抛物化Navier-Stokes方程在求解高超声速流动稳定性分析 的基本流中的应用

刘建新; 禹旻; 罗纪生

抛物化Navier-Stokes方程在求解高超声速流动稳定性分析的基本流中的应用

天津大学机械工程学院力学系,天津 300072

基金项目: 国家重点基础研究发展计划(2009CB724103); 国家自然科学基金重大研究计划(90716007); 国家自然科学基金重点项目(10632050)

计量
- 文章访问数: 1844
- HTML浏览量: 157
- PDF量: 24
- 被引次数: 0
出版历程
- 收稿日期: 2010-04-24
- 修回日期: 2010-07-10
- 刊出日期: 2011-05-28

Application of parabolized Navier-Stokes equations into basic flows for stability analysis of hypersonic flows

Department of Mechanics, School of Mechnical Engineering, Tianjin University, Tianjin 300072, China

摘要

摘要: 通过在边界层内部使用边界层上缘的流向压力梯度代替该处的流向压力梯度,对传统抛物化Navier-Stokes(PNS)方程求解中的流向压力梯度的处理方法进行改进,从而使它可以求解用于稳定性分析的高超声速流动的基本流,并分别计算了平板、零攻角钝锥和小攻角钝锥三种典型算例.对于流向没有分离,且横向流动不强的流动,使用PNS方程计算高超声速流动稳定性分析用的基本流是可靠的.特别是改进后的方法求得的基本流的稳定性分析结果与直接求解Navier-Stokes(N-S)方程的结果非常吻合,但计算的时间消耗和空间占用都减少了一个数量级.
- 抛物化Navier-Stokes(PNS) 方程 /
- 稳定性 /
- 高超声速 /
- 基本流 /
- 流向压力梯度
Abstract: By using streamwise pressure gradient on the edge of the boundary layer instead of that in the boundary layer,traditional solution for streamwise pressure gradient in parabolized Navier-Stokes (PNS) equations was improved and applied to PNS equations as basic flows for stability analysis of hypersonic flows.Three typical examples with flat,blunt cone at zero and small angle of attack,were calculated.For the blunt three-dimension flows or two-dimension flows,PNS equations are reliable to get the hypersonic basic flows for stability analysis,and the results of the stability analysis are in good agreement with those obtained by solving Navier-Stokes (N-S) equations directly,but expense of time and space is an order of magnitude lower than N-S equations.
- parabolized Navier-Stokes (PNS) equations /
- stability /
- hypersonic /
- basic flows /
- streamwise pressure gradient

HTML

参考文献(12)

[1]	Malik M R,Spall R E,Chang C L.Effect of nose bluntness on boundary layer stability and transition .AIAA Paper 1990-0112,1990.
[2]	Herbert T,Esfahanian V.Stability of hypersonic flow over a blunt body .AGARD,Theoretical and Experimental Methods in Hypersonic Flows 12p(SEE N94-10421 01-02),AGARD-CP-514,1993.
[3]	Kufner E,Dallmann U,Stilla J.Instability of hypersonic flow past blunt cones-effects of mean flow variations .AIAA Paper 1993-2983,1993.
[4]	闫溟,罗纪生.超声速流中圆锥头部钝度对边界层稳定性的影响[J].空气动力学学报,2008,26(4):430-434. YAN Ming,LUO Jisheng.The bluntness effect on stability of boundary layer over blunt cone in supersonic flow[J].Acta Aerodynamica Sinica,2008,26(4):430-434.(in Chinese)
[5]	苏彩虹,周恒.零攻角小钝头钝锥高超音速绕流边界层的稳定性分析和转捩预报[J].应用数学和力学,2007,28(5):505-513. SU Caihong,ZHOU Heng.Stability analysis and transition prediction of hypersonic boundary layer over a blunt cone with small nose bluntness at zero angle of attack[J].Applied Mathematics and Mechanics,2007,28(5):505-513.(in Chinese)
[6]	苏彩虹,周恒.小攻角高超音速尖锥边界层的转捩预测及e^N法的改进[J].中国科学(G辑:物理学力学天文学),2009,39(1):123-130. SU Caihong,ZHOU Heng.Transition prediction for supersonic and hypersonic boundary layers on a cone with angle of attack[J].Scientia Sinica Physica,Mechanica & Astronomica,2009,39(1):123-130.(in Chinese)
[7]	Anderson D A,Tannehill J C,Pletcher R H.Computational fluid mechanics and heat transfer[M].New York:Hemisphere Publishing,1984.
[8]	陈兵,徐旭,蔡国飚.一种求解抛物化Navier-Stokes方程的空间推进算法[J].力学学报,2008,40(2):162-170. CHEN Bing,XU Xu,CAI Guobiao.A space-marching algorithm for solving the parabolized Navier-Stokes equations[J].Chinese Journal of Theoretical and Applied Mechanics,2008,40(2):162-170.(in Chinese)
[9]	Lubard S C,Helliwell W S.Calculation of the flow on a cone at high angle of attack[J].AIAA Journal,1974,12(7):965-974.
[10]	Vigneron Y C,Rahich J V,Tannehill J C.Calculation of supersonic viscous flow over delta wings with sharp subsonic leading edges .AIAA Paper 1978-1137,1978.
[11]	Thivet F.The exact jacobian associated with steady PNS equations and its use to define new numerical schemes //Proceedings of the Sixteenth International Conference on Numerical Methods in Fluid Dynamics.France:Springer-Verlag,1998:320-325.
[12]	Hejranfar K,Esfahanian V,Darian H M.On the use of high-order accurate solutions of PNS schemes as basic flows for stability analysis of hypersonic axisymmetric flows[J].Journal of Fluids Engineering,2007,129(10):1328-1338.