Gamma-Re (γ-Re) transition model is a two equation
model
A model is an informative representation of an object, person, or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin , .
Models can be divided in ...
used in
Computational Fluid Dynamics
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid dynamics, fluid flows. Computers are used to perform the calculations required ...
(CFD) to modify turbulent transport equations to simulate
laminar
Laminar means "flat". Laminar may refer to:
Terms in science and engineering:
* Laminar electronics or organic electronics, a branch of material sciences dealing with electrically conductive polymers and small molecules
* Laminar armour or "bande ...
, laminar-to-turbulent and turbulence states in a fluid flow. The Gamma-Re model does not intend to model the physics of the problem but attempts to fit a wide range of experiments and transition methods into its formulation. The transition model calculated an
intermittency
In dynamical systems, intermittency is the irregular alternation of phases of apparently periodic and chaotic dynamics ( Pomeau–Manneville dynamics), or different forms of chaotic dynamics (crisis-induced intermittency).
Experimentally ...
factor that creates (or
extinguish
A fire extinguisher is a handheld active fire protection device usually filled with a dry or wet chemical used to extinguish or control small fires, often in emergencies. It is not intended for use on an out-of-control fire, such as one which ha ...
es) turbulence by slowly introducing turbulent production at the laminar-to-turbulent transition location.
R.B. Langtry. A Correlation-Based Transition Model using Local Variables for Unstructured Parallelized CFD Code. University of Stuttgart, PhD Thesis. May 31, 2006
Principle
The goal of developing the gamma-Re () transition model was to develop a transition model based on local variables which could be easily implemented into modern Computational fluid dynamics, CFD code with unstructured grids and massive parallel execution. The majority of earlier transition models such as the model needs to know the structure of the boundary layer
In physics and fluid mechanics, a boundary layer is the thin layer of fluid in the immediate vicinity of a Boundary (thermodynamic), bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces ...
and the integration along it; both concepts are hard to implement in three dimensions along many subdivisions of a grid. Another key insight to the formulation of this model is that the Reynolds vorticity
In continuum mechanics, vorticity is a pseudovector (or axial vector) field that describes the local spinning motion of a continuum near some point (the tendency of something to rotate), as would be seen by an observer located at that point an ...
number can be related to the Reynolds transition onset number so there is a local way to determine the transition location. The gamma-Re transition model has two equations and is based on the two-equation turbulence models in the context of turbulence modeling
In fluid dynamics, turbulence modeling is the construction and use of a mathematical model to predict the effects of turbulence. Turbulent flows are commonplace in most real-life scenarios. In spite of decades of research, there is no analytical ...
. This way both local and global trends can be modelled. The intermittency or gamma determines the percentage of time the flow is turbulent (0 = fully laminar, 1 = fully turbulent). The intermittency acts on the production term of the turbulent kinetic energy
In physics, the kinetic energy of an object is the form of energy that it possesses due to its motion.
In classical mechanics, the kinetic energy of a non-rotating object of mass ''m'' traveling at a speed ''v'' is \fracmv^2.Resnick, Rober ...
transport equation in the SST model to simulate laminar/turbulence flows.
Standard Gamma-Theta model
For intermittency
: