The computation of turbulent natural convection flows - Turbulence ...

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For the thermal boundary conditions, two different conditions have been
used in the current research. One is that of prescribed wall temperature, which
here can be constant, uniform, and non-uniform. The other thermal boundary
condition is that of an insulated wall. In order to simulate constant temper-
ature wall boundary conditions in low-Re-number computations, Twall is as-
signed to the temperature at the wall node. To simulate the insulated wall, the
wall heat flux must be zero and according to Fick’s law:
qwall = −λ
∂Θ
∂y wall
(5.39)
To have zero wall heat flux, the gradient of temperature at the wall must
therefore be zero. Therefore, in a low-Re-model, the temperature at the node
on the wall and the node adjacent to the wall are set equal.
For the high-Re-number computations, a different approach is adopted.
In the momentum equations, the wall shear stress(multiplied by the cell face
area), which is calculated from the wall-function equations, is added to the
source term of near wall cells, and the matrix coefficient which links the near
wall node and the wall is set to zero. For the turbulent kinetic energy transport
equation, the production and dissipation source terms for near wall cells are
calculated according to the wall-function equations. The ε transport equation
is not solved for near wall cells. Instead, the value of εP is assigned to near
wall cells,as:
εP = k3/2
P
clyP
(5.40)
Therefore, in the ε equation the near wall cell is effectively treated as the
boundary condition for the rest of the domain.
For the temperature transport equation, on boundaries at which the ther-
mal conditions are those of prescribed wall temperature, the wall heat flux
is calculated from the wall-function equations and then adding into the dis-
cretized source term as
SU = SU + qwall
Area (5.41)
cp