基于N-S方程的飞机静气动弹性计算方法研究
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摘要
本文分别基于传统的马蹄涡格网法以及N-S方程数值模拟弹性机翼的气动力,然后采用柔度法发展出了气动力作用下机翼静气动弹性特性的计算方法。
涡格法是升力面理论中一种比较实用的数值计算方法。它所采用的计算模型是:不仅沿展向分布离散的马蹄涡,在弦向也分布离散的马蹄涡,整个机翼用有限多个离散马蹄涡系来代替。控制点的诱导速度为附着涡和左右自由涡对控制点诱导速度之和。
在网格生成方面,采用代数方法及椭圆型方程优化相结合生成三维机翼的贴体网格,一种快捷的弹性变形技术用于生成弹性变形后的网格。
非定常渐近解法求解定常问题。基于Roe格式的有限体积法空间离散N-S方程、五步Runge-Kutta法进行显式时间推进。采用雷诺平均N-S方程模拟紊流,紊流模型选用SA一方程模型。应用了当地时间步长、焓阻尼、隐式残值光顺等加速收敛措施。
分别基于马蹄涡格网法和N-S方程,采用柔度法对机翼模型进行了考虑弹性影响的静气动弹性特性计算。不可压时两种方法计算得到的静气动弹性特性吻合较好,数值计算结果具有一定的实际参考价值。
In the present thesis, the traditional horse shoe vortex lattice method and the CFD method based on Navier-Stokes equations to numerically simulate the aerodynamic force of the elastic wings. Then the flexibility method is used to develop the method of calculating the static dynamic features of the wings of aircrafts under aerodynamic force.
The vortex lattice method is a practical numerical calculation method in the lift force area theory. Its calculation model is horse shoe vortexes distributed not only along the wingspan direction but also along the wing chord direction. The whole wing is represented by limited discrete vortex systems. The induced speed of the control point is induced by the attached vortex and the left and right free vortexes.
In regard to grid generation technology, algebraic approach and local part deformation technology are developed to generate 3 dimensional grid which sticks to the aircraft. And a quick elastic deformation technology is developed to generate the grid after the deformation.
The finite-volume method based on Roe scheme is applied to solve the three-dimensional N-S equations, and the five-stage Runge-Kutta explicit scheme is used for time marching. Spalat-Allmaras One-Equation turbulence model is employed to the simulations of turbulent flows. Local time-stepping, enthalpy damping and implicit residual smoothing are applied to accelerate the solution for stationary problems.
Basing on the horse shoe vortex lattice method and the Navier-Stokes equations, the flexibility method is developed to calculate the aerodynamic features of the aircraft wings when static areoelasticity is considered, and the results are compared with those that are calculated using the mode method. Computational results are valued pratically.
涡格法是升力面理论中一种比较实用的数值计算方法。它所采用的计算模型是:不仅沿展向分布离散的马蹄涡,在弦向也分布离散的马蹄涡,整个机翼用有限多个离散马蹄涡系来代替。控制点的诱导速度为附着涡和左右自由涡对控制点诱导速度之和。
在网格生成方面,采用代数方法及椭圆型方程优化相结合生成三维机翼的贴体网格,一种快捷的弹性变形技术用于生成弹性变形后的网格。
非定常渐近解法求解定常问题。基于Roe格式的有限体积法空间离散N-S方程、五步Runge-Kutta法进行显式时间推进。采用雷诺平均N-S方程模拟紊流,紊流模型选用SA一方程模型。应用了当地时间步长、焓阻尼、隐式残值光顺等加速收敛措施。
分别基于马蹄涡格网法和N-S方程,采用柔度法对机翼模型进行了考虑弹性影响的静气动弹性特性计算。不可压时两种方法计算得到的静气动弹性特性吻合较好,数值计算结果具有一定的实际参考价值。
In the present thesis, the traditional horse shoe vortex lattice method and the CFD method based on Navier-Stokes equations to numerically simulate the aerodynamic force of the elastic wings. Then the flexibility method is used to develop the method of calculating the static dynamic features of the wings of aircrafts under aerodynamic force.
The vortex lattice method is a practical numerical calculation method in the lift force area theory. Its calculation model is horse shoe vortexes distributed not only along the wingspan direction but also along the wing chord direction. The whole wing is represented by limited discrete vortex systems. The induced speed of the control point is induced by the attached vortex and the left and right free vortexes.
In regard to grid generation technology, algebraic approach and local part deformation technology are developed to generate 3 dimensional grid which sticks to the aircraft. And a quick elastic deformation technology is developed to generate the grid after the deformation.
The finite-volume method based on Roe scheme is applied to solve the three-dimensional N-S equations, and the five-stage Runge-Kutta explicit scheme is used for time marching. Spalat-Allmaras One-Equation turbulence model is employed to the simulations of turbulent flows. Local time-stepping, enthalpy damping and implicit residual smoothing are applied to accelerate the solution for stationary problems.
Basing on the horse shoe vortex lattice method and the Navier-Stokes equations, the flexibility method is developed to calculate the aerodynamic features of the aircraft wings when static areoelasticity is considered, and the results are compared with those that are calculated using the mode method. Computational results are valued pratically.
引文
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[77]郭同庆,陆志良,程芳,“一种静、动气动弹性的一体化计算方法”,振动工程学报2004年04期。
[2] H.W伏欣,沈克扬译,“气动弹性力学原理”,上海科学技术文献出版社。
[3]卢叔全编著,“气动弹性讲义”,南京航空学院,1991年11月。
[4] Kumar A, Hefner, J.N.: Future Challenges and Opportunities in Aerodynamics, The Aeronautical Journal, August 2000.
[5] Launder, B.E.: CFD for Aerodynamics Turbulent Flows: Progress and Problems, The Aeronautical Journal, August 2000.
[6]付德熏主编“流体力学数值模拟”,国防工业出版社,1993年1月。
[7]朱自强等编著,“应用计算流体力学”,北京航空航天大学出版社,1998年。
[8] Jameson A. et al.:Numerical Simulation of the Euler Equations by Finite Volume Methods Using Methods Using Runge-Kuta Time-Marching Schemes. AIAA paper 81-1295.
[9] MacCormack R.W.:The Effect of Viscosity on Hypervelocity Impact Cratering. AIAA paper 69-354.
[10] Lax P.D. and Wendroff B: System of Conservation Lows. Comm. Pure and Applied Mathematics. Vol.13,pp217-pp237.
[11]郑诚行,熊小依,“机翼跨音速非线性静气动弹性计算”,第六届全国气动弹性会议,1991。
[12] Beam R.W. and Warming R.F.: An Implicit Finite-Difference Algorithm for Hyperblic System in Conservation-Low-Form. Journal of Computational Physics. Vol.22.1976,pp87-110.
[13] Edwards, J.W; Malone J.B.: Current Status of Computational Methods for Transonic Unsteady Aerodynamics and Aeroelastic applications, NASA-TM-104191;A GARD-PAPER-1.
[14] Yang J.Y.:Third-order Nonoscillatory Schemes for the Euler Equations. AIAA J.Vol.29. No.10,1991, pp1661-1668.
[15] Van Leer et al.:A Comparison of Numerical Flux Formulation for the Euler and Navier-Stokes Equations. AIAA pp87-1104.
[16] Jameson A. and Turkel E.:Implicit Schemes and LU Decomposations. Mathematics of computation, Vo1.37,No.156,1981,pp385-397.
[17]管德,“非定常空气动力计算”,北京航空航天大学出版社。
[18]杨永年编,“气动弹性力学讲义”,西北工业大学。
[19] Patil, M.J. et al.: Nonlinat Aeroelasticity and Flight Dynamics of High-Altitude Long-Endurance Aircraft. AIAA 99-1470.
[20] Clark W.S.; Hall, Kenneth C.: A Time-Linearized Navier-Stockes Analysis of Stall Flutter , ASME Paper 99-GT-383.
[21] Manoj K. Bhardwa and Rakesh K. Kapania, et al.: ACED/CSD Interaction Methodology for Aircraft Wings. AIAA-98-4783.
[22] Raymond E. Gordnier and Reid B. Melville: Tansonic Flutter Simulations Using an Implicit Aeroelastic Slover. Journal of Aircraft, Vol.37,No.5, September-October 2000.
[23] S.A. Goodwin, C. Byun, M. Farhangnia: Aeroelastic Computations Using Parallel Computing Systems. AIAA99-0975.
[24] Shankaran, S. Jameson: A. Aerodynamic and Aeroelastic Applications of a Parallel Multi grid Unstrucured Flow Slover. AIAA Paper2003-0595.
[25] Sadeghi M., Yang S. Liu F., Tsai H.M.: Parallel Computation of with a Coupled Navier-Stokes /CSD method. AIAA Paper 3003-1347.
[26] Schweiger J., Weiss F., Kullrich T.: Active Aeroelastic Design of a Vertical Tail for a Fighter Aircraft. AIAA Paper 2000-4828.
[27] Kolonay R., Dindar M., Love M ,DeLa Garza A: A Methodology of Large Scale Computational Aeroelasticity for the MDA/MDOE environment. AIAA Paper 2000-4789.
[28] Jun Seungmoon, Tischler V.A., Venkayya, V.B.: Multidisciplinary Design Optimization of a Built-up Wing Structure with a Tip Missile. AIAA Paper 2002-1421.
[29] Chung Injae, Lee Duckjoo, Reu Taekyu: Prediction of Transonic Buffet Onset for an Airfoil with Shock Induced Separation Bubble Using Steady Navier-Stokes Slover. AIAA Paper 20 02-2934.
[30] Sheta E.F. Huttsell L.J.: Control of F/A-18 Vertical Tail Buffet by Vortial Blowing. AIAA Paper 2002-0948.
[31] Tang Deman, Kholodar, Denis, Dowell, Earl H.: Nolinear Aeroelastic Respans of a Typical Airfoil Section with Control Surface Freeplay. AIAA Paper 2000-1621.
[32] Gordnier, Raymond E. Visbal, Niguel R.: Computation of three-Dimensional NonlinearPan- -el Flutter. AIAA Paper 2001-0571.
[33] Sadeghi, Mani, Liu Feng: Investigation of Non-Linear Flutter by a Coupled Aerodynamics and structural Dynamics Method. AIAA Paper 2001-0573.
[34] Guruswamy G. P.: ENSAERO-A Multidisciplinary Program for Fluid/ Structural Interaction Studies of Aerospace Vehicles, Computing systems engineering, Vol.1, Nos.2-4, 1990 pp237-256.
[35] Thompson, J.F.; Thames, F.C.; Mastin, C.W.: Automatic Numerical Generation of Body-Fitted Curvilinear Coordinate System for Field Containing any Number of Arbitrary Two-Dimensional Bodies. J. Computational Physics, 15(1974), pp. 299-319.
[36] Sorenson, R.L.: A Computer Program to Generate Two-Dimensional Grids about Airfoils and other Shapes by the use of Poisson’s Equation. NASA TM-81198, 1980.
[37] Hsu, K.; Lee, S.L.: A Numerical Technique for Two-Dimensional Grid Generation with Grid Control at all of the Boundaries. J. Computational Physics, 96(1991), pp. 451-469.
[38] Starius, G.: Constructing Orthogonal Curvilinear Meshes by solving Initial Value Problems. Numerische Mathematik, 28(1977), pp. 25-48.
[39] Steger, J.L.; Chaussee, D.S.: Generation of Body-Fitted Coordinate Using Hyperbolic Partial Differential Equations. SIAM J. Sci. Stat. Comp., 1(1980), pp. 431-437.
[40] Haselbacher, A.C.; McGuirk, J.J.; Page, G.J.: Finite Volume Discretisation Aspects for Viscous Flows on Mixed Unstructured Grids. AIAA Paper 97-1946, 1997.
[41] Hilgenstock A.: A fast Method for the Elliptic Generation of Three Dimensional Grids with Full Boundary Control. Num. Grid Generation in CFM’88, Pineridge Press Ld., pp 137-146,1988.
[42] White J. A.: Elliptic Grid Generation with Orthogonality and Spacing Control on an Arbitrary Number of Boundaries. AIAA 90-1568, 1990.
[43] Batina J T.: Unsteady Euler airfoil Solutions using unstructured dynamic meshes. AIAA 8 9-0115,1989.
[44] Batina J T.: Implicit flux-split Euler schemes for unsteady aerodynamic analysis in volving unstructured dynamic meshes. NASA TM-102732,1990.
[45] Venkatakrishnan V, Mavriplis D J.:Implicit method for the computation of unsteady flows on unstructured grids. NASA CR-198206,1995.
[46]黄明恪编:计算空气动力学差分方法讲稿(-).南京航空学院6系.1991年12月.
[47] Stokes, G.G.: On the Theories of Internal Friction of Fluids in Motion. Trans.Cambridge Phil. Soc., 8(1845), pp. 287-305.
[48] Schlichting, H.: Boundary Layer Theory. 7th edition, McGraw-Hill, New York, 1979.
[49]唐登斌编:粘性流体力学.南京航空航天大学,1997年12月.
[50] Blazek, J.:Computational Fluid Dynamics: Principles and Applications. 2001.
[51] Roe, P.L.: Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes. J. Computational Physics, 43(1981), PP.339-374.
[52] Roe, P.L.; Pike,J.: Efficient Construction and Utilisation of Approximate Riemann Solutions. Computing Methods in Applied Sciences and Engineering, R.Glowinski, J.L. Lions(eds.), North Holland Publishing, The Netherlands,1984.
[53] VanLeer, B.: Towards the Ultimate Conservative Difference Scheme V. a Second Order Sequel to Godnuov’s Method. J. Computational Physics, 32(1979), PP.101-136.
[54] Venkatakrishnan, V.: Preconditioned Conjugate Gradient Methods for the Compressible Navier-Stokes Equations. AIAA Journal, 29(1991), PP.1092-1110.
[55] Van Albada, G.D.; Van Leer, B.; Roberts, W.W.: A Comparative Study of Computational Methods in Cosmic Gas Dynamics. Astronomy and Astrophysics, 108(1982), pp.76-84.
[56] Peery, K.M.; Imlay, S.T.: Blunt-Body Flow Simulations. AIAA Paper 88-2904, 1988.
[57] Lin, H.C.: Dissipation Additions to Flux-Difference Splitting. AIAA Paper 91-1544, 1991.
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