Substantial unbalance may be caused by fan blade off during the operation period of gas turbine engines,and related dynamic problems are very critical to the safety design of rotor system in aero-engine.This article a...Substantial unbalance may be caused by fan blade off during the operation period of gas turbine engines,and related dynamic problems are very critical to the safety design of rotor system in aero-engine.This article aims to understand lateral-torsional coupled vibration of the rotor system with substantial unbalance.The governing equation of a modified unbalanced rotor system is established based on Lagrangian approach.Then,a mathematical analytical method is proposed in which a linear approximation is derived and the Floquet theory and Hill’s method are incorporated,from which the modal characteristics of the unbalanced rotor are obtained.The modal characteristics of the unbalanced rotor system are revealed comprehensively for the first time.Furthermore,the relation between the modes and responses of the unbalanced rotor is discussed in detail.The results show that the lateral vibration and torsional vibration of the unbalanced rotor are coupled through the inertial terms in the governing equations.Due to the coupling,veering and lock-in phenomena occur between the frequencies of the forward whirl mode and the torsional mode.Furthermore,lock-in can lead to a kind of principal instability.With regard to the response of the unbalanced rotor,both natural vibration components and enforced vibration components appear in the lateral response,while only natural vibration components appear during torsional vibration.Moreover,natural vibration components play a crucial role in the response within the principal instability region and cause divergence of the vibration amplitudes in the lateral and torsional directions.展开更多
This paper experimentally investigates the pressure fluctuation induced by the unsteady attached cavitating flow, with special focus on the quasi-periodic cloud cavitation. A simultaneous sampling method is adopted fo...This paper experimentally investigates the pressure fluctuation induced by the unsteady attached cavitating flow, with special focus on the quasi-periodic cloud cavitation. A simultaneous sampling method is adopted for the synchronous measurement of the wall pressure signals and the cavitating flow images in a convergent-divergent channel. The results show that the pressure fluctuation is composed of three parts, the flow noise, the low-frequency fluctuation, and the cavity collapse induced impulse, and the pressure evolution of the quasi-periodic cloud cavitation is well consistent with the cavitation evolution. The statistical analysis of the pressure fluctuation shows that, when σ > 1.01, the probability density function (PDF) is nearly in the normal distribution, implying the randomness of the pressure fluctuation, when 0.84 < σ < 0.91, the PDF has a much larger variance than when σ > 1.01, when σ < 0.84, the PDF becomes narrow and asymmetric. In addition, the variance and the average value of the pressure indicate that the fluctuation intensity increases downstream along the cavity and reaches the maximum at the cavity closure and it also increases with the decrease of the cavitation number. The spectral analysis shows that the low-frequency pressure fluctuations mainly consist of two dominant components, the cavity shedding induced fluctuation and the lock-in fluctuation. The cavity shedding induced frequency decreases with the decrease of the cavitation number but the lock-in frequency is kept nearly constant. According to the spectral analysis of the cavity area fluctuation and the modal analysis of the flow system, the lock-in is possibly caused when the fluctuation frequency of the cavity volume approaches the natural frequency of the flow system.展开更多
The 2D incompressible Navier-Stokes equations arc solved based on the finite Flexible structure;Airfoil;Lock-in phenomenon;Lift coefficient;volume method and dynamic mesh technique is used to carry out partial fluid s...The 2D incompressible Navier-Stokes equations arc solved based on the finite Flexible structure;Airfoil;Lock-in phenomenon;Lift coefficient;volume method and dynamic mesh technique is used to carry out partial fluid structure interaction.The local flexible structure(hereinafter termed as flexible structure)vibrates in a single mode located on the upper surface of the airfoil.The Influence of vibration frequency and amplitude are examined and the corresponding fluid flow characteristics are investigated Computational fluid dynamics(CFD)which add complexity to the inherent problem in unsteady flow.The study is conducted for flow over NACA0012 airfoil at 600≤Re≤3000 at a low angle of attack.Vibration of flexible structure induces a secondary vortex which modifies the pressure distribution and lift performance of the airfoil.At some moderate vibration amplitude,frequency synchronization frequency of rigid airfoil.Evolution and shedding of vortices corresponding to the deformation of flexible structure depends on the Reynolds number.In the case of Re≤1000,the deformation of flexible structure is considered in-phase with the vortex shedding i.e.,increasing maximum lift is linked with the positive deformation of flexible structure.At Re=1500 a phase shift of about 1/π exists while they are out-of-phase at Re>1500.Moreover,the oscillation amplitude of lift coefficient increases with increasing vibration amplitude for Re£1500 while it decreases with increasing vibration amplitude for Re>1500.As a result of frequency lock-in,the average lift coefficient is increased with increasing vibration amplitude for all investigated Reynolds numbers(Re).The maximum increase in the average liftcoefficient is 19.72% within the range of investigated parameters.展开更多
基金the support from the National Natural Science Foundation of China(Nos.11772022,51575022 and 51475021)the support by the Academic Excellence Foundation of BUAA for Ph.D.Students。
文摘Substantial unbalance may be caused by fan blade off during the operation period of gas turbine engines,and related dynamic problems are very critical to the safety design of rotor system in aero-engine.This article aims to understand lateral-torsional coupled vibration of the rotor system with substantial unbalance.The governing equation of a modified unbalanced rotor system is established based on Lagrangian approach.Then,a mathematical analytical method is proposed in which a linear approximation is derived and the Floquet theory and Hill’s method are incorporated,from which the modal characteristics of the unbalanced rotor are obtained.The modal characteristics of the unbalanced rotor system are revealed comprehensively for the first time.Furthermore,the relation between the modes and responses of the unbalanced rotor is discussed in detail.The results show that the lateral vibration and torsional vibration of the unbalanced rotor are coupled through the inertial terms in the governing equations.Due to the coupling,veering and lock-in phenomena occur between the frequencies of the forward whirl mode and the torsional mode.Furthermore,lock-in can lead to a kind of principal instability.With regard to the response of the unbalanced rotor,both natural vibration components and enforced vibration components appear in the lateral response,while only natural vibration components appear during torsional vibration.Moreover,natural vibration components play a crucial role in the response within the principal instability region and cause divergence of the vibration amplitudes in the lateral and torsional directions.
基金supported by the Natural Science Foundation of Beijing Municipality(Grant Nos.3204056,3212023)supported by the National Natural Science Foundation of China(Grant Nos.51839001,51909002 and 52079004).
文摘This paper experimentally investigates the pressure fluctuation induced by the unsteady attached cavitating flow, with special focus on the quasi-periodic cloud cavitation. A simultaneous sampling method is adopted for the synchronous measurement of the wall pressure signals and the cavitating flow images in a convergent-divergent channel. The results show that the pressure fluctuation is composed of three parts, the flow noise, the low-frequency fluctuation, and the cavity collapse induced impulse, and the pressure evolution of the quasi-periodic cloud cavitation is well consistent with the cavitation evolution. The statistical analysis of the pressure fluctuation shows that, when σ > 1.01, the probability density function (PDF) is nearly in the normal distribution, implying the randomness of the pressure fluctuation, when 0.84 < σ < 0.91, the PDF has a much larger variance than when σ > 1.01, when σ < 0.84, the PDF becomes narrow and asymmetric. In addition, the variance and the average value of the pressure indicate that the fluctuation intensity increases downstream along the cavity and reaches the maximum at the cavity closure and it also increases with the decrease of the cavitation number. The spectral analysis shows that the low-frequency pressure fluctuations mainly consist of two dominant components, the cavity shedding induced fluctuation and the lock-in fluctuation. The cavity shedding induced frequency decreases with the decrease of the cavitation number but the lock-in frequency is kept nearly constant. According to the spectral analysis of the cavity area fluctuation and the modal analysis of the flow system, the lock-in is possibly caused when the fluctuation frequency of the cavity volume approaches the natural frequency of the flow system.
基金This work is supported by National Science Foundation of Zhejiang Province(LZ13E060001)National Natural Science Foundation of China(51210011)Zhejiang Provincial Public Projects(analysis and test)of Zhejiang Province(2015C37027).
文摘The 2D incompressible Navier-Stokes equations arc solved based on the finite Flexible structure;Airfoil;Lock-in phenomenon;Lift coefficient;volume method and dynamic mesh technique is used to carry out partial fluid structure interaction.The local flexible structure(hereinafter termed as flexible structure)vibrates in a single mode located on the upper surface of the airfoil.The Influence of vibration frequency and amplitude are examined and the corresponding fluid flow characteristics are investigated Computational fluid dynamics(CFD)which add complexity to the inherent problem in unsteady flow.The study is conducted for flow over NACA0012 airfoil at 600≤Re≤3000 at a low angle of attack.Vibration of flexible structure induces a secondary vortex which modifies the pressure distribution and lift performance of the airfoil.At some moderate vibration amplitude,frequency synchronization frequency of rigid airfoil.Evolution and shedding of vortices corresponding to the deformation of flexible structure depends on the Reynolds number.In the case of Re≤1000,the deformation of flexible structure is considered in-phase with the vortex shedding i.e.,increasing maximum lift is linked with the positive deformation of flexible structure.At Re=1500 a phase shift of about 1/π exists while they are out-of-phase at Re>1500.Moreover,the oscillation amplitude of lift coefficient increases with increasing vibration amplitude for Re£1500 while it decreases with increasing vibration amplitude for Re>1500.As a result of frequency lock-in,the average lift coefficient is increased with increasing vibration amplitude for all investigated Reynolds numbers(Re).The maximum increase in the average liftcoefficient is 19.72% within the range of investigated parameters.
