Sound from rotors in non-uniform flow

Geometric algebra and an acoustic space time for propagation in non-uniform flow

This study aims to make use of two concepts in the field of aeroacoustics; an analogy with relativity, and Geometric Algebra. The analogy with relativity has been investigated in physics and cosmology, but less has been done to use this work in the field of aeroacoustics. Despite being successfully applied to a variety of fields, Geometric Algebra has yet to be applied to acoustics. Our aim is to apply these concepts first to a simple problem in aeroacoustics, sound propagation in uniform flow, and the more general problem of acoustic propagation in non-uniform flows. By using Geometric Algebr…

Can Sound Waves be Slowed?

Dielectric fluids experience a striction force in the presence of an external electric field. Although the striction force on the entire body of the fluid is usually zero, it does contribute to its deformations. In this paper, I show that the speed of sound in dielectric fluids is reduced when they are exposed to uniform electric fields of sufficiently high magnitude. Ferrofluids also experience a similar striction force in presence of a magnetizing field. However, their low relative permeability makes the effect very small.

Slow sound in lined flow ducts

We consider the acoustic propagation in lined flow duct with a purely reactive impedance at the wall. This reacting liner has the capability to reduce the speed of sound, and thus to enhance the interaction between the acoustic propagation and the low Mach number flow ($M\simeq0.3$). At the lower frequencies, there are typically 4 acoustic or hydrodynamic propagating modes, with 3 of them propagating in the direction of the flow. Above a critical frequency, there are only 2 propagating modes that all propagate in the direction of the flow. From the exact 2D formulation an approximate 1D model …

有涡流体中声的波动方程

Wave Equation for Sound in Fluids with Vorticity

我们使用Clebsch势和作用原理推导出一个封闭的系统的规范不变方程叠加在一般的背景流的声音。当流动无旋或缓慢变化时，我们的系统简化为Unruh（1981）和Pierce（1990）波动方程。我们说明我们的形式主义，将其应用到波传播的均匀旋转的流体中的声音模式与惯性波杂交。

圆源的辐射部分

The radiating part of circular sources

分析开发链接的形式，从一个圆形的源的辐射状结构的源的声场，而不求助于远场或其他近似。结果表明，辐射到场中的信息是有限的，其极限由源的波数乘以源的半径（亥姆霍兹数）确定。声场是由一组线源产生的基本场来表示的，线源的形式由第二类切比雪夫多项式给出，其振幅由径向源项的加权积分给出。分析开发音调源，如转子，和，亥姆霍兹数小于2，随机磁盘源。在这种情况下，分析产生声场中两点之间的互谱。该分析适用于音调辐射，随机源辐射作为模型问题的喷气噪声的问题，和噪声消除，如在主动控制的噪声转子。它被发现，该方法给出了一个准确的辐射问题的模型，并明确地确定这些部分的源辐射。

An acoustic space-time and the Lorentz transformation in aeroacoustics

In this paper we introduce concepts from relativity and geometric algebra to aeroacoustics. We do this using an acoustic space-time transformation within the framework of sound propagation in uniform flows. By using Geometric Algebra we are able to provide a simple geometric interpretation to the space-time transformation, and are able to give neat and lucid derivations of the free-field Green's function for the convected wave equation and the Doppler shift for a stationary observer and a source in uniform rectilinear motion in a uniform flow.

Slow Sound in a duct, effective transonic flows and analogue black holes

We propose a new system suitable for studying analogue gravity effects, consisting of a gas flowing in a duct with a compliant wall. Effective transonic flows are obtained from uniform, low Mach number flows through the reduction of the one-dimensional speed of sound induced by the wall compliance. We show that the modified equation for linear perturbations can be written in a Hamiltonian form. We perform a one-dimensional reduction consistent with the canonical formulation, and deduce the analogue metric along with the first dispersive term. In a weak dispersive regime, the spectrum emitted f…