Acoustics within mean flows are governed by the linearized Euler equations, which possess a singularity wherever the local mean flow velocity is equal to the phase speed of the disturbance. Such locations are termed critical layers, and are usually ignored when estimating the sound field, with their contribution assumed to be negligible. This paper studies fully both numerically and analytically a simple yet typical sheared ducted flow in order to investigate the influence of the critical layer, and shows that the neglect of critical layers is sometimes, but certainly not always, justified. The model is that of a linear-then-constant velocity profile with uniform density in a cylindrical duct, allowing exact Green’s function solutions in terms of Bessel functions and Frobenius expansions. For sources outside the sheared flow, the contribution of the critical layer is found to decay algebraically along the duct as , where is the distance downstream of the source. For sources within the sheared flow, the contribution from the critical layer is found to consist of a non-modal disturbance of constant amplitude and a disturbance decaying algebraically as . For thin boundary layers, these disturbances trigger the inherent convective instability of the flow. Extra care is required for high frequencies as the critical layer can be neglected only in combination with a particular downstream pole. The advantages of Frobenius expansions over direct numerical calculation are also demonstrated, especially with regard to spurious modes around the critical layer.

This study investigates the sound produced when a jet, issued from a circular nozzle or hole in a plate, goes through a similar hole in a second plate. The sound, known as a hole tone, is encountered in many practical engineering situations. Direct computations of a hole tone feedback system were conducted. The mean velocity of the air jet was 10 m s−1. The nozzle and the end plate hole both had a diameter of 51 mm, and the impingement length between the nozzle and the end plate was 50 mm. The computational results agreed well with past experimental data in terms of qualitative vortical structures, the relationship between the most dominant hole tone peak frequency and the jet speed, and downstream growth of the mean jet profiles. Based on the computational results, the shear-layer impingement on the hole edge, the resulting propagation of pressure waves and the associated vortical structures are discussed. To extract dominant unsteady behaviours of the hole tone phenomena, a snapshot proper orthogonal decomposition (POD) analysis of pressure fluctuation fields was conducted. It was found that the pressure fluctuation fields and the time variation of mass flows through the end plate hole were dominantly expressed by the first and second POD modes, respectively. Integrating the computational results, an axisymmetric throttling mechanism linking mass flow rates through the hole, vortex impingement and global pressure propagation, is proposed.

This work belongs to the ongoing debate surrounding the mechanism responsible for low-angle sound emission from subsonic jets. The flow, simulated by large eddy simulation (Bogey & Bailly, Comput. Fluids, vol. 35 (10), 2006a, pp. 1344–1358), is a Mach 0.9 jet with Reynolds number, based on the exit diameter, of . A methodology is implemented to educe, explore and model the flow motions associated with low-angle sound radiation. The eduction procedure, which is based on frequency–wavenumber filtering of the sound field and subsequent conditional analysis of the turbulent jet, provides access to space- and time-dependent (hydrodynamic) pressure and velocity fields. Analysis of these shows the low-angle sound emission to be underpinned by dynamics comprising space and time modulation of axially coherent wavepackets: temporally localized energization of wavepackets is observed to be correlated with the generation of high-amplitude acoustic bursts. Quantitative validation is provided by means of a simplified line-source Ansatz (Cavalieri et al. J. Sound Vib., vol. 330, 2011b, pp. 4474–4492). The dynamic nature of the educed field is then assessed using linear stability theory (LST). The educed pressure and velocity fields are found to compare well with LST: the radial structures of these match the corresponding LST eigenfunctions; the axial evolutions of their fluctuation energy are consistent with the LST amplification rates; and the relative amplitudes of the pressure and velocity fluctuations, which are educed independently of one another, are consistent with LST.

We study the gas flow processes in ultra-tight porous media in which the matrix pore network is composed of nanometre- to micrometre-size pores. We formulate a pressure-dependent permeability function, referred to as the apparent permeability function (APF), assuming that Knudsen diffusion and slip flow (the Klinkenberg effect) are the main contributors to the overall flow in porous media. The APF predicts that in nanometre-size pores, gas permeability values are as much as 10 times greater than results obtained by continuum hydrodynamics predictions, and with increasing pore size (i.e. of the order of the micrometre), gas permeability converges to continuum hydrodynamics values. In addition, the APF predicts that an increase in the fractal dimension of the pore surface leads to a decrease in Knudsen diffusion. Using the homogenization method, a rigorous analysis is performed to examine whether the APF is preserved throughout the process of upscaling from local scale to large scale. We use the well-known pulse-decay experiment to estimate the main parameter of the APF, which is Darcy permeability. Our newly derived late-transient analytical solution and the late-transient numerical solution consistently match the pressure decay data and yield approximately the same estimated value for Darcy permeability at the typical core-sample initial pressure range and pressure difference. Other parameters of the APF may be determined from independent laboratory experiments; however, a pulse-decay experiment can be used to estimate the unknown parameters of the APF if multiple tests are performed and/or the parameters are strictly constrained by upper and lower bounds.

The wake of a flexible foil undergoing pitching oscillations in a low-speed hydrodynamic tunnel is used to examine the effect of chordwise foil flexibility in the dynamical features of flapping-based propulsion. We compare the regime transitions in the wake with respect to the case of a rigid foil and show that foil flexibility inhibits the symmetry breaking of the reverse Bénard–von Kármán wake reported in the literature. A momentum balance calculation shows the average thrust to be up to three times greater for the flexible foil than for the rigid foil. We explain both of these observations by analysing the vortex dynamics in the very near wake.