Ciência/Science NUMERICAL STUDIES OF NATURAL...

5
ABSTRACT In the present work a numeric study of thermal and fluid dynamics behavior of natural air convection in a bi-dimensional square cavity is presented, in a laminar flow. The square cavity has two walls heated with different temperatures and two isolated walls, the Boussinesq approximation is used and a constant Prandtl number. The Finite Volume Method is used for the discretization of flow equations. The staggered load of variables is adopted and Power-Law and SIMPLE models are used. The numeric simulation is 4 6 made up of several Rayleigh numbers, 10 Ra 10 , and the results of average Nusselt numbers are compared to values obtained in the literature. Flow and isotherm lines are presented and analyzed. The numerical results presented here in this work agree with the ones available in the literature and can be used by researchers who work in the convection problem numeric simulation area. Keywords: natural convection, square cavity, Finite Volume Method a Viviana Cocco Mariani , b and Ivan Moura Belo a Pontifícia Universidade Católica do Paraná Departamento de Engenharia Mecânica Bairro Prado Velho CP. 81611-970, Curitiba, Paraná, Brasil [email protected] b Pontifícia Universidade Católica do Paraná Departamento de Engenharia Mecânica CP. 81611-970, Curitiba, Paraná, Brasil [email protected] NUMERICAL STUDIES OF NATURAL CONVECTION IN A SQUARE CAVITY Nu Nu x c p D h g H k L p P Pr R Ra T u, v U, V x,y,z X,Y,Z Engenharia Térmica (Thermal Engineering), Vol. 5 - Nº 01 - July 2006 68 Ciência/Science

Transcript of Ciência/Science NUMERICAL STUDIES OF NATURAL...

ABSTRACT

In the present work a numeric study of thermal and fluid dynamics behavior of natural air convection in a bi-dimensional square cavity is presented, in a laminar flow. The square cavity has two walls heated with different temperatures and two isolated walls, the Boussinesq approximation is used and a constant Prandtl number. The Finite Volume Method is used for the discretization of flow equations. The staggered load of variables is adopted and Power-Law and SIMPLE models are used. The numeric simulation is

4 6made up of several Rayleigh numbers, 10 Ra 10 , and the results of average Nusselt numbers are compared to values obtained in the literature. Flow and isotherm lines are presented and analyzed. The numerical results presented here in this work agree with the ones available in the literature and can be used by researchers who work in the convection problem numeric simulation area.

Keywords: natural convection, square cavity, Finite Volume Method

aViviana Cocco Mariani ,band Ivan Moura Belo

a Pontifícia Universidade Católica do Paraná

Departamento de Engenharia Mecânica

Bairro Prado Velho

CP. 81611-970, Curitiba, Paraná, Brasil

[email protected] Pontifícia Universidade Católica do Paraná

Departamento de Engenharia Mecânica

CP. 81611-970, Curitiba, Paraná, Brasil

[email protected]

NUMERICAL STUDIES OF NATURAL CONVECTION IN A SQUARE CAVITY

NuNux

cp

Dh

gHkLpPPrRRaTu, v

U, Vx,y,zX,Y,Z

Engenharia Térmica (Thermal Engineering), Vol. 5 - Nº 01 - July 2006 68

Ciência/Science

)/(;/;/

H

uUHyYHxX

a=== (1)

)/( H

v

a 2

20 )(

ra

Hpp -

CH

C

TT

TT

-

-V = P = q = (2)

0)()(

¶+

Y

V

X

U (3)

UX

P

Y

VU

X

UU 2Pr)()(

Ñ+¶

¶-=

¶+

¶ (4)

)Pr(Pr)()(

02 qq -+Ñ+

¶-=

¶+

¶RaV

Y

P

Y

VV

X

UV (5)

qqq 2)()(

Ñ=¶

¶+

Y

V

X

U(6)

ra

m2

3 Pr)(

n

b HTTgRa CH -

= (7)

0=¶

Y

q

ò-

1

001 )(dYNu

Dhx

qqNu (8)

Engenharia Térmica (Thermal Engineering), Vol. 5 - Nº 01 - July 2006 69

Ciência/Science Mariani and Belo et al. Numerical Studies of ...

( ) 0=¶¶- XXq

5

,10max R -£×Ñ=

jiV (9)

UY

¶yV

X-=

¶y(10)

Figure 2. Streamlines (to the left) and isotherms (to the

4right) for Rayleigh = 10

maxy

Nu

4Table 1. Numerical results for Ra = 10 .

Engenharia Térmica (Thermal Engineering), Vol. 5 - Nº 01 - July 2006 70

Ciência/Science Mariani and Belo et al. Numerical Studies of ...

5Table 2. Numerical results for Ra = 10 .

6Table 3. Numerical results for Ra = 10 .

-1.0 -0.5 0.0 0.5 1.0U/Umax

0.0

0.2

0.4

0.6

0.8

1.0

Y

Ra = 104

Ra = 105

Ra = 106

0.0 0.2 0.4 0.6 0.8 1.0X

-1.0

-0.5

0.0

0.5

1.0

V/V

max

Ra = 104

Ra = 105

Ra = 106

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Engenharia Térmica (Thermal Engineering), Vol. 5 - Nº 01 - July 2006 72

Ciência/Science Mariani and Belo et al. Numerical Studies of ...