Lin Duo-min, Cai Shu-tang. Expressions for Pressure-Velocity-Gradient Correlations[J]. Applied Mathematics and Mechanics, 1991, 12(9): 777-785.
Citation: Lin Duo-min, Cai Shu-tang. Expressions for Pressure-Velocity-Gradient Correlations[J]. Applied Mathematics and Mechanics, 1991, 12(9): 777-785.

Expressions for Pressure-Velocity-Gradient Correlations

  • Received Date: 1990-09-14
  • Publish Date: 1991-09-15
  • The term for pressure-velocity-gradient correlation was initiated by Ratio's[21] 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[7] 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[7] and the three-vortex turbulence model[13].
  • loading
  • [1]
    Bradshaw,P.,D.H.Ferriss and N.P.Atwell,Calculation of boundary-layer development using the turbulent energy equation,J.Fluid Mech.,28(1967),593-616.
    [2]
    Chou,P.Y.,On the velocity correlations and the solutions of equations of turbulent fluctuation,Quart.Appli.Math.,3(1945) 38-54.
    [3]
    Daly,B.J.and F.H.Harlow,Transport equations of turbulence,Phys.Fluid,13(1970),2634-2649.
    [4]
    Donaldson,C.Dup,A computer study of an analytical model of boundary layer transition,AIAA Paper No.68-38(1968).
    [5]
    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.
    [6]
    Hanjalic,K.,Two-dimensional flow in an axisymmetric channel,Ph.D.thesis,Univ.of London(1970).
    [7]
    Hanjalic,K.and B.E.Launder,A Reynolds stress model of turbulence and its application to thin shear flows,J.Fluid Mech.,52(1972),609-638.
    [8]
    Hinze,J.O.,Turbulence,McGraw-Hill Book Company(1975).
    [9]
    Launder,B.E.,On the effects of gravitational field on the turbulent transport of heat and momentum,J.Fluid Mech.,67(1975),569-581.
    [10]
    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).
    [11]
    Launder,B.E.and D.B.Spalding,Lectures in Mathematical Models of Turbulence,Academic Press,New York(1972).
    [12]
    Launder,B.E.,G.J.Reece and W.Rodi,Progress in the development of a Reynolds stress turbulence closure,J.Fluid Mech.,68(1975),537-566.
    [13]
    Lin,D.M.and S.T.Tsai,The separation of large vortexes and the closed equation of turbulence model,Appli.Math,and Mech.,10,10(1989),853-864.
    [14]
    Lumley,J.L.and B.Khajeh-Nouri,Computational modelling of turbulent transport,Advances in Geophysics,18A,Academic Press,New York(1974),169-192.
    [15]
    Lumley,J.L.and G.R.Newman,The return to isotropy of homogeneous turbulence,J.Fluid Mech.,82(1977),161-178.
    [16]
    Naot,D.,A.Shavit and M.Wolfshtein,Two-point correlation model and the redistribution of Reynolds stresses,Phys.Fluids,16(1973),738-743.
    [17]
    Prandtl,L.,Bericht(?)ber Untersuchungen zur ausgebildeten Turbulenz,Z.Angew.Math.Mech.,5(1925),136-139.
    [18]
    Reece,G.J.,A generalized Reynolds stress model of turbulence,Ph.D.Thesis,Faculty of Engineering,Univ.of London(1977).
    [19]
    Reynolds,W.C.,Computation of turbulent flows-state-of-the-art,Stanford Univ.,Engng Dept.Rep.MD-27(1970).
    [20]
    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).
    [21]
    Rotta,J.C.,Statistische Theorie Nichthomogener Tubulenz,Z.Phys.,129(1951),547-572.
    [22]
    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.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (2066) PDF downloads(526) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return