Time-Domain Analysis of Body Freedom Flutter Based on 6DOF Equation

The reduced weight and improved efficiency of modern aeronautical structures result in a decreasing separation of frequency ranges of rigid and elastic modes.Particularly,a high-aspect-ratio flexible flying wing is prone to body freedomflutter(BFF),which is a result of coupling of the rigid body short-periodmodewith 1st wing bendingmode.Accurate prediction of the BFF characteristics is helpful to reflect the attitude changes of the vehicle intuitively and design the active flutter suppression control law.Instead of using the rigid body mode,this work simulates the rigid bodymotion of the model by using the six-degree-of-freedom(6DOF)equation.A dynamicmesh generation strategy particularly suitable for BFF simulation of free flying aircraft is developed.An accurate Computational Fluid Dynamics/Computational Structural Dynamics/six-degree-of-freedom equation(CFD/CSD/6DOF)-based BFF prediction method is proposed.Firstly,the time-domain CFD/CSD method is used to calculate the static equilibrium state of the model.Based on this state,the CFD/CSD/6DOF equation is solved in time domain to evaluate the structural response of themodel.Then combinedwith the variable stiffnessmethod,the critical flutter point of the model is obtained.This method is applied to the BFF calculation of a flyingwing model.The calculation results of the BFF characteristics of the model agree well with those fromthe modalmethod andNastran software.Finally,the method is used to analyze the influence factors of BFF.The analysis results show that the flutter speed can be improved by either releasing plunge constraint or moving the center ofmass forward or increasing the pitch inertia.

Aeroelastic prediction and analysis for a transonic fan rotor with the“hot”blade shape

This paper focuses on aeroelastic prediction and analysis for a transonic fan rotor with only its“hot”(running)blade shape available,which is often the case in practical engineering such as in the design stage.Based on an in-house and well-validated CFD solver and a hybrid structural finite element modeling/modal approach,three main aspects are considered with special emphasis on dealing with the“hot”blade shape.First,static aeroelastic analysis is presented for shape transformation between“cold”(manufacturing)and“hot”blades,and influence of the dynamic variation of“hot”shape on evaluated aerodynamic performance is investigated.Second,implementation of the energy method for flutter prediction is given and both a regularly used fixed“hot”shape and a variable“hot”shape are considered.Through comparison,influence of the dynamic variation of“hot”shape on evaluated aeroelastic stability is also investigated.Third,another common way to predict flutter,time-domain method,is used for the same concerned case,from which the predicted flutter characteristics are compared with those from the energy method.A well-publicized axial-flow transonic fan rotor,Rotor 67,is selected as a typical example,and the corresponding numerical results and discussions are presented in detail.

An Efficient Dynamic Mesh Generation Method for Complex Multi-Block Structured Grid

Aiming at a complex multi-block structured grid,an efficient dynamic mesh generation method is presented in this paper,which is based on radial basis functions(RBFs)and transfinite interpolation(TFI).When the object is moving,the multi-block structured grid would be changed.The fast mesh deformation is critical for numerical simulation.In this work,the dynamic mesh deformation is completed in two steps.At first,we select all block vertexes with known deformation as center points,and apply RBFs interpolation to get the grid deformation on block edges.Then,an arc-lengthbased TFI is employed to efficiently calculate the grid deformation on block faces and inside each block.The present approach can be well applied to both two-dimensional(2D)and three-dimensional(3D)problems.Numerical results show that the dynamic meshes for all test cases can be generated in an accurate and efficient manner.

Simulation of Viscous Flows Around A Moving Airfoil by Field Velocity Method with Viscous Flux Correction

Based on the field velocity method,a novel approach for simulating unsteady pitching and plunging motion of an airfoil is presented in this paper.Responses to pitching and plunging motions of the airfoil are simulated under different conditions.The obtained results are compared with those of moving grid method and good agreement is achieved.In the conventional field velocity method,the Euler solver is usually used to simulate the movement of the airfoil.However,when viscous effect is considered,unsteady Navier-Stokes equations have to be solved and the viscous flux correction must be taken into account.In this work,the viscous flux correction is introduced into the conventional field velocity method when non-uniform grid speed distribution is occurred.Numerical experiments for the flow around NACA0012 airfoil showed that the proposed approach can well simulate viscous moving boundary flow problems.

CFD/CSD-based flutter prediction method for experimental models in a transonic wind tunnel with porous wall

To predict the flutter dynamic pressure of a wind tunnel model before flutter test,an accurate Computational Fluid Dynamics/Computational Structural Dynamics(CFD/CSD)-based flutter prediction method is proposed under the conditions of a 2.4 m×2.4 m transonic wind tunnel with porous wall.From the CFD simulations of the flows through an inclined hole of this wind tunnel,the Nambu's linear porous wall model between the flow rate and the differential pressure is extended to the porous wall with inclined holes,so that the porous wall can be conveniently modeled as a boundary condition.According to the flutter testing approach for the current wind tunnel,the steady CFD calculation is conducted to achieve the required inlet Mach number.A timedomain CFD/CSD method is then employed to evaluate the structural response of the experimental model,and the critical flutter point is obtained by increasing the dynamic pressure step by step at a fixed Mach number.The present method is applied to the flutter calculations for a vertical tail model and an aircraft model tested in the current transonic wind tunnel.For both models,the computed flutter characteristics agree well with the experimental results.

A Three-Dimensional Gas-Kinetic BGK Scheme for Simulating Flows in Rotating Machinery

This paper focuses on the development and application of a threedimensional gas-kinetic Bhatnagar-Gross-Krook(BGK)method for the viscous flows in rotating machinery.For such flows,a rotating frame of reference is usually used in formulating the Navier-Stokes(N-S)equations,and there are two major concerns in constructing the corresponding BGK model.One is the change of the convective velocities in the N-S equations,which can be reflected through modification of the gas streaming velocity.The other one is the necessity to account for the effect of the additional Coriolis and centrifugal forces.Here,a specifically-designed acceleration term is added into the modified Boltzmann equation so that the source effects can be naturally included into the gas evolution process and the resulted fluxes.Under the finitevolume framework,the constructed BGK model is locally solved at each cell interface and then the numerical fluxes can be evaluated.When employing the BGK scheme,it is sometimes found that the calculated spatial derivatives of the initial and equilibrium distribution functions are sensitive to the mesh quality especially in complex rotating flow applications,which may significantly influence flux evaluation.Therefore,an improved approach for computing these slopes is adopted,through which the modeling capability for viscous flows is enhanced.For validation,several numerical examples are presented.The computed results show that the present method can be well applied to a wide range of flows in rotating machinery with favorable accuracy.