Turbulence

Turbulence modeling in STORM is accomplished using a two-equation k-epsilon model. This model solves transport equations for the turbulence kinetic energy k, and the dissipation rate e. The turbulent shear stresses in the Reynolds-averaged Navier-Stokes equations are then modeled using the Boussinesq hypothesis with an appropriate relation for the eddy or turbulent viscosity, based on the computed values of k and e.

STORM/CFD2000 provides seven (7) turbulence models:

           Standard k-epsilon  model

           RNG k-epsilon  model

           Chen-Kim k-epsilon   model

           Standard k-epsilon  model for low Reynolds number flows

           RNG k-epsilon  model for low-Reynolds number flows

           Chen-Kim k-epsilon  model for low Reynolds number flows

           LES - Smagorinsky's model

The Standard k-epsilon Turbulence Model

The k-e turbulence model is one of several two-equation models that have developed over the years.  It is probably the most widely and thoroughly tested of them all (Nallasamy, 1987). Based on simple dimensional arguments concerning the relationship between the size and the energetics of individual eddies in fully -developed, isotropic turbulence, the model employs the following diagnostic equation for the turbulent viscosity (Launder and Spalding, 1974).

where Cm is a dimensionless model constant, r is the local fluid density, and k and e are the specific turbulent kinetic energy (SI units: m2/s2) and turbulent kinetic energy dissipation rate (SI units: m2/s3), respectively.  These quantities are in turn computed using a pair of auxiliary transport equations of the form

 

and

 

 

 

where C1 and C2 are additional dimensionless model constants; Prk and Pre are the turbulent Prandtl numbers for kinetic energy and dissipation, respectively; Sk,p and Se,p are source terms for the kinetic energy and turbulent dissipation; and the turbulent production rate is