ation Metho d
An Example of Heatin g and Cool.in g Load Calcul
er
for Air-Co ndition ing of Buildi ng by Digita l Comput
1
Shoioh i Kuramo chi
Taieei Constr uction Co., Ltd., Tokyo, Japan
that the actual. load for air
Today, many air condit ioning engine ers recogn ize
tional heatin g and cooJ.in g
conven
the
by
ed
achiev
be
hardly
can
condit ioning system
a J.oad calcul ation system ,
out
worked
author
the
1966,
In
load ca1oul ation method .·
solve the problem on heat
to
d
adopte
was
in which the numeri cal calcul ation method
ation system for actual. use
transm ission, and has finally perfec ted- this calcul
ation method oan be summa rized
quite reoentJ .y. The charac teristi cs of this calcul
in majori ty operat ed interm itis
Japan
in
system
ioning
condit
as folJ.ow s: The air
during the early hours after
appear
ena
phenom
ular
tently in a day and quite partic
ation of operat ion. These
termin
the
after
the commencement of operat ion and right
d by the buildin g and air
retaine
heat
of
tion
transi
the
by
caused
are
ena
phenom
ation method worked out has
condit ioning system as heat capaci ty. The calcul
ina mentio ned. To be more
phenam
the
enting
repres
in
others
advant ages over the
need to be condit ioned
ularly
partic
't
doesn
system
specif ic, while any physic al
storag e heat load can
the
ission,
transm
linear or invari able for calcul ating heat
method . Moreov er, this calcube accura tely calcul ated by use of this oalcul. ation
g an accura cy within the allation system is marked by its reliab ility in securin easy unders tanding for the
s
permit
also
It
ation.
calcul
load
for
lowabl e· degree
widely useful for the profes sional
practi ce engine ers in genera l, hence it will be
calcul ation system can be also
this
to
cation
engine ers. Improv ement and modifi
system is mainly compos ed of two
made withou t much diffic ulties . This calcul ation
parts, namely ,
the heat source equipm ent
1. the calcul ation for obtain ing the output s of
er rate of thermal . medium
transf
heat
the
and
,
of air condit ioning system
atures, and
transp ortatio n system and the change s of room temper
load change s in the air2. the calcul ation for the heatin g and coolin g
condit ioned rooms.
d for this calcul ation are
In the text of this report , the equatio ns adopte
ation system is explain ed in
cal.cul
the
of
firstly Ulltstr ated 1 then the format ion
made for the model buildin g in exation
calcul
the
of
s
result
the
lastly
and
detail
the actual measur ements and by comistenc e are checke d and assure d by carryin g out
ed by the calcul ation system .
obtain
values
the
with
values
paring the measur ed
load, coolin g load,
Key Words: Compu ter, air condit ioning , heatin g
ature, simula tion,
numeri cal method , room temper ature, medium temper
evalua tion.
radiat ion, measur ement, interm ittent operat ion,
1.
Introd uction
is a heat that change s temper ature and humidi ty
The heatin g and coolin g load of air condit ioning
the
ed by an air-co nditio ning s,yetem . It occurs in
in the room being air-co nditio ned, other than produc
in the room.. The heat from the
ed
produc
heat
al
intern
an
or
room
the
g
ty
form of an extern al heat invadin
load, thereb y mainta ining the temper ature and humidi
air-co nditio ner absorb s this heatin g and coolin g
of the air in the room at a require d level.
in this paper is compos ed of the follow ing two
The calcul ation system that will be referre d to
princi pal parts:
1
Mecha nical Engine er
715
to heat sourc e equip chang e in room air temp eratu re relat ive
(1) Calc ulati on of heat trans fer and syste m.
tion
ment outp ut and heat medium trans porta
air-c ondi tione d.
ng and cooli ng load in the room being
(2) Calc ulati on of chang e in the heati
n syste m. Then,
start ing will the deta ils of the calcu latio be compared with
will
This pape r will deal with the subj ect,
ing
build
n upon appl icati on to an exist ing
the resu lt obtai ned from the calcu latio the exac tness of the calcu latio n. First of all, the featu res of
rm
confi
to
data
ent
urem
meas
al
the actu
ined:
the calcu latio n syste m will be expla
outpu t of air-c ondi tioneen cooli ng and heati ng load Qlt) and
(1) The syste m gives a relat ion betw
re 9i(t) unde r an eseratu
temp
air
room
the
of
n
latio
ling calcu
ing ~eat sourc 7 ~(t)' there with enab
tabl~shed cond~t~on.
in many cases in Japan ,
syste ms are opera ted inter mitte ntly
been much regar ded. By
Desp ite the fact that air-c ondi tioni ng
not
have
ation
oper ation and after the oper
therm al chang es at the early stage of es can be clari fied .
the said calcu latio n syste m, such chang
a prede termi ned
ired for room air temp eratu re ~. to reach
(2) A relat ion betw een the time t 4 requs oper ation and the capa city of~the air-c ondi tioni ng heat
m start
leve l after the air-c ondi tioni ng syste
medium trans porta tion syste ms.
perm itting reaso nable desig n of heat
sourc e ~ can be obtai ned, there by
1 This elim itrans fer by a nume rical metho d. { 1,2) latio n indeheat
with
deals
m
syste
n
latio
calcu
(3) The
perm its calcu
inva riabi lity of the therm al syste m and
nates the need for any linea rity or and temp eratu re. Also , the calcu latio n syste m is easy for prac tical
flow
heat
, thus offer ing wide use by
pend ent of such chang es in
appli ed and improved witho ut diffi culty
desig ners to unde rstan d, and can be
profe ssion al desig ners.
ept have been intro m, appro xima tion methods of new conc
(4) In making up the calcu latio n syste porta tion syste m in the air-c ondi tioni ng syste m, (b) simu m trans
duced ; (a) simu latio n of the heat mediuin the room, and (c) simu latio n of heat excha nging in the airlatio n of radia nt heat trans porta tion
cond ition ing syste m.
as a heat in a give- androom being air-c ondi tione d is defin ed re to incre ase is expr esThe heati ng and cooli ng load in the
eratu
temp
air
the heat causi ng the room
r defin ition s nece ssary in
take relat ion with the room air, where
e for the decre ase as "neg ative ". Othe
nsibl
respo
that
and
"
itive
"pos
as
sed
ired.
the calcu latio n will be given as requ
2.
on System
Prin cipa l Equa tions Adopted in Calc ulati
2.1
Exci tatio ns
can be obtai ned by means
r to achie ve the calcu latio n, which
formu lae are prepa red as
Exci tatio ns are used as an inpu t facto
from the desig n cond ition data. These
of nece ssary relat ive form ulae avail ableinvo lves solar radia tion, sky radia tion, other effec tive radia the exci tatio ns direc tly
subr utine . While the desig n cond ition
ligh ts and heat ers, their relat ion with
tions , atmo spher e, humanbody, anim als,
relat ed there to has been well known.
2.2 Num erica l method of heat trans fer
(1)
heat trans fer (2-di mens ional )
Fund amen tal equa tion of stead y state
~j = Kij (If~ - l)i)
)\ ,d
-."A
••• (1)
••• ( 1) '
d
ed dime nsion s (see
poin t j to adjac ent poin t i, d: Divid
wher e, Q.j: Rate of heat flow from
Assuming &-1 , (} , •••
ity.
uctiv
cond
al
poin ts i and j, )\: Therm
poin t 1, we ~ave,
to
flow
figur e 1), fi! ~1 : Temp eratu res at
heat
a
2, ••• and Q1 to be the rate of
to be the temper~tures at poin ts 1,
1
r.
atur e refer ence at the end of this pape
Figu res in brack ets indic ate the liter
716
••• (2)
For the steady-state heat transfer, the left member of the eq (2) is zero.
(2)
Fundamental equation of unsteady state heat transfer (2-dimensional)
••• (3)
••• (4)
4t.~ = C(~1.dt- 19-1)
19 1.dt
p(~2
+ 19-3 +
~4
+ li-5 +
(~- 4 l&;)
••• (5)
••• (6)
d. c(
N=--
••• (?)
A
where
1
~
At1
Temperature at point 1 after time interval of At,
capacity of element volume,
c:
Specific heat,
Specific weight,
(:
a: Thermal diffusivity,
.1t: Time interval, 0(:
0:
Heat
Heat
conductivity.
The various equations of heat transfer to be produced by the above fundamental equation and the
traditional equations will be illustrated in appendix.
(3)
Temperature variation in thermal medium transportation system ( 5)
With a tube as shown in a figure 2 (1) considered to be a model of the thermal medium transportation tube, it is assumed that the surface of the tube is insulated, and the temperatures of the tube and
thermal medium are equal at any contacting point and time. Next, changes in temperature with time at
respective points as shown in figure 2 (2) where the medium temperature is changed in step order as much
as 1:.. &- in the transportation system maintained at a constant temperature are replaced by linear changes
1
as shown in figure 2 (3), and it is assumed that & changes at a uniform rate during the period of 2m1.t:1t
to re~ch a final level, ~ corresponding to ~ th~t freely changes can be obtained by the following
equatJ.on.
2
1
2m1 2m1-m+1
t9:1(n • .1t-2m1.~t)
+
:E - - - i! IJ; ((n-2m1+1ll-1 Mtl
2m1
••• (8)
m=1
f
m1
c.r.v.llt
••• (q)
t):
fluid at inlet of system at time n.At, ~2 (
where, &
1 ( at): Temperature of medium
Temperature of ~edJ.um fluid at outlet of system at time n • .1.t, LlE;1 { At): Temperature dirlerence at
inlet during.t..t at time n.llt, n, m: Number showing time by multtitte 6f4t, f: Total heat capacity of
transportation system, p, v: Flow rate of medium fluid, c: Specific heat of medium fluid, {:
Specific weight of medium liquid.
When m1 is under a relation of 0.5~m1 f-1, it is regarded as 1, and if under a relation of m1 ~1,
an integer closet to the actual value is employed. Especially when m1 < 0.5 1 G-1 is always considered
equal to ~?~ This means that the effect of the heat capacity of the system is to be taken into account
when it is~arge, and such effect may be ignored when small.
3.
Change in Room Air Temperature and Heat Medium Transportation System
The calculation system dealt with in this Section takes the heating and cooling-load Q as the input
data, thereby computing the output of heat source equipment Qas and the change of room air temperature
9-i• Calculation system concerning Q will be explained in Section 4. Between_ the two calculation
systems for ~i and Q, input and output must be exchanged to carry out the calculation. The heat produced
717
tion system 1 and
the air-co nditio ning room by the trans porta
by the heat sourc e equipm ent is carrie d into
the same system a These heat
by
ent
equipm
e
sourc
heat
the
into
d
tion system
the heatin g or coolin g load is carrie
nce of: (1) Heat capac ity of the trans porta
trans porta tion phenomena are under the influe trans porta tion equipm ent power , and (3) Heat from outsid e
by
system will be
plus heat medium, (2) Therm al load cause d
therm al chara cteris tics of the trans porta tion
of the trans porta tion system , whereby the system is provi ded with autom atic contr ol unite With these
formeda In addit ion, the air-co nditio ning
desig n requi rewill be made up under restri ction s by the
facto rs, an air-co nditio ning proce ss system
ments .
will be
model as shown in figure 3 furth er expla nation
In this Secti on, assum ing a simpl e basic
made.
Cond itions for desig n calcu lation
3o1
(b) chilning system includ e (a) room tempe rature ~imt
Princ ipal contr ol value s for the air-co nditio
ictiv e condi tions,
restr
As
m•
~f
rature
tempe
air
g
1
tionin
condi
led or hot water tempe rature ~w1mand (c)
(c) flow rate of
(b) flow rate of chilli ed or hot water p,
there are (a) capac ity of heat sourc e GRBm, or air induc ed v , (e) time requi red for room air tempe ra0
air-co nditio ning air v 1 , (d) volume of outdo
sourc e outpu t to
of opera tion t4, (f) time requi red for heat
stage
early
at
level
e
stabl
a
reach
to
ture
elimi natio n of
ete
compl
till
red
requi
tion t 1 and (g) time
reach a stabl e level at early stage of opera
•
heat sourc e outpu t after opera tion stop t 5
indic ates
at early stage of opera tion, and figure 5
Figur e 4 shows the chang es in QL:rn, Q and t}i
ol value s and restr ictiv e condi tions
contr
The
over.
is
tion
opera
after
es
their trend of subsq uent chang
with outdo or and indoo r condi tions.
are appl.i ed as desig n requir emen ts toget her
are given as
tion and after the opera tion is over which
The chang es in Qm.[ at early stage of opera can be regard ed as linea r chang es in the case of
ment,
the chara cteris tic of the heat sourc e equip
r. Assuming
are treate d as a certa in restr ictiv e facto
ordin ary refrig erato rs and boile rs, and thus
at early stage of
ant
const
=
n
Qzmui
=
Ll~
have
we
t,
outpu
1
n 1 = t1/4t , and Qru3m = maximum heat sourc e
equat ion can be rewri tten as
opera tion. If n is betwe en 0 and n 1 , this
••• ( 10)
QRB(n .llt)
tion is t = 0, and n 5
Also, assum ing that the time to stop opera
n
and
0
be obtain ed if n is betwe en
5
n.<lruJ(o)
"rm<n.<lt)
=
ts(~t,
the fol.low ing relati on can
... (11)
n5
ity of suppl y
calcu lation , such as; W1 : Total heat capac heatin g
In addition-~ varia bles neces sary for the
g or
coolin
of
system
return
of
ity
capac
heat
system of coolin g or heatin g water , W2: Total duct system , V: Volume of room, c.r. V(l+~): Total efair
water , £ 1: Total heat capac ity of suppl y
room air must be asAddit ional coeff icien t of heat capac ity of
fectiv e heat capac ity of room air,
sumed for calcu lation o
the time of
al state of the air-co nditio ning system at
locat ion of
Initi al condi tions are relate d to the therm
by
d
guide
ents
judgem
eering
engin
h
throug
assumed
commencement of the calcu lation , and may be
data.
l
stica
stati
and
,
system
of build ing and
build ing, data, time, therm al chara cteris tics
the inl.et of
rature , ~"i is return air tempe rature at
Now, assum ing that !9-0 is outdo or air tempe on the side of the heat excha nger, t;. fZ can be obtain ed
rature
heat excha nger, and ~f 2 is mixed air tempe
from the follow ing equat ion.
e:
••• ( 12)
JoAq as,
are negligible~equent input data
tion
condi
al
initi
the
for
s
value
ed
start calcu lation
Sligh t error s in assum
itsel f has conve rgenc e and if the time to
are corre ct, becau se the calcu lation system
is advan ce.
3.2
Varia tion in room tempe rature
by the follow ing equat ion.
Varia tion in room tempe rature is obtain able
718
••• (13)
where, QRB(n.At): Rate of heat transported from air conditioning system to room at time n.~t,
Q(n.dt): Heating or cooling load in room at time n.dt,4~i(n.dt): Difference in room temperature
between 4t at time n.At. And if the supply air temperature at diffuser at time n.~t is &"rl(n.At),
••• (14)
'lru!(n.<lt)
According to the equation (14), it is noted that the room temperature at time (n.dt +dt) is obtainable from respective values at time n.At. This fact is of great significance for the subsequent
calculation. Apparent variation in retained heat of room air ~ relative to changes in room temperature
at the earlY period operation from 0 to t4 is given as,
••• ( 15)
where n4 = t4jdt. The decipive factor for the change in room temperature where the absolute value
of ~ is smaller than that of JlflQ}mdt is a balancing relation between Q and Q"'RB• With relative
increase in ~~ however, ita ef?ect on t4 can no longer be ignored, and must be given due consideration
in selecting the value of QRBm• At the early stage of usual intermittent air-conditioning operation,
the maximum output of the heat source equipment is required, and ~ is often determined by setting t4
at a required value. The relationship between t4 and ~ can be obtained. Today, there is no better
way than a trial and error method to find the relationship between t4 and ~·
3.3 Heat exchanger
Air must be used as final thermal medium when heat produced by the air-conditioning system is
transmitted into the room. Heat exchangers of the air-conditioning system in general use today employ
water as primary thermal medium and air as secondary thermal medium, excepting heat exchanger for heat
source equipment. The capacity and service condition of the heat exchanger are subject to the related
design specifications. In order to quantitatively find the characteristics of the heat exchanger under
other service conditions, it is necessary to intorporate complicated characteristic relationship as it
is into the calculation system. This, however, is so intricate to deal with that a practical simple
method will be employed here.
General usage and performance of the heat exchanger most used recently are as follows, with the
flow rate of air v 1 passing through the heat exchanger considered invariable, chilled or hot water at an
almost constant inlet temperature ~'w 1 m is supplied by controlling its flow rate p by means of a two-w~y
or three-way valve. Assuming the return water temperature to be 9'w2 ' the rate of exchanged heat is expressed as P (&'w 1 - ~'w2 ). This formula is equal, whether two-way or three-way valve is involved.
If the air temperatures at the inlet and outlet of the heat exchanger are ~£ 2 and ~L1 ' respectively,
the corresponding enthalpies are i 2 and i 11 and the latent heat load to be eliminated is~L' the rate of
exchanged heat is had as follows,
... ( 16)
While the values of &1 2 and &f are establiShed spontaneously during the air-conditioning operaserve ~s contra! valuesa Design values p and v 1 , therefore, must be adjusted so
and
tion, ~·
w1mcentro 1m
values may not be exceeded even under the maximum air-conditioning load.
that these
&f
Taking for example a cooling operation to simulate the action of this heat exchanger, the mutual
relation with temperatures is shown in figure 6. In figure 6 (1), a relationship under maximum load is
given, where the value of c/a is assumed to be invariable under medium load Shown in figure 6 (2).
Under this relation, a = &f 2 - 6l-'w 1 , b = &•w2 - &'w 1 , b' = ( G-'w2) - G-'w 1 and c = 8-f2 - 61-f1. The difference between ~·w 2 and (~'w~ is to correspond to the latent heat load Qt• The relation between c and b
is at given by the equation (16). The value of a becomes maximum when the load comes to the maximum, at
which point, it is necessary not to overestimate the value of~ 1 •
The values of ~·w 1 and ~·w 2 obtained from this simulation are not equal tO those actually measured.
But what is actually needed is the difference in temperature (&'w2 - 9'w1 ), and thus if near actual
values are desired, they can be obtained by comparing the value of ~·w 1 with ~·w 1 m and adjusting~w 2 as
719
much as the resultan t differen ce.
of operatio n is achieved as folSimulati on of the automati c control performa nce at the early stage
d till ()).i
m,
B-f
of
value
mined
predeter
the
toward
ed
1 andQR5 is increase
lows: The val.ue 9-f 1 iS'chang
the room
After
tamed.
main
is
state
this
RBmt
g~
reachin
reaches its predeter mined value. With QRM
correspo nding to the load variatio n is
tempera ture reaches the pre-dete rmined level, the differen ce in~i
and ~·w29 thereby controll ing the outfeed back to the heat source side with the medium tempera ture &f 1
put «Jm•
hed merely by reversin g the
The thermal relation s in the heating operatio n can also be establis
above.
given
heat
and
tures
tempera
for
symbols
3.4
Calculat ion of thermal relation in air conditio ning system
based on a simulati on model shown
Figure 7 shows a thermal relation in the air conditio ning system
To simplify and smoothly accompl ish
values.
various
obtain
to
e
procedur
ion
calculat
the
and
3,
in figure
follows:
as
set
are
ons
assumpti
the calculation~ some
(a)
Time required to transpor t heat medium is ignored.
'
system is proporti onal to the heat(b) Externa l heat load invading the heat medium transpo rtation
).
required
as
ion
calculat
by
le
obtainab
is
(this
ing or cooling load
for relative humidit ies. Thus,
(c) This calculat ion system includes no exact calculat ion method
maintain ed at 50%.
the relative humidity of the air in the room is consider ed always
referred to later) at same time are
(d) Room air temperat ures within one calculat ion unit (will be
all equal.
The calculat ion at t = n • .dt +.at
(e) Calculat ion is carried out at each step of time interval t& t.
t = n.dt is started with room
time
desired
at
ion
calculat
of
cycle
the
of
on
completi
the
subseque nt to
air tempera ture 9i(n.At + at)•
of room tempera ture, return air
(f) As shown in figure 7, calculat ion is carried out in the order
and supply air duct system, followed by
duct system, return water pipe system, supply water pipe system
calculat ion of room air temperat ure with time advanced as much as~t.
reversib le, the flow of heat trans(g) Although the heat flow of the cooling or heating load is
ible~
inrevers
ported by the heat medium transpor tation system is
system are calculat ed by the use of
(h) The tempera tures at various points of the air-cond itioning
general rule.
a
as
,
adyanced
most
is
time
when
known related tempera tures obtained
overall calculat ion accuracy .
Today, these assumpti ons are within the permiss ible range of the
ning system step by step.
The followin g will outline the transfer of heat in the air conditio
(1)
Return air system
ture. Assuming change in return
The return air temperat ure changes with changing room air tempera
be expresse d as f~llows:
can
it
(n.L]t),
A.9'
be
to
4t
+
n.tlt
and
n.dt
times
1
air tempera ture between
changed to 9 11i(n.llt + 4 t) at the
Suppose that the return air inlet temperat ure 9-'i(n.l] t +At) is heat qft invading the system and the
external
by
outlet. This temperat ure change can be caused to occur
1
and &"i can be obtained by the followin g
heat ca:pacity of the return air system. A relation between & i
account.
into
token
qf~
with
(9),
and
(8)
s
equation , using the equation
n.ll
~ i(n.4t~t)
=
2m1 2m1-m+1
(;'
i(n.4t+4 t-2m1.A t) + m'f1
2m1
t
Lli!l i{(n-2m1 -tm)tltj
+
qf2
<-~-)4t
Ceu•V
2
••• (18)
... (tq}
the equation (12).
from
le
obtainab
is
air
outdoor
and
air
return
this
of
The tempera ture of a mixture
ml =
(2)
f,j(c.a. Vz·At)
Return water system
ion now comes to the return
Accordin g to the given order of calculat ion in this paper, the calculat
720
water system at time (n.6t +~t). As shown in figure 3 1 the system contains a water1 pump, where the
flow rate of water is p, water temperature at the outlet of the beat exchanger is &w2 , and water temperature at the inlet of beat source equipment is &w 2 • It is also assumed that all the thermal changes
caused by the air at the inlet of the beat exchanger will be taken over by the return water system, which
will join the effects dependent on the rate of invading heat qwt• power load of the pump %WP and heat
capacity of the system in the return water system.
The effects of the mixed air will be taken over by the equation (16), and by applying equations (8)
and (9) to the above changes, the water temperature at the inlet of the heat source equipment
&w2(n.dt + ~t) can be obtained as follows:
2m2 2m2-m+1
1
+ m~
2m2
,
lf&-w2{(n-2m2-!m)~t}
+ (
m2=~
P•tlt
'\.2+ K~
p
-t ... (20)
••• (21)
where &-f 2 and ~·w 2 , and t9w 1 and &f 1 used in equation (16) are values expressed at times (n.Llt + 4t)
and n.4t, respectively.
(3) Supply water system
Thermal changes in the return waters system are carried over into the supply water system. The
heat source equipment is located between the two systems and is subjected to the change in temperature
depending on the output Qas• Assuming that the water temperatures at the inlet and outlet of the heat
source equipment are 9 2 and()- 1 , the relation ofQRBwith them isQRB = p(&: 1 - 8-' 2 ). With O.Wt assumed to be the water !emperat~e at the inlet of heat exchanger anu-temper~ture c~ange caused by heat
invading the system qw 1 taken into consideration, ~·w 1 can be expressed by the following equation in the
same manner as above.
+
m3
2m3
"" 2113-m-1 &
2m3 ~ w1(n-2m3-~mldt +
~1
w1
=p.l\t
••• (22)
••• (23)
(4) Supply air system
Thermal changes in the supply air system are taken Over by the supply air system via heat exchanger.
Values ~or ~f2 ! ~·w 1 and~~ 2 are all as measured at time (n.dt +dt), as well as ~f 1 • In the supply air
system ~s prov~ded a fan. l§suming that the air temperature at the outlet of the heat exchanger is ~£ 1 ,
average tempQ.ratur·e of the diffused air is 19'11f 1 , power load from the fan isQKWP' and heat invading tlie
system is ~l , we can obtain &"f 1 by the following equation in the same manner as above.
&"
4
2m4
,_. 2m -m+1 l\&
&
f1[(n-2m4-~m)llt) +
2m4
m;'
+
~t)
f1(n.At+dt-2m4,
f1(n,4t+At)=
1
••• (24)
... (25)
The four systems mentioned above are connected by (a) air-conditionin g room, (b) the heat e~changer
for air-conditionin g and (c) heat source equipment. The performance of these connected systems and heat
medium transportation system will serve as various basic components of an air-conditionin g system. Also,
the air-conditionin g system is available in other types using boost heater, dual duct system, three or
,
and Q
four piping system, etc. These cases can be handled in the theoretically same manner as Q
where subrutine is prepared for the calculation. By the combination of various basic mode~ and au~
routine as required, various types of air-conditionin g systems and associated heat medium transportation
systems can_ be made up.
4.
Heating and Cooling Load in Room
When the material of wall surrounding the room, dimensions, position and service condition of the
room, atmospheric condition and initial condition are given, and room temperature and humidity are
designated, the heating and cooling load tends to be determined. In this Section, the calculation
721
system whereby the transmitting course and thermal rate of the heating and cooling load can be obtained
will. be explained.
4.1
(1)
Preparation for calcUlation s,yatem
Calculation unit and area element
Unline the conventional method to calculate the load per each room, the calculation system being
referred to in this Section is such that a plurality of rooms that little differ in temperature and are
considered equal in temperature variation during the calculation are dealt with in one cal.culation unit.
In case one room has two or more typical temperatures, as many calculation units ae the number of typical
temperatures are provided in the building. Thus, while the calculation unit has something related to
the concept of zoning, it still depends on the typical room temperatures. Practicall.y, rooms where the
temperature difference is always within ± 1o5°C may be regarded as one calculation unit.
Heating or cooling load in the room is obtained by the calculation of trans:la:l.t heat transfer phenomena, except convection heat transfer, draft and latent heat that are directly obtainable. When the room
air absorbs the heating or cooling load, its temperature changes at a rate dependent on ita heat capacity. Ae the heat capacity of this room air, an apparent heat capacity c.r.V(1+p) is used. Walls, floor
and ceiling forming a room play a leading role in the transfer of heat, radiant heat that has invaded the
room cannot become a load without having been absorbed by the solid objects in the room.
The transmission course of the heating or cooling lead is formed as a thermal system chiefly by the
surrounding structural objects, and its thermal characteristics depend largely upon the construction and
composition of the structual surroundings, the load phenomenon occurs in largely different manner depending on whether the glass window is wide or narrow, or whether a curtain wall or concrete wall. is used.
A calculation of heat transfer does not necessarily require simulation exactly to the thermal com..
position of the room, in this calculation system, the areas of structural objects equal. in heat transfer
phenoemonea are totall.ed for calculation and the results are proportionally divided per area.. These
area are called area elements for calculation.
(2)
Thick wall and thin wall
Disturbances with large changes are caused by the external atmospheric condition, and response depends on the properies of the outer wall. To estimate the rate of heat transfer from the wall body,
thermal transmittance or thermal conductivity is used. The rate of temperature changes inside the solid
can be determined according to the thermal diffusivity. The wall bodies are available in many types,
such as concrete wall having a heat capacity with property of heat insulation, metal panels having a low
heat capacity with poor heat insulating power, a combination of metal panels with heat retaining material that is low in heat capacity yet has proper heat insulation, and glass plates that let radiant heat
penetrate through.
These wall bodies are classified by heat capacity per unit area, according to which those high in
heat capacity are call.ed a thick wall and those low in heat capacity are called a thin wall. The relation expressed by equation (6) is referred to for practical classification, whereby the divided measurement 11d11 relative to divided time .4 t is determinedo Accordingly, the wall whose thickness is divided
into two or leas portions is called a thin wall, and that with three or more divisions of its thickness
is called a thick wall. For the calculation on the thin wall, equation (1) or (48) is applied combined
with such an expedient as including part of the heat capacity of the wall body in that of room air ..
~.2
Course of heating or cooling load
The calculation of heating or cooling load in the room is aimed at clarification of the quantity of
heat transfer through the analysis of the transfer course of the heating or cooling load. The flow rate
and direction of heat always involves the temperature gradient on the course according to Fourier's low.
With a temperature change of the heat medium on the course, the rate of its retained heat increases or
decreases, and this behavior of the heat has an important bearing on the load. Kink of disturbance and
intensity of the heat flow are given as the design considerations, and various equations shown in the
a.}l}len.diX
are applied for the calculation of heat transfer inside the building. The application of
these equations is very simple, and will be outl.ined below in connection with the pointe particularly
considered in this calculation method.
(1)
Heat transfer on interior structural bodies
The room bas many pillars and beams in addition to the walls,. While these structural bodies do not
serve very much as the course of the external heat, they release or absorb the retained heat with changes
in room temperatureo Also the surrounding wall has a rugged surface, which has a similar thermal action ..
To compensate for these thermal actions, subrutines by the application of equations (5) and (36) through
722
(38) are prepared.
(2)
Radiant heat transfer in the room
Let us assume a film at the boundary dividing the exterior and interior structural bodies. This
assumed film represents a surface condition of the interior structual body, and its surface temperature
(MRT) is &'Im = ji Am X f;-r.nJ ~ Ain• The effective radiant heat transfer between the external surface and
the film can be obtained by equation (42). If there is no marked temperature difference over the entire
exterior structure, its average temperature (MRT) is B'om = Y: AonX G-or/fAon• The radiant heat transferred to the assumed film from the exterior can safely be considered to be received evenly by the whole
surface of the interior structure.
(3)
Radiation from interior heating bodies
Interior heating bodies are available locally and in the objects evenly scattered on the floor,
such as human bodies and lighting equipment. In the latter case, radiant heat is emitted evenly to the
ceiling and floor.
4.3 How to set up load variation calculation system
Tb achieve calculation by computer, the design conditions and area element per room are applied as
input data. Of the results from the calculation, necessary data are taken as output, and expressed with
a proper time intenal. The calculation system must be ready to take all kinds of possible input date
conditions. If any special conditions occur, and the system is not prepared to permit their application
thereto, an approximation method is emplyed in a form close to the existing method. If the effect of
the approximation is not permissible, then the calculation system itself must be improved for higher accuracy. Such instances often occur in respect to multi-layer wall, or when the air-conditioning room is
adjacent to a room under special condition.
5.
Example of Calculation
The calculation system being dealt with in this paper is based on the simulation of a air-conditioning system, and is a computer program intended to obtain design data. The details of the setup, however,
are the questions directly related to the prograrmning, and thus are omitted in this paper. Already, this
calculation method has provide to be able to provide permissible calculation data upon application to
several existing buildings and comparison with actual. values. The .following is an example of the practical application.
5.1
(1)
Application of calculation method
Preparation for calculation
Prior to calculation, ·the air-conditioning system is determined. Then, input data are prepared
from the related materials. Since the Capacities of the associated equipment are unknown prior to the
designing, they are estimated from the actual statistic values. The capacity of heat source equipment
.for intermittent air conditioning ~ is obtainable from ita relation with the time required to stabilize the room air temperature t4, and accordingly values for p and v 1 can also be determined. For the
operation of the calculation system, engineering decisions, such as initial conditions, are required.
Various values estimated at first are ·corrected to proper values upon investigation of the calculation
results, and are recalculated if' necessary. For example, the temperature change in room air temperature
in the adjacent part that will not be calculated is assumed and if this assumption is found far different
from the calculation result obtained later, the calculation is repeated from the beginning.
(2)
Application to building ( 6)
Location: Tokyo. Name: 0 Building. Purpose of use: to provide office spaces. Construction:
SRC (curtain waJ.ls used as outer walls at the south and east sides). Scale: Nine storied, 3 basement
floors and 3 penthouses. Total area: 7,260m2. Air-conditioning area: 3,400m2. Operation: Intermittent (8:30 to 17:30).
The application of this calculation method to the air conditioning of this building was attempted.
In this application, actual values were emplyed, instead of exterior and interior design conditions.
For the air-conditioning system, the model shown in figure 3 could be applied as it is, and the calculation was carried out in one calculation unit.
723
(3)
Results of calculat ion
building and at the respecti ve
By this calculat ion method, the tempera tures and heat flows in the over the given calculat ion
detail
in
ed
calculat
be
could
system
itioning
9
air-cond
components of the
heat flow is tremendo us and practica lperior. However, recordin g of all the data on the tempera ture and was selected from among these data
design
the
for
y
necessar
ed
ly meaning less. Thus 9 what was consider
up and diagrammed as given in figure
as the output, from which values for ~ 9 &i and only were pickedmedium tempera tures &f , &-r , &"r ,
heat
the
of
changes
The
1
2
line.
1
bracken
and
lines
full
with
8 (2)
calculat ion results, the followin g
&'w1 and &•w2 were as shown in figure 9 with full lines.. From these
were found out.
n to a predeter mined level,
(a) To bring the room air tempera ture at the early stage of operatio
Accordin g to the convent ional
time.,
a
for
output
full
with
operated
be
to
is
nt
equipme
the heat source
short. Thus, the output
becomes
system
air
supply
the
in
air
of
rate
design method, however, the flow
a result of a trial. calAs
level.
ture
tempera
air
room
mined
declines prior to arrival. at the predeter
full output operatio n
that
found
was
it
,
shortage
culation with increase d supply air rate to avoid the
level, as shown in figure
mined
predeter
the
reaches
ture
tempera
air
room
the
till
d
continue
has to be
10.
of operatio n represen ts what is
(b) The part indicate d with A in figure 8 (2) at the initial stage
in the cooling operation)~
heat
e
(negativ
nt
spent for the increase in the retained heat of the equipme
from the discharg e of this
results
finished
is
n
operatio
the
after
g
appearin
B
part
the
t,
In contras
heat. Both rates of heat are not always equal, however .
ning design, adequate value
(c) By the applicat ion of this calculat ion method to the air conditio medium transpo rtation system
l heat
for Qrum, can be discover ed. There are other advantag es that rationa can be set up.
plan
suited to ~ can be designed and that a proper air-cond itioning
for QRBm, p and v 1 of the system set up
In this example, calculat ion was made using known values
those for rationa l equipme nt.
than
results
other
by the convent ional design method, thus given
5·2 Comparison with measured values and evaluati on
ent in this building are
Changes of ~ and &-i obtained from the actual. air conditio ning measurem
8 (1). Changes of
figure
as
ns
conditio
exterior
given in figure 8-12) with dotted lines together with
correspo nding calculat ion results
The
lines~
dotted
with
9
figure
in
shown
are
tures
tempera
heat medium
A comparis on between both results
are as given in figure 8 (2) and 9 with full lines and bracken line. and trends.. Although the heat
values
similar
shows
time
with
&i
snows that the change of Qru3, Q and
differen ce in control method, the necesmedium tempera tures themselv es are a little differen t because of
sary tempera ture differen ce are in near agreement,.
air-cond itioning system is the
What calls for specific attentio n here is the fact that the existing Also, when it comes to the
method.
l
rationa
a
of
not
and
method
product of the convent ional design
and cooling load, such as that from
actual construc tion, there were unexpec tedly many causes of heating
these points taken into conside ration,
the heat medium transpo rtation system exposed on the roof. With
for ~ is upavoid able ..
a differen ce by 10% or so between the calculat ed and actual values
are such that IBM ,360 comFor referenc e, the time and labor required for this calculat ion method
day, and a little more
ion
calculat
one
per
seconds
60
to
puter took 20 to 130 seconds with6t at 300
tion.
labor than for convent ional method was required for input data prepara
ion method by degital comJudging from the above, we believe the practica l value of this calculat
puter is very high.
6.
Conclus ions
have to depend on compute rs by all
In the future, calculat ions of the type mentione d above will
function method, response
are weight
means. As the calculat ion methods for solid heat transfer , there
employed in our system.. All these
method
al
numeric
the
to
addition
in
method,
factor method and analog
and cooling load, and as to
heating
the
of
3096
than
less
on
problem
methods , however , pertain to the
heating and cooling load calcuthe
of
gist
The
differ.
to
remainin g part of the load, they have little
calculat ion, but in the systema tilation should lie, not in the methodology of the solid heat transfer
zation of the calculat ion method altogeth er ..
since several years ago, -inOur calculat ion method introduc ed in this paper has been systema tized too it is possible to reduce
method,
al
numeric
the
9
With
depende ntly of the progress in other methods .
is given, and satisfac tory results
the calculat ion time and memory capacity if proper conside ration
724
coul.d be !l'btained in respect to
accuracy~
Improvement of this calculation method itself and interchange with other methods are the problems
remaining to be solved,_
This paper limited clarification to the design problems ahead of the heat source equipment outputi
and has not dealt with the air conditioning energy. It, however, can be easily obtained using, the
handling of the heat medium transportation system as a guide, provided the performance of the system
components is already known.
WhUe it is still pre,ature to draw a conclusion because of insufficient data, the physical value
for the wall body, a ( = ~ ) is considered different between cooling and heating period. For such
phenomenon, this calculation method is more advantageously applicable than other methods as in the case
of intermittent air conditioning operation.
To conclude this report, the author expresses his profound appreciation to Dr. Kenichi Hiraga under
whom he works for the opportunity of compiling this paper and very helpful advicea and guidance.
7•
7.1
Appendix
Various equations related to unsteady state heat transfer
Temperature in one dimensional object, see figure 11 (1)
... (26)
One dimensional, surface temperature of object in contact with fluid with temperature of, see
figure 11 (2)
&1.6t = 2P(&2 +
N.~f
+
N.\9-f+2G;
N + 2
<zi. - N -
1)
&;)
... (27)
see figure 11 (3)
••• (28)
One dimensional, surface temperature of object subjected to heat flux q, see figure 11 (4)
... (29)
Heat produced at uniform rate inside object Q, see figure 11 (5)
.... (30)
One dimensional, surface temperature of object with heat produced at uniform rate inside Q, see
figure 11 (6)
.... (31)
One dimensional, heat conduction between two objectst aes figure 11 (7)
- 1)
725
e;)
••• (32)
where, t\I:
without point 1.
Thermal conductivity of object with point 1, Au:
Thermal conductivity of object
Two dimensional, irregular shape surface temperature of object
In case of figure 11 (8):
••• (33)
In case of figure 11 (9):
••• (34)
In ease of figure 11 (10):
&1.Jt = 4P (
$-2 + ~
2
+ N.er +
1
(lfP-
N-
')
1)$-~
••• (35)
Value for 0( used in equations (33) to (35) is a corrected heat transfer coefficient inversely proportionate to increase or decrease in area of the object surface.
7o2 Values of P and N
Because of the condition where multiplying coeffecient for ~1 in the right member of the equations
for G-1•(lt will not become minus, 4t has a permissible maximwn limit. For example, from equations (26)
and (27) given in the latter paragraphs, we have
p ~ 1/2
1
p 52( 1-INJ
inside object
••• (36)
on object surface
••• (37)
Also, the permissible range of P relative to any value of N is as follows:
P
~1/3
••• (38)
7o3 Surface heat transfer ( 3)
Q =
.w. -
••• (39)
11'1)
where, Q: Rate of heat transfer at surface, D<: Total heat transfer coefficient, CX 0 :
heat transfer coefficient, ~r: Radiation heat transfer coefficient.
7.4 Radiation (solar) temperature
Convection
&8
.... (41)
where,
I:
intensity of radiation,
a:
absorption rate.
7o5 Radiation ( 3)
••• (42)
726
••• (43)
••• (44)
••• (45)
••• (46)
where, Q12: Net rate of radiation from surface A1 to A2 , A1 , A2 : Areas of surfaces exchanging
heat by radiation opposite to each other, ~12 : Total shape factor between A1 and A2 , T1 , T2 : Surface
temperatures of A1 _end A2 , dA , ~: Small element areas in surfaces A and Az, ¢ , ¢> : Angles be1
1
2
tween normals on dA1 and dA2 and li.iie connecting dA 1 and
f,,
~:
Emissitivities of X1 and A2 •
7o6
&8
Equivalent out door temperature
110 = 11.,.
tll1o = &.,. +
+
~'
·a 1 , a 2 :
lbaorptJ.on factors of A1 and A2 ,
and equivalent temperature difference
t(l18 ('(") -Item)
r( Irs( 't)
( 4)
••• (47)
••• (48)
i9'sm) - 1)-1
-
~~e
1 23
&sm = 21+
where, & 1 : Room air temperature,
much as before time being calculated.
f:
1:
t=o
Decrement factor, \ :
B.
( 5)
Value of
9'8
s.
Kuramochi 1 An Calculation Method of
Heating and Cooling Load,
SHASHJ, Vol.43, No.12, Vo1.44 9 No.1
~Conditioning
P.394~416.
( 6)
( 3) K. Watanabe, others, Kenchiku
Time lag, &-a(L):
References
( 1) H. s. Carslow and J. J. Jarger, Conduction
of heat in Solid, P.467-478.
( 2) Y. Kudo, Dennetsu Gairon,
lf's(t)
Ke~
s. Kuramochi, Investigation and Measurements of Air-Conditioning on Buildings
(1)
Genron, P.29, 60.
( 4) H. Uchida, Kuuki Chyosei no Kihon
Keikaku, P.90, 91
727
(3), AHASEJ, Vol.44, No.2, No.3.
as
d
I_ J T~r----r-i
'
l
L __
I
I
I
---f--4 i
I
L_
__
1------I
i
y
I
I
I
I
IL
3
L_ _ _
I
__j _ __
1
I
I
lL __
~--
5
I
____ I
!
_
I
I
-r
I
_j ___
-,
i
I
f---~
2 !
I
1
r
I
--1
I
i
_ _j
'---X
Fig-1
Heat Cond uction in Solid , Two-Dimension
728
~--------------~--------------~
(}I
(t>O)
B'
0
l
....
Q:)
t
(h
(0)
~x
81 (t
()
I
10
11 L',tl
12/ltl
Fig-2(1)-(3)
Llt
llt
1
2 ilt
Simulation of Thermal Medium Transportation
System
729
v
0 -wv--j
8i
flwz p
vl flwl
H.X. v4
v3
Ref
Bwz
val ve for hea ting
fan
p pump
pl con tro l Pan el.
Pz pump
T1 the rm ost at
F
Fig- 3
ewl
"
II
II
If
for coo ling
"
thr ee way Va lve
A Model of
730
Air- cond ition ing Syste m
opera tion start
Bi'
B
I
Fig-4
Change of Thermal Medium Temp. just after
Operation Start
Qn.v.__ _ opera tion stop
QRs"'
Q
Ql
l
B (see Fi
-t
Fig-5
Change of Value of QRB, Q"RB and Q just after
Operation Stop
731
CD
I
~(
-.
.....
.....
1 )case atQm~
c:::
....
::::1
0
Fig-6(1),(2)
-....
~
( 2) case at Q
c:::
Simulation of Heat-exchanger Performance
732
.....
~
.....
::::1
0
out door air
rl®
r/ ®
return air system :
return water system
J
l
~
"'"'
leD
air conditionin g room
Y
I
l
(]) heat exchange r
@ supply air system
Fig-7
}-®--
Y
®
I
l G) heat
supply water system
Calculation Procedure Diagram
souce equipment
1
J
N
I
oc
s.
D.B.
tot al sk y .rc'J
W.B.
It
19 67 - 8 -1 0
.
~~
c4c'Jt.
loiJ .
1
bu lb temP·
~
5
~
:r
3
wind ve loc
ity
--. .._ __ __ _:.
.
W.V.
\
2
1
10
-h
Fig- 8
(1)
Con ditio ns of Wea ther
-+-'
~
9
-+-"
-+-"
cd
~
X
tn
operation stqp
QO
,~
'
6
-~-
~
• •• 0.
. . 0... .. 0......
calculatio n
5
w
'-"
.. •
A ,....,. -------- ---[----- --------
4
I
r---t..
3
/
I
I /
,
/
.i.Q
fresh airload
. ......... .
29
-------- - - - - - - - - - - - - - - - - - - - - '
28
27
calculatio n
Bi
2
..........................7···· ....... .
26
0 0 0 0 0 •• 0
25
measurem ent
1
/
B
....
8
OC Bi
-------
9
10
Fig-8 Cont.
11
12
13
14
15
16
17
18 h
(2) Values of QRB' Q and ei obtained by Calculation and Measurement
1
oc
30~peration start
- ,
-
25t
----
,_
operati on
fJr2
stop~
~~
------~-
B
l r
20
15r
11
fJ{l
__ ... ______ ........ - - - - · - - - - - - - - -
1
1
1
I
~
11
w
~
lOr
I
----
.
f)
------
I\1
--
_____ ;
...- --- - - --
I
51-
W2
- -- --
-----
f)
w1
----
-------
symbol --calc ulatio n
---meas uremen t
08
9
Fig-9
10
11
12
13
J
I
14
15
I_
16
Thermal Medium Temp. obtained by Calculation
and Measurement
L
17
-h
18
operation start
f-
6 f-
Q RB
oc
5f4
-
.-
-
3
-
ei
2
-
"'An.
-
1
8
Fig-10
-
I
I
9
10
29
28 1
27
26
25
24
I
11-time
Results of Calculation in case of enough Air
supply
737
e
I
I
I
I
I
2
1
3
Ld
I
I
I
I
I
d----i
d
(1)
f
2
1
I
lJ
(2)
Fig-11 (1 and 2) Variation of Heat Transfer to be adopted
738
I
I
I
/;
I
/
;:;
:;;
;:;
f s~
---1
11
1
I
~
V>
~
~·
/
3
I
I
I
·~d
I
I
I
I
I
I
4
r1
1
2
//A/#/@
I
I
d--1
I
I
I
I
d~-
One dimensionlal
Two dimensional
(3)
Fig-11 Cont. (3) Variation of Heat Transfer to be adopted
Q -.....
2
I
--~-<--d__,J
(4 )
Q
I
I
I
3
1
I
2
I
I
I
I
I
I
I
I
I
I
I
Ld
I'
I
d
d_J
(5)
Fig-11 Cont. (4 and 5) Variation of Heat Transfer to be adopted
740
Q
1
f
2
I
I
I
I
d-l----d~
2
(6)
I
I
I
I
I
l
3T
I
I
I
.L
1T
II
I
I
I
I
.l.
I
2TI
I
I
I
I
I
-d
d
I
I
d~
(7)
Fig-11 Cont. (6 and 7) Variation of Heat Transfer to be adopted
741
r~d-l
I
I
I
-~-1
I
_L __
-I
2 I
----~
~
"'"'
f
f
(8)
5
(9)
Fig-11 Cont. (8 and 9) Variation of Heat Transfer to be adopted
I
I
--r-1
I
f
I
1
__ j__
1
I
'i:l
'
I
--~-
_j
I
I
I
(10)
Fig-11 Cont. {10) Variation of Heat Transfer to be adopted
743