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Hybrid wall functions:
a step toward simplifying wall treatment
Julien de Charentenay,
STAR-CD Developer, CD-adapco
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We
have implemented a new treatment of near-wall boundary
conditions, developed by T. Rung [1], that removes
constraints on near wall mesh density. This "hybrid
wall function" treatment allows more accurate
solutions to be obtained when the near-wall mesh
is not optimized. If the mesh is fine enough, the
boundary layer is resolved in a similar way to a
low Reynolds number turbulence model. When the near-wall
cell is located in the fully developed part of the
boundary layer, adequate wall functions are applied.
This boundary condition is available for the following
turbulence models: k-epsilon linear/cubic/quadratic,
k-omega standard and SST; with heat and mass transfer.
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Fig. 1 presents a simulation of
flow over a hill. The wall distance of the near-wall
cell is constant along the bottom wall. However, the
normalized wall distance y+, shown in Fig. 1, varies
from 1 to 40 due to changes in flow velocity. Therefore,
the mesh is not optimized for either low-Reynolds or
high-Reynolds number turbulence models. However, using
a linear k-epsilon turbulence model with the hybrid
wall function, the agreement between predicted and
measured flow field is excellent, as shown in Fig.
2.
Velocity vectors for the simulation
of the turbulent flow and heat transfer in a cavity
are presented in Fig. 3. The inlet flow corresponds
to a fully developed boundary layer and can be accurately
modeled using a coarse mesh and wall functions. However,
a large re-circulation zone forms in the cavity. In
this region, the flow velocity is small and the boundary
layer must be resolved to accurately predict heat transfer.
Using the hybrid wall function, the wall treatment
automatically adapts to the near-wall mesh density
and the flow field is accurately predicted with a limited
number of cells. For this configuration, the predicted
Nusselt number on the bottom wall of the cavity agrees
well with experimental measurements, as shown in Fig.
4.
Fig. 5 shows the normalized wall
distance at wall boundaries for a HVAC geometry provided
by BEHR. The hybrid wall function has been successfully
applied to this test-case and a 5% difference in pressure
drop between inlet and outlet has been observed compared
to the high-Reynolds number turbulence model.
[1] T. Rung. Formulierung universeller
Wandrandbedingungen fur Transportgleichungsturbulenzmodelle.
Technische Universitat Berlin. Institutsbericht Nr.
02/99
Fig. 5: Normalized wall
distance y+ (scale from 0 to 100) for a HVAC system.
Courtesy of BEHR
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Fig. 1: Isocontours
of velocity magnitude and normalized wall distance
y+ (scale from 0 to 40) at the lower wall for flow
over a hill
Fig. 2: Comparison
of stream-velocity profile at two different sections
for flow over a hill
Fig. 3: Velocity vectors and Nusselt number on the cavity wall for flow
in a cavity
Fig. 4: Comparison of predicted
and measured Nusselt numbers on the cavity wall
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