Expressions for pressure-velocity-gradient correlations
- 41 Downloads
The term for pressure-velocity-gradient correlation was initiated by Rotta's rewriting the correlation between the pressure fluctuation gradient and velocity fluctuation. However, it is very difficult to consider the effect of this term. Since Rotta's work, Launder et al. has made some estimates of this term. In this paper according to the equations for velocity fluctuation, the pressure fluctuation is solved so that the average value of the product of the pressure fluctuation and the velocity fluctuation gradient is obtained. Thus, the whole expressions for the pressure-velocity-gradient correlation are derived. The result explains that the limited expressions by Rotta and Launder are reasonable to a certain degree. The whole expressions in this paper are discussed respectively in two situations: one is without a separate consideration of large and small vortexes; the other is with a separate consideration of three kinds of vortexes. Therefore, the paper gives the whole expressions for pressure-velocity-gradient correlation to the Reynolds stress turbulence model and the three-vortex turbulence model.
Key wordspressure-velocity-gradient correlation turbulence model theory second-order closure
Unable to display preview. Download preview PDF.
- Donaldson, C. Dup, A computer study of an analytical model of boundary layer transition,AIAA Paper No. 68-38 (1968).Google Scholar
- Fu, S., B. E. Launder and M. A. Leschziner, Modelling strongly swirling recirculating jet flow with Reynolds-stress transport closures,Proc. Sixth Symposium on Turbulent Shear Flows, Toulouse, France, September (1987), 17-6-1.Google Scholar
- Hanjalic, K., Two-dimensional flow in an axisymmetric channel, Ph. D. thesis, Univ. of London (1970).Google Scholar
- Hinze, J. O.,Turbulence, McGraw-Hill Book Company (1975).Google Scholar
- Launder, B. E., A. Morse, W. Rodi and D. B. Spalding, The prediction of free shear flows—a comparison of the performance of six turbulence models, NASA-SP-321 (1973).Google Scholar
- Launder, B. E. and D. B. Spalding,Lectures in Mathematical Models of Turbulence, Academic Press, New York (1972).Google Scholar
- Lumley, J. L. and B. Khajeh-Nouri, Computational modelling of turbulent transport,Advances in Geophysics,18A, Academic Press, New York (1974), 169–192.Google Scholar
- Reece, G. J., A generalized Reynolds stress model of turbulence, Ph. D. Thesis, Faculty of Engineering, Univ. of London (1977).Google Scholar
- Reynolds, W.C., Computation of turbulent flows-state-of-the-art, Stanford Univ., Engng Dept. Rep.MD-27 (1970).Google Scholar
- Rodi, W., The prediction of free turbulent boundary layers by use of a two-equation model of turbulence, Ph. D. dissertation, Mechanical Eng. Dept., Imperial College, London, December (1972).Google Scholar
- Tsai, S. T., and B. K. Ma, A new turbulence model with the separate consideration of large and small vortexes,Appli. Math. and Mech.,8, 10 (1987), 849–858.Google Scholar