Guidelines for Specification of Turbulence at Inflow Boundaries

In this user tip, we discuss how to calculate and set appropriate turbulence values for inflow boundary conditions (inlets or freestream boundaries). Rather than starting with the turbulence model variables themselves it is often easier to think of turbulence in terms of the more readily known turbulence intensity, turbulent viscosity ratio, and turbulence length scale parameters. With these parameters in hand you can calculate the appropriate boundary values for any RANS turbulence model in CFD-ACE+ or CFD-FASTRAN.

About Turbulence Intensity

The turbulence intensity, I, is defined as the ratio of the root-mean-square of the velocity fluctuations, u`, to the mean free stream velocity, u.

figure1 (1K)

For internal flows the value of turbulence intensity can be fairly high with values ranging from 1% - 10% being appropriate at the inlet. The turbulence intensity at the core of a fully developed duct flow can be estimated as:

figure2 (1K)

For external flows the value of turbulent intensity at the freestream can be as low as 0.05% depending on the flow characteristics. You may have a good estimate of the turbulence intensity at the freestream boundary from experimentally measured data.

Once you have obtained a reasonable estimate for l you can either use it to calculate the inlet value of turbulence kinetic energy, k, as described below or you can use it as a boundary value directly. All inlet boundary condition types allow you to specify the turbulence kinetic energy at the boundary.

About Turbulent Viscosity Ratio

The turbulent viscosity ratio is simply the ratio of turbulent to laminar (molecular) viscosity:

figure3 (1K)

For internal flows b may be scaled with the Reynolds numbers.  Some guidelines (determined with numerical experiments) for fully developed pipe flows are as follows:


Re

3000

5000

10,000

15,000

20,000

b

11.6

16.5

26.7

34.0

50.1


For a Reynolds number of 100,000 or greater a constant value of b = 100 is a reasonable estimate. For external flows the freestream turbulent viscosity will be on the order of laminar viscosity so small values of b are appropriate, say b = 0.1 – 0.2.

About Turbulence Length Scale

Sometimes it is easier to think in terms of turbulence length scale instead of turbulent viscosity ratio. The turbulence length scale, l, is a physical quantity which represents the size of the large eddies in turbulent flows. Empirical relationship between the physical size of the obstruction (or characteristic length), L, and the size of the eddy, l, can be used to get an approximate length scale.

figure4 (1K)

For internal flows you can choose the characteristic length (L) to be inlet duct width or hydraulic diameter (Dh).

Guidelines for choosing Hydraulic Diameter Dh or turbulence length scale l.

  • For fully developed internal flows, choose the Hydraulic Diameter specification method and specify the physical size of the hydraulic diameter.
  • For wall-bounded flows in which inlet involve a turbulent boundary layer, choose the Turbulent Intensity and Length Scale specification method and the use the boundary-layer thickness, d, to compute the turbulence length scale, l, from l = 0.4(d) .

For external flows, it is often not possible to determine a good characteristic length. In using the formulas below, pick a value of b and a value of u' and use the formulas on the left, the ones not involving the length scale. In the case of external aerodynamic flows, choose smaller values of b (0.1 to 1), whereas in the case of wind-tunnel external flows, choose larger values of b (1 to 10).

Calculating Turbulence Boundary Conditions Values

All the turbulence models (except Baldwin-Lomax Algebraic Model) require the specification of certain variable values at the boundaries. There are several methods used for turbulence specification at the boundaries available in the codes. For all of the models the user can directly specify the turbulence intensity, turbulence length scale or the hydraulic diameter. But it is important to know how these quantities are related to primary turbulence variables like k, epsilon and omega. In this note we address only the RANS turbulence models (LES turbulence models may be discussed in a future note). For full details of the turbulence models and equations please see the user manuals.

For the Standard k-epsilon model and variations (RNG, Kato-Launder, Two Layer)

Turbulent Kinetic Energy        figure5 (1K)

Turbulent Dissipation Rate       figure6 (1K)   or   figure7 (1K)

For the Spalart-Allmaras Model

Turbulent Kinematic Eddy Viscosity      figure8 (1K)   or   figure9 (1K)

For the k-omega and Menter SST Models

Specific Dissipation Rate     figure10 (1K)   or   figure11 (1K)

NOTE: For external flows it is very important to specify appropriate turbulent quantities at the freestream boundaries. If the values are unphysical it can cause the solution to be unrealistic and can lead to divergence or non-convergence. For internal flows the importance of the values is not as critical because usually there is much more turbulence generated internally in the flow field.

TIP: You can use the same methods as described above to calculate the initial condition values for the turbulence quantities. However, it can sometimes make for an easier simulation startup if the initial condition values generate higher turbulent viscosity. So consider using 10x greater values for b and I as the initial conditions. You can also use the Turbulence Start Control Feature for better convergence. Details on this feature can be found on the following link to the previous user tip titled "New Turbulence Startup Option in CFD-ACE-GUI and CFD-CADalyzer"

We welcome your discussion and comments about this note on the ESI CFD Community forum. A topic has already been started and you can find it here. [Access available only to customers under a current support contract.]

Amit Saxena
Senior Applications Engineer
ESI CFD Customer Support