t u r e (e.g. f i l m
temperature=(Tw+ T aw)/2.)
(c) I t i s k n o w n f r o m e arlier w o r k s that Nu is
affected by Tw in a way balancing changes in k.
O
B a s e d on the abo v e o b servations,
written as:
j
1
kNu
i.
the v a r i a t i o n of kNu w i t h W m a y be
I
k N u ( W-0)
I .
(RNu)i=O
+
I
9(1/kNu)
9W •
Jo
k3Nu
(kNu)2 I 9W
NuBk
3W
O
W
1=0
(28)
O
O
Substituting into (27),
the wire resistance becomes:
V R- +&
aw
a rR r
CWz
S-TTkflNu aw
(29)
Where
I 9Nu
Nu SW
Thus,
if w e
measure
Rw
and
W
+
I Skfl
kaSW
(30)
Ji=O
and
fit
the
data
to
a
second
order
polynomial
R= A q +A-^W+ A 2
(31)
then the hot wire heat loss characteristics (Num ) may be determined from
the known coefficients Ag, A^, A 2 and (29).
The recovery temperature is
obtained from
the i n t e r c e p t A g = R a w m and the re s i stanc e-t e m p e r a t u r e
relation (16).
From
the coefficient A^ and the evaluation of kaw using
T aw, the Nusselt number at T=O is determined from:
_
a r R
aw &7ik.
The
coefficient
provides
$1
the coefficient G=-P^
(30) provides the Nusselt number for W/0.
(30) results
(32)
/
Performing
and integration of
the integration of
in:
N u ( T ) _ k aw
B x p L - ( A 2 Z A 1 )W]
(33)
The above analysis was used in the present investigation.
The data were
fitted to a second order polynomial using the method of least squares in
computer codes LOFLOW02 and HIFLOW02 written by Demetriades and modified
for this i n v e s t i g a t i o n to include
presented
by
Dewey
(eqn
(21)).
the end loss c o r r e c t i o n p r o c e d u r e
These
codes
are
included
in
the
appendices.
i
O
21
Recovery Temperature
As
noted
earlier
in
temperature may vary from
this
a value
in incompressible continuum flow
chapter,
equal
the
hot-wire
to the free
stream
recovery
temperature
to a value greater than the stagnation
t e m p e r a t u r e in f r e e - m o l e c u l e flow.
In c o n t i n u u m flow,
the r e c o v e r y
t e m p e r a t u r e is m a i n l y a f u n c t i o n of the M a c h number. In slip flow and
free-molecule
flow,
Knudse n n u m b e r
the recovery
as w e l l
as the
temperature
Mach
number.
is
also
dependent
on
the
Vrebalovich proposed a
normalized recovery ratio given by
tIw
tiC
(34)
" " I f-Ic
w h e r e t|c is the e x p e r i m e n t a l
c o n t i n u u m r e c o v e r y factor and
theoretical f r e e - m o l e c u l e r e c o v e r y factor.
is the
The n o r m a l i z e d reco v e r y
factor minimizes the Mach number effect as was shown by Vrebalovich for
M > .4 .
Normalized recovery temperature
data
c o m p i l e d by D e w e y from
several sources is shown in figure 6 .
F fM -
ilfiom
Knuditn
Figure 6 . Normalized recovery factor data
number,
K n 00
(reproduced from (3)).
O
22
O
CHAPTER 3
EXPERIMENTAL APPARATUS AND PROCEDURE
O
Hot-wire Probes
The h o t - w i r e probes,
the MSU/SWT lab.
s h o w n in
at
The primary probe body is a 2 inch length of 1/16 inch
diameter 2-hole alumina tubing.
of 1/32
figures 7-8, were f a b r i c a t e d
inch diameter 2-hole
The secondary body is a 1/2 inch length
alumina
tubing.
'Pyroceram
glass
cement,
m a n u f a c t u r e d by Co r n i n g Gla s s W o r k s , is used to atta c h the s e c o ndary
body to the primary body.
Current
.012 inch d i am eter arm cured
is supplied to
the hot-wire
The
p o l y t h e r m a l e z e c o p p e r leads arc w e l d e d
supports are shaped with
to provide a suitable
contact
surface
an acid etch and fine
for
the hot-wires.
leads
rubber applied
enter
hel p s
to
at
the
end
prolong
the
of the
life
of
primary
Pyroceram
the
body
lead
is
where
wires
O
the
through
O
continued use.
Hot-wires
O
sandpaper
applied to the forward end of the probe to provide a smooth rounded tip.
Silicon
O
through
(using a thermocouple welder) to the .003 inch diameter nickel hot-wire
supports.
O
used
in .this
experiment
w i t h d i a m e t e r s of 20 pin. and 50 pin.
were 90% Platinum-10%. Rhodium
A l i q u i d gold resin a t e w as u s e d
to attach the hot-wires to the support prongs.
After mounting,
the hot­
O
wires were baked at IOOO0F to burn off the organic vehicle of the liquid
gold as w e l l as to anneal
the h o t - w i r e ^in an effort to e l i m i n a t e the
O
strain gage effects reported by previous researchers.
A
constant
current
control
fabricated
especially
for
O
23
Figure 8.
Photographs of hot-wire element and supports.
O
24
turbulence r e s e a r c h at P h i l c o - F o r d A e r o n u t r o n i c w a s used to heat the
hot-wire.
The
constant
15, indi v i d u a l l y
current
control
system
adju s t a b l e p u s h b u t t o n current
(model
O
ADP-13) provides
settings.
Pushbutton
operation is designed for quick disconnect current change and is ideally
O
suitable for automated data recording with swiching transients of only a
fraction of a second.
ten
10,000
automotive
Power is supplied to the heating circuit
mil I i a m p - h o u r
batteries.
mercury
batteries
The m e a n v o l t a g e
or
three
and current
12V
through
350
and current
recording.
signals were
Th e digital
later in this
amplified
as much
O
outputs m a y be
simultaneously recorded from jacks located on the rear of the unit.
voltage
amp
The
as 10 times before
O
c o n v e r s i o n and data r e c o r d i n g are d i s c u s s e d
chapter.
O
Supersonic Wind TunneI
The M o n t a n a State U n i v e r s i t y S u p e r s o n i c W i n d Tunnel,
s h o w n in
figures 9 and 10 is an open circuit
continuous, flow facility,
as the working
Mach numbers of 3.0 over a Reynolds
using air
O
n u m b e r range
normal
fluid and producing
of 4 8 5 0 0 - 1 4 5 0 0 0
operating
per
conditions,
in.
the
(19000 — 57000
SWT
is
per
capable
cm.).
of
Un d e r
stagnation
O
temperatures as high as 145 0F (620C) and stagnation pressures as low as
3 00 m m Hg absolute.
Automatic or manual
control of the flow conditions
is m a i n t a i n e d f r o m the control console l o c a t e d in the test area.
The
O
r e c t a n g u l a r test se c t i o n has a cross s e c t i o n a l area of 3.1x3 .2 inches
(7.87x8.13 cm.).
nozz l e w a s
For this investigation,
utilized.
The v a r i a t i o n
the entire
of
the
Mach
length of the Laval
number
with
axial
O
p o s i t i o n is s h o w n in figure 11.
The test s e c t i o n is a c c e s s e d t h r o u g h
O
25
Figure 10.
Test area of MSU/SWT laboratory.
26
XlO
=M
(MACH NUMBER)
V STATIC PRESSURE MEASUREMENT (£=600mm.H o )
-- THEORY CAZAh )
X
-50
-40
-30
-20
-10
XlO 1=x
Figure 11.
(in.
FROM THROAT)
Variation of Mach number with axial location in M S U /SWT
nozzle.
27
re m o v a b l e
nozzle.
optical-quality
glass p a n e l s
extending
the
length of the
A detailed description of the SWT may be found in (25).
Low Velocitv Tunnel
The L o w V e l o c i t y A p p a r a t u s
(LVT),
S h o w n in figure 13,
operated suction venturi m a n u f actured by A e r o l a b
LVT has a 12 inch (30.48 cm) diameter plexiglas
operating over a Reynolds number range
per cm) at room
cm/s).
flow
Supply
test
is a fan
Company.
section capable of
of 4300— 23000 per in.
(1700— 9000
t e m p e r a t u r e w i t h a m a x i m u m v e l o c i t y of 56 ft/s (1700
This corresponds to a Mach number range of .007(M(.05.
in the test
diffuser behind
The mass
se c t i o n is c o n t r o l l e d by a l l o w i n g air to enter the
the
test
section
thereby
decreasing mass
ahead of the test section at the intake manifold.
Figure 12.
The
Low velocity tunnel (LVT)
flow
entering
Flow M easurement Apparatus
Flow c o n d i t i o n s for tests c o n d u c t e d in the S W T were d e t e r m i n e d
from two separate sets of measured flow properties.
For tests conducted
at M=3, the flow conditions were determined by measuring the stagnation
temperature and pressure
shock P 02/P 0.
The
tube
for
the pressure ratio across a normal
stagnation conditions
nozzle using a type J
pitot
(T0lPo) and
the
thermocouple
for
determination
of
were
measured upstream
temperature
the
measurement,
s t a g n a t i o n pressure.
of the
and a
The
pressure Po 2 w a s m e a s u r e d us i n g a .029 inch i. d.-.063 inch o.d. pitot
tube positioned
in the same vertical
plane
as the hot-wire as shown in
figure 13.
Figure 13.
Probe configuration; MSU / SWT (M=3.0).
For tests conducted in the range .18 < M <2.2, where the hot-wire was
traversed th r o u g h the throat,
the flow
measuring
ratio
the
total
pressure ratio P / P Q.
press u r e
c o n d i t i o n s were d e t e r m i n e d by
and the static pressure-stagnation
The s t a g n a t i o n p r o p e r t i e s w e r e m e a s u r e d in the
same manner as in the M=3 tests while the static pressure was determined
using a static pressure probe attached
parallel
to the hot-wire
distance between
the
probe
and
in the
shown in figure 14.
static probe and
a .032 in o.d.
and
Four
at
the
tip.
.0145
plane and
The separation
the hot-wire was .90 inches.
probe was fabricated from
sealed
same horizontal
hollow
inch
The
tube tapered to a point
static
pressure
taps
drilled around the perimeter a distance of .25 inches from the tip.
were
The
h o t - w i r e w a s al i g n e d such that the e l e m e n t w a s at the same u p s t r e a m
location as the static p r e s s u r e taps.
Figure 14.
The p r e s s u r e transducers w e r e
Probe configuration; MSU/ SWT ( .I 8<M<2.2).
located o utside
the tunnel and w e r e c o n n e c t e d to the total and static
pressure probes by flexible tubing e x t e n d i n g
a nd
exiting
The pressure
the
tunnel
transducers
through
ports
through
located
the h o l l o w
in
c o n s i s t e d of a D y n i s c o 0-15
the
psi
sting
diffuser.
t r ansducer
energized by 5 vdc and a Kulite 0-15 psi transducer energized by 10 vdc.
The signals were
amplified 30 and 100
before recording.
The probes w e r e
using an electromechanical
actuating
diffuser sections of the tunnel
The flow
times and were dynamically damped
axially and vertically postitioned
system located above
the
test and
as seen in figure 10.
c o n d i t i o n s in the v i c i n i t y
of the h o t - w i r e
for tests
conducted in the LV T (M=O) were determined using the ambient temperature
and a pitot-static probe positioned in the same vertical plane and below
the hot-wire
Figure 15.
as shown in figure 15.
Probe configuration;
The pitot-static tube consisted of
LVT (M=0).
c o ncentric tubes, the s m a l l e r of w h i c h w a s a .04 inch i.d. tube o p e n at
the tip for total p r e s s u r e m e a s u r e m e n t and the outer tube, a .120 inch
o.d.
tube with
eight .0145
inch
static pressure taps drilled around the
p e r i m e t e r a d i s t a n c e of .6 inches from
dynamic pressures
were
the probe tip.
The static and
indicated on an inclined micromanometer
with
a
scale to .6 inches of H 2O and accuracy to .001 inch H2O using alcohol as
the working fluid.
Calibration Oven
The
temperature-resistance
characteristics
of
the hot-wires
were
cali b r a t e d in the c a l i b r a t i o n oven.
The oven, m a n u f a c t u r e d by S i g m a
Systems,
regulated
measures
temperature.
Figure 16.
1000
in^
and
is
A s i x - p o s i t i o n probe holder,
Oven calibration equipment.
to
maintain
constant
s h o w n in figure 16, a l l o w s
O
32
the
simultaneous
calibration
of
six hot-wires.
A
seventh
position
on
O
the holder allows for the calibration of a shorted hot-wire probe which
was used to account, for. resistances in the probe other than the hot-wire
element.
The h o l d e r is e n c l o s e d w i t h i n a tin b ox to isolate the h o t ­
wires from
the oven.
vicinity
the light air currents
caused by a small
O
circulation fan in
A type J t h e r m o c o u p l e m o n i t o r s the oven t e m p e r a t u r e in the
of
the
hot
described on page
wire.
23
The h o t - w i r e s
are h e a t e d by
the ADP-13
O
w i t h v o l t a g e and c u r r e n t r e c o r d e d in the same
manner as in the flow calibrations.
O
Data Acquisition
The b l o c k d i a g r a m of figure 17 s h o w s the e l e c t r o n i c c o m p o n e n t s
used
in data
acquisition.
The
hot-wire
signals
from
the
cons t a n t
O
current control panel w e r e a m p l i f i e d b e f o r e c o n v e r s i o n to a digital
signal for storage.
t ransducers
were
The signals f r o m
likewise
resistor-capacitor
analog to digital
linearly
converts
proportional
(R/C)
the
static and total
pressure
a m p l i f i e d and dynamically supressed with a
c ircuit
prior
to
digital
conversion.
The
O
(A/D) c o n v e r t e r ( a Spectral D y n a m i c s mod e l SD-133)
the
analog
to the voltage
input
range
signal
of the
to
a
digital
specified input
signal
channel.
The
O
SD-133 is a c c u r a t e to I part per 1000 over the input channel v o l t a g e
range.
The output
from
the SD-133
was
then recorded directly to 5 inch
disk using the I n t e r t e k S u p e r b r a i n m i c r o c o m p u t e r and also to a Te x a s
Instruments
Silent
700 ASR
computer
terminal
which provided temporary
b ack-up storage on cassette tape as w e l l as a h a r d copy of the
data.
The
flow
above
procedure
was
applied
to
oven
O
calibrations,
LVT
O
O
33
POWER
SUPPLY
H O T - W IR E
PR ESSU R E
SENSORS
CONSTANT
CURRENT
ANEMOMETER
TRANSDUCER
NO. 2
A M P L IF IE R
NO. 2
A/D
NO. 3
NO. 4
CONVERTER
TEMPORARY
STORAGE'CASSETTE
HARD COPY
STORAGE:
5 - INCH
Figure 17.
D IS K
Data Aquisition equipment diagram.
POWER
SUPPLY
O
■ 34
calibrations,
O
and SWT flow calibrations.
Experimental Procedure
The p r o c e d u r e for p r e p a r i n g the h o t - w i r e p r o b e s is d e s c r i b e d in
O
detail in {26}.
The P t - I 0% Rh W o l l a s t i n w i r e s w e r e first e t c h e d to
remove the silver coating,
m i c r o s cope,
then mounted on the probe with
and a n n e a l e d to r e m o v e
the
thermal
stress
the aid of a
effects
that
O
occure at high overheat.
any wi r e s
Each wire was checked under the microscope and
s h o w i n g ob v i o u s
imperfections
or i m p r o p e r
mounting were
discarded.
O
The wires were then
resistance
oven calibrated
characteristics
calibration utilized an
from
to determine the temperature-
equation
overheat traverse
(16).
.
This
method
of
The wires were placed in
O
the c a l i b r a t i o n oven and the r e s i s t a n c e m e a s u r e d at f i f t e e n pre-set
current settings.
Using the ADP-I3 as described on page 23,
current measurements were
obtained at
twelve
constant
voltage and
temperatures
in
O
15° C
increments
rangeing
from
room
temperature to 190° C.
temperature,
the R v s. W data w e r e f i t t e d to a quadratic.
shows typical
R(W)
vs.
T oven calibration data.
At each
Figu r e 18
The intercept
(W=O) of
O
each polynomial
provides
the resistance
of that p a r t i c u l a r overheat traverse.
of the wire
at
the temperature
The R(W=O) vs. T data w e r e then
linearly fit to obtain the coefficients Rr (Q) and ar (1/°C) of equation
O
(16).
Figure 19
shows the resistance-temperature
intercept data of f i gure 18.
correlation using the
C a l i b r a t i o n s s h o w i n g rms d e viations of
R(W) greater than .1 in the quadratic fit were
discarded.
A summary of
O
coe f f i c i e n t s R r and a r for h o t - w i r e s
u s e d in this
i n v e s t i g a t i o n is
O
35
OIX (U)H
Figure 18.
Oven calibration overheat traverse data.
36
6. 5
PROBE
2 6 /5 /1
R0 (O0C)= 4 6 . 5 2 (OHM)
a.
=1.562 X 1 0 - 3 ( | / ° c )
6
O
X
g
5. 5
CC
5
4. 5
O
.5
I
1 .5
2
T (T) XlCrZ
Figure 19.
Resistance-temperature correlation obtained from the
intercept data (R(W=O)) of figure 18.
given in the appendices.
the 0VENCAL5
code
included in the
The reduction of data was
accomplished using
written by Demetriade s and F i shbaugher.
The code
is
appendices.
The flow c a l i b r a t i o n p r o c e s s is s i m i l a r to the oven c a l i b r a t i o n
described above.
The purpose
heat transfer and flow
The
flow
traverse.
calibration,
For
the
flow
calibration is to obtain
the
data for the d e t e r m i n a t i o n of N u q (Re Q ,M, S = 00).
like
calibrations
were recorded along with P,
flow properties.
of
the
oven calibration,
in the LVT,
T,
overheat
utilizes
the overheat
traverse
measurements
and P 0 for the determination of the mean
In the L V T tests, the R e y n o l d s n u m b e r w a s v a r i e d by
Q
37
r e g ulating
the
velocity
characteristics were
W
data
and
Tpjq(S) w as
in
the
test
section.
The
heat
transfer
O
then determined using a quadratic fit of the R vs.
equations
determined
iteration procedure.
(29)-(33).
from
The
equation
end-loss
(18) usi n g
correction
factor,
an interval
halving
O
Data r e d u c t i o n w a s f a c i l i t a t e d using the code
LOFLOW02 listed in the appendices.
The p r o c e d u r e for the S W T c a l i b r a t i o n s w a s identical to the L V T
O
calibration except that variation of Reynolds number was accomplished by
regulating the total pressure in the tunnel.
The data recorded for the
M = 3 .0 tests i n c l u d e d i, R, P q, P 02 ’ and T 0 w h i l e
i, R, P q, P,
were
throat
region
data
shown in figure 20.
recorded
Typical
flow
for
calibrations
calibration overheat
in
the
traverse
Data for the S W T c a l i b r a t i o n s w e r e
is
r e d u c e d using the
and T q
O
(.18 < M < 2.2).
code H I F L O W 02
O
listed in the appendices.
Measurements
using hot-wires
of
10 pin.
were
attempted,
however,
consistent w i r e b r e a k a g e in the S W T p r e v e n t e d the c o l l e c t i o n of data.
Wire
failure has been a persistant problem
w i r e s and is c a u s e d by
O
in research using fine hot­
a n u m b e r of f a c t o r s i n c l u d i n g high p r e s s u r e
O
loading and collisions with the hot-wire element by dust particles.
F i s h b a u g h e r {27} a p p r o x i m a t e d the h o t - w i r e stress l o a d i n g using
s i m p l i f i e d b e a m and cable theories.
He d e t e r m i n e d that the m a x i m u m
aspect ratio for each theory may be obtained from
I
beam theory
I.
2
rnd ;
L4-
cable theory
O
:
(35)
'uDpdJ
I
Tr CTyp' s in 6
d
2
(36)
O
Ccfd
O
R(OHIVI) XIO
38
Figure 20.
Typical flow calibration overheat traverse data.
O
39
w h e r e ^yp is the m a x i m u m y i e l d stress (48000 psi for P t - 10% Rh wire),
C q is the drag coefficient,
is the d y n a m i c
angle of deflection due to loading.
O
press u r e and 9 is the
The beam theory models the hot-wire
as a uniformly loaded beam w i t h fixed
supports
while
the cable
theory
O
uses small angle approximation and a uniform load distribution model.
A comparison of the above
theory with actual conditions encountered
in this investigation showed the following.
O
M = 3 .0
R e 0= I .2
P (j=2 psi (min. dynamic pressure of M= 3 tests)
Cq (free-molecule)=4 (from {8})
Cn (continuum)=9 (from {28})
Conditions:
x
O
Results:
£/d
Beam
.80
120
continuum
free-molecule
Cable (9=.I)
7
16
(9=1)
73
164
O
The beam theory gives a better approximation,
is
quite
conservative
calibrations, w i r e s
unavoidable wire
of
for
&/d<250
failure
wire
v i o l a t i n g the
had
for 20 pin.
greater than a b o u t 350.
maximum
these
conditions.
a
good
wires
In o r d e r for
£ / d of 350,
however,
the val u e
the predicted %!d
In
the
survivability
M= 3
rate
SW T
and
Q
generally ocurred for wires
the cable
theory to pr e d i c t a
of 9is g reater than unity,
thus
Q
a s s u m p t i o n of small a n gles in the d e v e l o p m e n t of (36).
Note that (35) and (36) do not d e p e n d on the d i a m e t e r of the hot-wire.
In
practice,
however,
higher
aspect ratio
wires
show
better
Q
survivability for larger diameter wires.
O
O
O
40
O
CHAPTER 4
RESULTS
O
General
The
p urpose
transfer
of
this
characteristics
investigation
of
Reynolds n u m b e r air flows.
small
appendices,
In particular,
determine
the
hot-wires
heat
in low
O
it w a s d e s i r e d to evaluate
data in low Reynolds
less than 3. The results,
are d i s c u s s e d under
to
configuration
Nusselt number and recovery temperature
of M a c h n u m b e r
was
air
flows
w h i c h are t a b u l a t e d in the
the s u b h e a d i n g s
O
of
1.
End loss corrected Nusselt number N u q (ReQ,M, S=00)
2.
End loss correction
3.
Recovery Temperature Ttaw= ( T awZT0 )
O
tJ^(S)
The following discussion presents the results of this experiment in
comparative
form
with
previous
investigations.
The
presented by Dewey have been verified by data from
corr e l a t i o n s
several
O
sources and
are used as a basis for comparison of the compressible flow data of this
study.
The
correlation of Collis
velo c i t y f l o w s
was
used for
and Williams
for
c o m p a r i s o n of data
incompressible
low
O
o b t a i n e d in the L V T
(M=O).
O
Nusselt Number N u q (Re 0 .M . S=m )
The
number,
variation
of
the
end— loss-corrected
N u 0, w i t h R e y n o l d s number,
R e 0 , is
zero-current
s h o w n in f igures
Nu s s e l t
21-29.
O
Nusselt number
data
collected
in the M=3.0
test
section of the MSU / SWT
O
O
41
is s h o w n in figures 21 and 23.
Several d i s t i n c t c h a r a c t e r i s t i c s are
O
immediately apparent in these data.
Nu
1.
q
varies
inversely
with
%!d
even
though
conductive end losses have been theoretically
from
2.
axial
eliminated
the total heat loss.
Data
for
very
low
aspect
ratios
(&/d<130)
are
more
O
scatttered than data for wires of larger &/d.
3.
O
Data for high aspect ratio wires
converge
toward Dewey's
correlation.
P o s s i b l e c a u s e s for the o b s e r v a t i o n s I and 2 m a y be found in the
O
assumptions used in the solution of the heat loss equation (15) and the
end loss
correction factor
solution of (15) were:
equation (19).
The
assumptions used in the
(I) the heat transfer coefficient,
along the length of the wire,
h,
is constant
O
(2) Both hot-wire supports are maintained
at a t e m p e r a t u r e T g , (3) the t h e r m a l c o n d u c t i v i t y of the wire, k w , is
constant,
and (4) a uniform
the wire.
For this study,
temperature
exists
a s s u m p t i o n (2) w a s
at any cross section of
O
f u r t h e r r e s t r i c t e d to
T s= T aw (Ts=0)Assumption (I) requires that the flow be uniform over the length of
the wire.
If the flow near the supports
O
is affected by their presence,
the resulting effect on the measurement of N u q would be more pronounced
O
for smaller &.
The assumption T g=O may be questionable especially for small aspect
ratio wires.
Because
of the h o t - w i r e
temperature
of their relative
size,
the
supports b e h a v e s as a c o ntinuum,
of the support tips
should be equal
flow
in the vicinity
and therefore,
to or less
the
O
than the
O
-ry'-
I
.
8
" M=3
SYM.
.
O
D
Z
Il
O
7
I-
6
.
5
r
O
r~t
X
4
D =20
PROBE
/i.iN
L/D
►
t>
A
128
3 0 /4 /2
13 8
2 6 /4 /1
2 5 /3 /1
166
A
2 5 /3 /2
166
B
188
27 /3 /1
188
2 7 /3 /2
□
T
2 9 /3 /1
207
2 8 /3 /1
289
+
n
0 6 /2 /1
292
307
25 /4 /1
*
29/4/1
331
◄
----- h/>2 (DEWEY)
.3
.2
.I
. 25
. 75
XlO
Figure 21.
0
I. 2 5
Re0
End loss corrected heat transfer data; M=3, d=20|iin.
I.
MSU SWT CATALOG DATA
M=3
D = Z O zU-IN.
S Y M . PROBE
L/D
8
123
IO
123
7
144
9
150
5
191
DEWEY'S CORRELATION
O
3
Z
Il
XlO
O
I. 2 5
Figure 22.
End loss corrected heat transfer data; MSU/SWT catalog data
M=3, d=20 (iin.
I
.9
M-3
D = 50/-UN.
SYM.
PROBE UD
V
.8
.7
<
>
D
4A
-----
2 9 /7 /2
94
0 9 / 4 / 2 177
0 6 / 5 / 2 185
2 9 /5 /2 225
0 7 /7 /2 227
0 9 /3 /2 420
M >2 (DEWEY)
V
V
VV
Figure 23.
End loss corrected heat transfer data; M=3, d=50 pin.
O
45
s t a g n a t i o n t e m p e r a t u r e of the air stream, T q. For h o t - w i r e s in f r e e —
molecule flow,
theory and results from previous investigations indicate
T o < T aw-
the e v a l u a t i o n of
Thus,
lower calculated value of N u q.
O
a s s u m i n g T g= T 0 w o u l d result in a
Note, however,
that a higher proportion
O
of heat is conducted to the supports for smaller aspect ratio hot-wires,
tending to raise
the
support
temperature,
decreasing
in an increase in the calculated value of N u q.
\jj^ and resulting
The sensitivity of N u q
O
to the support t e m p e r a t u r e w a s c a l c u l a t e d and r e s u l t e d in d e v i a t i o n s
less than 2 %
for T g= ±.10 .
The codes H I F L O W 0 2 and L O F L O W 0 2 provide
for input of specifed values of r g.
O
The 20 pin. data (M=3.) are s h o w n . iu f i g u r e 21.
(1-3) noted on page 41 are clearly visible
The o b s e r v a t i o n s
in these data.
This behavior
was v e r i f i e d (in figure 22) by 20 pin. MSU/ SW T catalog data in M a c h 3
flow.
O
All corrected M S U / SWT catalog data show a general Z /d dependence.
Although figure 22
co r r e l a t i o n
for
indicates
a hot-wire
that end loss
of
&/ d= 2 00 ,
correction satisfies Deweys
the
data
i n v e s t i g a t i o n show a m u c h h i g h e r l i m i t on Z / d for a
correlation.
although the
The 50 pin.
data
(M=3) of figure 23
approach to Dewey's
show
correlation occur
of
fit
the
p resent
O
to Dewey's
similar behavior
at a lower value
of
O
Z/d (£/d=185).
The c o r r e c t e d N u s s e l t n u m b e r data p r e s e n t e d in figure 24 clearly
shows the effect of w i r e l e n g t h on the m e a s u r e d N u s s e l t number.
The
O
fact that the 50 pin. data conve r g e to Dewey's c o r r e l a t i o n at a l o w e r
Z/d than the 20 pin. data leads to the c o n c l u s i o n that the s e p a r a t i o n
distance b e t w e e n the supports a f f e c t s the f l o w d i s t r i b u t i o n over the
O
h o t - w i r e r e s u l t i n g in a h i g h e r h e a t loss than that m e a s u r e d by longer
O
O
46
wires.
It is i n t e r e s t i n g
to note
that an increase
in the heat loss
indicates a l o w e r local M a c h n u m b e r or h i g h e r R e y n o l d s number.
assume &/d =180
as the limit for 50 |iin wires where
If we
the support effect
dissipates then we would expect a limit of &/d=450 for the 20 pin. wires
in order to maintain the
mm).
However,
same
O
separation between prongs
(.0093
O
in./.235
figure 24 indicates a limit of approximately 300 at which
point the prongs no longer affect the measured Nusselt number for 20 pin
O
hot-wires.
• Verification
of Dewey's
correlation for M<2.
is shown in figures 25 and 26.
are
shown
in figure 25.
These
data agree w i t h Dewey's
aspect
Qualitatively,
ratio wires
Data
for a shorter
The higher heat loss that was
in the M= 3 measurements
wire
O
evident
is clearly evident.
O
in Mach number dependence of N u q with increasing M.
The h o t - w i r e h e a t — loss b e h a v i o r in lo w v e l o c i t y i n c o m p r e s s i b l e
flows (M=O) is p r e s e n t e d in f i g u r e s 27 and 28.
effect which was
evident in the compressible
to exist in the M = O calibrations,
The su p p o r t p r o x i m i t y
flow
calibrations
a l t h o u g h it is of l o w e r
less than 23 %.
magnitude.
29/6/1).
considering
O
A l t h o u g h the 50 pin. data of figure 28 agree w i t h i n 26
the data are e x t r e m e l y
(probe
O
appears
All the 20 pin. data d eviate f r o m Collis and W i l l i a m s ' c o r r e l a t i o n by
%,
O
correlation
the data of f i g u r e 26 agree w i t h Dewey's correlations,
showing a decrease
„
(&/d>280)
The data c o l l e c t e d at M= .2 agree
correlation shown.
(&/d=207) are shown in figure 26.
for low
hot-wires
Data for two longer hot-wires
w i t h i n 18 % at M= .4 and 14 % at M = I .
to 13 % with the empirical
and 20 pin.
the
The
scattered with
o r igin
uniformity
of
of
this
data
the e x c e p t i o n of one w i r e
sc a t t e r
from
is
unknown,
probe
29/6/1
however,
and
O
the
O
47
N u 0 DEWEY
7
XlD
=Nu0/
> 5
XlO
Figure 24.
=LXD
Support prong proximity effect on Nusselt number
(normalized with Dewey's correlation).
1.0
Figure 25.
End loss corrected heat transfer data; .2<M<1., d=20 pin.
1.0
.V '
"
\
>
/
J
+
J
C
/
_A-
= I :> £
D1
y
^
j /
/
k
,
r
/
i
",
Z
/
/
y
z
/
X
L/D=207
r)= ? (3 a N
/
PROBE
~ y
0.1 -------------- --- -- -- ----------------- --------------- ----- 1
----1
--- 1
-- 1
-- L-L
0.3
1.0
3.0
Re0
Figure 26.
2 9 /8
M
02
02
5
+U£“'
o
039
*
0.59
□
076
A
1.06
*1.41
4
2.13
------- DEWEY'S CORRELATION
SYM
End loss corrected heat transfer data; probe 29/8.
10
50
#
M-O
0 = 2 0 LUN
SYM. PROBE L/D
+3 0 /2 /2
H
2 5 /2 /1
V
2 7 /2 /2
k
2 6 /3 /1
w
2 6 /2 /1
□
2 9 /2 /1
----- COLLIS 8
132
216
246
2 74
334
404
WILLIAMS
XlO
#
V
□
XlO
1= R e o
S
Figure 27.
End loss corrected heat transfer data; M=O, d=20 gin.
51
I. 2
M=O
1. 1 -
SYM.
A
◄
►
<
+
H-
□
■
—
D = S O yLZ-IN.
PROBE
L/D
0 9 /4 /1
17 7
0 6 /5 /1
186
2 9 /5 /t
225
0 7 /7 /1
2 27
1 7 /4 /1
295
2 5 /4 /1
346
2 9 /6 /I
416
0 9 /3 /1
420
COLLIS 8 WILLIAMS
'nN=
8
OTX
7
.2
.8
.4
I. 2
XlO
Figure 28.
End loss corrected heat transfer data; M=O, d=50 pin.
I. 4
O
52
rela t i v e l y well b e h a v e d data of figure 27,
data are attributed to some external
source
the scatter in the 50 (iin.
(i.e.
electronics).
Figure 29 summarizes the data presented above.
Data for hot-wires
of aspect rat i o less than 1 85 for 50 pin w i r e s and less than 280 for 20
pin.
wires are not included in the figure because
proximity dependence for hot wires
of
5,/d less
of a definite
O
support
than these values.
The
data of figure 25 w a s used for the c o m p r e s s i b l e range of M<2. and the
scattered 50 pin.
O
O
low velocity data was not included.
End Loss Corrections
O
The v a r i a t i o n of
S) j,= q (e qn. (2)) is s h o w n in figure 30.
shorter w i r e s w h e r e the s upport p r o x i m i t y
wire,
the
For
affects the flow over the
correction equation is of little value
since the actual
flow
O
conditions in the vicinity of the hot-wire are not known.
The magnitude
of typical measured correction factors with Reynolds number is shown in
figures 31-34.
A correlation of
Tp ^ w i t h 5,/d was not attempted because,
O
as shown in the Nusselt number data,
Num may' vary considerably for hot­
wires of nearly equal aspect ratio.
Recovery Temperature
Recovery
O
temperature
r e c o v e r y fa c t o r s
data
are p r e s e n t e d
for 20 pin. h o t - w i r e s
used
in figures 35-38.
The
in this e x p e r i m e n t
are
compared in figure 35 with data of similar flow
D e m e t r i a d e s {29}.
the.pr e s e n t
data
conditions obtained by
No d e p e n d e n c e o n a s pect ra t i o is evident in either
or
the data
of D e m e t r iades.
Attempts
to correlate
Tia w (Kn) were not made considering the large variation of q aw in figures
35
O
O
and 36. A s u r p r i s i n g note is that these r e c o v e r y t e m p e r a t u r e data
O
k▻
, 50
3.0
3.0
----- DEWEYS CORRELATION
--------------- cOLLi s
_
Figure 29.
s
w il l ia m s
L /O > 185 FOR 5 0 /m
DATA
L / 0 > 2 8 0 FOR 2 0 /in
DATA
Summary
of heat transfer data
XlO
54
Figure 30.
Theoretical end loss correction function.
55
=3
-9
b
8
-
d=. 0 0 0 0 2
SYM
I /D
A
□
■*
D>
O
128
138
207
289
331
i n.
-5 ?
Ii
o
OIX
.
-7
b
C
D
^
d
□
.6
0
.25
.5
. 75
XlO
Figure 31.
0
I
1.25
=Re
Typical end loss correction data; M-3, d—20 pin.
I.
56
M=3
XlO
i f
d=. 0 0 0 0 5
L /D 4 2 0 >
^
in.
^
.8
a
0Ji
A
" ^ sv
a
l_/D=2 5 9
D
7
n
□ □U □
A 4 ^
L/D = 225 a
□
□ □
^
□ □
UD=I 85
□ □
.6
I. 5
2. 5
XlO
Figure 32.
=Rg ,
Typical end loss correction data; M=3, d=50 pin.
57
d=.00002
L/D = 4 0 4
V ^ 7V V
V
i n.
V
V
V
V
L/D= 3 3 4
Il
Q
QTX
□□
L /D =132
^
^
XlO
Figure 33.
D
1= R
g o
Typical end loss correction data; M=O, d=2O pin.
58
- - - - - - - - 1—
d=. 0 0 0 0 5
M=O
i n.
U d = 420
▼
A
▼
A
L/D =346
OTX
◄ L/D= 225
M
◄
-
£>
.
L/D = 186
-
▻
"> >
&
.4
CD
2
OO
▻
XlO
Figure 34.
I
I
I
1.2
0=Re0
Typical end loss correction data; M=O, d=50 pin.
I.
59
indicate
continuum
Stalder et.
ratio
or
slip f l o w
when
recovery
temperature
data of
al. at similar values of Kn (0.6<Kn<2.5) and molecular
(s^=2.5) s h o w e d r e c o v e r y
speed
factors consistently greater than unity
indicating f r e e - m o l e c u l a r flow.
The r e c o v e r y fact o r s for the M = O data are s h o w n in figures 37 and
38.
For
the
continuum
flow
conditions
of
these
tests
(.06<Kn<.12),
the
actual recovery temperature will not exceed the stagnation temperature.
R e c o v e r y t e m p e r a t u r e s for 20 pin. h o t - w i r e s in the l o w v e l o c i t y tests
were
consi stant at a value
of Tlaw = I .00 * .015,
probe n u m b e r 3 0/2/2 (figure 3 7).
number
38.
data
The
is also
recovery
indicates the total
evident
factors
with
the e x c eption of
The sc a t t e r of the 50 pin. Nusselt
in the recovery temperature data of figure
of
the w e l l - b e h a v e d
temperature with Tja w =I.Q ±.025 .
probe
(29/6/1)
also
12
D = Z O yUlN. M = 3
T0 = S G O o R
SYM.
▻
V
D
+
A
X
•
o
*
x
a
1.0
D
x
PROBE
06/2/1
28/3/1
29/ 4/1
25/4/1
25/3/1
25/3/2
27/ 3/ I
27 / 3 / 2
26/4/1
30/4/2
29/3/I
DEMETRIADES
l.5< Kn< 3.2
0.9
0.8
0.3
3.0
1.0
Re0
Figure 35.
Recovery temperature d a t a ; M = 3 , d=20yin
IO
1.2
D=50/xlN.
▻ ▻
M =3
16=560=R
SYM.
D
t>
r
1.0
+
■
A
P-
PRQRF
2 9 /7 /2
2 9 /5 /2
0 9 /4 /2
0 8 /3 /2
0 7 /7 /2
0 6 /5 /2
a a
Aa » ^
A a AA AAa A
T
T
■ D g D -B^B
0 . 6 < Kn <1.7
0 .9
0.8
03
1.0
3.0
Re0
Figure 36.
Recovery temperature data;
M=3,
d=50 yin.
10
62
I. 2
M =O 50/xin.
T0=SSOoR
I. I
PIi
°
I
OTX
■SYM
PRORF
S
▼
07/ 5/ I
07/5/2
17/4/1
25/ 4/ 1
29/ 5/ I
09/3/ I
29 /6 /1
07/ 7/ I
06/5 /I
09 /4 /1
<3
.9
+
o
O
A
□
V
.8
0
.2
.4
.6
.8
I
XlO °=Re0
Figure 37.
Recovery temperature data;
M= O , d=50 pin.
1.2
1.4
63
<JCJ<]<] <l< <]<]<]
O IX
Figure 38.
<
PROBE
Recovery temperature data; M=O, d=20 pin.
64
CHAPTER 5
CONCLUSION
The preceding results show that the heat loss characteristics for a
finite
hot-wire
with
configurations
of
investigation may not be accurately predicted,
the
type
used
in
this
and that individual flow
c a l i b r a t i o n is r e q u i r e d for each h o t - w i r e used in q u a n t i t a t i v e flow
study.
Specific
behavior
patterns
for
these
probes
are
summarized
in
the following discussion.
1.
The heat loss from
clearly
result
the hot-wires
affected by
the proximity
is an increase
decreasing
aspect
used in this investigation is
in the
ratio.
of
the
support prongs.
The
indicated Nusselt number with
An
increase
in
heat
transfer
i n d i c a t e s e i t h e r a decre a s e in the local M or an increase in
the local Re.
The e f fect is e vident in the c o m p r e s s i b l e flow
data for 50 pin. h o t - w i r e s w i t h &/d less t h a n a p p r o x i m a t e l y
200
and 20 pin.
uniform
heat
wires
transfer
with
&/d<300.
coefficient
The
theory
over the length
as s u m e s
a
of the wire
(i.e. uniform flow distribution) which may be a poor assumption
considering the actual geometry of the hot-wire.
2.
The compressible flow Nusselt number data of longer wires
general
agreement
dependence
indicated by previous
smaller hot-wires
for M >2.
w i t h D ewey's
correlation.
investigations
show
The Mach number
extends to the
indicating a Mach number independence of Nu q
65
3.
I n c o m p r e s s i b l e h e a t loss data also appear to be affec t e d by
a s p e c t ratio.
The g eneral tre n d is s i m i l a r to the effect at
higher velocity although a clear limit on £/d is not visible in
the data.
The
data for h i g h e r
aspect ratio w i r e s
values of N u q smaller than values
of Collis and Williams
4.
indicate
predicted by the correlation
(by 5% - 2 0%).
As w i t h the N u s s e l t n u m b e r data,
the r e c o v e r y t e m p e r a t u r e of
supersonic flow may not be accurately predicted and individual
h o t - w i r e c a l i b r a t i o n is n e c e s s a r y for q u a n t i t a t i v e recov e r y
temperature measurements. R e c o v e r y t e m p e r a t u r e s
•85 <Tia w < 1.12
were
measured
in
Mach
3
in the range
flow
at
5 60
0R.
Demetriades measured recovery factors in the range .94<qaw <(1.01
using similar probes subjected to similar flow conditions.
No
aspect ratio dependence is visible in either the data presented
here
or
the data of Demetriades.
Data obtained by Stalder et.
al. for h o t - w i r e s in a r a r e f i e d s u p e r s o n i c f l o w w i t h K n u d s e n
numbers
and m o l e c u l a r
speed
ratios
equal
to
those
of
this
experiment consistantly indicate a recovery factor greater than
unity.
P o s s i b l e causes for the d i s c r e p a n c y
f a c t o r s b e t w e e n the
t wo e x p e r i m e n t s
in the recovery
is (I) the flow in the
vicinity of the probe is affected by the support prongs so that
the actu a l R e y n o l d s n u m b e r and K n u d s e n n u m b e r are lower than
for ideal conditions,
and (2) the R vs. W polynomial fit of the
flow calibration data using the method suggested by Demetriades
incorrectly predicts the intercept R(W=O)
recovery
temperature.
which determines the
66
APPENDICES
M
67
APPENDIX A
OVEN CALIBRATION DATA REDUCTION CODE
IO
20
30
40
50
60
■70
80
REH
REH
REM
REM
REM
REM
REM
REM
0VENCAL5
This o ve n - c a l i b r a t i o n program uses Quadratic fit of resistance vs
current squared or c u r rent- s o u a r e d - t i roes-resistance to find the
Zero-cu rr e nt resistance at each temperature,
..,...,,Assumption: wire diaroeter - 0 .00002 i n c h , . , , ...........
Line 180 was added to correct wrong data file info during runs of
1/26/83. If line resistance is c o rr e c t l y written in future data file
s>
90 REM line 180 can be removed.
95 REM ............ UPDATED
MAY 6, 1984 ....................
100 DIM T ( 1 5 > , C 1 < 1 8 1 > , V 1 ( 1 8 1 > , C ( 1 8 1 ) , V ( 1 8 1 > , R ( 1 8 1 ) , C 2 (181).B (181),Bl(ISl)
120 DIM B2(181)fB3(181)
130 DIM R2(16)
140 DIM R 3(16)
150 DIM 69(16)
160 DIM R 6(16)
170 DIM C 3 (18 1 >
180 DIM D(20)rDl(20),D2(20>,00(20),A0(20> ,Al(20),A2(20)
190 DIM V0LT(1081,2)
191 DIM N 2 (7 )
200 INPUT "INPUT OVEN C A L IB RA T I ON DATA F I L E ? "?F1$
210 OPEN "I",*1,F1$
220 PRINT
230 PRINT "THIS IS A Q UA DRATIC R E S I S T A N C E - C U R R E N T FIT WITH O P T I O N S ? '
240 PRINT 1
TYPE 'I' TO FIT R - 12 (R = AtB I2 F C I 4) "
250 PRINT
260 PRINT "
TYPE '2' TO FIT R-RI2 (R=A+BRI2 +CR2I4)"
270 PRINT
280 PRINT "WHICH OPTION DO YOU WANT",290 INPUT Z
300 INPUT "INPUT THE NUMBER OF WIRES IN THIS OVEN CALIBRATION "!NI
310 INPUT "INPUT THE N UMBER OF CURRENTS PER WIRE PER TEMPERATURE "?A3
320 INPUT "INPUT THE N UMBER OF T E M P E RA T U R ES USED '!Tl
330 FOR I= I TO Tl
340 PRINT "INPUT T E M PE RA T UR E NUMBER "!I
350 INPUT T(I)
360 NEXT I
•370 PRINT
380 PRINT
i(roa) = D l t D 2 # ( D I G I T A L COUNTS)
390 PRINT
v (m v ) = D3 t D4 * ( D IG I TA L COUNTS)
400 PRINT
LINE RESISTANCE = D 5 + D6*(TEMP.
410 INPUT "INPUT BI"!BI
4 20 INPUT "INPUT D 2 !D2
430 INPUT ‘INPUT D 3 ! D 3
440 INPUT "INPUT D 4 ;D 4
450 INPUT "INPUT D 5 iR I
460 INPUT "INPUT D 6 !SI
470 FOR I = I TO NI
480 PRINT "INPUT THE INSTRUMENT NUMBER FOR POSITION NUMBER
490 INPUT N2( I >
500 NEXT I
510 INPUT ’INPUT STANDARD WIRE RES IS T A N CE (OHMS/FT) (CR = 2 7 7 9 7 0 )'!R6
520 IF R6 = 0 THEN R 6 = 2 7 7 9 7 0 !
530 FOR I = 1 TO A3*N1*T1
540 INPUT H , V O L T d , I), VOLT (1,2)
550 NEXT I
551 K = I
560 PRINT
570 X2 = l
68
.580 FOR I = I TO Tl
590 12=1-1
600 CIO = I2*N1*A3 + (K-1)*A3 +1
610 FOR J = ClO TO (Cl0 + A 3 - 1 )
620 V l <X2) = V O L T (J >I )
630 Cl (X2 ) = VOLT (J .•2 )
640 X2 = X 2 + I
641 NEXT J
642 NEXT I
650 PRINT
660 PRINT
670 PRINT ‘THIS IS '0VENCAL2' PROGRAM , Z E RO - C U RR E N T RESISTANCES C O M P U T E D ‘
680 IF Z=2 GOTO 710
690 PRINT ‘BY Q UA DRATIC FIT OF R VS 12"
700 GOTO 720
710 PRINT ‘BY Q UA DRATIC FIT OF R VS I 2 R ’
720 PRINT ‘-----------------------------------------------------------------------730 PRINT
740 PRINT
790 FOR J=I TO Tl
800 LET Gl=O
810 LET G2=0
820 LET G3=0
830 LET G 4=O
840 LET GS=O
850 LET G6=0
360 LET GS=O
870 LET G7=0
880 PRINT
890 PRINT
900 PRINT "R - 12 R DATA FOR T (DEG O = 1 JT(J)
910 PRINT ‘----------------------------------- 1
920 PRINT 1I ( M A ) ‘> ’V ( M V ) ‘> ,I 2 ( M A 2 ) * > ‘I 2 R ( M A 2 0 H M ) ‘i ‘R ( O H M ) ‘
930 PRINT
940 FOR N = ( J - I ) *A3+1 TO J*A3
950 LET C(N)=D1+D2*C1(N)
960 LET V ( N ) = D 3 + D 4 * VI(N)
970 LET R(N)=V(N)ZC(N) - (R1 + SI * T(J))
980 LET C2( N )= (C ( N> "2 > *R (N )
990 IF Z=I GOTO 1020
1000 LET C 3 (N >= C 2 (N )
1010 GOTO 1030
1020 LET C 3( N)=C(N)"2
1030 PRINT C ( N ) , V ( N ) , C ( N ) " 2 , R ( N ) * ( C ( N ) " 2 X , R(N)
1040 LET G l = G l + C 3 (N )
1050 LET G 2 = G 2 + C 3 (N )"2
1060 LET G 3 = G 3 + C 3 (N )"3
1070 LET G 4 = G 4 + C 3 ( N )"4
1080 LET G 5 = G 5 + R (N )
1090 LET G6=G6+R(N)*C3(N)
1100 LET G 7= G7 + (C3(N)"2)*R(N)
1110 NEXT N
1120 LET n ( J > = A 3 * G 2 * G 4 + 2 * G l * G 2 * G 3 - G 2 " 3 - A 3 * < G 3 " 2 ) - ( G l ~ 2 ) * G 4
1130 LET D 0( J) = G5 *G 2 *G 4+ G 2 * 0 3 * G 6 + G 1 * G 3 * G 7 - ( G 2 " 2 ) * G 7 - ( G 3 - 2 ) * G 5 - G 1 * G 4 * G 6
1140 LET D 1( J) = A3 * G 4 * G 6 + G 1 * G 2 * G 7 + G 2 * G 3 * G 5 - ( G 2 " 2 ) * G 6 - A 3 * G 3 * G 7 - G 1 * G 4 * G 5
1150 LET D 2( J) = A3 *G 2 * G 7 + G 1 * G 3 * G 5 P G 1 * G 2 * G 6 - ( G 2 " 2 ) * G 5 - A 3 * G 3 * G 6 - ( G 1 - 2 ) * G 7
1160 LET AO(J)=DO(J)ZD(J)
1170 LET Al(J)=Dl(J)ZD(J)
1180 LET A 2 ( J ) = D 2 (J)ZD(J)
1190 FOR N=(J-1)*A3+1 TO J*A3
1200 LET G 3 = G 8 + ( R ( N ) - A 0 ( J ) ~ A 1 (J ) * C 3 ( N ) - A 2 < J ) * ( C 3 ( N ) " 2 ) ) " 2
69
.1210
1220
.1230
1240
1250
1260
1270
1280
1290
1300
1310
1320
1330
1340
1350
1360
1370
1371
1372
1373
1374
1375
1376
1300
1390
1400
1410
1420
1430
1440
1450
1460
1470
1480
1490
1500
1510
1520
1530
1540
1550
1560
1570
1580
1590
1600
1610
1620
1630
1640
1650
1660
1670
1675
1677
1690
1700
NEXT N
LET G 9< J) = Sa R ( G 6 ) / A 3
PRINT
IF Z=I GOTO 1270
PRINT ’CURVE-FIT OF R VS I2R GIVES R ( I = O ) = 1 JAO(J)
GOTO 1280
PRINT 1CURVE FIT OF R VS 12 GIVES R(I=O) = 1JAO(J)
PRINT 1RMS D EV IA T IO N OF R FROM C U RV E - F IT AT THIS TEMP. (O H M S )= 1JGY(J)
PRINT
PRINT
NEXT J
PRINT "SUMMARY! ZERO-C UR RE NT RES IS T A N CE VS. TEMPERATURE 1
PRINT 1-----------------------------------------------------------1
PRINT
PRINT 1TdiEG O 11 1R(OHMS) 1
PRINT
PRINT
F=O
Fl=O
F 2=0
F 3 =O
F4=0
F5=0
FOR J=I TO Tl
PRINT T(J),AO(J)
LET F=FFT(J)
LET Fl=FlFAO(J)
LET F2=F2FT<J)*AO(J)
LET F 3 = F 3 F T (J )"2
NEXT J
LET R 4= (F * F1 -T 1 *F 2) / <F ~ 2- T1 * F 3)
LET R 5=(F1-R4*F)/T1
FOR J=I TO Tl
LET F 4 = F4F( A O ( J ) - R 5 - R 4 JKT(J) >"2
LET F5=F5FG9(J)
NEXT J
LET R7=(SQR(F4))/Tl
LET R8=F5/T1
PRINT
PRINT 1DATA FILE FOR THIS C A LI B R A T I O N IS 1JFl*
PRINT ‘INSTRUMENT N UMBER IS 1JNZ(K)
PRINT
PRINT 1CURVE-FIT OF R(I = O) VS T GIVES? 1
JR 8
PRINT 'AVERAGE R ES IS T AN C E - C U R R E N T D E VI ATION FOR ALL TEMPS (OHMS)
PRINT 1ROtOHMS, AT O DEG O = 1JRS
PRINT 1ARO (OHMS/DEG C)='JR4
PRINT "OVERALL RMS DEVIATION OF R FROM R-T CURVE ( O H M S ) = 1JRT
PRINT 1ALPHA (REFERRED TO RO AS A B O V E , PER DEG O = 1JR4/R5
PRINT 1L(Ciii) = 1 J (12* ( R5 F2 0 * R4 ) / R 6) * 2 . 54
PRINT 1L Z D = 1J1 2 * ( R 5 P 2 0 * R 4 > / < .0 0 0 0 2 * R 6 )
PRINT
PRINT 1HIT CR TO CONTINUE WITH NEXT W I R E 1)
INPUT ZlO
IF K=Nl THEN GOTO 1700
K = KFl
GOTO 560
CLOSE Tl
1710 END
Ok
70
APPENDIX B
FLOW CALIBRATION DATA REDUCTION CODE: INCOMPRESSIBLE FLOW
Iu
ECK
LOrLGV02
11
EZH
TlilZ
12
REH
THE
13
I <t
REM
REH
USING
DEUCY' Z
I T E R A T IO N
**«». * < : A r * * * y * « * * * * * * * * * ,
20
DIM
V ( 2 5 0 > , V l ( 2 5 0 1 , C ( 2 5 0 ) , C l ( 2 5 0 > , n < 2 5 0 ) , C 2 < 2 5 0 ) , C 3 i 2 5 0 )
30
DIM
F I ( 2 5 O) , P X (2 5 O ) , N <2 5 O > , J <2 O ) , B I 2 ( 2 O ) , M ( 2 OJ
“1 0
DIM
D ( 2 0 ) , DO ( 2 0 ) , D l ( 2 O ) , D 2 ( 2 0 ) , A O ( 2 O > , A l ( 2 O ) , A 2 ( 2 0 )
PROGRAM
UZEZ
H O T - U l RE
SO
DIM
BI? ( 2 0 )
60
DIM
M 4 ( 2 0 )
, T l
OATA
EROM
THE
CH AR ACTERIS TIC S.
( 2 0 )
, R 2 ( 2 0 )
, N O (Z O )
LOU
ZEEED
CALIBRATION
CORRECTIONS
FOR
END
TO
. T 2 ( 2 5 0 )
1T 3 ( 2 3 0 >
. H I
( 2 5 0 )
. N 1 ( 2 0 )
DIM
U (2 0)
DIM
T 4 ( 2 0 ) , M S ( 2 0 ) , R 3 k 2 0 ) , 1 1 6 ( 2 0 ) , R- i ( 2 0 ) , K I ( 2 0 ) , N 2 ( 2 0 > , R S ( 2 0 )
70
INPUT
FLOW
C A L IB R A T IO N
100
OPEN
I lO
INPUT
I I 5
LET
T - S / 7 » ( T t 460)
I 2 0
FOR
N - i
130
INPUT
I 40
NEXT
150
PRINT
160
FOR
#i
FOR
INPUT
, Al I , A U
TO
8 I ,Vl
MADE
, P3 < 2 0)
EO
" INPUT
ARE
PROCEDURE.
TO
E l i
DETERMINE
LOSSES
AZ
F IL E
, A i 3 , AS , D l
DATA
F I L E . " ; t I 5
it I
, D 2 . D 3 , D4 , R i
, P , A , - 5 , T , L , D , P 1 1
A 3 * P
( N ) , Cl ( N )
N
" INPUT
J-=I
TO
VELOCITY
PRESSURE
INFORMATION
( F O - F ) , ( F A - P ) "
F
170
INPUT
I SO
DPi =DP* I . 3 7 0 3 8
D F , DPA
1 70
DPA = D P A * I . 8 7 03 8
2 00
FZ = F l I - D P A
210
RI l O= F Z * . 00 1 35 9 4 / ( 29 2 5. 6 * T )
2 20
U ( J ) = ( D P * I.
230
NEXT
240
PRINT
250
PRINT
32 7 92 * 2 / R H O ) * . S
J
2 6 0
PRINT
"Till Z
270
PRINT
"SLOPES
IS
280
PRINT
" ----------------------------- —------------------------------------------------------------------------------------------------------------------------------------------------
290
PRINT
3 0 0
PRINT
3 I 0
PRINT
" PROBE
3 2 0
PRINT
"WIRE
THE
BY
' LOFLOUO I '
QUADRATIC
HOLDER
N O . : " ;
330
PRINT
"PLOW
PRINT
"ALL
DATA
350
PRINT
" AND
BAROMETRIC
360
PRINT
"THE
SUPPORT
370
INPUT
TS
3 8 0
PRINT
PRINT
4 U0
FOR
J - I
4 AC
LET
D=O
4 2 0
LET
Ei=O
430
LET
DZ=O
4 4 0
LET
B3 = 0
4 5 0
LET
C4 - 0
4 6 0
LET
35 - C
TO
4 7 0
LET
Bc=O
4 8 0
LET
B7 = 0
4 7 0
LET
BC=O
5 00
LET
Bf=O
CiO=O
5 I 0
LET
5 2 0
PRINT
5 30
PRiAi
5 4 0
f
5 5 0
L- R I N T
si : N T
CALIBR ATION
VIiICIi
( I . E .
COMPUTES
R= A
+
RESISTANCES
BI ZR
+ C ( I Z R ) 2)
Al I
SHOWN
NO
ARE
; Al 3
FOR
PRESSURE
TEMPERATURE
TEMPERATURE
( IN
MM
LOADING
HO
( I N
DEC
K >
OF: "HF
OF : " ; F l I
( T S - T E ) /TO
IS";
P
"OVERHEAT
' i (ha
F I T S
N O . : “ ; A I Z
3 4 0
390
PROGRAM
R - R 12
TRAVERSES
FOR
FLCV
SPEED
( I N
CM/SEC)
i : c r . A2 >• *, • • i Z R " , " R ( O l i M S ) " , " T U ( D E G
IO "
O F V i U ( J )
AND"
71
5 6 0
FOR
N = ( J - I ) * A3 + I
5 7 0
LET
V ( N ) = D 1 + D 2 * V 1 (N)
C ( N ) = D3 + D4 * C I ( N >
TO
A 3 * J
580
LET
590
LET
R ( N ) = ( V ( N ) Z C ( N ) ) - R l
6 0 0
LET
C Z ( N ) = C ( N ) "2
6 I C
LET
C 3 ( N ) = ( C ( N ) 1Z M R ( N )
6 20
LET
T 2 ( N ) =27 3.
6 3 0
PRINT
6 4 0
LET
E I = B I +C3 ( N )
6 50
LET
E 2 = G2 + C3 ( I i ) 1 2
6 6 0
LET
B 3 = B 3 + C 3 ( N ) 13
670
LET
3 4= B4 + C3 ( N > 14
6 3 0
LET
B5 = B5 + R ( N )
6 9 0
LET
B6 = 3 6 + R ( N ) * C 3 ( N >
700
LET
B 7 •- B 7 + ( C 3 ( N > 1 Z M R ( N )
7 I 0
NEXT’
7 2 0
LET
D ( J ) = A 3 * B 2 * B 4 + 2 * C i * G 2 * B 3 - B 2 - 3 - A 3 * ( B 3
1Z l - C B l
7 30
LET
D O ( J ) =- 3 5* B2 * B4 + 3 2 * D 3 * 36 + 3 1 * 3 3 * 3 7 - ( B 2
12 ) * 3 7 - ( 3 3 12 >* 3 5 - 3 1 * 3 4 * 3 6
C(N)
I 5 +R(N )
Z S - I ZA
, C2 ( N ) , C3 ( N ) , R U ! )
, T Z ( N )
N
740
LET
Dl ( J ) =A3 * 3 4* 36 + G 1 * 32 * 3 7 + 32 * 2 3 * 0 5 - (
7 50
LET
D 2 ( J ) = A 3 * 3 2 * 3 7 + 3 1 * 3 3 * 3 5 + 3 1 * 3 2 * 3 6 - ( 3 2
760
LET
A O ( J ) = D O ( J ) Z D ( J )
770
LET
A l ( J ) = D l ( J ) Z D ( J )
730
LET
A Z ( J ) = D Z ( J ) Z D ( J )
7 9 0
FOR
N = ( J - I ) * A3+1
8 0 0
LET
B8 = D3 + ( R ( N l - A Q ( J ) - A l
8 I 0
NEXT
8 2 0
LET
8 3 0
PRINT
TO
1Z ) *34
32 ' 2 ) * 3 6 - A 3 * 2 3 * 3 7 - D l * 2 4 * G 5
12 ) * 3 5 - A 3 * B 3 * 3 6 - (BI
12 M
37
J * A3
( J ) * C 3 ( N ) - A 2 ( J ) * ( C S ( N ) 1Z ) I 1Z
N
B l Z ( J ) - = S Q R ( CO ) Z A3
840
PRINT
"RESULTS
8 5 0
PRINT
" A O = " ; AG ( J )
860
PRINT
" A N D ;"
870
LET
8 9 0
PRINT
"RE( O K M S ,
9 00
PRINT
" X E ( C C S ) = " ; 6 0 + 8 . 5 8 3 * T 1
OF
TIiE
ASOVE
R(V)=R C
T l ( J ) = A O ( J ) Z S - C
I / A ) +2 7 3 .
, A O ( J )
( J )
910
LET
NO( J ) = I 0 * S Z (3 . I 4 I 6 * L * ( 4 4 6 .
REM
ZERO
930
NOC=NO(J)
940
XO= 4 . 4 6 5 + . 0 7 2 3 3 * T
" N o t= ;
k
2ND
CORRECTED
95 0
PRINT
9 60
K V = 3 02 3 0 * ( I + . 0 0 0 10 7 « ( T l
is
assumed
;T l
( J )
5
I
c o n s t .
NUMBER
=I ce
i n
9 9 0
N I ( J ) = N O ( J ) «( l - l ZSl * T A N K S )
IF
A S S ( D I F F )
IF
DIFFCO
1 0 30
IF
DI F E ) . 00 1
( . 0 0 I
THEN
GOTO
CJ ) / T
I Z S O R ( A M J ) )
c o n v e n t i o n . "
10 5 0
N O C = ( N i ( J ) + N C O
THEN
I=O(MA) = ";
CALCULATION
t h i s
S I = L / D * ( NO C * K G / K V ) 1 . 5
1 0 20
AT
( J > - 2 93 ) )
TANK S=( E X ? ( 3 l ) - E X ? ( - 3 1 ) ) Z ( E X P ( S l ) + E X P C - S l ) )
D i P F = N l ( J ) - N O C
, SI 7 (J)
+7 . 2 3 8 * T I ( J ) ) * A I C J > >
NUSSELT
9 70
1010
P I T : "
D E V l A T I ON=
, " REC . FACTOR=" ;Tl
, "BURNOUT
930
1000
DEGREE
15
, " T E ( D E G K ) - "
920
CURRENT
I 2 R )
" A l ; " ; A l ( J > , " A2 = " ; A 2 ( J ) , "RMS
Z2
NO C = N O C - D I P F Z 2
1040
GOTO
1050
PRINT
970
"EERO-CURRENT
1 0 60
PRINT
"CORRECTION
1070
PRINT
1080
PRINT
1090
PRINT
1100
PRINT
1110
PRINT
1120
PRINT
NUO
FACTOR
( C O R R E C T E D ) = " ; N F ( J ) ; "EXP.
P S l N = " ; NI
"OVERHEAT
DEPENDENCE
" I (MA)
NM
1130
FOR
M = ( J - I ) *AJ+1
1140
LET
NI
1150
N M = N l ( N ) «KC(J)
1160
LET
TO
NC
NUSSELT
FS IN
J * A3
(N)=EXPC ( - A 2 ( J )
EPS=O
OF
/ A l
( J ) )* C3 ( N ))
C = " ; - A : ( J ) Z A l (J;
( J ) Z N 0 (J)
NO.
NCZNE
AT
U ( C M Z S ) = " , U ( J )
TVZTC
( T V - T E ) Z T
PS I R "
72
1170
LCT
1160
KW^ 3 0 2 3 0 * ( 1 t . 0 0 0 1 0 7 * < T 2 < N > - 2 ? 3 > >
NC-MM
119 0
T V - ( T 2 ( N ) - T l
1 2 00
12 10
IF
T 2 (M) ( T l ( J )
CT A M - T 2 ( N ) Z T
I v ) ) / T
GOTO
14 7 0
1 2 20
ETAS. = T 5 t T 1 ( J ) Z T
12 3 0
T I -TW
1240
S 2 ^ A * T Z ( l + A * ( T l ( J > - 2 9 3 ) >
12 5 0
I t V = 4 * AO ( J ) Z ( 3 . 1 4 1 £ * D * 2 )
1260
? 5IC = 0
1 2 70
I t EM
1260
LA M BD A= LZD *( M G * ( K G Z K W ) ) ' .5
CALCULATE
THE
12 9 0
I l U= ( L A M B D A ' 2 - C <N > ' 2 * R V * L ' 2 * S 2 / ( 4 * K W * T ) ) ' . 5
(J) * ( T I - E F S )
CORRECTION
PARAMETERS
1 3 00
X l = N I
13 10
MUT =N U * ( I +S 2 * T V ) ' . 5 * X I
Z (TV*MM)
1 32 0
OMEGA=(EXP(NU) - E X P ( -NU > ) Z ( E X F ( N U ) +E X P ( - M U ) )
1 3 30
OMECAT=C E X P ( N U T ) - C X P ( - N U T )
1340
Cl=OMEGATZNUT
1 3 50
C 2 = O M E C A ZNU
1360
EPS = - T S * ( C l Z ( I - G l ) )
1 3 70
T I = ( T V - T S * G 2 ) Z ( I -G2 )
1380
T C = T V Z ( T I - E P S )
) Z ( C X P ( N U T ) - E X r i -NUT)
1 3 90
PS IN =T C * ( I +S 2 *T I >Z I I +S 2 * T V >
1 4 00
P S I R = I l - ETAS ZE T A M * C I J Z ( I - C l )
1410
IF
1420
REM
A D S ( P S I N - P S I C ) ( . 0 0 1
1430
NC = FS I M « N M
CALCULATE
1 4 40
PS I C = PS I N
1450
GOTO
1 460
PR IN T
THE
GOTO
MEV
)
1460
PARAMETERS
1230
USING
• • # . * * #
# . ###
S . S ft S
S . ft ft s
ft . f t f t f t
s. ft f tf t
ft . ft S ft
f t . Rf t f
&
(N)
, N M , N C , PS I N , NC ZNI ( J )
1 4 70
NE XT
1480
PRINT
, T Z ( N ) Z T l
(J)
, ( T Z ( H ) - T l
(J)
! Z T 1P S I R
N
1490
PRINT
1500
PR IN T
1510
PRINT
1520
NEXT
1530
PRINT
1540
PRINT
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
J
1550
PRINT
"SUMMARY:
15 6 0
PRINT
11M u s s e l
1570
PRINT
" -------------------------------------------------------------------------------------------------------------------------------- "
1580
PRINT
15 9 0
PRINT
1600
PRINT
1610
PRINT
1620
PRINT
t
NUSSCLT
r.o 5 .
" REYNOLDS
&
MO.
shown
NUSSCLT
"U(CMZSEC)
AND
RECOVERY
b e l o w
N O S .
RE
e r e
&
f o r
RCC .
NU
FACTORS"
the
FACTOR
PSIN
16 2 5
T = 9 Z5 * 7 - 4 6 0
1630
FOR
J= I
1 6 40
LET
R2 = I I 3 3 7 * P 1 I > Z ( 2 . 8 8 2 E + G 6 * ( T + 4 6 0 > * ( 5 Z 9 ) )
1650
LET
M 2 = . 0 0 0 0 109 * ( ( 4 6 0 + T )
1 6 60
LET
R 3 ( J ) = D * R 2 * U ( J ) ZM2
1 6 70
PRINT
TO
USING
1680
NEXT
CLOSE
1690
END
J
ft I
BASED
of
ON
zero
c u r r e n t . "
STAG.
CONDITIONS"
ETA"
P
" ft ft s ft . ft ft
' I . 5 > Z ( T + 6 5 9 >
f t . ftftft
N I i J ) , N I CJ ) Z N O ( J ) , T I ( J ) Z ( 5 * ( 4 6 0 + T ) Z 9 )
1 63 4
l i m i t
f t . ftftft
ft . o ft ft
ft . f t f t f t " .
U ( J )
, R S U
73
APPENDIX C
FLOW CALIBRATION DATA REDUCTION CODE: COMPRESSIBLE FLOWS
io
REi I
III
I 2
REM
TH IS
I 4
REM
HOT-WIRE
I6
18
REM
PROCEDURE.
REM
FLOUO 2
PROGRAM
USES
THE
TLO V
CH AR ACTERIS TIC S
DATA
USING
F I L E
TO
DEWEY'S
DETERMINE
THE
CORRECTION
CORRECTED
FACTOR
ITERATON
****************-A************************************** *.****** ***
20 DIM
V( 3 0 0 ) , V l
3 0
DIM
P l ( S O O ) 1P 2 ( 3 0 0 > , N ( 3 0 0 ) , 0 1 2 ( 2 0 ) , M ( 2 0 ) , J ( 2 0 )
( 3 0 0 )
, C ( 3 0 0 ) , C l ( 3 0 0 ) , R ( 3 0 0 ) , C2 ( 3 0 0 ) , C3 ( 3 0 0 )
40
DIM
D (2 0)
5 0
DIM
0 1 7 ( 2 0 ) , T 1 ( 2 0 ) , N O ( 2 0 ) , T 2 ( 3 0 0 ) , T 3 ( 3 0 0 ) , N 1 ( 3 0 0 ) , N I ( 2 0 )
, D 0 ( 2 0 )
, D I (2 0)
, D 2 ( 2 0)
, A 0 ( 2 0 >
,A l
( 2 0 )
,A 2 ( 2 0 >
60
DIM
M4 ( 2 0 ) , R2 ( 2 0 ) , P 3 ( 2 0 ) , KR ( 2 0 )
70
DIM
T 4 ( 2 0 ) , M 5 ( 2 0 ) , R 3 ( 2 0 ) , M 6 ( 2 0 ) , R 4 ( 2 0 ) , K 1 ( 2 0 ) . N 2 ( 2 0 ) , R 5 ( 2 0 )
8 0
INPUT
90
OPEN
" INPUT
F l 5
I 0 0
INPUT
I I 0
FOR
I20
INPUT
# I ,
M - I
I 30
NEXT
I 3 I
LET
I 4 0
PRINT
FLOW
FOR
C A LIBR ATION
INPUT
AS
F I L E
DATA
F I LE : " ; F I 5
41
A l l , A 1 2 , A 1 3 , A 3 , D 1 , D 2 , D 3 , D 4 , D 5 , D 6 , D 7 , D 8 , R 1 , P , A , S 1T 1 L 1 D
TO
A 3 * P
S l 1V l ( N ) , P l ( N ) , P 2 ( N ) , C l ( N )
N
T - 5 /9 * (T + 4 6 0 )
I 50
PRINT
I L0
PRINT
'TH I S
I 7 0
PRINT
'SLOPES
I 8 0
PRINT
1 90
PRINT
200
PRINT
IS
2 I 0
PRINT
"PROBE
220
PR I NT
"WIRE
THE
BY
HOLDER
2 3 0
PRINT
"FLOW
PR I NT
"ALL
DATA
2 4 5
PR I NT
"THE
SUPPORT
2 44
INPUT
TS
2 4 7
PRINT
" INPUT
2 4 8
INPUT
PR
2 5 0
PRINT
2 60
F I T S
WHICH
( I . E .
COMPUTES
R=A
+
RESISTANCES
B I 2R
AND"
+ C ( I 2 R )2) '
N O . :" ; A I I
PRINT
C A LIBR ATION
SHOWN
FOR
J =
280
LET
B= O
2 9 0
LET
Dl = O
3 0 0
LET
□ 2 = 0
3 I 0
LET
C3 = 0
3 2 0
LET
□ 4 = 0
330
LET
ES = O
3 4 0
LET
36= 0
3 5 0
LET
C7 = 0
3 6 0
LET
S8 = 0
3 7 0
LET
□9 = 0
3 8 0
L ET
□ 10 = 0
3 9 0
FOR
N = ( J - I ) * A3 + I
4 0 0
LET
3 9 = □9 + P I ( N )
B I Q -- E I 0 * P 2 ( N >
N O . : " ; Al 3
ARE
FOR
TEMPERATURE
PRESSURE
270
TO
PROGRAM
R-R I 2
N O . : " ; Al 2
2 4 0
I
' H I F L OWO I 1
QUADRATIC
MEASURED
STAG.
TEMPERATURE
LOADING
FOR
(DEG
( T S - T E ) Z T O
DETER MINATION
X)
O F : " ;T
I S ";
OF
M
( I -STATIC ,
CR-PI TOT >
P
TO
4 I 0
LET
420
NEXT
430
LET
BI I = B9 / A 3
4 4 0
LET
S I 2 ( J ) = D 5 + D 6 * 3 I I
4 5 0
LET
B I 3= B I 0/A3
4 6 0
LET
BI 4 = D 7 * D 0 * 3 1 3
4 7 0
LET
4 72
I F
480
LET
4 9 0
LET
500
IF
J * A3
N
BI S = C l 4 Z E l 2 ( J )
PR=I
GOTO
544
M= I + S O R ( - 5 * L O G ( C I 5 ) >
□ 1 6 = ( ( l + 1 . 1 6 6 7 * ( M ‘ 2 - l ) ) * ( - 2 . 5 ) ) * ( ( ( 2
( 3 I 5 - 3 I 6) Z3 I 5
(=
.00 1
GOTO
540
4 * ( M 2 ) ) Z ( . 4 * ( M 2 ) + 2 ) )
3 . 5 )
74
510
520
530
540
LCT M 1 - M * ( 1 - ( B 1 5 - B 1 6 ) / ( 4 * B 1 5 ) )
LET M=Ml
GOTO
490
LET M ( J ) = M
542
GOTO
544
M( J )=-(((
5
5 0
550
PRINT
560
PRINT
570
PRINT
5 8 0
PRINT
590
PRINT
I ZB I 5 ) ‘ . 2 8 5 7 I 4 - 1 ) * 5 ) "
"OVERHEAT
"LOCAL
TRAVERSES
" I ( M A ) " , " I 2 ( MA 2 ) "
POR
N = ( J - I >*A3 T I
0 I 0
LET
V ( N ) = D1 + D 2 * V 1 ( N )
TO
6 2 0
LET
C ( N ) =D3 + D 4 * C I ( N )
LET
R ( N ) = ( V ( N ) Z C ( N ) ) - R l
, " I 2 R" , " R ( OHMS)"
640
LET
C 2 ( N ) = C ( N ) "2
650
LET
Co(N ) = ( C ( N )
660
LET
T 2 ( N ) = 2 7 3 . I 5 + R ( N ) Z S - I / A
, " T W ( DCG
K>"
‘ 2 ) * R ( N >
670
PRINT
68 0
LET
BI = B l + C 3 ( N)
690
LET
B 2 = B 2 + C 3 ( N ) '2
700
LET
E 3 = 0 3 + C 3 ( N ) •3
710
LET
B 4 = 3 4 + C 3 ( N ) ‘ 4
C ( N ) , C 2 ( N ) , C 3 ( N ) , R ( N ) , T 2 (N)
720
LET
BS= 0 5 +R(N)
730
LET
B 6 = B 6 + R ( N ) * C 3 (M)
7 40
LET
E7 = E7 + ( C 3 ( N )
750
NEXT
6 0
H G ) = " ; BI 2 ( J )
A 3 * J
630
7
P O (MM
M =u JM (J)
60 0
770
.5
EOR
* 2 ) * R ( N )
N
LET
D ( J ) = A 3 * E 2 * E4 + 2 * E I * E 2 * E 3 - B 2 ‘ 3 - A3 * ( E 3 ‘ 2 ) - ( E I ‘ 2 ) * E 4
LET
D 0 ( J ) = 3 5 * B 2 * B 4 + E 2 * B 3 * B 4 + E 1 * E 3 * 3 7 - < E 2 * 2 ) * S 7 - ( 3 3 * 2 > * B 5 - E 1 * S 4 * B 6
7 8 0
LET
D I ( J > = A 3 * B 4 * E 6 + B t * B 2 * B 7 + B 2 * C 3 * B 5 - ( B 2 " 2 > * B 6 - A 3 * B 3 * B 7 - E l * D 4 * B 5
790
LET
D 2 ( J ) = A 3 * B 2 * B 7 + 3 1 * 3 3 * 3 5 + 3 1 * B 2 * 3 6 - C S 2 * 2 ) * 3 5 - A 3 * 3 3 * B 6 - ( B 1 * 2 ) * B 7
800
LET
A O ( J ) = D O ( J ) Z D ( J )
810
LET
A l ( J ) = D l ( J ) Z D ( J )
820
LET
A 2 ( J ) = D 2 ( J ) Z D ( J )
8 3 0
FOR
N = ( J - I ) * A3 + I
84 0
LET
B8 = B8 + ( R ( N ) - A O ( J ) - A I ( J ) * C 3 ( N ) - A 2 ( J ) * ( C 3 ( N ) ‘ 2 ) )
850
NEXT
TO
J* A3
86 0
LET
870
PRINT
BI 7 ( J ) = S O R ( E O )
PRINT
"RESULTS
8 9 0
PRINT
" AO = " ; A O ( J ) , " A l = " ; A l ( J > , " A 2 = " , A 2 ( J )
900
PRINT
“ AND:"
910
LET
9 20
PR IN T
30
T l
PRINT
OF
Z A3
880
9
‘ 2
N
( J ) = A O ( J )
THE
ABOVE
R ( V ) = R ( I 2 R )
Z S - ( I Z A ) +2 7 3 .
2ND
DECREC
, "RMS
F I T : "
D E V I A T I O N = " ; B 1 7 (J)
15
" R E (OHMS>=" ; A 0 ( J ) , "T E ( DECK) = " ; T I ( J ) , " R E C . F A C T O R = " ; T l
" K E ( C C S >=" ; 6 0 +8 . 5 8 3 * T 1 ( J ) , " B U R N O U T
940
LET
N O ( J ) = I O * S Z ( 3 . 1 4 1 6 * L * ( 4 4 6 . 5
950
REM
ZERO
960
NOC=MO(J)
970
KO= 4 . 4 6 5 + . 0 7 2 3 8 *T
975
KV= 3 0 2 3 0 * ( I + .0 0 0 I 0 7 * { T I ( J ) - 2 9 3 ) )
CURRENT
976
ETAMO = T S t T l
9 7 7
K R ( J ) = K O ZKV
CORRECTED
I
NUMBER
( J ) Z T
9 80
S I = L / D * ( N O C * KO Z K V ) 1 . 5
9 9 0
T AMI LS = ( E X F ( S l ) - E X r ( - S l > > Z ( E X F ( S l > + C X r ( - S l > >
NI ( J ) = N O ( J ) * ( 1 - 1 ZSl * T A N K S )
i o i o
D i r r = N i ( J ) -Noc
1020
IF
A B S ( D I F F )
1030
I r
D lFF
(
0
1040
IF
DIFF
>
.001
1050
GOTO
980
(
.001
THEN
GOTO
1060
NO C=( N I ( J ) + N O C ) Z2
THEN
N O C = N O C - D I F F Z 2
( J ) /T
I = 0 ( M A ) = " ; 1 Z 5 Q R ( Al ( J ) )
+ 7 . 2 3 8 * T 1 ( J ) ) * A 1 ( J ) >
NUSSELT
1 0 0 0
AT
CALCULATION
75
1060
THINT
" Z EHO-CURHEHT
1065
PRINT
"CORRECTION
1070
PRINT
1080
PRINT
1090
1110
PRINT
PRINT
112
0
"OVERHEAT
PRINT
"I
NUO
( C O R R E C T E D ) ;N I ( J )
FACTOR
DEPENDENCE
(MA)
MM
OF
NC
NUSSELT
PSIN
PRINT
1140
POR
N = ( J - I >* A 3 + I
116 0
LET
N I ( N ) = EXP ( ( - A2 ( J ) / A I ( J ) )* C3 ( N ) )
IlSO
N M = N l ( N ) * N 0 ( J )
1190
LET
EPS=O
1174
LET
HC=NM
KV=3 0 2 3 0 * ( I + . 0 0 0 1 0 7 * ( T Z ( N ) - 2 7 3 ) )
1230
T V = ( T Z ( N ) - T l ( J ) ) / T
1 2 35
I P
E T A M = T Z ( N ) / T
T Z ( N ) ( T l
( J )
GOTO
1241
E T A S = T S t T l ( J ) Z T
1245
T I = T V
1250
S 2 = A * T / ( I + A * ( T I ( J ) - 2 7 3 ) )
RV =4* AOCJ) / ( 3
1270
PSIC=O
1280
RCM
L A M S D A = L / D * ( NC * ( K O / K V ) ) 1 . 5
CALCULATE
THE
CORRECTION
1 300
N U = ( L A M B D A ' 2 - C ( N ) ' 2 * RV * L ' 2 * S 2 / ( 4 * K V * T >
X I = N I ( J ) *
1310
NUT =N U * ( I +32 * T V )
1 32 0
OMEGA= <E X P ( N U ) - E X P ( - N U ) ) /
1330
OMEGAT=( E X P ( N U T ) - E X P t -N U T)
1 3 40
G l = OME G A T / N U T
1350
GZ=OMCCAZNU
) / ( EXP ( NUT X - E X P t -NUT)
EPS = - T S * ( C l Z ( I - G l ) )
1385
T C = T V Z ( T I - E P S )
1 3 70
FSIN =T C * ( I + 5 2 ' T I
1 4 00
PS I R = ( I - E T A S Z E T A M * G I ) Z ( I - C l
1410
IF
1420
REM
1 4 60
NC = F S I N * NM
C (N)
) ' .5
( E X P ( N U ) + E X F ( - N U ) )
T I = ( T V -T S * G 2 ) /
CALCULATE
)
( I - G2 )
) / ( I +52 *TV)
A B S ( P S I N - P S I C )
PRINT
PSIR"
' . 5 * X I
1 3 80
1480
( T V - T E ) Z T
( T I - E P S ) / ( T V * Nil)
1 3 60
P S I c =P SIN
T V /TC
HG >=" ; B I 2 ( J >
PARAMETERS
1305
GOTO
P O ( MM
. I 4 I 6 * D • 2>
1 2 70
1470
AT
1470
1 260
1465
C = " ; - A 2 ( J ) Z A l ( J )
J * A3
1220
1240
NO.
NC / NE
1130
TO
;"EXT.
P S I N = " ; N I ( J ) / N O ( J )
( . 0 0
THE
I
NEV
)
GOTO
1480
PARAMETERS
1290
USING
" « . » # »
# . # # #
# . SS#
It . It # it
It . It it It
, N M 1N C , P S I N 1 N C Z N I ( J ) , T 2 ( N ) / T l ( J > , ( T 2 ( N ) - T l
1470
NEXT
1500
PRINT
4 . Ittttt
I t . Itl ttt
I t. Itittt
( J ) >/ T , PSIR
N
1510
PRINT
1520
NEXT
1530
PRINT
1540
PRINT
J
15 5 0
PRINT
" SUMMARY :
1560
PRINT
" -------------------------------------------------------------------------------------------------------------------------------- "
1570
PRINT
1580
PRINT
1570
PRINT
1 6 00
PRINT
1610
PRINT
" RE 0
6
"PO(MM)
NU SSELT
CORRECTED
NO.
NUSSELT
M
16 15
T= 7 Z5 * T - 4 6 0
1620
FOR
J = I
1630
LET
P3 ( J ) = I 3 3 7 * C I 2 ( J )
16 40
LET
M 2 = . 0 0 0 0 10 7* ( ( 4 6 0 + T )
TO
AND
RE
RECOVERY
N O S .
C
KU
P
' I . 5 ) Z ( T + 6 59 )
FACTORS"
REC .
PS IN
FACTOR
BASED
ETA
GN
P S I R
STAG.
COND. "
KN"
76
1650
LET
M 3 - .
1660
LET
1670
LET
114 <J) = < I » .2* <M< J >V 2 ) >
n2(J)^P3(J)*11(J>»( 1/M2)*M3*(K4(J) * (-
0006 7 6 / S O R ( ( 5 / 7 ) * ( T + 4
6 0 ))
1 . 5 ) ) * ( ( ( 1 / M 4 ( J ) ) + ( 1 ? 3
6 / ( 4 6 0 + T ) 6
) ) / ( ( ! + ! 7 8 . 6 / ( 4 6 0 + T l ) ) )
1680
L E T T 4 ( J ) = ( 5 / 7 > * ( T + 4 6 0 ) / 114 ( J )
1670
LET
M 5 ( J ) - . 0 0 0 0 1 G ? * ( < ( ? / 5 ) * T 4
1700
LET
R3(J) an 2 (J )* M 5( J) / M2
1710
LET
M 6 ( J ) = . 0 0 0 0 1 0 7 * < ( ( ? / 5 ) * T l < J ) ) ' 1 . 5 ) / (
1720
LET
R 4 ( J ) - R 2 ( J ) +1 1 5 ( J )
1730
LET
Kl ( J ) = 60 ! +8 . 5 S 3 * T I ( J )
1740
LET
K 2 - 6 0 + 8 . 5 8 3 * ( 5 / 9 ) * ( 4 6 0 + T >
1750
LET
N 2 ( J ) = N C ( J ) + K l ( J ) /XE
R 5 ( J ) =SOR( D * R 3 ( J ) )
<J > ) ‘ I . 5 > / < ( 7 / 5 ) * T 4 ( J ) + 1 7 8 . 6 )
( 7 / 5 ) * T 1 ( J ) + I 78 . 6 )
/ 116 ( J )
1760
LET
17 6 2
E T AM O = T l
1764
E T A S O = T S t T l ( J ) /T
17 7 0
NUO = L Z D * ( N I
1 78 0
O H E G AO = ( E X T ( N U O > - E K F ( - N U O ) ) / ( E X r ( N U 0 ) - r E X r ( - N U O ) )
(J)
/T
( J > * K R ( J ) ) ' .5
1 7 70
F S I R O = ( I - E T A 3 0 / ETAMO * O M E C A O / N U 0 ) / ( I - OME GA 0 / N U 0)
18 0 0
KN= I . 4 8 2 7 4 * M ( J )
1810
PRINT
BI 2 ( J )
USING
,M ( J )
1620
NEXT
1830
PRINT
1840
PRINT
1845
CLOSE
1850
END
/ ( R 2 ( J ) * D )
" SSS . # #
, D * R 3 ( J ) ,NI
J
SI
(J)
S . S8 S
S . S S S
8. #88
, N I ( J ) / H O ( J ) , T I ( J ) / (
8 . 8 8 8
5 * ( 4 6 0 +T > / 7 )
8 . 8 8 8
, P S I R O 1 KN
8 . 8 8 8
8 8 . 8
77
APPENDIX D
HOT-WIRE R E S ISTANCE-TEMPERATURE COEFFICIENTS
20 uin. Wires
PROBE
&/d
RrIOSDiiD
30/4/1
30/2/2
30/3/1
26/4/1
25/3/1
27/3/1
29/8/1
29/8/2
29/3/1
25/2/1
25/2/2
06/6/1
06/6/2
29/1/1
29/1/2
29/1/3
27/2/2
27/2/3
26 / 3/1
17/5/1
17/5/2
28/3/1
06/2/1
06/2/2
25/4/1
29/4/1
29/2/1
128
132
134
13 8
166
187
2 06
57.45
59.4
60.37
61.99
74.41
84.22
92.78
94.68
92.9
96.97
96.94
100.56
103.97
103.7
105.17
105.6
110.4
110.09
122.65
126.56
126.56
129.78
131.2
131.6
137.95
148.81
181.9
211
207
216
216
224
231
235
235
235
246
245
274
281
2 82
289
292
293
3 07
331
405
O 1xlO3 (I/ 0O
1.773
1.579
1.559
1.581
1.549
1.566
1.574
1.530
1.546
1.632
1.571
1.572
1.511
1.594
1.600
1.5 83
1.5 87
1.587
1 .705
1.547
1.567
1.613
1.568
1.565
1.573
1.568
1.567
78
50 uin. Wires
PROBE
&/d
R (0.0 0 0 0
29/7/1
29/7/2
09/4/1
06/5/1
29/5/1
07/7/1
26/5/1
07/4/1
17/4/1
06/4/1
29/6/1
09/3/1
07/6/1
94
94
176
186
225
227
259
293
295
413
416
419
448
16.96
16.74
31.7
33 .23
40.34
40.59
46.52
52.56
52.86
74.14
74.65
75.15
80.39
rer:cl03 (I/ O O
1.419
1.624
1.602
1.674
1.5 91
1.657
1.562
1.606
1.634
1.626
1.590
1.679
1.575
79
APPENDIX E
FLOW CALIBRATION RESULTS
M=3; d=20 yin.
FLOW
C A L I E R A T i OI F
N
RE
RESULTS ;
NUN
NUC
PROBE
ii
P S IN
. j 0 V <1 Z 2
LTA
KN
i /s
3 . 0 5 1
I .116
I .427
I .067
0 .7 46
0 .971
I . o i l
26o
3 . 0 5 1
I .0 76
I .378
I .023
C . 7 4 2
0 .965
. 6 / 2
.258
3 . 0 5 2
I .0 38
I .353
I .0 00
0 .739
0 .966
I
.7 33
.26 1
3 . 0 5 5
0 .9 98
I .38 1
I .026
0 . 7 4 3
0 .967
I .60 1
3 . 0 5 9
0
959
I .309
0 .961
0 . 7 3 4
0 .960
I . 8 74
.266
3 . 0 6 2
0 . 919
I .430
I .0 69
C . 7 4 8
0 .975
I .955
.252
3 . 0 6 6
0 .881
I .360
I .0 07
0 .740
0 .970
2 .037
.260
3 . 0 6 7
0 . 83 9
I .362
I .003
0 . 7 4 0
0 .970
2 .14 1
.260
3 . 0 6 ?
0 .306
I .227
0 .8 38
0 . 7 2 4
0 .959
2 . 2 28
.277
3 . 0 7 0
0 , 764
I .3 13
0 .965
0 . 7 3 5
0 .967
2 .350
.266
3 . 0 6 9
0 .7 28
I .243
0 .902
0 . 7 2 6
0 .963
2 ..4 6 4
. 2 75
3 . 0 6 4
G
,. 6 9 3
I .267
0 .923
0 . 7 2 9
0 .966
2 .59 1
.27,2
3 . 0 6 4
0 . 659
I .332
0 .932
0 . 7 3 7
0 . 9 75
2 . 7 25
.263
3 . 0 5 9
0 .63 0
I .327
0 .97 7
0 . 7 3 6
0 .976
2 .8 52
.264
3 . 0 6 0
0 . 589
I .134
0 . 3 49
0 . 7 1 7
0 . 9 59
3 .051
.283
KN
I ZS
F L O W'
CALIBR ATION
M
RE
RESULTS :
NUM
NUC
PROBE
#
F S IN
.256
: 26 Z 4 / I
ETA
3 . 0 4 0
I .. 0 6 7
0 . 7 22
0 .4 69
0 .6 49
0 .883
I .690
.353
3 . 0 4 0
I .. 0 3 0
0 .7 03
0 . 4 5 2
0 . 6 4 3
0 .8 79
I .75 1
.360
3 . 0 4 0
0 .994
0 .708
0 .4 56
0 . 6 45
0 .890
I .814
. 3 58
3 . 0 4 0
0 ,. 9 5 8
0 .689
0 .440
0 .6 39
0 .8 80
I .8 83
.364
3 . 0 4 0
0 .920
0 . 6 75
0 .4 27
0 . 6 3 4
0 .876
I .960
.370
3 . 0 4 0
0 .882
0 .656
0 .411
0 .627
0 .87 3
2 .0 44
.377
3 . 0 4 0
0 .8 45
0 . 6 62
0 .4 16
0 . 6 2 9
0 .884
2 .1 33
. 375
3 . 0 4 0
0 .610
0 .640
0 . 3 9 3
0 .621
0 .8 78
2 .22 5
.363
3 . 0 4 0
G .771
0 .652
0 .408
0 . 6 2 5
0 .882
2 .337
.378
3 . 0 4 0
0 .. 7 3 4
0 .646
0 .40 4
0 .624
0 .886
2
454
.380
3 . 0 4 0
C .696
0 .6 08
0 .3 69
0 .608
0 .860
2 .591
.398
3 . 0 4 0
0 ,, 6 6 0
0 .619
0 .379
0 . 6 1 2
0 .87 4
2 .732
.393
3 . 0 4 0
0 .6 22
0 . 6 26
0 .385
0 .615
0 .883
2 . 8 97
. 3 90
3 . 0 4 0
0 .. 5 8 5
0 .60 1
0 .36 4
0 .605
0 .87 3
3 .082
.40 1
I
80
FLuU CALIBRATION RESULTS. FKOEE (I . 25/ 3/ 1
M
RE
NUM
NUC
P S IN
ETA
G . 4 26
0 .25?
0 . 6 0 ?
0 . 3 8 6
I . 6 6 *1
G
SI ?
0
254
O.oOO
O.OSg
;
i
3 .031
I .033
3
031
I
3
033
I .30?
G
40?
0
245
0 . 5 7 ?
0 .667
3
035
C
?G S
0
400
0
-3 7
0 . 5 / 6
v . 6 8 —
3
0 40
0
3 2 7
C
3 I 4
0
2 32
0 . 5 3 6
0 . 3 8 2
3
043
0
36 5
0
3 ? Ci
0
2: 3
u . 5 3 o
0 .887
3
044
G
S 4 I
G
3 i 7
C
235
0 . 5 ; .
5 . 6 6 4
3
044
0
S I 0
G
3 76
Cl
2 I 6
0 . 5 7 5
3
047
G
7 7 3
U
3 7 I
0
2 I 2
3
045
0
733
0
3 7 0
G
3
044
G
6? 7
0
3 6 I
3
042
0
66 1
0
36 I
FLOW
0 4 7
CALIBRATION
M
RE
1/S
. 2 / 0
722
6 o I
.H
G/
.
; -i
7 -t O
. 'I A 7
I
0 3 4
.422
I 20
.416
0 . 6 7 3
2
222
.433
0 . 5 7 1
0 . 8 7 1
2
32?
.420
2 I I
0 . 5 7 1
0 . 6 6 0
2
45 7
.438
Cl
2 0 4
0 . 5 6 3
0 . 6 7 5
2
5 63
.447
0
203
0 . 5 6 3
0 . 3 7 ?
2
724
. 4 47
RE SU LTS:
NUM
KN
PROBE
NUC
#
PS IN
:
ETA
KN
I /S
I .1 18
0 . 4 5 3
0 .283
0 . 6 2 4
0 . 86 9
I . 6 08
.380
I . 0 75
0 . 4 5 0
0 .2 60
0 .622
0 . 6 9 5
I .67 1
.382
3 . 0 5 5
I .037
0 . 4 3 8
0 .270
0 .6 16
I . 7 33
.389
3 . 0 5 8
0 . ?? 7
0 . 4 3 1
C .263
0 .611
0 .891
I .80 1
.394
3 . 0 6 2
0 .95?
0 . 4 2 4
0 .257
C .6 07
0 . 8 9 2
I . 3 73
.398
3 . 0 6 5
0 .. ? I 7
0 . 4 0 4
0 .24 1
0 .59 5
0 . 6 6 5
I .9 53
.412
3 . 0 7 1
0 .877
0 . 4 1 0
0 .246
0
599
0 . 6 9 1
2 .047
.40 7
3 . 0 7 6
0 . 63 7
0 . 4 0 5
0 .241
0 . 5 95
0 . 8 9 0
2 .14 3
.411
3 . 0 7 6
0 .801
0 . 3 9 5
0 .2 33
0 .5 68
0 . 6 9 1
0 .760
C .2 37
0 . 5 9 2
0 . 9 0 0
2 .23?
I .36 1
.419
3 . 0 7 3
3 . 0 7 5
0
0 . 3 7 6
0 .216
0 .574
0 . 6 6 4
2 .461
.434
.443
729
:
3 . 0 5 4
3 . 0 5 3
.415
3 . 0 7 2
0 .69 1
0 . 3 6 7
0 .2 08
0 . 5 6 7
0 . 6 6 0
2 .5 95
3 . 0 7 0
0 .6 59
0 . 3 6 4
0 .2 05
0 .564
0 . 6 8 5
2 . 7 23
.446
3 . 0 6 1
0 . 619
0 . 3 4 ?
0 .19 3
0 .55 2
G . 860
2 .899
.460
FLOU
CALIBR ATION
H
RE
RESULTS:
NUli
NUC
PROBE
U
P S iN
: 27 / 3 / I
ETA
KN
1/S
3 . 0 3 /
I . 0 6/
G . 445
G . 302
G . o /6
G .. 6 6 5
I ., 6 0 6
.324
3 . 0 4 3
I . 02 9
ti . 4 4 9
G . 30 5
G . 6 7 v
0 . 6 7 1
I . 752
.322
3 . 0 4 5
0 . 9 90
0 .. 4 2 6
G ,. 2 6 5
0 . 666
0 .. 8 6 2
I . 6 2 1
.333
3 . 0 4 9
0 . 9 4 3
0 . 4 10
G .. 2 7 1
0 ., 6 6 1
0 .. 8 5 3
I . 9 0 1
.341
3 . 0 5 5
0 .. 9 0 8
0 ., 4 0 5
0 .266
G .. 6 5 8
G . 855
I . 9 82
.345
3 . 0 5 9
0 . 86 8
G .. 4 0 5
G .. 2 6 7
G . 656
0 . 660
2 .. 0 7 3
.344
3 . 0 6 2
0 ., 8 3 1
0 . 3 /3
0 .2 55
0 .. 6 5 1
0 .656
2 . 165
.352
3 . 0 6 3
0 .. 7 9 3
0 ., 3 9 4
G .. 2 5 7
0 . 652
0 . 665
2 . 26?
.35 1
3 . 0 6 1
0 .756
0 .385
0 . 2 49
0 .6 46
G .856
2 . 3 7?
. 356
3 . 0 6 1
0 . 716
0 . 275
0 .240
0 .. 6 4 0
0 .65 3
2 ,. 5 0 5
.363
3 . 0 5 ?
0
686
0 .360
0 . 2 45
G .643
G .864
2 . 6 25
.35?
3 . 0 5 6
0 .653
G. 356
G .22 4
0 .. 6 2 8
0 .65 4
2
. 3 76
3 . 0 5 6
0 .616
0 .336
0 . 2 08
Q .615
0 .647
2 .92 1
.390
3 . 0 5 5
0 . 576
U.345
0 . 214
0 . 621
0 .556
3 .116
.384
756
81
FLOV CALIBRATION RESULTS:
11
RE
PROBE
NUM
NUC
it :27/3/2
PS IN
ETA
RN
I / S
3 . 0 4 4
1 . 1 1 3
0 . 4 5 2
0 . 3 0 7
0 . 6 8 0
0 . 9 2 3
I .6 17
.322
3 . 0 4 6
1 . 0 7 0
0 . 4 2 2
0 . 2 8 0
0 . 6 6 5
0 . 9 1 6
I .6 82
.336
3 . 0 4 8
1 . 0 3 2
0.431
0 . 2 6 9
0 . 6 7 0
0 . 9 2 0
I .744
.332
3 . 0 5 1
0 . 7 ? I
0 . 4 0 6
0 . 2 6 9
0 . 6 5 6
0 . 9 1 2
I .815
.344
3 . 0 5 5
0 . ? 5 2
0 . 4 0 6
0 . 2 6 9
0 . 6 5 8
0 . 9 2 0
I .836
.344
3 . 0 5 ?
0 . ? I 2
0 . 3 6 7
0 . 2 5 0
0 . 6 4 7
0 . 9 1 1
I .9 70
.356
3 . 0 6 4
0 . 8 7 1
0 . 3 8 6
0 . 2 4 9
0 . 6 4 6
0 . 9 1 2
2 . 0 63
.35 7
3 . 0 6 5
0 . 8 3 4
0 . 3 7 5
0 . 2 4 0
0 . 6 3 9
0 . 9 1 3
2 .15 4
.364
3 . 0 6 c
0 . 7 9 6
0 .3 6 ?
0 . 2 3 3
0 . 6 3 4
0 . 9 10
I . 2 56
.36 9
3 . 0 6 2
0 . 7 5 2
0 . 3 5 3
0 . 2 2 1
0 . 6 2 5
0 . 9 0 7
2 .390
.379
3 . 0 6 5
0 . 7 2 0
0.341
0 . 2
10
0 . 6 1 c
0 . 9 0 0
. 4 95
. 3 88
3 . 0 c c
0 . oS 3
0 . 3 4 4
0 . 2 1 3
0 . 6 1 6
0 . 9 0 6
2 .6 30
. 3 8 o
3 . Cc I
0 . 6 5 1
0 . 3 3 ?
0 . 2 0 6
0 . 6 1 5
0 . 9 1 0
2 .7 66
.390
3 . 0 6 3
0 . 6 1 7
0 . 3 2 3
0 . 1 9 4
0 . 6 0 1
0 . 9 0 4
i .9 11
.404
3 . 0 6 0
0 . 5 7 7
0 . 3 : 6
0 . 1 9 7
0 . 6 0 4
0 . 9 1 1
3 .116
.40 1
FLOW
CA LI BRATI ON
H
RE
RE SULTS:
PROBE
NUM
NUC
it
P S IN
2 9 / 3 / 1
RN
ETA
I / S
3 . 0 4 2
I
070
0 . 4 7 2
C . 3 4 2
0 . 7 2 4
0 .892
I .6 83
.27 6
3 . 0 4 6
I
030
0 . 5 0 2
G . 3 o 9
0 . 734
0 .907
I .7 49
.266
3 . 0 4 3
0
9 9 I
0 . 4 7 1
0 . 3 4 I
0 . 7 2 4
0 .899
I .817
.276
3 . 0 5 4
0
9 4 9
0 . 4 6 6
0 . 338
0 . 7 23
0 .899
I .895
.273
3 . 0 5 3
0
9 07
0 . 4 5 0
0 . 322
0 . 7 I 6
0 .896
I .9 83
.284
3 . 0 6 4
0
865
0 . 4 5 5
0 . 32 7
0 . 7 I 8
0 .903
2 .07 8
.282
3 . 0 6 7
0
8 2 6
0 . 4 6 9
0 . 339
0 . 7 2 3
0 .907
2 .1 76
.277
3 . 0 7 1
0
7 5 I
0 . 4 4 7
0 . 3 2 0
0 . 7 I 5
0 .904
2 .3 90
.286
3 . 0 7 0
0
7 I 4
0 . 4 3 8
0 . 3 I I
0 . 7 I I
0 . 9 00
2 . 5 15
.289
3 . 0 6 9
0
67 S
0 . 4 1 9
0 . 29 4
0 . 7 0 3
0 .89 6
2 .6 50
.297
3 . 0 6 8
0
6 43
0 . 3 8 7
0 . 2 6 7
0 . 6 8 9
0 .884
2 .7 93
.312
3 . 0 6 9
0
6 0 4
0 . 3 9 5
0 . 27 3
0 . 6 9 2
0 .86 4
2 .9 73
.308
FLOW
CALIBR ATION
M
RE
RESULTS:
PROBE
NUM
NUC
tt
PS lN
2 3 / 3 / 1
ETA
RN
I /S
3 . 0 2 0
I
157
0 . 2 6 8
0 . I 9 8
0 . 7 40
I . 0 25
I .559
3 . 0 2 6
I
090
0 . 2 8 7
0 . I 9 7
0 .740
I .029
I -.65 3
3 . 0 2 8
I
0 4 9
0 . 2 7 4
0 . 204
0 . 7 4 4
I .034
I .718
. 257
3 . 0 3 2
I
009
0 . 2 4 7
0 . I 6 0
0 . 7 26
I .024
I .7 86
.273
3 . 0 3 3
0
9 7 I
0 . 2 6 3
0 . I ?4
0 . 7 3 7
I .027
I .655
.263
3 . 0 3 9
0
9 2 4
0 . 2o2
0 . I 9 3
0 . 7 3 7
I .037
I .9 49
.263
3 . 0 4 3
0
8 8 7
0 . 2 4 3
0 . I 7 6
0 . 7 25
I .034
2 . 0 30
.276
3 . 0 4 4
0
85 0
0 . 2 3 3
0 . I 6 7
C . 7 1 8
I .02 7
2 .1 17
.283
3 . 0 4 6
C
8 I 0
0 . 2 4 9
0 . 182
0 . 7 29
; .043
2 . 2 20
.272
3 . 0 4 5
0
7 7 7
0 . 2 2 7
C . \
it it
0 . 7 1 3
i .030
2 .316
.268
3 . 0 4 5
0
7 4 3
0 . 2 1 3
0 . I 4 7
0 .7 01
i .025
2 . 4 20
.299
3 . 0 4 2
0
705
0 . 2 : 8
0 . I O3
0 . 7 1 4
i .04 1
2 .55 3
.287
3 . 0 4 1
0
6 6 8
0 . 2 0 6
0 . I 4 4
0
696
i .03 1
2
. 6 93
.305
3 . 0 4 0
0
63 I
0 . 2 1 2
0 . I 4 y
0 .7 01
i .04 1
2 .85 2
.300
.26 1
,
82
FLOV C A L IBRATION RESULTS.
11
RE
NUM
NUC
PROBE
d .061211
PSlN
ETA
KN
I /S
3 . 0 3 5
I .1 34
0 .239
0 .17 4
0 . 7 26
I .0 17
I .5 89
.275
3 . 0 3 9
I .0 76
0 .228
0 .1 64
0 .7 18
I .017
I .67 4
.283
3 .041
I .037
0 .234
0 .16?
0 .7 22
I .026
I . 7 36
.27 7
3 . 0 4 2
I .000
0 .240
0 .17 4
0 .726
I .0 32
I .80 1
.274
3 . 0 4 6
0 .960
0 .207
0 .145
0 .7 00
I .0 13
I . 8 76
.301
3 . 0 4 9
U .917
0 .204
0 .14 2
0 .6 98
I .017
I .963
.303
3 . 0 5 2
0 .861
0 . 2 23
0 .159
0 .7 13
I .034
2 .041
.287
3 . 0 5 4
0 .84 2
C . 173
0 .132
0 .6 37
I .0 13
2 .1 36
.315
3 . 0 5 6
0 .SC?
0 .215
0 .152
Q .7 07
I .034
2 . 2 24
.294
.302
3 . 0 5 3
0 .. 7 7 1
0 .205
0 .14 3
0 .698
I .031
2 .3 34
3 . 0 5 2
G .735
0 .193
0 .133
0 .6 87
i .025
2 .4 47
.314
3 . 0 4 9
0 . 697
0 .17 2
0 .114
0 .6 64
I .019
2 .58 3
.333
3 . 0 4 8
0 . 664
0 .173
0 .115
0 .6 65
I .0 20
2 .711
.337
3 . 0 4 2
0 . 6 I 8
C .160
0 .10 3
0 .6 47
I .015
2 .914
.355
RN
I / S
FLOW
CA LI BRATI ON
M
RE
RESULTS:
iN U M
NUC
PROBE
S
: 2 5 / 4 / 1
ETA
FS I N
3 . 0 2 2
I . 1 5 3
0 .317
0 .247
0 .781
0 .9 73
I
564
.219
3 . 0 2 5
I . 069
0 .284
0 .2 18
U . 7 6 7
0 .968
I .6 56
.233
3 . 0 2 8
I . 0 4 9
0 . 3 26
0 .255
0 .7 84
0 .986
I . 7 1 8
. 2 16
3 . 0 2 ?
I .. 0 0 8
0 .29 4
0 .22 7
0 .77 1
0 .974
I . 7 8 7
.229
3 . 0 3 6
0 .923
0 .288
0 .221
0 .7 68
0 .983
I . 9 50
.232
3 . 0 4 3
0 ,649
0 .28 0
0 .2 14
0 .765
0 .963
2 .12 1
.235
3 . 0 4 2
0 .777
0 .2 60
0 .196
0 .7 54
0 .981
2 .317
. 2 46
3 . 0 3 8
0 . 733
0 .2 43
C .18 1
0 .744
0 .9 78
2 .45 3
.256
3 . 0 3 7
0 . 6 98
0 .242
0 .18 1
0 .744
0 .9 73
2 . 5 78
.256
3 . 0 3 7
0 .667
0 .245
0 .1 82
0 .745
0 .981
2 .700
.255
3 . 0 3 7
0 .630
0 .22 1
0 .16 2
0 .729
C .9 7 1
2 .659
.27 1
FLOW
CALIBRATION
M
RE
RESULTS:
NUM
NUC
PROBE
#
: 2 9 / 4 / 1
PSlN
ETA
KN
I /S
3 . 0 4 6
I .1 26
0 .232
0 . I 77
0 . 760
0 .980
I .59?
.240
3 . 0 4 7
I .06 8
0 .236
0 . I 8 0
0 . 762
0 .98 2
I .685
.238
3 . 0 4 8
I .03 1
0 . 2 24
0 . I 6 9
0 . 7 5 5
0 .979
I . 7 46
. 2 45
3 . 0 5 0
0 .9 93
0 .213
0 . I 5?
0 . 7 4 7
0 .973
I .312
.253
3 . 0 5 3
0 . 9 53
0 . 2 03
0 . I 55
0 . 7 4 4
0 .976
I .387
. 2 56
3 . 0 6 0
0 .911
0 .1 98
0 . I 46
0 . 7 3 7
0 .974
I . ?7 3
.264
3 . 0 6 4
0 .6 68
0 .189
0 . I 38
0 . 7 2 9
0
2 .071
.27 1
3 . 0 6 4
0 . 83 5
0 .1 95
0 . I 43
0 . 734
0 .975
2 .15 1
.266
3 . 0 6 6
0 .796
0 .193
0 . I 4 I
0 . 7 3 2
0 .997
2 . 255
.268
3 . 0 6 7
0 ,. 7 6 0
0. . 1 9 4
0 . I 4 2
0 . 7 3 3
I .00 1
2 .3 64
.267
966
3 . 0 6 6
0 .727
0 .192
0 . I 40
0 . 7 3 I
I .001
2 . 4 72
.269
3 . 0 5 7
0 .690
0 .18 9
0 . I 3 8
0 . 7 2 9
0
999
2 .607
.27 1
3 . 0 5 6
0 .656
0 .172
0 . I 23
0 . 7 I 3
0 .982
2 . 7 43
.283
3 . 0 5 3
0 , 619
0 .1 66
0 . I I 8
0 . 706
0 .9 85
2 .907
.294
3 . 0 5 3
0 ,. 5 8 3
0 .166
0 . I I 7
0 . 706
0 . 9 83
3 .034
. 2 95
.
83
M = 3 ; d=50 yin.
FLOW
CALIBR ATION
M
RESULTS.
RE
NUl I
NUC
. 7 76
PF v OEE
*
P S IN
. 2 9 / 7 ;
2
ETA
I ;s
KU
I .371
G .841
0 .614
U . 9 60
G .647
3 . 0 o 3
2 .632
I .20 9
0 .701
G . 5 8 0
0 .966
G .6 83
.426
3 . 0 6 5
2 . 5 37
I .286
0 . 7 t 7
0 .597
0 .973
0 . 7 06
.409
3 . 0 6 6
2 .435
I .238
0 . 7 2 6
0 .587
G .97 1
0 .73 7
.421
3 . 0 7 1
2 .337
I . 2 04
0
0 . 5 79
0 .966
0 .766
.429
3 . 0 7 4
2 . 246
I .1 78
0 .6 75
0 .57 2
0 .971
0 .79 9
.436
3 . 0 7 6
2 .145
I .167
C . g 65
0 .570
0 .973
G . 836
.440
3 . 0 6 2
2 . 05 2
I .2 12
0 . 7 0 3
0 . 5 8 0
0 .977
0 .8 74
. 4 27
3 . 0 5 9
696
.39 1
3 . 0 8 3
I . 966
I .080
0 . 5 90
0 .546
0 .9 60
0 .912
. 4o?
3 . 0 6 3
I . 870
I .14 1
G .642
0 . 5 6 3
0 .9 73
0 .9 56
.447
3 . 0 8 3
I ,. 7 8 7
I .139
0 .641
G .562
0 .962
I . 0 03
.443
3 . 0 3 2
I ,. 6 9 2
0 .986
0 .509
C . 5 1 6
0 .946
I .0 60
.502
3 . 0 8 0
I .618
I .088
0 .5 96
C .546
0 .964
I . I 03
.464
3 . 0 7 3
I . 519
I .06 2
0 . 5 7 4
C .54 1
0 .963
I
.18
1
.473
3 . 0 7 8
I .437
I . 0 62
0 . 5 74
0 .54 1
0 .964
I . 2 48
.473
3 . 0 7 6
I . 35 1
C .93 2
0 . 4 6 3
0 . 4 9 7
0 .939
I .32 8
.526
FLOW
CALIBR ATION
M
RE
RE SU LTS:
NUl I
HUC
PROBE
#
? S I N
; 0 9 / 4 / 2
ETA
KN
I / S
3 . 0 6 1
2 .7 67
0 .744
0 . 5 5 5
0 . 7 46
1 . 0 3 5
0 .650
.254
3 . 0 6 4
2 .6 19
0 .6 38
0 . 4 6 0
0 .7 21
1 . 0 2 4
0 .6 86
.279
3 . 0 6 6
2 . 5 20
0 .667
0 . 4 8 6
0 .72?
1 . 0 3 1
0 .713
.272
3 . 0 6 9
2 . 425
0 .4 76
0 . 3 1 6
C .666
0 . 9 9 0
0 . 7 40
. 33i .
3 . 0 7 3
2 .337
0 .500
0 . 3 3 8
0 .676
1 . 0 0 2
0 . 7 66
.326
3 . 0 7 7
2 .22 7
0 .5 69
0 . 3 9 9
0 .70 1
1 . 0 2 3
0 .806
.300
3 . 0 7 9
2 .139
0 .457
0 . 3 0 0
0 . 6 5 7
0 . 9 9 1
0 . 8 39
. 345
3 . 0 8 4
2 . 044
0 .5 56
0 . 3 8 7
0 .697
1.031
0 .8 77
.304
3 . 0 8 5
I . 957
C . 5 75
0 . 4 0 4
0 .703
1 . 0 3 8
0 .916
. 2 93
3 . 0 8 6
I .. 8 7 0
0 .50 4
0 . 3 4 2
0 .678
1 . 0 1 9
0 .9 59
.324
3 . 0 8 7
I . 7 82
0 .438
0 . 3 2 8
0 .67 1
1.021
I . 0 06
.331
3 . 0 3 4
I .. 6 9 2
0 .4 83
0 . 3 2 8
0 .67 1
1 . 0 2 6
I .0 60
.33 1
3 . 0 8 3
I . 615
0 .497
0 . 3 3 5
0 .674
1 . 0 3 0
I .111
.327
3 . 0 3 2
I . 5 19
0 .4 09
0 . 2 5 3
0 .631
1.001
I .18 1
.373
3 . 0 8 0
I . 423
G . 4 45
0 . 2 8 ?
0 .651
1 . 0 2 7
I . -60
.352
3 . 0 7 7
I . 320
0 .4 23
0 . 2 7 0
0 .63?
1.022
I .3 59
.364
84
FLOU CALIBRATION RESULTS.
M
RE
NUM
PROBE
NUC
K .06/5/2
PSIH
ETA
KN
1/S
3 .056
2 .791
0 . 6 2 7
0 .460
0 .734
I .048
0 .6 44
. 267
3 .058
2 .6 49
0 . 5 9 3
0 .4 30
0 . 7 2 5
I .052
0 .678
.276
3 . 0 60
2 .562
0 . 5 5 4
0 . 3 95
0 . 7 1 3
I .047
0 .701
.288
3 .06 1
2 .46 6
0 . 5 4 9
0 .390
0 . 711
I .048
0 . 728
.26 9
3 . 0 70
2 .347
0 . 5 3 3
0 .376
0 .7 06
I .050
0 .764
.295
3 .073
2 .258
0 . 5 1 0
0 .' 3 5 6
0 . OZO
I .043
0 .. 7 9 4
.303
3 . 0 76
2 .16 4
0 . 5 2 8
0 .371
0 .. 7 0 4
I .054
0 . 8 28
. 2 97
3 . 08 1
2 . 059
0 . 5 1 4
0 . 36 0
0 . 6??
I . 056
0 . 3 7 0
.30 1
3 .. 0 5 2
I . 9 72
0 . 4 8 4
0 . 3 33
0 ,6 33
I .049
0 . 909
.313
3 . 083
I . 55 5
0 . 4 5 5
0 . 307
0 . 6 7 5
I .. 0 4 6
0 . 96 6
.326
3 .. 0 8 2
I ., 7 3 d
0 . 4 3 3
0 . 2 58
0 . 6 6 5
I . 042
I . 0 03
.337
3 . 062
I . 69 1
0 . 4 5 2
0 . 287
0 . 6 6 5
I . 048
I . 060
.337
3 . 0 78
I . 6 15
0 . 4 2 0
0 . 2 7 7
0 . 65?
I . 050
I . I 10
.343
3 . 075
I . 52 I
0 . 3 8 9
0 . 250
0 . 6 4 2
I . 039
I . 179
.36 1
3 . 078
I . 4 42
O’ . 4 0 2
0 . 2 6 I
0 . 6 4?
I . 049
I . 2 43
.353
3 . 073
I . 33 9
0 . 3 9 9
0 . 258
0 . 647
I . 055
I . 339
.355
PLOW
CALIBR ATION
M
RE
RE SULTS:
N U lI
NUC
PROBE
#
F S iN
. 0 7 / 7 / 2
ETA
KN
1/S
3 .. 0 5 9
I . 78 3
C ., 4 o 0
0 . 3 4 4
0 . 748
0.964
0 . 6 45
.25 2
3 . 06 1
I.
0 . 296
3 .. 0 6 4
3 . 06 6
2 . 546
Cl . 4 G o
0 .. 4 3 4
0 . 7 29
0 . 739
0.952
0.967
0 . 68 0
G . 7 0S
.27 1
.26 1
2 . 45 3
0 . 424
0 . 3 12
0 . 732
.265
2 . 352
0 . 414
0 ., 3 0 2
0 . 736
0 .732
0.972
3 .069
0... 9 7 2
C .. 7
63
.268
3 . 073
2 . 25 2
0 .. 4 0 6
0 .. 2 9 6
0.972
3 .076
2 . 156
G . 3 79
0 . 2 72
0 . 7 2 9
0 .717
0.962
0 . 79 7
G . 8 32
.272
.283
3 . 060
2 .Ool
0 . 371
C . 282
C.722
0.977
G .. S o 9
.278
3 .083
I . 961
0 .368
0. 2 6 2
0.968
G.914
. 289
3 .03 3
I .872
u . 37 7
0 . 27 0
0 .712
0 .71o
0.979
.234
3 .08 1
I .7 83
0 .348
G .244
0 .702
0.968
0 .. 9 5 7
I . 0 05
3 .06 1
I .70 1
G. 347
0 .244
0.974
I .616
0 . 3 42
0 .239
3 .077
I .524
0 .310
G.211
0 .680
0.958
3 . 0 76
I .433
C .321
0 .221
0 .687
0.976
3 .076
I .348
0 .306
0 .207
0 .677
0.973
I ,. 0 5 3
I. 1 0 9
I. 1 7 6
I.251
I. 3 3 0
.299
3 . 0 78
0 .702
0 .699
I
64 I
0 . 3 2 1
0.976
. 299
.302
.32 1
.314
.324
85
FLOW CALI B R A T I O N R E S U L T S : FROBE
M
RE
NUH
NUC
# :29/5/2
PSIN
ETA
KN
I /S
3 . 0 5 5
2 . 8 1 1
0 . 5 1 8
0 . 3 9 5
0 . 7 6 3
1. 093
0 . 6 3 9
23 S
3 . 0 5 8
2 . 6 6 0
0 . 5 1 2
0 . 3 8 9
0 . 7 6 1
1. 10 3
0 . 6 7 5
239
3 . 0 5 8
2 . 5 7 2
0 . 4 8 7
0 . 2 6 7
0 . 7 5 4
1.10 1
0 . 6 9 6
246
3 . 0 5 9
2 . 4 7 3
0 . 4 6 9
0.251
0 . 7 4 6
1 . 0/6
0 . 7 2 6
252
3 . 0 5 9
2 . 3 3 4
0. 4 7 1
0 . 3 2 2
0 . 7 4 5
1. 10 7
0 . 7 5 3
2 5 I
3 . 0 6 1
2 . 2 6 8
5 . 4 5 7
0 . 3 4 2
0 . 7 4 5
1.10 6
0 . 7 6 5
2 5 5
3 . 0 6 2
2 . 1 7 5
0 . 4 2 5
0.211
0 . 7 3 3
I . 0 97
0 . 3
3 . 0 6 6
2.102
0 . 4 1 2
0 . 3 0 0
0 . 7 2 0
1. 097
0 . 3 5 3
13
266
2 72
3 . 0 7 3
1 . 9 7 8
0 . 3 9 7
0 . 2 3 6
0 . 7 2 1
1. 099
0 . 3 9 7
2 7 9
3 . 0 7 5
1 . 3 9 3
0 . 3 9 4
0 . 2 8 4
0 . 7 2 0
1. 105
0 . 9 4 4
260
3 . 0 7 5
1 . 3 0 7
0 . 3 8 3
0 . 2 7 4
0 . 7 1 5
1.110
0 . 9 9 2
285
3 . 0 7 6
1 . 7 1 4
0 . 3 7 0
0 . 2 6 2
0 . 7 0 9
1. 107
1 . 0 4 6
2 9 I
3 . 0 7 4
1.626
0 . 3 5 5
0 . 2 5 o
0 . 7 0 2
1. 108
1.102
2 9 9
3 . 0 7 2
1 . 5 2 9
0 . 3 4 5
0 . 2 4 1
0 . 6 / 7
1. 113
1 . 1 7 2
304
3 . 0 7 2
1 . 4 4 4
0 . 3 3-
0 . 2 2 9
0 . 6 8 9
1.112
1 . 2 42
3 I 2
3 . 0 7 2
1.362
0 . 3 1 3
0.212
0 . 6 7 6
1. 103
1 . 3 1 6
32 4
3 . 0 6 9
I .267
0 . 3 0 5
0 . 2 0 5
0 . 6 7 2
1. 115
1 . 4 1 5
329
3 . 0 7 0
1.15 1
0 . 2 3 5
0.186
0 . 6 5 8
1. 114
1 . 5 5 7
3 4 4
3 . 0 6 5
1. 051
0 . 2 6 0
0 . 1 6 5
0 . 6 3 7
1. 097
1 . 7 0 7
366
FLOW
C A LIB R A TIO N
RE
M
R E SU LTS:
NUH
NUC
PROBE
#
P S IN
: 0 9 / 3 / 2
ETA
KN
I / S
3 . 0 5 7
2 .796
0 . 4 58
0 . 4 00
0 . 3 74
I .087
0 . 643
.12 6
3 . 0 5 9
2 . 636
0 .442
0 . 385
0 .87 1
I . 0 / 3
0 . 662
.129
3 . 0 6 1
2 .5 43
0 . 423
0 . 367
0 . 368
I .094
0 .707
.132
3 . 0 6 2
2 ,. 4 5 1
0 .416
0 . 360
0 . 867
I .09 5
0 . 7 3 3
.133
3 . 0 6 4
2 .343
0 . 4 07
0 .352
0 .865
I .100
0 .767
. 135
3 . 0 6 6
2 . 24 1
0 .388
0 . 334
0 . 862
I .100
0 .801
.138
3 . 0 6 8
2 .16 1
0 .368
0 .316
0 .858
I . 0 97
0 .831
.142
3 . 0 7 4
2 .. 0 7 3
0 .333
0 . 283
0 . 850
I .038
0 . 866
.150
3 . 0 7 8
I . 975
0 . 3 42
0 .291
0 . 852
I .104
0 .906
.148
3 . 0 8 1
I ,. 8 8 1
0 .325
0 .27 6
0 . 848
I .10 1
0 . 953
.15 2
3 . 0 7 9
I .773
0 . 3 10
0 . 262
0 .844
I .103
I . 012
.156
3 . 0 7 8
I . 699
0 .306
0 . 2 5 8
0 . 843
I .111
I . 056
.157
3 . 0 7 8
I .609
0 . 3 00
0 .252
0 .84 1
I .114
I . 115
.159
3 . 0 7 8
I . 523
0 .23 1
0 . 235
0 .835
I .113
I . 178
.165
3 . 0 7 8
I
C .274
0 . 2 28
0 . 8 33
I .120
I .251
.167
3 . 0 7 7
I ,. 3 3 7
0 .25 1
0 . 207
0 . 325
I .113
I . 342
.17 5
434
86
.2<M<2.2; d=20 JJin.
FLOU
C A LIB R A TIO N
M
RE
RESULTS.
NUM
NUC
FKOEE
a
. I l i Z i l
?S I N
L , Ut
ETA
KN
I /' b
O
202
1 . 6 1 0
0 .809
0 . 6 9 3
0 . 8 3 7
1 . 0 1 1
U .165
. ANv
O
2 OI
1. 49 4
0 . 7 3 2
C . o 2 2
0 . 8 4 9
1. 0 0 0
0 . I 93
.15 1
O
197
1 . 3 5 2
0 . 6 9 0
0 . 5 8 3
0 . 8 4 4
1.001
0 .215
.156
O
I 9 9
1. 2 6 6
0 . 7 2 3
0 . 6 1 3
0 . 3 4 8
1. 009
0 .232
. i s :
U . 3. U fc
. I CN
O
I V9
1 . 1 4 6
0 . 6 2 8
0 . 5 2 5
0 . 3 3 6
0.9
C
I 9 9
1 . 0 5 0
0 . 6 4 2
0 . 5 3 8
0 . 3 3 6
1 . 0 0 7
0 . 260
16:
O
L 02
0 . 9 5 3
C . <, 20
0 . 5 : 6
0 . 8 3 5
I . 010
0 .312
. 165
O
20 7
0 . 8 6 3
0. 551
0 . 4 5 4
0 . 8 2 4
1 . 0 0 0
0 .354
. 1 7 c
C
2 I 2
0 . 7 6 3
0 . 5 1 ?
0 . 4 2 4
0 . 3 1 c
I . 006
0 . 4 : 0
. 132
FLOW
C A LIB R A TIO N
RE
M
RESULTS:
NUM
NUC
PROBE
9«.
E/ D = 252
1 7 / 5 / 2
K
=S IN
ETA
KN
I /s
I
I
076
4 . 6 8 9
0 . 8 9 5
0 . 7 7 4
0 . 8 6 5
0 . 9 99
0 .26?
.135
075
4 . 3 5 9
0 . 7 6 9
0 . 6 5 6
0 . 3 5 3
0 . 9 9 4
0 .209
.147
I
0 75
4 . 0 3 0
0 . 7 5 6
0 . 6 4 6
0 . 3 5 2
0 . 9 9 9
0 .232
. 146
I
075
3 . 7 5 1
0 . 7 2 4
0 . 6 1 5
0 . 8 4 9
1 . 0 0 3
0 .361
.15 1
I .075
3 . 4 2 6
0 . 6 7 4
0 . 5 6 3
0 . 8 4 2
I . 0 02
0 .396
.156
I
074
3 . 0 3 3
0 . 6 2 5
0 . 5 2 3
0 . 8 3 6
1 . 0 0 5
0 . 440
.164
I
074
2 . 3 3 8
0. 5 2 1
0 . 4 2 6
0 . 8 1 8
0 . 9 9 4
0 .477
.162
I
073
2 . 5 0 7
0 . 4 3 6
0 . 3 4 5
0 . 7 9 9
0 . 9 6 5
0 .540
.20 1
I
0 75
2 . 1 7 8
0 . 4 0 2
0 . 3 1 3
0 . 7 9 0
0 . 9 9 6
0 . c 22
.211
FLOW
C A LIB R A TIO N
M
RE
RESULTS :
NUM
NUC
FROBE
L / D= 33 1
: 0 7 / 8 / 1
ti
P S IN
ETA
KN
I /s
O
I 9 8
1. 591
0 . 8 4 7
0 . 7 4 8
0 . 8 8 3
0 . 9 9 1
0 .18 4
.117
O
I 9 9
1. 4 8 7
0 . 7 3 0
0 . 6 3 8
0 . 8 7 4
0 . 9 8 5
C . 197
.12 6
0 . 7 5 0
0 . 6 5 7
0 . 6 7 5
0. 99 c
0 .213
.125
0 . 5 6 8
0 . 6 6 6
0. 9 9 1
0 .23 1
.13 4
O
I 96
1 . 3 6 8
U
I r 9
1. 2 7 6
0
202
1 . 1 7 8
0 . 5 9 3
0 . 5 0 9
0 . 6 5 9
0 . 9 6 5
0 .252
Q
20 4
I . 073
0 . 5 3 7
0 . 4 5 7
0 . 6 5 1
0 . 9 6 2
0 .261
. *49
0
2 I 0
0 . 9 6 3
0 . 5 6 6
0 . 4 6 6
0 . 6 3 5
0 . 9 9 1
0 . 6 : 5
.145
O
2 I <-
0 . 9 0 4
0 . 5 1 4
0 . 4 3 5
0 . 6 4 7
0 . 9 9 6
0 . 355
.153
O
2 25
0 . 6 0 4
0 . 5 1 9
0 . 4 4 0
0
0 . 9 9 8
0 .412
.152
. 6
a
87
FLOW CALIBRATION RESULTS. PROBE S : 07/ 8/ 2
RE
M
NUM
NUC
P S lN
ETA
KN
I /s
0 . 8 5 1
4 . 6 44
0 . 7 63
0 . 669
0 .877
0
977
0 . 2 45
.12 3
0 . 8 5 1
4 . 327
0 . 782
0 . 686
0 . 878
0 .986
0 . 263
.122
0 . 8 5 1
4 .017
0 . 7 26
0 .634
0 .873
0 .984
0 .283
.12 7
0 . 8 5 2
3 .. 7 1 0
0 . 649
0 . 562
0 .665
0 .980
0 .30 7
.135
0 . 6 5 2
3 .414
0 . 6 85
0 . 5 95
0 .869
0 .987
0 .333
.13 1
0 . 6 5 3
3 . 037
0 . 598
0 . 514
0 .85 9
0 . 986
0 . 375
.14 1
0 . 8 5 4
2 . 766
0 . 5 28
0 .449
0 .649
Q .981
0 . 4 12
.15 1
0 . 8 5 6
2 . 430
0 . 496
0 . 419
C .34 4
0 . 966
0 . 470
.156
0 . 8 5 6
2 . 122
0 .491
0 .414
0 .843
0 . 9 94
0 . 539
.157
FLOW
C A LIB R A TIO N
M
RE
RESULTS:
NUM
PROBE
NUC
#
: 07 / 8 / 3
P S IN
ETA
KN
1 /S
I
6 0 9
3
754
0
8 0 I
0
705
0
880
U
99 }
0
455
. 120
I
5 6 4_
3
6 I I
0
709
0
6 I 8
0
87 2
0
99 6
0
46 7
. 128
I
5 I I
3
4 43
0
6 98
G
608
0
8 7 I
0
998
0
481
. 129
I
457
3
282
0
73 1
0
639
0
874
I
002
0
49 7
.126
I
392
3
093
0
6 95
G
605
0
8 70
I
Cl 0 I
0
5 I 5
. 130
I
32 I
2
89 I
0
59 9
0
5 I 5
0
659
0
9 9 7
0
535
.14 1
I
246
2
685
0
578
0
4 95
0
857
0
999
0
556
.143
I
I 4 9
2
430
0
566
0
483
0
855
I
003
0
584
.145
I
033
2
I 33
0
458
0
3 8 4
0
837
0
9 9 I
0
6 16
. 163
FLOW
C A LIB R A TIO N
M
RE
RESULTS:
NUM
PROSE
NUC
S
F S IN
: 0 7 / 8 / 4
ETA
KN
I / S
0 . 4 0 0
2 .964
0 .741
0 . 6 48
0 . 8 75
0 . 9 8 3
0 .19 5
.125
0 . 4 0 0
2 .765
0 .808
0 .711
0 . 880
0 . 9 9 5
0 . 210
.120
0 . 4 0 0
2 .57 1
0 .659
0 .571
0 . 867
0 . 9 8 5
0 . 2 25
.133
0 . 4 0 0
2 . 372
G .799
0 . 7 0 3
0 . 860
0 . 9 9 7
U . 2 44
. I 2u
0 . 4 0 0
2 . 163
0 .733
0 .641
0 .87 4
0 . 9 9 6
0 . 2 68
.lit,
0 . 4 0 0
I .. 9 6 7
0 . 704
0 . 613
0 .37 1
0 . 9 99
0 .29 4
.129
0 . 4 0 0
I . 761
G .656
G .569
0 . 866
0 . 9 9 5
0 . 3 29
.134
0 . 4 0 0
I . 53 1
G .530
0 .49 7
U . 8 5 7
0 . 9 9 4
0 . 378
143
0 . 4 0 0
I . 3 48
0 . 5 46
0 . 465
0 .852
0 . 9 9 7
0 . 430
. 146
88
FLOV CALIBRATION RESULTS: PROBE # : 2 9 / 8 / I
M
RE
NUM
NUC
P S IN
ETA
L / D=2O7
KN
I ZS
0 . 2 0 0
1 . 5 8 6
0 . 9 9 1
0 . 8 1 3
0 . 8 2 0
I .020
0 . 1 8 6
.180
0 . 2 0 0
1 . 4 8 3
0 . 9 3 5
0 . 7 6 1
0 . 8 1 4
I .02 1
0 . 1 9 9
. 186
0 . 2 0 0
1 . 3 7 0
0 . 8 4 4
0 . 6 7 8
0 . 8 0 3
I .0 09
0 . 2 1 5
.197
0 . 2 0 3
1 . 2 8 6
0 . 8 9 9
0 . 7 2 8
0 . 8 1 0
I .022
0 . 2 3 3
.190
0 . 2 0 7
1 . 1 9 2
0 . 8 6 8
0 . 7 0 0
0 . 8 0 6
I . 0 23
0 . 2 5 5
.194
0 . 2 1 0
1 . 0 8 8
0 . 7 9 3
0 . 6 3 2
0 . 7 9 6
I .018
0 . 2 3 5
.204
0 . 2 1 5
0 . 9 9 7
0 . 7 6 1
0 . 6 0 2
0 . 7 9 1
I .013
0 . 3 1 8
.20 9
0 . 2 2 3
0 . 9 1 7
0 . 6 6 5
0 . 5 1 5
0 . 7 7 4
I . 005
0 . 3 5 6
.Z2o
0 . 2 3 3
0 . 8 1 5
0 . 6 7 0
0 . 5 2 0
0 . 7 7 6
I .021
0 . 4 2 0
.225
KN
I ZS
FLOW
C A LIB R A TIO N
M
RE
RESULTS:
PROBE
NUM
NUC
S
: 2 9 / 8 / 2
P S IN
ETA
I .061
4 , 68?
I .138
0 . 7 4 9
0 .8 3 4
I . 0 10
0 . 286
.AOO
I .06 1
4 . 384
I .04 4
0 . 8 6 2
0 .826
I .019
0 . 306
.17 4
I . 060
4 .069
I .031
0 . 8 5 0
0 .8 2 4
I .023
0 .330
.176
I .06 1
3 . 737
0 .903
0 . 7 5 2
0 .8 I I
I . 015
0 .35 9
.169
I .06 1
3 .433
0 .867
0 . 6 9 9
0 .6 06
I .020
0 .39 1
.194
I . 063
3 , 08 2
0 .809
0 . 6 4 6
0 .799
I .022
0 . 436
.20 1
I .064
2 .776
0 .761
0 . 6 2 0
0 .794
I . 0 28
0 .455
.206
I .Ooo
2 ,. 4 4 2
0 . 696
0 . 5 4 4
0 .780
I .020
0 . 552
.220
I .083
2 .092
0 . o '2 4
0 . 4 7 5
C .766
I . 023
0 . 6 45
.224
FLOW
C A LIB R A TIO N
M
RE
RESULTS:
NUM
NUC
PROBE
U
P S IN
: 2 9 / 8 / 3
ETA
KN
I /S
0 . 168
I . 5 02
1 . 0 7 9
0 . 8 9 4
0 . 829
I .034
0 . 165
.17 1
0 . 186
i .. 3 3 1
0 . 8 5 6
0 . 68 9
0 . 805
I . 030
0 . 206
.195
0 ,. 1 8 2
I . 2 05
0 . 9 5 4
0 . 779
0 . 8 I 6
I .036
0 . 223
.184
0 .. 1 8 3
I ., 1 1 1
0 . 6 1 2
0 . 649
0 . 799
I .029
0 . 242
.201
0 . 184
I . 016
0 . 8 1 3
0 . 650
0 . 799
I .032
0 .266
.201
0 . 182
0 .908
0 . 7 1 0
0 . 556
0 . 7 8 3
I .026
0 . 296
.217
0 . 183
0 .600
0 . 7 6 3
0 . 604
0 . 7 9 2
I . 0 35
0 . 337
.208
0 . 18 7
0 . 717
0 . 7 4 2
0 . 585
0 . 783
I .035
0 . 335
.212
0 .18 9
0 .624
0 . 6 7 6
0 . 5 25
0 . 7 76
I .034
0 . 4 48
.224
89
FLOW CALIBRATION RESULTS: PKubL # .Lilli*
11
ETA
F S IH
HUC
HUM
RE
I/s
KN
.16
7
.17 7
0. 23V
I.633
I .013
0
633
0 . 6 23
I .030
0
0 . 2 3 5
I .65?
3 . E?2
0 .60 9
I .029
0 . 208
0 . 824
I . 0 35
0 . 2 24
.176
0 . 804
I .030
0 . 245
.19 6
0.23<i
I.537
I .030
0 . 722
0 .649
0 . 2 3 5
I .410
0 . 653
0 . 666
0 . 2 3 5
I .28?
0 . 8 76
0 . 7 06
0 . 8 08
I .024
0
0 . 2 3 3
I . 150
0 . 700
0 . 620
U . 7 9 4
0 . 299
0 . 2 3 3
I .013
0 . 7 c6
0 . 607
0 . 792
I. 0 2 9
I. 0 26
0 . 2 3 5
0 . 696
0 . 722
0 . 567
0 . 785
I .030
0
0 . 2 3 7
0 .770
0 .691
0 .539
0 . 779
I. 031
0 . 4 53
FLOW
C A LIB R A TIO N
M
RESULTS:
RE
HUM
HUC
PROBE
tt
.2 68
0 . 338
.36 6
.19 1
.193
. 2 0 o
.206
.215
.22 1
: 2 9 / E/ 5
ETA
F S IM
I /s
KN
0 . 3 9 5
2 .9 45
0 . 9 1 5
0 . 7 43
0 . 8 I 2
I .018
0
194
.138
0 . 3 9 4
2 . o24
1 . 0 2 6
0 . 8 4 5
0 . 8 2 4
I .028
0 . 2 1 7
.176
0 . 3 9 3
2 . 4 26
0 . 9 8 4
0 . 607
0 . 8 20
I . 0 28
0 . 2 35
.130
0 . 3 9 3
2 . 214
0 . 9 0 7
0 . 735
0 . 8 I I
I .027
0 . 257
.16?
0 . 3 5 2
2 .0 03
0 . 9 0 2
0 . 8 I I
I .027
0 . 284
.18?
0 . 3 9 2
I .. 8 2 3
0 . 8 1 9
0 . 6 0 0
I .02 4
0 . 312
.200
0 . 3 9 2
I . 607
0 . 7 6 9
0 . 6 09
0 . 7 9 3
I .022
0 . 3 53
.207
0 . 3 9 2
I . 385
0 . 6 9 0
0 . 5 3 7
0 . 7 7 9
I .01?
0 . 411
.22 1
FLOV
C A LIB R A TIO N
M
RE
' 0 . 7 3 2
0 . 656
RESULTS.
HUM
HUC
PROBE
Ii
: 2 9 / 8 / 6
P S IK
ETA
KN
I / 5
0 . 5 9 1
3 . 946
0 . 9 2 5
0 .75 2
0.813
I
.211
.137
0. 5 9 1
3 . 5 35
1 . 0 2 7
0 .846
0 . 8 24
I .020
0 . 2 35
.176
0 . 5 9 0
3 . 257
1 . 0 2 6
0 . 846
0 . 5 2 4
I .02 1
0 . 2 5 5
.176
0 . 5 6 ?
2 .974
0. 9 7 1
0 . 795
0 . 818
I .02 1
0 . 2 79
.182
0 . 5 6 9
2 . 680
1.000
0 .82 1
I .025
0 . 3 1 0
.17?
2 . 447
0 . 9 3 5
0. 3 2
0. 76
1
0 . 5 8 8
1
0.614
I . 0 25
0 . 339
. 186
0 . 5 6 8
2 . 17 1
0 . 7 9 3
0 .63 1
0 . 796
I .019
0. 3 8 2
.204
0 . 5 8 9
I ., 9 0 2
0. 7 9 1
0 . 629
0 . 7 96
I .023
0 . 4 36
.204
KN
I / S
FLOW
C A LIB R A TIO N
M
RE
RESULTS:
HUM
HUC
PROBE
H
P S IN
.012
0
. 2 9 / 8 / 7
ETA
0. 7&6
4
4 6 2
1 . 1 0 3
0 . 9 I 6
0 .331
I .Glo
0 . 234
.16?
0 . 7 6 4
4
0 I 7
1 . 0 7 9
0 . 8 9 4
G . 629
I .Olo
J . 259
.171
0 . 7 6 4
3
705
0 . 9 0 1
0 . 7 30
0 .611
I .00 7
U
0 . 7 6 3
3
4 I I
1 . 0 1 3
0 . 634
0 . 823
I .013
a. 30
.261
5
.16 7
. I 7 7
0 . 7 6 3
3
0 96
0 . 9 4 1
0 . 7 c 7
■3 . 6 1 5
I .02 1
0 . 3 56
.133
0 . 7 o2
2
755
0 . 6 7 c
0 . 70 7
G . 607
I . L i ;
0 .37 7
.193
0. 761
2
4 8 I
0 . 6 7 7
0 . 526
0 . 7 77
I .005
0 . 416
. 2 25
0 . 7 6 2
2
I 8 0
0. 8 1 1
0 . c 48
0
I .02 1
0 . 4 7o
.20 1
799
90
FLOW CALIBRATION R E S U L T S . PROBE
H
I
RVIl
RE
NUC
* :2 9/8/6
?S I N
ETR
KR
I / S
037
4 . 0 9 6
0
793
0 . 3 1 5
0 . 8 2 1
I .002
0 . 2 8 5
.17 9
: . OSo
4 . 2 0 9
C .640
0.O7S
0 . 3 0 3
•: . 9 9 9
0 . 3 1 7
.197
0 . 6 3 0
i .011
0 . 3 4 4
.170
i .014
0 . 3 7 5
.ISL
OSS
3. cdO
i .094
0 . 9 0 6
i . OSS
i
3. Soj
U .937
0 . 7c 3
i . GSS
3 . 2 0 3
U . V S5
0 . 7 6 0
0 . 3 1 7
: .017
0 . 4 1 1
.183
i .CLt
. . / C O
C .911
0 . 7 4 3
0 . 3 1 2
i .021
0 . 4 6 1
.166
: .003
- . S ;2
U . / 1 7
0 . 3 7 1
0 . 7 3 6
i . C U
0 . 5 16
.214
. . . 9 7
0 .740
0 . 3 3 3
0 . 7 3 3
I . 0 . 9
0 . 5 3 2
.212
KN
I / S
. Oi 4
FLCw
CRL I B R A T l ON
11
R ESU LTS:
NUM
RE
PROBE
NUC
4
P S IN
2 9 / 8 / 9
ETA
4
2 I 4
1 . 1 9 8
i . 0 0 4
0 . 8 33
I .017
0 . 380
.132
40 9
3
7 8 I
0 . 9 4 9
0 . 7 7 4
0 . a i o
I .015
0 .42 4
.134
I
408
3
4 9 o
0 . 9 0 1
G . 73 1
0 .811
I . 0 22
G . 458
.139
I
406
3
205
0 . 3 1 0
0 . 347
0 .799
I . 017
0 . 5 0 0
.20 1
I
4 08
2
9 3 6
0 . 8 1 3
0 . 353
0 . 300
I . 0 22
0 . 5 43
.200
I
407
2
335
0 . 7 4 s
0 . 58 7
0 . 789
I . 023
0 . 3 0 8
.211
I
4 0 6
2
345
0 . 3 2 4
0 . 4 6 7
0 . 733
I .017
0 . 383
.232
I
406
2
02 2
0 . 46 I
0 . 737
I .023
0 . 792
.23 3
KN
I / S
FLOW
L-
I .409
I
C A LIB R A TIO N
11
RE
RESULTS:
NUlI
PROBE
NUC
#
P S IN
: 2 9 / 3 /
10
ETA
2
I 25
2
5 I 5
0 . 7 2 7
0 .571
0 . 786
,. 0
30
0 .7 35
.214
2
123
2
2 4 3
0 . 7 2 9
0 . 573
0 . 733
I .035
0 . 325
.214
2
I 23
2
09 I
0 . 3 6 3
0 . 5 16
0 . 775
I .033
0 . 334
. 223
2
125
I
9 2 0
0. 6 0 9
0 . 435
G . 733
I .032
0 . 983
.233
2
I 23
I
7 48
0 . 6 0 0
0 .456
0 . 730
I .034
I . 0 53
. 2 40
2
I 2 7
I
53 2
0 . 5 5 3
0 . 414
G . 74?
I .035
I . 203
.252
2
I 2 4
I
399
0 . 5 2 1
0 .385
0 . 7 40
I .03 7
I . 3 22
.28 1
2
I 2 2
I
2 2 7
0 . 4 7 7
0 .346
0 . 725
I .50 7
. 2 75
’ I .03c
91
M = O ; d=20 yin.
FLOV
C A LIB R A TIO N
U <CU/ S EC )
RE
RESULTS :
FROEE
if
NUM
NUC
F S IN
0 . 5 4 3
16 36 . 63
0 . 4 3 3
0 . 8 2 0
14 5 0 . 05
0 . 3 9 4
0 . 8 0 4
3 0 / 2 / 2
L / D= I 3 2
ETA
I /S
0 . 6 5 4
. 0 78
.348
0 . 6 4 7
I . 074
.355
12 0 1 . 82
0 . 3 4 4
0 . 7 9 ?
0 . 5 1 6
0 . 6 4 6
I .076
.357
2 *- . 2 5
. G4
0 . 2 7 7
c . : c 5
0 . 5 0 4
0 . 6 4 2
I . 075
. 36:
-
634
. 9 2
0 . 2 6 0
0 . 7 7 6
0 . 4 9 6
0 . 6 3 9
I .075
.364
0 . 2 3 4
0 . 7 7 2
0 . 4 7 2
0 . 6 3 8
I .076
.365
8 I 4 . 10
0 . 2 1 5
0 . 7 6 5
0 . 4 8 6
0 . 6 3 6
I . 0 75
.363
7 2 8 . 87
0 . 1 7 3
0 . 7 7 1
0 . 4 9 2
0 . 6 3 8
.366
.37 1
6 6 3 . 27
0 . 1 7 7
0 . 7 6 0
0 . 4 8 2
0 . 6 3 4
I . 077
I .076
558 . 2 I
0 . 1 4 8
0 . 7 5 5
0 . 4 7 8
0 . 6 3 3
I . 077
.369
5 0 I . 00
0 . 132
0 . 7 4 ?
0 . 4 7 2
0 . 6 3 0
I
448 . 6 8
0 . 1 1 9
0 . 7 4 9
0 . 4 7 2
0 . 6 3 0
I .08 1
.373
4 I I . 02
0 . 1 0 9
0 . 7 4 4
0 . 4 6 3
0 . 6 2 9
I . 07?
. 3 75
FLOW
C A LIB R A TIO N
UC C M / S E C )
RE
RESULTS :
FROBE
#
NUM
NUC
P S IN
073
2 5 / 2 / 1
. 3 73
L / D= 2 I
ETA
I /S
16 42 . 6 9
0 . 4 3 7
0 . 7 3 5
0 . 5 8 4
0 . 7 9 5
I .009
. 2 05
1521
. 9 8
0 . 4 0 5
0 . 7 3 0
0 . 5 7 9
0 . 7 9 4
I . 007
.206
1 2 ? I . 66
0 . 3 4 4
0 . 7 0 6
0 . 5 5 7
0 . 7 9 0
I .002
.210
1 1 1 5 . 45
0 . 2 9 7
0 . 6 8 5
0 . 5 3 8
0 . 7 8 6
I . 003
.214
10 13 . 00
0 . 2 7 0
0 . 6 7 8
0 . 5 3 2
0 . 7 8 5
I .003
.215
8 ?2 . 7 7
0 . 2 3 8
0 . 6 6 3
0 . 5 1 ?
0 . 7 3 2
I .00 4
.218
6 32 . 57
0 . 2 2 2
0 . 6 5 7
0 . 5 1 3
0 . 7 8 1
I .003
.219
6 73 . 77
0 . 1 7 9
0 . 6 4 4
0 . 5 0 1
0 . 7 7 8
I .005
.222
5 6 I . 87
0 . 1 5 0
0 . 6 2 7
0 . 4 8 6
0 . 7 7 5
I . 004
.225
4 8 6 . 02
0 . 1 2 ?
0 . 6 2 6
0 . 4 8 5
0 . 7 7 5
I .006
.225
4 3 6 . 54
0 . 1 1 6
0 . 6 1 4
0 . 4 7 4
0 . 7 7 2
I .004
.228
404 . 27
0 . 1 0 8
0 . 6 1 1
0 . 4 7 1
0 . 7 7 2
I
005
.229
3 6 ? . 20
0 . 0 9 8
0 . 6 0 6
0 . 4 6 7
0 . 7 7 1
I .006
. 2 30
RESULTS.
FROBE
S
NUM
MUC
F S IN
F L OV
2AL IB R A T IG N
U v C M. s e c :
RE
L / D = 246
2 7 / 2 / 2
ETA
I / S
16 4 4.
7 I
0 . 4 2 5
0 . 6 5 2
0 . 5 2 8
0 . 3 1 1
0 . ?9 S
. 139
1 5 2 2.
30
0 . 4 0 3
0 . 6 2 8
0 . 5 0 6
0 . 8 0 7
0 . ?9 4
.19 3
1 2 8 0.
6 9
0 . 3 3 9
0. 6 2 0
0 . 4 9 9
0 . 8 0 5
0 . 9 9 5
. 195
1127.
8 2
0 . 2 9 ?
0. 6 1 8
0 . 4 9 7
0 . 8 0 5
0 . 9 9 8
. 195
10 05 . 3 I
0 . 2 6 6
0. 611
0 . 4 9 1
0 . 8 0 4
0 . 9 9 6
. 197
8 92 . 50
0 . 2 3 6
0 . 6 0 7
0 . 4 8 7
0 . 8 0 3
0 . 998
.19 7
2 7
0 . 2 1 6
0 . 5 9 8
0 . 4 7 9
0 . 8 0 1
0 . 9 9 7
.199
6 73 . 5 I
0 . 1 7 9
0. 591
0 . 4 7 3
0 . 8 0 0
0 . 99 8
. 200
571
. 2 6
0 . 1 5 1
0 . 5 8 6
0 . 4 6 8
0 . 7 9 9
5 02 . 28
0 . 1 3 3
0 . 5 7 8
0 . 4 6 1
0 . 7 9 7
.0 • 9 9 8
0 . 9 9 8
. 203
6 16.
.201
03
0 . 1 1 9
0 . 5 7 5
0 . 4 5 8
0 . 7 9 7
0 . 9 9 9
.203
4 0 5 . 92
0 . 1 0 7
0 . 5 7 2
0 . 4 5 6
0 . 7 9 6
0 . 999
. 204
3 83 . I 7
0 . 1 0 1
0 . 5 6 9
0 . 4 5 2
0 . 7 9 5
0 . 9 9 8
.2 05
4 49.
92
RE S U I T E
L. A zi
F L OV
i!
MVM
MUC
FS IM
3 .673
C . wL6
0 . S2 S
C . ? ?S
I f ci
0 . 6 ?0
0 .577
0 . 3 2 6
0 .973
I 6 4
688
0 . 575
5 . 8 3 4
I . C- 3 4
I fc S
C
G . 5 20
0 . 8 : 7
C .735
RE
U < C M / SEC
I t S l
51
. 4 : 0
i s a s
56
C . SOT
L / C=
ERCBE
2 6 / :• ' *
ETA
1/ s
1133
Ofc
C
152
C
i ; : i
20
0 . OCT
C
1313
39 2
20
37
0 .275
0 . 2 *’ C
0
0:5
0 . 6 1 '
0 . 5 26
0 . 50 •
0 . 8 2 5
0 . 5 2 5
G . • ? 9
0 .997
6 25
25
0 . 2 2fc
0 . 6 20
0 .512
0 . 3 2 4
I .002
I 7 S
6 74
5 4
0 .105
0
C .43?
0 . 8 2 4
I
OCi
i : 6
.
4
v
6 0 6
I 72
I 75
5 80
24
0 .15?
G .53 7
0 .431
0 . 8 2 0
I . co:
I 3 Q
S I 4
9 0
0 .14 1
0
C
0 . 8 1 5
C . ?? S
i s :
57 3
SoS
S6S
6 I
C .127
C .55?
G . S5 6
0 . 6 1 5
G
4 2?
5 2
0 .113
0 .556
C . 453
0 . 3 1 5
I .cos
I 5 5
4 02
37
C .110
0 . 5 S2
3 . 4 46
0 . 8 1 2
I . C0 I
I 87
FLGV
C A LIB R A TIO N
U(CM ZSEC)
RE
RESULTS.
MUM
FROSE
8
MUC
F S IM
L < D= 3 3 4
0 4 / : /
ETA
1 /S
0 . 4 2 0
0
5 3 4
C
8 6 I
I
0 0 0
.129
0 . 5 3 1
0
4 ? 7
0
35 4
0
9 9 9
.14 4
125 7 . 0 8
0 .S 3 7
0 . 3? 5
0 . 324
0 . 5 4 5
0
- 18 3
0
3 54
0
999
.14 4
1133.?:
0 . -3 0 3
0 . 5 5 7
0
475
0
85 3
I
000
. 147
? 37 . 33
0 . 5 4 4
0
4 6 3
C
S5 I
0
99?
IS?
0 . 5 3 7
0
0
£5 0
I
CO I
. 150
0 . 5 2 ?
0
4 4 3
0
3 4 9
I
COG
.15 1
4 4 7 . 2 3
C 265
0 .3 3 5
C . 2 15
C . 177
0.510
0
4 : I
0
3 4 6
I
COC
.15 4
5 5 3 . 3 1
0 .147
0 . 5 0 2
C
4:4
C
3 4 4
I
0 0 I
.154
5 0 1 . 3 1
0 .13 3
0 . S
0
4 I 2
0
8 4 2
I
00 1
.15 8
S 4 3 .33
0.11?
C.10?
Q.10 1
0 . 4 3 4
0
4 0 7
0
84 1
I .002
0 . 4 7 0
0
394
C
838
0
I4 S5
.
I4
1 4 8 7 . 8 7
3 3 5 . 17
8 1 0 . 2 7
4 1 0 . 7 6
3 3 1 . 7 4
FLOW
C A LIB R A TIO N
U ( C M /SEC)
RE
?0
0 . 4 4 7
■ 0 .392
RESULTS:
0 . 3 38
?9 8
.159
.162
I .000
PROSE
8
2 9 / 2 / 1
LZD=SOS
MUM
MUC
FS I M
ETA
I /S
1636
85
0 .444
0 . 6 1 5
0 . 545
0 . 8 3 6
0 . 9 ? 7
.114
1 5 11
9 7
0 .416
0 . 5 9 3
0 . 527
0 . 8 8 4
0 .995
.116
1303
63
0 . 358
0 . 5 3 4
0 .515
0 . 3 6 3
C . 9 95
.117
114 4
45
0 .315
0 . 5 7 1
0 . 504
0. 381
C . 993
.119
25
0 .282
0 . 5 5 2
0 . 4 85
0 . 8 7 ?
0
994
.12 1
87
0 .25 3
0 . 5 4 *
C
47?
0 . 6 7 8
0 . 997
.12 2
1024
9 I 3
8 3:
93
0 .22?
0 . 5 3 7
0 .471
0 . 6 7 7
0 .994
.123
695
4 I
0 .19 1
0 . 5 1 3
0 .45 3
0 . 8 7 5
0
. 1 : 5
5 94
99
0 .164
0 . 3 0 3
0 . 444
0 . 8 7 3
0 .993
.127
5 I 9
27
0 .14 3
0 . 4 9 3
0 . 42?
0. 3 7 1
G . 995
. 1 : ?
995
45?
0 ?
C .126
0 . 4 3 8
0 . 125
G .996
.129
434
9 I
0 . 120
0 . 4 7 5
0 . 413
0 . 3 6 9
0 .996
.13 1
3 35
7 I
0 .10 9
0 . 4 7 3
C .411
G
0
.13 2
8 6 6
997
93
M = O ; d=50 pin.
FLOV
C A LIB R A TIO N
U(CM ZSEC)
RESULTS:
RE
PROBE
NUH
NUC
# 0 9 / 4 / 1
L / D = 1 7 7
P S IN
ETA
1 /S
1 6 3 3 .. 4 9
I . 117
C . 873
0 ., 6 6 7
0 . 764
0 . 984
.236
1 4 89 . 4 B
I . 019
I . 15 4
0 . 92 1
0 . 799
I . 0 I 9
.20 1
12 4 1.
9 3
0 . 863
0 . 8 36
0 . 6 34
0 . 756
0 . 9 86
. 2 43
112 2.
2 6
0 . 763
0 . BI 9
0 . 6 I 8
0 . 755
0 . 985
.246
9 80.
B2
0 . 6 71
I . 0 4 3
0 . 7 8 7
I . 0 22
. 213
C S 3 . 49
0 .604
0 .799
0 . 8 2 1
0 . 600
0 .75 1
0 .970
.249
. 3 I
0 .549
0 .782
0 .5 85
0 .748
0 .986
.252
o 6 5 . 6 0
0 .455
0 .79 4
0 . 575
0 .750
0 . 99 5
.25 0
5 76 . 39
0 .394
0 .919
0 . 7 08
0 . 7 70
I .024
.230
49 I . 54
0 .336
0 ,. 8 9 1
0 ,. 6 8 2
0 . 766
I . 020
. 234
802
4 43 . 05
0 .303
0 .897
0 . 688
0 .767
I .027
.233
4 0 I . 32
0 .275
0 .737
0 . 545
0 . 739
0 .997
. 262
382
0 .261
0 .769
0 . 573
0 .745
I . 0 12
.255
FLOV
. 04
C A LIB R A TIO N
UC C M / S E C )
RESULTS:
RE
HUM
PROBE
# 0 6 / 5 / 1
NUC
ETA
0
0
0
0
0
0
I
0
I
0
0
0
0
0
0
0
032
9 I5
069
956
9 12
95 6
86I
86 9
7 I4
84 3
94
0
306
0
868
0
0
6 74
797
783
3G I
G 7 SC
0 7 82
C 788
0 7 75
0 776
0 749
C 772
0 7 76
4 I 3
89
0
282
0
79 1
0
6 0 4
0
763
388
7 8
0
265
0
772
0
5 8 7
0
7 6 0
45
66
63
0
994
892
787
699
567
4 96
448
II
43
39
I8
90
90
FLOW
I
I
C A LIB R A TIO N
U(CM ZSEC)
RE
0
0
0
G
0
0
C
0
P S IH
I I7
008
85?
75 2
6 78
609
537
477
383
339
16 37
1 476
1258
G
RESULTS:
NUM
8 23
7 I6
3 56
753
7 I4
753
6 68
675
5 35
65 I
L A B = I S i
0
0
0
PROBE
#
NUC
P S IN
I
006
99 4
0 23
CII
008
C I0
I 0 02
I 0 I2
0 969
I 0 I4
0
I
I
I
I
1 /S
.2 03
.217
. 19 9
.212
.2 18
.212
.225
.224
.25 1
.228
I
0 22
. 224
'I
0 I 2
.237
I
0 I 4
. 2 40
2 7 / 5 / 1
L / D = 2 Z 5
ETA
1 /S
1 6 3 4 . 0 9
1 . 1 4 9
0 9 7 2
0 . 808
0 .330
I .087
.170
1 4 5 7 . 5 7
1 . 0 2 5
0 . 8 1 7
0 . 665
0 .813
I . 074
.18 7
1226
. 6 7
0 . 8 63
0 . 9 26
C . 764
0 .826
I .088
. 174
1068
. 90
0 .75 2
0 .789
0 .63 9
0 . 809
I .077
.19 1
9 56 . 78
0 . 6 73
0 . 8 23
0 . 6 70
0 .814
I .039
.186
855 . 9 6
0 .602
0 .849
0 .694
0 . 8 17
I . 093
.18 3
7 77 . 03
0 . 5 47
0 .706
0 . 562
0 . 7 97
I .0 73
.203
65 1 . 77
0 . 458
0 . 776
0 . 627
0 . SOB
I ,. 0 8 8
.192
5 38 . 6 5
0 .379
0 .769
0 .62 1
0 . 8 07
I .091
.193
4 8 2 . 99
0 . 34 0
0 . 724
0 . 579
0 . 800
I .. 0 8 7
.200
4 2 4. , 39
0
0 .677
0 . 536
0 . 7 92
I .084
. 2 08
3 7 8 . 86
0 . 267
0 . 63 1
0 . 4 9 5
0 . 784
I . 076
.216
3 55.
0 . 2 50
0 . 703
0 . 565
0 . 797
I . 071
.203
86
299
94
FLOW CALIBRATION R E S U L T S : PROBE
Ut CM/ S E C )
1626
M
RE
NUM
NUC
#07/7/1
L/0=227
P S IN
ETA
I / S
. 74
1 . 1 1 0
0 . 3 9 7
0 . 7 4 0
0 . 3 2 5
0 . 9 3 7
.175
7 S . 4?
1. 00?
1 . 0 5 5
0 . 8 8 6
0 . 8 4 0
1. 013
. 160
0 . 8 4 4
0 . 9 3 ?
0 . 7 7 ?
0 . 8 2 9
0 . 9 9 9
.17 1
. 24
0 . 7 5 1
0 . 9 0 8
0 . 7 5 0
0 . 8 2 6
1. 0 0 6
.17 4
9 63 . 9 9
0. 4 7 1
. 173
B
12 48 . 7 0
1100
38 I . I 6
7 8 7 . 4 4
0 . 5 3 7
0 . 9 1 3
0 . 7 5 5
0 . 8 2 7
1. 012
0 . 8 4 9
0 . 6 9 6
0 . 8 2 0
0 . 9 9 9
I SO
0 . 7 4 5
0 . 4 1 ?
0 . 8 0 9
0 . 9 8 5
.19 1
. I ? 2
6 6 6. , 0 I
0 . 4 5 4
0 . 7 4 0
0 . 6 1 4
0 . 8 0 3
0 . 9 7 1
5 7 4.
0 . 3 ? 3
0 . 7 9 1
0 . 6 4 2
0 . 8 1 2
1. 003
.13 3
0 . 3 4 2
0 . 7 8 2
0 . 6 3 4
0 . 8 1 1
1. 0 1 0
.13?
0 . 9 9 ?
75
5 0 1. 78
4 i 3 .
3 3
0
3 02
0 . 7 5 1
0 . 6 0 6
0 . 8 0 7
401.
5 7
0 . 2 7 4
0 . 7 4 4
0 . 6 1 ?
0 . 8 0 ?
3 8 2. 2 8
0. 2 4 1
0 . 7 0 7
0 . 5 4 6
0 . 6 0 0
CAL : B R A T IO N
U <C M /SEC)
I 6
i
t.
1474
RESULTS
RE
PROBE
UUC
hum
-6
I .15?
0 . 8 0 7
0 . 6 75
4 4
I
0 . 7 4 3
C . 6 35
033
* 1 7 / 4 /
ps Hf
5. 8 5 5
. 200
1 . 0 0 0
Cl
FLOV
. I ?3
.19 1
ZTA
2 ?5
I /S
1 . 0 2 0
I 29
1. 0 1 6
I 4 5
I 2 6 2
5 I
C .85?
0 . 7 I S
0 .612
0 . 8 5 2
1. 0 1 3
I 4 8
H O ?
4 0
0 .98 1
0 . 8 2 4
0 . 710
5 .862
1. 0 2 4
I 3 7
1. 0 3 8
I 33
1. 027
I 4 9
?
?
U
88 C
?
?E
I £
0 .697
0 . 8 1 1
C . 704
0
0 I
0 .619
0. 711
0 . 6 35
0 . 3 5 1
0
0 .624
0 . 5 5 3
I
032
I 47
G . 620
0 . 8 5 3
1. 0 3 7
I 4 7
I 9
0 .562
6 7 I
42
0
55?
9 T
0
4 £ ?
?6
0 .345
0
0 .312
0 .279
V
.2 70
44: 6?
375 93
3 63 3 5
FLOW
.473
394
C A LIB R A TIO N
U CC M / S E C )
7 3 I
0 . 7 2 7
3 6 2
0 . 4 2 ?
0 . 5 33
0 . 8 4 2
1. 0 2 6
I 5 3
6
66
0.474
0 . 565
0 . 5 4 4
1 0
I 5 4
O .571
0 .552
0 . 4 73
0.347
0.344
0 .836
1. 043
I 5 3
0 . 4 5 5
1. 041
156
1. 02?
I 6 4
0 . 5 ?4
PROBE
#
MUM
NUC
P S IN
R ESU LTS:
RE
3 6
L / B= 346
2 5 / 4 / 1
ETA
I / S
1 4 6 9 . 6 6
1. 2 0 3
0 . 9 7 4
0 . 8 7 2
0 . 8 9 3
0 . 9 9 4
I 0 7
1 4 9 2 . 3 2
1 . 0 7 5
0 . 9 4 2
0 . 3 4 0
0 . 8 9 1
0 . 9 ?3
I 09
1 2 8 3 . 5 3
0 . 9 2 3
0
0 . 7 8 1
0 . 8 3 7
0 . 9 9 5
I I 3
1 1 3 9 . 7 6
0 . 3 5 1
0 . 9 1 6
0 . 8 1 5
0 . 8 9 0
1. 0 0 3
I I 0
3 3 0
9 9 8 . 2 3
0 . 7 1 9
0 . 8 3 3
0 . 7 3 7
0 . 8 8 4
0 . 9 9 9
I I 6
8 9 4 . 4 7
0 . 4 4 4
0
0 . 7 0 3
0 . 8 8 2
0 . 9 9 7
I I 8
3 0 1 . 8 4
0 . 5 7 3
0 . 8 0 3
0 . 7 0 8
0 . 8 6 2
1 . 0 0 3
I I 6
6 3 2 . 9 6
0 . 4 9 2
0 . 7 4 4
0 . 4 5 2
0 . 8 7 7
1 0
I 2 2
5 6 9 . 4 6
0 . 4 1 0
0. 7 1 1
0 . 4 2 1
0 . 8 7 4
0 . 9 9 7
I 26
4 9 4 . 0 9
0 . 3 5 6
0. 4 9 1
0 . 6 0 3
0 . 8 7 2
0 . 9 9 7
123
80 3
0 0
4 4 2 . 8 8
0 . 3 1 ?
0 . 4 9 2
0 . o03
0 . 8 7 2
1 . 0 0 2
I 28
4 0 0 . 7 8
0 . 2 3 ?
0 . 4 5 2
0 . 5 6 6
0 . 8 6 8
0 . 9 9 8
I 3 2
3 8 5 . 3 3
0 . 2 7 8
0 . 6 o9
0 . 5 3 2
0 . 8 7 0
1 . 0 0 6
I 30
95
r LOW CALIBRATION R E S U L T S : FROEE
UC C M / S E C )
RE
NUM
NUC
#29/6/1
L / D = 4 I6
F S IM
ETA
1/S
16 34
98
1. 1 1 3
0 .744
0
6 70
0
900
0 .93?
.10 0
1469
65
1. 000
0
0
6 9?
0
902
I
00 2
.098
775
12 67
00
0 . 8 6 2
0
762
0
6 3 7
0
9 0 I
I
0 04
. 099
1096
5 I
0 . 7 4 6
0
68 6
0
6 I 5
0
8 9 6
0
990
.10 4
. 102
9 85
2 5
0 . 6 7 0
0
70?
0
6 3 7
0
3 98
I
004
8 7 4
2 8
0 . 5 9 5
0
6 65
C
6 I 3
C
83 6
I
00 4
.10 4
8 05
3 7
0 . 5 4 3
0
6 9 7
C
6 2 5
0
397
I
009
. 103
672
65
0 . 4 5 7
0
6 4 4
0
5 75
C
892
I
00 4
.10 8
5 58
24
0 . 3 8 0
0
6 I 5
0
5 4 7
0
8 8 9
I
0 03
.111
49 I
I 9
0 . 3 3 4
0
59 3
0
52 6
0
86 7
0
996
.113
4 37
03
0 . 2 9 7
0
5 65
0
5 0 0
0
3 8 4
0
? 8 ?
4 0 I
04
0
0
58 3
0
5 I 7
C
5 8 6
I
004
.114
3 75
I 3
0 . 2 5 5
0
5 3 6
0
4 72
0
8 8 I
0
9 3 I
. i i ?
FLOW
2 7 3
C A LIB R A TIO N
U ( CM/ SEC)
R ESU LTS:
RE
MUM
FROEE
NUC
# 0 9 / 3 / 1
116
L / D = 4 2 0
P S IN
ETA
I / S
16 33
36
I .108
0 . 7 7 4
0 . 718
0
9 0 4
1. 0 2 2
. 096
14 7 4
47
I .000
0 . 7 3 7
0 . 664
0
90 I
1. 0 1 7
.099
12 6 0
22
0
0 . 7 7 2
0 . 6 97
0
903
I . 0 32
. 097
1122
S I
0 .76 1
0 . 7 6 0
0 . 665
0
9 3 2
1. 035
. 098
854
9 9 I
2 7
0 .672
0 . 6 6 9
0 . 599
0
6 9 5
1 . 0 1 4
. 105
89 7
83
C .609
0 . 7 0 0
0 . 628
0
6 9 8
1. 0 2 8
.10 2
7 93
52
G . 5 38
0 . 6 8 7
0 .616
0
3 97
1. 0 3 4
.10 3
6 73
2 7
0
456
0 . 6 2 6
0 . 556
0
8 9 2
1 . 0 1 8
.10 8
5 o7
72
0 .365
0 . 5 9 6
0 . 5 30
0
8 3 9
1. 014
.111
4 96
7 4
0
0
636
0 . 567
0
69 2
I
039
. 108
4 4 3
I 5
C .300
0. 561
0 . 4 97
0
885
I
009
. 115
4 0 I
4 I
0
0. 561
0 . 515
0
66 7
1. 0 2 2
. 113
:• 6 6
66
0 .263
C
0 . 524
0
3 8 8
I . 0 35
. 112
33 7
272
590
REFERENCES CITED
97
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7th
Problems
STATE UNIVERSITY LIBRARIES
MAIN
R378
HU42 Hertel, P. S.
cop.2
Heat transfer characteris­
tics of small configuration.
DATE
ISSUED TO
i
TAIH
N378
H442
cop.2