基于动态变形网格的非定常粘性流动数值分析
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摘要
飞行器的定常和非定常气动力的准确数值求解,特别是跨音速范围内的准确数值求解及研究,一直以来都是飞行器设计工作者必须面对的重要研究难题。本文主要对亚音速、跨音速和超音速定常和非定常粘性绕流的数值模拟进行深入的研究。
利用代数生成法中的沿物面边界法向外推法和结合源项修正技术的偏微分方程生成法共同生成高质量的贴体正交粘性网格。以此作为初始网格,运用无限插值法(TFI)生成任意时刻的非定常动态变形网格。非定常动态变形网格的变形过程与初始网格的生成毫无关系,它维持了初始网格的整体特征,在流场剧烈变化的区域内的网格由最小程度的扭曲变形而得到。尤其重要的是,在靠近物面的区域尽量保持了网格的固定,并允许靠近远场的网格扭曲变形,或至少是在流场变化不明显的小梯度范围内变形。
对于定常和非定常绕流,本文均将Navier-Stokes方程在中心有限体积法离散格式下,利用以Runge-Kutter迭代法为内迭代的双时间推进法进行求解。所谓双时间推进指同时采用真实时间步和虚拟时间步,即在每个真实时间步上采用虚拟时间进行定常迭代,从而不但使时间迭代具有二阶精度,计算时间大大缩短,而且非定常与定常程序相差不大,使程序修改简洁、方便。湍流计算采用了Baldwin-Lonax代数紊流模型。运用当地时间步长和隐式残值光顺等加速技术,加速了收敛过程;用虚拟边界改进了边界域的处理,提高了效率。
以NACA0012、RAE2822、NACA64A010翼型为例,进行亚音速、跨音速定常和非定常粘性绕流数值模拟,计算结果同实验结果进行比较,吻合良好,验证了本文方法及程序的正确性
In aircraft design, efficacious and accurate numerical simulation for steady or unsteady flow, especially for transonic flow is a crucial problem for designers. And the research of this dissertation is focused on how to efficaciously accurately simulate numerically the unsteady subsonic and transonic viscous flows.Solving the elliptic grid generation together with an algebraic method marching along the normal-to-wall direction, viscous grids around complex geometries are generated. By using TFI of displacements, we can get the unsteady viscous grid in any time. And the grid deformation process becomes completely independent of the generation of the initial grid; an important feature of the deforming grid procedure is that it must maintain the overall quality of the initial grid by introducing minimal distortion of the cells in the regions where the flow is likely to be changing rapidly. It is particularly important to keep the grid as rigid as possible in the near-wall regions and allow cell distortion towards the far-field, or at least in the regions of low gradients where the flow is not changing rapidly.The steady and unsteady viscous flow solvers based on Jameson's cell-centred finite volume method, and Jameson's dual method with Runge-Kutter scheme as inner iteration scheme have been development in this dissertation. In dual time method, there are real time and the pseudo-time, at each real time step marches the solution in a pseudo-time to steady state through an explicit time marching scheme, and the equation have two-order accuracy in time. We can make the solver more laconic and spend less time to get the numerical result. Baldwin-Lomax turbulence model is implemented in Navier-Stokes flow solver. In order to efficacious simulate the Navier-Stokes flow, some standard convergence acceleration techniques, such as local time stepping and implicit residual smoothing, and "ghost" cells which make complex boundary conditions simply have been used.To confirm the validity, effectivity and reliability of developed flow solvers, test
cases of steady/unsteady subsonic and transonic flow of NACA0012、 RAE2822、 NACA64A010 airfoils. The result of flow field computation is good agreement with experiment; the method and the procedure presented in this paper are verified.
利用代数生成法中的沿物面边界法向外推法和结合源项修正技术的偏微分方程生成法共同生成高质量的贴体正交粘性网格。以此作为初始网格,运用无限插值法(TFI)生成任意时刻的非定常动态变形网格。非定常动态变形网格的变形过程与初始网格的生成毫无关系,它维持了初始网格的整体特征,在流场剧烈变化的区域内的网格由最小程度的扭曲变形而得到。尤其重要的是,在靠近物面的区域尽量保持了网格的固定,并允许靠近远场的网格扭曲变形,或至少是在流场变化不明显的小梯度范围内变形。
对于定常和非定常绕流,本文均将Navier-Stokes方程在中心有限体积法离散格式下,利用以Runge-Kutter迭代法为内迭代的双时间推进法进行求解。所谓双时间推进指同时采用真实时间步和虚拟时间步,即在每个真实时间步上采用虚拟时间进行定常迭代,从而不但使时间迭代具有二阶精度,计算时间大大缩短,而且非定常与定常程序相差不大,使程序修改简洁、方便。湍流计算采用了Baldwin-Lonax代数紊流模型。运用当地时间步长和隐式残值光顺等加速技术,加速了收敛过程;用虚拟边界改进了边界域的处理,提高了效率。
以NACA0012、RAE2822、NACA64A010翼型为例,进行亚音速、跨音速定常和非定常粘性绕流数值模拟,计算结果同实验结果进行比较,吻合良好,验证了本文方法及程序的正确性
In aircraft design, efficacious and accurate numerical simulation for steady or unsteady flow, especially for transonic flow is a crucial problem for designers. And the research of this dissertation is focused on how to efficaciously accurately simulate numerically the unsteady subsonic and transonic viscous flows.Solving the elliptic grid generation together with an algebraic method marching along the normal-to-wall direction, viscous grids around complex geometries are generated. By using TFI of displacements, we can get the unsteady viscous grid in any time. And the grid deformation process becomes completely independent of the generation of the initial grid; an important feature of the deforming grid procedure is that it must maintain the overall quality of the initial grid by introducing minimal distortion of the cells in the regions where the flow is likely to be changing rapidly. It is particularly important to keep the grid as rigid as possible in the near-wall regions and allow cell distortion towards the far-field, or at least in the regions of low gradients where the flow is not changing rapidly.The steady and unsteady viscous flow solvers based on Jameson's cell-centred finite volume method, and Jameson's dual method with Runge-Kutter scheme as inner iteration scheme have been development in this dissertation. In dual time method, there are real time and the pseudo-time, at each real time step marches the solution in a pseudo-time to steady state through an explicit time marching scheme, and the equation have two-order accuracy in time. We can make the solver more laconic and spend less time to get the numerical result. Baldwin-Lomax turbulence model is implemented in Navier-Stokes flow solver. In order to efficacious simulate the Navier-Stokes flow, some standard convergence acceleration techniques, such as local time stepping and implicit residual smoothing, and "ghost" cells which make complex boundary conditions simply have been used.To confirm the validity, effectivity and reliability of developed flow solvers, test
cases of steady/unsteady subsonic and transonic flow of NACA0012、 RAE2822、 NACA64A010 airfoils. The result of flow field computation is good agreement with experiment; the method and the procedure presented in this paper are verified.
引文
1.李杰,“先进民用飞机复杂外形跨音速绕流数值分析”,西北工业大学博士学位论文,1999年
2.朱自强等,《应用计算流体力学》,北京航空航天大学出版社,1998
3.杨国伟,“大迎角定常与非定常绕流数值模拟”,西北工业大学博士学位论文,1996
4.梁强,非定常气动力的N-S方程解及其应用,西北工业大学硕士学位论文,2001年
5.陈海昕,“复杂外形绕流Euler/N-S方程数值分析”,西北工业大学博士学位论文,1999年
6.肖志祥,“复杂流动Navier-Stokes方程数值模拟及湍流模型研究”,西北工业大学博士学位论文,2003年
7. Thompson, J. F., Weatherill, N. P., "Aspects of Numerical Grid Generation: Current Science and Art", AIAA Paper 93-3539-CP, 1993
8. J. A. White, Hampton. "Elliptic Grid Generation With Orthogonality And Spacing Control On An Arbitrary Number Of Boundaries", AIAA paper 90-1568
9. Z. D. QIAO, A. M. YANG, B. ZHU. "NUMERICAL SIMULATION OF NAVIER-STOKES EQUATIONS FOR HELICOPTER ROTOR IN FORWARD FLIGHT USING MOVING CHIMERA GRIDS", 航空学报(英文版), 1997, 第10期, 第3卷
10. L. Dubuc, F. Cantariti, M. Woodgate, B. Gribben, K. J. Badcock and B. E. Richards, "A grid deformation technique for unsteady flow computations", INTERNATIONAL JOURNAL FOR NUMERICAL METHODS int. J. Numer. meth Fluids 2002; 32:285-311
11. Jie Li, Fengwei Li and Qing E, "A fully implict method for steady and unsteady viscous flow simulations", INTERNATIONAL JOURNAL NUMERICAL METHODS IN FLUIDS, int. J. Numer. Meth. Fluids 2003; 43:147-163
12. John M. Hsu, Antony Jameson, "An Implicit-Explict Hybrid Scheme for Calculating Complex Unsteady Flows", AIAA paper 2002-0714
13. L. Dubuc, et al. "Solution of the Unsteady Euler Equations Using an Implicit Dual-time Method", AIAA Journal 36(8): 1417-1424, August 1998.
14. C. Q. LIN and K. PAHLKE, "Numerical solution of Euler equation for aerofoils in arbitrary unsteady motion", Aeronautical Journal, June/July 1994
15.张正科,李凤蔚,罗时均,“用椭圆型偏微分方程生成三维贴体与边界正交网格”,西北工业大学学报,Vol.13,No.1,1995
16.宋文萍,杨永,等,“双时间法求解大迎角翼型绕流非定常N—S方程”,空气动力学学报,1999,第17卷,第4期。
17.蔡晋生,“跨音速大迎角欧拉方程数值模拟”,西北工业大学博士学位论文,1992年
18.肖志祥,李凤蔚,鄂秦,“三种湍流模型模拟能力的对比”,西北工业大学学报,Vol.30,No.3,2002年
19.桑为民,“基于自适应直角叉树切割网格的Euler及N-S方程数值模拟”,西北工业大学博士学位论文,2003年
20.蒋胜矩,“基于N-S方程的大迎角分离流及翼型结冰数值模拟”,西北工业大学硕士学位论文,2004年
21.罗时均,《跨音速无粘有旋流和有限体积法》,西北工业大学,上海交通大学讲义,1984年
22.李凤蔚,鄂秦,李杰,杨国伟,陈海昕,“真实飞行器网格生成策略及在航空CFD中的应用”,第一届全国计算网格生成方法研讨会论文集,1997年,陕西西安
23. Zhenghong Gao, Boris Laschka, "Numerical Investigation of Euler Equations for the Rigid and Flexible Wings in arbitrary Motion", AIAA -95-2262.
24. Jameson, A., et al, "Numerical Solutions of Euler Equations by Finite Volume Methods with Runge-Kutta Time Stepping Schemes", AIAA Paper 81-1259,1981
25. Hilgenstock, A., "A Fast Method for the Elliptic Generation of Three Dimensional Grids with Full Boundary Control", Numerical Grid Generation in Computational Fluid Mechanics' 88, Pineridge Press Limited, pp. 137-146, 1988
26. Roe, P.L., "Approximate Riemann Solver, Parameter Vectors, and difference schemes", Journal of Computational Physics, Vol.43, pp.357-372,1981
27. Arnone, A., et al., "Integration of Navier-Stokes Equations Using Dual Time Stepping and a Multigrid Method", AIAA Journal, Vol.33, pp.985-990,1995
28. Jameson,A. "Time Dependent Calculations Using Multigrid with Applications to Unsteady Flow Past Airfoils and Wings", AIAA paper 91-1596
29. Thomas, P.D., and Middlecoff, J.F., "Direct Control of Grid Point Distribution in Meshes Generated by Elliptic Equations", AIAA Journal, Vol.18, No.6, 1979
30. Sonar, Th., "Grids Generation Using Elliptic Partial Differential Equations", DFVLR-IB 129-88/11,1988
31. Jameson, A., "Success and Challenge in Computational Aerodynamics", AIAA Paper 87-1184, 1987
32. Thompson, J.F., et al, "Automatic Numeric Generation of Body-Fitted Curvilinear Coordinates for a Field Containing any Number of Arbitrary Two-Dimensional Bodies", Journal of Computational Physics, Vol.15, No.3, 1974
33. Volpe, G. and Jameson, A., "An Efficient Solution for Computing Transonic and Supersonic Flows about Aircraft", ICAS-88-4.8.3, 1988
34. Yoon, S., Jameson, A., and Kwak, D., "Effect of Artificial Diffusion Scheme on Multi-Grid Convergence", AIAA Paper 95-1670, 1995
35. E,Q., Li,F.W., and Yang G.W. "Numerical Solution of the Euler Equations for Transonic Flow about the Complete Aircraft", AIAA-96-2406, 1996.
36. Johnson, D.A., King, L.S., "A Mathematical Simple Turbulence Closure Model for Attached and Separated Turbulent Boundary Layers", AIAA Journal, 23:1684-1692,1985.
37. A.L. Gaitonde. A dual-time method for the solution of the unsteady Euler equations, Aeronautical Journal, October 1994.
38.李杰,“三维非定常Navier-Stokes方程数值求解格式研究”,西北工业大学博士后研究报告,2001年
39.杨青,“超临界翼型、机翼的定常和非定常流场数值模拟”,西北工业大学硕士学位论文,2004年
40.李凤蔚,鄂秦,李杰,杨国伟,“复杂外形网格生成技术”,空气动力学学报,Vol.16,No.1,1998年
41. Davis, s., "NACA 64A010(NASA AMES Model)oscillatory Pitching", AGARD Compendium of Unsteady Aerodynamic Measurements AGARD-R-702,1982
42. Swanson, R. C., and Turkel, E., "A Multistage Time-Stepping Scheme for the Navier-Stokes Equations, AIAA Paper 85-0035,1985
43. Rumsey, C. L., et al, "Efficiency and Accuracy of Time-Accurate Turbulent Navier-Stokes Computations", AIAA Paper 95-1835-CP, 1995
44.朱自强等著,现代飞机设计中的空气动力学.北京:北京航空航天大学出版社,1995
45.北京空气动力研究所编,空气动力学发展论文集.北京:国防工业出版社,1997.
46. McMasters, J. H., and Cummings, R. M., "Airplane Design—Past, Present, andFuture", Journal of Aircraft, Vol. 39, No. 1, 2002, pp. 10-17.
47.陈海昕,李凤蔚,鄂秦,高超.“复杂外形网格生成及在流场数值模拟中的应用”,第九届全国计算流体力学会议论文集,1998年11,云南景洪.
48.梁强,复杂流场的非定常气动力计算以及气动弹性研究。西北工业大学博士学位论文,2003。
49. Swanson, R. C., Turkel, E., "Artificial Dissipation and Central difference schemes for Euler and N-S Equations", AIAA Paper 87-1107, 1987
50. Thomas, P. D., and Lombard, C. K., "Geometric Conservation Law and Its Application to Flow Computations on Moving Grids", AIAA Journal, Vol. 17, No. 10, 1979, pp. 1030-1037.
51.徐华舫,《空气动力学基础》,国防工业出版社,1979年
2.朱自强等,《应用计算流体力学》,北京航空航天大学出版社,1998
3.杨国伟,“大迎角定常与非定常绕流数值模拟”,西北工业大学博士学位论文,1996
4.梁强,非定常气动力的N-S方程解及其应用,西北工业大学硕士学位论文,2001年
5.陈海昕,“复杂外形绕流Euler/N-S方程数值分析”,西北工业大学博士学位论文,1999年
6.肖志祥,“复杂流动Navier-Stokes方程数值模拟及湍流模型研究”,西北工业大学博士学位论文,2003年
7. Thompson, J. F., Weatherill, N. P., "Aspects of Numerical Grid Generation: Current Science and Art", AIAA Paper 93-3539-CP, 1993
8. J. A. White, Hampton. "Elliptic Grid Generation With Orthogonality And Spacing Control On An Arbitrary Number Of Boundaries", AIAA paper 90-1568
9. Z. D. QIAO, A. M. YANG, B. ZHU. "NUMERICAL SIMULATION OF NAVIER-STOKES EQUATIONS FOR HELICOPTER ROTOR IN FORWARD FLIGHT USING MOVING CHIMERA GRIDS", 航空学报(英文版), 1997, 第10期, 第3卷
10. L. Dubuc, F. Cantariti, M. Woodgate, B. Gribben, K. J. Badcock and B. E. Richards, "A grid deformation technique for unsteady flow computations", INTERNATIONAL JOURNAL FOR NUMERICAL METHODS int. J. Numer. meth Fluids 2002; 32:285-311
11. Jie Li, Fengwei Li and Qing E, "A fully implict method for steady and unsteady viscous flow simulations", INTERNATIONAL JOURNAL NUMERICAL METHODS IN FLUIDS, int. J. Numer. Meth. Fluids 2003; 43:147-163
12. John M. Hsu, Antony Jameson, "An Implicit-Explict Hybrid Scheme for Calculating Complex Unsteady Flows", AIAA paper 2002-0714
13. L. Dubuc, et al. "Solution of the Unsteady Euler Equations Using an Implicit Dual-time Method", AIAA Journal 36(8): 1417-1424, August 1998.
14. C. Q. LIN and K. PAHLKE, "Numerical solution of Euler equation for aerofoils in arbitrary unsteady motion", Aeronautical Journal, June/July 1994
15.张正科,李凤蔚,罗时均,“用椭圆型偏微分方程生成三维贴体与边界正交网格”,西北工业大学学报,Vol.13,No.1,1995
16.宋文萍,杨永,等,“双时间法求解大迎角翼型绕流非定常N—S方程”,空气动力学学报,1999,第17卷,第4期。
17.蔡晋生,“跨音速大迎角欧拉方程数值模拟”,西北工业大学博士学位论文,1992年
18.肖志祥,李凤蔚,鄂秦,“三种湍流模型模拟能力的对比”,西北工业大学学报,Vol.30,No.3,2002年
19.桑为民,“基于自适应直角叉树切割网格的Euler及N-S方程数值模拟”,西北工业大学博士学位论文,2003年
20.蒋胜矩,“基于N-S方程的大迎角分离流及翼型结冰数值模拟”,西北工业大学硕士学位论文,2004年
21.罗时均,《跨音速无粘有旋流和有限体积法》,西北工业大学,上海交通大学讲义,1984年
22.李凤蔚,鄂秦,李杰,杨国伟,陈海昕,“真实飞行器网格生成策略及在航空CFD中的应用”,第一届全国计算网格生成方法研讨会论文集,1997年,陕西西安
23. Zhenghong Gao, Boris Laschka, "Numerical Investigation of Euler Equations for the Rigid and Flexible Wings in arbitrary Motion", AIAA -95-2262.
24. Jameson, A., et al, "Numerical Solutions of Euler Equations by Finite Volume Methods with Runge-Kutta Time Stepping Schemes", AIAA Paper 81-1259,1981
25. Hilgenstock, A., "A Fast Method for the Elliptic Generation of Three Dimensional Grids with Full Boundary Control", Numerical Grid Generation in Computational Fluid Mechanics' 88, Pineridge Press Limited, pp. 137-146, 1988
26. Roe, P.L., "Approximate Riemann Solver, Parameter Vectors, and difference schemes", Journal of Computational Physics, Vol.43, pp.357-372,1981
27. Arnone, A., et al., "Integration of Navier-Stokes Equations Using Dual Time Stepping and a Multigrid Method", AIAA Journal, Vol.33, pp.985-990,1995
28. Jameson,A. "Time Dependent Calculations Using Multigrid with Applications to Unsteady Flow Past Airfoils and Wings", AIAA paper 91-1596
29. Thomas, P.D., and Middlecoff, J.F., "Direct Control of Grid Point Distribution in Meshes Generated by Elliptic Equations", AIAA Journal, Vol.18, No.6, 1979
30. Sonar, Th., "Grids Generation Using Elliptic Partial Differential Equations", DFVLR-IB 129-88/11,1988
31. Jameson, A., "Success and Challenge in Computational Aerodynamics", AIAA Paper 87-1184, 1987
32. Thompson, J.F., et al, "Automatic Numeric Generation of Body-Fitted Curvilinear Coordinates for a Field Containing any Number of Arbitrary Two-Dimensional Bodies", Journal of Computational Physics, Vol.15, No.3, 1974
33. Volpe, G. and Jameson, A., "An Efficient Solution for Computing Transonic and Supersonic Flows about Aircraft", ICAS-88-4.8.3, 1988
34. Yoon, S., Jameson, A., and Kwak, D., "Effect of Artificial Diffusion Scheme on Multi-Grid Convergence", AIAA Paper 95-1670, 1995
35. E,Q., Li,F.W., and Yang G.W. "Numerical Solution of the Euler Equations for Transonic Flow about the Complete Aircraft", AIAA-96-2406, 1996.
36. Johnson, D.A., King, L.S., "A Mathematical Simple Turbulence Closure Model for Attached and Separated Turbulent Boundary Layers", AIAA Journal, 23:1684-1692,1985.
37. A.L. Gaitonde. A dual-time method for the solution of the unsteady Euler equations, Aeronautical Journal, October 1994.
38.李杰,“三维非定常Navier-Stokes方程数值求解格式研究”,西北工业大学博士后研究报告,2001年
39.杨青,“超临界翼型、机翼的定常和非定常流场数值模拟”,西北工业大学硕士学位论文,2004年
40.李凤蔚,鄂秦,李杰,杨国伟,“复杂外形网格生成技术”,空气动力学学报,Vol.16,No.1,1998年
41. Davis, s., "NACA 64A010(NASA AMES Model)oscillatory Pitching", AGARD Compendium of Unsteady Aerodynamic Measurements AGARD-R-702,1982
42. Swanson, R. C., and Turkel, E., "A Multistage Time-Stepping Scheme for the Navier-Stokes Equations, AIAA Paper 85-0035,1985
43. Rumsey, C. L., et al, "Efficiency and Accuracy of Time-Accurate Turbulent Navier-Stokes Computations", AIAA Paper 95-1835-CP, 1995
44.朱自强等著,现代飞机设计中的空气动力学.北京:北京航空航天大学出版社,1995
45.北京空气动力研究所编,空气动力学发展论文集.北京:国防工业出版社,1997.
46. McMasters, J. H., and Cummings, R. M., "Airplane Design—Past, Present, andFuture", Journal of Aircraft, Vol. 39, No. 1, 2002, pp. 10-17.
47.陈海昕,李凤蔚,鄂秦,高超.“复杂外形网格生成及在流场数值模拟中的应用”,第九届全国计算流体力学会议论文集,1998年11,云南景洪.
48.梁强,复杂流场的非定常气动力计算以及气动弹性研究。西北工业大学博士学位论文,2003。
49. Swanson, R. C., Turkel, E., "Artificial Dissipation and Central difference schemes for Euler and N-S Equations", AIAA Paper 87-1107, 1987
50. Thomas, P. D., and Lombard, C. K., "Geometric Conservation Law and Its Application to Flow Computations on Moving Grids", AIAA Journal, Vol. 17, No. 10, 1979, pp. 1030-1037.
51.徐华舫,《空气动力学基础》,国防工业出版社,1979年
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