Comparison Between One-dimensional And Three-dimensional Acoustic Numerical Solution And Shape Optimization For Pipes

Pipeline is a very common structure in engineering, which is widely used in construction, aerospace, military and other fields. This paper focuses on the research of one-dimensional wave equation Webster equation in pipe, and explores the scope of application in 3D pipeline, and optimize the pipes in two different aspects according to the result of analysis.Firstly, linear equations are solved with finite difference method to obtain one dimensional numerical solution of Webster equation. With compared with the existing analytical solutions of the one-dimensional Webster equation for straight, conical, index and catenary pipes, the feasibility and computational accuracy of the numerical method is verified.Then, the three dimensional finite element analyses of acoustical fields for the three above-mentioned pipes with gradual change cross sections are implemented by using the LMS Virtual. Lab software, and the three dimensional simulating results are compared with the analytical solution of the three kinds of pipes. The applied scope of the one dimensional Webster equation is analyzed and discussed for describing the three kinds of pipes.Optimize the pipeline in two different aspects. In first part of optimization, a horn pipe is designed by the cubic spline interpolation method. Analyze by changing the pipe curve shape to illustrate the existence of a pipe, whose one-dimensional speed on input and output is closer to the three-dimensional pipe’s speed, comparing with straight, conical, index and catenary pipes. And this kind of pipe’s one dimensional numerical solution of Webster equation can predict the actual 3D pipeline transmission problem more accurately. What’s more, the process of 3D modeling could be avoided to greatly reduce the amount of computation and improve the computational efficiency.In second part of optimization, the pipe is built by parametric modeling with ANSYS--a finite element analysis platform. The acoustic wave flatness is introduced as the objective function of optimization.Finally, the acoustic wave of the pipe outlet, which is the closest to the plane wave in specific parameters, is found to provide a reference to the pipe design, which requires plane wave on the outlet.