A Chebyshev spectral element approximation of acoustic propagation problems based on linearized Euler equations is introduced, and the numerical approach is based on spectral elements in space with first-order Clayton–Engquist–Majda absorbing boundary conditions and implicit Newmark method in time. An initial perturbation problem has been solved to test the accuracy and stability of the numerical method. Then the sound propagation by source terms is also studied, including the radiation of a monopole and dipolar source in both stationary medium and uniform mean flow. The numerical simulation leads to good results in both accuracy and stability. Compared with the analytical solutions, the numerical results show the advantages in spectral accuracy even with relatively fewer grid points. Moreover, the implicit Newmark method in time marching also presents its superiority in stability. Finally, a problem of sound propagation in pipes is simulated as well.
An optimization strategy called response surface methodology (RSM) is applied to a centrifugal fan impeller optimization design in this paper. RSM is used to generate an approximated model of objective function, for which a second-order polynomial function is chosen. The Design of experiment (DOE) technique coupled with CFD analysis is then ran to generate the database. The least-squares regression method (LS) is used to determine the coefficient of the RSM function. Finally, the Genetic Algorithms (GA) is applied to the objective function in order to obtain the optimal configuration. This paper also presents a solution to the problem of imprecise fitting of second-order RSM model by dividing the zone into several subzones which is proved to be effective in this paper. The optimization result shows that RSM is an effective and feasible optimization strategy for the centrifugal fan impeller design, and the complexity of the objective function and the overall optimization time could be significantly reduced.
One centrifugal compressor is applied for refrigeration and its working substance is R134a. The operating points obtained by using similar conversion at different rotation speeds are compared with the numerical results. They keep consistent with each other while the rotation speeds are lower, but the error between them will become large with the increasing of the rotation speed. Then the operating points are obtained when the working substance is air by using two similar conversion methods separately. Based on the comparison, it can be obtained that the result of keeping the specific volume ratio of inlet and outlet is more accurate than the result of maintaining Ma number. Then the test result is compared with the similarity result and the numerical result when the working substance is air. It is obtained that the similarity result is more consistent with the test result better than the numerical result and the trend of efficiency and pressure ratio change with the flow rate is consistent with the test result. In the process of similar conversion, the efficiency η is no useful for similitude design and it has less influence on the conversion result.
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