Building Heat Load Calculation 魏晓永.docx
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Building Heat Load Calculation 魏晓永.docx
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BuildingHeatLoadCalculation魏晓永
AircraftEnvironmentalControlSystems
Project:
BuildingHeatLoadCalculation
Pro:
方贤德
Name:
魏晓永
No.:
SQ10018075001
2011-8
CONTENTS
1.Objectives1
2.Information1
3.RadiantTimeSeries(RTS)Method3
3.1calculatesol-airtemperature
3
3.2calculateheatgain
3
3.3calculate
and
3
3.4calculatecoolingload
from
4
3.5calculatecoolingload
4
3.6calculatecoolingload
4
4.CalculationresultsofRTS4
4.1Sol-airtemperature
4
4.2calculateheatgain
6
4.3calculatecoolingload
7
5.HeatBalanceMethod8
6.ComparisonoftheTwoMethods13
7.ProgramofRTSmethodandHBmethod14
7.1ProgramofRTSmethod14
7.2ProgramofHBmethod18
Project:
BuildingHeatLoadCalculation
1.Objectives
∙Estimationoftheroomcoolingloadduetoanexteriorwall.
∙Comparisonoftwomethods:
(a)theHeatBalancemethodusingtheConductionTransferFunctions(CTFs),and(b)theRadiantTimeSeriesmethod.
2.Information
ThefollowingspecificationsofanofficespacelocatedinAlbany(N.Y.)aregiven:
(1)Concretefloorof20cmthickness,withtotalfloorareaof160m2(16mx10m).
(2)Oneexteriorwall,facingsouth,16mx3.8m,composedofthefollowinglayers(fromoutsidetoinside):
brick,aircavity,metalstudswiththecavityfilledwithfiberglassbattinsulationof75mmthickness,andgypsumboard.
(3)Noexteriorwindowsanddoors.
(4)Airinfiltrationrateisequalto0ACH.Nointernalgains(people,lights,equipment).
(5)Thermostatsetpointequalto24℃,withthrottlingrangeof0.5℃.
(6)Datafortheoutsidesurfaceofexteriorwall:
hconvection=17W/m2K;α=0.8.
(7)Datafortheinsidesurfaceofexteriorwall:
hconvection=4W/m2K;hradiation=3W/m2K.
(8)Insidesurfacetemperaturesofallpartitions,floor,ceiling,andfurnitureis24.0℃.
(9)Table1showstheweatherdataforasummerdesignday.
Table1.Weatherdataforasummerdesignday
Hour
OutdoorairtemperatureT0[℃]
Totalsolarradiationnormaltotheexteriorwall[W/m2]
1
19.9
0
2
19.7
0
3
18.5
0
4
18.5
0
5
18.0
0
6
19.0
0
7
19.6
0
8
21.0
300
9
27.0
800
10
27.5
970
11
30.7
1200
12
35.0
1300
13
38.7
1200
14
42.8
970
15
38.8
800
16
37.1
300
17
35.0
0
18
29.0
0
19
25.0
0
20
23.5
0
21
22.6
0
22
21.2
0
23
21.0
0
24
20.2
0
3.RadiantTimeSeries(RTS)Method
3.1calculatesol-airtemperature
:
Outdoorairtemperature℃
:
outersurfaceflowheattransfercoefficientW/(m2.k)
:
outersurfaceofsolarradiationabsorptioncoefficient
:
IntensityofsolarradiationW/m2
:
Outersurfaceofthelong-waveradiationcoefficient
:
Poorlong-waveradiationW/m2
3.2calculateheatgain
:
ConductiveheatinputforthesurfacenhoursagoW
:
OverallheattransfercoefficientforthesurfaceW/(m2.k)
:
Surfaceaream2
:
Sol-airtemperaturenhoursago℃
:
Presumedconstantroomairtemperature℃
:
Conductiontimefactors
j=0meanscurrenthour
3.3calculate
and
Conductiveheatgainthroughwallscontainstwoparts:
convectivecoolingload(
)andradiantcoolingload(
).BysearchingthetableofconvectiveandradiantpercentagesofTotalSensibleHeatGain,wecanget:
Becauseoftime-delayeffects,radiantcoolingload(
)forthecurrenthour(θ)
3.4calculatecoolingload
from
:
RadiantheatgainnhoursagoW
3.5calculatecoolingload
3.6calculatecoolingload
4.CalculationresultsofRTS
4.1Sol-airtemperature
TheresultsofSol-airtemperature
areshownasTable2:
Table2Sol-airtemperature
Hour
Outdoorairtemperaturet0[℃]
sol-airtemperature
[℃]
1
19.9
19.9
2
19.7
19.7
3
18.5
18.5
4
18.5
18.5
5
18.0
18
6
19.0
19
7
19.6
19.6
8
21.0
35.11765
9
27.0
64.64706
10
27.5
73.14706
11
30.7
87.17059
12
35.0
96.17647
13
38.7
95.17059
14
42.8
88.44706
15
38.8
76.44706
16
37.1
51.21765
17
35.0
35
18
29.0
29
19
25.0
25
20
23.5
23.5
21
22.6
22.6
22
21.2
21.2
23
21.0
21
24
20.2
20.2
Figure1showstheresultsofRTSmethod
Figure1Theresultsofthesol-airtemperature
4.2calculateheatgain
Wehavethefigure2:
Figure2Theresultsoftheheatgain
4.3calculatecoolingload
Figure3showstheresultsof
Figure3Comparisonofheatgainandcoolingload
Fromthefigureswecangetthattheheatgainat16:
00isthehighest,1946Wandwithaphasedelayandattenuationofpeak,thecoolingloadat17:
00isthehighest,1634W.
5.HeatBalanceMethod
HBmethodcanbeviewedasfourdistinctprocedures:
(1)outside-faceheatbalance;
(2)wallconductionprocess;
(3)inside-faceheatbalance;
(4)airheatbalance.
Equationofoutside-faceheatbalanceis:
(1)
Where
=absorbeddirectanddiffusesolarradiationflux(q/A),W/m2.
=Netlong-waveradiationfluxexchangewithairandsurroundings,W/m2.
convectiveexchangefluxwithoutsideair,W/m2.
=Conductiveflux(q/A)intowall,W/m2.
Equationofinside-faceheatbalanceis:
(2)
Where
netlong-waveradiantfluxexchangebetweenzonesurfaces,W/m2.
=Netshort-waveradiationfluxtosurfacefromlights,W/m2.
=Long-waveradiationfluxfromequipmentinzone,W/m2.
=Conductivefluxthroughthewall,W/m2.
=Transmittedsolarradiantivefluxabsorbedatsurface,W/m2.
=Convectiveheatfluxtozoneair,W/m2.
Equationofairheatbalanceis:
(3)
Where
=Convectiveheattransferfromsurfaces,W.
=Convectivepartsofinternalloads,W.
=Sensibleloadcausedbyinfiltrationandventilationair,W.
=Heattransferto/fromHVACsystem,W.
Thegeneralformfortheinsideheatfluxis:
(4)
Foroutsideheatflux,theformis:
(5)
Where
=outsideCTF,k=0,1,…nz;
=crossCTF,k=0,1,…nz;
=insideCTF,k=0,1,…nz;
=fluxCTF,k=0,1,…nq;
=time;
δ=timestep;
=inside-facetemperature,℃;
=outside-facetemperature,℃;
=conductiveheatfluxoninsideface,W/m2;
=conductiveheatfluxonoutsideface,W/m2;
①formulas:
=outside-facetemperature,℃,i=1,2,…,12;j=1,2,…,24
=inside-facetemperature,℃,i=1,2,…,12;j=1,2,…,24
=coolingload,j=1,2,…,24
Fromequations
(1)and(4),wecanget:
Where:
=outsideairtemperature
=outsideconvectionheattransfercoefficient
Fromequations
(2)and(5),wecanget:
where:
=roomairtemperature
=insideconvectionheattransfercoefficient
Fromtheequation
(2),wecanobtain:
and
areallequalto0.Sowecansimplifyqsys.
②WecanobtaintheCTFsandRadiantTimeSeriesvaluesbyusingthePRFgen.CTFsvaluesareputinTable3,whileCTSandRTSvaluesareputinTable4.
Table3.CTFsvalues
CTF
X-Exterior(W/m2K)
Y-Cross(W/m2K)
Z-Interior(W/m2K)
Flux
0
11.28142452
0.000322116
4.947700024
0
1
-17.19666862
0.014172389
-9.024801254
1.250475287
2
6.705113411
0.031286769
4.501733303
-0.399797946
3
-0.757661641
0.009221151
-0.377397597
0.028814277
4
0.023245038
0.000358497
0.008133379
-0.000552414
5
-9.0643E-05
9.96527E-07
-6.20116E-06
3.33923E-08
6
2.71818E-09
6.65832E-11
3.34581E-10
-2.62222E-13
7
-1.53771E-14
8.40115E-17
-2.27363E-15
-4.46136E-19
Table4.CTSandRTSvalue
Hour
CTS
RTS
1
1.58%
31.3%
2
24.55%
20.1%
3
32.26%
13.6%
4
19.45%
9.49%
5
10.43%
6.78%
6
5.53%
4.92%
7
2.92%
3.60%
8
1.54%
2.65%
9
0.82%
1.96%
10
0.43%
1.46%
11
0.23%
1.08%
12
0.12%
0.81%
13
0.06%
0.60%
14
0.03%
0.45%
15
0.02%
0.33%
16
0.009%
0.25%
17
0.005%
0.19%
18
0.003%
0.14%
19
0.001%
0.10%
20
0.0007%
0.08%
21
0.0004%
0.06%
22
0.0002%
0.04%
23
0.0001%
0.03%
24
0.00006%
0.02%
Figure4showstheresultsofRTSandCTS:
Figure4TheresultsofRTSandCTS
③Theresultsofcalculation
Table5showstheresultsofcoolingload.
Table5Theresultsofthecoolingload
Time(h)
Outside-facetemperature
Tso(K)
Inside-facetemperature
Tsi(K)
Coolingload
qsys(W)
1
298.63
297.213
15.2346
2
297.766
297.198
11.6499
3
296.393
297.184
8.3094
4
295.753
297.17
4.8799
5
294.917
297.155
1.1814
6
295.023
297.14
-2.4561
7
295.028
297.127
-5.6086
8
304.074
297.119
-7.6353
9
322.59
297.126
-5.8035
10
330.08
297.185
8.4085
11
340.692
297.314
39.7975
12
348.762
297.483
80.8947
13
350.836
297.661
124.341
14
348.901
297.822
163.414
15
343.073
297.936
191.086
16
328.413
297.984
202.816
17
317.623
297.955
195.67
18
312.421
297.844
168.808
19
308.5
297.685
130.188
20
306.129
297.527
91.6669
21
304.283
297.4
60.8144
22
302.28
297.314
39.8644
23
301.077
297.262
27.233
24
299.667
297.232
19.8665
6.ComparisonoftheTwoMethods
Figure5Comparisonofthetwomethods
Figure5showsthecomparisonofthetwomethods.Fromcomparisonwecanget,themaximumvaluesandtheminimumvaluesarealmostatthesametime.Butthevaluesofcoolingloadalmosthavedifferencesateachtime.
7.ProgramofRTSmethodandHBmethod
7.1ProgramofRTSmethod
hour=1:
24;%时间序列
U=0.4983269;%总传热系数
A=60.8;%传热面积
trc=24;%室内计算温度
a=0.8;%吸收系数
ho=17;%墙外表面传热系数
%室外气温
to=[20.2,19.9,19.7,18.5,18.5,18,19,19.6,21,27,27.5,30.7,35,38.7,42.8,38.8,37.1,35,29,25,23.5,22.6,21.2,21];
%综合温度
te=[19.9,19.7,18.5,18.5,18,19,19.6,35.11765,64.64706,73.14706,87.17059,96.17647,95.17059,88.44706,76.44706,51.21765,35,29,25,23.5,22.6,21.2,21,20.2];
plot(h,to,'--r+',h,te,'-bd');
h=legend('airtemperature','Sol-airtemperature',2)
xlabel('hour(h)')
ylabel('temperature(℃)')
title('AirandSor-airtemperature')
gridon
%太阳辐射强度
I=[0,0,0,0,0,0,0,0,300,800,970,1200,1300,1200,970,800,300,0,0,0,0,0,0,0];
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