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Documentation

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:

geometry of the buoyant flow between two plates with different temperature
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 :

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 \((\nu)\) = 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)
    • 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 \(m \over \ s^2 \)

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 \(m\):
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.

Last updated: July 18th, 2022

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