Quick and accurate determination of the optimal synchrophase angle is crucial for synchrophasing control of multi-propeller aircraft with low noise.This paper proposes a novel noise prediction and optimization strateg...Quick and accurate determination of the optimal synchrophase angle is crucial for synchrophasing control of multi-propeller aircraft with low noise.This paper proposes a novel noise prediction and optimization strategy,developing a continuous and accurate noise prediction model and obtaining its minimum by solving the Hessian matrix and Fourier-Frobenius matrix.Firstly,a novel propeller noise prediction method uses acoustic simulation pressure signals and improved propeller signatures theory to accurately estimate noise for all synchrophase angles and receiving points.Secondly,a novel optimization approach is proposed to solve the analytical solution of the minimum propeller noise:(A)A noise objective function is established,and use its first derivatives’zeros and Hessian matrix to determine the function minimum.(B)A novel Euler formula transform method is proposed to convert trigonometric polynomials into algebraic polynomials,changing the zeros of the former into those of the latter.(C)Utilize the Fourier-Frobenius matrix method to solve the zeros of algebraic polynomials.To assess the computation time and accuracy,a turboprop aircraft with two six-bladed propellers was analyzed using the computational fluid dynamics and acoustic analogy method,providing acoustic pressure signals at 20 receivers for noise prediction and optimization.The Durand-Kerner and Fourier-Frobenius matrix methods were compared.Results demonstrate that improved propeller signatures theory is more accurate,and the Hessian matrix+Fourier-Frobenius matrix method is faster and more precise than the Hessian matrix+Durand-Kerner method.展开更多
基金supported by the National Natural Science Foundation of China(Nos.51576097,51976089)the Funding for Outstanding Doctoral Dissertation in Nanjing University of Aeronautics and Astronautics,China(No.BCXJ24-05)the Aeronautical Science Foundation of China(No.2023L060052001).
文摘Quick and accurate determination of the optimal synchrophase angle is crucial for synchrophasing control of multi-propeller aircraft with low noise.This paper proposes a novel noise prediction and optimization strategy,developing a continuous and accurate noise prediction model and obtaining its minimum by solving the Hessian matrix and Fourier-Frobenius matrix.Firstly,a novel propeller noise prediction method uses acoustic simulation pressure signals and improved propeller signatures theory to accurately estimate noise for all synchrophase angles and receiving points.Secondly,a novel optimization approach is proposed to solve the analytical solution of the minimum propeller noise:(A)A noise objective function is established,and use its first derivatives’zeros and Hessian matrix to determine the function minimum.(B)A novel Euler formula transform method is proposed to convert trigonometric polynomials into algebraic polynomials,changing the zeros of the former into those of the latter.(C)Utilize the Fourier-Frobenius matrix method to solve the zeros of algebraic polynomials.To assess the computation time and accuracy,a turboprop aircraft with two six-bladed propellers was analyzed using the computational fluid dynamics and acoustic analogy method,providing acoustic pressure signals at 20 receivers for noise prediction and optimization.The Durand-Kerner and Fourier-Frobenius matrix methods were compared.Results demonstrate that improved propeller signatures theory is more accurate,and the Hessian matrix+Fourier-Frobenius matrix method is faster and more precise than the Hessian matrix+Durand-Kerner method.
基金Supported by Natural Science Foundation of China(11571329)the Natural Science Foundation of Anhui Province(1708085MA01)Project of University Natural Science Research of Anhui Province(KJ2015A101)
