Study On Volterra Kernel Aerodynamic Reduction Of Transonic Wings

The reduced order model of unsteady aerodynamics not only needs to accurately describe the unsteady characteristics of aerodynamics,but also needs to reflect its nonlinear characteristics.Because of the strong ability of Volterra series to describe the nonlinearity,at present,some researchers have used the three-order Volterra kernel based on multi wavelet to reduce the unsteady aerodynamics of two-dimensional airfoil in the transonic stage with single degree of freedom This model can accurately predict the aerodynamic force of airfoil with single degree of freedom and reflect the nonlinear characteristics of the aerodynamic force.However,it is limited to describe the motion of twodimensional airfoil with one degree of freedom.In fact,it is more practical to do two-dimensional airfoil pitching and plunging two-dimensional motion.In this work,aerodynamic reduction model is established for two-dimensional airfoil pitching and plunging two-dimensional motion in transonic stage.Firstly,the aerodynamic force of the airfoil in a given pitching motion is calculated by the dynamic grid method of fluent,and compared with the experimental data of wind tunnel,the reliability of unsteady aerodynamic force calculated by FLUENT is verified.Secondly,the piecewise quadratic multiwavelet basis function is constructed and applied to the expansion of Volterra kernel.According to the Volterra series,the multi input and multi output model of three Volterra cores is derived and constructed.The design of the input signal is to use the sweep input signal,take the airfoil as the sweep motion of pitching and plunging two degrees of freedom as the system input,and Fluent calculates the aerodynamic coefficient of the airfoil as the system output.The least square method is used to identify the coefficients before the multiwavelet basis function in the Volterra kernel,so as to establish the aerodynamic reduced order model,and use the model to predict the pitching and plunging of the airfoil.The aerodynamic coefficients of two degrees of freedom motion with constant frequency are compared with the results of Fluent calculation,and the prediction effect is better.The reduced order aerodynamic model has a strong prediction ability for the unsteady aerodynamic prediction of two-dimensional airfoil in the transonic stage.