using software gambit 2.0 and fluent 6.0 for simulation of heat mass transfer problems

7/27/2019 Using Software Gambit 2.0 and Fluent 6.0 for Simulation of Heat Mass Transfer Problems

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Using software Gambit 2.0 and Fluent 6.0 for simulation of heat mass transfer problems.

Progress report (June, 2002), A. I. F.

1. Natural convection in a square cavity.

Buoyancy driven flow in a square cavity with vertical sidewalls, which are differentially heated is a

suitable object for testing and validating computer code and getting start of GAMBIT [1] and FLUENT

[2].

Model and boundary conditions

The problem considered here is that of two-dimensional flow of an air as a Boussinesq fluid.

Figure 1 shows geometry and boundary conditions of the enclosure used for modeling flow inside the

enclosure. Rayleigh number of this problem is 106.

0.07 m

u = v = 0

T/n= 0u = v = 0

T1 = 0oC

u = v = 0

T2 = 25.2oC

Figure 1. Square enclosure and boundary conditions.

The mesh for this problem has been generated by GAMBIT and depicted in Figure 2. The mesh

density near the enclosure walls must be able to resolve both the thermal and velocity boundary layers

developing on the walls. The generated mesh contains 35 x 35 quadrilateral elements and with defined

in GAMBIT boundary zones was saved in the file sqrtst1.mshfor using in FLUENT.

Solution procedure

For solution of the problem we used segregated solver with default settings: implicit formulation,

steady (time-independent) calculation, laminar model and energy equation. We used PRESTO as

pressure interpolation scheme, SIMPLE as the pressure-velocity coupling method and Second- Order

Upwind scheme for density and momentum equations. For under-relaxation factors and convergence

criterion were used default values. The solution reached convergence after approximately 250 iterations.

Results

The graphical results are obtained using post process features of FLUENT. Figure 3 through Figure 5

show the velocity and temperature fields in the enclosure. The profile of vertical velocity at y = 0.035 mis shown in Figure 6.


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Figure 2. Mesh generated by Gambit 2.0.

Figure 3. Velocity vector field.


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Figure 4. Streamline contours.

Figure 5. Temperature contours.


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Figure 6. Vertical velocity at y = 0.035 m (middle height line).

The heat fluxes on define surfaces can be calculated and plotted by using Fluent reporting options.

In Figure 7 is shown local Nusselt number distribution along cold wall of the enclosure. Predicted

average Nusselt number is compared with benchmark solution of De Vahl Davis [4] very well. For Ra

= 106, Pr = 0.71, De Vahl Davis obtained a value of average Nusselt number of 8.798 for fine mesh. The

average Nusselt number using Fluent with a 35x35 graded elements mesh was found to be Nu = 8.883

(FIDAP [3] gives for this problem Nu = 9.199 with 12x12 element mesh).

Figure 7. Nusselt number distribution along cold wall.


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1. Natural convection in an enclosure with opening.

The next problem is example of applying Low-Reynolds-Number k-turbulence model with

radiation surface-to-surface (S2S) model for purpose of simulation of heat transfer and air flows inside

skylight well with glazing at an angle of 20o.

Model and boundary conditions

The problem considered here is modeling of two-dimensional flow and heat transfer in a skylight

well. Figure 9 shows geometry and boundary conditions of the skylight well model. Rayleigh number of

this problem approximately is 1.0x109. Initial conditions: operating (mean) temperature 13oC; kinetic

energy 0.001 m2/s2; dissipation of kinetic energy 0.0012 m2/s3.

0.5 m

0.2 m

0.6 m

0.8 m

hwall= 5 W/m2o

Csimulated thermalresistance of wellwall insulation

T = 21o

C

hwall= 2 W/m2o

Csimulated thermal

resistance ofskylight frame

T = -10

o

C

hglz= 2.8 W/m2o

C

simulated thermalresistance of glazing andouter film coefficient

T = -10oC

Fluents BC :Pressure outlet

T = 21oC

Figure 9. Geometry and boundary conditions of the skylight model.

In Figure 10 it is shown mesh generated by Gambit and consisted from structured boundary layers

along glazing and well walls and unstructured other part. Boundary layer has 10 elements and thickness19 mm (size of the first element is 0.5 mm and increasing coefficient is 1.2).


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Figure 10. Mesh generated by Gambit 2.0.

Solution procedure and strategy

We used segregated solver with the next settings: implicit formulation, unsteady calculation, energy

equation. Viscous model was defined as standard k-omega model with options: transitional flows andshear stress. Radiation model was defined as surface-to-surface model (S2S).

Solution controls: under-relaxation factors (RF) for all equations (variables) were defined as default

excluding energy equation where was used RF = 0.8.

Method discretization: pressure equation PRESTO; pressure-velocity coupling SIMPLEC;

momentum POWER LAW; energy first order scheme.

Time step: 0.5 s. (Maximal number iterations on each time step is 20).

After 220 steps when it was clear that flow and temperature fields were stabilized relaxation factors

for pressure and momentum equations were changed (RFpress= 0.7 and RFmoment= 0.3) and time step

was redefined (0.2 s).

The solution reached convergence after 400 time steps.


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Results

Figure 11 through Figure 15 show the velocity and temperature fields in the enclosure. Significant

flows exist only along walls and glazing and directions of flow depend from surface temperature: near

the skylight frame air moves to top of the well and the well walls moves to the well bottom. The central

part of the well is zone of temperature stratification (Figure 15) and turbulence intensity (Figure 16).

Maximum value of no dimensional turbulent viscosity is 48. Maximal predicted velocity is 0.066 m/s.

Figure 11. Velocity vector field in the top left part of the model.


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Figure 12. Velocity vector field in the top right part of the model.

Figure 13. Velocity magnitude field.


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Figure 14. Plot of streamline function.

Figure 15. Temperature distribution in the skylight well.


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Figure 15. No dimensional turbulent viscosity distribution in the skylight well.

Figure 16. Temperature distribution along skylight glazing (left point is sharp skylight angle).


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Figure 17. Local heat transfer coefficient distribution along skylight glazing (left point is sharp skylight

angle).

Distribution of temperature and local heat transfer coefficient along glazing surface are shown in

Figure 16 and Figure 17. Mean temperature of the skylight well is 13.25oC. Average heat transfer

coefficient on skylight glazing is 5.25 W/m2oC. Average heat transfer coefficients on well walls are from

6.9 W/m2oC to 3.8 W/m2oC.

References

1. FDI 2000. Gambit 1.3.2 Users and Reference Manual. Fluid Dynamics International, Fluid

Dynamics Analysis Package Revision 1.3.2, Evanston, IL.

2. FDI 2001. FLUENT 6.0. Users and Reference Manual. Fluid Dynamics International, Fluid

Dynamics Analysis Package. Fluent Inc. November 2001.

3. FDI 2000. FIDAP 8.52 Users and Reference Manual. Fluid Dynamics International, Fluid Dynamics

Analysis Package Revision 8.52, Evanston, IL.

4. G. de Vahl Davis, Natural Convection of Air in a Square Cavity: A Bench Mark NumericalSolution, Int. J. Numer. Meth. Fluids, vol. 3, pp. 249-264, 1983.

using software gambit 2.0 and fluent 6.0 for simulation of heat mass transfer problems

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