The Proceedings Fifth International Conference on Numerical Ship Hydrodynamics (1990) / Chapter Skim
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RNG Modeling Techniques for Complex Turbulent Flows
RNG Modeling Techniques for Complex Turbulent Flows
Pages 35-44
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From page 35... ...
Yakhoti Ben-Gurion University of the Negev, Beesheva, Istael V Yakhot Princeton University, Princeton, USA Permanent address: Ben-Gurion University of the Negev Beesheva, Israel Abstract In this paper, we combine RNG modeling techniques with spectral element discretization procedures to formulate an algorithm appropriate for simulating high Reynolds number turbulent flows in complex geometries.
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From page 36... ...
RNG k-e Model This is a differential model based on differential recursion relations discussed in t13. It is free of adjustable parameters, however two additional equations are derived for the turbulent kinetic energy k, and the rate of dissipation e.
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From page 37... ...
A typical elliptic equation for a field variable ~ can be put in a standard Helmholtz equation form with variable coefficients as follows ~ `p 6+ ~ >2¢ = f in Q for j = 1,2 (14) In addition, let us assume homogeneous boundary conditions ~ = 0 on Q
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From page 38... ...
We have found that, for spectral element discretizations involving elements of low aspect ratio, multigird methods converge much faster than conjugate gradient methods; their convergence rate, however, is greatly deteriorated for large aspect ratio or very deformed spectral elements. A more quantitative analysis of the computational complexity as well as of the convergence properties of the aforementioned iterative methods in spectral element approximations, and in particular in the context of parallel implementation, is given in A
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From page 39... ...
Indeed, direct numerical simulations on the same mesh at Reynolds number R = 10, 000 shows regions of multiple small and large size instantaneous eddies (figure 43; the time-a~reraged flow however exhibits only very small recirculation zones sirrular to the ones shown in figures 2-3.
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From page 40... ...
= 45, 000~. In this simulation the computational domain includes the walls, where we impose the zero flux condition for the disipation rate e; at the outflow Neumann conditions are specified for all field variables.
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From page 41... ...
The results of our simulation are essentially identical with the results of the direct simulation as shown in figures 12 and 13, and in close agreement with the experiments t14~. The agreement extends also to higher order statistics as well as to flow structure and the streak spacing; the results of our simulations are plotted in figure 14 as color contour plots of the fluctuating velocity component at a plane close to the wall (here red indicates low velocity; blue high velocity)
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From page 42... ...
This methodology is very robust and can be applied to a variety of flows as a totally prognostic tool of analysis, since it requires no apriori known parameters or any experimental input, which is typically the case with the currently used turbulence modeling techniques. A computationally efficient implementation of the RNG methodology is obtained if it is combined with spectral or spectral element discretization methods, which are used today primarily in direct computations of transitional and turbulent flows.
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From page 43... ...
and EckelmAn H Behavior of the three fluctuating velocity components in the wall region of a turbulent channel flow.
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From page 44... ...
This is true for both free surface and other flows. However, in developing turbulence models for free surface flows, it may be best to "tune" the model using experimental observations of free surface turbulence.
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