高超声速飞行器气动力气动热数值模拟和超声速流动的区域推进求解
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摘要
本文围绕超声速流动气动力气动热的准确求解和超声速流动的高效数值求解及其应用展开研究,研究包括两方面的内容:一是超声速流动壁面摩阻、热流的准确预测技术及其在吸气式高超声速飞行器气动力气动热预测中的应用,二是伪时间迭代的空间推进求解技术和复杂超声速流动的高效区域推进求解技术研究及其在复杂工程问题和气动优化设计中的应用。
关于超声速流动中壁面摩阻、气动热准确数值预测技术及应用研究。由于在超声速流动中,气流和固壁之间存在较大的相对运动速度,壁面会产生大的速度梯度和温度梯度,导致气流对物体产生较大的摩擦阻力和气动加热;同时在大多数的超声速流动中,存在层流和湍流两种流动状态,数值模拟要准确的预测超声速流动的气动力和气动热,必须足够准确的预测出在层流和湍流两种流动状态下物面的速度梯度和温度梯度。
本文的时间迭代求解方法,采用有限体积方法在结构网格上离散守恒型的流动控制方程。时间离散采用LU-SGS方法;空间离散中,无粘通量采用3阶MUSCL插值和AUSMPW+格式构造,粘性偏导数采用基于Guass定理的方法构造。在边界上采用两层虚点的2阶精度处理。湍流模型采用Kok修正的k ?ωTNT两方程模型,并在湍流计算中耦合了在湍流边界层内一致有效、考虑可压缩和热传导效应的先进壁面函数边界条件。
运用以上数值模拟技术,对于超声速层流(超声速圆柱驻点法向网格雷诺数Re n<80内);亚、超声速状态下的湍流(等应力层等假设的前提下,在y +<200~300范围内),可以得到较为准确的壁面压力、摩阻和热流信息。对吸气式高超声速飞行器流场中的典型流态进行了详细的验证和确认,以确保在整体飞行器数值模拟中结果的可靠性。在此基础上对典型高超声速飞行器在无动力巡航飞行状态下的气动力和气动热进行了数值预测。获得飞行器外表面和内流道的热流分布及峰值区域,峰值区热流可达3MW/m2以上;得到了飞行器的气动力特性,其中摩擦阻力(包括内流道摩阻)占总阻力的62.7%。这些数据对飞行器的热防护和气动设计十分关键。
关于超声速流动的伪时间空间推进求解技术、复杂超声速流动的区域推进求解技术及应用研究。
在确认了对超声速流动的气动力、气动热准确数值模拟的基础上,实现了对超声速占主导的层流、湍流和多组分有限速率化学反应流动的空间推进进求解。空间推进求解采用伪时间迭代方法,在一个推进面上迭代求解抛物化NS方程。在推进面上的隐式时间迭代采用修正的LU-SGS方法,推进方向的无粘通量采用一阶或二阶的迎风离散方法,法向和展向无粘通量采用3阶MUSCL插值和AUSMPW+格式构造,推进方向的粘性耗散项被舍弃,其它方向的粘性耗散项采用基于Gauss积分的方法构造。空间推进方法成功的应用到了二维、轴对称和三维超声速无粘、层流、湍流和多组分有限速率化学反应流动的推进求解中。数值试验表明空间推进方法在求解超声速占主导的流动时,所得结果与实验一致且和时间迭代方法结果具有相当的准确性,求解速度比时间迭代方法提高了1~2个数量级。
对于复杂超声速流动,提出并实现了复杂超声速流动的区域推进求解方法,并运用在实际工程问题的求解中。复杂超声速流动的区域推进求解,按照流动的物理特征,沿主流方向划分为超声速占主导的区域或回流、亚声速占主导的区域。在超声速占主导的区域采用空间推进求解PNS方程的方法求解,在回流和亚声速占主导的区域采用时间迭代求解完全NS方程的方法求解。区域推进求解了典型二维复杂超声速流动,表明区域推进求解方法在求解复杂超声速流动时和时间迭代方法具有相同的准确性,且求解速度提高了数倍。在此基础上对吸气式高超声速飞行器的三维进气道、氢燃料三维超燃冲压发动机和碳氢燃料二维一体化整机进行了区域推进求解,以显示该方法的高效性以及在处理复杂工程问题中的灵活性。计算得到的结果和实验测量值以及时间迭代方法的结果一致,在求解效率上,对于三维氢燃料发动机,整个流场采用时间迭代方法求解,需要256个CPU(0.8GHz),5天时间得到一个状态的结果,而采用区域推进方法求解相同的流动状态,空间推进区域仅采用1个CPU(2.8GHz),时间迭代区域采用8个CPU(2.8GHz),总共只需要3天左右时间。
区域推进求解方法具有高效、灵活和可靠的特点。把区域推进方法做为自动优化设计过程中的CFD分析工具,结合优化外形的参数化描述以及计算网格的自动化生成,使用成熟的优化工具,实现了吸气式高超声速飞行器尾喷管的单目标和多目标自动优化设计。高效准确的湍流流动的CFD分析工具,使得一个设计循环仅需40秒左右时间,优化循环1000次仅耗时11个小时左右,整个优化过程在单个CPU上得以快速完成。优化后的尾喷管的升力和推力都有了较大的提高。
本文包含七章内容。第一章是引言,介绍研究工作的意义和国内外进展以及本文的研究内容。第二章介绍流动的时间迭代求解方法以及本文采用的先进壁面函数边界条件,验证了壁面函数边界条件在亚跨声速和超声速流动中的准确性以及本文采用的热完全气体模型。第三章采用本文开发的CFD软件,验证和确认了吸气式高超声速飞行器典型流态的气动热和气动力分布,计算了一体化高超声速飞行的气动热和气动力,为工程设计提供了可靠的气动热、气动力数据。第四章介绍了求解包含超声速层流、湍流和有限速率化学反应流动的空间推进求解方法,并对开发的空间推进程序进行了严格的验证确认和应用。第五章提出和实现了复杂超声速流动的区域推进求解,把该方法应用在了实际工程问题的求解中,取得了较好的计算结果和较高的求解效率。第六章结合流动的区域推进求解方法,完成了高超声速飞行器单壁膨胀尾喷管的自动优化设计,使尾喷管的性能得到了大的提高。第七章是本文的结束语。
The aims of this thesis are studying methods for accurate simulating aerodynamic heat&force of hypersonic/supersonic flows and the efficient numerical method for hypersonic/supersonic flows. There are two parts of works included in this thesis. The first part is the technologies of accurately simulating aerodynamic force and aerodynamic heat of supersonic flow and its applications in predicting the aerodynamic force and aerodynamic heat of hypersonic vehicle. The second part is the high efficient methods in solving supersonic flow, they are space marching and region marching methods, and their applications in solving complex engineering problems and in automatical aerodynamic optimization design.
Studying work related to accurate numerical simulation of aerodynanic force and heat and its apllications are as follows:
There is comparatively large velocity gradient between flow and solid surface in supersonic flow field, which leads to large velocity and temperature gradients producing comparatively large skin friction and aerodynamic heat. At the same time, there are laminar and turbulent flow conditions in most of supersonic flows. Numerical simulating technologies must have sufficient accuracy to predict the velocity and temperature gradients in laminar and turbulent conditions for accurately predicting the aerodynamic heat and force.
The time dependent methods of this thesis use cell-averaged finite volume techniques to solve the conservative form governing equations on structured grid. LU-SGS method is used in time-marching. In space terms difference, inviscid fluxes construction use third order MUSCL interpolation method and AUSMPW+ scheme, viscous fluxes use central difference method which base on the Gauss Law. Turbulence simulations use Kok’s modified k ?ωTNT 2-equation turbulence mode coupled with an advanced wall function boundary condition considering modification of compressibility and heat transfer and being valid in whole turbulence boundary layer.
Basing on the techniques introduced above, the accurate wall skin friction and wall heat flux can be gotten for laminar flows (normal grid Reynolds number Re n<80 for hypersonic cylinder flow) and for the turbulence flows (y+<200~300 assuming the constant shear stress hypothesis in the lower part of the boundary layer etc.) . For accurately predicting hypersonic vehicle’s flow fields, the characteristic flows in hypersonic vehicles are confirmed and validated by present CFD tool. The aerodynamic force and heat of a hypersonic vehicle are predicted in the power off, cruise conditions basing on the numerical confirmations described above. Wall heat flux and its maximum locations are obtained. In the maximum heat flux region, the maximum heat flux can beyond 3MW/m2. At the same time, aerodynamic force characters are acquired. The skin friction force, including inner inlet and combustion chamber friction force, possesses 62.7% of the whole drag force. Those data is very crucial to the heat protection and aerodynamic design of hypersonic vehicles.
Studying work related to pseudo-temporal space marching methods and region marching methods for complex supersonic flows and their applications are as follows: As having obtained accurate numerical prediction abilities for aero force and heat flux of supersonic flows, space marching ability of supersonic dominated flow field is fulfilled. Space marching methods use pseudo-temporal iteration and iteratively solve parabolic NS equations in the marching plane. The time iterating method in the marching plane uses modified LU-SGS methods. Inviscid fluxes of the space marching direction use first order or second order upwind difference. The construction of normal direction and spanwise inviscid fluxes uses third order MUSCL interpolation and AUSMPW+ scheme. Viscous and dissipation fluxes in the space marching direction are neglected and the remainder directions dissipation gradients of viscous fluxes are constructed basing on Guess Law. Space marching techniques are successfully used in supersonic dominated inviscid, laminar, turbulence and multi-species finite rate chemical reaction flow fields in 2D/3D and axisymmetric cases. Numerical results show that the space marching algorithms are agree well with experiment and have the same level of accuracy in solving supersonic dominated flow fields in comparison with time iteration methods, furthermore, present space marching algorithms are 1~2 orders faster than time iteration methods.
For complex supersonic flows, region marching methods are established and used in engineering problems. The region marching methods for complex supersonic flow fields divide the flow field in streamwise direction into supersonic flow dominated regions or reverse and subsonic flow dominated regions according to their physical characters. In the supersonic flow dominated region, flow field is solved by space marching algorithms and in the reverse and subsonic flow dominated region time iterating method is used. The 2D characteristic complex supersonic flow fields are solved using region marching methods. It shows that region marching method have the same level of accuracy as time iterating algorithms in dealing with complex supersonic flow, furthermore, region marching method accelerate the convergence speed several times compared with time iterating algorithms. The 3D inlet and hydrogen fueled Scramjet engine of hypersonic vehicle and 2D kerosene fuled whole areo-breathing engine are numerically simulated with region marching method to illustrate its high efficiency and easily using in complex engineering problems. The region marching results have good agreements with experimental results and time iterating results.
Considering about the computational efficiency, for 3D hydrogen fueled Scramjet case, it takes 5 days with 256 CPU processors (0.8GHz) to get on condition’s result for time iterating algorithm in the entire flow field. But it only takes 3 days with 1 CPU processor in the space marching regions and 8 CPU processors (2.8GHz) in the time iterating regions to get the same result for region marching method.
Because it’s high efficiency and easy using and accuracy, region marching method is used as the turbulence CFD analysis tool during the cycle of automatic design optimization. Combined with parametric description of optimization geometry and automatic grid generation, single and multi-objects automatic optimizations of single expansion ramp nozzle (SERN) of hypersonic vehicle are fulfilled using the sophisticated optimization tools. Because of using cheap and accurate CFD analysis software, only about 40 seconds are needed for one optimization cycle and 11 hours are needed for about 1000 optimization cycles. The optimization procedures can run quickly in a single CPU processor. The lift and propulsion force of the nozzle have improved significantly after the optimization.
Seven chapters are included in this thesis. The First chapter is the introduction. The meaning and development of researching work are introduced. In chapter 2, time iterating algorithms are introduced and wall function boundary conditions and thermally perfect gas model are validated. In the third chapter, the aerodynamic force and heat flux of the hypersonic vehicle and the characteristic flow conditions of hypersonic vehicle are simulated, those work provide reliable datum of heat flux and aero-force for engineering design. In chapter 4, the space marching algorithms of supersonic turbulent and chemical reaction flow included their validations are fulfilled. In chapter 5, the region marching method for complex supersonic flow fields and their applications in engineering problems are fulfilled. In chapter 6, combining region marching method for solving supersonic flow fields, automatic optimization design of hypersonic vehicle’s SERN nozzle is conducted. Chapter 7 is the conclusion of this thesis.
关于超声速流动中壁面摩阻、气动热准确数值预测技术及应用研究。由于在超声速流动中,气流和固壁之间存在较大的相对运动速度,壁面会产生大的速度梯度和温度梯度,导致气流对物体产生较大的摩擦阻力和气动加热;同时在大多数的超声速流动中,存在层流和湍流两种流动状态,数值模拟要准确的预测超声速流动的气动力和气动热,必须足够准确的预测出在层流和湍流两种流动状态下物面的速度梯度和温度梯度。
本文的时间迭代求解方法,采用有限体积方法在结构网格上离散守恒型的流动控制方程。时间离散采用LU-SGS方法;空间离散中,无粘通量采用3阶MUSCL插值和AUSMPW+格式构造,粘性偏导数采用基于Guass定理的方法构造。在边界上采用两层虚点的2阶精度处理。湍流模型采用Kok修正的k ?ωTNT两方程模型,并在湍流计算中耦合了在湍流边界层内一致有效、考虑可压缩和热传导效应的先进壁面函数边界条件。
运用以上数值模拟技术,对于超声速层流(超声速圆柱驻点法向网格雷诺数Re n<80内);亚、超声速状态下的湍流(等应力层等假设的前提下,在y +<200~300范围内),可以得到较为准确的壁面压力、摩阻和热流信息。对吸气式高超声速飞行器流场中的典型流态进行了详细的验证和确认,以确保在整体飞行器数值模拟中结果的可靠性。在此基础上对典型高超声速飞行器在无动力巡航飞行状态下的气动力和气动热进行了数值预测。获得飞行器外表面和内流道的热流分布及峰值区域,峰值区热流可达3MW/m2以上;得到了飞行器的气动力特性,其中摩擦阻力(包括内流道摩阻)占总阻力的62.7%。这些数据对飞行器的热防护和气动设计十分关键。
关于超声速流动的伪时间空间推进求解技术、复杂超声速流动的区域推进求解技术及应用研究。
在确认了对超声速流动的气动力、气动热准确数值模拟的基础上,实现了对超声速占主导的层流、湍流和多组分有限速率化学反应流动的空间推进进求解。空间推进求解采用伪时间迭代方法,在一个推进面上迭代求解抛物化NS方程。在推进面上的隐式时间迭代采用修正的LU-SGS方法,推进方向的无粘通量采用一阶或二阶的迎风离散方法,法向和展向无粘通量采用3阶MUSCL插值和AUSMPW+格式构造,推进方向的粘性耗散项被舍弃,其它方向的粘性耗散项采用基于Gauss积分的方法构造。空间推进方法成功的应用到了二维、轴对称和三维超声速无粘、层流、湍流和多组分有限速率化学反应流动的推进求解中。数值试验表明空间推进方法在求解超声速占主导的流动时,所得结果与实验一致且和时间迭代方法结果具有相当的准确性,求解速度比时间迭代方法提高了1~2个数量级。
对于复杂超声速流动,提出并实现了复杂超声速流动的区域推进求解方法,并运用在实际工程问题的求解中。复杂超声速流动的区域推进求解,按照流动的物理特征,沿主流方向划分为超声速占主导的区域或回流、亚声速占主导的区域。在超声速占主导的区域采用空间推进求解PNS方程的方法求解,在回流和亚声速占主导的区域采用时间迭代求解完全NS方程的方法求解。区域推进求解了典型二维复杂超声速流动,表明区域推进求解方法在求解复杂超声速流动时和时间迭代方法具有相同的准确性,且求解速度提高了数倍。在此基础上对吸气式高超声速飞行器的三维进气道、氢燃料三维超燃冲压发动机和碳氢燃料二维一体化整机进行了区域推进求解,以显示该方法的高效性以及在处理复杂工程问题中的灵活性。计算得到的结果和实验测量值以及时间迭代方法的结果一致,在求解效率上,对于三维氢燃料发动机,整个流场采用时间迭代方法求解,需要256个CPU(0.8GHz),5天时间得到一个状态的结果,而采用区域推进方法求解相同的流动状态,空间推进区域仅采用1个CPU(2.8GHz),时间迭代区域采用8个CPU(2.8GHz),总共只需要3天左右时间。
区域推进求解方法具有高效、灵活和可靠的特点。把区域推进方法做为自动优化设计过程中的CFD分析工具,结合优化外形的参数化描述以及计算网格的自动化生成,使用成熟的优化工具,实现了吸气式高超声速飞行器尾喷管的单目标和多目标自动优化设计。高效准确的湍流流动的CFD分析工具,使得一个设计循环仅需40秒左右时间,优化循环1000次仅耗时11个小时左右,整个优化过程在单个CPU上得以快速完成。优化后的尾喷管的升力和推力都有了较大的提高。
本文包含七章内容。第一章是引言,介绍研究工作的意义和国内外进展以及本文的研究内容。第二章介绍流动的时间迭代求解方法以及本文采用的先进壁面函数边界条件,验证了壁面函数边界条件在亚跨声速和超声速流动中的准确性以及本文采用的热完全气体模型。第三章采用本文开发的CFD软件,验证和确认了吸气式高超声速飞行器典型流态的气动热和气动力分布,计算了一体化高超声速飞行的气动热和气动力,为工程设计提供了可靠的气动热、气动力数据。第四章介绍了求解包含超声速层流、湍流和有限速率化学反应流动的空间推进求解方法,并对开发的空间推进程序进行了严格的验证确认和应用。第五章提出和实现了复杂超声速流动的区域推进求解,把该方法应用在了实际工程问题的求解中,取得了较好的计算结果和较高的求解效率。第六章结合流动的区域推进求解方法,完成了高超声速飞行器单壁膨胀尾喷管的自动优化设计,使尾喷管的性能得到了大的提高。第七章是本文的结束语。
The aims of this thesis are studying methods for accurate simulating aerodynamic heat&force of hypersonic/supersonic flows and the efficient numerical method for hypersonic/supersonic flows. There are two parts of works included in this thesis. The first part is the technologies of accurately simulating aerodynamic force and aerodynamic heat of supersonic flow and its applications in predicting the aerodynamic force and aerodynamic heat of hypersonic vehicle. The second part is the high efficient methods in solving supersonic flow, they are space marching and region marching methods, and their applications in solving complex engineering problems and in automatical aerodynamic optimization design.
Studying work related to accurate numerical simulation of aerodynanic force and heat and its apllications are as follows:
There is comparatively large velocity gradient between flow and solid surface in supersonic flow field, which leads to large velocity and temperature gradients producing comparatively large skin friction and aerodynamic heat. At the same time, there are laminar and turbulent flow conditions in most of supersonic flows. Numerical simulating technologies must have sufficient accuracy to predict the velocity and temperature gradients in laminar and turbulent conditions for accurately predicting the aerodynamic heat and force.
The time dependent methods of this thesis use cell-averaged finite volume techniques to solve the conservative form governing equations on structured grid. LU-SGS method is used in time-marching. In space terms difference, inviscid fluxes construction use third order MUSCL interpolation method and AUSMPW+ scheme, viscous fluxes use central difference method which base on the Gauss Law. Turbulence simulations use Kok’s modified k ?ωTNT 2-equation turbulence mode coupled with an advanced wall function boundary condition considering modification of compressibility and heat transfer and being valid in whole turbulence boundary layer.
Basing on the techniques introduced above, the accurate wall skin friction and wall heat flux can be gotten for laminar flows (normal grid Reynolds number Re n<80 for hypersonic cylinder flow) and for the turbulence flows (y+<200~300 assuming the constant shear stress hypothesis in the lower part of the boundary layer etc.) . For accurately predicting hypersonic vehicle’s flow fields, the characteristic flows in hypersonic vehicles are confirmed and validated by present CFD tool. The aerodynamic force and heat of a hypersonic vehicle are predicted in the power off, cruise conditions basing on the numerical confirmations described above. Wall heat flux and its maximum locations are obtained. In the maximum heat flux region, the maximum heat flux can beyond 3MW/m2. At the same time, aerodynamic force characters are acquired. The skin friction force, including inner inlet and combustion chamber friction force, possesses 62.7% of the whole drag force. Those data is very crucial to the heat protection and aerodynamic design of hypersonic vehicles.
Studying work related to pseudo-temporal space marching methods and region marching methods for complex supersonic flows and their applications are as follows: As having obtained accurate numerical prediction abilities for aero force and heat flux of supersonic flows, space marching ability of supersonic dominated flow field is fulfilled. Space marching methods use pseudo-temporal iteration and iteratively solve parabolic NS equations in the marching plane. The time iterating method in the marching plane uses modified LU-SGS methods. Inviscid fluxes of the space marching direction use first order or second order upwind difference. The construction of normal direction and spanwise inviscid fluxes uses third order MUSCL interpolation and AUSMPW+ scheme. Viscous and dissipation fluxes in the space marching direction are neglected and the remainder directions dissipation gradients of viscous fluxes are constructed basing on Guess Law. Space marching techniques are successfully used in supersonic dominated inviscid, laminar, turbulence and multi-species finite rate chemical reaction flow fields in 2D/3D and axisymmetric cases. Numerical results show that the space marching algorithms are agree well with experiment and have the same level of accuracy in solving supersonic dominated flow fields in comparison with time iteration methods, furthermore, present space marching algorithms are 1~2 orders faster than time iteration methods.
For complex supersonic flows, region marching methods are established and used in engineering problems. The region marching methods for complex supersonic flow fields divide the flow field in streamwise direction into supersonic flow dominated regions or reverse and subsonic flow dominated regions according to their physical characters. In the supersonic flow dominated region, flow field is solved by space marching algorithms and in the reverse and subsonic flow dominated region time iterating method is used. The 2D characteristic complex supersonic flow fields are solved using region marching methods. It shows that region marching method have the same level of accuracy as time iterating algorithms in dealing with complex supersonic flow, furthermore, region marching method accelerate the convergence speed several times compared with time iterating algorithms. The 3D inlet and hydrogen fueled Scramjet engine of hypersonic vehicle and 2D kerosene fuled whole areo-breathing engine are numerically simulated with region marching method to illustrate its high efficiency and easily using in complex engineering problems. The region marching results have good agreements with experimental results and time iterating results.
Considering about the computational efficiency, for 3D hydrogen fueled Scramjet case, it takes 5 days with 256 CPU processors (0.8GHz) to get on condition’s result for time iterating algorithm in the entire flow field. But it only takes 3 days with 1 CPU processor in the space marching regions and 8 CPU processors (2.8GHz) in the time iterating regions to get the same result for region marching method.
Because it’s high efficiency and easy using and accuracy, region marching method is used as the turbulence CFD analysis tool during the cycle of automatic design optimization. Combined with parametric description of optimization geometry and automatic grid generation, single and multi-objects automatic optimizations of single expansion ramp nozzle (SERN) of hypersonic vehicle are fulfilled using the sophisticated optimization tools. Because of using cheap and accurate CFD analysis software, only about 40 seconds are needed for one optimization cycle and 11 hours are needed for about 1000 optimization cycles. The optimization procedures can run quickly in a single CPU processor. The lift and propulsion force of the nozzle have improved significantly after the optimization.
Seven chapters are included in this thesis. The First chapter is the introduction. The meaning and development of researching work are introduced. In chapter 2, time iterating algorithms are introduced and wall function boundary conditions and thermally perfect gas model are validated. In the third chapter, the aerodynamic force and heat flux of the hypersonic vehicle and the characteristic flow conditions of hypersonic vehicle are simulated, those work provide reliable datum of heat flux and aero-force for engineering design. In chapter 4, the space marching algorithms of supersonic turbulent and chemical reaction flow included their validations are fulfilled. In chapter 5, the region marching method for complex supersonic flow fields and their applications in engineering problems are fulfilled. In chapter 6, combining region marching method for solving supersonic flow fields, automatic optimization design of hypersonic vehicle’s SERN nozzle is conducted. Chapter 7 is the conclusion of this thesis.
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