Unsteady aerodynamics modeling using Volterra series expansed by basis function

Senlin Chen,Zhenghong Gao,Huafeng Ding,Hongliang Yuan

doi:10.1051/matecconf/201819803002

Senlin Chen, Zhenghong Gao + Show 2 more

Open Access

https://doi.org/10.1051/matecconf/201819803002

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Abstract

Unsteady aerodynamics modeling must accurately describe nonlinear aerodynamic characteristics in addition to unsteady aerodynamic characteristics. The Volterra series has attracted increasing attention as a powerful tool for nonlinear system modeling. It is essential to incorporate the influence of the second-order Volterra kernel or higher-order kernels to build a nonlinear unsteady aerodynamics model. The main difficulty in the identification of higher-order kernels is that the number of parameters to be identified increases exponentially with the order of a kernel. This paper expands the Volterra kernels with the four-order B-spline wavelet on the interval as the basis function, converts the problem into the solution of low-dimensional equations, and obtains a stable solution. A nonlinear unsteady aerodynamics model is built by identifying the second-order and third-order kernels of the lift, drag, and pitching moment coefficients of the NACA0012 airfoil. Then the model is verified at different reduced frequencies using CFD.

Highlights

Aerodynamics exhibit evident nonlinear unsteady hysteresis characteristics when a complex flow of shock waves, flow separation, vortices, etc. occurs in a flow field [1]
Most existing studies only use the first-order Volterra kernel or the truncated second-order Volterra kernel [10]. Such methods are only suitable for aerodynamic modeling with linear or weak nonlinearities and are difficult to apply for strongly nonlinear aerodynamic modeling
The Volterra series theory [15] shows that the input output relation of any continuous-time, causal, time-invariant, fading memory, and nonlinear system can be formulated as an infinite sum of multidimensional convolution integrals

Summary

Introduction

Aerodynamics exhibit evident nonlinear unsteady hysteresis characteristics when a complex flow of shock waves, flow separation, vortices, etc. occurs in a flow field [1]. Most existing studies only use the first-order Volterra kernel or the truncated second-order Volterra kernel [10] Such methods are only suitable for aerodynamic modeling with linear or weak nonlinearities and are difficult to apply for strongly nonlinear aerodynamic modeling. Regarding the difficulties in Volterra kernel identification, Silva [11] and Balajewicz [12] proposed a truncation method that preserves the main diagonal of a high-order kernel or its nearby elements. As this approach neglects a large number of coupling factors in the Volterra kernel, it reduces the ability of the Volterra series to express nonlinearities. The ability of the Volterra series to describe nonlinear unsteady aerodynamics is verified by predicting the lift coefficient, drag coefficient, and pitching moment coefficient of the NACA0012 airfoil in plunging motion at transonic speed

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