三维曲面激波反问题的参考平面解法
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摘要
为了进一步探索三维超声速气动反问题的求解方法,从降维的三维特征线方法出发,推导出适用于参考平面法的特征方程和相容方程,并提出曲面激波反问题的求解方法。该设计方法可以把三维流场切为多个横截平面。在参考平面内,通过局部迭代求解准二维的特征方程和相容方程;在垂直于参考平面方向,通过引入整体迭代法来确定解面上的交叉导数,使结果达到二阶精度。采用泰勒-麦科尔流动和斜激波关系式验证了该设计方法的精度,其中压力的相对误差分别为1.3×10~(-3),6.1×10~(-5)。为了进一步验证设计方法的可靠性,设计了在3°来流攻角情况下,产生圆锥激波的三维型面,并采用商用软件Fluent验证所设计的三维构型。对比结果表明:所设计的流场与CFD数值模拟结果符合得较好,且流场参数最大误差不超过2%。
In order to explore valid methods for three-dimensional supersonic aerodynamics inverse problems,the characteristics equations and compatible equations of the reference plane method were deduced based on the method of descending three-dimensional characteristics. And a method for solving the inverse problem of three-dimensional curved shock wave was proposed. The design method could cut the three-dimensional flow field into multiple transverse planes,and solve characteristic equations and the compatibility equations in the reference plane which had a same form of two-dimensional MOC. The integral iteration method was applied in the direction of perpendicular to the reference plane in order to determine the cross derivations of solution point,which could insure the second-order accuracy. The accuracy order of the reference plane method is tested by comparing numerical solutions with analytical results of Taylor-Maccoll flow and curved shock theory. By contrast,it could be found that the pressure maximum relative error is 1.3×10~(-3) and 6.1×10~(-5),respectively. In order to further verify the reliability of the method,a three-dimensional wall surface generating a conical shock wave at 3 degrees of attack angle was design. And the reliability of the design result is verified using commercial software Fluent. It could be found that the numerical solutions of the solver are good in agreement with those of CFD numerical simulations,and the maximum error of flow field is no more than 2%. Therefore,the proposed method would be reliable and might provide new ideas for three-dimensional supersonic aerodynamic design.
In order to explore valid methods for three-dimensional supersonic aerodynamics inverse problems,the characteristics equations and compatible equations of the reference plane method were deduced based on the method of descending three-dimensional characteristics. And a method for solving the inverse problem of three-dimensional curved shock wave was proposed. The design method could cut the three-dimensional flow field into multiple transverse planes,and solve characteristic equations and the compatibility equations in the reference plane which had a same form of two-dimensional MOC. The integral iteration method was applied in the direction of perpendicular to the reference plane in order to determine the cross derivations of solution point,which could insure the second-order accuracy. The accuracy order of the reference plane method is tested by comparing numerical solutions with analytical results of Taylor-Maccoll flow and curved shock theory. By contrast,it could be found that the pressure maximum relative error is 1.3×10~(-3) and 6.1×10~(-5),respectively. In order to further verify the reliability of the method,a three-dimensional wall surface generating a conical shock wave at 3 degrees of attack angle was design. And the reliability of the design result is verified using commercial software Fluent. It could be found that the numerical solutions of the solver are good in agreement with those of CFD numerical simulations,and the maximum error of flow field is no more than 2%. Therefore,the proposed method would be reliable and might provide new ideas for three-dimensional supersonic aerodynamic design.
引文
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[2] Eyi S,Yumusak M. Three Dimensional Rocket Nozzle Design Using Adjoint Method[R]. AIAA 2013-4086.
[3]刘红阳.特征线追踪方法和应用[D].长沙:国防科技大学,2015.
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[8] Rakich J V. Calculation of Hypersonic Flow over Bodies of Revolution at Small Angles of Attack[J]. AIAA Journal,1965,3(3):458-464.
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[14] Thompson H D and Murthy S N B. Design of Optimized Three-Dimensional Nozzles[J]. Journal of Spacecraft,1966,3(9):1384-1393.
[15] Wang X,Damodaran M. Optimal Three-Dimensional Nozzle Shape Design Using CFD and Parallel Simulated Annealing[J]. Journal of Propulsion and Power,2015,18(1):217-221.
[16] Xing X Q,Damodaran M. Design of Three-Dimensional Nozzle Shapes Using NURBS,CFD and Hybrid Optimization Strategies[R]. AIAA 2004-4368.
[17] Meenaksh R,Hoffman J D,Murthy S N B. Design and Performance Computations in Complex 3-D Nozzles[R].AIAA 99-0882.
[18]覃粒子,王长辉,刘宇,等.三维喷管设计[J].推进技术,2005,26(6):499-521.(QIN Li-zi,WANG Chang-hui,LIU Yu,et al. Three-Dimensional Nozzle Design[J]. Journal of Propulsion Technology,2005,26(6):499-521.)
[19] Smart M K. Design of Three-Dimensional Hypersonic Inlets with Rectangular-to-Elliptical Shape Transition[J]. Journal of Propulsion and Power,1999,15(3):408-416.
[20] Gollan R J,Smart M K. Design of Modular Shape-Transition Inlets for a Conical Hypersonic Vehicle[J]. Journal of Propulsion and Power,2013,29(4):832-838.
[21] Molder S Szipiro. Busemann Inlet for Hypersonic Speeds[J]. Journal of Spacecraft and Rockets,1966,3(8):1303-1304.
[22]尤延铖,梁德旺,黄国平.一种新型内乘波进气道初步研究[J].推进技术,2006,27(3):252-256.(YOU Yan-cheng,LIANG De-wang,HUANG Guo-ping. Investigation of Internal Waverider-Derived Hypersonic Inlet[J]. Journal of Propulsion Technology,2006,27(3):252-256.)
[23] Mo J W,Xu J L,Gu R,et al. Design of an Asymmetric Scramjet Nozzle with Circular to Rectangular Shape Transition[J]. Journal of Propulsion and Power,2014,30(3):812-819.
[24] Jones K D,Sobieczky H,Seebass A R,et al. Waverider Design for Generalized Shock Geometries[J]. Journal of Spacecraft and Rockets,1995,32(6):957-963.
[25]赵博.乘波体飞行器气动外形设计及其数值验证[D].哈尔滨:哈尔滨工程大学,2013.
[26]尤延铖,梁德旺.基于内乘波概念的三维变截面高超声速进气道[J].中国科学(E辑),2009,39(8):1483-1494.
[27]卢鑫,岳连捷,肖雅彬,等.超燃冲压发动机三维变截面尾喷管设计[C].无锡:第三届高超声速科技学术会议,2010.
[28] Moretti G. Three-Dimensional Supersonic Flow Computations[J]. AIAA Journal,1963,1(9):2192-2193.
[29] Katskova O N,Chushkin P I. Three-Dimensional Supersonic Equilibrium Flow of a Gas Around Bodies at Angles of Attack[R]. NASA TT F-9790,1965.
[30] Taylor G I,Maccoll J W. The Air Pressure on a Cone Moving at High Speeds[J]. Proceeding of the Royal Society of London,Series A,1933,139:279-311
[31] Maccoll J W. The Conical Shock Wave Formed by a Cone Moving at High Speed[J]. Proceeding of the Royal Society of London,Series A,1937,159:459-472.
[2] Eyi S,Yumusak M. Three Dimensional Rocket Nozzle Design Using Adjoint Method[R]. AIAA 2013-4086.
[3]刘红阳.特征线追踪方法和应用[D].长沙:国防科技大学,2015.
[4]易仕和,赵玉新,何霖,等.超声速与高超声速喷管设计[M].北京:国防工业出版社,2013.
[5]左克罗M J,霍夫曼J D.气体动力学[M].王汝涌等译.北京:国防工业出版社,1984.
[6]童秉纲,孔祥言,邓国华.气体动力学[M].北京:高等教育出版社,1990.
[7] Rakich J V. Theoretical and Experimental Study of Supersonic Steady Flow around Inclined Bodies of Revolution[J]. AIAA Journal,1970,8(3):511-518.
[8] Rakich J V. Calculation of Hypersonic Flow over Bodies of Revolution at Small Angles of Attack[J]. AIAA Journal,1965,3(3):458-464.
[9] Fong J, Sirovich L. Supersonic Inviscid Flow—A Three-Dimensional Characteristics Approach[J]. Journal of Computational Physics,1987,68(2):378-392.
[10] Butler D S. The Numerical Solution of Hyperbolic Systems of Partial Differential Equations in Three Independent Variables[J]. Proceedings of the Royal Society of London A:Mathematical,Physical and Engineering Science,1960,255(1281):232-252.
[11] Ransom V H,Hoffman J D,Thompson H D. A SecondOrder Numerical Method of Characteristics for Three-Dimensional Supersonic Flow[D]. USA:Purdue University,1970.
[12] Cline M C,Hoffman J D. Comparison of Characteristic Schemes for Three-Dimensional, Steady, Isentropic Flow[J]. AIAA Journal,1972,10(11):1452-1458.
[13]蓝庆生,赵玉新,赵一龙,等.三维超声速流动的压力反问题[J].空气动力学学报,2017,35(3):429-435.
[14] Thompson H D and Murthy S N B. Design of Optimized Three-Dimensional Nozzles[J]. Journal of Spacecraft,1966,3(9):1384-1393.
[15] Wang X,Damodaran M. Optimal Three-Dimensional Nozzle Shape Design Using CFD and Parallel Simulated Annealing[J]. Journal of Propulsion and Power,2015,18(1):217-221.
[16] Xing X Q,Damodaran M. Design of Three-Dimensional Nozzle Shapes Using NURBS,CFD and Hybrid Optimization Strategies[R]. AIAA 2004-4368.
[17] Meenaksh R,Hoffman J D,Murthy S N B. Design and Performance Computations in Complex 3-D Nozzles[R].AIAA 99-0882.
[18]覃粒子,王长辉,刘宇,等.三维喷管设计[J].推进技术,2005,26(6):499-521.(QIN Li-zi,WANG Chang-hui,LIU Yu,et al. Three-Dimensional Nozzle Design[J]. Journal of Propulsion Technology,2005,26(6):499-521.)
[19] Smart M K. Design of Three-Dimensional Hypersonic Inlets with Rectangular-to-Elliptical Shape Transition[J]. Journal of Propulsion and Power,1999,15(3):408-416.
[20] Gollan R J,Smart M K. Design of Modular Shape-Transition Inlets for a Conical Hypersonic Vehicle[J]. Journal of Propulsion and Power,2013,29(4):832-838.
[21] Molder S Szipiro. Busemann Inlet for Hypersonic Speeds[J]. Journal of Spacecraft and Rockets,1966,3(8):1303-1304.
[22]尤延铖,梁德旺,黄国平.一种新型内乘波进气道初步研究[J].推进技术,2006,27(3):252-256.(YOU Yan-cheng,LIANG De-wang,HUANG Guo-ping. Investigation of Internal Waverider-Derived Hypersonic Inlet[J]. Journal of Propulsion Technology,2006,27(3):252-256.)
[23] Mo J W,Xu J L,Gu R,et al. Design of an Asymmetric Scramjet Nozzle with Circular to Rectangular Shape Transition[J]. Journal of Propulsion and Power,2014,30(3):812-819.
[24] Jones K D,Sobieczky H,Seebass A R,et al. Waverider Design for Generalized Shock Geometries[J]. Journal of Spacecraft and Rockets,1995,32(6):957-963.
[25]赵博.乘波体飞行器气动外形设计及其数值验证[D].哈尔滨:哈尔滨工程大学,2013.
[26]尤延铖,梁德旺.基于内乘波概念的三维变截面高超声速进气道[J].中国科学(E辑),2009,39(8):1483-1494.
[27]卢鑫,岳连捷,肖雅彬,等.超燃冲压发动机三维变截面尾喷管设计[C].无锡:第三届高超声速科技学术会议,2010.
[28] Moretti G. Three-Dimensional Supersonic Flow Computations[J]. AIAA Journal,1963,1(9):2192-2193.
[29] Katskova O N,Chushkin P I. Three-Dimensional Supersonic Equilibrium Flow of a Gas Around Bodies at Angles of Attack[R]. NASA TT F-9790,1965.
[30] Taylor G I,Maccoll J W. The Air Pressure on a Cone Moving at High Speeds[J]. Proceeding of the Royal Society of London,Series A,1933,139:279-311
[31] Maccoll J W. The Conical Shock Wave Formed by a Cone Moving at High Speed[J]. Proceeding of the Royal Society of London,Series A,1937,159:459-472.