Using the concept of the base forces, a new finite element method （base force element method, BFEM） based on the complementary energy principle is presented for accurate modeling of structures with large displacemen...Using the concept of the base forces, a new finite element method （base force element method, BFEM） based on the complementary energy principle is presented for accurate modeling of structures with large displacements and large rotations. First, the complementary energy of an element is described by taking the base forces as state variables, and is then separated into deformation and rotation parts for the case of large deformation. Second, the control equations of the BFEM based on the complementary energy principle are derived using the Lagrange multiplier method. Nonlinear procedure of the BFEM is then developed. Finally, several examples are analyzed to illustrate the reliability and accuracy of the BFEM.展开更多
Blade rubbing faults cause detrimental impact on the operation of aeroengines. Most of the existing studies on blade rubbing in the shaft-disk-blade-casing(SDBC) system have overlooked the elastic deformation of the b...Blade rubbing faults cause detrimental impact on the operation of aeroengines. Most of the existing studies on blade rubbing in the shaft-disk-blade-casing(SDBC) system have overlooked the elastic deformation of the blade, while some only consider the whirl of the rotor, neglecting its spin. To address these limitations, this paper proposes a dynamic model with large rotation for the SDBC system. The model incorporates the spin and whirl of the rotor, enabling the realistic reproduction of multiblade rubbing faults. To verify the accuracy of the SDBC model with large rotation and demonstrate its capability to effectively consider the rotational effects such as the centrifugal stiffening and gyroscopic effects, the natural characteristics and dynamic responses of the proposed model are compared with those obtained from reported research and experimental results. Furthermore, the effects of the rotating speed, contact stiffness,and blade number on the dynamic characteristics of the SDBC system with multi-blade rubbing are investigated. The results indicate that the phase angle between the rotor deflection and the unbalance excitation force increases with the increasing rotating speed,which significantly influences the rubbing penetration of each blade. The natural frequency of the SDBC system with rubbing constrain can be observed in the acceleration response of the casing and the torsional response of the shaft, and the frequency is related to the contact stiffness. Moreover, the vibration amplitude increases significantly with the product of the blade number under rubbing, and the rotating frequency approaches the natural frequency of the SDBC system. The proposed model can provide valuable insight for the fault diagnosis of rubbing in bladed rotating machinery.展开更多
The large eddy simulation method was employed to investigate the film-cooling performance in a low-speed rotor blade of a 1-1/2 turbine stage.The rotor blade height and axial chord length were 99 mm and 124.3 mm,respe...The large eddy simulation method was employed to investigate the film-cooling performance in a low-speed rotor blade of a 1-1/2 turbine stage.The rotor blade height and axial chord length were 99 mm and 124.3 mm,respectively.Two rows of film holes were placed on the rotor blade surface,one each on the pressure and suction surfaces.Each row had three cylindrical film holes with a diameter of 4 mm and a tangential injection angle of 28°on the pressure side and 361 on the suction side.The Reynolds number was fixed at Re=1.92×10^(5)and the coolant-to-mainstream density ratio(DR)was about 2.0.Simulations were carried out for three different rotating speeds of 1800,2100,and 2400 rpm with the blowing ratio(BR)varying from 0.3 to 3.0.The commercial CFD code STAR-CCM+was used to run the simulations using the WALE subgrid-scale model for modelling the turbulence.The results show that on the pressure side,the film coverage and filmcooling effectiveness decrease with increasing rotation number(Ro)and increase with increasing blowing ratio(BR).A higher Ro and lower BR result in a stronger film deflection.The film injection with higher BR produces better film attachment.The film deflects centrifugally where the deflection becomes greater with increasing Ro.On the suction side,the film coverage and film-cooling effectiveness increase with increasing either Ro or BR and a centripetal deflection of the film is observed.The deflection of the film path could be amplified by either increasing the Ro at a constant BR or decreasing the BR at a constant Ro.Increasing the rotation weakens the film deflection towards the hub on the suction surface.Overall,it was found that both rotation number and blowing ratio play significant roles in determining the film-cooling effectiveness distributions of the rotor blade surface.展开更多
基金supported by the China Postdoctoral Science Foundation Funded Project (20080430038) the Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (05004999200602)
文摘Using the concept of the base forces, a new finite element method （base force element method, BFEM） based on the complementary energy principle is presented for accurate modeling of structures with large displacements and large rotations. First, the complementary energy of an element is described by taking the base forces as state variables, and is then separated into deformation and rotation parts for the case of large deformation. Second, the control equations of the BFEM based on the complementary energy principle are derived using the Lagrange multiplier method. Nonlinear procedure of the BFEM is then developed. Finally, several examples are analyzed to illustrate the reliability and accuracy of the BFEM.
基金Project supported by the National Science and Technology Major Project of China (No. 2017-V-0009)the National Natural Science Foundation of China (Nos. 12032015 and 12121002)the National Funding Program for Postdoctoral Researchers of China (No. GZC20231586)。
文摘Blade rubbing faults cause detrimental impact on the operation of aeroengines. Most of the existing studies on blade rubbing in the shaft-disk-blade-casing(SDBC) system have overlooked the elastic deformation of the blade, while some only consider the whirl of the rotor, neglecting its spin. To address these limitations, this paper proposes a dynamic model with large rotation for the SDBC system. The model incorporates the spin and whirl of the rotor, enabling the realistic reproduction of multiblade rubbing faults. To verify the accuracy of the SDBC model with large rotation and demonstrate its capability to effectively consider the rotational effects such as the centrifugal stiffening and gyroscopic effects, the natural characteristics and dynamic responses of the proposed model are compared with those obtained from reported research and experimental results. Furthermore, the effects of the rotating speed, contact stiffness,and blade number on the dynamic characteristics of the SDBC system with multi-blade rubbing are investigated. The results indicate that the phase angle between the rotor deflection and the unbalance excitation force increases with the increasing rotating speed,which significantly influences the rubbing penetration of each blade. The natural frequency of the SDBC system with rubbing constrain can be observed in the acceleration response of the casing and the torsional response of the shaft, and the frequency is related to the contact stiffness. Moreover, the vibration amplitude increases significantly with the product of the blade number under rubbing, and the rotating frequency approaches the natural frequency of the SDBC system. The proposed model can provide valuable insight for the fault diagnosis of rubbing in bladed rotating machinery.
文摘The large eddy simulation method was employed to investigate the film-cooling performance in a low-speed rotor blade of a 1-1/2 turbine stage.The rotor blade height and axial chord length were 99 mm and 124.3 mm,respectively.Two rows of film holes were placed on the rotor blade surface,one each on the pressure and suction surfaces.Each row had three cylindrical film holes with a diameter of 4 mm and a tangential injection angle of 28°on the pressure side and 361 on the suction side.The Reynolds number was fixed at Re=1.92×10^(5)and the coolant-to-mainstream density ratio(DR)was about 2.0.Simulations were carried out for three different rotating speeds of 1800,2100,and 2400 rpm with the blowing ratio(BR)varying from 0.3 to 3.0.The commercial CFD code STAR-CCM+was used to run the simulations using the WALE subgrid-scale model for modelling the turbulence.The results show that on the pressure side,the film coverage and filmcooling effectiveness decrease with increasing rotation number(Ro)and increase with increasing blowing ratio(BR).A higher Ro and lower BR result in a stronger film deflection.The film injection with higher BR produces better film attachment.The film deflects centrifugally where the deflection becomes greater with increasing Ro.On the suction side,the film coverage and film-cooling effectiveness increase with increasing either Ro or BR and a centripetal deflection of the film is observed.The deflection of the film path could be amplified by either increasing the Ro at a constant BR or decreasing the BR at a constant Ro.Increasing the rotation weakens the film deflection towards the hub on the suction surface.Overall,it was found that both rotation number and blowing ratio play significant roles in determining the film-cooling effectiveness distributions of the rotor blade surface.
