The Reynolds stress model (RSM) determines the turbulent stresses by solving a
transport equation for each stress component.
The RSM accounts for the effects of flow history and streamline curvature, as well as
system rotation and stratification (Wilcox, 2000). Reynolds stress models are known to give
superior results over one and two equation models when dealing with flows with streamline
curvature, flows with sudden change in strain rate, and flows with secondary motions, all at
the cost of an increased computing time (Bradshaw, 1997). There are many types of Reynolds
stress models, the two most common being the RSM based on the dissipation rate
(ε) and the RSM based on the eddy frequency
(ω). In this section the dissipation rate
(ε) model is discussed.
Transport Equations
Reynolds Stresses
(1)
Turbulent Dissipation Rate
ε(2)
Production Modeling
Reynolds Stresses
(3)
Turbulent Dissipation Rate
ε
(4)
Dissipation Modeling
Reynolds Stresses
(5)
Turbulent Dissipation Rate
ε
(6)
Molecular Diffusion Modeling
Reynolds Stresses
(7)
Turbulent Diffusion Modeling
Reynolds Stresses
(8)
Pressure-Strain Modeling
Reynolds Stresses
(9)
where
,
,
,
,
,
,
where
is the
component of the unit normal to the wall and
is the normal distance from the wall.
Modeling of Turbulent Viscosity
Model Coefficients
= 1.44,
= 1.92,
= 0.09,
= 1.0,
= 1.0,
= 1.8,
= 0.6,
= 0.5,
= 0.3,
=