One drawback of the eddy-viscosity models is that these models are insensitive to streamline curvature and system rotation, which play a significant role in many turbulent flows of practical interest. A modification to the turbulence production term is available to sensitize the following standard eddy-viscosity models to the effects of streamline curvature and system rotation:

Note that both the RNG and Realizable (-) turbulence models already have their own terms to include rotational or swirl effects (see RNG Swirl Modification and Modeling the Turbulent Viscosity, respectively, for more information). The curvature correction option should therefore be used with caution for these two models and is offered mainly for completeness for RNG and Realizable (-).

Spalart and Shur [623] and Shur et al. [595] have derived a modification of the production term for the Spalart-Allmaras one-equation turbulence model to take streamline curvature and system rotation effects into account. Based on this work, a modification of the production term has been derived that allows you to sensitize the standard two-equation turbulence models to these effects (Smirnov and Menter [604]). The empirical function suggested by Spalart and Shur [623] to account for streamline curvature and system rotation effects is defined by

(4–420)

It is used as a multiplier of the production term and has been limited in Ansys Fluent in the following way:

(4–421)

with

(4–422)

(4–423)

The original function is limited in the range from 0 corresponding to, for example, a strong convex curvature (stabilized flow, no turbulence production) up to 1.25 (strong concave curvature, enhanced turbulence production). The lower limit is introduced for numerical stability reasons, whereas the upper limit is needed to avoid over-generation of the eddy viscosity in flows with a destabilizing curvature/rotation. The specific limiter 1.25 provides a good compromise for different test cases that have been considered with the SST model (such as U-turn flow, flow in hydro cyclone, NACA 0012 wing tip vortex [604]).

in Equation 4–422 has been introduced to allow you to influence the strength of the curvature correction if needed for a specific flow. By default, the coefficient is constant and the value of is equal to 1. It is accessible in the Viscous Model dialog box or via text command, and you may also specify an expression or a User Defined Function (see DEFINE_CURVATURE_CORRECTION_CCURV in the Fluent Customization Manual). This offers additional flexibility to provide zonal dependent values. The coefficient should be positive.

Assuming that all the variables and their derivatives are defined with respect to the reference frame of the calculation, which is rotating with a rate , the arguments and of the function are defined in the following way:

(4–424)

(4–425)

Where the first term in brackets is equivalent to the second velocity gradient (in this case the Lagrangian derivative of the strain rate tensor) and the second term in the brackets is a measure of the system rotation. The strain rate and vorticity tensor are defined as

(4–426)

(4–427)

with

(4–428)

(4–429)

The denominator in Equation 4–425 takes the following form for the Spalart-Allmaras turbulence model (Shur et al. [595]):

(4–430)

(4–431)

and for all other turbulence models (Smirnov and Menter [604]) :

(4–432)

(4–433)

are the components of the Lagrangian derivative of the strain rate tensor. The Einstein summation convention is used.

The empirical constants , and involved in Equation 4–420 are set equal to

To enable curvature correction, see Including the Curvature Correction for the Spalart-Allmaras and Two-Equation Turbulence Models in the User's Guide.