热流固耦合下的螺旋槽干气密封特性及失稳分析
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摘要
干气密封系统可靠运行的关键在于保证干气密封系统内气膜动态稳定性。端面密封内润滑气膜的稳定性与其温度、动力学特性密切相关,从干气密封系统热流体非线性动力学分析；系统轴向运动失稳分析；系统角向摆动失稳分析；实验验证,这四个方面来进行研究,对应不同的角度分析了系统稳定运行的条件,通过试验验证了所建立模型和数值计算的正确性。
首先,从热流体力学理论出发,对干气密封系统内密封气膜的热力过程进行了研究,分析了系统内部产生的热导致的密封环的热弹变形,从而对密封性能的影响。基于滑移边界条件下的雷诺方程,不考虑密封环的变形,求解获得气膜压力函数式；根据气膜微尺度流体流动过程中熵变方程,得到螺旋槽内气膜温度场分布；考虑微槽道内气流在不同阶段的熵变过程,分析了气膜温度场在不同多变指数下的分布规律；进而在不同多变指数下计算出密封环的热弹变形量及气膜厚度近似表达式；求出无变形时理论泄漏量和考虑不同多变指数下热弹变形的泄漏量,并与实验值进行比对,验证了泄漏量在采用不同多变指数时更接近试验数据。
其次,基于非线性振动理论,研究了系统轴向非线性稳定性问题。建立轴向振动下系统流固耦合动力学模型,求解振动方程,分析失稳点振动非线性动力学行为。利用数值算法找到失稳点域,并在特定的螺旋槽结构参数范围内发现了混沌运动,通过选择合理的螺旋槽结构参数进行控制混沌。得到控制系统稳定运行的结构参数区域。在特例下计算并拟合非线性气膜轴向刚度,得到了一个含二次、三次项的非线性受迫振动微分方程。在无外激励情况下,通过求Floquet指数讨论了系统分岔问题,分析了螺旋角对系统稳定性的影响,给出了使干气密封系统稳定运行的螺旋角范围。
再次,研究了系统角向非线性稳定性问题。建立了角向振动下系统的动力学模型,求解角向摆动的二维振动方程,获得了密封系统失稳时的密封结构参数,分析了临界转动惯量与螺旋角之间的定量关系及失稳点振动的非线性动力学行为,同样得到控制系统稳定运行的结构参数区域。同时建立了气膜-密封环系统角向摆动动力学模型,将气膜厚度表示为含有摆角的变量,在特例下计算并拟合非线性气膜角向刚度,得到了一个含二次、三次项的非线性受迫振动微分方程。在无外激励情况下,通过求Floquet指数讨论了系统分岔问题,分析了螺旋角对系统稳定性的影响,给出了使干气密封系统稳定运行的螺旋角范围。
最后,在密封试验台上对干气密封样机进行了试验研究,完成了气体端面密封试验台的测试系统的总体方案设计、测试系统的硬件配置。测试了泄漏量、气膜轴向刚度和振动位移,给出了气体端面密封试验的测试结果,并与理论计算近似值比较,进行误差分析。试验测出数值与计算结果较为吻合,表明所建立的螺旋槽干气密封气膜密封环系统的数学和力学模型是正确的,所编制的近似计算程序可行。
It is the key point to ensure reliable and safe operation of gas seal system to keep the dynamic stability of the gas film. The stability of the face seal film is closely related to its temperature and dynamical characteristics, from four aspects:thermal fluid nonlinear dynamical analysis of gas seal system, instability analysis of axial for the dry gas seals system, instability analysis of angular wobbly for the system, experimental validation, the safe operation conditions of the system are analysized form different angles, the accuracy of the mode and the numerical calculation are proved through experiments.
First, thermal process of the lubricated gas film for the system was stadied based on the thermal hydrodynamics theory, the thermo-elastic deformation of the seals ring caused by the heat of the system and its effect on the seal properties are analysized. The pressure distributions function is obtained not considering the seal rings' deformation based on the Reynolds equation under the slid boundary conditions, the entropy variation equations of fluid in the spiral groove are derived and the temperature field distributions of the gas film are obtained. The temperature distribution of the gas film under the different polytropic exponent is analyzed considering the process of entropy change of the fluid in the spiral groove. The thermo-elastic deformation of the seal rings and the approximate analytic of the gas film thickness is obtained under the different polytropic exponent, the theoretical leakages considering and not considering the thermo-elastic deformation are obtained, then compared with the experimental measurements, the leakage by using the different polytropic exponent is closer to the experimental measurements than the theoretical value.
Secondly, nonlinear stability of axial for the system was studied based on the nonlinear vibration theory. A fluid-structure interaction dynamic model of axial vibration of the system was established, the vibration equation was solved and the nonlinear dynamics behavior of the instability point was analyzed. Instability point-fields is obtained using the numerical method, the chaotic motion was found under the specific spiral grooved parameters of the structure, and then the chaotic motion was controlled by select reasonable parameters. Nonlinear forced vibration differential equation contains the second and the third order was derived while the nonlinear axial rigidity of the gas film was calculated and simulated, The bifurcation question was discussed according to solve the Floquet exponent unconsidering the outer excitation, and the stability influenced by spiral angle was analyzed in the system, the range of the spiral angle enable system stable was given.
Again, nonlinear stability of angular wobbly for the system was studied. The dynamic model of the angular wobbly of the system was established, and the angular wobbly two-dimensional vibration equations were solved, then instability parameters of the system were obtained, quantitative relation of critical moment of inertia and the angle and the nonlinear dynamic behavior of the instability point was analyzed, parameters of the structure enable system stable is obtained also. The dynamical angular wobbly vibration model of the gas film and seal rings in the system of dry gas seals was established, a nonlinear forced vibration differential equation contains the second and the third order was derived while the rigidity of the gas film is expressed as a variable containing the swing angle, The bifurcation question was discussed according to solve the Floquet exponent unconsidering the outer excitation, and the stability influenced by spiral angle was analyzed in the system, the range of the spiral angle enable system stable was given.
At last, the experimental investigation of dry gas seal prototype was conducted on the sealing test device, and the overall plan design and the hardware configuration of the test system is proposed. Leakage, gaseous film axial rigidity and sealing ring axial vibration displacement are tested, test results are obtained and the error between test and calculation data is analyzed.The results show that dynamical and mathematical model for the system of gas film and seal rings of the spiral groove dry gas seal is validated correctly comparing the data from experiments with the approximate calculation, and the developed program of approximate analysis method is practicable.
首先,从热流体力学理论出发,对干气密封系统内密封气膜的热力过程进行了研究,分析了系统内部产生的热导致的密封环的热弹变形,从而对密封性能的影响。基于滑移边界条件下的雷诺方程,不考虑密封环的变形,求解获得气膜压力函数式；根据气膜微尺度流体流动过程中熵变方程,得到螺旋槽内气膜温度场分布；考虑微槽道内气流在不同阶段的熵变过程,分析了气膜温度场在不同多变指数下的分布规律；进而在不同多变指数下计算出密封环的热弹变形量及气膜厚度近似表达式；求出无变形时理论泄漏量和考虑不同多变指数下热弹变形的泄漏量,并与实验值进行比对,验证了泄漏量在采用不同多变指数时更接近试验数据。
其次,基于非线性振动理论,研究了系统轴向非线性稳定性问题。建立轴向振动下系统流固耦合动力学模型,求解振动方程,分析失稳点振动非线性动力学行为。利用数值算法找到失稳点域,并在特定的螺旋槽结构参数范围内发现了混沌运动,通过选择合理的螺旋槽结构参数进行控制混沌。得到控制系统稳定运行的结构参数区域。在特例下计算并拟合非线性气膜轴向刚度,得到了一个含二次、三次项的非线性受迫振动微分方程。在无外激励情况下,通过求Floquet指数讨论了系统分岔问题,分析了螺旋角对系统稳定性的影响,给出了使干气密封系统稳定运行的螺旋角范围。
再次,研究了系统角向非线性稳定性问题。建立了角向振动下系统的动力学模型,求解角向摆动的二维振动方程,获得了密封系统失稳时的密封结构参数,分析了临界转动惯量与螺旋角之间的定量关系及失稳点振动的非线性动力学行为,同样得到控制系统稳定运行的结构参数区域。同时建立了气膜-密封环系统角向摆动动力学模型,将气膜厚度表示为含有摆角的变量,在特例下计算并拟合非线性气膜角向刚度,得到了一个含二次、三次项的非线性受迫振动微分方程。在无外激励情况下,通过求Floquet指数讨论了系统分岔问题,分析了螺旋角对系统稳定性的影响,给出了使干气密封系统稳定运行的螺旋角范围。
最后,在密封试验台上对干气密封样机进行了试验研究,完成了气体端面密封试验台的测试系统的总体方案设计、测试系统的硬件配置。测试了泄漏量、气膜轴向刚度和振动位移,给出了气体端面密封试验的测试结果,并与理论计算近似值比较,进行误差分析。试验测出数值与计算结果较为吻合,表明所建立的螺旋槽干气密封气膜密封环系统的数学和力学模型是正确的,所编制的近似计算程序可行。
It is the key point to ensure reliable and safe operation of gas seal system to keep the dynamic stability of the gas film. The stability of the face seal film is closely related to its temperature and dynamical characteristics, from four aspects:thermal fluid nonlinear dynamical analysis of gas seal system, instability analysis of axial for the dry gas seals system, instability analysis of angular wobbly for the system, experimental validation, the safe operation conditions of the system are analysized form different angles, the accuracy of the mode and the numerical calculation are proved through experiments.
First, thermal process of the lubricated gas film for the system was stadied based on the thermal hydrodynamics theory, the thermo-elastic deformation of the seals ring caused by the heat of the system and its effect on the seal properties are analysized. The pressure distributions function is obtained not considering the seal rings' deformation based on the Reynolds equation under the slid boundary conditions, the entropy variation equations of fluid in the spiral groove are derived and the temperature field distributions of the gas film are obtained. The temperature distribution of the gas film under the different polytropic exponent is analyzed considering the process of entropy change of the fluid in the spiral groove. The thermo-elastic deformation of the seal rings and the approximate analytic of the gas film thickness is obtained under the different polytropic exponent, the theoretical leakages considering and not considering the thermo-elastic deformation are obtained, then compared with the experimental measurements, the leakage by using the different polytropic exponent is closer to the experimental measurements than the theoretical value.
Secondly, nonlinear stability of axial for the system was studied based on the nonlinear vibration theory. A fluid-structure interaction dynamic model of axial vibration of the system was established, the vibration equation was solved and the nonlinear dynamics behavior of the instability point was analyzed. Instability point-fields is obtained using the numerical method, the chaotic motion was found under the specific spiral grooved parameters of the structure, and then the chaotic motion was controlled by select reasonable parameters. Nonlinear forced vibration differential equation contains the second and the third order was derived while the nonlinear axial rigidity of the gas film was calculated and simulated, The bifurcation question was discussed according to solve the Floquet exponent unconsidering the outer excitation, and the stability influenced by spiral angle was analyzed in the system, the range of the spiral angle enable system stable was given.
Again, nonlinear stability of angular wobbly for the system was studied. The dynamic model of the angular wobbly of the system was established, and the angular wobbly two-dimensional vibration equations were solved, then instability parameters of the system were obtained, quantitative relation of critical moment of inertia and the angle and the nonlinear dynamic behavior of the instability point was analyzed, parameters of the structure enable system stable is obtained also. The dynamical angular wobbly vibration model of the gas film and seal rings in the system of dry gas seals was established, a nonlinear forced vibration differential equation contains the second and the third order was derived while the rigidity of the gas film is expressed as a variable containing the swing angle, The bifurcation question was discussed according to solve the Floquet exponent unconsidering the outer excitation, and the stability influenced by spiral angle was analyzed in the system, the range of the spiral angle enable system stable was given.
At last, the experimental investigation of dry gas seal prototype was conducted on the sealing test device, and the overall plan design and the hardware configuration of the test system is proposed. Leakage, gaseous film axial rigidity and sealing ring axial vibration displacement are tested, test results are obtained and the error between test and calculation data is analyzed.The results show that dynamical and mathematical model for the system of gas film and seal rings of the spiral groove dry gas seal is validated correctly comparing the data from experiments with the approximate calculation, and the developed program of approximate analysis method is practicable.
引文
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