叶轮机械中若干气流激振问题的流固耦合数值研究
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摘要
流体激振是造成叶轮机械安全性问题的重要原因。本文发展了一种流固耦合数值计算方法来研究叶轮机械的流体激振问题。该方法采用了准确的数学物理模型，在流体区域求解二维、三维Favre平均的非定常Navier-Stokes方程，在固体区域对于不同的问题求解体振动模型，每一个计算时间步完成后，流体和固体之间传递一次边界条件。在计算网格移动下的非定常流场时采用了高精度、高分辨率的数值计算方法——LU-SGS-GE隐式格式和高阶MUSCL TVD格式。在固体区域针对不同的固体振动模型采用了四阶Rounge-Kutta法或Lax法求解。采用这套数值方法研究了叶轮机械中三种典型的流体激振问题。
首先研究了二维翼型的古典颤振(小攻角)、失速颤振(失速攻角)和动力响应问题(大攻角)，得到以下结论：在静态失速攻角附近的一定来流速度范围内，分离涡会发生频率锁定现象，分离流的频率与固有频率趋于相同，这时的振动呈现自激振动的特点；远离失速攻角时分离流频率则摆脱固有频率的影响，此时的振动具有强迫振动的特点。这种频率锁定规律可以清楚地解释失速颤振的各种非线性现象。在大攻角下分离涡脱落的频率没有一个明显的频率锁定区域，流体振动属于稳定的动力响应问题，但在大来流速度下会出现振幅突跳的现象。在机理研究的基础上深入研究了振荡射流减振技术，得到了振荡射流参数对减振效果和升力系数的影响规律。
其次研究了密封转子的流体激振问题。采用本文的流固耦合方法成功地捕捉到频率锁定的现象，且发现随着转速的提高，固有频率也增大，从而证明高转速下密封转子会发生自激振动，传统的刚度阻尼方法对此是无法解释的。另外，本文还得到了压比、预旋度对密封转子自激振动的影响规律。
最后研究了三维透平叶片的流体激振问题，在模拟大负攻角下的颤振时发现，传播失速响应频率向固有频率靠近是振动发散的一个重要判据。它不但可用于判断流体激振的稳定性，而且可以研究颤振的强度。这对于叶轮机械的设计和运行是很有意义的。
研究成果证明本文发展的流固耦合方法具有先进性、有效性和实用价值，所得到的研究成果对叶轮机械的工程设计具有重要的理论意义和工程价值。
Fluid induced Oscillation is one of the most important problems that threaten the turbomachinery's safety. A new fluid-structure coupling numerical method is developed in the present dissertation. 2D/3D Navier-Stokes equations and low Renolds number turbulence model are solved in the fluid zone, while the structure models are solved in the solid zone. The boundary conditions are transferred between the two zones after each time step. A high accuracy, high resolution numerical method (LU-SGS-GE scheme and 4th order MUSCL TVD scheme) is applied to calculate the unsteady flow field. Various numerical methods are used to solve the structure models, such as Fourth order Rounge-Kutta method and Lax method. This numerical approach is used to analyze three typical fluid-induced vibration problems in turbomachinery.
Firstly, the airfoil's classic flutter (at small attack angle), stall flutter (near the static stall angle) and response (at large attack angle) are analyzed. It is found from the numerical results that "lock-in" will occur at certain freestream velocity range near the static stall angle, where the frequency of the vortex will be equal to the natural frequency and the flutter has the characteristic of self-induced oscillation. When the attack angle is far from the static stall angle, the vortex will have its own frequency, which differs from the natural frequency, and the flutter has the characteristic of forced oscillation. The characteristic of "lock-in" can be used to explain all kinds of nonlinear phenomenon of the stall flutter. At large attack angle the frequency of the vortex hasn't a apparent zone of "lock-in". The fluid-induced vibration at large attack angle belongs to the stable dynamic response problems. But a sudden skip of amplitude will occur at large inlet velocity. The oscillatory blowing technique to control the flutter is also studied. The influence of the blowing factors to the flutter and the lift coefficient is analyzed.
Secondly, the self-induced vibration of seals are analyzed by fluid-structure coupling numerical method. The self-induced oscillation of the seals will occur at large rotational speed, however, this phenomenon can't be simulated with the
custom linear aerodynamic model. The seal's fluid-induced vibration is studied by the present fluid-structure coupling method. The "lock-in" of the frequency is obtained from the study and the amplitude of the natural frequency will increase with the rotational speed, which verifies that the self-induced oscillation will occur at large rotational speed. In addition, the influence of the pressure ration and the pre-swirling to the fluid-induced vibration is also studied.
Finally, the fluid-structure interaction problems of a 3-d turbine blade are studied. During the numerical simulation of flutter at large negative attack angle, it is found that the frequency of the propagating stall will move to the natural frequency gradually, which is an important signal of the flutter. The figures, which indicate the influence of the attack angle and pressure ratio to the fluid, are obtained, from which we can learn not only the stability of the oscillation, but also the oscillation's intensity.
The study have shown the advantage, efficiency and usage of the present fluid-structure coupling numerical method. The numerical results will be very useful in the design and theory of turbomachinery.
首先研究了二维翼型的古典颤振(小攻角)、失速颤振(失速攻角)和动力响应问题(大攻角)，得到以下结论：在静态失速攻角附近的一定来流速度范围内，分离涡会发生频率锁定现象，分离流的频率与固有频率趋于相同，这时的振动呈现自激振动的特点；远离失速攻角时分离流频率则摆脱固有频率的影响，此时的振动具有强迫振动的特点。这种频率锁定规律可以清楚地解释失速颤振的各种非线性现象。在大攻角下分离涡脱落的频率没有一个明显的频率锁定区域，流体振动属于稳定的动力响应问题，但在大来流速度下会出现振幅突跳的现象。在机理研究的基础上深入研究了振荡射流减振技术，得到了振荡射流参数对减振效果和升力系数的影响规律。
其次研究了密封转子的流体激振问题。采用本文的流固耦合方法成功地捕捉到频率锁定的现象，且发现随着转速的提高，固有频率也增大，从而证明高转速下密封转子会发生自激振动，传统的刚度阻尼方法对此是无法解释的。另外，本文还得到了压比、预旋度对密封转子自激振动的影响规律。
最后研究了三维透平叶片的流体激振问题，在模拟大负攻角下的颤振时发现，传播失速响应频率向固有频率靠近是振动发散的一个重要判据。它不但可用于判断流体激振的稳定性，而且可以研究颤振的强度。这对于叶轮机械的设计和运行是很有意义的。
研究成果证明本文发展的流固耦合方法具有先进性、有效性和实用价值，所得到的研究成果对叶轮机械的工程设计具有重要的理论意义和工程价值。
Fluid induced Oscillation is one of the most important problems that threaten the turbomachinery's safety. A new fluid-structure coupling numerical method is developed in the present dissertation. 2D/3D Navier-Stokes equations and low Renolds number turbulence model are solved in the fluid zone, while the structure models are solved in the solid zone. The boundary conditions are transferred between the two zones after each time step. A high accuracy, high resolution numerical method (LU-SGS-GE scheme and 4th order MUSCL TVD scheme) is applied to calculate the unsteady flow field. Various numerical methods are used to solve the structure models, such as Fourth order Rounge-Kutta method and Lax method. This numerical approach is used to analyze three typical fluid-induced vibration problems in turbomachinery.
Firstly, the airfoil's classic flutter (at small attack angle), stall flutter (near the static stall angle) and response (at large attack angle) are analyzed. It is found from the numerical results that "lock-in" will occur at certain freestream velocity range near the static stall angle, where the frequency of the vortex will be equal to the natural frequency and the flutter has the characteristic of self-induced oscillation. When the attack angle is far from the static stall angle, the vortex will have its own frequency, which differs from the natural frequency, and the flutter has the characteristic of forced oscillation. The characteristic of "lock-in" can be used to explain all kinds of nonlinear phenomenon of the stall flutter. At large attack angle the frequency of the vortex hasn't a apparent zone of "lock-in". The fluid-induced vibration at large attack angle belongs to the stable dynamic response problems. But a sudden skip of amplitude will occur at large inlet velocity. The oscillatory blowing technique to control the flutter is also studied. The influence of the blowing factors to the flutter and the lift coefficient is analyzed.
Secondly, the self-induced vibration of seals are analyzed by fluid-structure coupling numerical method. The self-induced oscillation of the seals will occur at large rotational speed, however, this phenomenon can't be simulated with the
custom linear aerodynamic model. The seal's fluid-induced vibration is studied by the present fluid-structure coupling method. The "lock-in" of the frequency is obtained from the study and the amplitude of the natural frequency will increase with the rotational speed, which verifies that the self-induced oscillation will occur at large rotational speed. In addition, the influence of the pressure ration and the pre-swirling to the fluid-induced vibration is also studied.
Finally, the fluid-structure interaction problems of a 3-d turbine blade are studied. During the numerical simulation of flutter at large negative attack angle, it is found that the frequency of the propagating stall will move to the natural frequency gradually, which is an important signal of the flutter. The figures, which indicate the influence of the attack angle and pressure ratio to the fluid, are obtained, from which we can learn not only the stability of the oscillation, but also the oscillation's intensity.
The study have shown the advantage, efficiency and usage of the present fluid-structure coupling numerical method. The numerical results will be very useful in the design and theory of turbomachinery.
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