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Constraints for the Pressure-Strain Correlation tensor derived from Spectral Representation

Constraints for the Pressure-Strain Correlation tensor derived from Spectral Representation. S.R.Bogdanov T.J.Jongen. Outline DRSM, PSC models The derivation of the restrictions on the “rapid” part of PSC. Direct checking of the models for

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Constraints for the Pressure-Strain Correlation tensor derived from Spectral Representation

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  1. Constraints for the Pressure-Strain Correlation tensor derived from Spectral Representation S.R.Bogdanov T.J.Jongen EFMC-6, Stockholm, 2006

  2. Outline • DRSM, PSC models • The derivation of the restrictions on the “rapid” part of PSC. • Direct checking of the models for • Predicting the available areas of the parameters of stationary states • Others: (Implicit) checking of the models for non-linear part of PSC, non-uniform turbulence … EFMC-6, Stockholm, 2006

  3. Differential Reynolds stress models, DRSM Spectra of ideas, connected with the study of fully developed turbulence and calculations of the flows with the anisotropy is extremly wide: from the theory of fractals and renormalization group methods to direct numeric simulations and semiempirical modelling. At the same time nowadays the so-called first (with the turbulent viscosity as the key concept) and second-order closure (or full differential Reynolds stress models, DRSM). models are the most popular in practice. EFMC-6, Stockholm, 2006

  4. A lot of models were proposed for PSC. One of the most popular and well-known (quasi-linear) semi-empirical approximations for PSC looks like: EFMC-6, Stockholm, 2006

  5. Realizability criteria EFMC-6, Stockholm, 2006

  6. The derivation of the restrictions on the “rapid” part of PSC. EFMC-6, Stockholm, 2006

  7. Illustration of the basic idea EFMC-6, Stockholm, 2006

  8. EFMC-6, Stockholm, 2006

  9. EFMC-6, Stockholm, 2006

  10. EFMC-6, Stockholm, 2006

  11. Direct checking of the models for PSC EFMC-6, Stockholm, 2006

  12. EFMC-6, Stockholm, 2006

  13. EFMC-6, Stockholm, 2006

  14. EFMC-6, Stockholm, 2006

  15. It's convenient to present the available areas for the set ofparameters B with graphic on B_3 - {B_2}/R plane. Available is the insidearea of the triangle ABC. 2-D turbulence corresponds to the sides ofthe triangle; points A,B,C correspond to 1-dimensional turbulence(with pulsations along axes 3,1,2).BE, CF, AD - present axisymmetric turbulence;At last, point O presents isotropic turbulence. The set of hyperbola (B_1 - isolines) isalso presented on the picture.When B_1 is fixed, the area of available values of theparameters B_2 и B_3/R is restricted with correspondent hyperbolaand BC- line. Y – axis: B3= -b33/2 X-axis: B2/R = (b11 – b22)/2 EFMC-6, Stockholm, 2006

  16. EFMC-6, Stockholm, 2006

  17. EFMC-6, Stockholm, 2006

  18. EFMC-6, Stockholm, 2006

  19. The available domain on invariant map EFMC-6, Stockholm, 2006

  20. B3 - isolines EFMC-6, Stockholm, 2006

  21. B2 - isolines, for B1=0 EFMC-6, Stockholm, 2006

  22. «Forbidden» areas on invariant map (SSG model, R=0, B1=0 and -0.1 correspondently) EFMC-6, Stockholm, 2006

  23. EFMC-6, Stockholm, 2006

  24. Stationary state analysis, SSG EFMC-6, Stockholm, 2006

  25. Conclusion • Possibilities of direct checking (and improving, hopefully: at least, through the proper choice of the set of the model constants) of PSC models • Direct analysis of the parameters of stationary states. • The link between spectral approach and one-point closures. • Most probably turbulence is more non-local than it’s usually assumed within second-order closures. EFMC-6, Stockholm, 2006

  26. Thank you EFMC-6, Stockholm, 2006

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