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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
Face Type
ABCD Bottom
EFGG Top
ABFE Hot Wall
DCGH Cold Wall
BCGF Front
ADHE Back

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 type Number of volumes Type
snappyHexMesh 5.95×106

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
Parameter Top and Bottom Front and Back Hot Wall Cold Wall
Velocity 0.0 ms1

0.0 ms1

 

0.0 ms1

0.0 ms1

 

0.0 ms1

0.0 ms1

 

0.0 ms1

0.0 ms1

 

Modified Pressure FFP ( 105

105

 Pa)

FFP ( 105

105

 Pa)

FFP ( 105

105

 Pa)

FFP (105

105

 Pa)

Temperature Zero Gradient Zero Gradient 307.85

307.85

 K

288.25

288.25

 K

k

k

 

Wall Function Wall Function Wall Function Wall Function
ω

ω

 

Wall Function Wall Function Wall Function Wall Function
αt

αt

 

Wall Function Wall Function Wall Function Wall Function
μt

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.

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.

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