A simplified two-dimensional boundary element method with arbitrary uniform mean flow

To reduce computational costs, an improved form of the frequency domain boundary element method（BEM） is proposed for two-dimensional radiation and propagation acoustic problems in a subsonic uniform flow with arbitrary orientation. The boundary integral equation（BIE） representation solves the two-dimensional convected Helmholtz equation（CHE） and its fundamental solution, which must satisfy a new Sommerfeld radiation condition（SRC） in the physical space. In order to facilitate conventional formulations, the variables of the advanced form are expressed only in terms of the acoustic pressure as well as its normal and tangential derivatives, and their multiplication operators are based on the convected Green＇s kernel and its modified derivative. The proposed approach significantly reduces the CPU times of classical computational codes for modeling acoustic domains with arbitrary mean flow. It is validated by a comparison with the analytical solutions for the sound radiation problems of monopole,dipole and quadrupole sources in the presence of a subsonic uniform flow with arbitrary orientation.

Numerical quadrature for singular and near-singular integrals of boundary element method and its applications in large-scale acoustic problems

The numerical quadrature methods for dealing with the problems of singular and near-singular integrals caused by Burton-Miller method are proposed, by which the conventional and fast multipole BEMs （boundary element methods） for 3D acoustic problems based on constant elements are improved. To solve the problem of singular integrals, a Hadamard finite-part integral method is presented, which is a simplified combination of the methods proposed by Kirkup and Wolf. The problem of near-singular integrals is overcome by the simple method of polar transformation and the more complex method of PART （Projection and Angular ＆ Radial Transformation）. The effectiveness of these methods for solving the singular and near-singular problems is validated through comparing with the results computed by the analytical method and/or the commercial software LMS Virtual.Lab. In addition, the influence of the near-singular integral problem on the computational precisions is analyzed by computing the errors relative to the exact solution. The computational complexities of the conventional and fast multipole BEM are analyzed and compared through numerical computations. A large-scale acoustic scattering problem, whose degree of freedoms is about 340,000, is implemented successfully. The results show that, the near singularity is primarily introduced by the hyper-singular kernel, and has great influences on the precision of the solution. The precision of fast multipole BEM is the same as conventional BEM, but the computational complexities are much lower.

An improved series expansion method on the multi-frequency analysis of acoustic boundary element

For the multi-frequency acoustic analysis, a series expansion method has been introduced to reduce the computation time of the frequency-independent parts, but the Runge phenomenon will arise when this method is employed in high frequency band. Therefore, this method is improved by analyzing the application condition and proposing the selection principle of the series truncation number. The argument interval can be adjusted with the wavenumber factor. Therefore, the problem of unstable numeration and poor precision can be solved, and the application scope of this method is expanded. The numerical example of acoustic radiation shows that the improved method is correct for acoustic analysis in wider frequency band with less series truncation number and computation amount.

Noise comparison of centrifugal pump operating in pump and turbine mode

Investigations regarding the relation of noise performance for centrifugal pump operating in pump and turbine modes continue to be inadequate.This paper presents a series of comparisons of flow-induced noise for both operation modes.The interior flow-borne noise and structure modal were verified through experiments.The flow-borne noise was calculated by the acoustic boundary element method(ABEM),and the flow-induced structure noise was obtained by the coupled acoustic boundary element method(ABEM)/structure finite element method(SFEM).The results show that in pump mode,the pressure fluctuation in the volute is comparable to that in the outlet pipe,but in turbine mode,the pressure fluctuation in the impeller is comparable to that in the draft tube.The main frequency of interior flow-borne noise lies at blade passing frequency(BPF)and it shifts to the 9th BPF for interior flow-induced structure noise.The peak values at horizontal plane appear at the 5th BPF,and at axial plane,they get the highest sound pressure level(SPL)at the 8th BPF.Comparing with interior noise,the SPL of exterior flow-induced structure noise is incredibly small.At the 5th BPF,the pump body,cover and suspension show higher SPL in both modes.The outer walls of turbine generate relatively larger SPL than those of the pump.