The propagation of acoustic waves in a slowly varying duct with radially sheared axial mean flow

We consider the propagation of acoustic waves along a cylindrical duct carrying radially sheared axial mean flow, in which the duct radius is allowed to vary slowly along the axis. In previous work [A.J. Cooper & N. Peake, Journal of Fluid Mechanics 445 (2001) 207-234.] radially sheared axial mean flow with nonzero swirl in a slowly varying duct was considered, but in this paper we set the swirl to zero, thereby allowing simplification of the calculations of both the mean and unsteady flows. In this approach the acoustic wavenumber and corresponding eigenfunction are determined locally, while the wave amplitude is found by solving an evolution equation along the duct. Sample results are presented, including a case in which, perhaps surprisingly, the number of cut-on modes increases as the duct radius decreases. © 2013 Elsevier Ltd. All rights reserved.

The rhythm of fountains: The length and time scales of rise height fluctuations at low and high Froude numbers

The magnitude and frequency of vertical fluctuations of the top of an axisymmetric miscible Boussinesq fountain forms the focus of this work. We present measurements of these quantities for saline-aqueous fountains in uniform quiescent surroundings. Our results span source Froude numbers 0.3 ≤ Fr 0 ≤ 40 and, thereby, encompass very weak, weak, intermediate and forced classes of fountain. We identify distinct scalings, based on known quantities at the fountain source, for the frequency of fountain height fluctuations which collapse our data within bands of Fr0. Notably, our scalings reveal that the (dimensionless) frequency takes a constant value within each band. These results highlight characteristic time scales for the fluctuations which we decompose into a single, physically apparent, length scale and velocity scale within each band. Moreover, within one particular band, spanning source Froude numbers towards the lower end of the full range considered, we identify unexpectedly long-period fluctuations indicating a near balance of inertia and (opposing) buoyancy at the source. Our analysis identifies four distinct classes of fluctuation behaviour (four bands of Fr 0) and this classification matches well with existing classifications of fountains based on rise heights. As such, we show that an analysis of the behaviour of the fountain top alone, rather than the entire fountain, provides an alternative approach to classifying fountains. The similarity of classifications based on the two different methods confirms that the boundaries between classes mark tangible changes in the physics of fountains. For high Fr0 we show that the dominant fluctuations occur at the scale of the largest eddies which can be contained within the fountain near its top. Extending this, we develop a Strouhal number, Strtop, based on experimental measures of the fountain top, defined such that Strtop = 1 would suggest the dominant fluctuations are caused by a continual cycle of eddies forming and collapsing at this largest physical scale. For high- Fr 0 fountains we find Strtop ≈ 0. 9. © 2013 Cambridge University Press.

An experimental study of loss sources in a fan operating with continuous inlet stagnation pressure distortion

The viability of Boundary Layer Ingesting (BLI) engines for future aircraft propulsion is dependent on the ability to design robust, efficient engine fan systems for operation with continuously distorted inlet flow. A key step in this process is to develop an understanding of the specific mechanisms by which an inlet distortion affects the performance of a fan stage. In this paper, detailed full-annulus experimental measurements of the flow field within a low-speed fan stage operating with a continuous 60-degree inlet stagnation pressure distortion are presented. These results are used to describe the three-dimensional fluid mechanics governing the interaction between the fan and the distortion and to make a quantitative assessment of the impact on loss generation within the fan. A 5.3 percentage point reduction in stage total-to-total efficiency is observed as a result of the inlet distortion. The reduction in performance is shown to be dominated by increased loss generation in the rotor due to off-design incidence values at its leading edge, an effect which occurs throughout the annulus despite the localised nature of the inlet distortion. Increased loss generation in the stator row is also observed due to flow separations that are shown to be caused by whirl angle distortion at rotor exit. By addressing these losses, it should be possible to achieve improved efficiency in BLI fan systems. Copyright © 2012 by ASME.

Lock-in and quasiperiodicity in a forced hydrodynamically self-excited jet

The ability of hydrodynamically self-excited jets to lock into strong external forcing is well known. Their dynamics before lock-in and the specific bifurcations through which they lock in, however, are less well known. In this experimental study, we acoustically force a low-density jet around its natural global frequency. We examine its response leading up to lock-in and compare this to that of a forced van der Pol oscillator. We find that, when forced at increasing amplitudes, the jet undergoes a sequence of two nonlinear transitions: (i) from periodicity to T{double-struck}2 quasiperiodicity via a torus-birth bifurcation; and then (ii) from T{double-struck}2 quasiperiodicity to 1:1 lock-in via either a saddle-node bifurcation with frequency pulling, if the forcing and natural frequencies are close together, or a torus-death bifurcation without frequency pulling, but with a gradual suppression of the natural mode, if the two frequencies are far apart. We also find that the jet locks in most readily when forced close to its natural frequency, but that the details contain two asymmetries: the jet (i) locks in more readily and (ii) oscillates more strongly when it is forced below its natural frequency than when it is forced above it. Except for the second asymmetry, all of these transitions, bifurcations and dynamics are accurately reproduced by the forced van der Pol oscillator. This shows that this complex (infinite-dimensional) forced self-excited jet can be modelled reasonably well as a simple (three-dimensional) forced self-excited oscillator. This result adds to the growing evidence that open self-excited flows behave essentially like low-dimensional nonlinear dynamical systems. It also strengthens the universality of such flows, raising the possibility that more of them, including some industrially relevant flames, can be similarly modelled. © 2013 Cambridge University Press.

An experimental study of loss sources in a fan operating with continuous inlet stagnation pressure distortion

The viability of boundary layer ingesting (BLI) engines for future aircraft propulsion is dependent on the ability to design robust, efficient engine fan systems for operation with continuously distorted inlet flow. A key step in this process is to develop an understanding of the specific mechanisms by which an inlet distortion affects the performance of a fan stage. In this paper, detailed full-annulus experimental measurements of the flow field within a low-speed fan stage operating with a continuous 60 deg inlet stagnation pressure distortion are presented. These results are used to describe the three-dimensional fluid mechanics governing the interaction between the fan and the distortion and to make a quantitative assessment of the impact on loss generation within the fan. A 5.3 percentage point reduction in stage total-to-total efficiency is observed as a result of the inlet distortion. The reduction in performance is shown to be dominated by increased loss generation in the rotor due to off-design incidence values at its leading edge, an effect that occurs throughout the annulus despite the localized nature of the inlet distortion. Increased loss in the stator row is also observed due to flow separations that are shown to be caused by whirl angle distortion at rotor exit. By addressing these losses, it should be possible to achieve improved efficiency in BLI fan systems. © 2013 by ASME.

The evolution of a stratified turbulent cloud

Localized regions of turbulence, or turbulent clouds, in a stratified fluid are the subject of this study, which focuses on the edge dynamics occurring between the turbulence and the surrounding quiescent region. Through laboratory experiments and numerical simulations of stratified turbulent clouds, we confirm that the edge dynamics can be subdivided into materially driven intrusions and horizontally travelling internal wave-packets. Three-dimensional visualizations show that the internal gravity wave-packets are in fact large-scale pancake structures that grow out of the turbulent cloud into the adjacent quiescent region. The wave-packets were tracked in time, and it is found that their speed obeys the group speed relation for linear internal gravity waves. The energetics of the propagating waves, which include waveforms that are inclined with respect to the horizontal, are also considered and it is found that, after a period of two eddy turnover times, the internal gravity waves carry up to 16 % of the cloud kinetic energy into the initially quiescent region. Turbulent events in nature are often in the form of decaying turbulent clouds, and it is therefore suggested that internal gravity waves radiated from an initial cloud could play a significant role in the reorganization of energy and momentum in the atmosphere and oceans.©2013 Cambridge University Press.

Scaling arguments for the fluxes in turbulent miscible fountains

For established axisymmetric turbulent miscible Boussinesq fountains in quiescent uniform environments, expressions are developed for the fluxes of volume, momentum and buoyancy at the outflow from the fountain: the outflow referring to the counterflow at the horizontal plane of the source. The fluxes are expressed in terms of the fountain source conditions and two dimensionless functions of the source Froude number, Fr0: a radial function (relating a horizontal scale of the outflow to the source radius) and a volume flux function (relating the outflow and source volume fluxes). The forms taken by these two functions at low Fr0 and high Fr0 are deduced, thereby providing the outflow fluxes and outflow Froude number solely in terms of the source conditions. For high Fr0, the outflow Froude number, Frout, is shown to be invariant, indicating (by analogy with plumes for which the 'far-field' Froude number is invariant with source Froude number) that the outflow may be regarded as 'far-field' since the fluxes within the fountain have adjusted to attain a balance which is independent of the source conditions. Based on Frout, the fluxes in the plume that forms beyond the fountain outflow are deduced. Finally, from the results of previously published studies, we show that the scalings deduced for fountains are valid for 0.0025 ≲ Fr0 ≲ 1.0 for low Fr0 and Fr0≳ 3.0 for high Fr0. © 2014 Cambridge University Press.

On the laminar-turbulent transition of the rotating-disk flow: The role of absolute instability

© 2014 Cambridge University Press. This paper describes a detailed experimental study using hot-wire anemometry of the laminar-turbulent transition region of a rotating-disk boundary-layer flow without any imposed excitation of the boundary layer. The measured data are separated into stationary and unsteady disturbance fields in order to elaborate on the roles that the stationary and the travelling modes have in the transition process. We show the onset of nonlinearity consistently at Reynolds numbers, R, of ∼ 510, i.e. at the onset of Lingwood's (J. Fluid Mech., vol. 299, 1995, pp. 17-33) local absolute instability, and the growth of stationary vortices saturates at a Reynolds number of ∼ 550. The nonlinear saturation and subsequent turbulent breakdown of individual stationary vortices independently of their amplitudes, which vary azimuthally, seem to be determined by well-defined Reynolds numbers. We identify unstable travelling disturbances in our power spectra, which continue to grow, saturating at around R=585, whereupon turbulent breakdown of the boundary layer ensues. The nonlinear saturation amplitude of the total disturbance field is approximately constant for all considered cases, i.e. different rotation rates and edge Reynolds numbers. We also identify a travelling secondary instability. Our results suggest that it is the travelling disturbances that are fundamentally important to the transition to turbulence for a clean disk, rather than the stationary vortices. Here, the results appear to show a primary nonlinear steep-fronted (travelling) global mode at the boundary between the local convectively and absolutely unstable regions, which develops nonlinearly interacting with the stationary vortices and which saturates and is unstable to a secondary instability. This leads to a rapid transition to turbulence outward of the primary front from approximately R=565 to 590 and to a fully turbulent boundary layer above 650.

Modelling of submarine landslides and generated water waves

The slide of unstable sedimentary bodies and their hydraulic effects are studied by numerical means. A two-dimensional fluid mechanics model based on Navier-Stokes equations has been developed considering the sediments and water as a mixture. Viscoplastic and diffusion laws for the sediments have been introduced into the model. The numerical model is validated with an analytical solution for a Bingham flow. Laboratory experiments consisting in the slide of gravel mass have been carried out. The results of these experiments have shown the importance of the sediment rheology and the diffusion. The model parameters are adjusted by trial and error to match the observed “sandflow”.