Mechanism of Indoor Vertical Temperature Profile in Nature Ventilation BuildingNumerical Calculation on Vertical Temperature Profile with Block Model

Student Member: †Cheng ZHANG(Osaka University) SHASE Technical Fellow: Toshio YAMANAKA(Osaka University) SHASE Technical Fellow: Hisashi KOTANI(Osaka University) Member: Yoshihisa MOMOI (Osaka University)

SHASE Technical Fellow:Kazunobu SAGARA (Osaka University)

Using chimneys for natural ventilation is considered as an effective way to save energy in summer and intermediate seasons. However, the effect of the chimney on indoor thermal environment in wintertime still remains unknown well. In this study, an environmental measurement and a simple mathematical model is applied to figure out whether the indoor vertical temperature difference in wintertime is due to the chimney`s open state or it's affected by some other factors.

1.Introduction Nowadays, the passive environmental control methods are becoming more and more popular on the background of global warming. The chimney is adopted in many buildings for its advantage to promote ventilation effectiveness by stack effect in summer and intermediate seasons. However in the buildings where the chimney was open all the time, the chimney`s effect on indoor thermal environment in wintertime remained unknown. In the previous study, the open chimney was suspected to be the reason of the large vertical temperature gradient in wintertime. So the mechanism of the indoor vertical temperature profile in a particular building, where staircases are used as chimneys, is studied in this research, to figure out the factors that cause the vertical temperature difference.2.Background The target building is a schoolhouse in Takamatsu, Kagawa. Figure-1 shows the 3rd plan of the building and the sections of east and west chimneys are given in Figure-2 and Figure-3 respectively. Figure-4 demonstrates the scheme of the natural ventilation system in summer and intermediate seasons. In winter of 2009, Wakamatsu et al.1) conducted an environmental measurement in the same building, finding that a large indoor vertical temperature difference existed. Moreover, it was recognized that about 80% residents felt cool in corridor and staircase space, according to the results of a questionnaire survey. At that time, the chimneys` open state was suspected to contribute to the vertical temperature profile, for cold air might flow into the building from the upper vents of the chimneys. To figure out the chimneys` effect on indoor thermal environment, two steel doors are installed in both upper vents of the chimneys, then another environmental

Period 2/3 ～ 2/6 2/7 ～ 2/17

Steel Doors Open Shut

Temperature in Each Parts Measured Measured

Temperature Stratification Measured Measured

Air Change Rate in a Roomby Tracer Gas Method

Feb.3ndTested

Feb.9thTested

Table-1 Items of the measurements

West Chimney

Section-164000

17400

Section-2

East Chimney

Room B

Room A

Figure-1 Plan of the 3rd Floor

N

Aluminum Louvres Aluminum Louvres

Aluminum Louvre

Figure-3 Section-2

Steel DoorSteel Door

Figure-2 Section-1

east

chi

mne

ynatural draft

wes

t chi

mne

y

induced draft

Figure-4 Natural Ventilation Scheme

measurement is conducted in February, 2013.　 3.Details of the measurements Table-1 shows the items of the measurements. In the measurements of temperature stratification, thermometers (TR-71S &.TR-72S, T&D Corp.) are attached to vertical bars at the height of 100mm, 600mm, 1100mm, 1700mm and 2200mm above floor. Figure-5 shows the plan of Room A, where temperature stratification is measured. T h e m e a s u r e m e n t s o f a i r c h a n g e r a t e a r e conducted in Feb.3rd and 9th, by setting portable CO 2 ana lyzers (RTR-575 , T&D Corp . ) to the designated points (shown in Figure-6). Tracer gas method(concentration decay method) with CO2 is adopted under several experimental conditions given in Table-2. Figure-6 shows the plan of Room B, where the measurements are done.4.Results of the measurements Figure-7 shows the contrast of vertical temperature profiles between the chimneys` open and close states. It indicates that the vertical temperature difference exists both when the chimneys are opened and shut, with the air conditioner under heating operation. Besides, without heating operation, the temperature at the height of 100mm above floor near the window is lower than that near the corridor, which may be the result of the infiltration from a ventilation vent. Figure-8 and Figure-9 show the concentration variation of CO2 in Room B on Feb. 3rd and Feb. 9th, in which the measurements periods are marked. Dealing with the data by least-squares method, the air change rate for each case can be calculated. The results are given in Table-3. Comparing the results of Case 1 and Case 3, due to closing chimneys, the decreasing tendency on air change rate is observed. Besides, from the results of Case 3 and Case 5, the air change rate drops when ventilators are blocked, which verifies the increase of infiltration through ventilators. By the environmental measurements, it`s confirmed that though shutting the steel doors reduces the air change rate, the vertical temperature profile is rarely influenced, i.e. the effect of solar chimneys on vertical temperature profile is not significant. Relatively, the data warrant us the possibility of cold draft near the window and infiltration through ventilators, which may contribute to the vertical temperature difference.5.Introduction of Block Model

Table-2 Experiment Conditions

15003200

7200

900

2000

1100

1400

2700

outdoors

Figure-6 Plan of Room B

1200 1000500

Legendair conditioner sampling point

tracer gas dispersion pointventilating opening

Figure-5 Plan of Room A

3200

300350 3000

7200

1200

450

outdoors

aisle

aisle sidemeasure pointpoint-a

point-b

window sidemeasure point

Figure-7 Indoor Vertical Temperature Distribution

Temperature[℃]10 15 20 25

14:00

18:00

12:0016:00

10:0012:00

10 15 Temperature[℃]20 25

14:00

18:00

16:00

12:00

10:00

Hei

ght a

bove

Flo

or[mm]

10 15 20 25

14:00

18:00(Open air:5.5℃～10.3℃)

(Open air:9.8℃～10.5℃)

16:00

10:00

0100

600

1100

1700

2200

10 15 20 250100

600

1100

1700

2200

14:00

18:00

16:00

12:0010:00

Hei

ght a

bove

Flo

or[mm]

Feb.6OpenPoint-a

Feb.6OpenPoint-b

Feb.15ClosePoint-a

Feb.15ClosePoint-b

AveragedVelocity

PrevailingDirection

1 2/3 Open On Off 1.6m/s North2 2/3 Open Off Off 2.4m/s North3 2/9 Shut On Off 2.6m/s North4 2/9 Shut Off Off 3.0m/s North5 2/9 Shut On Off, blocked 2.5m/s North

Case DateSteel

DoorsMix Ventilator

External Wind

0 10:30

5000

3000

1000

11:00 11:30 12:00 12:30Figure-8 CO2 Concentration Variation on Feb.3

Indoor CO2 Concentration [ppm]

Case1 Case2

Figure-9 CO2 Concentration Variation on Feb.9

50011:00 11:40 12:20 13:00 13:40 14:20 15:00 15:40

1500

2500

Indoor CO2 Concentration [ppm]

Case3 Case4 Case5

0

To predict indoor vertical temperature profile in large atria, Togari et al.3) created a simple block model in the previous research. We have based the model on it, for its validity on simulating the property of cold draft in rather small rooms. Figure-10 shows the calculation algorithm and Figure-11 demonstrates the scheme of the model. The formulas used in the model are given in Table-4. Also, the values of physical parameters are listed in Table-5. In this model, given the initial block temperatures, the temperatures of each surface contacting the blocks as boundary conditions, the flow rate and the heat transported between blocks are calculated in every 0.05s. After that, the block temperatures are renewed and the time progress of vertical temperature profile can be obtained by forward difference method. However, the infiltration

Table-3 Measured Air Change Rates

Case Period[s] Air ChangeRate[1/h]

Coefficient of Determination

1 3060 0.721 0.99342 1500 0.842 0.99953 3600 0.522 0.99784 3600 0.688 0.99515 3600 0.394 0.9985

Figure-11 the Schematic Construction of Block Model

Figure-10 Algorithm of Calculation by Block Model

Nomenclatures in Fig.11T(I): the temperature of block ITc: ceiling temperatureTf: floor temperatureVin(I,W): the amount of the flow returned from the mixed flow in block I on W-sideQin(I,W): the amout of the heat returned from the mixed flow in block I on-W sideTm(I,W): the temperature of the mixed flow in block I on W-sideTg(I): the surface temperature of G-side in block IVout(I,G): the amount of flow involved in mixed flow in block I on G-sideQout(I,W): the amout of the heat involved in the mixed flow in block I on-W sideVc(I): the amount of the flow between block I and block I+1Qc(I): the amount of heat carried by the flow between block I and block I+1Qb(I): the convective heat between block I and block I+1 VBLOCK(I): the volumn of block I

No

Flow Amount of Cold DraftHeat Transferred by Cold DraftHeat Transferrd by Diffusion

Flow Amount Transferred by AdvectionHeat Transferred by Advection

End

EquilibriumYes

Flow Amount Balance in Each Block

Start

Imput Physical

Parameters

Initial Block TemperatureGlass Surface TemperatureWall Surface Temperature

Model SpecificationAir Properties

Heat Transfer Coefficient

Imput Boundary Condition

OutputPrimaryResult

OutputSecondary

Result

New Block Temperaturein Each Block

Heat Balance in Each BlockOutputTertiaryResult

TNEW(I)=TOLD(I)

Floor Tf

BLOCK-1

Ceiling Tc

T(1)

Tg(1)

Vout(1,G)Qout(1,G)

Vout(1,W)Qout(1,W)

Vout(2,W)Qout(2,W)

Vout(3,W)Qout(3,W)

Vout(4,W)Qout(4,W)

Vout(5,W)Qout(5,W)

Vin(5,W)Qin(5,W)Tm(5,W)

Vin(4,W)Qin(4,W)Tm(4,W)

Vin(3,W)Qin(3,W)Tm(3,W)

Vin(2,W)Qin(2,W)Tm(2,W)

Vin(1,W)Qin(1,W)Tm(1,W) Vin(1,G)

Qin(1,G)Tm(1,G)

Vin(2,G)Qin(2,G)Tm(2,G)

Vin(3,G)Qin(3,G)Tm(3,G)

Vin(4,G)Qin(4,G)Tm(4,G)

Vin(5,G)Qin(5,G)Tm(5,G)

Qb(1)

Qb(0)

Qb(5)

Vc(1)Qc(1)

Vc(2)Qc(2)

Vc(3)Qc(3)

Vc(4)Qc(4)

Qb(2)

Qb(3)

Qb(4)

Vout(2,G)Qout(2,G)

Vout(3,G)Qout(3,G)

Vout(4,G)Qout(4,G)

Vout(5,G)Qout(5,G)

Tw(1)

Tg(2)Tw(2)

Tg(3)Tw(3)

Tg(4)Tw(4)

Tg(5)Tw(5)

BLOCK-2 T(2)

BLOCK-3 T(3)

BLOCK-4 T(4)

BLOCK-5 T(5)

[ ]1

1 1

1/( ) ( )1/ / 1/

( )aisle i

i iW

i

T I T I T Sl

T IS

αα λ α

− − + + =∑

∑

Table-4 Formulas Used in Calculation by Boundary ConditionFlow Amount Balance for Each Block

Heat Balance for Each Block

Temperature and Amount of Downward Flow On Glass Surface

Temperature and Amount of Mixing Flow on Glass Surface

Heat Transferred between Blocks by Turbulent Diffusion

Heat Transfer CoefficientGlass・Wall Surface Temperature

Distribution of Mixing Flow

Boundary Condition( , ) ( , ) ( , ) ( , ) ( 1) ( ) 0IN IN OUT OUT C CV I G V I W V I G V I W V I V I+ − − + − − = (1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(13)(11) (12)

( , ) 0.75 ( ) 0.25 ( )D WT I G T I T I= +( 1, ) ( 1, ) ( , ) ( , )( , )

( , )MD M OUT D

MM

V I G T I G V I G T I GT I GV I G

− − +=

( , ) ( 1, ) ( , )M MD OUTV I G V I G V I G= − +

( , )INV I G

( , ) ( )MT I G T I≥

( , ) ( 1)MT I G T I≤ +

( ) ( , ) ( 1)MT I T I G T I> > +

( , )MV I G=

( , ) ( )( , )( ) ( 1)

MM

T I G T IV I GT I T I

−=

− −

0=

{ }( ) ( ) ( ) ( ) ( 1)b B BQ I C I A I T I T I= − +

[ ]1

1 1 1 0

1/( ) ( ) ( )1/ / 1/g OUTT I T I T I T

lα

α λ α= − −

+ +

4 ( , ) ( , )( , ) C WOUT

I G A I GV I GCρ

α ⋅=

( )B t BC I a C Lρ=

( , ) ( , ) ( , ) ( , ) ( 1) ( ) ( 1) ( ) ( )IN IN OUT OUT C C b b BlockQ I G Q I W Q I G Q I W Q I Q I Q I Q I C V I Tρ ρ+ − − + − − + − − = ∆

through ventilators is not taken into account. 6.Results and Discussion Figure-12 shows the variation in 80 minutes of vertical temperature profile in Room B in a natural cooling procedure, while Figure-13 shows the calculation results under the same boundary condition. It's important to mention that the ceiling and floor temperatures are adopted by minimizing the sum of squared deviation of the data. Comparing the results of the measurements and calculation, it 's found that both of the vertical temperature difference decrease during the procedure of natural cooling. It confirms that cold draft affects the indoor vertical temperature profile dominantly. Furthermore, in the measurements results, there is a conspicuous discrepancy between the temperatures of Block 3 and Block 4. This discrepancy can be explained

as follows. A ventilator is installed at the height of Block 3, and infiltration through its opening drops by density difference, leading to an decrease in temperature of Block 4, while the other ventilator installed at the height of Block 1 lets out equal amount of indoor air to maintain the pressure balance in the room.7.Summary After excluding the effect from chimneys by environmental measurements, block model is adopted to verify the argument that cold draft near the window and the infiltration through ventilators are the possible causes for the vertical temperature difference in the studied building in wintertime. Finally, it is our aim to develop a new model, which can estimate the effect of infiltration quantitatively.

Reference1)N.Wakamatsu, H.Kotani, K.Sagara, T.Yamanaka, Y.Momoi, T.Fujimoto, T.Sakaguchi, K.Tanaka: Natural Ventilation Performance of School Building with Staircase Chimney Part.5, Transactions of the Japan Society of Heating, Air Conditioning and Sanitary Engineers, pp285-288, 20092)Zhang, T.Sakaguchi, T.Yamanaka, H.Kotani, Y.Momoi, K.Sagara: Natural Ventilation Performance of School Building with Staircase Chimney Part.8, Transactions of the Japan Society of Heating, Air Conditioning and Sanitary Engineers (Kinki Branch) No.43, pp289-292, 20143)S.Togari, Y.Arai, K.Miura: Simplified Prediction Model of Vertical Air Temperature Distribution in a Large Space Part1. Study on a Thermal Environment Design System for Large Spaces, Journal of Archit, Plann, Environ, Engng, AIJ, No.427, 1991

Acknowledgement The technical support from Mr. Sakaguchi (Graduate Student of Osaka University) is greatly appreciated.

9

11

13

15

17

19

21

23

25

27

0 600 1200 1800 2400 3000 3600 4200 48009

11

13

15

17

19

21

23

25

27

0 600 1200 1800 2400 3000 3600 4200 4800

Figure-12 Decay of Block Temperature (Measured Value)

9 9 90 0 01200 1200 12002400 2400 24003600 3600 36004800 4800 4800

13 13 13

17 17 17

21 21 21

25 25 25Case 1 Case 3Case 2Feb.3rd Feb.9thFeb.6th

block1block3

block2

block4block5

block1block2

block3 block1block2

block3

[℃ ]

block5 block5block4block4

9

11

13

15

17

19

21

23

25

27

0 600 1200 1800 2400 3000 3600 4200 4800

Figure-13 Decay of Block Temperature (Calculated Value)

9 9 90 0 01200 1200 12002400 2400 24003600 3600 36004800 4800 4800

13 13 13

17 17 17

21 21 21

25 25 25Case 1 Case 3Case 2Feb.3rd Feb.9thFeb.6th

block1block2

block3

[℃ ]

block1block3block2

block1block3

block2

block5 block5

block4

block4 block4block5

Table-5 List of ParametersParameter Value Explanation

h 0.580[m] height of blocksAw,Ag 1.830[m2] area between block and glass(wall)

S 23.040[m2] area between blocks(floor area)Cp 1006[J/(kg・℃ )] specific heat of air

ρ 1.295[kg/m3] density of air

αc 3.5[W/(m2・℃ )] convective heat transfer coefficient of glass( wall)

CB 2.18[W/(m2・℃ )] heat transfer coefficient by turbulent diffusion

α0 23.3[W/(m2・℃ )] outdoor heat transfer coefficientin winter

α1 9.3[W/(m2・℃ )] indoor heat transfer coefficient

λ1 0.793[W/(m・℃ )] thermal conductivity (glass)

λ2 0.163[W/(m・℃ )] thermal conductivity (wood)

λ3 1.63[W/(m・℃ )] thermal conductivity (concrete)