空间推进算法及超燃冲压发动机部件优化设计研究
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摘要
超燃冲压发动机是以高超声速巡航导弹、高超声速飞机和未来低成本可重复使用天地往返运输系统为应用背景的。以美国为首的各航天大国,都在加紧对其研究,并取得了一些技术突破。但就世界范围来说,目前关于这种发动机的许多技术难题仍然没有完全解决,在其工作规律、流场数值模拟,以及流动通道尤其是进气道和尾喷管的气动优化设计等方面,有许多问题需要进一步深入研究。其中,传统的时间迭代CFD方法计算效率太低,是亟待解决的关键技术之一,它严重影响了发动机流场大规模数值模拟的计算效率,制约了高精度CFD技术在发动机部件及一体化设计中的广泛应用。
围绕这一问题,论文主要开展了三方面的研究工作,即高性能(高效、低存储量和高精度)的超声速/高超声速流场计算方法SSPNS(Single-Sweep Parabolized Navier- Stokes Algorithm)的研究,多种优化方法的对比分析研究,以及超燃冲压发动机进气道和尾喷管气动优化设计研究。具体来说,论文主要开展了以下一些工作:
详细地介绍了LU-SGS(Lower-Upper Symmetric Gauss-Seidel)隐式积分方法及其改进形式,以及其在全NS方程(Full Navier-Stokes Equations,FNS)的时间迭代求解方法中的应用。通过5个算例的计算考察了典型迎风格式,包括矢通量分裂、通量差分分裂和混合型迎风格式,以及二阶NND格式,在超声速/高超声速流动中的粘性分辨率和间断分辨率的高低。结果表明,以AUSM系列格式和LDFSS格式为代表的混合型迎风格式分辨率较高,在超声速/高超声速流动数值模拟中综合性能最优。
讨论了抛物化NS方程(Parabolized Navier-Stokes Equations,PNS)的数学性质,对比分析了多种处理流向压力梯度的方法的优缺点。以此为基础,成功地将LU-SGS隐式时间积分方法推广到了PNS方程的流向空间积分上,发展了基于PNS方程的单次扫描空间推进算法SSPNS。在该算法中,横向无粘数值通量和粘性通量分别采用混合型迎风格式和中心格式求解。同时,对多次扫描空间推进算法FBIPNS进行了公式推导和初步算例研究。用SSPNS算法计算了5个典型流场,包括超声速平板流、15°压缩楔板流、带攻角的锥形流、双向垂直压缩角流和激波-边界层干扰平板流。前4个算例的SSPNS计算结果,与NASA UPS程序计算结果、相关文献提供的实验数据及理论分析结果,符合得很好。在对激波-边界层干扰平板流计算时,SSPNS算法没有模拟出平板上的流向分离现象;FBIPNS算法虽能准确给出分离点位置,但仍然未预测出再附点位置。进一步用SSPNS算法计算了4个高超声速进气道和2个尾喷管流场,得到的结果也与文献中相关数值解和实验结果基本一致,表明SSPNS法能够准确地模拟超燃冲发动机进气道和尾喷管内的高超声速流动。对比研究表明,SSPNS法与传统时间迭代法相比,二者计算精度相当,而SSPNS计算速度快1~2个量级,存储量至少低1个量级。
对比分析了基于梯度的传统优化方法和GA等全局优化方法的寻优机制,指出传统方法多属确定性方法,局部搜索能力强而全局搜索能力较弱,优化结果在很大程度上依赖于所选初值;GA则属于启发式随机搜索方法,全局搜索能力强而局部搜索能力较弱。与传统方法相比,遗传算法更适合求解多目标优化问题;组合优化方案则可提高优化设计的效率。此外,论文还较详细地分析了气动优化设计中的一些主要影响因素。
数值计算表明,文献中常采用的进气道设计方案(方案I),不能保证进气道低马赫数自起动。为此,论文给出了进气道设计方案II,从而很好地解决了进气道指定马赫数自起动问题。以进气道设计方案II为基础,将序列二次规划法(SQP)、多岛遗传算法(MIGA)、多目标遗传算法(NCGA和NSGA-II)等优化方法,与SSPNS流场计算方法相结合,在巡航点(Ma = 7.0)对二维高超声速进气道进行了单目标和多目标优化设计研究,包括总压恢复最大模型、有效动能效率最大模型和多目标优化模型等。优化设计结果表明,在有效动能效率最大模型中,由于过分强调阻力系数的作用,往往在阻力系数降低的同时,也使得进气道总压恢复和流量系数较低。较之单目标优化设计,多目标优化设计得到的进气道Pareto最优前沿,为设计者提供了关于各性能参数的更全面、更可靠的权衡信息。为了兼顾巡航点和加速爬升段的综合性能,采用多目标优化方法,对进气道进行了多点优化设计,并开展了基于等动压弹道的设计点选择问题研究。计算结果表明,若将设计点选在巡航点,则进气道爬升段的流量系数相对较低,且可变范围较小;若将设计点选在6.5左右,则进气道的综合性能较好。
采用相同的优化方法和流场数值模拟技术,对某二维高声速尾喷管即单壁扩张喷管进行了单目标和多目标气动优化设计,分别得到了喷管的最大推力设计和关于多个目标性能的Pareto最优前沿分布情况。以这些结果为基础,分析了尾喷管推力系数、升力系数和俯仰力矩系数的主要影响因素。
As a candidate powerplant for the hypersonic flight vehicles, scramjet has been studied extensively all over the world, but there are still many technical problems remaining unsolved, such as efficient flowfield simulation tools and aerodynamic integrated design tools, etc. The traditional CFD methods, i.e. time iterative algorithms based on Full Navier-Stokes (FNS) Equations, have achieved great development and been widely used in scramjet integrated design. But it is so time-consuming that it is very difficult to integrate them into the aerodynamic optimization design process of scramjet and its components.
A new single-sweep Parabolized Navier-Stokes algorithm (SSPNS), a highly accurate, highly efficient supersonic/hypersonic flowfield simulation method, is developed. And it is successfully used in the aerodynamic optimization design process of scramjet inlets and single expansion ramp nozzles (SERNs).
Firstly, a time iterative FNS algorithm is presented. It is a finite volume method (FVM) based on implicit lower-upper symmetric Gauss-Seidel (LU-SGS) time integration, and several typical upwind schemes, including van Leer scheme, Roe scheme, AUSM-family schemes, LDFSS schemes, and 2-order NND schemes, etc. Five typical flows, including 1D Sod tube, colliding flow, laminar/turbulent flat plate boundary flow, shock-boundary interaction on a flat plate and hypersonic inlet flow, are investigated using this method. Results show that the hybrid upwind schemes, such as AUSM-family schemes and LDFSS schemes, have higher viscous resolution and discontinuities resolution. They are applicable to supersonic/hypersonic flowfield simulations.
Secondly, theoretical analysis is focused on the mathematic properties about the Parabolized Navier-Stokes (PNS) Equations, especially on the treatment of streamwise pressure gradient. Then the original implicit time iterative LU-SGS method is successfully extended to integrate the PNS Equations in the streamwise space direction. And the space-marching algorithm SSPNS is formulated. Five typical flows, including supersonic flat plate flow, 15°ramp hypersonic flow, cone flows with different angles of attack, hypersonic corner flow, and shock-boundary interaction flow on a flat plate, are computed with the SSPNS codes. Numerical results of the first 3 examples agreed well with those obtained from NASA’s UPS PNS codes and experimental results by Tracy or Holden et al. The five-shock structure of the corner flow is also computed well. But the separation zone of the shock-boundary interaction flow is not captured satisfactorily. Several scramjet component flowfields, including 4 hypersonic inlet flows and 2 SERN flows, are also obtained with the SSPNS codes. Results of inlets, such as flow structures, wall pressure distributions, and friction coefficients, show good agreement with numerical results of UPS, SCRAMIN NS codes, and experimental results by NASA. SSPNS results of the 2D and 3D SERN flows also agree well with NASA’s experimental results. By comparison with the FNS flow solvers, the SSPNS codes show at least 1~2 order of magnitude speed faster and 1 order of magnitude of storage saving in the 3D side-compression hypersonic inlet flowfield simulation. All these numerical results prove that SSPNS is a highly efficient, highly accurate algorithm for steady supersonic/ hypersonic flows, especially for 3D cases.
Thirdly, theoretical comparison analysis is carried out between traditional gradient based optimization methods and global random optimization methods, such as Genetic Algorithms (GAs), etc. It is concluded that GAs are typical random heuristic methods, and more suitable for nonlinear discontinuous optimization problems than traditional methods.
Fourthly, a novel 2D inlet which can self-start at relay Mach number (Ma = 3.5) is designed. Then single- or multi-objective optimization designs of this 2D inlet are carried out on cruise operation point (Ma=7.0) by Sequential Quadratic Programming (SQP), Multi-Island GA (MIGA), and multi-objective GAs, including NCGA and NSGA-II. The inlet flowfields are calculated with SSPNS in these optimization design processes. Single objective optimization results show pressure recovery maximum model is better than effective kinetic energy coefficient maximum model. Multi-objective optimization results reveal the tradeoffs of pressure recovery, static pressure rise, and drag coefficients. Based on multi-objective design process, a two-point design and a design point choosing process are investigated. Results show if design point is set at cruise point, the off-design mass capture coefficients is relatively low; whereas if the design Mach number is 6.5, the 2D inlet will get good overall operation performances along the constant dynamic pressure trajectory.
Lastly, the same optimization design methods are applied to design several 2D SERNs. The single objective optimization design result shows that the objective, thrust coefficient is improved, but the lift coefficient is too small. In the 2- and 3-objective optimization design, tradeoffs of thrust coefficient, lift coefficient and pitching moment coefficient, are obtained.
围绕这一问题,论文主要开展了三方面的研究工作,即高性能(高效、低存储量和高精度)的超声速/高超声速流场计算方法SSPNS(Single-Sweep Parabolized Navier- Stokes Algorithm)的研究,多种优化方法的对比分析研究,以及超燃冲压发动机进气道和尾喷管气动优化设计研究。具体来说,论文主要开展了以下一些工作:
详细地介绍了LU-SGS(Lower-Upper Symmetric Gauss-Seidel)隐式积分方法及其改进形式,以及其在全NS方程(Full Navier-Stokes Equations,FNS)的时间迭代求解方法中的应用。通过5个算例的计算考察了典型迎风格式,包括矢通量分裂、通量差分分裂和混合型迎风格式,以及二阶NND格式,在超声速/高超声速流动中的粘性分辨率和间断分辨率的高低。结果表明,以AUSM系列格式和LDFSS格式为代表的混合型迎风格式分辨率较高,在超声速/高超声速流动数值模拟中综合性能最优。
讨论了抛物化NS方程(Parabolized Navier-Stokes Equations,PNS)的数学性质,对比分析了多种处理流向压力梯度的方法的优缺点。以此为基础,成功地将LU-SGS隐式时间积分方法推广到了PNS方程的流向空间积分上,发展了基于PNS方程的单次扫描空间推进算法SSPNS。在该算法中,横向无粘数值通量和粘性通量分别采用混合型迎风格式和中心格式求解。同时,对多次扫描空间推进算法FBIPNS进行了公式推导和初步算例研究。用SSPNS算法计算了5个典型流场,包括超声速平板流、15°压缩楔板流、带攻角的锥形流、双向垂直压缩角流和激波-边界层干扰平板流。前4个算例的SSPNS计算结果,与NASA UPS程序计算结果、相关文献提供的实验数据及理论分析结果,符合得很好。在对激波-边界层干扰平板流计算时,SSPNS算法没有模拟出平板上的流向分离现象;FBIPNS算法虽能准确给出分离点位置,但仍然未预测出再附点位置。进一步用SSPNS算法计算了4个高超声速进气道和2个尾喷管流场,得到的结果也与文献中相关数值解和实验结果基本一致,表明SSPNS法能够准确地模拟超燃冲发动机进气道和尾喷管内的高超声速流动。对比研究表明,SSPNS法与传统时间迭代法相比,二者计算精度相当,而SSPNS计算速度快1~2个量级,存储量至少低1个量级。
对比分析了基于梯度的传统优化方法和GA等全局优化方法的寻优机制,指出传统方法多属确定性方法,局部搜索能力强而全局搜索能力较弱,优化结果在很大程度上依赖于所选初值;GA则属于启发式随机搜索方法,全局搜索能力强而局部搜索能力较弱。与传统方法相比,遗传算法更适合求解多目标优化问题;组合优化方案则可提高优化设计的效率。此外,论文还较详细地分析了气动优化设计中的一些主要影响因素。
数值计算表明,文献中常采用的进气道设计方案(方案I),不能保证进气道低马赫数自起动。为此,论文给出了进气道设计方案II,从而很好地解决了进气道指定马赫数自起动问题。以进气道设计方案II为基础,将序列二次规划法(SQP)、多岛遗传算法(MIGA)、多目标遗传算法(NCGA和NSGA-II)等优化方法,与SSPNS流场计算方法相结合,在巡航点(Ma = 7.0)对二维高超声速进气道进行了单目标和多目标优化设计研究,包括总压恢复最大模型、有效动能效率最大模型和多目标优化模型等。优化设计结果表明,在有效动能效率最大模型中,由于过分强调阻力系数的作用,往往在阻力系数降低的同时,也使得进气道总压恢复和流量系数较低。较之单目标优化设计,多目标优化设计得到的进气道Pareto最优前沿,为设计者提供了关于各性能参数的更全面、更可靠的权衡信息。为了兼顾巡航点和加速爬升段的综合性能,采用多目标优化方法,对进气道进行了多点优化设计,并开展了基于等动压弹道的设计点选择问题研究。计算结果表明,若将设计点选在巡航点,则进气道爬升段的流量系数相对较低,且可变范围较小;若将设计点选在6.5左右,则进气道的综合性能较好。
采用相同的优化方法和流场数值模拟技术,对某二维高声速尾喷管即单壁扩张喷管进行了单目标和多目标气动优化设计,分别得到了喷管的最大推力设计和关于多个目标性能的Pareto最优前沿分布情况。以这些结果为基础,分析了尾喷管推力系数、升力系数和俯仰力矩系数的主要影响因素。
As a candidate powerplant for the hypersonic flight vehicles, scramjet has been studied extensively all over the world, but there are still many technical problems remaining unsolved, such as efficient flowfield simulation tools and aerodynamic integrated design tools, etc. The traditional CFD methods, i.e. time iterative algorithms based on Full Navier-Stokes (FNS) Equations, have achieved great development and been widely used in scramjet integrated design. But it is so time-consuming that it is very difficult to integrate them into the aerodynamic optimization design process of scramjet and its components.
A new single-sweep Parabolized Navier-Stokes algorithm (SSPNS), a highly accurate, highly efficient supersonic/hypersonic flowfield simulation method, is developed. And it is successfully used in the aerodynamic optimization design process of scramjet inlets and single expansion ramp nozzles (SERNs).
Firstly, a time iterative FNS algorithm is presented. It is a finite volume method (FVM) based on implicit lower-upper symmetric Gauss-Seidel (LU-SGS) time integration, and several typical upwind schemes, including van Leer scheme, Roe scheme, AUSM-family schemes, LDFSS schemes, and 2-order NND schemes, etc. Five typical flows, including 1D Sod tube, colliding flow, laminar/turbulent flat plate boundary flow, shock-boundary interaction on a flat plate and hypersonic inlet flow, are investigated using this method. Results show that the hybrid upwind schemes, such as AUSM-family schemes and LDFSS schemes, have higher viscous resolution and discontinuities resolution. They are applicable to supersonic/hypersonic flowfield simulations.
Secondly, theoretical analysis is focused on the mathematic properties about the Parabolized Navier-Stokes (PNS) Equations, especially on the treatment of streamwise pressure gradient. Then the original implicit time iterative LU-SGS method is successfully extended to integrate the PNS Equations in the streamwise space direction. And the space-marching algorithm SSPNS is formulated. Five typical flows, including supersonic flat plate flow, 15°ramp hypersonic flow, cone flows with different angles of attack, hypersonic corner flow, and shock-boundary interaction flow on a flat plate, are computed with the SSPNS codes. Numerical results of the first 3 examples agreed well with those obtained from NASA’s UPS PNS codes and experimental results by Tracy or Holden et al. The five-shock structure of the corner flow is also computed well. But the separation zone of the shock-boundary interaction flow is not captured satisfactorily. Several scramjet component flowfields, including 4 hypersonic inlet flows and 2 SERN flows, are also obtained with the SSPNS codes. Results of inlets, such as flow structures, wall pressure distributions, and friction coefficients, show good agreement with numerical results of UPS, SCRAMIN NS codes, and experimental results by NASA. SSPNS results of the 2D and 3D SERN flows also agree well with NASA’s experimental results. By comparison with the FNS flow solvers, the SSPNS codes show at least 1~2 order of magnitude speed faster and 1 order of magnitude of storage saving in the 3D side-compression hypersonic inlet flowfield simulation. All these numerical results prove that SSPNS is a highly efficient, highly accurate algorithm for steady supersonic/ hypersonic flows, especially for 3D cases.
Thirdly, theoretical comparison analysis is carried out between traditional gradient based optimization methods and global random optimization methods, such as Genetic Algorithms (GAs), etc. It is concluded that GAs are typical random heuristic methods, and more suitable for nonlinear discontinuous optimization problems than traditional methods.
Fourthly, a novel 2D inlet which can self-start at relay Mach number (Ma = 3.5) is designed. Then single- or multi-objective optimization designs of this 2D inlet are carried out on cruise operation point (Ma=7.0) by Sequential Quadratic Programming (SQP), Multi-Island GA (MIGA), and multi-objective GAs, including NCGA and NSGA-II. The inlet flowfields are calculated with SSPNS in these optimization design processes. Single objective optimization results show pressure recovery maximum model is better than effective kinetic energy coefficient maximum model. Multi-objective optimization results reveal the tradeoffs of pressure recovery, static pressure rise, and drag coefficients. Based on multi-objective design process, a two-point design and a design point choosing process are investigated. Results show if design point is set at cruise point, the off-design mass capture coefficients is relatively low; whereas if the design Mach number is 6.5, the 2D inlet will get good overall operation performances along the constant dynamic pressure trajectory.
Lastly, the same optimization design methods are applied to design several 2D SERNs. The single objective optimization design result shows that the objective, thrust coefficient is improved, but the lift coefficient is too small. In the 2- and 3-objective optimization design, tradeoffs of thrust coefficient, lift coefficient and pitching moment coefficient, are obtained.
引文
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