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How to estimate turbulence quantities to specify at inlet 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 a measure of the strength of the velocity fluctuations, u, compared to the strength of the bulk velocity, U. By definition, I is equal to the ratio of the root-mean-square of the velocity fluctuations to the mean freestream velocity.

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The best way to get values for inlet turbulence quantities specification is to have experimental data, from which turbulence intensity can be calculated. When experimental data is not available, an educated guess based on the type of flow may be sufficient. The following section provides some guidelines for a broad category of flows (internal/external).

Internal flows usually have high turbulence intensity. Good values for inlet turbulence intensity are 0.01 to 0.1 (i.e. velocity fluctuations are about 1% - 10% of the mean bulk velocity. For high speed flows in complex geometries such as turbomachinery, the turbulence intensity values could be much higher than 10%. For a fully developed flow inside a duct, the turbulence intensity can be estimated as:

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Here, Re is the Reynolds number based on the hydraulic diameter.

External flows are unconstrained and therefore have smaller values of turbulence intensity. Inlet values can go down to 0.0005.

Once you have obtained a reasonable estimate for I, you can either use it to calculate the inlet value of turbulent kinetic energy, k, as described in later sections, or you can use it as a boundary value directly.

About Turbulent Viscosity Ratio

The turbulent viscosity ratio is the ratio of turbulent to laminar (molecular) viscosity, and is defined as:

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For internal flows, β 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 value of 100 is a reasonable estimate for β.

For external flows the freestream turbulent viscosity is of the order of laminar viscosity, so small values of β are appropriate, say β = 0.1 1.

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 that 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. For a fully developed pipe flow, the turbulence length scale is given by:

l = 0.07L

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

  • In the case of fully-developed internal flows, it is better to choose the Hydraulic Diameter specification method.
  • In the case of wall-bounded flows, the Turbulent Intensity and Length Scale specification methods are preferred. Then use the boundary-layer thickness, δ, to estimate the turbulence length scale, l, as l = 0.4δ.

For external flows, it is often not possible to determine a good characteristic length. In using the formulas below, pick a value of β and a value of I 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 β (0.1 to 1), whereas in the case of wind-tunnel external flows, choose larger values of β (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. 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:

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Turbulent Dissipation Rate:

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or

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For the Spalart-Allmaras Model

Turbulent Kinematic Eddy Viscosity:

Image

or

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For the k-omega and Menter SST Models

Specific Dissipation Rate:

Image

or

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NOTE: For external flows, it is very important to specify appropriate turbulence 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. Hence, consider using 10x greater values for β and I for the initial conditions. You can also use the Turbulence Start Control feature for better convergence.

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Last update: 2011-08-31 17:05
Author: ESI-CFD Support Team
Revision: 1.5

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