多腔充液晃动及其飞行器系统耦合动力学研究
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摘要
本文以火箭飞行器系统外弹道设计为背景,对携带几十个装填液体子腔体的非旋转多充液腔飞行器系统外弹道特性和腔内液体晃动特性进行了系统深入的研究。
根据充液系统(液体-刚体)的数学模型,以圆柱形腔体为例,论述了非旋转充液系统腔内液体基本流动和复杂流动的理论、数值模拟与实验研究状况。主要取得了如下研究成果：
(1)在单腔充液晃动等效力学模型基础上,建立了多腔充液晃动等效力学模型,得出了多充液腔对飞行器的反作用力和力矩计算公式。
(2)建立了计算腔内液体小幅晃动固有频率和阻尼的有限元计算方法,对带球形底圆柱容器中不同液深情况下水平激励的液体小幅晃动进行了实验研究,获得了晃动第一阶固有频率和阻尼比,验证了有限元计算结果。
(3)对半球形容器中不同液深情况下液体第一阶侧向晃动自由衰减过程进行了实验,初步发现其非线性大幅晃动表现出的软特性,且阻尼比随振幅的变化关系是复杂的。对带球形底的圆柱容器中竖直激励下的液体非线性晃动进行了实验观测,显示了液珠喷射与最大激励加速度的关系,表明了液珠喷射和激励频率、表面张力系数的关系,及其液面重力波和毛细波的作用机制。
(4)对竖直和水平激励情形下的多充液腔晃动进行了实验研究。竖直和水平激励均可观察到超谐振动、共振晃动、马鞍型模态晃动、钟形模态共振和液珠喷射等现象。对竖直激励,当频率较低时,晃动幅度上层大下层小,当激励频率较高时,晃动幅度的层间差异反而不大。对水平激励,当频率较低时,晃动幅度层间差异不大,而当激励频率较高时,上层液体振动幅度普遍较下层液体大。
(5)应用Rumjantsev部分变量理论,建立了充液飞行器系统的耦合动力学数学模型,证明腔内液体主要通过壁面压力的作用力、力矩和质量力、力矩影响系统行为。
结合多腔充液火箭飞行器系统建立了飞行弹道仿真模型,对设计样机进行了仿真实验和计算。结果表明,对腔内所充液体量较小的飞行稳定飞行器,其飞行攻角小腔内液体的激励幅值小,因而液体晃动对飞行器弹道的影响也较小。而由于充液质心与飞行器质心不重合,却使液体质量力矩的影响变大。当充液质心与飞行器质心的距离较大时,对飞行器弹道的影响较严重,甚至导致飞行不稳定。相反减小充液质心与飞行器质心的距离,包括充液质量,可以减小腔内液体对飞行器弹道的影响。
In the dissertation, with the background of flight design to a rocket with several decade sub-cavities filled with liquid, the flight ballistic properties of rocket with liquid-filled multi-containers and liquid sloshing properties in container were investigated systemically.
Based on the mathematical models of liquid-filled system (liquid-rigid container), to the situations that the shape of container is cylindrical, an overview of the theoretical, numerical and experimental investigations on the basic flow and complicated flow in non-rotating liquid-filled system were presented.
Main results are as follows:
(1) On the basis of equivalent mechanical models for liquid sloshing in a single tank, the equivalent mechanical models for liquid sloshing in multi-tank were proposed, and the calculating formulas for forces and moments acting on flight vehicle due to liquid sloshing of multi-tank were obtained.
(2) A finite element method (FEM) for calculating eigenfrequencies and damping ratios of liquid sloshing with small amplitude was proposed. Some experiments on small amplitude liquid sloshing forced by horizontal excitations for different liquid depth in a circular cylindrical tank with spherical bottom were carried out. The first order eigenfrequency and damping ratio from experiments validated the calculating results by FEM.
(3) By the experiments results about attenuation process of first order lateral free sloshing in a hemisphere container for different liquid depth, it was founded primarily that the nonlinear sloshing with large amplitude shows softening behavior and the relationships between damping ratios and amplitudes are complex. Based on the experimental observations on liquid nonlinear sloshing forced by vertical excitation in a circular cylindrical tank with spherical bottom, the relationships between liquid drop ejecting and maximum exciting accelerations are given. And it was also indicated that the mechanism of liquid drop ejecting depends on excited frequencies and surface tension coefficients relying on gravitational waves and capillary waves on liquid surface.
(4) The experiments on liquid sloshing excited by vertical and horizontal excitations in multi-tank were performed. The phenomena about super-harmonic oscillation, resonant mode sloshing, saddle mode sloshing, campaniform mode sloshing, liquid drop ejecting etc. were observed in vertical and horizontal excitations. In the vertical situation, if the exciting frequency is low, the amplitude of sloshing in tank on top-layer is larger than that on bottom-layer. If the exciting frequency is high, the differences among amplitudes of sloshing in any layer are slight. In the horizontal situation, the case is opposite, which is that if the exciting frequency being low, the differences among amplitudes of sloshing in any layer are not evident, otherwise if the exciting frequency being high, the amplitude of sloshing in tank on top-layer is larger than that on bottom-layer.
(5) By applying the Rumjantsev's Partial Variable Theory (PVT), the mathematical models of coupling dynamics of liquid-filled flight vehicle were proposed. It was demonstrated that the behavior of flight system is mainly affected by the force and moment due to the pressure from the wall and the gravity of the liquid.
Combining with the design of rocket with liquid-filled sub-cavities, the simulating models of flight ballistics were established, and simulation calculations for planning model projectiles were processed. Following conclusions were obtained. In a situation that the flight of rocket filled with small liquid mass is stable, because the attack angle and the excited amplitude to liquid within container are small, so the influences of liquid sloshing to rocket flight ballistics are also small. However, if the mass center of liquid is not coincided with that of flight vehicle, the influences of liquid gravity moment become large. When the distance between the mass center of liquid and the mass center of flight vehicle is large, the influences to rocket flight ballistics become serious, which even induce flight instability. In reverse, reducing the distance and the liquid mass, the influences to rocket flight ballistics may be decreased.
根据充液系统(液体-刚体)的数学模型,以圆柱形腔体为例,论述了非旋转充液系统腔内液体基本流动和复杂流动的理论、数值模拟与实验研究状况。主要取得了如下研究成果：
(1)在单腔充液晃动等效力学模型基础上,建立了多腔充液晃动等效力学模型,得出了多充液腔对飞行器的反作用力和力矩计算公式。
(2)建立了计算腔内液体小幅晃动固有频率和阻尼的有限元计算方法,对带球形底圆柱容器中不同液深情况下水平激励的液体小幅晃动进行了实验研究,获得了晃动第一阶固有频率和阻尼比,验证了有限元计算结果。
(3)对半球形容器中不同液深情况下液体第一阶侧向晃动自由衰减过程进行了实验,初步发现其非线性大幅晃动表现出的软特性,且阻尼比随振幅的变化关系是复杂的。对带球形底的圆柱容器中竖直激励下的液体非线性晃动进行了实验观测,显示了液珠喷射与最大激励加速度的关系,表明了液珠喷射和激励频率、表面张力系数的关系,及其液面重力波和毛细波的作用机制。
(4)对竖直和水平激励情形下的多充液腔晃动进行了实验研究。竖直和水平激励均可观察到超谐振动、共振晃动、马鞍型模态晃动、钟形模态共振和液珠喷射等现象。对竖直激励,当频率较低时,晃动幅度上层大下层小,当激励频率较高时,晃动幅度的层间差异反而不大。对水平激励,当频率较低时,晃动幅度层间差异不大,而当激励频率较高时,上层液体振动幅度普遍较下层液体大。
(5)应用Rumjantsev部分变量理论,建立了充液飞行器系统的耦合动力学数学模型,证明腔内液体主要通过壁面压力的作用力、力矩和质量力、力矩影响系统行为。
结合多腔充液火箭飞行器系统建立了飞行弹道仿真模型,对设计样机进行了仿真实验和计算。结果表明,对腔内所充液体量较小的飞行稳定飞行器,其飞行攻角小腔内液体的激励幅值小,因而液体晃动对飞行器弹道的影响也较小。而由于充液质心与飞行器质心不重合,却使液体质量力矩的影响变大。当充液质心与飞行器质心的距离较大时,对飞行器弹道的影响较严重,甚至导致飞行不稳定。相反减小充液质心与飞行器质心的距离,包括充液质量,可以减小腔内液体对飞行器弹道的影响。
In the dissertation, with the background of flight design to a rocket with several decade sub-cavities filled with liquid, the flight ballistic properties of rocket with liquid-filled multi-containers and liquid sloshing properties in container were investigated systemically.
Based on the mathematical models of liquid-filled system (liquid-rigid container), to the situations that the shape of container is cylindrical, an overview of the theoretical, numerical and experimental investigations on the basic flow and complicated flow in non-rotating liquid-filled system were presented.
Main results are as follows:
(1) On the basis of equivalent mechanical models for liquid sloshing in a single tank, the equivalent mechanical models for liquid sloshing in multi-tank were proposed, and the calculating formulas for forces and moments acting on flight vehicle due to liquid sloshing of multi-tank were obtained.
(2) A finite element method (FEM) for calculating eigenfrequencies and damping ratios of liquid sloshing with small amplitude was proposed. Some experiments on small amplitude liquid sloshing forced by horizontal excitations for different liquid depth in a circular cylindrical tank with spherical bottom were carried out. The first order eigenfrequency and damping ratio from experiments validated the calculating results by FEM.
(3) By the experiments results about attenuation process of first order lateral free sloshing in a hemisphere container for different liquid depth, it was founded primarily that the nonlinear sloshing with large amplitude shows softening behavior and the relationships between damping ratios and amplitudes are complex. Based on the experimental observations on liquid nonlinear sloshing forced by vertical excitation in a circular cylindrical tank with spherical bottom, the relationships between liquid drop ejecting and maximum exciting accelerations are given. And it was also indicated that the mechanism of liquid drop ejecting depends on excited frequencies and surface tension coefficients relying on gravitational waves and capillary waves on liquid surface.
(4) The experiments on liquid sloshing excited by vertical and horizontal excitations in multi-tank were performed. The phenomena about super-harmonic oscillation, resonant mode sloshing, saddle mode sloshing, campaniform mode sloshing, liquid drop ejecting etc. were observed in vertical and horizontal excitations. In the vertical situation, if the exciting frequency is low, the amplitude of sloshing in tank on top-layer is larger than that on bottom-layer. If the exciting frequency is high, the differences among amplitudes of sloshing in any layer are slight. In the horizontal situation, the case is opposite, which is that if the exciting frequency being low, the differences among amplitudes of sloshing in any layer are not evident, otherwise if the exciting frequency being high, the amplitude of sloshing in tank on top-layer is larger than that on bottom-layer.
(5) By applying the Rumjantsev's Partial Variable Theory (PVT), the mathematical models of coupling dynamics of liquid-filled flight vehicle were proposed. It was demonstrated that the behavior of flight system is mainly affected by the force and moment due to the pressure from the wall and the gravity of the liquid.
Combining with the design of rocket with liquid-filled sub-cavities, the simulating models of flight ballistics were established, and simulation calculations for planning model projectiles were processed. Following conclusions were obtained. In a situation that the flight of rocket filled with small liquid mass is stable, because the attack angle and the excited amplitude to liquid within container are small, so the influences of liquid sloshing to rocket flight ballistics are also small. However, if the mass center of liquid is not coincided with that of flight vehicle, the influences of liquid gravity moment become large. When the distance between the mass center of liquid and the mass center of flight vehicle is large, the influences to rocket flight ballistics become serious, which even induce flight instability. In reverse, reducing the distance and the liquid mass, the influences to rocket flight ballistics may be decreased.
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