How do I Select a Turbulent Mixing Length, TLEN?
The default value of TLEN, the turbulent mixing length, has recently changed. Previously, the value of TLEN was computed based on the computational grid. This method was fairly arbitrary and did not consider the flow scale which is more important in determining the turbulent length scale than the computational grid. In general, the hydraulic diameter, if it can be defined, provides a better estimate of the turbulent flow scale.
The default value of TLEN is now computed as 0.07 of the smallest domain dimension, excluding any mesh direction which has only 1 cell. For example, if the simulation contains 3 mesh blocks and the smallest dimension of all mesh blocks is 1 meter, the default value of TLEN would be 0.07m. However, this is a simple estimate of length scale and does not include geometry effects or the actual flow-field scales.
The Effect of TLEN on Simulations
TLEN is used by the k-ε and RNG turbulence models to limit the turbulent dissipation so that the turbulent viscosity does not become excessively large. It is important that users understand the effect of TLEN on their simulations. If TLEN is too large, the dissipation will be under-predicted and the turbulent viscosity will be unrealistically large. If TLEN is too small, the dissipation will be large and turbulence will be excessively damped out. In most cases, the user should input an appropriate value for TLEN. For example, in a spillway simulation, a good selection for the length scale would be the depth of the flow over the spillway. In a high pressure die casting simulation, a good choice for the length scale is the width of the inlet runner. For flows in pipes and ducts, the length scale should be the hydraulic diameter of the flow channel. Once the length scale is determined, TLEN is then input at 0.07 or 7% of the length scale.
Example: Flow in a Conduit
The effect of the turbulent mixing length is clearly seen in this case of a flow in a conduit.
Geometry and mesh block configuration:
The effect of the turbulent mixing length is clearly seen in this case of a flow in a conduit
Left boundary: Velocity inlet (210 cm/s), fluid height = 5 cm
Right boundary: Pressure outlet
Results--Case A (TLEN = 0.35 cm):
TLEN is calculated as 7% of the fluid height at the boundary.
TLEN = 0.35
TLEN = 0.35
Results--Case B (Default TLEN):
The code calculates TLEN as 7% of smallest domain dimension. In this case, the z direction represents the smallest domain direction.
TLEN = 0.07 * 15 = 1.05 cm
Default TLEN = 1.05
Default TLEN = 1.05
The results show that the default value of TLEN (1.05 cm) increases the dynamic viscosity by a factor of 3, which results in the over prediction of turbulent diffusion and leads to a large change in the free-surface profile. When dealing with water flows having depths of several centimeters and speeds of meters per second, for example, the filling of a bathtub, you expect to see considerable turbulence (i.e., a highly unsteady free surface, lots of eddy structures, etc.). Such experiences lead us to question the relatively smooth results compluted with the larger TLEN value.
This conclusion is also suggested by the comparison of the time-step sizes of the two cases:
- When TLEN = 0.35 cm, the time step is always limited by convection.
- When the default value for TLEN (1.05 cm) is used, the time step is limited by viscosity, which means that the turbulence viscosity generated is probably unphysically large and the turbulence length scale needs to be changed to a smaller value.
Specified value of TLEN based on hydraulic diameter: dt controlled by advection.
Default value of TLEN based on hydraulic diameter: dt controlled by viscosity.