RNG kepsilon model
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+  { class="infobox bordered" style="verticalalign: top; textalign: left;"  
+  + style="background: #ccf; fontsize: larger;" align="center"  '''[[Turbulence modeling]]'''  
+    
+   '''[[Turbulence]]'''  
+    
+    
+  * [[What is turbulence%3FIntroduction]]  
+  * [[Elements of statistical analysisStatistical analysis]]  
+  * [[Reynolds averaged equations and the turbulence closure problemReynolds averaging]]  
+    
+   '''[[Algebraic turbulence modelsAlgebraic models]]'''  
+    
+    
+  * [[CebeciSmith model]]  
+  * [[BaldwinLomax model]]  
+  * [[JohnsonKing model]]  
+    
+   '''[[One equation turbulence modelsOne equation models]]'''  
+    
+    
+  * [[Prandtl's oneequation model]]  
+  * [[BaldwinBarth model]]  
+  * [[SpalartAllmaras model]]  
+    
+   '''[[Two equation models]]'''  
+    
+    
+  * [[kepsilon models]]  
+  :[[Standard kepsilon model]]  
+  :[[Realisable kepsilon model]]  
+  :[[RNG kepsilon model]]  
+  :[[Nearwall treatment for kepsilon modelsNearwall treatment]]  
+  *[[komega models]]  
+  :[[Wilcox's komega model]]  
+  :[[Wilcox's modified komega model]]  
+  :[[SST komega model]]  
+  :[[Nearwall treatment for komega modelsNearwall treatment]]  
+  * [[Two equation turbulence model constraints and limitersContraints and limiters]]  
+  :[[KatoLaunder modification]]  
+  :[[Durbin's realizability constraint]]  
+  :[[Yap correction]]  
+  }  
+  
==Background==  ==Background==  
The RNG model was developed using ReNormalisation Group (RNG) methods by [[#ReferencesYakhot et al]] to renormalise the NavierStokes equations, to account for the effects of smaller scales of motion. In the standard kepsilon model the eddy viscosity is determined from a single turbulence length scale, so the calculated turbulent diffusion is that which occurs only at the specified scale, whereas in reality all scales of motion will contribute to the turbulent diffusion. The RNG approach, which is a mathematical technique that can be used to derive a turbulence model similar to the kepsilon, results in a modified form of the epsilon equation which attempts to account for the different scales of motion through changes to the production term.  The RNG model was developed using ReNormalisation Group (RNG) methods by [[#ReferencesYakhot et al]] to renormalise the NavierStokes equations, to account for the effects of smaller scales of motion. In the standard kepsilon model the eddy viscosity is determined from a single turbulence length scale, so the calculated turbulent diffusion is that which occurs only at the specified scale, whereas in reality all scales of motion will contribute to the turbulent diffusion. The RNG approach, which is a mathematical technique that can be used to derive a turbulence model similar to the kepsilon, results in a modified form of the epsilon equation which attempts to account for the different scales of motion through changes to the production term. 
Revision as of 07:42, 12 June 2007
Turbulence 
Algebraic models 
One equation models 
Two equation models 

Contents 
Background
The RNG model was developed using ReNormalisation Group (RNG) methods by Yakhot et al to renormalise the NavierStokes equations, to account for the effects of smaller scales of motion. In the standard kepsilon model the eddy viscosity is determined from a single turbulence length scale, so the calculated turbulent diffusion is that which occurs only at the specified scale, whereas in reality all scales of motion will contribute to the turbulent diffusion. The RNG approach, which is a mathematical technique that can be used to derive a turbulence model similar to the kepsilon, results in a modified form of the epsilon equation which attempts to account for the different scales of motion through changes to the production term.
Transport Equations
There are a number of ways to write the transport equations for k and , a simple interpretation where bouyancy is neglected is
where
and and
With the turbulent viscosity being calculated in the same manner as with the standard kepsilon model.
Constants
It is interesting to note that the values of all of the constants (except ) are derived explicitly in the RNG procedure. They are given below with the commonly used values in the standard kepsilon equation in brackets for comparison:
 (0.09)
 (1.0)
 (1.30)
 (1.44)
 (1.92)
 (derived from experiment)
Applicability and Use
Although the technique for deriving the RNG equations was quite revolutionary at the time, it's use has been more low key. Some workers claim it offers improved accuracy in rotating flows, although there are mixed results in this regard: It has shown improved results for modelling rotating cavities, but shown no improvements over the standard model for predicting vortex evolution (both these examples from individual experience). It is favoured for indoor air simulations.
References
Yakhot, V., Orszag, S.A., Thangam, S., Gatski, T.B. & Speziale, C.G. (1992), "Development of turbulence models for shear flows by a double expansion technique", Physics of Fluids A, Vol. 4, No. 7, pp15101520.