Turbulent flows through rectangular channels, pipes of non-circular cross-section, and wing-body-junction type geometries exhibit secondary flows in the plane normal to the main flow direction into the corner along the bisector. These flows are known as "secondary flow of the second kind" [533] and are of much lower magnitude than the flow in the main direction. These secondary flows are driven by the anisotropy (meaning differences in normal stresses) of the turbulence stress tensor. They can have a subtle effect on flow separation under adverse pressure gradient conditions, where the additional momentum transport into the corner can help the flow remain attached.
Eddy-viscosity models cannot account for this effect, as they do not model the anisotropy of the normal stresses. They therefore have a tendency to over-predict corner flow separation zones. Differential Reynolds stress models are the most consistent RANS-based formulations able to take anisotropy into account, but are often too time consuming and not robust enough in complex flow situations. A simplified quadratic non-linear algebraic extension for the Spalart-Allmaras and two-equation models has been implemented that drives momentum into the corner and can reduce corner separation effects. The additional terms do not affect the basic model calibration for simple generic flows (like flat plates). A tunable model parameter is introduced which allows you to optimize the strength of the quadratic term for your application.
The corner flow correction is available for the following turbulence models:
Spalart-Allmaras (SA,SA-DES)
Standard k-ω model (and combination of this model with SAS)
BSL, SST, GEKO, and Transition-SST models (and combination of these models with SAS, DES, and SBES)
For the definition of the Reynolds stress tensor in the momentum equation, a quadratic model is used based on [619], but augmented for the Spalart-Allmaras model:
 | (4–434) |
and for two-equation models:
 | (4–435) |
where 
denotes the kinematic eddy viscosity. The strain-rate and vorticity tensor are
defined as:
.
with 
and 
.
The factor 1.2 is from 0.3*4, where 0.3 is the model constant 
introduced by Spalart [619] and 4 is due to
the utilization of strain-rate and vorticity tensors in Equation 4–434 and Equation 4–435. Instead of giving access to 
, a tunable parameter 
is available in Fluent.
By default, the coefficient 
is constant and the value is equal to 1. It is accessible in the Viscous Model
dialog box or via text command. There is also the possibility to specify an expression or a User
Defined Function which offers additional flexibility to provide zonal-dependent values.
Note: One-equation models like Spalart-Allmaras are missing the 
- term which can lead to negative normal stresses.
To enable corner flow correction, see Including Corner Flow Correction in the Fluent User's Guide.