Investigation Of Transonic Nonlinear Flutter And Efficient Analysis Approach

In transonic regime,flutter behavior of flight vehicles are highly nonlinear becuase of shock wave and boundary layer separation.Transonic nonlinear flutter problems influence flight safety and target performance of flight vehicles significantly.Transonic dipin the flutter boundary and limit cycle oscillation are typical phenomena.The common approach of unsteady aerodynamics in engineering application is doublet-lattice method,whose precision is very low at transonic speed.While RANS equations can predict transonic complex flow field successfully.Therefore,time-domain aeroelastic approach,which couples unsteady RANS solver and structural equations of motion,could offer favorableinstrumentsto the analysis and improvement of transonic flutter characteristics.However,efficiency,precision and robustness of time-domain aeroelastic method restrict its engineering application.In order to resolve above challenges,the main researches are as follows:(1)Apreciseunsteady aerodynamic analysis method is developed.Firstly,the computational and acceleration methods of three-dimensional(3D)unsteady RANS equations are introduced.Secondly,existent mesh moving methods are studied.Two efficient and robust mixed mesh deformation methods are constructed,which can update spatial mesh after the deformation of geometry availably.MPI parallel method is applied to enhance the efficiency of mesh deformation.Lastly,precision of transonic unsteady aerodynamics are validated by forced pitch cases of NACA64A010 and RSW configuration.(2)A precise time-domain aeroelastic analysis system is constructed.Firstly,the data exchange between aerodynamics and structures based on mode shapes is built,which is proved by virtual work theory.Reduction method of RBF interpolation points based on greedy algorithm is developed,which fulfills the data interpolation of 3D complex structure configuration and improves interpolation efficiency significantly.Secondly,aeroelastic timedomain analysis method is constructed by two-order Euler prediction-correction method,which couples unsteady RANS equations and structural equations of motion.At last,flutter analysis of BSCW and AGARD445.6 wings are employed to validate the analysis method.(3)Transonic nonlinear flutter problems are studied.Flutter mechanism is investigated by energy approach and bifurcation theory.It is demonstrated that inviscid results of transonic LCO of 2D plunge/pitch airfoil are shown to be subcritical Hopf bifurcation,while viscous results are supercritical Hopf bifurcation.The flutter critical mode and flutter boundary of 2D airfoil with control surface changes remarkably in transonic region.Freeplay nonlinearity makes flutter speed decrease enormously,and induces nonperiodic response and LCO.The flutter speed of store configuration of 3D Goland+ wing falls obviously at transonic region.Inviscid results are manifested as complex multiple LCO with some stable and unstable branches and fold bifurcation.LCOs of different stable branches have significant different unsteady flow mechanism.Viscous LCOs are shown as supercritical Hopf bifurcation without unstable branches.(4)In order to improve efficiency of aeroelastic analysis,reduced-order model based on high dimensional harmonic balance method is built.The stability and precision of HDHB method are investigated in details.Firstly,HDHB method is deduced based on the generalized form of one-order partial differential equation.The time-derivative term is transformed to HDHB source term.Secondly,the influences of HDHB source term on numerical stability and damping characteristics are investigated based on Von Neumann stability analysis method.It is demonstrated that no matter explicit or implicit time-marching algorithm is employed,HDHB source terms must be treated implicitly.Next,the source of non-phyiscal solution is investigated through Duffing oscillator.The simple treatment of nonlinear terms results in non-physical solution,which can be resolved by expansion of subtime levels of nonlinear terms.Lastly,HDHB method is applied in Duffing oscillator,Van der Pol oscillator and aeroelastic system with freeplay nonlinearity,which exhibit the precision of HDHB method.(5)HDHB solver of flow field is constructed based on RANS solver.HDHB solver is built by the modification of storage content and analysis process of existing RANS solver.The residual of all subtime levels are calculated by iterative cycle.The precision of HDHB solver is validated by three forced motion cases.Comparing with unsteady RANS equations,twoorder HDHB solver can increase efficiency by 6 times.(6)Efficient aeroelastic analysis method based on HDHB method is developed.As for flutter problem,HDHB method can be employed to build Aerodynamic Influence Coefficients matrix efficiently and accurately.Flutter boundary problem can be transformed to a complex eigenvalue problem by AICs matrix.Thus,efficient frequency-domain flutter analysis method are created.However,AICs are not suitable for LCO problem.LCO responses can be analyzed by the coupling of HDHB solver and frequency-domain structural equations of motion.Comparing with time-domain analysis method,analysis efficiency of aeroelastic problems is improved markably by frequency-domain method.