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physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which rel ...
, the Spalart–Allmaras model is a one-equation model that solves a modelled transport equation for the kinematic eddy
turbulent In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between ...
viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...
. The Spalart–Allmaras model was designed specifically for
aerospace Aerospace is a term used to collectively refer to the atmosphere and outer space. Aerospace activity is very diverse, with a multitude of commercial, industrial and military applications. Aerospace engineering consists of aeronautics and astrona ...
applications involving wall-bounded flows and has been shown to give good results for boundary layers subjected to adverse pressure gradients. It is also gaining popularity in
turbomachinery Turbomachinery, in mechanical engineering, describes machines that transfer energy between a rotor (turbine), rotor and a fluid, including both turbines and gas compressor, compressors. While a turbine transfers energy from a fluid to a rotor, a ...
applications. In its original form, the model is effectively a low- Reynolds number model, requiring the viscosity-affected region of the boundary layer to be properly resolved ( y+ ~1 meshes). The Spalart–Allmaras model was developed for aerodynamic flows. It is not calibrated for general industrial flows, and does produce relatively larger errors for some free shear flows, especially plane and round jet flows. In addition, it cannot be relied on to predict the decay of homogeneous, isotropic turbulence. It solves a transport equation for a viscosity-like variable \tilde. This may be referred to as the ''Spalart–Allmaras variable''.


Original model

The turbulent eddy viscosity is given by : \nu_t = \tilde f_, \quad f_ = \frac, \quad \chi := \frac : \frac + u_j \frac = C_ - f_\tilde \tilde + \frac \ - \left _ f_w - \frac f_\right\left( \frac \right)^2 + f_ \Delta U^2 : \tilde \equiv S + \frac f_, \quad f_ = 1 - \frac : f_w = g \left \frac \right, \quad g = r + C_(r^6 - r), \quad r \equiv \frac : f_ = C_ g_t \exp\left( -C_ \frac d^2 + g^2_t d^2_t\right) : f_ = C_ \exp\left(-C_ \chi^2 \right) : S = \sqrt The
rotation Rotation, or spin, is the circular movement of an object around a '' central axis''. A two-dimensional rotating object has only one possible central axis and can rotate in either a clockwise or counterclockwise direction. A three-dimensional ...
tensor In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tens ...
is given by : \Omega_ = \frac ( \partial u_i / \partial x_j - \partial u_j / \partial x_i ) where d is the distance from the closest surface and \Delta U^2 is the norm of the difference between the velocity at the trip (usually zero) and that at the field point we are considering. The constants are : \begin \sigma &=& 2/3\\ C_ &=& 0.1355\\ C_ &=& 0.622\\ \kappa &=& 0.41\\ C_ &=& C_/\kappa^2 + (1 + C_)/\sigma \\ C_ &=& 0.3 \\ C_ &=& 2 \\ C_ &=& 7.1 \\ C_ &=& 1 \\ C_ &=& 2 \\ C_ &=& 1.1 \\ C_ &=& 2 \end


Modifications to original model

According to Spalart it is safer to use the following values for the last two constants: : \begin C_ &=& 1.2 \\ C_ &=& 0.5 \end Other models related to the S-A model: DES (1999

DDES (2006)


Model for compressible flows

There are two approaches to adapting the model for
compressible flow Compressible flow (or gas dynamics) is the branch of fluid mechanics that deals with flows having significant changes in fluid density. While all flows are compressible, flows are usually treated as being incompressible when the Mach number (the ...
s. In the first approach, the turbulent dynamic viscosity is computed from : \mu_t = \rho \tilde f_ where \rho is the local density. The
convective Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the convec ...
terms in the equation for \tilde are modified to : \frac + \frac (\tilde u_j)= \mbox where the right hand side (RHS) is the same as in the original model.


Boundary conditions

Walls: \tilde=0 Freestream: Ideally \tilde=0, but some solvers can have problems with a zero value, in which case \tilde \leq \frac can be used. This is if the trip term is used to "start up" the model. A convenient option is to set \tilde=5 in the freestream. The model then provides "Fully Turbulent" behavior, i.e., it becomes turbulent in any region that contains shear. Outlet: convective outlet.


References

* ''Spalart, P. R. and Allmaras, S. R.'', 1992, "A One-Equation Turbulence Model for Aerodynamic Flows" ''AIAA Paper 92-0439''


External links

* This article was based on th
Spalart-Allmaras model
article i
CFD-Wiki


from kxcad.net

at NASA's Langley Research Center Turbulence Modelling Resource site {{DEFAULTSORT:Spalart-Allmaras turbulence model Turbulence models