高超声速弹头气动热工程算法与数值传热
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摘要
采用有限体积法,在非结构化网格上离散稳态导热方程,耦合迭代计算法向扩散项和切向扩散项,以满足高精度离散格式的要求。运用可视化语言Fortran95模块化完成了数值传热计算程序的编制,采用C++编写网格文件的接口程序,并对来自与Tecplot和GAMBIT的网格文件重新进行读取与编号,实现了网格前处理的兼容性。
在标准大气环境下,对球锥型弹头在5～8马赫高超声速来流时,采用工程算法计算弹头表面热通量。基本公式为费-里德尔(Fay-Riddell)平衡边界层驻点热流密度公式,李斯(Lees)层流热流分布公式。在二维零攻角来流情况下,考虑了两种流动状况,一种是完全层流无转捩；另一种为采用Batt边界层转捩准则来确定边界层转捩点。完全湍流区采用湍流热流计算公式确定其热流值,转捩过渡区热流由层流传热与湍流传热的加权平均值计算得到。
在三维有攻角来流情形下,弹体周向热流不再对称,结合上面的基本公式与经过适当修正的等价锥法,分析攻角对层流传热的影响。然后,采用一种简化的轴对称比拟法计算相同攻角来流条件下的弹体热流分布,并与等价锥法以及实验值相互比较,并得到了令人满意的一致性。
最后,在验证了自编气动热程序的正确性后,将上述工程算法得到的弹体表面热流值,线性化后作为第三类边界条件耦合到弹体热分析程序中,对弹体的温度场进行了数值模拟。
计算结果表明,湍流边界层传热会导致弹头高温区扩大,表面温度上升；随着攻角的增大,迎风面的热流值会增大,而且温度也会上升；而背风面的热流值会随着攻角的增大而减小,温度也会相应的有所降低。上述所得结论将为弹箭气动热设计和热防护提供了有价值的参考。
The steady state conduction equation is discretized by using the finite volume method (FVM) in the unstructured grid. For the diffusion terms, the normal direction scalar and the tangent direction scalar were coupled iterated to meet the high precision demand. The programs have been complied by visual Fortran95.The mesh generation that come from Tecplot and GAMBIT are searched and ranged again by the code complied by C++.
The engineering methods have been applied to calculate the heat flux of the spherically blunted cone on the condition of the standard atmosphere and the coming flow is on 5-8 Mach number. The basic formulas are Fay-Riddell balance boundary layer stagnation point heat flux formula and Lees' formula. There are two states to be considered here. One is the complete laminar boundary layer and the other is the boundary layer transition. The transition point is confirmed by Batt boundary layer transition criteria. The turbulent heating-rate expression is applied in the area of turbulence boundary layer. The transition region's heat flux is calculated with weighed average of laminar and turbulence heat transfer.
Integrated with equivalence conical method, the influence of the angle of attack is considered in calculating the heat flux of the projectile's head in 3D situation. And another simplified method is applied for calculating laminar heat transfer over bodies at the same angle of attack as being mentioned. The result is compared with experiment and the equivalence conical method.
The heat flux was linearizated as the third kind of boundary conditions and coupled with the numerical thermal conduction in the projectile's head. The temperature of the projectile's head is simulated. The result indicate that:turbulence boundary layer will enhance the heat conduction and the temperature of the surface will go up. The larger the angles of attack the bigger the heat flux over the surface on the windward, and the higher the temperature on the windward. But on the surface of the leeward, the trend is the opposite.
在标准大气环境下,对球锥型弹头在5～8马赫高超声速来流时,采用工程算法计算弹头表面热通量。基本公式为费-里德尔(Fay-Riddell)平衡边界层驻点热流密度公式,李斯(Lees)层流热流分布公式。在二维零攻角来流情况下,考虑了两种流动状况,一种是完全层流无转捩；另一种为采用Batt边界层转捩准则来确定边界层转捩点。完全湍流区采用湍流热流计算公式确定其热流值,转捩过渡区热流由层流传热与湍流传热的加权平均值计算得到。
在三维有攻角来流情形下,弹体周向热流不再对称,结合上面的基本公式与经过适当修正的等价锥法,分析攻角对层流传热的影响。然后,采用一种简化的轴对称比拟法计算相同攻角来流条件下的弹体热流分布,并与等价锥法以及实验值相互比较,并得到了令人满意的一致性。
最后,在验证了自编气动热程序的正确性后,将上述工程算法得到的弹体表面热流值,线性化后作为第三类边界条件耦合到弹体热分析程序中,对弹体的温度场进行了数值模拟。
计算结果表明,湍流边界层传热会导致弹头高温区扩大,表面温度上升；随着攻角的增大,迎风面的热流值会增大,而且温度也会上升；而背风面的热流值会随着攻角的增大而减小,温度也会相应的有所降低。上述所得结论将为弹箭气动热设计和热防护提供了有价值的参考。
The steady state conduction equation is discretized by using the finite volume method (FVM) in the unstructured grid. For the diffusion terms, the normal direction scalar and the tangent direction scalar were coupled iterated to meet the high precision demand. The programs have been complied by visual Fortran95.The mesh generation that come from Tecplot and GAMBIT are searched and ranged again by the code complied by C++.
The engineering methods have been applied to calculate the heat flux of the spherically blunted cone on the condition of the standard atmosphere and the coming flow is on 5-8 Mach number. The basic formulas are Fay-Riddell balance boundary layer stagnation point heat flux formula and Lees' formula. There are two states to be considered here. One is the complete laminar boundary layer and the other is the boundary layer transition. The transition point is confirmed by Batt boundary layer transition criteria. The turbulent heating-rate expression is applied in the area of turbulence boundary layer. The transition region's heat flux is calculated with weighed average of laminar and turbulence heat transfer.
Integrated with equivalence conical method, the influence of the angle of attack is considered in calculating the heat flux of the projectile's head in 3D situation. And another simplified method is applied for calculating laminar heat transfer over bodies at the same angle of attack as being mentioned. The result is compared with experiment and the equivalence conical method.
The heat flux was linearizated as the third kind of boundary conditions and coupled with the numerical thermal conduction in the projectile's head. The temperature of the projectile's head is simulated. The result indicate that:turbulence boundary layer will enhance the heat conduction and the temperature of the surface will go up. The larger the angles of attack the bigger the heat flux over the surface on the windward, and the higher the temperature on the windward. But on the surface of the leeward, the trend is the opposite.
引文
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[8]H.H. Hamilton and K.J. Weilmuenster, Hampton, VA and F.R. DeJarnette. Application of Axisymmetric Analogue for Calculating Heating in Three-Dimensional Flows. AIAA-85-0245,1985.
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[10]Eli Reshotko. Roughness-Induced Transition, Experiment and Modeling. AIAA 2008-4294,2008.
[11]Scott A. Berry, Thomas J. Horvath. Discrete Roughness Transition for Hypersonic Flight Vehicles. AIAA-2007-0307,2007.
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[44]张敏,戴春林,范悦宏.圆环域中结构与非结构网格的热传导数值计算[J].东北电力学院学报(自然科学版).2004.24(6)：15-19
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[2]卞荫贵,徐立功.气动热力学[M].力学学报.合肥：中国科学技术大学出版社,1997.
[3]Fred R. DeJarnette and Ruby M. Davis. A Simplified Method for Calculating Laminar Heat Transfer over Bodies at an Angle of Attack. NASA TN D-4720,1968.
[4]Joseph W. Cleary. Effects OF Angle OF Attack and Bluntness on Laminar Heating-rate Distribution of a 15" Cone at a Mach Number of 10.6.NASATN D-5450,1969.
[5]E.V. Zoby. Approximate Heating Analysis for the Windward-Symmetry Plane of Shuttle-like Bodies at Large Angle-of-Attack.AIAA-81-1042,1981.
[6]J.D. Waskiewicz and C.H.Lewis. Hypersonic Viscous Flows over Sphere-Cones at High Angles of Attack. AIAA. January 16-18,1978.
[7]Christopher J.Riley, Fred R. DeJarnette. An Engineering Aerodynamic Heating Method for Hypersonic Flow. AIAA 92-0499,1992.
[8]H.H. Hamilton and K.J. Weilmuenster, Hampton, VA and F.R. DeJarnette. Application of Axisymmetric Analogue for Calculating Heating in Three-Dimensional Flows. AIAA-85-0245,1985.
[9]Michael S. Holden, Erik P. Mundy, Timothy P. Wadhams. A Review of Experimental Studies of Surface Roughness and Blowing on the Heat Transfer and Skin Friction to Nosetips and Slender Cones in High Mach Numbers Flows. AIAA 2008-3907,2008.
[10]Eli Reshotko. Roughness-Induced Transition, Experiment and Modeling. AIAA 2008-4294,2008.
[11]Scott A. Berry, Thomas J. Horvath. Discrete Roughness Transition for Hypersonic Flight Vehicles. AIAA-2007-0307,2007.
[12]Catherine B. McGinley. Scott A. Berry. Review of Orbiter Flight Boundary Layer Transition Data. AIAA 2006-2921,2006.
[13]Nathaniel B. Cohen. Correlation Formulas and Tables of Density and some Transport Properties of Equilibrium Dissociating Air for Use in Solutions of the Boundary-Layer Equations. NASA TN D-194,1960.
[14]ROGER A.SVEHLA. Estimated Viscosities and Thermal Conductivities of Gases AT High Temperatures. NASATR R-132,1962.
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[16]Warren F. Ahtye and Tzy-Cheng Peng. Approximations for the Thermodynamic and Transport Proerties of High-temperature Nitrogen with Shock-tube Applications. NASATND-1303,1962.
[17]Kennetb Sutton and Randolpb A. Graves, Jr. A General Stagnation-Point Convective Heating Equation for Arbitrary Gas Mixtures. NASATR R-376,1971.
[18]Chul Park. Calculation of Stagnation-Point Heating Rates Associated with Stardust Vehicle. AIAA 2005-190,2005.
[19]F. De Filippis R. Savino and A. Martucci. Numerical-experimental correlation of stagnation point heat flux in high enthalpy hypersonic wind tunnel. AIAA 2005-3277
[20]Convective Heat-Transfer Rate Distributions Over A 140 Blunt Cone at Hypersonic Speeds in Different Gas Environments. AIAA 93-2787,1993.
[21]Joseph W. Cleary. An Experimental and Theoretical Investigation of the Pressure Distribution and Flow Fields of Blunted Cones at Hypersonic Mach Numbers. NASA TND-2969,1965.
[22]John V. rakich and Joseph W. Cleary. Theoretical and Experimental Study of Supersonic Steady Flow around Inclined Bodies of Revolution. AIAA Paper 69-187,1969.
[23]G.T.CHRUSCIEL and L. D. HULL. Theoretical Method for Calculating Aerodynamic Characteristics of Spherically Blunted Cones. AIAA Paper 68-674,1968.
[24]杨世铭,陶文铨.传热学[M].北京：高等教育出版社,1998
[25]陶文铨.计算传热学的近代进展[M].北京：科学出版社,2001
[26]陶文铨.数值传热学[M].西安：西安交通大学出版社,2001
[27]张洪济.热传导[M].高等教育出版社,1990
[28]张鲁民.载人飞船返回舱空气动力学[M].北京：国防工业出版社,2002.
[29]赵梦熊.载人飞船空气动力学[M].北京：国防工业出版社,2000.
[30]王希季.航天器进入与返回技术(上册)[M].北京：中国宇航出版社,2007.
[31]王国雄.弹头技术(上)[M].北京：宇航出版社,1993.
[32]黄志澄.高超声速飞行器空气动力学[M].第1版.北京：国防工业出版社,1995
[33]张家荣,赵廷元.工程常用物质的热物理性质手册[M].北京：新时代出版社,1987
[34]B.K.科什金.航空与火箭技术中的传热原理[M].北京：科学出版社,1963
[35]乐嘉陵,詹妮迈德芙,曼彻娜娅,维特拉斯基.高超声速飞行器表面气动热和粘性摩擦力计算[J].流体力学实验与测量,2002.
[36]吕红庆,王振清,王永军,张翠娥,靳承滨.高超声速钝头体气动热分析[J].导弹与航天运载技术,2008.3
[37]耿湘人,桂业伟,王安龄.微型凸起物高超声速气动热特性研究[J].空气动力学学报,2006.2
[38]周成平,涂素平,蔡超,张义广.高超音速飞行器头罩气动热流场数值模拟[J].华中科技大学学报
[39]娄文忠,刘爱丽,秦跃.超音速火箭弹激光引信气动热特性仿真研究[J].红外与激光工程.2008.8.
[40]欧阳水吾,苏玉宏.高超音速有攻角钝头体三维化学非平衡粘性激波层流动数值计算[J].宇航学报,1992.7
[41]刘伟,杨小亮,赵海洋,陈景兵.高超声速圆锥边界层转捩数值研究[J].空气动力学报,2008.12
[42]王希季.航天器进入与返回技术(下册)[M].北京：中国宇航出版社,2007
[43]张敏,黄庆宏.非结构化网格中导热和辐射复合传热的数值计算[J].南京师范大学学报(工程技术版),2005,5(3)：5-7
[44]张敏,戴春林,范悦宏.圆环域中结构与非结构网格的热传导数值计算[J].东北电力学院学报(自然科学版).2004.24(6)：15-19
[45]武淑萍,张敏,商立英.结构化与非结构化网格中的导热计算[J].南京工程学院学报(自然科学版).第3卷第2期,2005.3(2)：11-16
[46]吕丽丽.高超声速气动热工程算法研究[D].西安：西北工业大学硕士论文,2005
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