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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 analyzed:

• 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

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

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

${y}^{+}={u}^{\ast }y/\nu$

. 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
$30⩽{y}^{+}⩽300$

.

y+

${y}^{+}$

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

$k-\omega$

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

$5.95×{10}^{6}$
3D hex

## 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

${c}_{p}$

J/kgK

$J/kgK$
mu

$mu$

N/ms

$N/ms$
Pr

$Pr$
28.9

$28.9$
1005

$1005$
1.831×105

$1.831×{10}^{-5}$
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

Modified Pressure FFP ( 105

${10}^{5}$

Pa)

FFP ( 105

${10}^{5}$

Pa)

FFP ( 105

${10}^{5}$

Pa)

FFP (105

${10}^{5}$

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

$\omega$
Wall Function Wall Function Wall Function Wall Function
αt

${\alpha }_{t}$
Wall Function Wall Function Wall Function Wall Function
μt

${\mu }_{t}$
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.

h=872 mm

h=218 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

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

h=872 mm

## 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: January 26th, 2021