液体火箭POGO振动的多体动力学建模及稳定性分析
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摘要
液体火箭POGO振动本质上是液路系统与结构系统耦合产生的一种不稳定现象，是载人航天任务需要特别关注的问题。传统方法需人工选择几阶重要结构模态，这在研究模态密集的大型捆绑火箭的POGO稳定性时给建模与分析带来困难，因此有必要发展更有效的分析方法。此外，火箭实飞数据表明POGO振动对工作参数非常敏感。因此，找出具有POGO鲁棒性的参数区域具有重要意义。针对这两大类问题，本文主要进行了如下三项研究：
提出用三个无量纲数表征单结构振子和单液路振子耦合的稳定性。并解析/半解析地研究了各工作参数对POGO稳定性的影响。结果表明，将液路频率降至低于结构频率有利于减弱稳定性对参数的敏感度，从而获得POGO鲁棒性，即对一定质量范围的有效载荷和不同工况都稳定。
提出了一种一维流-管耦合动力学的有限元建模方法，用于描述空间任意构型输运管路的大范围运动。管壁由本文发展的Euler-Bernoulli梁单元建模，该单元采用四元数描述截面姿态，从根本上避免了用Euler角做广义坐标引入的三维奇异性问题，并在插值位移场时通过次序插值保证了Euler-Bernoulli梁的直法线假设，即中心切向与截面垂直。流体单元的控制体与运动的梁单元时刻重合，对流体可压与不可压两种情况分别建立控制方程，并考虑对结构的作用力。算例表明，该方法能很好的描述一维流-管的耦合动力学。
建立了基于多体动力学系统方程的液体火箭POGO稳定性分析方法。解决了流固耦合求解不收敛问题，将推进剂系统的各单元引入多体动力学求解框架中，使得可通过求解线化系统方程的特征值来判断系统稳定性。然后，建模并研究了某大型液体捆绑火箭在推进剂完全轴对称构型和局部非轴对称构型下的POGO稳定性。结果表明，除纵向模态外，即使在轴对称布局下，助推推进剂与结构的耦合也可能导致非轴对称的整体弯曲模态或局部模态的失稳，这可通过蓄压器调频来消除；管路的局部非轴对称构型也有可能引起系统不稳定，这种不稳定性需从管路设计上而非蓄压器调频来消除。
POGO vibration, resulted from the closed-loop instability between propulsionsystem and structure modes, is highly concerned in manned space flight. In analysis,only few important structure modes should be artificially selected, this complex themodeling work for checking stability of powerful bundled liquid rocket since a lot ofdensity structure modes has to be considered carefully. Hence, it is very necessary todevelop another easier and efficient approach for stability analysis. Besides, an idealrocket should be pogo robust, which means pogo free for a certain kind of payload andwide range of working conditions. While, flight data show that pogo stability behaviorsmission-specific and is highly sensitive to the dynamical working conditions. Therefore,it will be meaningful to qualitatively investigate the effect of physical factors onstability, and figure out the important parameters domain for achieving robust pogostability. This thesis is aimed at studying these two major problems.
Firstly, the effects of physical parameters on pogo stability are qualitativelyinvestigated through analytically approach. In the analysis, coupling between rocketstructure and a single-propellant system is transformed to a number of two coupledoscillators, which describe the involved structure mode and the propulsion mode,respectively. Analytical results on the pogo stability are obtained in terms of3dimensionless parameters. The effects of these three dimensionless parameters and alldimensional physical parameters on pogo stability are extensively discussed. Resultsshow that regulating the frequency of propulsion with accumulator until it is lower thanthat of structure is an efficient way to achieve robust pogo stability.
Secondly, a finite element approach of analyzing one dimensional fluid-structureinteraction problem is developed for modeling the suction line with arbitrary spatialconfigurations subjecting to large deformation. The pipe structure is divided through thenewly proposed Euler-Bernoulli beam element based on quaternion. Quaternionsinstead of Euler angles are adopted as nodal variables to avoid the traditional singularityproblem when describing the attitude of cross section. To meet the Euler-Bernoullibeam requirement, a requital interpolation method is also specially developed toguarantee the perpendicularity of cross section and tangent. The liquid in pipe isformulated through finite volume method whose control volume keeps on coinciding with the corresponding beam element during deformation. The governing equation ofcompressible and uncompressible liquid is established, and the reaction force tostructure is formulated. Numerical results show this approach is suitable for modelingfluid-structure interaction in one dimensional pipe.
Finally, a multibody dynamic approach of modeling liquid rocket is proposed forpogo stability analysis. All of components in propulsion system are successfullyimplemented into multibody dynamic program after fixing the converging problem metat solving motion equations of liquid and structure simultaneously. POGO stability of apropulsion system with both axisymmetric and non-axisymmetric configurations isnumerically addressed. Results show that, on the one hand, except longitudinalvibration modes, instability might happen at the bending modes or local models evenwith axisymmetric propulsion configuration, and this kind of instability could bemitigated by accumulator. On the other hand, non-axisymmetric configuration offeedline might introduce another kind of instability, which could be eliminated throughdesign of feedline instead of accumulator.
提出用三个无量纲数表征单结构振子和单液路振子耦合的稳定性。并解析/半解析地研究了各工作参数对POGO稳定性的影响。结果表明，将液路频率降至低于结构频率有利于减弱稳定性对参数的敏感度，从而获得POGO鲁棒性，即对一定质量范围的有效载荷和不同工况都稳定。
提出了一种一维流-管耦合动力学的有限元建模方法，用于描述空间任意构型输运管路的大范围运动。管壁由本文发展的Euler-Bernoulli梁单元建模，该单元采用四元数描述截面姿态，从根本上避免了用Euler角做广义坐标引入的三维奇异性问题，并在插值位移场时通过次序插值保证了Euler-Bernoulli梁的直法线假设，即中心切向与截面垂直。流体单元的控制体与运动的梁单元时刻重合，对流体可压与不可压两种情况分别建立控制方程，并考虑对结构的作用力。算例表明，该方法能很好的描述一维流-管的耦合动力学。
建立了基于多体动力学系统方程的液体火箭POGO稳定性分析方法。解决了流固耦合求解不收敛问题，将推进剂系统的各单元引入多体动力学求解框架中，使得可通过求解线化系统方程的特征值来判断系统稳定性。然后，建模并研究了某大型液体捆绑火箭在推进剂完全轴对称构型和局部非轴对称构型下的POGO稳定性。结果表明，除纵向模态外，即使在轴对称布局下，助推推进剂与结构的耦合也可能导致非轴对称的整体弯曲模态或局部模态的失稳，这可通过蓄压器调频来消除；管路的局部非轴对称构型也有可能引起系统不稳定，这种不稳定性需从管路设计上而非蓄压器调频来消除。
POGO vibration, resulted from the closed-loop instability between propulsionsystem and structure modes, is highly concerned in manned space flight. In analysis,only few important structure modes should be artificially selected, this complex themodeling work for checking stability of powerful bundled liquid rocket since a lot ofdensity structure modes has to be considered carefully. Hence, it is very necessary todevelop another easier and efficient approach for stability analysis. Besides, an idealrocket should be pogo robust, which means pogo free for a certain kind of payload andwide range of working conditions. While, flight data show that pogo stability behaviorsmission-specific and is highly sensitive to the dynamical working conditions. Therefore,it will be meaningful to qualitatively investigate the effect of physical factors onstability, and figure out the important parameters domain for achieving robust pogostability. This thesis is aimed at studying these two major problems.
Firstly, the effects of physical parameters on pogo stability are qualitativelyinvestigated through analytically approach. In the analysis, coupling between rocketstructure and a single-propellant system is transformed to a number of two coupledoscillators, which describe the involved structure mode and the propulsion mode,respectively. Analytical results on the pogo stability are obtained in terms of3dimensionless parameters. The effects of these three dimensionless parameters and alldimensional physical parameters on pogo stability are extensively discussed. Resultsshow that regulating the frequency of propulsion with accumulator until it is lower thanthat of structure is an efficient way to achieve robust pogo stability.
Secondly, a finite element approach of analyzing one dimensional fluid-structureinteraction problem is developed for modeling the suction line with arbitrary spatialconfigurations subjecting to large deformation. The pipe structure is divided through thenewly proposed Euler-Bernoulli beam element based on quaternion. Quaternionsinstead of Euler angles are adopted as nodal variables to avoid the traditional singularityproblem when describing the attitude of cross section. To meet the Euler-Bernoullibeam requirement, a requital interpolation method is also specially developed toguarantee the perpendicularity of cross section and tangent. The liquid in pipe isformulated through finite volume method whose control volume keeps on coinciding with the corresponding beam element during deformation. The governing equation ofcompressible and uncompressible liquid is established, and the reaction force tostructure is formulated. Numerical results show this approach is suitable for modelingfluid-structure interaction in one dimensional pipe.
Finally, a multibody dynamic approach of modeling liquid rocket is proposed forpogo stability analysis. All of components in propulsion system are successfullyimplemented into multibody dynamic program after fixing the converging problem metat solving motion equations of liquid and structure simultaneously. POGO stability of apropulsion system with both axisymmetric and non-axisymmetric configurations isnumerically addressed. Results show that, on the one hand, except longitudinalvibration modes, instability might happen at the bending modes or local models evenwith axisymmetric propulsion configuration, and this kind of instability could bemitigated by accumulator. On the other hand, non-axisymmetric configuration offeedline might introduce another kind of instability, which could be eliminated throughdesign of feedline instead of accumulator.
引文
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