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Old   November 11, 2000, 02:23
Default Reynolds Stress equation ???
Abhijit Tilak
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hi everybody

my question is regarding Reynolds stress equation. Anyone who has tried deriving RS-equation and hence k and e equation in k-e turbulence model, knows that in order to get the equation in the desired form, the manipulation of the derivative terms (especially the convective terms) requires density to be assumed as constant. Otherwise u will have 6 more terms for u'rho'. I tried deriving the equation in conservative form but could'nt get any where without those assumptions (Note that most of the books derive RS equation in non-conservative form). My question is can this have serious implications in variable density /compressible flows? What is to be done if i want to retain the conservative form?

thanx in advance

Abhijit Tilak
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Old   November 12, 2000, 12:50
Default Re: Reynolds Stress equation ???
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you try to refer "computational fluid mechanics and heat transfer" by Dale anderson,Tannenhill and Fletcher. In that book, for two dimensional,incompressible flow, reynolds equations of motion derivation given. Hope, your problem will be solved.

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Old   November 12, 2000, 19:18
Default Re: Reynolds Stress equation ???
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REGARDING THE EQUATION (T-9){48,FG,H(6+T[G'J''K''']} INVOLVING ABNORMAL STRESS BREAK FLUID ANALISYS, DIMENSONAL EQUATION:--()'[(1[45])]-- FLUID ANALI/??? SYS:ESA,DEYG.99/8UIT>[T-8.65/WRG>(-+)/ETA>0.1TW)] T-1:H2O>0.1T>>3>7.0967:C2 T-2:H2O=0.34T29/H2O+H2M2T>W2---E T-3:??? T-4:??? WT-01:??? WT-02:??? QUANTIM:26'78TTW''

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Old   November 15, 2000, 00:34
Default Re: Reynolds Stress equation ???
Abhijit Tilak
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ur message seems illegible to me. i cant read it. guess some problem with format or ur browser.
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Old   November 15, 2000, 07:01
Default Re: Reynolds Stress equation ???
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Fluctuations of density (rho') are often neglicted even for compressible flow, since the turbulence mach number (sqrt(k)/c - where c is the speed of the sound) is low (<0.2).

To derive a turbulence model for compressible flow, you should use the Favre averaging method :

$ \tilde{\phi}= \frac{\overlined{\rho \phi}}{{\overlined{\rho}}$

where $\overlined{\phi}$ is the Reynolds average of $\phi$

You should look for papers from Sarkar or Mansour or Launder in the JFM (years 1990-1996).
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