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Documentation

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×0.52 m

2.18 m×0.076 m×0.52 m

, and the face details have been given in Table 1.

Fig.1. Geometry used in the study
Table 1: Domain Details
FaceType
ABCDBottom
EFGGTop
ABFEHot Wall
DCGHCold Wall
BCGFFront
ADHEBack

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+

 (“y-plus”) value, which is defined as the non-dimensionalized distance to the wall; it is given by y+=uy/ν

y+=uy/ν

. A y+

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+

    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 30y+300

    30y+300

    .

y+

y+

 value of 30 was used for the inflation layer. The kω

kω

 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
snappyHexMesh5.95×106

5.95×106
3D hex
Fig.2. Mesh used for the SimScale case

Simulation Setup

Fluid:

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

Table 3: Fluid Properties
m

m

 g/mol

g/mol
cp

cp

 J/kgK

J/kgK
mu

mu

 N/ms

N/ms
Pr

Pr
28.9

28.9
1005

1005
1.831×105

1.831×105
0.705

0.705

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 ms1

0.0 ms1
0.0 ms1

0.0 ms1
0.0 ms1

0.0 ms1
0.0 ms1

0.0 ms1
Modified PressureFFP ( 105

105

 Pa)

FFP ( 105

105

 Pa)

FFP ( 105

105

 Pa)

FFP (105

105

 Pa)

TemperatureZero GradientZero Gradient307.85

307.85

 K

288.25

288.25

 K

k

k
Wall FunctionWall FunctionWall FunctionWall Function
ω

ω
Wall FunctionWall FunctionWall FunctionWall Function
αt

αt
Wall FunctionWall FunctionWall FunctionWall Function
μt

μt
Wall FunctionWall FunctionWall FunctionWall 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.

Fig.3.a. Velocity profile at h=872 mm

h=872 mm

h=872 mm
Fig.3.b. Velocity profile at h=218 mm

h=218 mm

h=218 mm
Fig.3.c. Velocity profile at h=109 mm

h=109 mm

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 mm

109 mm

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

Fig.4. Temperature profile at h=872 mm

h=872 mm

h=872 mm

References

[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

Disclaimer

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: October 7th, 2020

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