Calculating Dynamic Derivative And Modeling Nonlinear Unsteady Aerodynamics Based On CFD

Most of the problems in aircraft design are closely related to unsteady aerodynamics.As the rapid development of aerial technology,the conventional ideas based on static aerodynamics cannot satisfy the demand for modern military and civil flight vehicles design,while the new synthetic design methods considering the unsteady aerodynamic characteristics attract more attentions and have been widely used in current studies.Two significant issues in unsteady aerodynamics design are dynamic stability analysis and aerodynamics modeling at high angle of attack,and the former one mainly affects the flight quality analysis and the flight control system design,while the latter is one of the most important ways to evaluate the flight performance at high angle of attack.Therefore,it is very valuable to study the dynamic stability simulation and unsteady aerodynamics modeling for modern aircraft.However,there are deficiencies in present work on these two aspects.The analysis of dynamic stability still remains in the relatively coarse level,and the existed mathematical models for unsteady aerodynamics are not so accurate,as well as their weak applicability.Aiming at improving the actualities,this paper proposes a series investigation on new methods to simulate dynamic stability and model unsteady aerodynamics based on the high-fidelity Computational Fluid Dynamics(CFD)methods.By using the conventional method,the static and dynamic aerodynamics of flight vehicle under complicated environments are evaluated,and then several new methods to finely calculate the dynamic derivatives are built and validated,finally a new mathematical model based on physical characteristics of flow field at high angle of attack is developed.The major research topics and achievements are listed as below:1)The application range of the conventional method to calculate dynamic derivatives is extended to simulate the static and dynamic aerodynamic characteristics of flight vehicles in more complicated flow fields.Based on several dynamic mesh techniques,the small oscillation method is applied in four cases: ground/ water effect,wake flows of wing-tip vortex,jet flow and propeller slipstream,formation with two UAVs and the effect of intake and exhaust,respectively.The static and dynamic aerodynamics of the vehicles with these influences are detailedly analyzed,and the corresponding derivatives are identified and compared to those of ideal environment without any interference.The results indicate that the effect caused by ground is similar to that of water.However,unlike the rigid characteristic of ground,the soft water surface makes significant numerical differences on both the static and dynamic aerodynamics.Three wake flows of the large aircraft act with different phenomenon on the aerodynamics of small aircraft,among which the wing-tip vortex mainly shows shear effect,while the jet flow and propeller slipstream lead to acceleration and rotation effects on the flow field respectively.All the wake flows have heavily affected the aerodynamics of the rear small aircraft and even change its flight quality.When the UAVs fly at a forming column,the lateral distance between the aircrafts is proved to be one of the most important factors in the aerodynamic derivatives.Moreover,it is found that the powered effect of fly wing may increase the dynamic damping of itself when considering the engine as intake and exhaust model,as well as the ventilating model.2)Several new methods to achieve fine results of static and dynamic derivatives are developed and validated based on CFD technique.Firstly,combined with harmonic balance and time spectral models,two new methods to rapidly compute the dynamic derivatives with periodic oscillation are presented.With the aerodynamic results at several sample point times,these methods can rebuilt the whole periodic process of the dynamic motion and further obtain the derivatives efficiently.Secondly,four new methods: plunging oscillation method,flow field rotating method,differential method and step response method,are proposed to finely identify the combined and single derivatives of aircraft.Similar to conventional way,the first method based on plunging oscillation can directly calculate one of the single derivatives-the lag of wash derivative or the acceleration derivative,while the flow field rotating method is realized by simulating the steady pull-up motion with arc tube domain to achieve the other damping derivative or the rotatory derivative.By imposing the aircraft pitching to the same angle of attack with two different pitching angular velocities,or translating it to the same additional angle of attack with two different rates of angle of attack,the combined dynamic derivative and the acceleration derivative can be respectively obtained with the differential method.The last method begins from steady calculation,and then the combined dynamic derivative,the acceleration derivative and the rotary derivative can be calculated by employing the step response motion of angle of attack,rate of angle of attack and pitching angular velocity,respectively,which is a systematic method for dynamic derivative simulation.Various models including Finner,SACCON,HBS and SDM are used to testify the new methods.Numerical results of all cases achieve good agreement with reference values or experimental data.Moreover,all the new methods can be extended to the simulation of combined and single stability derivatives of directional and lateral.3)The applicability of the traditional derivative model for unsteady aerodynamics modeling at small and high angles of attack is evaluated and analyzed.This model is established based on the static and dynamic derivatives calculated with above methods,and then it is employed to predict the unsteady aerodynamic forces of NACA 0015 airfoil at small and high angles of attack.The results at small angle of attack closely coincide with those of reference data.However,as the increase of angle of attack,bad agreement occurs between the predicted and reference results,which shows that the original model may be not applicable to the cases with strong nonlinearity.To improve the status,the original model is modified to a new one with the expansion of higher order terms and the consideration of reduced frequency on derivatives.The new model can describe some nonlinear characteristics at high angle of attack,which is validated by using the aerodynamic data of NACA 0015 airfoil.Even so,the foundation of these models is still not changing,which cannot explain the serious coupling action between the dynamic motion and aerodynamics of complicated configurations at high angle of attack.4)Several models are compared to calculating the static aerodynamics of a delta wing at high angle of attack.Moreover,further validation and comparison on the selected model are carried out by simulating the dynamic motion of NACA0015 at high angle of attack.Firstly,it takes the 70°sharp leading edge delta wing as example,and the calculating mesh is generated based on the analysis of flow filed.The inviscid model,laminar model,S-A one-equation model,k-? two-equations model,k-? SST two-equations model and the SAS model are used to calculate the static aerodynamic forces and moments of the delta wing at high angle of attack.Compare to wind tunnel data,the lift obtained with turbulence models is larger due to the reason that these models may increase the strength of the vortex.The laminar model achieves better results than those of turbulence models.The inviscid method cannot capture the accurate position of vortex breakdown.The computational results of SAS model get the best agreement with the experimental data.Then we use the dynamic motion of NACA0015 to further testify the SAS model at high angle of attack.The comparison of the SAS model,DES model and SST model indicates that the calculation results of the first two models fit the experimental data well,and more accurate results can be obtained from SAS model than DES model with less computational meshes.5)Based on high-precise CFD method,the influential factors on unsteady aerodynamics at high angle of attack are detailedly analyzed and added to the conventional state space model to develop a new mathematical model for unsteady aerodynamics modeling.Focus on the original state space model which established on the internal physical characteristics of flow field,the high-precise SAS method is used to firstly testify the ability of the original model to predict the aerodynamic forces and moments at high angle of attack.To avoid its shortcomings of few factors and weak applicability,with the analysis of the nonlinear flow field in the dynamic process,three influential factors,including the pitching angular velocity,the reduced frequency and the amplitude,are determined and added into the original state space model for a more comprehensive description of the dynamic flow field.Then a new mathematical model modified from the state space model by weighing the three factors comprehensively is presented.The identifiability parameters and the performance of the new model are validated with a delta wing and a scaling geometry of F-18 aircraft.Results show that the new model can achieve more accurate aerodynamic loads compared to the original model.The new state space model is demonstrated to be a more efficient and widely used approach for unsteady aerodynamics modeling.