Buoyant Flow: Natural convection between heated plates
Overview
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.
Geometry
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.
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.
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¶
Parameter
Top and Bottom
Front and Back
Hot Wall
Cold Wall
Velocity
0.0 ms−1
0.0 ms−1
0.0 ms−1
0.0 ms−1
Modified Pressure
FFP (105 Pa)
FFP (105 Pa)
FFP (105 Pa)
FFP (105 Pa)
Temperature
Zero Gradient
Zero Gradient
307.85K
288.26K
K
Wall Function
Wall Function
Wall Function
Wall Function
ω
Wall Function
Wall Function
Wall Function
Wall Function
αt
Wall Function
Wall Function
Wall Function
Wall Function
μt
Wall Function
Wall Function
Wall Function
Wall Function
Results
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.
BuoyantFlow-results-V-y872
Fig.3.a. Velocity profile at h=872mm
BuoyantFlow-results-V-y872
Fig.3.b. Velocity profile at h=218mm
BuoyantFlow-results-V-y109
Fig.3.c. Velocity profile at h=109mm
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.
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.
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