Analysis of interzonal natural convective heat and mass flow: Benchmark evaluation

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Analysis of interzonal natural convective heat and mass flow:

Benchmark evaluation

Said, M. N.; Barakat, S. A.

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Ana lysis of int e rzona l na t ura l c onve c t ive he a t a nd m a ss flow :

Be nc hm a rk e va lua t ion

N R C C - 3 8 5 5 2

S a i d , M . N . ; B a r a k a t , S . A .

F a l l 1 9 9 4

A version of this document is published in / Une version de ce document se trouve dans:

Building Research Journal,

3, (2), Fall, pp. 35-53, 1994

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Volume 3, Number 2, 1994 ₃₅

Analysis of Interzonal Natural Convective Heat and Mass

Flow-Benchmark Evaluation

M.N.A. Said and S.A. Barakat

ABSTRACT

This paper presents an analysis of inter-zonal natural convective heat and mass trans-fer through doorway Apertures using a three-dimensional computation. The main ob-jectives of the study were to benchmark evalu-ate a public domain Computational Fluid Dynamics (CFD) computer program in predict-ing interzonal convective heat and mass trans-fer, and also to analyze the interzonal

convective air flow patterns in a two-zone enclo-sure in order to better understand the effect of the aperture size on the natural convective in-terzonal heat and air mass flow.

Computational results are compared to measurements from full scale experiments in a

two zone realistic building. The experiments

in-volved natural convective interzonal heat and mass transfer through various doorway-like ap-erture configurations between two zones in a building. The air flow through the aperture was driven primarily by a small zone-to-zone temperature differential in the range l°C to 2.5°C, Computations are reported for air

(Pr = 0. 71), aperture height relative to the

en-closure height in the range 0. 75 to 1, and aper-ture width relative to the enclosure width in the range 0.29 to 0. 79. Computed temperature and velocity of the indoor air agree reasonably well with the measured data. Computed coeffi-cient of discharge and Nusselt number for natu-ral convective interzonal air mass and heat flow also agree quite well with those measured and with theoretically derived coefficients in the literature.

The authors are with the Institute for Research in Construc-tion, National Research Council Canada, Ottawa, Ontario,

Canada KIA ORB.

NOMENCLATURE

c

cd

Cp F

F.

Ft g gi GrH h H

H,

k K constant in correlations

volumetric coefficient of discharge specific heat of air (Jikg· K)

volumetric air flow rate (m3/s)

computed volumetric air flow rate (m3/s)

theoretical volumetric air flow rate (m 3/s)

gravitational acceleration, 9.81 (m/s 2)

gravitational acceleration in xi direction (m/s 2)

Grashofnumber,

ｧｪＳｈ

Ｓ

ｾｔＯｶＲ＠

(dimension-less)

convective heat transfer coefficient, pF 0CrfHW

2

(W/m ·K)

aperture height (m)

room (enclosure) height (m)

turbulent kinetic energy (J/kg or m 2/s 2)

thermal conductivity of air (W/m·K) NuH Nusselt number, hHIK (dimensionless)

P pressure (Pa)

P, Prandtl number (dimensionless)

q volumetric heat generation rate {W/m

l)

ｾ＠ aperture height ratio,

H1H,.

Rw

aperture width ratio, W/W,

t time (sec.)

U; mean velocity component in X; direction (m/s)

u.

velocity component normal to wall surface

(m/s)

Ut velocity component parallel to wall surface

(m/s)

W aperture width (m)

w

r partition width (m)

36

X; Cartesian coordinate

thermal diffusivity of air (m 2/s)

coefficient of thermal expansion (IlK)

AT. difference between average air

tempera-tures in each zone at a level of half the

en-closure height (K)

AT m difference between air temperatures at the center of each zone at a level of half the

enclosure height (K)

ATv difference between average air

tempera-tures of a vertical grid of nodes at the

cen-tre of each zone (K)

e dissipation rate of turbulent kinetic energy

(Jikg·s)

v kinematic viscosity (m 2/s)

a

temperature difference between local temp·

erature and a reference one (K)

p air density (kg;lm 3)

INTRODUCTION

Natural convective interzonal heat and air mass transfer through doorway-like apertures

in vertical partitions is an important process by

which thermal energy and indoor contaminants

are transported from one zone (room)

to

an-other in buildings. Computational Fluid Dy-namics (CFD) numerical techniques are now viable tools for the analysis of interzonal heat and air flow in buildings. The main objectives

of this study were

to

benchmark evaluate a

pub-lic domain CFD computer program in predict-ing interzonal convective heat and mass

transfer, and also

to

analyze the air flow

pat-tern in a two-zone enclosure. The results as-sisted in better understanding the effect of the aperture size on the natural convective inter-zonal heat and air mass flow and air distribu-tion in a two zone enclosure.

Three-dimensional computational results

are compared

to

measurements from full scale

experiments in a two-zone realistic building. The experiments (SaYd, Barakat, and Whidden 1993) involved natural convective interzonal heat and mass transfer through various door-way-like aperture configurations under small zone-to-zone temperature differentials. The en-closure aspect ratio (the ratio of enen-closure

height

to

enclosure length) of the test building

Building Research Journal

is 0.26. The aperture configurations included aperture height ratio (Rh) in the range 0.75 to 1, and aperture width ratio <Rw) in the range

0.29

to

0. 79. The partition thickness was in the

range 0.021

to

0.028 of the aperture height.

The natural convective air flow through the ap-erture was driven primarily by a small

zone-to-zone temperature differential in the range 1

•c

to 2.5•c.

Computation studies that have examined in-terzonal natural convection are limited. Slavko and Hanjalic (1989) computed laminar and tur-bulent natural convective air flow patterns and temperature distribution in a two-dimensional rectangular enclosure with and without parti-tion simulating solar or heated buildings. Slavko and Hanjalic compared computed re-sults to measurements by Nansteel and Greif (1981) involving a two-dimensional laminar free convective in a water filled scale model rec-tangular enclosure with an aspect ratio of 0.5,

aperture height ratio in the range 0.25

to

0. 7 5,

and partition thickness in the range 0.083 to 0.25 of the aperture height (note that for the 2-D enclosure, the aperture width ratio is 1.0). For the turbulent flow cases, they used a low-Re-number k-e turbulence model to simulate a two-zone enclosure with an aspect ratio of 0.37 that mimics a solar heated building.

Haghighat eta!. (1989) used a high-Re-number k-e turbulence model to study the effect of door height and its location in the partition on natu-ral convection and air flow pattern in a three-di-mensional partitioned rectangular enclosure dimensioned 10 x 4 x 3m. The interzonal con-vective air flow through the aperture was un-der the influence of the hot and cold

temperatures of the two opposite end walls

that are parallel

to

the partition. These walls

were assumed to be isothermal. The other walls were assumed to be adiabatic. Haghighat et a!. evaluated their numerical scheme by com-paring computed Nusselt numbers to those measured by Nansteel and Greif(1984) in a water fllled scale model rectangular enclosure (aspect ratio of 0.5) and aperture

configura-tions ofRh

=

0. 75 and Rw

=

0.093 which is

rather a narrow opening. In the present study, computed air temperature, velocity, vertical temperature stratification, coefficient of

dis-charge, and Nusselt number are compared

to

measured data from experiments conducted in a realistic building.

Volume 3, Numlier 2, 1994

EXPERIMENTS

This section, briefly, describes the interzonal experiments. The experiments (Sai:d, Barakat, and Whidden 199S) were performed in a full

scale test house facility. Figure 1 shows the floor

plan and the aperture configuration of the tqst

facility used in the experiments and the

nu-merical simulations. The partition wall separat-ing the two zones was constructed of 0.0508 m (2 in) polystyrene. The aperture was situated

in the middle of the partition and did not have

a sill. Table 1 lists the aperture configurations. All interior surfaces of the test house were practically isothermal. Direct solar radiation was blocked from entering the two test zones. Three baseboard heaters were located at the back wall of each test cell (one in the hot zone

and two in the cold zone, Figure 1 ). The heaters

were used to maintain nominal zone-to-zone

temperature differences between 1

•c

and

2.5°C. Power consumption of each heater (Table 1) was measured with a kWh pulse me-ter.

The velocity and temperature distributions of the air at the aperture were measured with a

vertical grid of 7 to 101 omnidirectional

ane-mometers (with velocity and temperature meas-uring sensors). The accuracy of the omni-directional anemometers was estimated to be ±2.5 percent for the velocity range 0.05-1.0 rnls

and the absolute accuracy of temperature

meas-urements was ±0.5°C. Trees consisting of nine copper-constantan thermocouples were located

37

at the centre of each zone along the centre line

of the aperture (Figure 1 ). The air temperature

in surrounding rooms and outdoors were also monitored in the experiments. The maximum uncertainty in measured temperatures by the copper-constantan type thermocouples was

esti-mated to be ±Q.1

•c.

Measurements were

col-lected continuously over at least a 24 hour period. Steady-state conditions were desig-nated when there was negligible change in room air temperatures for at least 4 hours. The results were then averaged over a 12 hour steady-state period.

SIMULATION METHOD

The public domain CFD computer program

EXACTS was used in this study. Kurabuchi,

Fang, and Grot (1990) describes EXACTS in

de-tail. EXACTS is a three-dimensional finite

dif-ference computer program for simulating buoyant turbulent air flow within buildings. The buoyancy effect is accounted for by Boussi-nesq approximation. The program solves the conservation equations for continuity, momen-tum, and energy as well as the equations for the turbulent kinetic energy and its dissipation rate. The high-Reynolds-number k-e

turbu-lence closure is used in EXACT3. The

govern-ing equations can be written in the general elliptic form for an incompressible fluid as:

(1)

Table 1. Tests (Sai'd, Barakat, and Whidden 19931 Configuration

Aperture Heater Power Watt)

Test _(m)

w

_(m) H

Rw

Rh

DTa

H1

H2

H3

(OC\

ｾ＠

1.49

2.41

0.49

1.00

1.8

1300.5

1.49

2.11

0.49

0.88

2.2

ＱＲＹＴＮｾ＠

1.49

1.81

0.49

0.75

2.0

570.6

D

0.88

2.41

0.29

1.00

2.2

886.0

E

0.88

2.11

0.29

0.88

2.3

711.0

F

0.88

1.81

0.29

0.75

2.5

665.1

G

0.88

2.41

0.29

1.00

1.1

368.2

196.3

207.0

H

0.88

2.11

0.29

0.88

1.1

388.6

190.5

199.2

I

1.49

1.81

0.49

0.15

1.2

315.9

160.1

168.8

J

2.41

2.11

0.79

o.aa

1.2

739.3

154.6

164.6

38 Building Research J oumal

(a) Floor Plan

9.27m

,.,

' ｾ＠

Hot Zone

ｾ＠

E

"'

-:1: Cll

2:.

A:f:l

A

ｾｩﾷＭＭＭＭ［ＭＭＭＭＭＭｾ＠

_{ＱＭＭＭＭＭＭＭ［ＭＭＭＭＭｾ＠}

- Cll _Thermocouple

J

C') ｾ＠ Thermocouple ｾ＠

:z:

Tree Tree

:z:

E

Cold Zone

•

N

I -M'

2:.

ｾ＠ Cll

ｾｺ＠

1'5

:'

Cll :1:

...

4.57m

,.,

y

(b) Aperture configuration

ｾ＠

E

...

'II:

C\1

w

3.05m

Figure 1. Geomelry and coordinate syslem

Volume ｡Ｌｎｵｭｾｲ＠ 2, 1994

where the parameters

q,,

r,

and

s,

are

identi-fied for each equation in Table 2, Wall boundary conditions used by EXACT3 are also listed in Table 2.

marker and cell method by Harlow and Welch

(1965). A staggered grid and a hybrid up-wind/central differencing combination scheme

are used in EXACTS.

39

A pressure relaxation method is used to sat-isfy the Poisson equation for mass conserva-tion. The governing equations are solved by an explicit time marching technique using the

In the simulation, measured power

consump-tion of the baseboard heaters (see Table 1) was

simulated as nodal heat sources. Thus, the heat input into the flow domain was assumed

Table 2. Values ｯｦｾＬ＼＾Ｎ＠ and S• associated with equallan (I)

$

r$

s$

1 0 0 (Continuity)

u,

V +Vt (-1/p) ilP/ilxi • ｾ＠ 9i 9 9 _{ex+ vt!a9} q/p Cp k V + VtfCJk vt + G- e e v +vvae (C1 Vt

s -

c2 e + c3 G) e

I

k Vt = c₁₁ k2t e, eddy viscosity

S = (ilUjlilXj • ilUjilxi) ilUjlilXj

G = ｾ＠ 9i (vtfa9)il9/ilxi

Empirical coefficients :

Cll= 0.09, C1= 1.44, C2= 1.92, C3= 1.0,

C1k= 1.0, ae= 1.3, ae= 0.9

Wail Boundary Conditions:

Un

=

0.0

auvay

=

Ut1 2m/y

ilkliln

=

0.0

e = Cu314 k312t y, where:

m

=

1/7, is the exponent of the velocity 1/7th power-law relation,

y is the length from wail surface to centre of the fluid cell immediately adjacent to wail, and

Ut1 is the velocity component parallel to wail surface at the centre of the fluid cell immediately adjacent to wall

40

to be transmitted immediately to the fluid cells

adjacent to the heaters. All walls, except the

floor, were assumed to be isothermal. The floor was assumed to be adiabatic because it was very well insulated, and the space below was heated to 2o•c. The temperature of the wall surfaces was estimated from known thermal re-sistance of the walls and measured ambient air temperatures. Wall surface temperatures (aver-age for all tests) for the floor, ceiling, north wall, east wall, south wall, and west wall were respectively 25.6, 25.2, 24.6, 25.2, 25.6 and 24.6°C for the hot zone, and 24, 23.5, 24, 23, 23.3 and 23°C for the cold zone. The wall sur-face conductance was taken from

ASHRAE(1989) as 9.26 and 8.29 W/m2 _{K for}

the ceiling and vertical walls respectively. These values account for the convective as well as radiative heat transfer from the surfaces, and were chosen because EXACT3 does not cal-culate radiative heat transfer. The chosen val-ues assume non-reflective surfaces with a surface emittance of0.9 (ASHRAE 1989). It is

(a) Horizontal Plane

)o _N

A

z

(b) Venical Plane A·A through apenure centre

Figure 2. Grid 119 x 40 x 36) distribution

Building Research Joumal

noted that recent correlations by Khalifa and Marshall (1990) suggest that the surface con. vective heat transfer coefficient, for a tempera-ture difference between the surface and

ambient air of 2 to 3°C, would be about 3.1 and

2.8 W/m2 K for the ceiling and vertical walls

re-spectively. These correlations are based on measurements in a 2.95 x 2.35 x 2.08m (length x width x height) indoor test cell facility.

Computations were performed using a

non-uniform grid, Figure 2, of,19 x 40 x 36 (a total of

27,360 nodes) for the two-zone enclosure

(Figure I) and .the aperture configurations listed in Table I. To check grid independence of com-puted results, computations were conducted us-ing a non-uniform grid of 19 x 5lx 56 (a total of 54,264 nodes) and found no significant differ-ences in computed air temperatures and

veloci-ties (see Figure 3). Computation time, on an

IBM-3090 main frame computer, was about 6

120 80 E 40

"

""

J: .!2'

..

0 :r:

...

.ao ·120

...

120

§ ..

-' J: .!2'

..

0 :r:

....,

.ao ·120 --.-6---. Computed 19x40x36 .... 0 ... Computed 19x51x56 .(1.1 0.0 0.1 Velocity, m/s

"'

23 24 25 28 Temperature, 'C TestA R..-0.49 ｒｾ＠ ... 1.0 .:\T ... 1.8aC

,.

TestA R,-0.49 27

Figure 3. Grid effect on computed veloclly and temperature at aperature

o.a

Volume 3, Number ,2, 1994

hours for the fine grid ( 19 x 51 x 56) as com-pared to 2. 5 hours for the 19x 40 x 36 grid. It is noted that a much coarser grid has been used in the literature, e.g., Haghighat et al. (1989) used a uniform grid of 16 x 10 x 10.

RESULTS AND DISCUSSION

Temperature and Velocity Distributions

Figure 4 compares computed and measured (Said, Barakat, and Whidden 1993) vertical dis-tributions of the air temperature at the

thermo-couple tree location (Figure 1) of each of the hot

and cold zones. Predicted air temperatures are generally in good agreement with those meas-ured. The air temperature is essentially

strati-fied (Figure 5). Linear regression was used to

evaluate computed temperature stratification in each zone. Temperature stratification,

80

e

40

"

:'E . 21 0 ｾ＠

_...

...

--- Computed,ColdZone "'/,

...

... ···

•

•

TestA R ... 0.49 ｒｾﾷＱＮＰ＠ ll.T ... 1.8 oc ,.

Computed, Hot Zone

Expt [11, Co1d Z.rio ... ,

.

'

Expl [1], Hot Zone

' / ,/ j ｾ＠

....

.. i

_{ＮＯＧｾ＠}

...

' ' ｾＯ＠

/

.

"".' i•

:

.' ' i AI ! •

1

_/

...

_:

,' _/

"

.. ;../

·120 ｌＮＮＮＮｾＭ ... _. _ ｟Ｎ｟｟ｾ＠ .... _,_ _ _,_ ... _...l...l 18 19 20 21 22 23 24 25 26 27 Temperature, 'C ＱＲＰｲＭｾＭＭｾｾＭｾＮｾＭｲｾｲＭｾＭＭｾｾＭＮ＠ 80

5

40

t!

·il'

0 :I:

...

...

•

•

TestE R,.-0.29 R,.-0.88 ar •• a.s.oc

Computed, Cold Zone .. ｾ＠ .. · .':/

Computed, Hot Zone•/

.

/

Expt. [1], Cold Zone : Expt. (1], Hot Zone./ .

:

I !

:/

;/

.. :'

i

: ,/

""/

/

... i • ,/ ' ' ' / .. : ,i ＭＱＲＰＧＭｾＭＺＺＺＭＭＭＺＺＧＺｾＭ］ｾﾷ＠ ＺＺＭＭﾷＢＢＧＢＺＧＭｾＭ

...

ｾ＠ 18 19 20 21 22 23 24 25 26 27 Temperature, 'C 41

Table 3, was between 0.43 and 1.21 °C/m at the

cold zone centre, and between 0.63 and 1.93°C/m at the hot zone centre. The lower

level of temperature stratification being for the

tests with the lower zone-to-zone temperature

Table 3. Temperature stratlhcatlon, S, °C/m

Cold Zone Hot Zone

Test Computed (Expt. [1]) Computed [Expt. [1]) A B c D E F G H I J 5 (OC/m) R2 5 (OC/m) R2 1.21 (1.17) 0.90 (0.97) 1.93 (1.42) 0.97 (0.96) 1.18 (1 .03) 0.93 (0.96) 1.86 (1.38) 0.99 (0.94) 0.86 (1.02) 0.90 (0.97) 1.30 (1.44) 0.98 (0.91) 0.88 (0.97) 0.86 (0.95) 1.42 (1.28) 0.99 [0.95) 0.73 (0.86) 0.87 (0.90) 1.35 (1 .23) 0.98 (0.90) 0.64 (0.83) 0.89 (0.92) 1.39 (1.28) 0.94 (0.89) 0.54 (0.50) 0.90 (0.93) 0.63 (0.62) 0.98 (0.88) 0.43 (0.46) _{0.88 ＨＰＮＹｾＡ＠} 0.66 (0.65) 0.98 (0.88) 0.48 ｾｾ＠ .. ｾｾ＠ ＰＮＹＲＡｾﾷＹＲ＠

o.1o

ｾｾﾷＶｧ｜＠ 0.97 ｾｾＮＸｾ｜＠ 0.81 0.65 0.99 0.95 1.06 1.10 0.95 0.95 120 ｲＭＮＮＮＬＮＮＭＮＬＭＢＧＢＧｔｾＮＬＮＮＮＮＭ

... ...,..-..-"'"'T-"1""1

80 ... .

5

••I-E

ﾷｾ＠ 0 :I:

...

...

•

•

TestS A.-0.49 R,.-0.88 AT.-2.2"C ",

.

/

Computed, Cold Zone / /

Computed, Hot Zone .._.,.,. • /

Expt. [1], Cold Zone -'

Expt. [1], Hot Zone ｊｾ＠ ＮＧｾ＠

,1

ＮＯﾷｾﾷﾷﾷ＠ '

,...

/

.

:•

/·

' ' ,' / I A. / I

:

/ Ｚｾ＠

/

.

' ·' ' r ' ; .... / . -120 ｾＮＮＮ＠ ... _ . . _ _ . _ ｟Ｎ｟ＮＮｾＮ＠ ...

l._,_,__.._ ...

_..J.-.1 18 19 20 21 22 23 24 25 26 27 80

...

...

•

•

Te11H R,.-0.29 R,.•0.88 .6.T1•1.1 OC Temperature, °C

Computed, Cold Zone

Computed, Hot Zone

Expt. [1], Cold Zone

Expt [11. Hot Zone

ｾ＠_{i /}

'

. . I • I l ! ' l A I • : i ' I

ｾＯ＠

:l

.: • i : I I I ｾ＠

'

: !

....

' : !

: /

I I

A:,.

-120 L...-L.-.i.----.J.--'--'-'--'-.!.L...i.---..1.-.J..;J 18 19 ｾ＠ ｾ＠ ｾ＠ ｾ＠ ｾ＠ ｾ＠ u ｾ＠ Temperature, 'C

42

Building Research Journal

Test A: Rw=0.49, Rh=1.0, aT.=1.8

•c

I/

ｾ＠

) \

ｉｾ＠

Cold

Zone

3

ｾＺＺＺＺＺ＠

_--s:

_:.

Cold Zone

ｾ］Ｍ］］］］｟ＮＮ［ＬＺＭＺＭｾｈＺｯｾｴｾｚ］ｾｾｮｾｾ

Ｖ＠

__ .--../

ｾＭ

---J

ｾｾｾ＠ ｾＭＭＭＭ｟Ｍ｟Ｍ｟Ｍ

___

Ｍｈ｟ｾ｟Ｎｺ｟ｯＭｮ･ＭＭＺＺＺ［［Ｚ］］ＬＯ＠

ｾ＠

Hot

Zone

Figure 5. Temperature ､ｩｳｾｩ｢ｵｬｬｯｮ＠ In plane A-A lhraugh aperature centre

Level T ("C) B 27.0 A 26.5 9 26.0 8 25.5 7 25.0 6 24.5 5 24.0 4 23.5 3 23.0 2 22.5 22.0 Level T ('C) B 27.0 A 26.5 9 28.0 8 25.5 7 25.0 6 24.5 5 24.0 4 23.5 3 23.0 2 22.5 22.0 Level T ("C) B 27.0 A 26.5 9 26.0 8 25.5 7 25.0 8 24.5 5 24.0 4 23.5 3 23.0 2 22.5 22.0 level T ('C) B 27.0 A 26.5 9 26.0 8 25.5 7 25.0 6 24.5 5 24.0 4 23.5 3 23.0 2 22.5 22.0

Volume 3, Numbet 2, 1994

difference ＨｾｔＮ＠

=

1.0°C). Predicted temperature

stratification values agree reasonably well with

measured data, Table 3. Measured stratification

was between 0.46 and 1.17°C/min. in the cold zone, and between 0.62 and 1.44°C/min. in the hot zone. Computed results suggest that for the

tests with ｾｔＮ＠ = 1.8 to 2.5°C, stratification

de-creased with decreasing aperture height. For

the tests with ｾｔＮ＠ = 1•c, aperture height

ap-pears to have little effect on stratification. Pre-dicted stratification values are also consistent with those measured by Balcomb and Jones (1985). They reported temperature stratifica-tion levels in the range 0.91 to 2.19°C/m (0.5 to

ＱＮＲｾＯｦｴＩ＠ in passive solar buildings.

Computed air temperatures along the centre

line of the aperture, Figure 6, are within 1 •c of

measured data. The discrepancy between

com-puted and measured temperature proflles is

probably due to the difficulty in duplicating the actual thermal boundary conditions of the ex-periments at the aperture. However, computed proflles of the horizontal component of the air velocity along the centre line of the aperture

agree very well with measured data, Figure 7.

The neutral plane (the plane of no horizontal flow) is nearly at the aperture mid-height

(height = 0, Figures 4 and 6). It is noted that the

vertical distributions of the horizontal velocity component are symmetric with respect to the neutral plane, and are similar to the theoreti-cal velocity proflle based on the Bernoulli equa-tion by Brown and Solvason (1962).

Air Flow Pattern

Figure

a

shows typical air flow patterns in a vertical plane through the centre of the

aper-ture (Plane A-A, Figure 1 ). A counterclockwise

air circulation cell dominates the hot zone. The upward boundary layer flow by the north wall

in the hot zone reaches the top of the enclosure

where it turns horizontally and moves toward the aperture to the cold zone. The air flow accel-erates as it moves through the aperture. After entering the cold zone, the air, along with en-trained cooler air, move upward to the enclo-sure top then horizontally toward the south wall in the cold zone. This air flow pattern in the hot zone indicates that the interzonal natu-ral convective flows were primarily under the influence of the so-called bulk-density flow re-gime in which the air flow through the

aper-43

ture is driven by the zone-to-zone temperature

difference.

The air flow pattern in the cold zone de-pended on the status of the heaters H2 and H3

by the south wall (Figure 1). For Tests A, Band

E, shown in Figure

a,

heaters H2 and H3 were

off (see Table 1 ). One circulation cell occupies

the top half of the enclosure. The air descends along the south wall to the floor. Then immedi-ately turns up to about mid-height of the enclo-sure where it moves horizontally toward the aperture to the hot zone. This is believed to be

due to the asymmetry caused by the irregular

extension of the cold zone. It is worth noting that this L-shaped arrangement of the two zones is typical in Canadian doweling. As can

be seen from Figures 9 and 10, unlike the hot

zone, a counter-clockwise air circulation cell dominates the cold zone. This air circulation cell is fed from the relatively high momentum of the air accelerating out of the aperture

(Plane x!H, = 0.786, Figure 9 and Plane x!H, =

0. 718, Figure 1 0). This relatively high

momen-tum area across the aperture in the cold zone induces air entrainment upwards from the bot-tom where some air turns towards the aper-ture, and others follow the main air circulation cell.

For Test H, Figure

a,

where heaters H2 and

H3 were on (Table 1 ), the air ascends along the

south wall up to the enclosure top where it moves horizontally until it is deflected down-ward by the warmer air stream from the hot zone. This results in two circulation cells in the

cold zone. Figure 11 shows the effect of the heat

supplied by heaters H2 and H3 on the air flow pattern in the cold zone. The counter-clockwise air circulation cell noted earlier in the oold

zone (Figures 9 and 10) is not present when

heaters H2 and H3 are on.

For the aperture/enclosure configUrations studied, the natural convective interzonal air flow through the aperture appears to be

three-dimensional, Figure 12. This is consistent with

the,finding ofMahajan (1987). Above the neu-tral plane, two airflow circulation cells appear at the top of the aperture. Below the neutral plane, the convective air flows appear to be bi-ased towards.the bottom right corner of the ap-erture. This difference in the airflow pattern above and below the neutral plane at the aper-ture is clearly due to the fact that the hot and

44 120 r-T"" ... ＭｲＭＮＮＮＭＭＬＬｲＭＺＭＱＭＭｯＭＭＭＧＱＮＮＭｾＮＮＮＬＮＮ＠ ... ,..., CCmputod •••• • 80 ₀ -80-Expt.[1) >-o--l •• ••

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Building Research Journal

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Figure 6. Vertloallemperalure dlslrlbullons al aperture cenlre line

1

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VoltJIIle 3, Number 2, 1994 80 E40 0

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-J -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 Velocity, m/s Figure 7. Vertical diatributlon of horizontal velocity component, V, at aperature centerline

46 ,

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Building Research Journal

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Fieuro 9. Velocity distribution in horizontal ｰｬ｡ｮ･ｳｾＧ＠ =0.786 and 0.193 Test A, R.. • 0.49, Rh • 1.0, ＼ｾＮｔ｡＠ = 1.a•c

47

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48 Building Research Journal

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Volume 3, Number 2, 1994 '

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50 0.1 m/s \ ' ' ' ' ' \ 1 / / -0.1 m/s

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Building Research Journal

0.1 m/s

Test B: Rw=0.49, Rh=0.88, .1.T,=2.2

•c

0.1 m/s

>

Test H: Rw=0.29, Rh=0.88, .1.T,=1.1

•c

Volume 3, Number 2, 1994

cold zones are different in shape. The air flow

from the cold zone to the hot zone (Figure• 9 and

10, Plane xiH, = 0.193) appears to be biased

to-ward the side of the aperture nearest to the ir-regular extension of the cold zone. The air flow from the hot zone to the cold zone, however, pears to diffuse symmetrically through the

ap-erture (Figure 9, Plane x/H, = 0. 786, and

Figure 10, Plane x!H, = 0. 718).

Coefficient of Discharge

Using the computed results, the volumetric

air flow rate through one-half the aperture (with respect to the neutral plane) was com-puted by summing the product of the local ve-locity component normal to the plane of the aperture {Y-direction component) and the corre-sponding incremental area. Computed volumet-ric air flow rates, F •• out of the hot zone (above the neutral plane) and that into the hot zone (below the neutral plane) were identical. The theoretical volumetric flow rate, F,, was calcu-lated with the relation derived by Brown and Solvason (1962):

_ _3 0.5

Ft=W/3 (g ｾＱＱ＠ ｾ＠ T)

(2)

where the symbols are as defined in the nomen-clature. The fluid properties were taken at the overall mean air temperature of both zones. Two definitions for the characteristic tempera-ture differential, AT, were considered:

• ｾｔ＠ m is the difference between air

temperatures at the centre

(thermo-couple tree location, Figure 1) of each

zone at a level of half the enclosure height, and

• ｾｔｶ＠ is the difference between

aver-age air temperatures of a vertical

grid of nodes at the centre of each

zone.

The difference between average air tempera-tures in each zone at a level of half the

enclo-sure height, ｾｔＮＬ＠ was also considered.

Computed results using ｾｔＮ＠ were similar

to

those using ｾｔｭＮ＠

The volumetric coefficient of discharge, Cd, was then calculated from the computed volu-metric flow rate, F •• divided by the theoretical

one, F,. The values ofCd were found

to

be in

51

the range 0.57 to 0.81. Computed Cd values are in good agreement with measured results

(Sard, Barakat, and Whidden 1993), see Table 4.

Computed Cd values also compare favorably with those reported by Brown and Solvason (1962). They experimentally determined cd to be in the range 0.6 to 1.0. Their experiments in-volved a partitioned square enclosure, openings

with a maximum size of 0.305 x 0.305 m, and

temperature differentials across the opening be-tween 8.3 and 4 7.2 •c.

Table 4. Coefficient of discharge, computed vs. measured (Sa'id, Barakat, and Whtdden 1993), Rw•0.29 and 0.49,

Rh=0.75-l.O, ｾｔＮ］ｬＮｬＭＲＮｳ｣＠

.

L\Tm .:\Tv

Test Computed Expt.[11 Computed Expt.[t]

A 0.81 0.74 0.75 0.75 B 0.68 0.67 0.69 0.73

c

0.57 0.59 0.66 0.66 D 0.67 0.65 0.72 0.70 E 0.63 0.66 0.70 0.74 F 0.60 0.69 0.67 0.75 G 0.64 0.67 0.72 0.63 H 0.65 0.78 0.68 0.72 I 0.60 0.65 0.66 0.64

Using an average Cd value of 0.67 in conjunc-tion with Equaconjunc-tion (2) gives the following corre-lation for computing air flow rates through a doorway-like aperture:

F= 0.223 W(g

ｾｉｉｾ＠

T) 0'5 (3)

Equation (3) correlates computed (from EX-ACT3 results) volumetric air flow rates with a

goodness of fit R2 = 0.85 for ｾｔ＠ = ｾｔｭＬ＠ and R2 =

0.95 for ｾｔ＠ ］ｾｔｶＮ＠ The results (Cd and Nusselt

number) for Test J were not included in the

cor-relation. The aperture size in Test J

<Rw

= 0. 79

and Rh = 0.88) was such that the two zones were almost like a single zone.

Nusselt Correlation

The natural convective heat flow rate through the aperture was computed from com-puted air mass flow rate through the aperture and the temperature differential across the ap-erture. The results are presented in terms of Nusselt number, Nu. In accordance with the conclusion reported by the authors (Sald,

52

Barakat, and Whidden 1993), the following cor-relation was considered:

G

0.6p

Nu=C r r (4)

The aperture height, H, was used as the characteristic length in Nu and Gr numbers. Correlation Equation (4) is the theoretical form derived by Brown and Solvason (1962) in which the coefficient C = C,.l3. This correlation was based on the inviscid Bernoulli equation.

Similar

to

the measured results (Sa'id, Barakat, and Whidden 1993), the characteristic temperature difference that led

to

the most ac-curate Nu correlation (R2 = 0.98) was Ll.Tv as compared to R2 = 0.87 when Ll.Tm was used. The temperature differential Ll.Tm (the difference be-tween air temperatures at the centre of each zone at a level of half the enclosure height) is, however, convenient

to

measure in practice. Thus, the following is the least squares fit re-sult for the correlation Equation ( 4) in which

Ll.Tm was used. 0.6 Nun=0.215Grn Pr 15000 0 (5) Computed, EXACT3

l:SUU<itng .ttesearcn ..1 ouma1

Figure 13 compares the correlation Equation (5)

to

that from the experiments (Sa'id,

Barakat, and Whidden 1993) (C = 0.22 ) and the lower and upper limits (C

=

0.2 and 0.33) by Brown and Solvason (1962). As can be seen, the correlation Equation (5) agrees very well with that derived from the full scale experi-ments (Sa'id, Barakat, and Whidden 1993). The correlation Equation (5) is also in close agree-ment with the lower limit (C

=

0.2) of the corre· lation by Brown and Solvason(1962).

CONClUSIONS

• The three-dimensional computation results facilitated better under· standing of the air flow pattern and the natural convective flow regime in the two-zone enclosure.

• Computed results for temperature and velocity agree reasonably well with measured data from full scale experiments (Sai:d, Barakat, and Whidden 1993) in a realistic build-ing.

ＱｾＰＰＰ＠

11000

- - - Nu=0.215 PrGr'·', present study, AT • . . · ... · ·. . . Nu=0.222 Pr Gr'·', Expt.[1] - - - . NU=0.2 Pr Gr'·', [11] __________ , Nu=0.33 PrGr", [11] 9000 :I: ::l

z

7000 5000

-0 .. ··· '

' 0

0 _{.. ···} .. ·

.··

ｾ＠ｾＰＭＧ＠ ＳＰＰＰｌＭＭＭＮ｟ｾＭＭｾＭＭｾｾＭＭＭＭＭＭＭＭＭＭｾＭＭＭＭＭＭＭＭＭＭＭＭｾＭＭＭ

4.0E8 7.0E8 1.0E9 4.0E9

vo1wne 6, ＮＱＺｾｵｭｯ･ｲ＠ z, ＮｌｾｾＧｩ＠

• Coefficients of discharge were found

to range between 0.57 and 0.81 for

the aperture configurations studied. An average Cd value of 0.67 corre-lates very well with all computed data. Computed temperature strati-fication, coefficient of discharge, and Nusselt number agree quite well with those measured. REFERENCES

ASHRAE. 1989. Fundamentals handbook (SI), Chap-ter 22, Table 1.

Balcomb, J.D. and G.F. Jones. 1986. Natural convec-tion air flow and heat transfer in buildings: Ex-perimental Results, Proceedings: 10th National

Passive Solar Conference. Raleigh. 88-92.

Brown, W.G. and K.R. Solvason.1962. Natural con-vection through rectangular openings in parti-tions -vertical partiparti-tions. International JourTUJl

of Heat and Mass Transfer. (6)859-881.

Haghighat, F., Z. Jiang and J.C.Y. Wang. 1989. Natural convection and air flow pattern in a parti-tioned room with turbulent flow. ASHRAE

Trans-actions. 6(2)600.

Harlow, F.H. and J.E. Welch. 1965. Numerical calcu-lation of time-dependent viscous incompressible flow of fluid with free surface. Ths Physics of

Fluids. 8(1)2182-2189.

Khalifa, A.J.N. and R.H. Marshall. 1990. Validation of heat transfer coefficients on interior surfaces using a real-sized indoor test cell. International

Journal of Heat Mass Transfer. 33(10)2219-2236.

Kurabuchi, T., J. B. Fang, and R.A. Grot.1990. A nu-merical method for calculating indoor air flows us-ing a turbulence model. N a tiona) Institute of Standards and Technology. Gaithersburg, MD 20899. Report No. NISTIR 89-4211. January. Mahajan, B.M. 1987. Measurements of air velocity

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