Enhanced wall treatment is a nearwall modeling method that combines a
twolayer model with enhanced wall functions. If the nearwall mesh is fine
enough to be able to resolve the laminar sublayer (typically
),
then the enhanced wall treatment will be identical to the traditional twolayer
zonal model (see below for details). However, the restriction that the
nearwall mesh must be sufficiently fine everywhere might impose too large a
computational requirement. Ideally, then, one would like to have a nearwall
formulation that can be used with coarse meshes (usually referred to as
wallfunction meshes) as well as fine meshes (lowReynoldsnumber meshes). In
addition, excessive error should not be incurred for intermediate meshes that
are too fine for the nearwall cell centroid to lie in the fully turbulent
region, but also too coarse to properly resolve the sublayer.
To achieve the goal of having a nearwall modeling approach that will possess
the accuracy of the standard twolayer approach for fine nearwall meshes
and that, at the same time, will not significantly reduce accuracy for
wallfunction meshes,
FLUENT can combine the twolayer model with
enhanced wall functions, as described in the following sections.
TwoLayer Model for Enhanced Wall Treatment
In
FLUENT's nearwall model, the viscosityaffected nearwall region is
completely resolved all the way to the viscous sublayer. The twolayer approach
is an integral part of the enhanced wall treatment and is used to specify both
and the turbulent viscosity in the nearwall cells. In this approach,
the whole domain is subdivided into a viscosityaffected region and a
fullyturbulent region. The demarcation of the two regions is determined by a
walldistancebased, turbulent Reynolds number, Re
, defined as
(12.1018)
where
is the normal distance from the wall at the cell centers. In
FLUENT,
is interpreted as the distance to the nearest wall:
(12.1019)
where
is the position vector at the field point, and
is
the position vector on the wall boundary.
is the union of all the
wall boundaries involved. This interpretation allows
to be uniquely defined
in flow domains of complex shape involving multiple walls. Furthermore,
defined in this way is independent of the mesh topology used, and is definable
even on unstructured meshes.
In the fully turbulent region
(
;
),
the

models or the RSM (described in Sections
12.4
and
12.7) are employed.
In the viscosityaffected nearwall region (
), the
oneequation model of Wolfstein [
406] is employed. In the
oneequation model, the momentum equations and the
equation are retained
as described in Sections
12.4 and
12.7.
However, the turbulent viscosity,
, is computed from
(12.1020)
where the length scale that appears in Equation
12.1020
is computed from [
54]
(12.1021)
The twolayer formulation for turbulent viscosity described above is used as a
part of the enhanced wall treatment, in which the twolayer definition is
smoothly blended with the highReynoldsnumber
definition from the outer
region, as proposed by Jongen [
168]:
(12.1022)
where
is the highReynoldsnumber definition as described in
Section
12.4 or
12.7 for the

models or the RSM.
A blending function,
, is defined in such a way that it
is equal to unity far from walls and is zero very near to walls.
The blending function chosen is
(12.1023)
The constant
determines the width of the blending function. By defining a
width such that the value of
will be within 1% of its
farfield value given a variation of
, the result is
(12.1024)
Typically,
would be assigned a value that is between 5%
and 20% of
. The main purpose of the blending function
is to prevent solution convergence from being impeded
when the

solution in the outer layer does not match with the twolayer
formulation.
The
field is computed from
(12.1025)
The length scales that appear in Equation
12.1025 are again
computed from Chen and Patel [
54]:
(12.1026)
If the whole flow domain is inside the viscosityaffected region
(
),
is not obtained by solving the transport
equation; it is instead obtained algebraically from Equation
12.1025.
FLUENT uses a procedure for
the
specification that is similar to the
blending in order to ensure a
smooth transition between the algebraicallyspecified
in the
inner region and the
obtained from solution of the transport
equation in the outer region.
The constants in the length scale formulas, Equations
12.1021 and
12.1026, are taken from [
54]:
(12.1027)
Enhanced Wall Functions
To have a method that can extend its applicability throughout the nearwall
region (i.e., laminar sublayer, buffer region, and fullyturbulent outer region)
it is necessary to formulate the lawofthe wall as a single wall law for the
entire wall region.
FLUENT achieves this by blending linear (laminar) and
logarithmic (turbulent) lawsofthewall using a function suggested by
Kader [
170]:
(12.1028)
where the blending function is given by:
(12.1029)
where
and
.
Similarly, the general equation for the derivative
is
(12.1030)
This approach allows the fully turbulent law to be easily modified and
extended to take into account other effects such as pressure gradients
or variable properties. This formula also guarantees the correct asymptotic
behavior for large and small values of
and reasonable representation of
velocity profiles in the cases where
falls inside the wall buffer region
(
).
The enhanced wall functions were developed by smoothly blending an enhanced
turbulent wall law with the laminar wall law. The enhanced turbulent
lawofthewall for compressible flow with heat transfer and pressure gradients
has been derived by combining the approaches of White and
Cristoph [
402] and Huang et al. [
149]:
(12.1031)
where
(12.1032)
and
(12.1033)
(12.1034)
(12.1035)
where
is the location at which the loglaw slope will remain fixed.
By default,
. The coefficient
in Equation
12.1031
represents the influences of pressure gradients while the
coefficients
and
represent thermal effects. Equation
12.1031 is an ordinary differential equation and
FLUENT will provide an appropriate analytical solution. If
,
, and
all equal 0, an analytical solution
would lead to the classical turbulent logarithmic lawofthewall.
The laminar lawofthewall is determined from the following expression:
(12.1036)
Note that the above expression only includes effects of pressure gradients
through
, while the effects of variable properties due to heat
transfer and compressibility on the laminar wall law are neglected.
These effects are neglected because they are thought to be of minor importance
when they occur close to the wall. Integration of
Equation
12.1036 results in
(12.1037)
Enhanced thermal wall functions follow the same approach developed for the
profile of
. The unified wall thermal formulation blends the laminar and
logarithmic profiles according to the method of Kader [
170]:
(12.1038)
where the notation for
and
is the same as for standard thermal
wall functions (see Equation
12.105). Furthermore, the blending factor
is defined as
(12.1039)
where
is the molecular Prandtl number, and the coefficients
and
are defined as in Equation
12.1029.
Apart from the formulation for
in Equation
12.1038, enhanced thermal wall functions
follow the same logic as for standard thermal wall
functions (see Section
12.10.2), resulting in the following
definition for turbulent and laminar thermal wall functions:
(12.1040)
(12.1041)
where the quantity
is the value of
at the fictitious "crossover"
between the laminar and turbulent region. The function
is defined in the same
way as for standard wall functions.
A similar procedure is also used for species wall functions when the enhanced
wall treatment is used. In this case, the Prandtl numbers in Equations
12.1040 and
12.1041 are
replaced by adequate Schmidt numbers. See Section
12.10.2 for details about species wall functions.
The boundary condition for turbulence kinetic energy is the same as for
standard wall functions (Equation
12.109). However, the production of
turbulence kinetic energy
is computed using the velocity gradients that
are consistent with the enhanced lawofthewall (Equations
12.1028 and
12.1030), ensuring a formulation that is valid throughout the
nearwall region.
The enhanced wall treatment is available with the following viscous models:
Kepsilon
Reynolds Stress
Enhanced wall functions are available with the following viscous models: