Natural convection at high Rayleigh number within a cubic cavity. Influence of inclination.

MECHANICS RESEARCH COMMUNICATIONS 0093-6413/86 $3.00 + .00

Voi.13(4), 215-220, 1986. Printed in the USA Copyright (c) 1986 Pergamon Journals Ltd.

NATURAL CONVECTION AT HIGH RAYLEIGH NUMBER WITHIN A CUBIC CAVITY. INFLUENCE OF INCLINATION.

F. Chabchoub, D. Lemonnier and Doan-Kim-Son Laboratolre de Thermique de I'E.N.S.M.A.

(L.E.S.T.E., U.A. 1098 au C.N.R.S.),

20 rue Guillaume VII, 86034 Poitiers Cedex, France.

(Received 28 April 1986; accepted for print 27 June 1986

Introduction

The experimental knowledge of natural convection within enclosures is still nowadays far from complete. From the thermal point of view, only papers by ECKERT and CARLSON /I/ and by YIN et al. /2/ are available in the literature. In the dynamic fleld, the only references are MORRISSON and TRAN /3/ or, more recently LINTHORST et al. /4/, all of them for rather small sized configurations. We are not aware of any experimental investigation of both thermal and dynamic fields except for the study by RENAULT et al. /5/ in a cavity with hlgh aspect ratio and a Raylelgh number up to 7.107 . W l t h regard to the effects of inclination, as yet only laminar flows have been considered and only for Raylelgh numbers not exceeding 106 . The present paper aims at p r o v i d i n g some i n f o r m a t i o n on t h e t h e r m a l a n d d y n a m i c natural convection within a cubic enclosure (A = 1 ) , higher than 2.108 and for various inclination angles.

characteristics of at Rayleigh number

Experimental apparatus and technics of measurement

Our experimental model consists of a cubic cavity (see figure 1) : each side is

400 mm l o n g .

The a s p e c t

ratio

is

thus

fixed

a t A ffi L/D = B/D ffi 1.

This cavity includes two "active" walls, set out face to face. The first one ("hot wall") is kept isothermal, at a temperature T H ffi 75°C, by means of 215

216

F. CHABCHOUB,

D. LEMONNIER and DOAN-KIM-SON electrical heating.

On the other hand,

second

wall")

water

one

("cold

circulation

remains

is

so that

uniformly

at

T

the

cooled

by

its temperature

=

15°C.

The

four

C

other walls

("passive walls")

double-glazing

in

proper

insulation

the

thermal

use

of

order

laser

are made of

to

insure

and

Doppler

to

a

allow

anemometry

for

velocity measurements. An

appropriate

whole in

cavity

the

apparatus

to take

several

range

0°

<

around

an

axis

rotation

~

= 90°corresponds

the

inclinations

<

180 ° ,

after

perpendicular

the vertical passive walls

FIG. i Configuration

allows

to

(note that

to the vertical

position). Due

to

the

fairly

large

T H - T C = 60 K is sufficient

of

size

our model, a

temperature

reference

to provide us with a Raylelgh number,

Ra D equal

to 2.75 108 .

Temperature

measurements

informations

on

this

were

performed

procedure

itself are given in reference

and

an

with

a

cold-wlre

accurate

probe.

description

of

Detailed the

probe

/6/.

The velocity field has been investigated by mean of Laser Doppler Anemometry. The

optical

described

system

and

the

operating

technique

were

the

in a previous paper by RENAUI, T and DOAN-KIM-SON

same

as

those

/5/.

Results and discussion

The

thermal

through

the

inclinations,

and

dynamic

shape

isothermal

and

of

the

iso-~

flow lines

~, of the cavity. 4 is the non-dimensional

i

~ ( x , y)

of

characteristics

0 u

y

D f o p(T) u dy' max

are

here

obtained quantity

illustrated at :

various

NATURAL CONVECTION IN A CUBIC CAVITY which,

for

function.

a

bidlmensional

All

the

median plane, velocity density

results

z = D/2.

matches

presented

(Umax d e n o t e s

i n t h e whole p l a n e of air,

flow,

variable

the

217

definition

hereafter

have

been

t h e maximum v a l u e

of

the

obtained

of the

stream in

the

longitudinal

( x , y) where m e a s u r e m e n t s a r e p e r f o r m e d . 0 i s t h e

with the temperature

T).

a) Vertical cavity (~ = 90 ° )

It appears from figures 2-a and 3-a that the flow has separated thermal and dynamic boundary layers (strong thermal gradients and most of the iso-$ lines are confined to the vicinity of the walls).

One may point out that such a

pattern of flow is more likely to happen with a high value of Ra D since it decreases the boundary layer thicknesses. Figure 2-a also clearly displays of vertical cavity.

stratification The

shape

of

of the

the

thermal

iso-~

lines

field drawn

in in

the

central

figure

3-a

area

of

the

indicates

the

existence of secondary motions, located on the cold wall side half way up and at the bottom of the cavity (x/D ~ 0.5 and 0.145). According to MALLINSON et al. /7/ this phenomenon may be closely connected with the dlstorsion of the thermal field

(note that the strongest

are encountered Just beneath

near the cold wall).

the upper horizontal

horizontal

gradients

A recirculating

wall

Furthermore,

(x/D % 0.9)

active wall

to the other.

iso-~ lines

(in other words ~ does not match

of temperature

area also takes place and

streches

from one

the lack of closure of many of the zero at the cold wall,

as a

stream function should) indicates a three dimensional behaviour of the flow. This is also clearly evidenced by the strong dissymmetry of the mean velocity profiles, measured respectively on the hot wall and the cold wall, at a same altitude x/D (see figure 4, for # ffi 90°). This dissymmetry is here far more important

than

consequently,

the the

one

observed

classical

~n

previous

attribution

of

the

studies

(/3/,

phenomenon

/8/...)

to heat

through the passive wall is no longer sufficient : three-dlmensionality

and, losses seems

more likely to be a specific characteristic of the flow itself. At least, it is worth pointing out that, despite a high value of RaD, the flow is found to remain laminar throughout the whole measurement plane.

218

F. CHABCHOUB,

D, LEMONNIER

TH

and DOAN-KIM-SON

TC

iH

TC

(a)

•

=

90 °

II

=

3() o

9

~ ~oro

,

o., o.,, o.~ o.,, o., o., o., o.,,ro.,io., o.,io.,, o.,1o.,1o.,1o.85io.,[o., ~

FIG. 2 Distribution of isotherms

FIG. 3 Distribution of iso-~ lines

Ol

(D_y)(m)

005

T

|

°

Ira/s:

D

~,5

r~

30

G

o

• ° °°

o°

Ll []

60

•

e °

x/L -05

02 _5Ira/s)

[] :]

i

D

O o o ooQgo

®

0.05

Profiles

S

•

,

.

°-

~

01

of longitudinal

I

a

015

mean velocity

a

y(m)

( ~ ~

02

90 ° )

NATURAL CONVECTION IN A CUBIC CAVITY

219

b) Inclined cavity (~ <,90°,)

The inclination of the cavity (at angles smaller than 90 °) makes secondary motions disappear and produces a gradual thlckenning of the dynamic boundary layer /9/ so that, at $ = 30 ° , a mono-cellular pattern of flow is reached (see

figure

thermal

3-b).

boundary

Thus, layers

the boundary become

layer regime

thinner

and,

is lost.

in

the

However,

same

the

way,

the

stratification of temperature vanishes as ~ decreases. Another effect of inclination is to weaken the three dimensional behavlour of the flow, and now we observe a symmetrlsatlon of the mean velocity profiles (see figure 4, ~ < 90°). The

last point

is that inclination favours

the appearance of turbulence.

Particularly, with regard to the flow on the hot wall side, both the thermal and dynamic intensity of turbulence profiles (figures 5 and 6) converge to an unique

curve,

as

x/D

exceeds

0.5.

This

behaviour

characterizes

a

fully

turbulent flow, according to the criteria established in the case of a single plate /i0/.

• A

059 050

,

023

! I-ll •

~ ' ~ .

w;ll ¸

IO~'

o 'OM o 1050 6

"--

, :.::

-4

.

~gO

4

...

2

0

FIG. 5 Thermal intensity of turbulence

O~

-

-

0;2

-

-

-

-

-

-

013

y (m)

FIG. 6 Dynamic intensity of turbulence

O&

F. CHABCHOUB, D. LEMONNIER and DOAN-KIM-SON

220 Conclusion

The

results

presented

above

provide

a

contribution

to

the

knowledge

of

natural convection flows in cavities at Ra D > 2.108 . The flow confined in a vertical cubic cavity is found to be strongly three-dimenslonal,

but remains

laminar and has separated thermal and dynamic boundary layers. As

inclination

occurs,

three-dimensional

effects

vanish

and

turbulence

gradually appears, but the dynamic boundary layer regime has been lost.

References

1

E.R.G. Eckert, W.O. Carlson, Int. J. Heat Mass Transf. 2, 106 (1961).

2

S.H. Yin, J.Y. Wung, Int. J. Heat Mass Transf. 21, 307 (1978).

3

G.L. Morrisson, V.Q. Tran, Int. J. Heat Mass Transf. 21, 203 (1978).

4

S.J.M. Linthorst, W.M.M. Shinkel, C.J. Hoogendoorn, J. Heat Mass Transf.

5

C. Renault, Doan-Kim-Son, Mech. Res. Comm. I0, 245 (1983).

6

Doan-Kim-Son, J. Coutanceau, Acta Astronautica,

7

G.D. Mallinson, G. De Vahl Davis, J. Fluid Mech. 83, I (1977).

8

W.M.M. Shinkel, Dutch efficiency Bureau, Pijnakeer (1980).

9

F. Chabchoub, Th@se de 3~me Cycle, Univ. Poitiers

I0

Doan-Kim-Son, Thgse Docteur @s Sciences, Univ. Poitiers (1977).

103, 535 (1981).

8, 123 (1981).

(1986).