脉动压力脉动速度变形平均项的表达式
Expressions for Pressure-Velocity-Gradient Correlations
-
摘要: 脉动压力脉动速度变形平均项,最初是Rotta[21]改写压力梯度做功项得来的.但是,这项处理起来都很困难,从Rotta开始,以后Launder等人都对这项做过一些假定.本文根据脉动速度所满足的方程解出脉动压力,然后进而求出脉动压力乘上脉动速度变形的平均值,得到了脉动压力脉动速度变形平均项的完整表达式.这个表达式说明了Rotta和Launder等人的有限表达式是有一定道理的.本文所得的完整表达式分为两种情形加以讨论.一种是几种涡旋不分开的情形,另一种是三种涡旋分开考虑的情形.由此,本文为雷诺应力模式和三涡旋模式等湍流模式提供了完整的脉动压力脉动速度变形平均项的表达式.Abstract: 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].
-
[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.
点击查看大图
计量
- 文章访问数: 2071
- HTML全文浏览量: 68
- PDF下载量: 526
- 被引次数: 0