
Enhanced wall treatment is a nearwall modeling method that combines a twolayer model with socalled enhanced wall functions. If the nearwall mesh is fine enough to be able to resolve the viscous sublayer (typically with the first nearwall node placed at
), 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, 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 the intermediate meshes where the first nearwall node is placed neither in the fully turbulent region, where the wall functions are suitable, nor in the direct vicinity of the wall at
, where the lowReynoldnumber approach is adequate.
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, ANSYS FLUENT can combine the twolayer model with enhanced wall functions, as described in the following sections.
TwoLayer Model for Enhanced Wall Treatment
In ANSYS 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
(4.1220) 
where is the wallnormal distance calculated at the cell centers. In ANSYS FLUENT, is interpreted as the distance to the nearest wall:
(4.1221) 
where
is the position vector at the field point, and
is the position vector of 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.
In the fully turbulent region (
;
), the

models or the RSM (described in Sections
4.4 and
4.9) are employed.
In the viscosityaffected nearwall region ( ), the oneequation model of Wolfstein [ 382] is employed. In the oneequation model, the momentum equations and the equation are retained as described in Sections 4.4 and 4.9. However, the turbulent viscosity, , is computed from
where the length scale that appears in Equation 4.1222 is computed from [ 51]
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 [ 153]:
(4.1224) 
where is the highReynoldsnumber definition as described in Section 4.4 or 4.9 for the  models or the RSM. A blending function, , is defined in such a way that it is equal to unity away from walls and is zero in the vicinity of the walls. The blending function has the following form:
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
(4.1226) 
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 value of
obtained in the outer layer does not match with the value of
returned by the Wolfstein model at the edge of the viscosityaffected region.
The field in the viscosityaffected region is computed from
The length scales that appear in Equation 4.1227 are computed from Chen and Patel [ 51]:
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
4.1227.
ANSYS FLUENT uses a procedure for the blending of
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 Equations 4.1223 and 4.1228, are taken from [ 51] and are as follows:
Enhanced Wall Functions
To have a method that can extend its applicability throughout the nearwall region (i.e., viscous 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. ANSYS FLUENT achieves this by blending the linear (laminar) and logarithmic (turbulent) lawsofthewall using a function suggested by Kader [ 155]:
where the blending function is given by:
where and .
Similarly, the general equation for the derivative is
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 [ 378] and Huang et al. [ 134]:
where
and
(4.1235)  
(4.1236)  
(4.1237) 
where
is the location at which the loglaw slope is fixed. By default,
. The coefficient
in Equation
4.1233 represents the influences of pressure gradients while the coefficients
and
represent the thermal effects. Equation
4.1233 is an ordinary differential equation and
ANSYS 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:
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 4.1238 results in
(4.1239) 
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 [ 155]:
where the notation for
and
is the same as for standard thermal wall functions (see Equation
4.126). Furthermore, the blending factor
is defined as
where
is the molecular Prandtl number, and the coefficients
and
are defined as in Equation
4.1231.
Apart from the formulation for in Equation 4.1240, the enhanced thermal wall functions follow the same logic as for standard thermal wall functions (see Section 4.12.2), resulting in the following definition for turbulent and laminar thermal wall functions:
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 the 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
4.1242 and
4.1243 are replaced by adequate Schmidt numbers. See Section
4.12.2 for details about the species wall functions.
The boundary conditions for the turbulence kinetic energy are similar to the ones used with the standard wall functions (Equation 4.1210). However, the production of turbulence kinetic energy, , is computed using the velocity gradients that are consistent with the enhanced lawofthewall (Equations 4.1230 and 4.1232), ensuring a formulation that is valid throughout the nearwall region.

The enhanced wall treatment is available with the following turbulence closures:
The enhanced wall functions are available with the following turbulence models:
However, the enhanced wall functions are not available with SpalartAllmaras model.
