Numerical Investigations Of Unsteady Aerodynamics And Aeroelasticity Of Turbomachines

Aeroelastic problem is a key factor affecting the performance and safety of turbomachiney,especially aero engines.As a cross-disciplinary,turbomachiney aeroelasticity involves the studies of steady/unsteady flow characteristics,flutter mechanism and mathematical modeling of all kinds of aeroelastic behavior.In this thesis,based on the computational fluid dynamics(CFD)technique,an integrated computing and analysis platform for steady/unsteady flows,static aeroelasticity and flutter problems in turbomachinery is established,through which numerical studies on several kinds of aeroelastic problems are performed.The main research contents and academic contributions are as follows:Because turbomachiney aeroelasticity is closely related to the aerodynamic characteristics,one of the emphasis of current research is to accurately simulate internal flow fields.Based on solving the Reynolds-averaged Navier-Stokes(RANS)equations in a rotating frame of reference,an in-house CFD code is developed for the flows in rotating machinery.Particularly,for simulation of unsteady flows caused by the blade vibration,the dynamic mesh method is adopted,where the dynamic mesh generation is achieved by an efficient RBF–TFI approach.For simulation of unsteady flows caused by the rotor/stator interaction,the domain scaling method is applied and a flux transfer-based rotor/stator interface treatment is used to exchange the flow information between the adjacent blade rows.Results from numerical examples validate the computational accuracy and efficiency of the present CFD code,which lays the foundation for the following aeroelastic studies.The static aeroelastic analysis is an important part in the design optimization process and is also a premise of flutter analysis.Based on the CFD technique and the idea of fluid-structure interaction,a highly accurate method is developed for static aeroelastic calculations.For the ?cold-to-hot? aeroelastic forward problems,the total blade deformation is decomposed into two components: one caused by the centrifugal force and the other one caused by the aerodynamic force.They are obtained by the nonlinear finite element analysis and the modal method,respectively.For the ?hot-to-cold? aeroelastic inverse problems,a predictor-corrector iterative approach based on solving the previous ?cold-to-hot? problems is employed,from which the unknown ?cold? shape can be determined with high accuracy and efficiency.By applying the developed method to the two typical rotors,we carefully study the differences between ?cold? and ?hot? shapes and the influences of blade deformation on aerodynamic performance.As for flutter calculation,the CFD technique and the energy approach are first used to predict the unsteady flows around oscillating blades and to analyze the flutter characteristics.The emphasis is put on how to deal with an arbitrary Inter blade phase angle(IBPA),which is a special factor in turbomachinery.Because of the various disadvantages of the simple multi-passage simulation method and conventional phase-lagged methods,based on the original single-passage shape correction(SPSC)method,a novel double-passage shape correction(DPSC)method is proposed.In the DPSC method,the flow variables at circumferential boundaries are corrected through the Fourier series while the corresponding Fourier coefficients are updated from flow variables at interior boundaries.From both the theoretical analysis and the numerical tests,it is proven that the DPSC method can not only deal with any IBPA in a unified way,but also significantly improve the convergence performance and robustness as compared with the original SPSC method.The flutter characteristics of typical oscillating cascades/blades are quantitatively studied and also the potential flutter mechanism is analyzed from the perspective of energy transferring.In order to more accurately calculate the actual vibration response to the structural disturbance,a CFD/CSD coupled time-domain method is developed,where the unsteady aerodynamic force is obtained from the aforementioned CFD method and the structural equations of motion are solved by using the modal method.A hybrid predictor-corrector scheme is used to guarantee that the flow field and the structural filed can be advanced in time accurately and efficiently.The calculated results for Rotor67 show that the rotor blade is free of flutter under any operating condition.The calculated results for a fan rotor show that the subsonic/transonic stall flutter could happen at some specific speeds.Also for this rotor,the flutter margins at different rotational speeds are obtained and the mechanism of stall flutter is briefly analyzed.Then the time-domain method is further extended to solve several practical flutter problems of turbomachines.By constructing specific approaches or using simplified models,we study the flutter problem with non-zero IBPAs,the flutter problem for a transonic fan rotor with part-span shrouds and the flutter problem for a multi-stage compressor.Because the unsteady aerodynamic force plays an important role in studying aeroelasticity and also in order to improve the capability of flow simulation,a novel gas-kinetic scheme(GKS)is extended to solve typical turbomachinery flows.Three aspects are considered.Firstly,a rotating reference frame-based GKS is constructed for the flows in rotating machinery.The main idea is to add a particle acceleration term into the Bhatnagar–Gross–Krook(BGK)model so that the non-inertial(source)effects can be naturally included into the gas evolution process and the resulting fluxes.Secondly,a new version of GKS on moving grids is constructed for the unsteady flows through oscillating cascades.The main idea is to account for the mesh movement through the change of the particle streaming velocity.Thirdly,in order to overcome the disadvantage of slow convergence speed in the original explicit GKS,an efficient implicit GKS by using the Jacobian–Free Newton–Krylov(JFNK)method is proposed for the first time,making it possible for the GKS to be applied in complex engineering problems.