Natural Convection: Buoyant Flow Between Heated Plates

This validation case belongs to fluid dynamics. The aim of this test case is to validate the following parameters for a buoyant flow simulation between heated plates, and specifically a hot and cold wall:

Velocity parallel to the plates ( $U_{y}$ )and temperature profiles

The simulation results from SimScale were compared to the experimental results presented in a research article on turbulent natural convection in a closed cavity by Betts et. al. $^{1}$

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Geometry

The geometry is constructed based on the reference case $^{1}$ , as shown below:

It is basically a rectangular block with dimensions 0.076 $m \times$ 2.18 $m \times$ 0.52 $m$ .

Analysis Type and Domain

Tool Type: OpenFOAM®

Analysis Type: Steady-state, incompressible, Convective heat transfer

Mesh and Element Types:

SimScale’s Standard algorithm was used for the creation of this mesh :

details of the mesh created with the standard meshing algorithm — Figure 2: The generated mesh for the whole flow region (top) and meshing details after zooming in (bottom)

Simulation Setup

Fluid:

Air
- Kinematic viscosity $(ν)$ = 1.529 e-5 $\frac{m^{2}}{s}$
- Density $(ρ)$ = 1.196 $\frac{k g}{m^{3}}$

Boundary Conditions:

Wall conditions
- No-slip walls with wall function for all faces
Temperature conditions
- 34.65 $° C$ on the hot wall (face ABFE)
- 15 $° C$ on the cold wall (face DCGH)
- Zero gradient/Adiabatic on the rest of the faces

Initial Conditions:

Uniform temperature of 19.85 $° C$

Model:

Gravity towards the negative y direction $g_{y}$ = – 9.81 $\frac{m}{s^{2}}$

Result Comparison

In the graphs below the velocity profile data that is parallel to the plates, $(U_{y})$ , extracted with ParaView, is plotted against the experimental findings $^{1}$ at different heights. The reference lines are located at the mid-plane normal to the z-direction:

$U_{y}$ at 0.109 $m$ :

comparison of velocity profiles between a hot and a cold wall with buoyant flow at a height of 0.109 meters — Figure 3: The $U_{y}$ comparison across the x direction, mid-plane normal to the z direction, and at a height of 0.109 $m$

$U_{y}$ at 0.218 $m$ :

comparison of velocity profiles between a hot and a cold wall with buoyant flow at a height of 0.218 meters — Figure 4: The $U_{y}$ comparison across the x direction, mid-plane normal to the z direction, and at a height of 0.218 $m$

$U_{y}$ at 0.654 $m$ :

comparison of velocity profiles between a hot and a cold wall with buoyant flow at a height of 0.654 meters — Figure 5: The $U_{y}$ comparison across the x direction, mid-plane normal to the z direction, and at a height of 0.654 $m$

$U_{y}$ at 0.872 $m$ :

comparison of velocity profiles between a hot and a cold wall with buoyant flow at a height of 0.872 meters — Figure 6: The $U_{y}$ comparison across the x direction, mid-plane normal to the z direction, and at a height of 0.872 $m$

$U_{y}$ at 1.09 $m$ :

comparison of velocity profiles between a hot and a cold wall with buoyant flow at a height of 1.09 meters — Figure 7: The $U_{y}$ comparison across the x direction, mid-plane normal to the z direction, and at a height of 1.09 $m$

Shown below is the comparison of the temperature profile between the two plates obtained from SimScale simulation results with the reference paper $^{1}$ at a height of 0.109 $m$ . The reference line is located at the mid-plane normal to the z-direction:

comparison of temperature profiles between a hot and a cold wall with buoyant flow at a height of 0.109 meters — Figure 8: The temperature comparison across the x direction, mid-plane normal to the z direction, and at a height of 0.109 $m$

The $U_{y}$ distribution mid-plane normal to the z-direction can be seen in the following figure:

parallel to the plates velocity distribution for buoyant flow between plates — Figure 9: The $U_{y}$ distribution mid-plane normal to the z-direction

On the same plane, the temperature is also visualized:

temperature distribution for buoyant flow between plates — Figure 10: The temperature distribution mid-plane normal to the z-direction

All results are in good agreement with the reference.

References

Last updated: July 18th, 2022

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