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Buoyant Flow: Natural convection between heated plates


The aim of this test case is to validate the following parameters of steady-state natural convection between two plates maintained at different temperatures. The incompressible, turbulent case is validated with the experimental results of Betts and Bokhari [1] as archived in the ERCOFTAC database [2]. The following parameters have been analysed:

  • Velocity Profiles
  • Temperature Profiles

The geometry is uploaded on to the SimScale platform and meshed using the snappyHexMesh tool.

This project could be imported from the library upon request.


The geometry is constructed based on the reference case [1], as shown in Fig.1.Its dimensions are 2.18 m×0.076 m×0.52m and the face details have been given in Table 1.


Fig.1. Geometry used in the study

Table 1: Domain Details
ABFEHot Wall
DCGHCold Wall

Analysis type and Domain

The snappyHexMesh tool was used to generate a uniform mesh (see Fig.2. and Table 2.).

A typical property of the generated mesh is the y+(“y-plus”) value, which is defined as the non-dimensionalized distance to the wall; it is given by y+=u∗y/ν. A y+ value of 1 would correspond to the upper limit of the laminar sub-layer.

  • Explicit resolution of the near-wall region: The first cell lies at most at the boundary of the laminar sub-layer and no further. Here, y+ value is 1 or below.
  • Use of wall-functions to resolve the near-wall region: There is no need to place cells very close to the laminar sub-layer, and typically 30⩽y+⩽300.

A y+ value of 30 was used for the inflation layer. The k−ω SST turbulence model was chosen, with wall functions for near-wall treatment of the flow.

Tool Type : OPENFOAM®

Analysis Type : buoyantSimpleFoam

Mesh and Element types :

Table 2: Mesh Metrics
Mesh typeNumber of volumesType
snappyHexMesh5.95×1063D hex

Fig.2. Mesh used for the SimScale case

Simulation Setup


Table 3 encapsulates the properties of fluids used in the subsonic and supersonic case simulations.

Table 3: Fluid Properties
m g/molcp J/kgKmu N/msPr

The boundary conditions for the simulation are shown in Table 4. Note: FFP stands for Fixed Flux Pressure.

Boundary Conditions:

Table 4: Boundary Conditions for Ahmed Body simulation
ParameterTop and BottomFront and BackHot WallCold Wall
Velocity0.0 ms−10.0 ms−10.0 ms−10.0 ms−1
Modified PressureFFP (105 Pa)FFP (105 Pa)FFP (105 Pa)FFP (105 Pa)
TemperatureZero GradientZero Gradient307.85K288.26K
KWall FunctionWall FunctionWall FunctionWall Function
ωWall FunctionWall FunctionWall FunctionWall Function
αtWall FunctionWall FunctionWall FunctionWall Function
μtWall FunctionWall FunctionWall FunctionWall Function


Velocity Profiles

Shown below are comparisons of velocity profile between the two plates from SimScale simulation results with the reference [1]at different heights. The reference lines are located at the mid-plane normal to the z-direction.


Fig.3.a. Velocity profile at h=872 mm


Fig.3.b. Velocity profile at h=218 mm


Fig.3.c. Velocity profile at h=109 mm

Temperature Profiles

Shown below is the comparison of the temperature profile between the two plates from SimScale simulation results with the reference [1] at a height of 109 m.

The reference line is located at the mid-plane normal to the z-direction.


Fig.4. Temperature profile at h=872 mm


[1](1234) Betts, P.L. & Bokhari, I.H., 2000, Experiments on turbulent natural convection in an enclosed tall cavity. Int. J. Heat & Fluid Flow, Vol 21, pp 675-683.
[2]ERCOFTAC Database: Turbulent Natural Convection in an Enclosed Tall Cavity


This offering is not approved or endorsed by OpenCFD Limited, producer and distributor of the OpenFOAM software and owner of the OPENFOAM® and OpenCFD® trade marks. OPENFOAM® is a registered trade mark of OpenCFD Limited, producer and distributor of the OpenFOAM software.

Last updated: January 29th, 2019

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part of: Flow Analysis of a Butterfly valve

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