旋翼绕流的高效数值计算方法及主动流动控制研究
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摘要
本文研究了适用于复杂非定常粘性流动的高效数值计算方法及其微射流主动流动控制技术。通过使用隐式求解、引入预处理方法、多重网格法等数值模拟技术，发展了一套适用于从不可压缩流动到超声速流动的Navier-Stokes(N-S)方程统一求解方法和高效计算程序。在发展高效数值模拟技术基础上，开展了直升机旋翼前飞非定常粘性流动以及翼型和旋翼微射流主动流动控制的数值模拟研究，并结合N-S方程和气动声学Ffowcs Williams-Hawkings(FW-H)方程开展了旋翼悬停和前飞气动噪声的高效预测方法研究。本文的研究为新型旋翼气动和声学设计提供了一种高效计算分析工具，并探讨了一种基于MEMS技术的旋翼主动流动控制技术的实现途径。
本文完成的研究工作主要表现在如下几个方面：
(1)发展了一套适用于定常／非定常粘性流动的全速域高效、高精度数值计算方法和计算程序(命名为PMNS3D)。在有限体积法的基础上，空间离散以改进的JST格式和基于MUSCL方法的高阶AUSM+-up格式为主，时间推进以改进的LU-SGS格式和全隐式双时间法为主，并引入预处理方法和多重网格法等高效率加速收敛技术。为了提高LU-SGS格式在粘性流动计算中的效率和稳定性，本文引入粘性修正，给出了一种牛顿型LU-SGS迭代方法。为了提高非定常粘性流动的计算效率，发展了含牛顿型LU-SGS子迭代的全隐式双时间法，并提出了一种采用直接LU-SGS方法进行子迭代初场预估的预报校正法。
(2)为了改善现有可压缩计算方法在低马赫数流动计算中面临的收敛困难和收敛精度低的问题，本文对矩阵预处理方法进行了深入研究，并通过与多重网格方法结合，发展了同时适用于从不可压流动到超声速流动的高效、高精度计算方法。推导了针对显式时间推进和隐式时间推进以及双时间推进格式的预处理方法，同时也发展了适用于JST格式和AUSM+格式的预处理方法。将AUSM+-up空间离散格式同预处理时间推进方法相结合，发展了一种预处理AUSM+-up格式，可实现从极低马赫数流动(如Ma=10~(-5))到超声速流动的高效、高精度数值模拟。通过二维／三维、定常／非定常流动数值模拟算例，表明所发展的预处理方法既能显著提高计算效率，又能提高计算精度。
(3)研究发展了适用于N-S方程数值求解的隐式多重网格方法。在课题组原有的定常流动显式多重网格技术基础上，发展了适用于定常和非定常粘性流动的LU-SGS隐式多重网格技术。研究表明，隐式多重网格方法计算效率和计算稳定性明显优于显式多重网格方法。对隐式多重网格技术的循环方式进行了研究，总结出了比较有效的多重网格循环方式。针对预处理方法的应用，发展了程序改动量小、通用性强且易于实现的预处理多重网格技术，并给出了该技术的流程图。
(4)研究发展了适用于前飞直升机旋翼非定常粘性流动计算的隐式多重网格方法。针对运动嵌套网格技术，提出了一种改进的贡献单元搜索方法，并发展了一种高效实用的嵌套多重网格技术。将多重网格方法与含牛顿型LU-SGS子迭代的全隐式双时间法相结合，发展了适用于前飞旋翼粘性绕流的高效数值计算方法和计算程序(命名为FORWARD)。算例研究表明，本文所发展的计算方法显著地提高了计算效率，减少了计算时间。
(5)研究发展了翼型微射流主动流动控制的数值模拟技术及相应的控制参数优化方法。在翼型表面施加非定常吹／吸气边界条件，发展了微射流与翼型干扰流动的数值分析方法。对NACA0015翼型、YLSG107高升力翼型、VR-7B旋翼翼型的失速控制进行了数值模拟，并对OA212R旋翼翼型的动态失速控制进行了数值模拟，深入研究了零质量射流技术在翼型主动流动控制方面的控制效果、控制机理和参数影响规律。研究表明：近切向射流比法向射流具有更好的分离控制效果，可有效增加翼型升力、减小分离阻力和减小力矩绝对值；射流动量系数达到0.001以上可获得较明显的控制效果。为实现最优控制，还提出了一种基于“代理模型”的控制参数优化方法。该方法将均匀试验设计与二次响应面、Kriging模型以及径向基神经网络等近似技术相结合，构造出目标函数和状态变量的代理模型，并采用序列二次规划方法和遗传模拟退火算法进行优化。以NACA0015翼型和VR-7B旋翼翼型的失速控制为例验证了该方法的有效性。
(6)在发展前飞旋翼高效数值模拟方法的基础上，开展了三维旋翼微射流控制的探索性研究。提出了三维非定常吹／吸气边界条件，并对悬停旋翼的定常射流控制、有升力前飞旋翼的零质量射流增升以及前进桨激波-附面层干扰的零质量射流控制进行了初步研究，表明主动流动控制在提高旋翼气动性能方面具有很好的应用前景。
(7)在国内首次开展了结合RANS方程和可穿透数据面FW-H方程(简称RANS／FW-H_(pds)方法)的直升机旋翼气动噪声预测方法研究。首先通过RANS方程数值模拟获得旋翼近场噪声，然后通过求解FW-H_(pds)方程得到远场气动噪声。悬停旋翼和前飞旋翼气动噪声算例研究表明，RANS／FW-H_(pds)方法能更准确地预测高速脉冲(HSI)噪声，并具有一定桨涡干扰噪声预测能力。
In present dissertation, efficient simulation of complex unsteady viscous flowsand active flow control based on synthetic jet technology are studied. By usingLU-SGS implicit method and introducing preconditioning method coupling withmultigrid scheme, an efficient and robust numerical method solving Navier-Stokesequations for flows at all speed is presented and investigated. Based on this method,the unsteady viscous flows past helicopter rotors in forward flight are simulated, andactive flow control over airfoils and rotor blades are conducted. At last, theaeroacoustic nosie generated by helicopter rotor and in hover and forward flight arepredicted by solving Navier-Stokes equations and Ffowcs Williams/Hawkingsequation with penetrable data surface. This dissertation develops an efficient analysismethod for aerodynamic and aeroacoustic design of advanced helicopter rotors andalso presents a new-concept flow control techniques based on synthetic jettechnology.
The main research work and increasing contribution of this dissertation are listedas follows:
1) An efficient, robust and accurate method for simulating steady/unsteadyflows at all speed is developed and applied to solve a variety of two-dimensional andthree-dimensional viscous flows. All methods are implemented within the frameworkof Finite-Volume method. Revised JST scheme and high-order AUSM+-up schemeare employed for spatial discretization. Improved LU-SGS scheme and fully implicitdual-time stepping method are utilized for time integral. Preconditioning method andmultigrid method is used as the highly efficient techniques for accelerating theconvergence of residual. To improve the efficiency and stability for viscous flows, aviscous correction is introduced into LU-SGS scheme and a Newton-like scheme isobtained. A fully implicit dual-time stepping method is developed to improve theefficiency of unsteady flow simulation and a prediction-correction method is proposedby predicting the initial flow field of sub-iteration with the direct LU-SGS method.
2) To overcome the he difficult in solving compressible equations for low Machnumber flows, preconditioning method is investigated and successfully applied intoour code. The preconditioning scheme for explicit and implicit time steppingmethod and also for JST and AUSM+ scheme is derived and discussed. Coupling thespatial discretization with AUSM+-up scheme and time stepping usingpreconditioning method, efficient and accurate simulation of flows from extremelylow speed (Ma=10~(-5)) to supersonic speed has been realized.
3) An implicit muligrid scheme for solving Navier-Stokes equations ispresented. It is proved by numerous examples that implicit multigrid method is moreefficient and robust than explicit multigrid method. Introducing preconditioningmethod, this paper develops a preconditioning multigrid method, and the flow chart ofthis general technique is presented and discussed.
4) A chimera multigrid method and a fully implicit dual-time stepping method for simulating the viscous flows over helicopter rotors in forward flight is presented,and an efficient code named FORWARD is developed. To improve the efficiency androbustness of moving-over-set-grid technique, a revised method for searchingcontributing cell is proposed. A new technique for implementing multigrid cycle onmoving-over-set grid is also proposed. The flows past hovering rotor, non-lifting andlifting forward flight rotor are simulated. The computed pressure distribution iscompared with experimental data and good agreement has been achieved. It's shownthat the present method markedly improves the efficiency and reduces the CPU timeof numerical simulation of viscous flow past helicopter rotor in forward flight.
5) Numerical analysis method for active flow control over airfoils withsynthetic jet is presented, and optimization method for control parameters based on"surrogate model" is proposed. By imposing unsteady blowing/suction boundarycondition on airfoil, the numerical method considering the interaction betweensynthetic jet and the flow around airfoil is developed. The simulations of stall controlover NACA0015 airfoil, YLSG107 high-lift airfoil and VR-7B rotor airfoil anddynamic stall over OA212R rotor airfoil are conducted. The income and mechanismof synthetic jet as well as the effect of control parameters are analyzed and discussed.In order to optimize the control parameters, a method based on "surrogate model" isproposed. The numerical examples for NACA0012 and VR-7B airfoil shows that thismethod is efficient and engineering applicable.
6) Based on the developed efficient numerical method for flows over helicopterrotors, the active flow control on three-dimensional rotor blades is investigated.Three-dimensional unsteady blowing/suction boundary condition is developed anddefinitions of momentum coefficient, non-dimensional frequency and jet angle arepresented. The active flow control on hovering rotor and forward flight rotor forincreasing thrust and removing the chock wave/boundary layer interaction isnumerically studied.
7) The RANS/FW-H_(pds) method is applied to predict the aeroacoustic noisegenerated by helicopter rotors in hover and forward flight for the first time. Thenear-filed noise is obtained by solving Reynolds-Averaged Naiver-Stokes equations,and far-field noise is predicted by solving Ffowcs Williams-Hawking equation.Numerical examples shows that RANS/FW-H_(pds) method can predict High-SpeedImpulsive noise more accurately and also this method can be used to predict theBlade-Vortex-Interaction noise.
本文完成的研究工作主要表现在如下几个方面：
(1)发展了一套适用于定常／非定常粘性流动的全速域高效、高精度数值计算方法和计算程序(命名为PMNS3D)。在有限体积法的基础上，空间离散以改进的JST格式和基于MUSCL方法的高阶AUSM+-up格式为主，时间推进以改进的LU-SGS格式和全隐式双时间法为主，并引入预处理方法和多重网格法等高效率加速收敛技术。为了提高LU-SGS格式在粘性流动计算中的效率和稳定性，本文引入粘性修正，给出了一种牛顿型LU-SGS迭代方法。为了提高非定常粘性流动的计算效率，发展了含牛顿型LU-SGS子迭代的全隐式双时间法，并提出了一种采用直接LU-SGS方法进行子迭代初场预估的预报校正法。
(2)为了改善现有可压缩计算方法在低马赫数流动计算中面临的收敛困难和收敛精度低的问题，本文对矩阵预处理方法进行了深入研究，并通过与多重网格方法结合，发展了同时适用于从不可压流动到超声速流动的高效、高精度计算方法。推导了针对显式时间推进和隐式时间推进以及双时间推进格式的预处理方法，同时也发展了适用于JST格式和AUSM+格式的预处理方法。将AUSM+-up空间离散格式同预处理时间推进方法相结合，发展了一种预处理AUSM+-up格式，可实现从极低马赫数流动(如Ma=10~(-5))到超声速流动的高效、高精度数值模拟。通过二维／三维、定常／非定常流动数值模拟算例，表明所发展的预处理方法既能显著提高计算效率，又能提高计算精度。
(3)研究发展了适用于N-S方程数值求解的隐式多重网格方法。在课题组原有的定常流动显式多重网格技术基础上，发展了适用于定常和非定常粘性流动的LU-SGS隐式多重网格技术。研究表明，隐式多重网格方法计算效率和计算稳定性明显优于显式多重网格方法。对隐式多重网格技术的循环方式进行了研究，总结出了比较有效的多重网格循环方式。针对预处理方法的应用，发展了程序改动量小、通用性强且易于实现的预处理多重网格技术，并给出了该技术的流程图。
(4)研究发展了适用于前飞直升机旋翼非定常粘性流动计算的隐式多重网格方法。针对运动嵌套网格技术，提出了一种改进的贡献单元搜索方法，并发展了一种高效实用的嵌套多重网格技术。将多重网格方法与含牛顿型LU-SGS子迭代的全隐式双时间法相结合，发展了适用于前飞旋翼粘性绕流的高效数值计算方法和计算程序(命名为FORWARD)。算例研究表明，本文所发展的计算方法显著地提高了计算效率，减少了计算时间。
(5)研究发展了翼型微射流主动流动控制的数值模拟技术及相应的控制参数优化方法。在翼型表面施加非定常吹／吸气边界条件，发展了微射流与翼型干扰流动的数值分析方法。对NACA0015翼型、YLSG107高升力翼型、VR-7B旋翼翼型的失速控制进行了数值模拟，并对OA212R旋翼翼型的动态失速控制进行了数值模拟，深入研究了零质量射流技术在翼型主动流动控制方面的控制效果、控制机理和参数影响规律。研究表明：近切向射流比法向射流具有更好的分离控制效果，可有效增加翼型升力、减小分离阻力和减小力矩绝对值；射流动量系数达到0.001以上可获得较明显的控制效果。为实现最优控制，还提出了一种基于“代理模型”的控制参数优化方法。该方法将均匀试验设计与二次响应面、Kriging模型以及径向基神经网络等近似技术相结合，构造出目标函数和状态变量的代理模型，并采用序列二次规划方法和遗传模拟退火算法进行优化。以NACA0015翼型和VR-7B旋翼翼型的失速控制为例验证了该方法的有效性。
(6)在发展前飞旋翼高效数值模拟方法的基础上，开展了三维旋翼微射流控制的探索性研究。提出了三维非定常吹／吸气边界条件，并对悬停旋翼的定常射流控制、有升力前飞旋翼的零质量射流增升以及前进桨激波-附面层干扰的零质量射流控制进行了初步研究，表明主动流动控制在提高旋翼气动性能方面具有很好的应用前景。
(7)在国内首次开展了结合RANS方程和可穿透数据面FW-H方程(简称RANS／FW-H_(pds)方法)的直升机旋翼气动噪声预测方法研究。首先通过RANS方程数值模拟获得旋翼近场噪声，然后通过求解FW-H_(pds)方程得到远场气动噪声。悬停旋翼和前飞旋翼气动噪声算例研究表明，RANS／FW-H_(pds)方法能更准确地预测高速脉冲(HSI)噪声，并具有一定桨涡干扰噪声预测能力。
In present dissertation, efficient simulation of complex unsteady viscous flowsand active flow control based on synthetic jet technology are studied. By usingLU-SGS implicit method and introducing preconditioning method coupling withmultigrid scheme, an efficient and robust numerical method solving Navier-Stokesequations for flows at all speed is presented and investigated. Based on this method,the unsteady viscous flows past helicopter rotors in forward flight are simulated, andactive flow control over airfoils and rotor blades are conducted. At last, theaeroacoustic nosie generated by helicopter rotor and in hover and forward flight arepredicted by solving Navier-Stokes equations and Ffowcs Williams/Hawkingsequation with penetrable data surface. This dissertation develops an efficient analysismethod for aerodynamic and aeroacoustic design of advanced helicopter rotors andalso presents a new-concept flow control techniques based on synthetic jettechnology.
The main research work and increasing contribution of this dissertation are listedas follows:
1) An efficient, robust and accurate method for simulating steady/unsteadyflows at all speed is developed and applied to solve a variety of two-dimensional andthree-dimensional viscous flows. All methods are implemented within the frameworkof Finite-Volume method. Revised JST scheme and high-order AUSM+-up schemeare employed for spatial discretization. Improved LU-SGS scheme and fully implicitdual-time stepping method are utilized for time integral. Preconditioning method andmultigrid method is used as the highly efficient techniques for accelerating theconvergence of residual. To improve the efficiency and stability for viscous flows, aviscous correction is introduced into LU-SGS scheme and a Newton-like scheme isobtained. A fully implicit dual-time stepping method is developed to improve theefficiency of unsteady flow simulation and a prediction-correction method is proposedby predicting the initial flow field of sub-iteration with the direct LU-SGS method.
2) To overcome the he difficult in solving compressible equations for low Machnumber flows, preconditioning method is investigated and successfully applied intoour code. The preconditioning scheme for explicit and implicit time steppingmethod and also for JST and AUSM+ scheme is derived and discussed. Coupling thespatial discretization with AUSM+-up scheme and time stepping usingpreconditioning method, efficient and accurate simulation of flows from extremelylow speed (Ma=10~(-5)) to supersonic speed has been realized.
3) An implicit muligrid scheme for solving Navier-Stokes equations ispresented. It is proved by numerous examples that implicit multigrid method is moreefficient and robust than explicit multigrid method. Introducing preconditioningmethod, this paper develops a preconditioning multigrid method, and the flow chart ofthis general technique is presented and discussed.
4) A chimera multigrid method and a fully implicit dual-time stepping method for simulating the viscous flows over helicopter rotors in forward flight is presented,and an efficient code named FORWARD is developed. To improve the efficiency androbustness of moving-over-set-grid technique, a revised method for searchingcontributing cell is proposed. A new technique for implementing multigrid cycle onmoving-over-set grid is also proposed. The flows past hovering rotor, non-lifting andlifting forward flight rotor are simulated. The computed pressure distribution iscompared with experimental data and good agreement has been achieved. It's shownthat the present method markedly improves the efficiency and reduces the CPU timeof numerical simulation of viscous flow past helicopter rotor in forward flight.
5) Numerical analysis method for active flow control over airfoils withsynthetic jet is presented, and optimization method for control parameters based on"surrogate model" is proposed. By imposing unsteady blowing/suction boundarycondition on airfoil, the numerical method considering the interaction betweensynthetic jet and the flow around airfoil is developed. The simulations of stall controlover NACA0015 airfoil, YLSG107 high-lift airfoil and VR-7B rotor airfoil anddynamic stall over OA212R rotor airfoil are conducted. The income and mechanismof synthetic jet as well as the effect of control parameters are analyzed and discussed.In order to optimize the control parameters, a method based on "surrogate model" isproposed. The numerical examples for NACA0012 and VR-7B airfoil shows that thismethod is efficient and engineering applicable.
6) Based on the developed efficient numerical method for flows over helicopterrotors, the active flow control on three-dimensional rotor blades is investigated.Three-dimensional unsteady blowing/suction boundary condition is developed anddefinitions of momentum coefficient, non-dimensional frequency and jet angle arepresented. The active flow control on hovering rotor and forward flight rotor forincreasing thrust and removing the chock wave/boundary layer interaction isnumerically studied.
7) The RANS/FW-H_(pds) method is applied to predict the aeroacoustic noisegenerated by helicopter rotors in hover and forward flight for the first time. Thenear-filed noise is obtained by solving Reynolds-Averaged Naiver-Stokes equations,and far-field noise is predicted by solving Ffowcs Williams-Hawking equation.Numerical examples shows that RANS/FW-H_(pds) method can predict High-SpeedImpulsive noise more accurately and also this method can be used to predict theBlade-Vortex-Interaction noise.
引文
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