高超声速多场耦合及其GPU计算加速技术研究
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摘要
高超声速飞行器，由于其飞行环境中存在激波边界层干扰、高温流动等复杂物理现象，给研制工作带来了一系列新的课题，尤其体现在气动热弹性等问题中，也是目前国际上的研究热点之一。解决这些问题的基础已经远远超出常规的气动弹性力学范畴，必须计入高温气体效应、边界层效应、结构热传导和热辐射等研究内容。它们具有流-固-热多场耦合和计算密集型特点，需要计算流体力学（CFD）、计算结构动力学（CSD）、计算传热学（CTD）等多个学科的相互配合，对理论分析和计算能力都是一个很大的挑战，目前已有的成功分析还较少。本文针对上述问题开展了以下研究工作：
针对化学反应非平衡流N-S方程，对隐式时间离散格式中的对流项、粘性项及源项的雅可比矩阵表达式进行了推导。采用Menter’SST两方程湍流模型、Roe格式、AUSM+-up格式及LUSGS方法编制了高超声速CFD计算程序，并通过典型算例验证其正确性，为后续研究工作提供基本计算手段。
从GPU架构特点出发，发展了基于数据并行的隐式CFD求解方法，适用于结构和非结构网格。采用CUDA技术，通过数据结构和算法优化，在GPU上成功实现了高超声速CFD计算。分别在Intel Core2Quad3.0GHz CPU和NVIDIA GTX280GPU上进行了数值仿真，结果表明隐式格式计算速度是显式格式6倍以上，采用显式格式的加速比达到28倍，采用隐式格式加速比达到了28.7倍，同时加速比随问题规模的增加而增加。仿真结果和实验值吻合良好。该工作可为后续研究提供快速计算手段。
依据几何关系及插值特点，提出了一种带旋转修正的TFI动网格方法，用来解决传统TFI方法在粘性网格和网格大变形时引起的网格正交性问题。以典型二维及三维粘性网格为例进行了方法的有效性研究。结果表明，在显著大变形情况下，引入旋转修正得到了正交性和光顺性良好的变形网格。方法的计算效率虽然较传统TFI有所降低，但相比弹簧方法能提高1到2个量级。
在位移和温度插值方法上，鉴于常规的基于薄板变形理论的样条方法（TPS/IPS）对于复杂结构外形存在插值困难，且对于温度插值没有明显的物理意义，提出了采用高阶等参单元形函数代替TPS/IPS的方法。算例表明，本文方法不仅成功解决了温度插值问题，而且位移插值精度也优于TPS/IPS方法，并更具普适性。此外，针对压力和热流插值需要保持守恒性的特点，从有限元法和有限体法的单元特性出发，提出一种具有局部守恒特性的界面载荷插值方法，并通过算例验证了方法的有效性。
采用共享内存技术开发了适用于通用有限元分析（FEA）和计算流体力学（CFD）软件的多场耦合计算平台，并基于分区耦合方式实现了流固耦合传热计算。作为算例，计算了外壁冷却的喷管和高超音速圆柱绕流的耦合传热问题，结果与实验值吻合良好。针对类X-34飞行器的头部热防护结构，考虑材料非线性和辐射效应，对高超音速巡航状态下驻点温度和结构冷却系统功率随热防护层厚度的变化规律进行了研究。计算结果表明，驻点温度随厚度的变化并不明显，而冷却系统功率随厚度增加急剧降低。此外材料发射率非线性对结果影响较大。
采用Euler方程和N-S方程研究了超声速和高超声速壁板颤振中的湍流边界层效应。低超声速条件下的计算结果表明，湍流边界层对颤振边界影响较为明显，在马赫数1.2左右达到最大值，随后这种差别随马赫数增大而逐渐减小，颤振边界计算结果和试验值吻合较好。在高超声速阶段，湍流边界层效应对颤振动压仍有较明显影响。在马赫数8时，N-S方程的结果高出Euler方程20%左右。这说明，对于高超声速壁板颤振，湍流边界层效应是不可忽略的影响因素。
采用三阶活塞理论、Euler方程和N-S方程三种气动力模型对二元双楔翼型的气动弹性问题进行了研究。结果表明采用Euler和三阶活塞理论的颤振速度非常接近，但和N-S方程结果差别较大。这可以归结为两方面原因：一是激波边界层干扰引起流场特征发生变化，二是边界层厚度间接改变了结构外形。因此，粘性效应对此类高超声速气弹稳定性有显著影响。
对典型吸气式高超声速飞行器机翼的三维气动热弹性问题进行了研究。将其分解为静气动热弹性配平和气动热弹性响应问题。其中，对于静气动热弹性配平问题，为避免计算过程不收敛，提出了采用动态过程代替静态过程的计算方法。在海拔10公里标准大气条件下，对一典型非对称高超声速机翼结构进行了气动热弹性计算，其中，气动力模型采用理想气体和化学反应非平衡气体。为进行比较，还采用活塞理论和Euler方程计算了相应的颤振速度。结果表明，采用理想气体时，用活塞理论和Euler方程得到的颤振速度比N-S方程结果分别高164.3和98.7%。而同样在N-S方程中，采用理想气体比化学反应非平衡气体的颤振速度低6.1%。造成上述结果的主要原因是高温引起的热应力及材料特性变化改变了结构的动力学特性。对于这类气动热弹性问题需要采用包含化学反应非平衡效应的N-S方程来求解。
Hypersonic flow with shock-boundary layer interaction, high temperature flow and othercomplex phenomena is significantly different from low speed flows, which bring lots of difficultiesand new problems for vehicle design, especially in aerothermoelastic behavior. Solving theseproblems must take into count the effects of high temperature, boundary layer, structure thermalconduction and thermal radiation, which is in excess of tridiantional aeroelastic problems. Thesemulti-field coupled and high arithmetic intensity problems are depend on the cooperation ofcomputational fluid dynamics (CFD), computational structure dynamics (CSD) and computationalthermal dynamics (CTD), and produce a big challenge for analysis and computing capacity. Thecontributions to the state-of-the-art made in this dissertation are summarized below:
A details description of the finite speed non-equilibrium chemical reaction Navier-Stokesequations is present and computational methods of gas transport properties and chemical reactionsource term are provied. The formulas of explicit and implicit time discretisation method are derived,the full system Jacobi matrix which contains convective/viscous/source terms is also provided. Acomputer program, which using Roe and AUSM+-up schemes and Menter’s SST two equationsturbulence model and implicit LUSGS method, is developed for solving hypersonic CFD problems,and also verified by some test cases.
Based on the features of the GPU architecture, an implicit data-parallel scheme has beendeveloped for solving CFD problems. The presented method is applicable to structured andunstructured mesh and uses upwind scheme to achieve more accurate results. The method has beenimplemented on NVIDIA GTX280GPU by employing CUDA technology and compared with IntelCore2Quad3.0GHz CPU. The results indicate that the implicit scheme proposed in this paper is6times faster than the explicit scheme with same hardware and the computation is speed-up to28.7x byusing GPU and implicit scheme, which will be more efficient for larger scale problems. At last, theresults provide good agreement with the existing experimental data.
Based on analysis of geometric relationship and interpolation features, an improvement forpresent transfinite interpolation (TFI) method with a rotation correction is proposed to solve theorthogonal problem with large mesh deformation. The computational results of typical two and threedimensional viscous grids indicate that good orthogonal and smoothing properties can be achieved byrotation correction for large mesh deformation. In addition, the computational efficiency is slightlydecreased than the traditional TFI method, but improved by1or2orders of magnitude compared tothe spring analogy method.
The thin-plate spline (TPS) or infinte-plate spline (IPS) methods are not suitable for complexstructure, and have no physical meanings for temperature interpolating. A new interpolating methodusing high order isoparameter finite element shape function is presented for solving these problems,and validated by some test cases. A local conservative remapping method is presented for thermal fluxand aerodynamic loads interpolation, based on analysis of the element features of finite element andfinite volume. It’s availability is also identified by some test cases.
A multi-field coupled computing platform using multi-zone iteration method is developed for solving multi-disciplinary problems. Shared memory method is employed for faster data exchange forgeneral finite element analysis (FEA)/computational fluid dynamics (CFD) software. The problems ofconjugate heat transfer for a cooled converging-diverging nozzle and a cylindrical leading edge inhypersonic flow are studied. Effects of mesh density, nonlinear material properties and radiationeffects are considered during the computation，and the results indicate good agreement with theexisting experimental data. The relationship between stagnation temperature, cooling power and thethickness of nose thermal protection structures (TPS), which resemble X-34hypersonic vehicle, underhypersonic cruise condition are emphatically investigated. The results indicate that the thicknessvariations have much less influences on stagnation temperature, while the cooling power dropssharply as the thickness increases. Furthermore, the nonlinear material emission properties havesignificant influences on the analysis results.
A coupled CFD/CSD method was used to solve supersonic and hypersonic panel flutter problemin time domain using Euler and Navier-Stokes equations. Flutter dynamic pressure was calculatedunder different boundary layer thickness and Mach number; the results show that boundary layerthickness has a large stabilizing influence on the flutter of flat panels. The effect on flutter dynamicpressure is maximum near Ma=1.2and decrease rapidly with increasing Mach number, which agreedwell with experimental data. The dynamic pressure is20%higher than the Euler results at Ma=8, theinfluence of turbulent boundary layer thickness can not be neglected at hypersonic flow.
Aeroelastic behavior of a typical double-wedge airfoil in hypersonic flow was investigated. Theeigenvalue method using3rdpiston theory, Euler equations, Navier-Stokes equations with adiabaticand isothermal wall boundary were employed to determinate the flutter boundary under differenceflight altitude. The results indicated that Euler equations is very closed to3rdpiston theory, butsignificant difference from Navier-Stokes, and result with difference wall temperature conditaionusing Navier-Stokes is agree well with each other. This conclusion results from two reasons:shock-boundary layer interaction changes the characteristics of flow field, and the thickness ofboundary layer modifies the geometric shape indirectly. Therefore, the viscous effects play a key rolein this aeroelastic problem and can not be neglected.
Analysis of aerothermoelastic behavior for the nonsymmetric wing structure of typicalairbreathing hypersonic vehicle was accomplished using multi-field coupled method. It can be dividedinto static aerothermoelastic trim and transient aerothermoelastic response. A new iterative methodusing transient coupling method instead of steady method is present to avoid some numericaldifficulties of convergence. The free-stream condition is10km standard atmosphere. Ideal gas andnon-equilibrium chemical reaction gas model are adopted, piston theory and Euler equations are alsoemploy for comparsion. The results indicated that flutter speed calculated with ideal gas is6%higherthan non-equilibrium chemical reaction Navier-Stokes equations. A very large error exists betweenEuler/3rdpiston and Navier-Stokes. The main reason is the modification of structure dynamicproperties produced by the thermal-stress and variation of materials properties under high temperature.The non-equilibrium chemical reaction Navier-Stokes equations must be used for thisaerothermoelastic problem.
针对化学反应非平衡流N-S方程，对隐式时间离散格式中的对流项、粘性项及源项的雅可比矩阵表达式进行了推导。采用Menter’SST两方程湍流模型、Roe格式、AUSM+-up格式及LUSGS方法编制了高超声速CFD计算程序，并通过典型算例验证其正确性，为后续研究工作提供基本计算手段。
从GPU架构特点出发，发展了基于数据并行的隐式CFD求解方法，适用于结构和非结构网格。采用CUDA技术，通过数据结构和算法优化，在GPU上成功实现了高超声速CFD计算。分别在Intel Core2Quad3.0GHz CPU和NVIDIA GTX280GPU上进行了数值仿真，结果表明隐式格式计算速度是显式格式6倍以上，采用显式格式的加速比达到28倍，采用隐式格式加速比达到了28.7倍，同时加速比随问题规模的增加而增加。仿真结果和实验值吻合良好。该工作可为后续研究提供快速计算手段。
依据几何关系及插值特点，提出了一种带旋转修正的TFI动网格方法，用来解决传统TFI方法在粘性网格和网格大变形时引起的网格正交性问题。以典型二维及三维粘性网格为例进行了方法的有效性研究。结果表明，在显著大变形情况下，引入旋转修正得到了正交性和光顺性良好的变形网格。方法的计算效率虽然较传统TFI有所降低，但相比弹簧方法能提高1到2个量级。
在位移和温度插值方法上，鉴于常规的基于薄板变形理论的样条方法（TPS/IPS）对于复杂结构外形存在插值困难，且对于温度插值没有明显的物理意义，提出了采用高阶等参单元形函数代替TPS/IPS的方法。算例表明，本文方法不仅成功解决了温度插值问题，而且位移插值精度也优于TPS/IPS方法，并更具普适性。此外，针对压力和热流插值需要保持守恒性的特点，从有限元法和有限体法的单元特性出发，提出一种具有局部守恒特性的界面载荷插值方法，并通过算例验证了方法的有效性。
采用共享内存技术开发了适用于通用有限元分析（FEA）和计算流体力学（CFD）软件的多场耦合计算平台，并基于分区耦合方式实现了流固耦合传热计算。作为算例，计算了外壁冷却的喷管和高超音速圆柱绕流的耦合传热问题，结果与实验值吻合良好。针对类X-34飞行器的头部热防护结构，考虑材料非线性和辐射效应，对高超音速巡航状态下驻点温度和结构冷却系统功率随热防护层厚度的变化规律进行了研究。计算结果表明，驻点温度随厚度的变化并不明显，而冷却系统功率随厚度增加急剧降低。此外材料发射率非线性对结果影响较大。
采用Euler方程和N-S方程研究了超声速和高超声速壁板颤振中的湍流边界层效应。低超声速条件下的计算结果表明，湍流边界层对颤振边界影响较为明显，在马赫数1.2左右达到最大值，随后这种差别随马赫数增大而逐渐减小，颤振边界计算结果和试验值吻合较好。在高超声速阶段，湍流边界层效应对颤振动压仍有较明显影响。在马赫数8时，N-S方程的结果高出Euler方程20%左右。这说明，对于高超声速壁板颤振，湍流边界层效应是不可忽略的影响因素。
采用三阶活塞理论、Euler方程和N-S方程三种气动力模型对二元双楔翼型的气动弹性问题进行了研究。结果表明采用Euler和三阶活塞理论的颤振速度非常接近，但和N-S方程结果差别较大。这可以归结为两方面原因：一是激波边界层干扰引起流场特征发生变化，二是边界层厚度间接改变了结构外形。因此，粘性效应对此类高超声速气弹稳定性有显著影响。
对典型吸气式高超声速飞行器机翼的三维气动热弹性问题进行了研究。将其分解为静气动热弹性配平和气动热弹性响应问题。其中，对于静气动热弹性配平问题，为避免计算过程不收敛，提出了采用动态过程代替静态过程的计算方法。在海拔10公里标准大气条件下，对一典型非对称高超声速机翼结构进行了气动热弹性计算，其中，气动力模型采用理想气体和化学反应非平衡气体。为进行比较，还采用活塞理论和Euler方程计算了相应的颤振速度。结果表明，采用理想气体时，用活塞理论和Euler方程得到的颤振速度比N-S方程结果分别高164.3和98.7%。而同样在N-S方程中，采用理想气体比化学反应非平衡气体的颤振速度低6.1%。造成上述结果的主要原因是高温引起的热应力及材料特性变化改变了结构的动力学特性。对于这类气动热弹性问题需要采用包含化学反应非平衡效应的N-S方程来求解。
Hypersonic flow with shock-boundary layer interaction, high temperature flow and othercomplex phenomena is significantly different from low speed flows, which bring lots of difficultiesand new problems for vehicle design, especially in aerothermoelastic behavior. Solving theseproblems must take into count the effects of high temperature, boundary layer, structure thermalconduction and thermal radiation, which is in excess of tridiantional aeroelastic problems. Thesemulti-field coupled and high arithmetic intensity problems are depend on the cooperation ofcomputational fluid dynamics (CFD), computational structure dynamics (CSD) and computationalthermal dynamics (CTD), and produce a big challenge for analysis and computing capacity. Thecontributions to the state-of-the-art made in this dissertation are summarized below:
A details description of the finite speed non-equilibrium chemical reaction Navier-Stokesequations is present and computational methods of gas transport properties and chemical reactionsource term are provied. The formulas of explicit and implicit time discretisation method are derived,the full system Jacobi matrix which contains convective/viscous/source terms is also provided. Acomputer program, which using Roe and AUSM+-up schemes and Menter’s SST two equationsturbulence model and implicit LUSGS method, is developed for solving hypersonic CFD problems,and also verified by some test cases.
Based on the features of the GPU architecture, an implicit data-parallel scheme has beendeveloped for solving CFD problems. The presented method is applicable to structured andunstructured mesh and uses upwind scheme to achieve more accurate results. The method has beenimplemented on NVIDIA GTX280GPU by employing CUDA technology and compared with IntelCore2Quad3.0GHz CPU. The results indicate that the implicit scheme proposed in this paper is6times faster than the explicit scheme with same hardware and the computation is speed-up to28.7x byusing GPU and implicit scheme, which will be more efficient for larger scale problems. At last, theresults provide good agreement with the existing experimental data.
Based on analysis of geometric relationship and interpolation features, an improvement forpresent transfinite interpolation (TFI) method with a rotation correction is proposed to solve theorthogonal problem with large mesh deformation. The computational results of typical two and threedimensional viscous grids indicate that good orthogonal and smoothing properties can be achieved byrotation correction for large mesh deformation. In addition, the computational efficiency is slightlydecreased than the traditional TFI method, but improved by1or2orders of magnitude compared tothe spring analogy method.
The thin-plate spline (TPS) or infinte-plate spline (IPS) methods are not suitable for complexstructure, and have no physical meanings for temperature interpolating. A new interpolating methodusing high order isoparameter finite element shape function is presented for solving these problems,and validated by some test cases. A local conservative remapping method is presented for thermal fluxand aerodynamic loads interpolation, based on analysis of the element features of finite element andfinite volume. It’s availability is also identified by some test cases.
A multi-field coupled computing platform using multi-zone iteration method is developed for solving multi-disciplinary problems. Shared memory method is employed for faster data exchange forgeneral finite element analysis (FEA)/computational fluid dynamics (CFD) software. The problems ofconjugate heat transfer for a cooled converging-diverging nozzle and a cylindrical leading edge inhypersonic flow are studied. Effects of mesh density, nonlinear material properties and radiationeffects are considered during the computation，and the results indicate good agreement with theexisting experimental data. The relationship between stagnation temperature, cooling power and thethickness of nose thermal protection structures (TPS), which resemble X-34hypersonic vehicle, underhypersonic cruise condition are emphatically investigated. The results indicate that the thicknessvariations have much less influences on stagnation temperature, while the cooling power dropssharply as the thickness increases. Furthermore, the nonlinear material emission properties havesignificant influences on the analysis results.
A coupled CFD/CSD method was used to solve supersonic and hypersonic panel flutter problemin time domain using Euler and Navier-Stokes equations. Flutter dynamic pressure was calculatedunder different boundary layer thickness and Mach number; the results show that boundary layerthickness has a large stabilizing influence on the flutter of flat panels. The effect on flutter dynamicpressure is maximum near Ma=1.2and decrease rapidly with increasing Mach number, which agreedwell with experimental data. The dynamic pressure is20%higher than the Euler results at Ma=8, theinfluence of turbulent boundary layer thickness can not be neglected at hypersonic flow.
Aeroelastic behavior of a typical double-wedge airfoil in hypersonic flow was investigated. Theeigenvalue method using3rdpiston theory, Euler equations, Navier-Stokes equations with adiabaticand isothermal wall boundary were employed to determinate the flutter boundary under differenceflight altitude. The results indicated that Euler equations is very closed to3rdpiston theory, butsignificant difference from Navier-Stokes, and result with difference wall temperature conditaionusing Navier-Stokes is agree well with each other. This conclusion results from two reasons:shock-boundary layer interaction changes the characteristics of flow field, and the thickness ofboundary layer modifies the geometric shape indirectly. Therefore, the viscous effects play a key rolein this aeroelastic problem and can not be neglected.
Analysis of aerothermoelastic behavior for the nonsymmetric wing structure of typicalairbreathing hypersonic vehicle was accomplished using multi-field coupled method. It can be dividedinto static aerothermoelastic trim and transient aerothermoelastic response. A new iterative methodusing transient coupling method instead of steady method is present to avoid some numericaldifficulties of convergence. The free-stream condition is10km standard atmosphere. Ideal gas andnon-equilibrium chemical reaction gas model are adopted, piston theory and Euler equations are alsoemploy for comparsion. The results indicated that flutter speed calculated with ideal gas is6%higherthan non-equilibrium chemical reaction Navier-Stokes equations. A very large error exists betweenEuler/3rdpiston and Navier-Stokes. The main reason is the modification of structure dynamicproperties produced by the thermal-stress and variation of materials properties under high temperature.The non-equilibrium chemical reaction Navier-Stokes equations must be used for thisaerothermoelastic problem.
引文
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