The aim of this test case is to validate the following parameters of steadystate 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×0.52 m
$2.18\text{}m\times 0.076\text{}m\times 0.52\text{}m$, and the face details have been given in Table 1.
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+
${y}^{+}$(“yplus”) value, which is defined as the nondimensionalized distance to the wall; it is given by y+=u∗y/ν
${y}^{+}={u}^{\ast}y/\nu $. A y+
${y}^{+}$value of 1 would correspond to the upper limit of the laminar sublayer.
 Explicit resolution of the nearwall region: The first cell lies at most at the boundary of the laminar sublayer and no further. Here, y+
${y}^{+}$
value is 1 or below.
 Use of wallfunctions to resolve the nearwall region: There is no need to place cells very close to the laminar sublayer, and typically 30⩽y+⩽300
$30\u2a7d{y}^{+}\u2a7d300$
.
A y+
${y}^{+}$value of 30 was used for the inflation layer. The k−ω
$k\omega $SST turbulence model was chosen, with wall functions for nearwall treatment of the flow.
Tool Type : OPENFOAM®
Analysis Type : buoyantSimpleFoam
Mesh and Element types :
Mesh type  Number of volumes  Type 

snappyHexMesh  5.95×106
$5.95\times {10}^{6}$

3D hex 
Fluid:
Table 3 encapsulates the properties of fluids used in the subsonic and supersonic case simulations.
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
$1005$

1.831×10−5
$1.831\times {10}^{5}$

0.705
$0.705$

The boundary conditions for the simulation are shown in Table 4. Note: FFP stands for Fixed Flux Pressure.
Boundary Conditions:
Parameter  Top and Bottom  Front and Back  Hot Wall  Cold Wall 

Velocity  0.0 ms−1
$0.0\text{}m{s}^{1}$

0.0 ms−1
$0.0\text{}m{s}^{1}$

0.0 ms−1
$0.0\text{}m{s}^{1}$

0.0 ms−1
$0.0\text{}m{s}^{1}$

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 
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 midplane normal to the zdirection.
h=872 mm
$h=872\text{}mm$
h=218 mm
$h=218\text{}mm$
h=109 mm
$h=109\text{}mm$
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
$109\text{}mm$. The reference line is located at the midplane normal to the zdirection.
h=872 mm
$h=872\text{}mm$
[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 675683. 
[2]  ERCOFTAC Database: Turbulent Natural Convection in an Enclosed Tall Cavity 
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