超超临界汽轮发电机组气流激振机理分析及实验研究
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摘要
随着超超临界汽轮机技术的发展，汽轮发电机组蒸汽参数不断地提高以及负荷不断增加，气流激振对汽轮机转子的影响日益突出，严重影响了汽轮机安全稳定的运行。由于超超临界汽轮机组内部流场十分复杂，气流激振对转子的作用力含有严重的非线性因素，因此对气流激振机理分析存在一定的困难。在国家自然科学基金重点项目：“超超临界汽轮发电机组转子系统的若干非线性动力学问题”的资助下，本文应用流体计算动力学(CFD)分析方法和通过转子-密封系统动力学实验，研究了密封中气流激振力对转子的影响。并应用相关非线性动力学的方法，从理论上分析了超超临界汽轮发电机组轴端密封中气流激振的机理。本论文的主要研究内容如下：
针对超超临界汽轮发电机组轴端密封建立了二维流场模型和全三维流场模型，基于CFD计算模拟了密封流场的内部结构，并分析了密封流场特性。进一步研究了转子相对偏移量、转速和进出口压比对密封流场的影响，得到了气流激振力与这些参数的非线性关系。根据CFD技术计算得到的密封流场结果，对Muszynska气流激振力模型中的经验参数和实验参数进行系统辨识，解决了模型中相关经验参数和实验系数难以确定的问题，得到了适用于超超临界汽轮发电机组轴端密封气流激振力模型的相关系数，为超超临界汽轮发电机组转子-密封系统非线性动力学分析奠定了基础。
随后利用辨识经验系数和实验系数，对转子-密封系统进行幂级数展开得到了系统幂级数模型，先根据Hopf分岔定理和稳定性理论，研究了超超临界汽轮机组转子-密封自治系统在平衡点失稳的机理，结果表明当系统转速达到临界值时，系统开始出现Hopf分岔，并进入周期涡动状态。并进一步研究了转子存在不平衡质量时系统的非线性动力学特性，应用多尺度法计算得到了超超临界汽轮机组转子-密封非自治系统1:2亚谐共振的分岔方程，对分岔方程进行了奇异性分析，研究了转子-密封系统1:2亚谐共振的工程开折问题，得到了奇异性参数空间上的转迁集，并根据转迁集划分的不同参数区域分别计算了系统分岔曲线。结果表明：超超临界汽轮机组系统在不同的参数区域上存在超临界Hopf分岔和亚临界Hopf分岔现象。之后并通过计算Floquet乘子来研究超超临界汽轮机组转子-密封系统周期解的稳定性。
为了更好的研究在参数取值范围内，超超临界汽轮机组转子-密封系统的非线性动力学特性，对系统进行了全局分岔研究。利用系统1:1主共振，1:2亚谐共振和1:3亚谐共振幅频方程实数解的存在条件构造出系统的Arnold舌头解析曲线，根据Arnold舌头是否存在叠加来判断系统出现混沌的可能性。并通过数值计算研究了Arnold舌头叠加区域与非叠加区域内系统动力学行为，研究结果表明：当转子-密封系统的参数处于Arnold舌头叠加区域内时，系统会出现多倍周期，拟周期以及混沌等动力学特性。并应用最大Lyapunov指数进一步判断了系统是否出现混沌现象。
本文设计并建立了哈尔滨工业大学转子-密封系统实验台，进一步研究密封中气流激振的机理。在现有的实验室条件下，通过流场计算和理论分析设计了转子-密封实验台的结构参数。实验密封结构采用了哈尔滨汽轮机厂超临界汽轮机组轴端密封结构，自主设计了径向间隙可调的密封机械结构，实现了在同一转子实验台上进行不同密封间隙的测量工作。应用影响系数法对实验台转子进行了高精度的动平衡，使得转子系统可以稳定运行在高转速下。并测试了系统在不同进气压力以及在不同径向密封间隙下的振动数据，并观测到了密封中气流激振力对转子的影响。
With development of ultra-supercritical steam technology, the parameters andthe load of steam turbine unit have been continuously improved, and gas exctingforce is increasingly prominent, which influences the stablility of the steam turbineseriously. Since the flow flied of the steam turbine are complex and the gas exctingforce on the rotor has much nonlinear factors, it is difficult to reseach the gasexciting force of the turbine. The paper is supported by the National Natural Sciencefoundation of key projects,“some nonlinear dynamics problems ofultra-supercritical turbine generator rotor system”. The effect of the gas flow in theseals for the rotor is researched by Comutational Fluid Dynamics (CFD) technologyand the experimemtal study of the rotor-seal system. By nonlinear dynamicsmethods, the mechnanism of the gas exciting force in the seal for the steam tubineunite are studied. The main content and conclusions of the paper are as follows:
The two-dimension model and three-dimension model of the seals on the shaftare established. Based on the calculation of interior flow field of the seals using theCFD method, the charateristics of the seals are analyzed. And then, the paperresearches the effect of relative eccentricity, rotating speed of the rotor and thepressure ratio of the seal on the gas exciting force, which shows the nonlinearrelationship between the gas exciting force and the paramters. Lastly the empiricalparameters and experimental parameters of the Muszynska gas exciting force modelare identified to solve the problem that the parameters of the model are difficult todetermine. The identified coefficients of the shaft seal model on the steam turbineunit are suitalbe. The results mentiond above provide the basis for the nonlineardynamic analysis of the rotor-seal system.
The power series model of the rotor-seal system of the ultra-supercritical steamturbine are obtained by Taylor expansion. According to Hopf bifurcation theory andstability theory, the paper researches the mechanism of the instability of therotor-seal autonomous system of the ultra-supercritical steam turbine on theequilibrium position. The results shows that system has the Hopf bifurcationphenomenon at the sloved theshold speed, and have the periodic orbit after the Hopfbifurcation. The multiple scale method are used to obtain the bifurcation equationsof the rotor-seal non-autonomous system of the ultra-supercritical steam turbine, forstudying the effects of the rotor’s imbalance excitation on the nonlinear dynamiccharacteristic of the system, in the1:2subharmonic resonance case. Through thesingularity analysis of the1:2subharmonic resonance bifurcation equations, the paper studied engineering unfolding problems of the rotor-seal system. Thetransition sets and the local bifurcations diagrams of the system parameter space areobtained. The results show that system has the supercritical Hopf bifurcation andsubcritical Hopf bifurcation in the different parameters regions. Lastly, Floquetmultiplier is applied to the study on the stabilities and dynamic behaviors of theperiodic solutions of the systems by shooting method.
According to the real solution conditions of the bifurcation equations in the1:1main resonance,1:2subharmonic resonance and1:3subharmonic resonance, theArnold tongue are constructed to study the global bifurcation of the system by theanalytical method. Then the paper studies the dynamic characteristics of the systemin the Arnold tongues overlap and non-overlap. The results show that when thesystem parameters are in the Arnold tongues overlap region, the system appearmulti-times cycle motion and chaotic motion for the coexistence of the resonancesolutions. And the chaotic motion is confirmed by the largest Lyapunov exponent.
Finally, the dynamic testing rig of the rotor-seal system are designed and builtin the Harbin Institute of Technology for further studying the effect of the gasexcitation on the rotor-seal system. According to the current condition of experiment,the structure parameters of the rig are confirmed by CFD calculation and theoreticalanalysis. The seal structure simulates the current structure of the steam turbines ofHarbin steam turbine factory, and independent seal facility with adjustable clearanceis designed to achieve the dynamic tests of the system with the different clearancesin the same rig. By using effect coefficient method, the dynamic balance of the rotorreaches a good level and the rotor can work at high rotating speed. The vibrationtests of the rotor are done when the input pressure is zero and different values, tostudy the influence of the gas excitation.
针对超超临界汽轮发电机组轴端密封建立了二维流场模型和全三维流场模型，基于CFD计算模拟了密封流场的内部结构，并分析了密封流场特性。进一步研究了转子相对偏移量、转速和进出口压比对密封流场的影响，得到了气流激振力与这些参数的非线性关系。根据CFD技术计算得到的密封流场结果，对Muszynska气流激振力模型中的经验参数和实验参数进行系统辨识，解决了模型中相关经验参数和实验系数难以确定的问题，得到了适用于超超临界汽轮发电机组轴端密封气流激振力模型的相关系数，为超超临界汽轮发电机组转子-密封系统非线性动力学分析奠定了基础。
随后利用辨识经验系数和实验系数，对转子-密封系统进行幂级数展开得到了系统幂级数模型，先根据Hopf分岔定理和稳定性理论，研究了超超临界汽轮机组转子-密封自治系统在平衡点失稳的机理，结果表明当系统转速达到临界值时，系统开始出现Hopf分岔，并进入周期涡动状态。并进一步研究了转子存在不平衡质量时系统的非线性动力学特性，应用多尺度法计算得到了超超临界汽轮机组转子-密封非自治系统1:2亚谐共振的分岔方程，对分岔方程进行了奇异性分析，研究了转子-密封系统1:2亚谐共振的工程开折问题，得到了奇异性参数空间上的转迁集，并根据转迁集划分的不同参数区域分别计算了系统分岔曲线。结果表明：超超临界汽轮机组系统在不同的参数区域上存在超临界Hopf分岔和亚临界Hopf分岔现象。之后并通过计算Floquet乘子来研究超超临界汽轮机组转子-密封系统周期解的稳定性。
为了更好的研究在参数取值范围内，超超临界汽轮机组转子-密封系统的非线性动力学特性，对系统进行了全局分岔研究。利用系统1:1主共振，1:2亚谐共振和1:3亚谐共振幅频方程实数解的存在条件构造出系统的Arnold舌头解析曲线，根据Arnold舌头是否存在叠加来判断系统出现混沌的可能性。并通过数值计算研究了Arnold舌头叠加区域与非叠加区域内系统动力学行为，研究结果表明：当转子-密封系统的参数处于Arnold舌头叠加区域内时，系统会出现多倍周期，拟周期以及混沌等动力学特性。并应用最大Lyapunov指数进一步判断了系统是否出现混沌现象。
本文设计并建立了哈尔滨工业大学转子-密封系统实验台，进一步研究密封中气流激振的机理。在现有的实验室条件下，通过流场计算和理论分析设计了转子-密封实验台的结构参数。实验密封结构采用了哈尔滨汽轮机厂超临界汽轮机组轴端密封结构，自主设计了径向间隙可调的密封机械结构，实现了在同一转子实验台上进行不同密封间隙的测量工作。应用影响系数法对实验台转子进行了高精度的动平衡，使得转子系统可以稳定运行在高转速下。并测试了系统在不同进气压力以及在不同径向密封间隙下的振动数据，并观测到了密封中气流激振力对转子的影响。
With development of ultra-supercritical steam technology, the parameters andthe load of steam turbine unit have been continuously improved, and gas exctingforce is increasingly prominent, which influences the stablility of the steam turbineseriously. Since the flow flied of the steam turbine are complex and the gas exctingforce on the rotor has much nonlinear factors, it is difficult to reseach the gasexciting force of the turbine. The paper is supported by the National Natural Sciencefoundation of key projects,“some nonlinear dynamics problems ofultra-supercritical turbine generator rotor system”. The effect of the gas flow in theseals for the rotor is researched by Comutational Fluid Dynamics (CFD) technologyand the experimemtal study of the rotor-seal system. By nonlinear dynamicsmethods, the mechnanism of the gas exciting force in the seal for the steam tubineunite are studied. The main content and conclusions of the paper are as follows:
The two-dimension model and three-dimension model of the seals on the shaftare established. Based on the calculation of interior flow field of the seals using theCFD method, the charateristics of the seals are analyzed. And then, the paperresearches the effect of relative eccentricity, rotating speed of the rotor and thepressure ratio of the seal on the gas exciting force, which shows the nonlinearrelationship between the gas exciting force and the paramters. Lastly the empiricalparameters and experimental parameters of the Muszynska gas exciting force modelare identified to solve the problem that the parameters of the model are difficult todetermine. The identified coefficients of the shaft seal model on the steam turbineunit are suitalbe. The results mentiond above provide the basis for the nonlineardynamic analysis of the rotor-seal system.
The power series model of the rotor-seal system of the ultra-supercritical steamturbine are obtained by Taylor expansion. According to Hopf bifurcation theory andstability theory, the paper researches the mechanism of the instability of therotor-seal autonomous system of the ultra-supercritical steam turbine on theequilibrium position. The results shows that system has the Hopf bifurcationphenomenon at the sloved theshold speed, and have the periodic orbit after the Hopfbifurcation. The multiple scale method are used to obtain the bifurcation equationsof the rotor-seal non-autonomous system of the ultra-supercritical steam turbine, forstudying the effects of the rotor’s imbalance excitation on the nonlinear dynamiccharacteristic of the system, in the1:2subharmonic resonance case. Through thesingularity analysis of the1:2subharmonic resonance bifurcation equations, the paper studied engineering unfolding problems of the rotor-seal system. Thetransition sets and the local bifurcations diagrams of the system parameter space areobtained. The results show that system has the supercritical Hopf bifurcation andsubcritical Hopf bifurcation in the different parameters regions. Lastly, Floquetmultiplier is applied to the study on the stabilities and dynamic behaviors of theperiodic solutions of the systems by shooting method.
According to the real solution conditions of the bifurcation equations in the1:1main resonance,1:2subharmonic resonance and1:3subharmonic resonance, theArnold tongue are constructed to study the global bifurcation of the system by theanalytical method. Then the paper studies the dynamic characteristics of the systemin the Arnold tongues overlap and non-overlap. The results show that when thesystem parameters are in the Arnold tongues overlap region, the system appearmulti-times cycle motion and chaotic motion for the coexistence of the resonancesolutions. And the chaotic motion is confirmed by the largest Lyapunov exponent.
Finally, the dynamic testing rig of the rotor-seal system are designed and builtin the Harbin Institute of Technology for further studying the effect of the gasexcitation on the rotor-seal system. According to the current condition of experiment,the structure parameters of the rig are confirmed by CFD calculation and theoreticalanalysis. The seal structure simulates the current structure of the steam turbines ofHarbin steam turbine factory, and independent seal facility with adjustable clearanceis designed to achieve the dynamic tests of the system with the different clearancesin the same rig. By using effect coefficient method, the dynamic balance of the rotorreaches a good level and the rotor can work at high rotating speed. The vibrationtests of the rotor are done when the input pressure is zero and different values, tostudy the influence of the gas excitation.
引文
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