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:

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 :

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 \(m\):

• \(U_y\) at 0.218 \(m\):

• \(U_y\) at 0.654 \(m\):

• \(U_y\) at 0.872 \(m\):

• \(U_y\) at 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:

The \(U_y\) distribution mid-plane normal to the z-direction can be seen in the following figure:

On the same plane, the temperature is also visualized:

All results are in good agreement with the reference.

Last updated: July 18th, 2022