In addition to the standard wall function described above (which is the default
near-wall treatment) a two-layer-based, non-equilibrium wall
182] is also available. The key elements in the non-equilibrium
wall functions are as follows:
Launder and Spalding's log-law for mean velocity is sensitized to
The two-layer-based concept is adopted to compute the budget of turbulence
kinetic energy (
) in the
The law-of-the-wall for mean temperature or species mass fraction remains the
same as in the standard wall function described above.
The log-law for mean velocity sensitized to pressure gradients is
is the physical viscous sublayer thickness, and is computed from
The non-equilibrium wall function employs the two-layer concept in computing the
budget of turbulence kinetic energy at the wall-adjacent cells, which is needed
to solve the
equation at the wall-neighboring cells. The wall-neighboring
cells are assumed to consist of a viscous sublayer and a fully turbulent layer.
The following profile assumptions for turbulence quantities are made:
is the dimensional thickness
of the viscous sublayer, defined in Equation
Using these profiles, the cell-averaged production of
the cell-averaged dissipation rate,
, can be computed from
the volume average of
of the wall-adjacent cells. For
quadrilateral and hexahedral cells for which the volume average can be
approximated with a depth-average,
is the height of the cell (
). For cells with other
shapes (e.g., triangular and tetrahedral grids), the appropriate volume averages
12.10-17, the turbulence kinetic energy
budget for the wall-neighboring cells is effectively sensitized to the
proportions of the viscous sublayer and the fully turbulent layer, which varies
widely from cell to cell in highly non-equilibrium flows. It effectively
relaxes the local equilibrium assumption (production = dissipation) that is
adopted by the standard wall function in computing the budget of the turbulence
kinetic energy at wall-neighboring cells. Thus, the non-equilibrium
wall functions, in effect, partly account for non-equilibrium
effects neglected in the standard wall function.
Limitations of the Wall Function Approach
The standard wall functions give reasonably accurate predictions for the
majority of high-Reynolds-number, wall-bounded flows. The non-equilibrium wall
functions further extend the applicability of the wall function approach by
including the effects of pressure gradient and strong non-equilibrium. However,
the wall function approach becomes less reliable when the flow conditions depart
too much from the ideal conditions underlying the wall functions. Examples are
Pervasive low-Reynolds-number or near-wall effects (e.g., flow through a
small gap or highly viscous, low-velocity fluid flow).
Massive transpiration through the wall (blowing/suction).
Severe pressure gradients leading to boundary layer separations.
Strong body forces (e.g., flow near rotating disks, buoyancy-driven flows).
High three-dimensionality in the near-wall region (e.g., Ekman spiral
flow, strongly skewed 3D boundary layers).
If any of the items listed above is a prevailing feature of the flow you are
modeling, and if it is considered critically important to capture that feature
for the success of your simulation, you must employ the near-wall modeling
approach combined with adequate mesh resolution in the near-wall region.
FLUENT provides the enhanced wall treatment for such situations.
This approach can be used with the three
models, and the RSM.
Standard Wall Functions vs. Non-Equilibrium Wall Functions
Because of the capability to partly account for the effects of pressure
gradients and departure from equilibrium, the non-equilibrium wall functions are
recommended for use in complex flows involving separation, reattachment, and
impingement where the mean flow and turbulence are subjected to severe pressure
gradients and change rapidly. In such flows, improvements can be obtained,
particularly in the prediction of wall shear (skin-friction coefficient) and
heat transfer (Nusselt or Stanton number).
Non-equilibrium wall functions are available with the following viscous models: