高超声速气动热数值模拟方法及大规模并行计算研究
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摘要
气动热一直是设计人员极为关切的重要问题。高速飞行器以超声速或高超声速在空中飞行,对前方气体剧烈压缩和粘性阻滞,使温度急剧升高,并产生离解、电离等反应,带来“热障”和“黑障”等一系问题。气动热对飞行器带来较大影响,必须准确预测飞行器的热环境,为热防护提供指导和参考。
本文对高超声速气动热开展了数值模拟研究。考虑量热完全气体条件和高温热化学非平衡条件建立了数值模拟方法,基于消息传递库,发展了两种气体模型的高超声速气动热并行计算方法,编制了相应的计算程序,开展了气动热并行计算研究。
通过对8种差分格式的计算分析,对比了各种格式对膨胀波、激波及接触间断的分辨率,讨论了各种格式的粘性机理和优劣。计算表明,差分格式对间断和粘性的处理,是提高格式精度和影响格式优劣的关键。其中迎风类格式具有符合信息的传播方向和耗散性能的天然优势,是当今格式发展的主流。其中AUSM类格式兼有FVS和FDS的优势,表现出良好的性能。应用五种限制器针对激波管Riemann问题进行了计算分析,研究表明采用限制器,通过MUSCL高阶插值方法,可以有效提高的计算效率和计算精度。使用中,应权衡压缩性和耗散性,合理选择限制器。
建立了量热完全气体模型的气动热数值模拟方法,对气动热数值模拟中的网格因素和收敛性进行了深入研究。气动热的数值模拟中,网格因素非常关键,计算结果对网格,特别是壁面附近的法向网格间距十分敏感。近壁面的巨大温度梯度是网格相关性敏感的主要原因。气动热数值模拟实践经验表明,壁面第一层网格雷诺数小于10的网格判别标准相对简单有效。气动热计算的收敛比压力缓慢的多,以压力和方程残值下降量级作为热流收敛判别标准是不适合的;而以机器零点为判别保证收敛,但太过耗时。相对而言,直接观察气动热数据的收敛是比较有效的方法。
建立了高温热化学非平衡条件下的气动热数值模拟方法,采用包含Park双温模型、Gupta空气多组分和有限速率化学反应模型的全NS方程进行气动热数值求解。对化学生成和振动能源项采用了隐式处理,发展了带有源项的LU-SGS数值求解方法,提高了计算效率。利用所建立的数值模拟方法,对二维和三维算例进行了气动热数值模拟研究,分析了热化学非平衡条件下,不同非平衡模型、热流构成及催化壁的影响。计算表明所建立的热化学非平衡流数值模拟方法具有较高的精度。
基于消息传递库(MPI),对量热完全气体模型和热化学非平衡模型的气动热数值模拟程序并行化处理,发展了适合复杂外形的多区大规模并行气动热计算软件。在自行搭建的PC集群并行系统和高性能集群系统上,通过多个算例,开展了气动热计算与分析,计算结果表明所发展的气动热并行计算软件具有较高的计算精度、并行效率和良好可扩展性,可以应用下进一步的工程计算中。
Aeroheating has been an important issue for hypersonic vehicles. As hypersonic vehicles fly through the atmosphere, the kinetic energy associated with high velocity is converted into increasing the temperature of the air and into endothermic reactions, such as dissociation and ionization of the air near the vehicle surface. High temperature causes“thermal barrier”and“black barrier”problems which will bring a great impact on the aircraft. Thus we must accurately predict thermal environment and provide guidance and reference for thermal protection.
The present dissertation is about research of numerical simulation methods and hypersonic aerothermal computations. Numerical methods were conducted for calorically perfect gas and high temperature thermochemical nonequilibrium gas. Using MPI(Message Passing Interface), parallel methods were developed. Hypersonic computation softwares based on the above methods for the two gas models were coded, and massive parallel computations were carried out for hypersonic aeroheating problem.
Eight difference schemes and five limiters are applied in numerical computation of Riemann problem. Performance of each scheme is compared for expansion wave, shock discontinuity and contact discontinuity simulation. Numerical dissipation and it’s expediency are discussed. The computation shows that the ability to resolve viscosity and discontinuity is vital to improve scheme’s accuracy and quality. The upwind schemes which accord with feature wave propagating direction and avoid the use of artificial viscosity by being inherently dissipative have been the mainstream of current scheme development. AUSM scheme, combining the efficiency of FVS(Flux Vector Splitting) and the accuracy of FDS(Flux Difference Splitting) has favorable properties. MUSCL method is effective to increase computational efficiency and precision. Limiter should be selected appropriately by balancing compressive and diffusive performance.
Hypersonic aerothermal simulation method for calorically perfect gas flow is conducted, Grid effect and iteration convergence are investigated using CFD(Computational Fluid Dynamics) method in blunt flow. Grid effect is crucial to aerothermal simulation. Heat transfer prediction is very sensitive to grid spacing in normal direction near the wall. Great temperature grad result in grid sensitivity for heat transfer simulation. The computation showed that the Cell Reynolds Numbers<10 is the effective criterion for computation mesh. Aeroheating computation converged slower than pressure and flow field significantly. When accurate surface-pressure is worked out it can not guarantee converged heat-transfer values. Judging with Machine Zero can guarantee heat flux convergence but is a little time-consuming. Observing convergence of heat flux directly is an effective method. It is considered that viscosity charging in boundary layer induce to slow heat transfer convergence.
Hypersonic aerothermal simulation method for High temperature thermochemical nonequilibrium flow is developed. The reacting Navier-Stokes equations including Park’s two temperature model, Gupta’s air multi-species reaction model and vibrational relaxation were solved to compute aerothermal load. chemical and vibrational source terms are calculated implicitly which diminishs the stiffness of the calculation, accelerates the calculation’s convergence. The LU-SGS numerical method with source terms was deduced to do the hypersonic aerothermal computation in thermochemical nonequilibrium flow which improves the calculation’s efficiency. The researches on different nonequilibrium models, heat flux constitute and surface catalysis property were discussed. The numerical results are compared to available experimental data, which proved that the proposed methods are of higher-order accuracy.
Parallel computation of hypersonic flow field was performed with computational fluid dynamics method. Based on MPI(Message Passing Interface) the CFD parallel aeroheating computation program both for ideal gas flow and high temperature nonequilibrium flow was developed. Multi-blocks parallel aeroheating computation for several cases were performed in PC cluster and high performance cluster system. The computation results indicate that the program and method were acceptable, and could be used for following massive parallel computation and engineering application.
本文对高超声速气动热开展了数值模拟研究。考虑量热完全气体条件和高温热化学非平衡条件建立了数值模拟方法,基于消息传递库,发展了两种气体模型的高超声速气动热并行计算方法,编制了相应的计算程序,开展了气动热并行计算研究。
通过对8种差分格式的计算分析,对比了各种格式对膨胀波、激波及接触间断的分辨率,讨论了各种格式的粘性机理和优劣。计算表明,差分格式对间断和粘性的处理,是提高格式精度和影响格式优劣的关键。其中迎风类格式具有符合信息的传播方向和耗散性能的天然优势,是当今格式发展的主流。其中AUSM类格式兼有FVS和FDS的优势,表现出良好的性能。应用五种限制器针对激波管Riemann问题进行了计算分析,研究表明采用限制器,通过MUSCL高阶插值方法,可以有效提高的计算效率和计算精度。使用中,应权衡压缩性和耗散性,合理选择限制器。
建立了量热完全气体模型的气动热数值模拟方法,对气动热数值模拟中的网格因素和收敛性进行了深入研究。气动热的数值模拟中,网格因素非常关键,计算结果对网格,特别是壁面附近的法向网格间距十分敏感。近壁面的巨大温度梯度是网格相关性敏感的主要原因。气动热数值模拟实践经验表明,壁面第一层网格雷诺数小于10的网格判别标准相对简单有效。气动热计算的收敛比压力缓慢的多,以压力和方程残值下降量级作为热流收敛判别标准是不适合的;而以机器零点为判别保证收敛,但太过耗时。相对而言,直接观察气动热数据的收敛是比较有效的方法。
建立了高温热化学非平衡条件下的气动热数值模拟方法,采用包含Park双温模型、Gupta空气多组分和有限速率化学反应模型的全NS方程进行气动热数值求解。对化学生成和振动能源项采用了隐式处理,发展了带有源项的LU-SGS数值求解方法,提高了计算效率。利用所建立的数值模拟方法,对二维和三维算例进行了气动热数值模拟研究,分析了热化学非平衡条件下,不同非平衡模型、热流构成及催化壁的影响。计算表明所建立的热化学非平衡流数值模拟方法具有较高的精度。
基于消息传递库(MPI),对量热完全气体模型和热化学非平衡模型的气动热数值模拟程序并行化处理,发展了适合复杂外形的多区大规模并行气动热计算软件。在自行搭建的PC集群并行系统和高性能集群系统上,通过多个算例,开展了气动热计算与分析,计算结果表明所发展的气动热并行计算软件具有较高的计算精度、并行效率和良好可扩展性,可以应用下进一步的工程计算中。
Aeroheating has been an important issue for hypersonic vehicles. As hypersonic vehicles fly through the atmosphere, the kinetic energy associated with high velocity is converted into increasing the temperature of the air and into endothermic reactions, such as dissociation and ionization of the air near the vehicle surface. High temperature causes“thermal barrier”and“black barrier”problems which will bring a great impact on the aircraft. Thus we must accurately predict thermal environment and provide guidance and reference for thermal protection.
The present dissertation is about research of numerical simulation methods and hypersonic aerothermal computations. Numerical methods were conducted for calorically perfect gas and high temperature thermochemical nonequilibrium gas. Using MPI(Message Passing Interface), parallel methods were developed. Hypersonic computation softwares based on the above methods for the two gas models were coded, and massive parallel computations were carried out for hypersonic aeroheating problem.
Eight difference schemes and five limiters are applied in numerical computation of Riemann problem. Performance of each scheme is compared for expansion wave, shock discontinuity and contact discontinuity simulation. Numerical dissipation and it’s expediency are discussed. The computation shows that the ability to resolve viscosity and discontinuity is vital to improve scheme’s accuracy and quality. The upwind schemes which accord with feature wave propagating direction and avoid the use of artificial viscosity by being inherently dissipative have been the mainstream of current scheme development. AUSM scheme, combining the efficiency of FVS(Flux Vector Splitting) and the accuracy of FDS(Flux Difference Splitting) has favorable properties. MUSCL method is effective to increase computational efficiency and precision. Limiter should be selected appropriately by balancing compressive and diffusive performance.
Hypersonic aerothermal simulation method for calorically perfect gas flow is conducted, Grid effect and iteration convergence are investigated using CFD(Computational Fluid Dynamics) method in blunt flow. Grid effect is crucial to aerothermal simulation. Heat transfer prediction is very sensitive to grid spacing in normal direction near the wall. Great temperature grad result in grid sensitivity for heat transfer simulation. The computation showed that the Cell Reynolds Numbers<10 is the effective criterion for computation mesh. Aeroheating computation converged slower than pressure and flow field significantly. When accurate surface-pressure is worked out it can not guarantee converged heat-transfer values. Judging with Machine Zero can guarantee heat flux convergence but is a little time-consuming. Observing convergence of heat flux directly is an effective method. It is considered that viscosity charging in boundary layer induce to slow heat transfer convergence.
Hypersonic aerothermal simulation method for High temperature thermochemical nonequilibrium flow is developed. The reacting Navier-Stokes equations including Park’s two temperature model, Gupta’s air multi-species reaction model and vibrational relaxation were solved to compute aerothermal load. chemical and vibrational source terms are calculated implicitly which diminishs the stiffness of the calculation, accelerates the calculation’s convergence. The LU-SGS numerical method with source terms was deduced to do the hypersonic aerothermal computation in thermochemical nonequilibrium flow which improves the calculation’s efficiency. The researches on different nonequilibrium models, heat flux constitute and surface catalysis property were discussed. The numerical results are compared to available experimental data, which proved that the proposed methods are of higher-order accuracy.
Parallel computation of hypersonic flow field was performed with computational fluid dynamics method. Based on MPI(Message Passing Interface) the CFD parallel aeroheating computation program both for ideal gas flow and high temperature nonequilibrium flow was developed. Multi-blocks parallel aeroheating computation for several cases were performed in PC cluster and high performance cluster system. The computation results indicate that the program and method were acceptable, and could be used for following massive parallel computation and engineering application.
引文
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