高超声速流动的磁流体力学控制数值模拟研究
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摘要
采用MHD(磁流体动力学)方法实现高超声速流动控制是一种新颖的流动控制概念,与常规空气动力学方法采用的飞行器表面气流接触式干扰不同,MHD方法不改变飞行器外形,而是通过电磁场对电离流场进行有距离影响,这是MHD流动控制方法具有的最大优点。此类方法具有较大地改善高超声速飞行器性能的潜力,包括防热控制,增加进气道流量捕获、增强燃烧室燃烧效率等。
本文针对高超声速MHD流动控制概念,基于磁流体动力学数值模拟方法研究,结合理论分析进行了数值模拟与控制机理分析。工作包括高超声速MHD数值方法研究和高超声速MHD流动控制模拟与机理研究两大部分。
第一部分为MHD数值模拟方法研究。MHD流动依据特征磁雷诺数分为高磁雷诺数和低磁雷诺数两大类,分别对应于全MHD方程组形式和低磁雷诺数近似方程组形式。本文分别针对这两种形式发展了相应的数值模拟方法。
全MHD方程组形式对应于磁雷诺数较高情况,针对当前研究中存在的伪磁场散度问题、方程组奇性和修正形式的守恒性问题,本文提出了八波形式方程附加源项的模拟形式,该方法同时具备八波形式和原七波MHD方程组的优点,既可以采用八波形式特征向量,同时又保证方程组整体守恒。在数值方法上,将CFD模拟中采用的有限体积方法、Roe的近似Riemann求解器、OC-TVD限制器以及时间格式推广到MHD模拟中。此外,作为全MHD模拟的辅助步骤,本文建立了三维投影方法,能够有效清除磁场的伪散度。
低磁雷诺数MHD方程组的求解形式较全MHD方程组形式简单,为了使之能够更好地实现高超声速复杂流场结构变化的精细捕捉,提高计算效率,本文发展了一套完整的三维自适应各向异性叉树网格方法应用于低磁雷诺数MHD流动模拟。该网格方法的工作主要包括:建立了三维叉树形网格的数据结构,以及在此基础上完善了包括自适应判别、合并/分裂、网格级别审查等步骤,并提出了对流场结构进行“保护”性加密等网格优化方式,实现了对激波等流场结构的细致捕捉。
针对上述发展的数值模拟方法,本文编制了三维结构网格全MHD流动模拟程序FMHD,三维结构网格低磁雷诺数MHD流动模拟程序LSMHD,以及三维各向异性叉树网格低磁雷诺数MHD流动程序LTMHD。这些程序经过了多个经典算例的计算,验证了其有效性和准确性,能够应用于针对高超声速飞行器MHD流动控制的模拟中。
第二部分为高超声速MHD流动控制机理研究。本文主要结合理论分析,开展了钝体MHD防热控制和斜激波MHD控制的模拟研究,并对控制机理进行了分析。
对于马赫5来流,考虑理想气体,且假设激波层内电导率均布的高超声速钝头绕流,气动热MHD控制的数值模拟结果显示,随着控制磁场的加强,弓形激波脱体距离增大,壁面压强变化很小,而热流降低比较明显,在驻点互涉参数Q=6时热流下降了26%。
基于高温空气电导率模型和化学平衡热力学关系,成功进行了40km高空马赫15钝头MHD绕流数值模拟。结果显示考虑空气化学平衡效应的驻点热流小于理想气体。随着互涉参数Q的增大,弓形激波脱体距离增大,但很小,而热流降低比较明显,在驻点互涉参数Q=6时热流下降了24%。模拟结果说明了MHD钝体热流控制在很高马赫数下的可行性。
数值研究了高磁雷诺数的理想无粘斜激波MHD流动控制规律。模拟清晰地捕捉到激波结构。磁场大小和方向对流场和激波影响较大。在多数磁场较大情况下得到了MHD流动特有的快—慢激波结构;而磁场垂直于来流方向时,始终未有慢激波产生。这些现象都通过群速度图方法进行了理论上的解释。
数值研究了低磁雷诺数无粘MHD斜激波流动控制规律,自由来流马赫数6,考虑电子束激发使局部区域产生电导率,采用自适应各向异性叉树网格。结果显示,MHD作用能够使斜激波向远离壁面的方向偏离,激波控制效应明显。磁场和电导率的大小是MHD作用的决定性因素,且磁场垂直与来流时,MHD作用更明显。
高超声速进气道前体MHD激波控制是一项重要的MHD应用,本文将MHD斜激波控制方法应用于二级马赫6进气道前体激波控制,结果显示,在飞行器飞行马赫数大于设计马赫数时,MHD激波控制可使激波偏折,两级激波重新交汇到进气道唇缘上,使流动状态更佳。来流马赫数增大时,增大控制磁场仍可很好达到这一效果。该结果对进气道的优化设计具有参考价值。
MHD (Magnetohydrodynamics) flow control is a new concept for hypersonic vehicle. In ordinary aerodynamics, flow control has to disturb flow by touching. But in MHD concept, it could be carried out by magnetic field and electric field, with the advantage of not modify configuration of vehicle. In the aerospace community, the MHD research has shown great potential in flow control associated with hypersonic vehicles and propulsion systems. The applications mainly include heating reduction, air capture increase and combustion mixing enhancement.
In this thesis, basing on MHD numerical technologies and theoretical analytical methods, hypersonic flow control phenomena and mechanisms were investigated. There are two main parts in this work, research of MHD numerical algorithms and analysis of MHD phenomena.
The first part is the research of MHD numerical technologies. MHD flow is distinguished into two types, high Re_m (Magnetic Reynolds Number) and low Re_m. They correspond to full MHD equations and low Re_m equations respectively. Numerical algorithms for these two types were developed.
For full MHD equations, aiming at spurious magnetic field divergence problem, equations singularity and conservation problem, a form of eight-waves with source term was proposed. This form has the advantages of eight-wave eigenvectors and monolithic conservation of equations. Numerically, a 3-D Roe solver by means of finite volume formulation, OC-TVD scheme and temporal scheme were applied. 3-D projection scheme was used to modify magnetic field from basic scheme, which could clear the spurious magnetic field divergence effectively.
It is simpler in numerical algorithms for Low Re_m MHD equations than that for full MHD equations. In order to capture hypersonic flow field structures clearly, and to improve computational efficiently, a 3-D anisotropic self-adaptive tree mesh technology was built for low Re_m MHD flow simulation. A suit of algorithms for tree mesh were developed, including data structure form for 3-D tree mesh, self-adaptive distinguishing, mergence/ cleavage, and audit for levels of adjacent cells. Some other steps, protective refinement and local mergence/ cleavage control, were used for mesh optimization.
Forementioned numerical algorithms were realized in Fortran codes, including FMHD(3-D full MHD code with structural mesh), LSMHD(3-D low Re_m MHD code with structural mesh), LTMHD(3-D low Re_m MHD code with tree mesh). These codes were validated to be accurate by multiple classical MHD problems. It shows they could be used for hypersonic vehicle MHD flow control.
The second part is mechanism research for hypersonic MHD flow control. Heating reduction control for flow over blunt and oblique shock control were investigated, and results were compared with that for theoretical analysis.
Cases for Mach 5 perfect gas flow over a 3-D blunt were studied. The assumption is that electric conductivity is unique in post-shock area. Simulation results show that shock standoff distance increases significantly. And it shows obvious reduction effect on wall heat transfer in the vicinity of the stagnation point (26% reduction for the interaction parameter Q = 6), but a slight variation on wall pressure.
Cases for Mach 15 flow over a 3-D blunt were studied. The altitude is 40km. Models for electric conductivity of air and high temperature chiemical equilibrium relations were developed for MHD simulation. Results show heat transfer in stagnation point is lower than that of perfect gas. Shock standoff distance increases, but it is not insignificantly. There is 24% reduction for the interaction parameter Q = 6.
Full-MHD numerical investigation for Mach 10 flow over a perfectly conducting corner was carried out. Shock structure was captured clearly. Results show that magnitude and direction of magnetic field have important impact on MHD effect. Fast-slow shock structure appears in the field in most cases of high magnetic field. When magnetic field vector is perpendicular to free stream, there's no slow shock. These phenomena were all explained by group velocity diagram method.
Research for low Re_m Mach 6 MHD inviscous oblique shock was carried out. A partial area of flow field was ionized by electron beam. Results show that the magnetic field compels shock deflexed obviously. Magnitudes of magnetic field and electric conductivity were determinant. When magnetic field vector is perpendicular to free stream, shock deflexes more obviously.
MHD control for inlet of hypersonic vehicle is one important application. MHD oblique control was applied to a two-stage Mach 6 inlet. Results show that, when free Mach number is higher than designed, MHD oblique shock control method can be used to change inlet shocks, and make them converging in cowl slip, which is the optimal case desired by designers. With the increase of velocity of free stream, if magnitude of magnetic field increases properly, the optimal case can also realize.
本文针对高超声速MHD流动控制概念,基于磁流体动力学数值模拟方法研究,结合理论分析进行了数值模拟与控制机理分析。工作包括高超声速MHD数值方法研究和高超声速MHD流动控制模拟与机理研究两大部分。
第一部分为MHD数值模拟方法研究。MHD流动依据特征磁雷诺数分为高磁雷诺数和低磁雷诺数两大类,分别对应于全MHD方程组形式和低磁雷诺数近似方程组形式。本文分别针对这两种形式发展了相应的数值模拟方法。
全MHD方程组形式对应于磁雷诺数较高情况,针对当前研究中存在的伪磁场散度问题、方程组奇性和修正形式的守恒性问题,本文提出了八波形式方程附加源项的模拟形式,该方法同时具备八波形式和原七波MHD方程组的优点,既可以采用八波形式特征向量,同时又保证方程组整体守恒。在数值方法上,将CFD模拟中采用的有限体积方法、Roe的近似Riemann求解器、OC-TVD限制器以及时间格式推广到MHD模拟中。此外,作为全MHD模拟的辅助步骤,本文建立了三维投影方法,能够有效清除磁场的伪散度。
低磁雷诺数MHD方程组的求解形式较全MHD方程组形式简单,为了使之能够更好地实现高超声速复杂流场结构变化的精细捕捉,提高计算效率,本文发展了一套完整的三维自适应各向异性叉树网格方法应用于低磁雷诺数MHD流动模拟。该网格方法的工作主要包括:建立了三维叉树形网格的数据结构,以及在此基础上完善了包括自适应判别、合并/分裂、网格级别审查等步骤,并提出了对流场结构进行“保护”性加密等网格优化方式,实现了对激波等流场结构的细致捕捉。
针对上述发展的数值模拟方法,本文编制了三维结构网格全MHD流动模拟程序FMHD,三维结构网格低磁雷诺数MHD流动模拟程序LSMHD,以及三维各向异性叉树网格低磁雷诺数MHD流动程序LTMHD。这些程序经过了多个经典算例的计算,验证了其有效性和准确性,能够应用于针对高超声速飞行器MHD流动控制的模拟中。
第二部分为高超声速MHD流动控制机理研究。本文主要结合理论分析,开展了钝体MHD防热控制和斜激波MHD控制的模拟研究,并对控制机理进行了分析。
对于马赫5来流,考虑理想气体,且假设激波层内电导率均布的高超声速钝头绕流,气动热MHD控制的数值模拟结果显示,随着控制磁场的加强,弓形激波脱体距离增大,壁面压强变化很小,而热流降低比较明显,在驻点互涉参数Q=6时热流下降了26%。
基于高温空气电导率模型和化学平衡热力学关系,成功进行了40km高空马赫15钝头MHD绕流数值模拟。结果显示考虑空气化学平衡效应的驻点热流小于理想气体。随着互涉参数Q的增大,弓形激波脱体距离增大,但很小,而热流降低比较明显,在驻点互涉参数Q=6时热流下降了24%。模拟结果说明了MHD钝体热流控制在很高马赫数下的可行性。
数值研究了高磁雷诺数的理想无粘斜激波MHD流动控制规律。模拟清晰地捕捉到激波结构。磁场大小和方向对流场和激波影响较大。在多数磁场较大情况下得到了MHD流动特有的快—慢激波结构;而磁场垂直于来流方向时,始终未有慢激波产生。这些现象都通过群速度图方法进行了理论上的解释。
数值研究了低磁雷诺数无粘MHD斜激波流动控制规律,自由来流马赫数6,考虑电子束激发使局部区域产生电导率,采用自适应各向异性叉树网格。结果显示,MHD作用能够使斜激波向远离壁面的方向偏离,激波控制效应明显。磁场和电导率的大小是MHD作用的决定性因素,且磁场垂直与来流时,MHD作用更明显。
高超声速进气道前体MHD激波控制是一项重要的MHD应用,本文将MHD斜激波控制方法应用于二级马赫6进气道前体激波控制,结果显示,在飞行器飞行马赫数大于设计马赫数时,MHD激波控制可使激波偏折,两级激波重新交汇到进气道唇缘上,使流动状态更佳。来流马赫数增大时,增大控制磁场仍可很好达到这一效果。该结果对进气道的优化设计具有参考价值。
MHD (Magnetohydrodynamics) flow control is a new concept for hypersonic vehicle. In ordinary aerodynamics, flow control has to disturb flow by touching. But in MHD concept, it could be carried out by magnetic field and electric field, with the advantage of not modify configuration of vehicle. In the aerospace community, the MHD research has shown great potential in flow control associated with hypersonic vehicles and propulsion systems. The applications mainly include heating reduction, air capture increase and combustion mixing enhancement.
In this thesis, basing on MHD numerical technologies and theoretical analytical methods, hypersonic flow control phenomena and mechanisms were investigated. There are two main parts in this work, research of MHD numerical algorithms and analysis of MHD phenomena.
The first part is the research of MHD numerical technologies. MHD flow is distinguished into two types, high Re_m (Magnetic Reynolds Number) and low Re_m. They correspond to full MHD equations and low Re_m equations respectively. Numerical algorithms for these two types were developed.
For full MHD equations, aiming at spurious magnetic field divergence problem, equations singularity and conservation problem, a form of eight-waves with source term was proposed. This form has the advantages of eight-wave eigenvectors and monolithic conservation of equations. Numerically, a 3-D Roe solver by means of finite volume formulation, OC-TVD scheme and temporal scheme were applied. 3-D projection scheme was used to modify magnetic field from basic scheme, which could clear the spurious magnetic field divergence effectively.
It is simpler in numerical algorithms for Low Re_m MHD equations than that for full MHD equations. In order to capture hypersonic flow field structures clearly, and to improve computational efficiently, a 3-D anisotropic self-adaptive tree mesh technology was built for low Re_m MHD flow simulation. A suit of algorithms for tree mesh were developed, including data structure form for 3-D tree mesh, self-adaptive distinguishing, mergence/ cleavage, and audit for levels of adjacent cells. Some other steps, protective refinement and local mergence/ cleavage control, were used for mesh optimization.
Forementioned numerical algorithms were realized in Fortran codes, including FMHD(3-D full MHD code with structural mesh), LSMHD(3-D low Re_m MHD code with structural mesh), LTMHD(3-D low Re_m MHD code with tree mesh). These codes were validated to be accurate by multiple classical MHD problems. It shows they could be used for hypersonic vehicle MHD flow control.
The second part is mechanism research for hypersonic MHD flow control. Heating reduction control for flow over blunt and oblique shock control were investigated, and results were compared with that for theoretical analysis.
Cases for Mach 5 perfect gas flow over a 3-D blunt were studied. The assumption is that electric conductivity is unique in post-shock area. Simulation results show that shock standoff distance increases significantly. And it shows obvious reduction effect on wall heat transfer in the vicinity of the stagnation point (26% reduction for the interaction parameter Q = 6), but a slight variation on wall pressure.
Cases for Mach 15 flow over a 3-D blunt were studied. The altitude is 40km. Models for electric conductivity of air and high temperature chiemical equilibrium relations were developed for MHD simulation. Results show heat transfer in stagnation point is lower than that of perfect gas. Shock standoff distance increases, but it is not insignificantly. There is 24% reduction for the interaction parameter Q = 6.
Full-MHD numerical investigation for Mach 10 flow over a perfectly conducting corner was carried out. Shock structure was captured clearly. Results show that magnitude and direction of magnetic field have important impact on MHD effect. Fast-slow shock structure appears in the field in most cases of high magnetic field. When magnetic field vector is perpendicular to free stream, there's no slow shock. These phenomena were all explained by group velocity diagram method.
Research for low Re_m Mach 6 MHD inviscous oblique shock was carried out. A partial area of flow field was ionized by electron beam. Results show that the magnetic field compels shock deflexed obviously. Magnitudes of magnetic field and electric conductivity were determinant. When magnetic field vector is perpendicular to free stream, shock deflexes more obviously.
MHD control for inlet of hypersonic vehicle is one important application. MHD oblique control was applied to a two-stage Mach 6 inlet. Results show that, when free Mach number is higher than designed, MHD oblique shock control method can be used to change inlet shocks, and make them converging in cowl slip, which is the optimal case desired by designers. With the increase of velocity of free stream, if magnitude of magnetic field increases properly, the optimal case can also realize.
引文
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