Wall Treatment

Simcenter STAR-CCM+ In-cylinder provides various wall treatment models for the calculation of the wall heat flux.

By default, Simcenter STAR-CCM+ In-cylinder calculates the wall heat flux q ˙ w as given by Eqn. (1629). The Angelberger and the GruMO-UNiMORE wall treatment modify the wall heat flux computation as follows:

Angelberger Wall Treatment

The wall treatment suggested by Angelberger [146] takes into account the variation of thermophysical properties in the near-wall region for high-Reynolds number turbulence models.

In Simcenter STAR-CCM+ In-cylinder, the Angelberger wall heat flux is calculated depending on the type of engine as:

Engine Type q ˙ w
Gasoline
Figure 1. EQUATION_DISPLAY
ρ C p u * T ^ C ln ( T ^ C T w ) T ^ C +
(643)
Diesel
Figure 2. EQUATION_DISPLAY
ρ C p u * ( T ^ C + T w ) ln ( T ^ C T w ) 2 T ^ C +
(644)

with:

Figure 3. EQUATION_DISPLAY
T ^ C + = f ( y + , Pr )
(645)

where:

  • ρ is the density.
  • C p is the specific heat capacity.
  • u * is the Velocity Scale.
  • T ^ C is the RANS averaged or LES filtered temperature at the centroid of the near-wall cell.
  • T w is the temperature at the wall.
  • y + is the non-dimensional wall distance as given by Eqn. (1584).
  • Pr is the Prandtl number given by Eqn. (1141).
  • f is the Wall Function for Temperature that is used to approximate T ^ C + .
GruMo-UniMORE Wall Treatment

If the variables appearing in a wall function are made dimensionless using near-wall mean thermodynamic properties instead of wall properties, an isothermal law of the wall can be applied to non-isothermal problems. This formulation leads to an improvement in wall heat flux and local temperature field predictions in studies of turbocharged / highly-downsized engines [147], [148].

The GruMO-UniMORE wall treatment modifies the wall heat flux to account for variations in the Prandtl number as it follows instantaneous local conditions as:

Figure 4. EQUATION_DISPLAY
q ˙ w = ρ C p u * T ^ C T w T ^ C +
(646)

with:

Figure 5. EQUATION_DISPLAY
T ^ C + = 2.075 ln ( y + ) + 13.2 Pr 5.34
(647)