Initialization and Inflow for RANS Turbulence Models

The specification of realistic initial and inflow boundary values is important for good convergence and accurate simulation results.

For a one-equation turbulence model, only a single value is required, for the other turbulence models, a minimum of two values are required.

For many engineering applications, two-equation models are used. The k-epsilon models for example require two boundary conditions: one for the turbulent kinetic energy $k$ and one for the turbulent dissipation rate $ε$ . Measured data for $k$ and $ε$ are usually not available, but there are equations that calculate $k$ and $ε$ from values that you can measure or estimate such as turbulence intensity and length scale. In Simcenter STAR-CCM+, three turbulence specification methods are typically available (depending on the turbulence model):

Direct specification of the turbulence variables (such as $k$ and $ε$ )
Specification of turbulence intensity and turbulent length scale
Specification of turbulence intensity and turbulent viscosity ratio

For initialization, the last two methods also require the specification of a turbulent velocity scale.

Specification of Turbulence Values

It does not matter which turbulence specification method you use to set the boundary conditions, Simcenter STAR-CCM+ converts these values to $k$ and $ε$ values automatically. To avoid divergence during the initial iterations, it also helps to have reasonable initial values for the turbulence quantities. Admittedly, it might be hard to find a single number that describes the turbulence adequately throughout the domain.

Turbulent Length Scale

Turbulence length scale is a physical quantity describing the size of the large energy-containing eddies in a turbulent flow. It is typically set to be about 5% of the characteristic dimension of the inflow, so for a 30 mm diameter pipe it would be 1.5 mm.

Turbulence Intensity

Turbulence intensity is a measure of the root mean square of the local velocity fluctuations relative to the mean velocity and is typically estimated as follows:

High-turbulence case: High-speed flow inside complex geometries like heat-exchangers and flow inside rotating machinery (turbines and compressors). Typically the turbulence intensity is between 5% and 20%
Medium-turbulence case: Flow in not-so-complex devices like large pipes or ventilation flows, or low speed flows (low Reynolds number). Typically the turbulence intensity is between 1% and 5%
Low-turbulence case: Flow originating from a fluid that is stagnant, like external flow across cars, submarines and aircrafts. High-quality wind-tunnels can also reach very low turbulence levels. Typically the turbulence intensity is low, below 1%.

Turbulent Viscosity Ratio

The turbulent viscosity ratio is typically set in the range

10 < μ_{t} / μ < 100

. However, for SKE LRe, RKE, RKE 2L, and EBL models, the turbulent viscosity ratio that you specify on flow boundaries, or for initialization purposes, differs from the value that the model uses inside the domain.

For these models, the turbulent viscosity is not only a function of turbulence quantities and model coefficients, but also of the damping function

f_{μ}

(see for example Eqn. (1163)), which varies in space and is, therefore, unknown before running the simulation. For this reason, Simcenter STAR-CCM+ can not use Eqn. (1163) to calculate

ε

from the specified turbulent viscosity ratio on flow boundaries or for initialization. Instead, Simcenter STAR-CCM+ approximates

ε

using Eqn. (1359).

When you analyse the turbulent viscosity ratio after initialization, you can see the difference between the specified values and the values that Simcenter STAR-CCM+ applies. To get the desired turbulent viscosity ratio on a flow boundary or for initialization, follow these steps:

Set the desired turbulent viscosity ratio value, ${T V R}_{s p e c i f i e d}$ .
Initialize the solution.
Create a scalar scene and plot the field function Turbulent Viscosity Ratio, ${T V R}_{a p p l i e d}$ , on the flow boundary or in the fluid domain, respectively.
Set the turbulent viscosity ratio value to $\frac{{T V R}_{s p e c i f i e d}^{2}}{{T V R}_{a p p l i e d}}$ .
Clear the solution, then initialize again.
The scalar scene now displays the desired turbulent viscosity ratio.

Turbulent Velocity Scale

The turbulent velocity scale is a representative velocity that Simcenter STAR-CCM+ requires to convert the specified turbulence quantities to the transported turbulence quantities. Typically, you set this value equal to the initial velocity in the domain. However, if the initial velocity equals zero, leave the turbulent velocity scale at its default value (1 m/s) to ensure a good convergence of the turbulence quantities.