考虑毛细效应的液体小幅晃动问题研究
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摘要
随着航天工程的深入发展,航天器所携带的液体燃料以及液体载荷越来越多,而另一方面对其姿态保持和机动的要求也越来越高,这就需要对航天器中液体的晃动行为进行更为深入细致的研究。为此本文从航天工程应用的实际出发,从理论、计算和实验三方面对考虑毛细效应的液体小幅晃动问题进行了系统的研究。
在理论方面,本文以改进的方式重新推导了考虑毛细效应的液体小幅晃动问题的方程和边界条件。对液体小幅晃动的阻尼理论进行了总结和发展,提出了计算接触线处以及表面活性物质带来的能量耗散的新方法,以便于工程应用。通过量纲分析的方法揭示了采用不考虑毛细效应的边界条件和零重力两种特殊情况下,晃动频率和阻尼随各特征量的变化关系,得到了一些有用和有趣的结论。
在计算方面,本文对考虑毛细效应的液体小幅晃动的有限元模态分析方法进行了系统的研究,按照应用对象将研究分成两部分。一部分是在计算液体晃动频率和模态时不考虑毛细效应的影响,但在随后计算晃动阻尼时将毛细效应引入进来。在算得的晃动频率、模态和阻尼的基础上本文还进一步研究了建立液体小幅晃动等效力学模型的方法。值得一提的是,这部分的有限元计算曾成功地应用于我国某大型卫星燃料箱液体晃动的建模之中。另一部分是在晃动频率、模态、晃动阻尼比的计算中均考虑了毛细效应的影响。由于不同的接触线边界条件下液体小幅晃动的有限元分析方法也有所不同,因此本文分别对接触线为固定端、自由端和浸润边界条件三种情形,建立了相应的有限元计算方法。另外,还对表面活性物质引起能量耗散的精确计算方法进行了研究。
本文对带有半球形底的圆柱容器中液体的小幅晃动和半球形容器中液体自由衰减晃动非线性效应进行了实验研究。测量了小幅晃动的频率、阻尼和自由衰减晃动的时间历程,验证了本文有限元模态分析方法的有效性,并观察到了一些有理论意义的非线性现象。
As the developing of aerospace engineering, spacecrafts bring more and more propellant and liquid charge, on the other hand the attitude keeping and maneuvering are required to be more and more accurate, so the liquid sloshing on spacecraft needs to be studied deeply. From the perspective of aerospace engineering, this thesis studys the liquid sloshing with small amplitude considering capillary effect by theoretical , numerical and experimental methods.
In the part of theoretical research the equation and boundary conditions of liquid sloshing with small amplitude considering capillary effect are derived in a new way . The damping theory of liquid sloshing is summarized and developed, new methods of calculation the energy dissipation at contact line and surfactant are proposed. The relationship of characteristic parameters and sloshing frequency , damping in two special case is studied by demensional ananlysis method, some useful results are obtained.
In the part of numerical research the FEM modal analysis method of liquid small amplitude sloshing considering capillary effect is studied systematically. According to the different application objects the study is composed of two parts. One is the FEM using boundary conditions without capillary effect. In this case the calculation of frequcies and modals doesn’t consider capillary effect, but the calculation of damping considers it. The numerical method of this part has been used in the slohing modeling of a Chinese large satellite successfully. The other part of numercal research is the FEM using boundary conditions with capillary effect. In this case the calculation of frequencies, modal and damping all take capillary effect into account. Because differete contact line boundary conditons make the numerical method different, the pin-end, free-end and wetting boundary conditions of contact line are dealt with separately. The accurate calculation of surfactant dissipation is also consider in this thesis.
In the part of experimental research the small amplitude liquid sloshing in a cylindrical container with hemisphere bottom and the nonlinear effect of liquid freely sloshing in a hemisphere container are studied. The experiment results prove the effectiveness of the FEM modal analysis method and show some interesting nonlinear phenomenon.
在理论方面,本文以改进的方式重新推导了考虑毛细效应的液体小幅晃动问题的方程和边界条件。对液体小幅晃动的阻尼理论进行了总结和发展,提出了计算接触线处以及表面活性物质带来的能量耗散的新方法,以便于工程应用。通过量纲分析的方法揭示了采用不考虑毛细效应的边界条件和零重力两种特殊情况下,晃动频率和阻尼随各特征量的变化关系,得到了一些有用和有趣的结论。
在计算方面,本文对考虑毛细效应的液体小幅晃动的有限元模态分析方法进行了系统的研究,按照应用对象将研究分成两部分。一部分是在计算液体晃动频率和模态时不考虑毛细效应的影响,但在随后计算晃动阻尼时将毛细效应引入进来。在算得的晃动频率、模态和阻尼的基础上本文还进一步研究了建立液体小幅晃动等效力学模型的方法。值得一提的是,这部分的有限元计算曾成功地应用于我国某大型卫星燃料箱液体晃动的建模之中。另一部分是在晃动频率、模态、晃动阻尼比的计算中均考虑了毛细效应的影响。由于不同的接触线边界条件下液体小幅晃动的有限元分析方法也有所不同,因此本文分别对接触线为固定端、自由端和浸润边界条件三种情形,建立了相应的有限元计算方法。另外,还对表面活性物质引起能量耗散的精确计算方法进行了研究。
本文对带有半球形底的圆柱容器中液体的小幅晃动和半球形容器中液体自由衰减晃动非线性效应进行了实验研究。测量了小幅晃动的频率、阻尼和自由衰减晃动的时间历程,验证了本文有限元模态分析方法的有效性,并观察到了一些有理论意义的非线性现象。
As the developing of aerospace engineering, spacecrafts bring more and more propellant and liquid charge, on the other hand the attitude keeping and maneuvering are required to be more and more accurate, so the liquid sloshing on spacecraft needs to be studied deeply. From the perspective of aerospace engineering, this thesis studys the liquid sloshing with small amplitude considering capillary effect by theoretical , numerical and experimental methods.
In the part of theoretical research the equation and boundary conditions of liquid sloshing with small amplitude considering capillary effect are derived in a new way . The damping theory of liquid sloshing is summarized and developed, new methods of calculation the energy dissipation at contact line and surfactant are proposed. The relationship of characteristic parameters and sloshing frequency , damping in two special case is studied by demensional ananlysis method, some useful results are obtained.
In the part of numerical research the FEM modal analysis method of liquid small amplitude sloshing considering capillary effect is studied systematically. According to the different application objects the study is composed of two parts. One is the FEM using boundary conditions without capillary effect. In this case the calculation of frequcies and modals doesn’t consider capillary effect, but the calculation of damping considers it. The numerical method of this part has been used in the slohing modeling of a Chinese large satellite successfully. The other part of numercal research is the FEM using boundary conditions with capillary effect. In this case the calculation of frequencies, modal and damping all take capillary effect into account. Because differete contact line boundary conditons make the numerical method different, the pin-end, free-end and wetting boundary conditions of contact line are dealt with separately. The accurate calculation of surfactant dissipation is also consider in this thesis.
In the part of experimental research the small amplitude liquid sloshing in a cylindrical container with hemisphere bottom and the nonlinear effect of liquid freely sloshing in a hemisphere container are studied. The experiment results prove the effectiveness of the FEM modal analysis method and show some interesting nonlinear phenomenon.
引文
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