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The stability of laminar symmetric separated wakes
Full text linkTime-dependent computations of the two-dimensional incompressible uniform-velocity laminar flow past a normal flat plate (of unit half-width) in a channel are presented. Attention is restricted to cases in which the well-known anti-symmetric (von Kármán-type) vortex shedding is suppressed by the imposition of a symmetry plane on the downstream plate centreline. With a further symmetry plane at the channel's upper boundary, the only two governing parameters in the problem are the channel half-width, H, and the Reynolds number, Re (based on the body half-width and the upstream velocity, U). The former is restricted to the range 3?H?30 and the interest lies in determining the nature of the initial instability which occurs in the separated wake as Re is gradually increased. It is found that for sufficiently large H and at a critical Re, a long-time-scale global (supercritical) instability is initiated, which in its saturated (limit) state takes the form of ‘lumps’ of vorticity being periodically shed from the tail end of the separated bubble. Stability calculations of corresponding mean flow profiles (typical of those found in the separated wake) are undertaken by examining the impulse response of particular profiles via appropriate solution of the Orr–Sommerfeld equation. The results of this analysis extend those available from related published work and are consistent with the behaviour found from the numerical computations. Taken together, all the results suggest that this type of global instability may be generic to many kinds of separated wakes and, indeed, may provide the fundamental explanation for the very low-frequency oscillations often noticed in fully turbulent wake bubbles
Turbulence intensity in wall-bounded and wall-free flows
No full textTurbulence intensity variations in the outer region of turbulent shear flows are considered, in the context of the diagnostic plot first introduced by Alfredsson et al. (Phys. Fluids, vol. 23, 2011, 041702) and for both (smooth and rough) wall-bounded flows and classical free shear flows. With U U
defined as the mean velocity within the flow, U e Ue
as a suitable reference velocity and u ′ u′
as the root mean square of the fluctuating velocity, it is demonstrated that, for wall flows, the attached eddy hypothesis yields a closely linear diagnostic plot ( u ′ /U u′/U
versus U/U e U/Ue
) over a certain Reynolds number range, explaining why the relation seems to work well for both boundary layers and channels despite its lack of any physical basis (Castro et al., J. Fluid Mech., vol. 727, 2013, pp. 119–131). It is shown that mixing layers, jets and wakes also exhibit linear variations of u ′ /U u′/U
versus U/U e U/Ue
over much of the flows (starting roughly from where the turbulence production is a maximum), with slopes of these variations determined by the total mean strain rate, characterised by Townsend’s flow constant R s Rs
. The diagnostic plot thus has a wider range of applicability than might have been anticipated.</p
Near wall flow over urban-like roughness
No full textIn this study, comprehensive measurements over a number of urban-type surfaces with the same area density of 25% have been performed in a wind tunnel. The experiments were conducted at a free stream velocity of 10 m s-1 and the main instrumentation was 120 ° x-wire anemometry, but measurement accuracy was checked using laser Doppler anemometry. The results have confirmed the strong three-dimensionality of the turbulent flow in the roughness sublayer and the depths of the inertial sublayer (log-law region) and roughness sublayer for each surface have been determined. Spatial averaging has been used to remove the variability of the flow in the roughness sublayer due to individual obstacles and it is shown that the spatially averaged mean velocity in the inertial sublayer and roughness sublayer can, together, be described by a single log-law with a mean zero-plane displacement and roughness length for the surface, provided that the proper surface stress is known. The spatially averaged shear stresses in the inertial sublayer and roughness sublayer are compared with the surface stress deduced from form drag measurements on the roughness elements themselves. The dispersive stress arising from the spatial inhomogeneity in the mean flow profiles was deduced from the data and is shown to be negligible compared with the usual Reynolds stresses in the roughness sublayer. Comparisons have been made between a homogeneous (regular element array) surface and one consisting of random height elements of the same total volume. Although the upper limits of the inertial sublayer for both surfaces were almost identical at equivalent fetch, the roughness sublayer was much thicker for the random surface than for the uniform surface, the friction velocity and the roughness length were significantly larger and the 'roughness efficiency' was greater. It is argued that the inertial sublayer may not exist at all in some of the more extreme rough urban areas. These results will provide fundamental information for modelling urban air quality and forecasting urban wind climates
Axisymmetric jets impinging on porous walls
No full textThe flow of axisymmetric turbulent jets impinging on porous walls has been studied experimentally. It is shown how the overall flow structure depends on the porosity of the surface. For high porosities (open area ratios, β, in excess of around 40% say) the porous wall, or screen, leads to a sudden increase in jet width and decrease in mean and fluctuating velocities, a direct consequence of the momentum flux extracted because of the screen drag. Lower porosities can lead to the appearance of radial wall jets on the upstream side of the screen but, in contrast to the corresponding case of planar jet impingement (Cant et al. in Exp Fluids 32:16–26, 2002), such wall jets never occur on the downstream side. The axial downstream velocities thus remain positive for all porosities. Jet growth rates for β ≥ 0.45 are initially increased by the screen, but once β ≤ 0.4 momentum extraction by the screen is virtually complete, so that velocities become very small. Again, unlike in the corresponding planar case (for β ~ 0.4), recirculating regions upstream of the screen never occur. A simple argument is suggested to explain the fundamental differences in flow behaviour between planar and axisymmetric jet impingement onto porous screens and it is concluded that in the latter case the effects of the screen are generally more benign and unsurprising. Nonetheless, these axisymmetric flows, like the corresponding planar ones, provide a serious challenge for computational modelling
Direct numerical simulation of axisymmetric wakes embedded in turbulence
No full textDirect numerical simulation has been used to study the effects of external turbulence on axisymmetric wakes. In the absence of such turbulence, the time-developing axially homogeneous wake is found to have the self-similar properties expected whereas, in the absence of the wake, the turbulence fields had properties similar to Saffman-type turbulence. Merging of the two flows was undertaken for three different levels of external turbulence (relative to the wake strength) and it is shown that the presence of the external turbulence enhances the decay rate of the wake, with the new decay rates increasing with the relative strength of the initial external turbulence. The external turbulence is found to destroy any possibility of self-similarity within the developing wake, causing a significant transformation in the latter as it gradually evolves towards the forme
The critical Reynolds number for rough-wall boundary layers
No full textRough-wall boundary layers become aerodynamically smooth if the ‘roughness Reynolds number’ Re*=u*z0/? becomes sufficiently small. Conventional wisdom is that Re* should exceed at least two and perhaps be as much as five before viscous effects are insignificant. This criterion is assessed for the types of rough wall commonly used in laboratory simulations of atmospheric boundary layers—arrays of sharp-edged obstacles with significant separation between each obstacle. It is demonstrated that for such surfaces the roughness length z0 remains constant for falling roughness Reynolds numbers down to at least Re*=1. Viscous effects are shown to change the near-wall Reynolds stresses only for Re* below similar values, so that z0-scaling (rather than scaling based on ?/u*) remains appropriate down to at least Re*=1. One of the practical implications of this result is that wind-tunnel simulations of atmospheric boundary layers can be successful at lower wind speeds (or with smaller roughness elements) than previously supposed
Secondary motions in turbulent ribbed channel flows
No full textWe present data from direct numerical simulations (DNS) of the fully turbulent flow through nominally two-dimensional channels containing longitudinal, surface-mounted, rectangular ribs whose widths (W) are either one third of or equal to the gap (S − W) between consecutive ribs across the domain, where S is the span (centre-to-centre spacing) of the ribs. A range of the ratio of channel half-height (H) to span (S) is considered, covering 0.25 ⩽ H/S ⩽ 2.5. In each case, a fixed rib height (h) of 0.1H was used, but a number of cases with much smaller heights, h/H = 0.025 or 0.05 were also studied. The secondary flows resulting from the presence of the ribs are examined, along with their sources in terms of the axial vorticity transport equation, which highlights the effects of spanwise inhomogeneity in the Reynolds stresses. We show that the strength of the secondary flows depends strongly on H/S (and, correspondingly, on W/S) and that the major sources of axial vorticity arise near the top corners of the ribs, with convection of that vorticity dominating its spread. We also show that for smaller ribs the secondary flow strengths are similar to those predicted by Zampino et al. (2022) using a linearised model of the Reynolds-averaged equations, which does not include the vorticity convection process; the behaviour of secondary flow topology and strength with varying W/H is thus noticeably different
Three-dimensional flow in circular cavities of large spanwise aspect ratio
No full textExperimental data are presented for the vortex flow in a nominally two-dimensional circular cavity. The vortex is driven by a separated shear layer along an open section of the cavity circumference. It is shown that the core vortex flow is perturbed three-dimensionally. An inviscid analysis of an ideal core (solid body) vortex is given and it is shown that this flow contains a steady perturbation whose characteristics are almost exactly those identified in the experiments. Viscous effects reduce (by a few per cent) the spanwise wavelength of the perturbation and also lead, via spatial variations in Reynolds stress, to a modification of the core flow so that the radial profile of the circumferential velocity is ‘S’-shaped, rather than linea
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