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:
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
| Face | Type |
|---|---|
| ABCD | Bottom |
| EFGG | Top |
| ABFE | Hot Wall |
| DCGH | Cold Wall |
| BCGF | Front |
| ADHE | Back |
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 :
| Mesh type | Number of volumes | Type |
|---|---|---|
| snappyHexMesh | 5.95×106 | 3D hex |
Fig.2. Mesh used for the SimScale case
Fluid:
Table 3 encapsulates the properties of fluids used in the subsonic and supersonic case simulations.
| m g/mol | cp J/kgK | mu N/ms | Pr |
|---|---|---|---|
| 28.9 | 1005 | 1.831×10−5 | 0.705 |
The boundary conditions for the simulation are shown in Table 4. Note: FFP stands for Fixed Flux Pressure.
Boundary Conditions:
| 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 |
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] | (1, 2, 3, 4) 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 |
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