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# 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. $$^1$$

## Geometry

The geometry is constructed based on the reference case $$^1$$, as shown below: Figure 1: The geometry for the buoyant flow between heated plates consists of a rectangular block.

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 : Figure 2: The generated mesh for the whole flow region (top) and meshing details after zooming in (bottom)

## Simulation Setup

Fluid:

• Air
• Kinematic viscosity $$(\nu)$$ = 1.529 e-5 $$m^2 \over \ s$$
• Density $$(\rho)$$ = 1.196 $$kg \over \ m^3$$

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)

Initial Conditions:

• Uniform temperature of 19.85 $$°C$$

Model:

• Gravity towards the negative y direction $$g_y$$ = – 9.81 $$m \over \ s^2$$

## 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 $$m$$: 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 $$m$$: 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 $$m$$: 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 $$m$$: 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 $$m$$: 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: 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: Figure 9: The $$U_y$$ distribution mid-plane normal to the z-direction

On the same plane, the temperature is also visualized: