Abstract
Sound field prediction has practical significance in the control of noise generated by sources in a flow, for example, the noise in aero-engines and ventilation systems. Aiming at accurate and flexible prediction of time-dependent sound field, a finite-difference wavenumber-time domain method for sound field prediction in a uniformly moving medium is proposed. The method is based on the second-order convective wave equation, and the wavenumber-time domain representation of the sound pressure field on one plane is forward propagated via a derived recursive expression. In this paper, the recursive expression is first deduced, and then numerical stability and dispersion of the proposed method are analyzed, based on which the stability condition is given and the correction of dispersion related to the transition frequency is made. Numerical simulations are conducted to test the performance of the proposed method, and the results show that the method is valid and robust at different Mach numbers.
Highlights
Sound field prediction is exactly an effective way to comprehend such properties and can provide a basis for noise reduction. Several methods, such as parabolic equation approximations [1, 2], fast field program [3, 4], nearfield acoustic holography [5,6,7], and finite-difference time-domain (FDTD) method [8,9,10], have been presented for sound field prediction in a moving medium. e first two methods are performed in the frequency domain, while the rest can be performed in the time domain
In the FDTD method, the wave propagation equations are directly solved in the space-time domain and the acoustic quantities at each spatial point are calculated in terms of those at nearby points. erefore, the FDTD method is usually regarded as a local method [14]
The second-order convective wave equation is first transformed into the wavenumber-time domain by taking the 2D spatial Fourier transform, the first-order and second-order derivatives of sound pressure in the wavenumber-time domain are approximated by the central finite difference in second order, and a recursive expression is deduced for the sound field prediction
Summary
Z-transform. e wavenumber spectrum P(kz, n) of pressure P(m, n) can be obtained from the spatial discrete. To obtain the explicit expression of the stability condition, inequality (12) can be discussed in two different cases, according to the relationship between the magnitudes of a2 and 1 + V2k2xΔt2. It can be analyzed briefly as follows. E transition frequency will be deviated from that in the continuous case caused by discretization, and it is expected to be corrected in the following analysis. The theoretical value of wavenumber kz in the continuous case normalized by k0 in the propagation direction can be represented as. It is expected that the correction can be made by assuming that ft/fs equals ft/fs, and
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