飞行器多自由度耦合摇滚运动数值模拟研究
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摘要
摇滚是现代战斗机大攻角运动下的常见问题，是一种以大振幅自由滚转为主，同时耦合如俯仰、侧滑、沉浮等自由度的复杂运动，密切关系到飞行器的作战效能和飞行包线，是飞行器在选型设计阶段就需要重点关注的动态稳定性问题之一。国内外对飞行器大攻角摇滚现象及其蕴含的物理机理极为关注，开展了大量的研究，但目前仍有大量的问题亟待解决。摇滚现象本质上是多自由度耦合的运动，但从国内外已发表的文献看来，采用单自由度假设的研究占绝大多数，直接研究多自由度耦合摇滚现象的文献十分少见。本文针对飞行器的动态摇滚现象，通过耦合求解N-S方程组和欧拉刚体动力学方程组，数值模拟飞行器不同自由度耦合条件下的非定常摇滚运动过程，研究大攻角摇滚特性及非定常复杂流动机理。
首先，耦合求解流体运动方程组和飞行器刚体动力学方程组建立飞行器多自由度耦合运动数值模拟的高效计算方法和软件。①根据摇滚运动的特点，分析运动的主要自由度，建立耦合运动的非定常动力学模型；②基于有限体积法采用二阶迎风型NND格式和含双时间步的LU-SGS方法离散流动控制方程组，基于刚性动网格技术，耦合求解流动控制方程组和刚体动力学方程组，发展适用于复杂飞行器多自由度耦合摇滚运动的数值模拟软件；③基于MPI环境发展并行算法，提高计算效率；④采用典型算例对发展的软件进行分类考核，计算结果和相关文献的实验结果或数值模拟结果吻合，验证了方法及软件的可靠性。
其次，针对战斗机大攻角俯仰运动时的横侧向稳定性问题，研究细长三角翼强迫俯仰、自由滚转的耦合运动特性。结果表明：俯仰运动的存在，使得滚转运动不能形成极限环形式的等幅振荡；俯仰/滚转耦合将导致三角翼升力显著降低，对机动飞行安全不利，还将导致三角翼横向稳定性变差。此外，多种敏感因素对俯仰/滚转耦合运动特性具有显著影响：转动惯量影响三角翼滚转运动的频率特性，转动惯量越小，频率越高；轴承的机构阻尼影响双自由度运动的振幅，阻尼越大振幅越小，当阻尼过大时，可能观察不到机翼的自由滚转现象；实验观察到三角翼强迫俯仰、自由滚转耦合运动过程中表征滚转停滞状态的台阶状曲线，是湍流、转动惯量以及轴承摩擦等多种影响因素共同作用的结果。
再次，针对动态特性研究中自由度相似的问题开展自由状态下细长三角翼滚转/侧滑双自由度和滚转、侧滑及沉浮三自由度耦合运动的研究。对滚转/侧滑双自由度耦合运动的研究表明：滚转运动表现为极限环形式的周期性等幅摇滚振荡，侧滑与摇滚同频率，反相位，具有左滚右侧滑、右滚左侧滑的耦合运动机制；与单自由度翼摇滚相比，耦合摇滚振幅更大，频率更低，摇滚分岔攻角显著减小，可能出现单自由度滚转运动稳定，而滚转/侧滑双自由度耦合运动不稳定的情况，因此，应将自由度相似作为动态特性研究中重要的相似准则予以满足。对滚转、侧滑及沉浮三自由度耦合运动的研究表明：重力显著小于垂向气动力时，三角翼可能因爬升而改出摇滚；重力显著大于垂向气动力时，三角翼快速下沉导致名义攻角增大，摇滚振幅呈现出先快速增大，再在涡破裂影响下减小的变化过程；重力和垂向气动力相当时，三角翼呈现上浮、下沉交替的运动。在垂向气动力和重力相当的情况下，沉浮运动幅度较小，三自由度的耦合运动可简化为滚转/侧滑两自由度的耦合运动，若质量很大，则三角翼侧滑的效应也可以被忽略，运动可进一步简化为单自由度摇滚，因此单自由度摇滚是本质上多自由度耦合运动在特定条件下的合理性简化假设。
最后，针对战斗机全机摇滚背景开展复杂翼体外形单自由度摇滚运动特性研究。“气动弹簧”式非对称振荡的前体分离集中涡与破裂机翼涡的非线性复杂干扰是维持翼体外形大幅度摇滚的主要流动机理，在多涡流结构的强相互干扰下，复杂翼体外形不能形成规则的等幅摇滚振荡（如单三角翼摇滚），振幅存在明显波动，可能伴有间歇、猝发特征，应当关注平均滚转振幅的变化。复杂翼体外形的动态摇滚特性受到部件构型和布局的影响：前体截面形状的影响极为显著，严重影响翼体模型的横向动态稳定性；尾翼能够对翼体摇滚起到一定的动态稳定性作用，稳定的程度与尾翼的布局有关；与简单三角翼的静态特性不同，机翼前缘形状的变化对翼体外形动态摇滚运动特性的影响较小。
Rock is a universal problem of modern combat aircraft maneuvering in high angleof attack, it is a complex motion which is dominated by large amplitude free-roll andcoupled with pitch, sideslip and vertical movement. Rock has significant influence oncombat effectiveness and envelope, and is treated as a key problem that should be fixedin designing phase. A lot of researches focus on rock phenomenon and its mechanism,but many problems are still need to be solved. Rock is a motion essentially coupled withmultiple degrees of freedom (DOF), but in literature, researches on the assumption ofsingle DOF are in absolutely dominant, it is seldom investigated with multiple DOFssimultaneously. This paper concerns with dynamic coupling rock of aircraft, solves N-Sequations and Euler rigid body dynamic equations by coupling method, numericallysimulates the unsteady rock motion in multiple DOFs, and investigates the motioncharacteristics and complex flow mechanism of aircraft in high angle of attack.
Firstly, high performance numerical simulation method and relevant software areestablished by sequentially solving the flow control equations and rigid body dynamicequations in a coupling way.①In terms of the characteristics of rock motion, analysesof main movement freedoms are conducted, and then the unsteady dynamic model ofcoupling motions is constructed.②The2nd-order, upwind, finite volume NNDscheme and LU-SGS method with dual time steps are employed to discretize the flowcontrol equations, based on rigid dynamic mesh technology, a coupling method isemployed to solve the flow control equations and rigid body dynamic equations, thedynamic simulation software suitable for multiple DOFs motion of complicate aircraftis developed consequently.③Parallel algorithm based on MPI environment isdeveloped for higher efficiency.④Typical validating examples are employed toassess the method and software developed in this paper, and the outcomes show goodagreement with relevant experimental or reference results.
Secondly, investigation of the coupling characteristics of slender delta wing incombined force-pitch and free-roll motion focus on the the transverse/lateral stabilitiesof combat aircraft pitching maneuver in high angle of attack. Results show: thehysteresis of pitching motion lags the variations of roll amplitudes, no limit cycle rolloscillation is observed; the coupling effect of pitch and roll motion leads to significantlydecrease of lift force, which is harmful to maneuvering safety and worsens thetransverse stabilities of delta wings. Additionally, the investigation shows that severalsensitive factors have profound influence on the characteristics of coupling motion inpitching and rolling: the moment of inertial affects the roll frequency, the smaller rollmoment of inertial, the higher roll frequency; the structural damp of bearing affects the amplitudes, the larger structural damp, the smaller roll amplitudes, enough large dampeven eliminates the rock phenomenon of delta wing; the plateau curve of roll angleobserved in experiment is result of the collaboration of turbulence, moment of inertialand bearing friction, et al.
Thirdly, numerical investigation of the characteristics of double DOFs motion incombined free-roll and free-sideslip and three DOFs motion in combined roll, sideslipand vertical movement are conducted focusing on the DOFs similarity in dynamicproblem. Results show: motion in combined free-roll and free-sideslip behaves asperiodic limit cycle oscillation, sideslip is observed to oscillate with roll in the samefrequency and opposite phase, the coupling mechanism of roll and sideslip can bedescribed as right sideslip with left roll and left sideslip with right roll; compared withthe single DOF wing rock, larger roll amplitudes, lower roll frequencies and smallerbifurcation attack angle are observed in double DOFs motion, which indicates apossibility that the delta wing is stable in single DOF wing rock, but unstable incombined roll and sideslip wing rock, therefore, DOFs similarity should be take as animportant similarity rule to be satisfied in dynamic characteristics researches. Theinvestigation of three DOFs motion in combined roll, sideslip and vertical movementshows: when the gravity is obviously lower than the vertical force, the delta wing rockmay eliminate owing to fiercely climb up; when the gravity is obviously larger than thevertical force, the swift sinking of delta wing lead to an increase of nominal attack angle,as a result, the roll amplitudes may significantly decrease with the increasing dampeffect of vortex burst; when the gravity and vertical force are comparative, small rangeof climbing up and sinking may emerge sequentially. In the case of gravity is equivalentto vertical force, the movement in vertical direction could be neglected, then the threeDOFs motion can be simplified to double DOFs motion in combined roll and sideslip, ifa large mass of delta wing is enforced, the coupling motion can be further simplified tosingle DOF wing rock, that is to say single DOF wing rock is a rational simplification ofessentially multiple DOFs motion in some special conditions.
Finally, investigation of single DOF wing/body rock phenomenon on the ground ofcomplicate combat aircraft is conducted. The nonlinearly interaction between theunsymmetrical oscillating fore-body vortexes and the burst vortical flow on wings is themechanism which sustains the roll amplitudes of wing/body configuration. Under thestrong interactions among vortexes, no regular roll oscillation (such as slender singledelta wing) is built. The history curves of roll angle are accompanied with amplitudesfluctuation, even with intermittent and abrupt characteristics, thus the averageamplitudes should be concerned with. Additionally, the results show that thecharacteristics of wing/body rock phenomenon are influenced by the local configuration:the influence of fore-body configuration is primary, it has profound influence ontransverse stabilities; to some extent, tail wings enforce the dynamic stabilities of static stabilities of simple delta wings, the influences of leading edge of wing on thewing/body dynamic characteristics are secondary, no obvious impact is observed.
首先，耦合求解流体运动方程组和飞行器刚体动力学方程组建立飞行器多自由度耦合运动数值模拟的高效计算方法和软件。①根据摇滚运动的特点，分析运动的主要自由度，建立耦合运动的非定常动力学模型；②基于有限体积法采用二阶迎风型NND格式和含双时间步的LU-SGS方法离散流动控制方程组，基于刚性动网格技术，耦合求解流动控制方程组和刚体动力学方程组，发展适用于复杂飞行器多自由度耦合摇滚运动的数值模拟软件；③基于MPI环境发展并行算法，提高计算效率；④采用典型算例对发展的软件进行分类考核，计算结果和相关文献的实验结果或数值模拟结果吻合，验证了方法及软件的可靠性。
其次，针对战斗机大攻角俯仰运动时的横侧向稳定性问题，研究细长三角翼强迫俯仰、自由滚转的耦合运动特性。结果表明：俯仰运动的存在，使得滚转运动不能形成极限环形式的等幅振荡；俯仰/滚转耦合将导致三角翼升力显著降低，对机动飞行安全不利，还将导致三角翼横向稳定性变差。此外，多种敏感因素对俯仰/滚转耦合运动特性具有显著影响：转动惯量影响三角翼滚转运动的频率特性，转动惯量越小，频率越高；轴承的机构阻尼影响双自由度运动的振幅，阻尼越大振幅越小，当阻尼过大时，可能观察不到机翼的自由滚转现象；实验观察到三角翼强迫俯仰、自由滚转耦合运动过程中表征滚转停滞状态的台阶状曲线，是湍流、转动惯量以及轴承摩擦等多种影响因素共同作用的结果。
再次，针对动态特性研究中自由度相似的问题开展自由状态下细长三角翼滚转/侧滑双自由度和滚转、侧滑及沉浮三自由度耦合运动的研究。对滚转/侧滑双自由度耦合运动的研究表明：滚转运动表现为极限环形式的周期性等幅摇滚振荡，侧滑与摇滚同频率，反相位，具有左滚右侧滑、右滚左侧滑的耦合运动机制；与单自由度翼摇滚相比，耦合摇滚振幅更大，频率更低，摇滚分岔攻角显著减小，可能出现单自由度滚转运动稳定，而滚转/侧滑双自由度耦合运动不稳定的情况，因此，应将自由度相似作为动态特性研究中重要的相似准则予以满足。对滚转、侧滑及沉浮三自由度耦合运动的研究表明：重力显著小于垂向气动力时，三角翼可能因爬升而改出摇滚；重力显著大于垂向气动力时，三角翼快速下沉导致名义攻角增大，摇滚振幅呈现出先快速增大，再在涡破裂影响下减小的变化过程；重力和垂向气动力相当时，三角翼呈现上浮、下沉交替的运动。在垂向气动力和重力相当的情况下，沉浮运动幅度较小，三自由度的耦合运动可简化为滚转/侧滑两自由度的耦合运动，若质量很大，则三角翼侧滑的效应也可以被忽略，运动可进一步简化为单自由度摇滚，因此单自由度摇滚是本质上多自由度耦合运动在特定条件下的合理性简化假设。
最后，针对战斗机全机摇滚背景开展复杂翼体外形单自由度摇滚运动特性研究。“气动弹簧”式非对称振荡的前体分离集中涡与破裂机翼涡的非线性复杂干扰是维持翼体外形大幅度摇滚的主要流动机理，在多涡流结构的强相互干扰下，复杂翼体外形不能形成规则的等幅摇滚振荡（如单三角翼摇滚），振幅存在明显波动，可能伴有间歇、猝发特征，应当关注平均滚转振幅的变化。复杂翼体外形的动态摇滚特性受到部件构型和布局的影响：前体截面形状的影响极为显著，严重影响翼体模型的横向动态稳定性；尾翼能够对翼体摇滚起到一定的动态稳定性作用，稳定的程度与尾翼的布局有关；与简单三角翼的静态特性不同，机翼前缘形状的变化对翼体外形动态摇滚运动特性的影响较小。
Rock is a universal problem of modern combat aircraft maneuvering in high angleof attack, it is a complex motion which is dominated by large amplitude free-roll andcoupled with pitch, sideslip and vertical movement. Rock has significant influence oncombat effectiveness and envelope, and is treated as a key problem that should be fixedin designing phase. A lot of researches focus on rock phenomenon and its mechanism,but many problems are still need to be solved. Rock is a motion essentially coupled withmultiple degrees of freedom (DOF), but in literature, researches on the assumption ofsingle DOF are in absolutely dominant, it is seldom investigated with multiple DOFssimultaneously. This paper concerns with dynamic coupling rock of aircraft, solves N-Sequations and Euler rigid body dynamic equations by coupling method, numericallysimulates the unsteady rock motion in multiple DOFs, and investigates the motioncharacteristics and complex flow mechanism of aircraft in high angle of attack.
Firstly, high performance numerical simulation method and relevant software areestablished by sequentially solving the flow control equations and rigid body dynamicequations in a coupling way.①In terms of the characteristics of rock motion, analysesof main movement freedoms are conducted, and then the unsteady dynamic model ofcoupling motions is constructed.②The2nd-order, upwind, finite volume NNDscheme and LU-SGS method with dual time steps are employed to discretize the flowcontrol equations, based on rigid dynamic mesh technology, a coupling method isemployed to solve the flow control equations and rigid body dynamic equations, thedynamic simulation software suitable for multiple DOFs motion of complicate aircraftis developed consequently.③Parallel algorithm based on MPI environment isdeveloped for higher efficiency.④Typical validating examples are employed toassess the method and software developed in this paper, and the outcomes show goodagreement with relevant experimental or reference results.
Secondly, investigation of the coupling characteristics of slender delta wing incombined force-pitch and free-roll motion focus on the the transverse/lateral stabilitiesof combat aircraft pitching maneuver in high angle of attack. Results show: thehysteresis of pitching motion lags the variations of roll amplitudes, no limit cycle rolloscillation is observed; the coupling effect of pitch and roll motion leads to significantlydecrease of lift force, which is harmful to maneuvering safety and worsens thetransverse stabilities of delta wings. Additionally, the investigation shows that severalsensitive factors have profound influence on the characteristics of coupling motion inpitching and rolling: the moment of inertial affects the roll frequency, the smaller rollmoment of inertial, the higher roll frequency; the structural damp of bearing affects the amplitudes, the larger structural damp, the smaller roll amplitudes, enough large dampeven eliminates the rock phenomenon of delta wing; the plateau curve of roll angleobserved in experiment is result of the collaboration of turbulence, moment of inertialand bearing friction, et al.
Thirdly, numerical investigation of the characteristics of double DOFs motion incombined free-roll and free-sideslip and three DOFs motion in combined roll, sideslipand vertical movement are conducted focusing on the DOFs similarity in dynamicproblem. Results show: motion in combined free-roll and free-sideslip behaves asperiodic limit cycle oscillation, sideslip is observed to oscillate with roll in the samefrequency and opposite phase, the coupling mechanism of roll and sideslip can bedescribed as right sideslip with left roll and left sideslip with right roll; compared withthe single DOF wing rock, larger roll amplitudes, lower roll frequencies and smallerbifurcation attack angle are observed in double DOFs motion, which indicates apossibility that the delta wing is stable in single DOF wing rock, but unstable incombined roll and sideslip wing rock, therefore, DOFs similarity should be take as animportant similarity rule to be satisfied in dynamic characteristics researches. Theinvestigation of three DOFs motion in combined roll, sideslip and vertical movementshows: when the gravity is obviously lower than the vertical force, the delta wing rockmay eliminate owing to fiercely climb up; when the gravity is obviously larger than thevertical force, the swift sinking of delta wing lead to an increase of nominal attack angle,as a result, the roll amplitudes may significantly decrease with the increasing dampeffect of vortex burst; when the gravity and vertical force are comparative, small rangeof climbing up and sinking may emerge sequentially. In the case of gravity is equivalentto vertical force, the movement in vertical direction could be neglected, then the threeDOFs motion can be simplified to double DOFs motion in combined roll and sideslip, ifa large mass of delta wing is enforced, the coupling motion can be further simplified tosingle DOF wing rock, that is to say single DOF wing rock is a rational simplification ofessentially multiple DOFs motion in some special conditions.
Finally, investigation of single DOF wing/body rock phenomenon on the ground ofcomplicate combat aircraft is conducted. The nonlinearly interaction between theunsymmetrical oscillating fore-body vortexes and the burst vortical flow on wings is themechanism which sustains the roll amplitudes of wing/body configuration. Under thestrong interactions among vortexes, no regular roll oscillation (such as slender singledelta wing) is built. The history curves of roll angle are accompanied with amplitudesfluctuation, even with intermittent and abrupt characteristics, thus the averageamplitudes should be concerned with. Additionally, the results show that thecharacteristics of wing/body rock phenomenon are influenced by the local configuration:the influence of fore-body configuration is primary, it has profound influence ontransverse stabilities; to some extent, tail wings enforce the dynamic stabilities of static stabilities of simple delta wings, the influences of leading edge of wing on thewing/body dynamic characteristics are secondary, no obvious impact is observed.
引文
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