# Research on aeroacoustics inverse problem of rotor static interference

** Aerodynamic Acoustic Counter-Research on Rotor Static Interference Luo Jun, Li Xiaodong Beijing University of Aeronautics and Astronautics, 40, Beijing 100083, lined up Euler equation, the sound pressure of finite space is related to the unsteady pressure distribution of stationary blade surface. 1.6 The form of this 0-integral equation In view of the ill-posedness of the question, this paper uses the least-multiply method combining singular value decomposition and 1 punctualization to solve the problem, and uses discrete, 1 condition for solvability analysis, and optimal regularization. The selection of the parameters is based on the generalized mutual check method 1 and the inversion is feasible when the signal-to-noise ratio is not very low. 1 Introduction The prediction and control of the aeronautical engine rotor tweezer interference noise is aerodynamics. Very important research directions are existing and numerical simulations, most of which require the pressure distribution of the blade surface from experimental or numerical calculations. Although computational fluid dynamics has developed rapidly in recent years, experimental measurements are still indispensable. This traditional contact measurement method is often difficult when applied to the turbine. This is mainly due to the fact that the blade is very thin at the tip and has dimensions. Complex shapes, which make the implementation of the experiment very difficult and this measurement method has interference with the real flow field, and can only obtain the pressure distribution of some points, so it is very necessary to develop the non-contact measurement method. Sound source reconstruction through the sound field reverse sound Yuanmiao Acoustics has a long history of research, and in recent years, significant progress has been made due to non-contact measurement technology! In this paper, the aeroacoustic inquisition research on rotor static interference is carried out, and the feasibility of inversion of the static leaf pressure distribution through the sound pressure at a limited point in space is discussed. The mathematical model of the 2 questions is received. The date of the 20010,015, revised date 2000 Fund Project National Natural Science Foundation of China Milk, 59606003; Aviation Science Foundation funded project 397502. **

** The base model assumes that the blade-shooting wheel is closer to the lower one, so that the blade can be simplified into a series of plane-blade body-breaking control equations. The linearized Euler equation is also used in the No. 1 plant, after a series of transformations, the blade surface is unsteady and its sleeve The sound field is related to the first class 1.10 integral equation, pressure, for each point of hunger, + respectively, the sound wave to 1 swim and. The analysis and solution of the travel 1 3 cross-question divides the micro-element in the cascade and the surface, and discriminates the 2-form, and abstracts the abstraction into the matrix to see the sound pressure at the point as the model matrix. After introducing the singular value decomposition and the regularization solution to obtain 1; the singular value of the matrix, and the left and right singular vectors of the matrix are classified as regularization parameters. The above regularization method must satisfy the discreteness. Condition 7. That is, the Fourier coefficient of the casting matrix is â€‹â€‹faster than the singular value. In the above regularization method, the selection of regularization parameters is very important. Good regularization parameters can properly balance the disturbance error with The error of the solution caused by regularization, so as to obtain a good regularization solution. This paper uses the generalized mutual calibration method to select the regularization parameters. Its basic formula can be written as 1. In the case of regularization, the transformation 2 =; 7.6 can be written as the factory input = the singular value decomposition of the household is completed, the optimum value can be determined by the above formula, and the progress can be calculated by the formula 4 as the simulated sound pressure. The signal is accurate sound pressure, çž§ nbsp ;; mean value is zero, the covariance is bow =, the perturbation vector, the signal-to-noise ratio of the observed noise is calculated as the following steps: Method 1 is used to calculate the cascade surface in the literature 4 Unsteady pressure, cloth; 3 Calculate the radiated sound field from Equation 2 and add the above-mentioned Gaussian distribution noise as the hypothetical measurement, and solve the unsteady distribution of the cascade surface by solving the problem. **

** 4 Examples and discussion The parameters of this example are as follows: the blade pitch chord length ratio is 3.8, and the blade mounting angle is the inter-blade phase angle. The incoming Mach number is 0.5. The number of swim and downstream observation points is 1 and 7 respectively, and the number of micro-members in the cascade is 30. In order to simulate the measurement error, in the condition of 31æ±1.31 of the different letter-to-examination ratio of the winter 21, For the case where the signal-to-noise ratio is large, you = 579. On the left side of the singular value curve 16, the Fourier coefficient approaches the zero faster than the singular value, which indicates that the discrete 1 condition is better and the pass ratio is lower. The observed data is gradually controlled by the disturbance error. The satisfaction of the discrete 1 condition becomes worse and worse, and the inversion effect becomes worse and worse. **

** In the general school of the Court 3, the function can see that the regularization selected by the method is obvious, and the number increases with the decrease of the noise-to-noise ratio. This is the regularization introduced by the increase of the disturbance. The parameters must be larger and larger so that the disturbance error can be properly balanced. **

** Which can be. , 0 soil phase network 1 æ›° ä¸ ç“œ ç“œ.è‚“YouXun 1 does not contain enough information for the required inversion, and the inversion result is worse than the high frequency. The inversion result obtained when the dog takes the observation point from the near field. Since the near-field acoustic signal contains some information about the high-frequency dissipative waves, although these waves are quickly attenuated and do not contribute to the far-field, they contain more information about the sound source, so the inversion results are farther than the far-field. it is good. **

** 5 Conclusions The calculation results show that the inversion result and the exact solution are better when the signal-to-noise ratio is not very low, which proves that the mathematical physics model and the enthalpy method are the same, and the inversion results in the high frequency case are lower. The situation is good. **

** The inversion results of the near field observation points are better than the far field. **

** Sun Xiaofeng, Zhou Sheng. Pneumatic acoustics. Beijing National Defense Industry Press, 1994. **

** Li Xiaodong. A new type of counter-exploration in the gas turbine gas dynamics. 0. Beijing University of Aeronautics and Astronautics, 1995. **

** Responsible editor Yang Zairong 6, Du Jiu 3, 100 generations of literature 4 results. **

** 0, near field observation point **

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