Non-uniqueness in wakes and boundary layers

1984 ◽  
Vol 391 (1800) ◽  
pp. 1-26 ◽  
Keyword(s):  
Boundary Layer ◽  
Large Scale ◽  
Reynolds Numbers ◽  
Near Wake ◽  
Algebraic Decay ◽  
Scale Separation ◽  
Boundary Layer Equations ◽  
Classical Boundary ◽  
Streamlined Flow ◽  
High Reynolds

In streamlined flow past a flat plate aligned with a uniform stream, it is shown that ( a ) the Goldstein near-wake and ( b ) the Blasius boundary layer are non-unique solutions locally for the classical boundary layer equations, whereas ( c ) the Rott-Hakkinen very-near-wake appears to be unique. In each of ( a ) and ( b ) an alternative solution exists, which has reversed flow and which apparently cannot be discounted on immediate grounds. So, depending mainly on how the alternatives for ( a ), ( b ) develop downstream, the symmetric flow at high Reynolds numbers could have two, four or more steady forms. Concerning non-streamlined flow, for example past a bluff obstacle, new similarity forms are described for the pressure-free viscous symmetric closure of a predominantly slender long wake beyond a large-scale separation. Features arising include non-uniqueness, singularities and algebraic behaviour, consistent with non-entraining shear layers with algebraic decay. Non-uniqueness also seems possible in reattachment onto a solid surface and for non-symmetric or pressure-controlled flows including the wake of a symmetric cascade.

On the laminar flow in a free jet of liquid at high Reynolds numbers

1968 ◽  
Vol 32 (2) ◽  
pp. 273-292 ◽  
Author(s):  
J. P. K. Tillett
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Applied Pressure ◽  
Reynolds Numbers ◽  
Momentum Balance ◽  
Free Jet ◽  
Contraction Ratio ◽  
Asymptotic Contraction ◽  
Classical Boundary ◽  
High Reynolds

This paper is concerned with the jet of liquid, open to the atmosphere, that emerges from a two-dimensional channel in which there is Poiseuille flow far upstream, the flow being driven by an applied pressure gradient. The problem is discussed with the aid of the method of matched asymptotic expansions; the small parameter involved is the inverse Reynolds number. A boundary layer forms adjacent to the free surface, and a classical boundary-layer analysis is applied to find the flow there (for moderate distances downstream); the influence of this boundary layer on the flow in the core of the jet is then investigated. Higher-order boundary-layer effects, such as indeterminacy and eigensolutions, are also discussed. The first few terms are found of an asymptotic expansion for the equation of the free surface, and considerations of momentum balance are applied to find the asymptotic contraction ratio of the jet.

Highly separated axisymmetric step shock-wave/turbulent-boundary-layer interaction

2017 ◽  
Vol 828 ◽  
pp. 236-270 ◽  
Author(s):  
Gaurav Chandola ◽  
Xin Huang ◽  
David Estruch-Samper
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Turbulent Boundary Layer ◽  
High Speed ◽  
Large Scale ◽  
Scale Separation ◽  
Time Resolved ◽  
Layer Interaction ◽  
Boundary Layer Interaction ◽  
High Reynolds

The unsteadiness of a shock-wave/turbulent-boundary-layer interaction induced by an axisymmetric step (cylinder/$90^{\circ }$-disk) is investigated experimentally at Mach 3.9. A large-scale separation of the order of previously reported incoming turbulent superstructures is induced ahead of the step ${\sim}30\unicode[STIX]{x1D6FF}_{o}$ and followed by a downstream separation of ${\sim}10\unicode[STIX]{x1D6FF}_{o}$ behind it, where $\unicode[STIX]{x1D6FF}_{o}$ is the incoming boundary-layer thickness. Narrowband high-frequency instabilities shift gradually to more moderate frequencies along the upstream separation region exhibiting a strong predominance of shear-induced disturbance levels – arising between the outer high-speed flow and the subsonic bubble. Through spectral/time-resolved analysis of this high Reynolds number and large-scale separation, results offer new insights into the shear layer’s inception and evolution (convection, growth and instability) and its influence on interaction unsteadiness.

Effects of Reynolds Number and Free-Stream Turbulence on Boundary Layer Transition in a Compressor Cascade

2000 ◽  
Author(s):  
Heinz-Adolf Schreiber ◽  
Wolfgang Steinert ◽  
Bernhard Küsters
Keyword(s):  
Boundary Layer ◽  
Free Stream ◽  
Reynolds Numbers ◽  
Boundary Layer Transition ◽  
Bypass Transition ◽  
Layer Transition ◽  
Free Stream Turbulence ◽  
High Reynolds Numbers ◽  
High Turbulence ◽  
High Reynolds

An experimental and analytical study has been performed on the effect of Reynolds number and free-stream turbulence on boundary layer transition location on the suction surface of a controlled diffusion airfoil (CDA). The experiments were conducted in a rectilinear cascade facility at Reynolds numbers between 0.7 and 3.0×106 and turbulence intensities from about 0.7 to 4%. An oil streak technique and liquid crystal coatings were used to visualize the boundary layer state. For small turbulence levels and all Reynolds numbers tested the accelerated front portion of the blade is laminar and transition occurs within a laminar separation bubble shortly after the maximum velocity near 35–40% of chord. For high turbulence levels (Tu > 3%) and high Reynolds numbers transition propagates upstream into the accelerated front portion of the CDA blade. For those conditions, the sensitivity to surface roughness increases considerably and at Tu = 4% bypass transition is observed near 7–10% of chord. Experimental results are compared to theoretical predictions using the transition model which is implemented in the MISES code of Youngren and Drela. Overall the results indicate that early bypass transition at high turbulence levels must alter the profile velocity distribution for compressor blades that are designed and optimized for high Reynolds numbers.

Turbulent flow between counter-rotating concentric cylinders: a direct numerical simulation study

2008 ◽  
Vol 615 ◽  
pp. 371-399 ◽  
Author(s):  
S. DONG
Keyword(s):  
Turbulent Flow ◽  
Large Scale ◽  
Outer Cylinder ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Taylor Vortex ◽  
Small Scale ◽  
Mean Flow ◽  
Concentric Cylinders ◽  
High Reynolds

We report three-dimensional direct numerical simulations of the turbulent flow between counter-rotating concentric cylinders with a radius ratio 0.5. The inner- and outer-cylinder Reynolds numbers have the same magnitude, which ranges from 500 to 4000 in the simulations. We show that with the increase of Reynolds number, the prevailing structures in the flow are azimuthal vortices with scales much smaller than the cylinder gap. At high Reynolds numbers, while the instantaneous small-scale vortices permeate the entire domain, the large-scale Taylor vortex motions manifested by the time-averaged field do not penetrate a layer of fluid near the outer cylinder. Comparisons between the standard Taylor–Couette system (rotating inner cylinder, fixed outer cylinder) and the counter-rotating system demonstrate the profound effects of the Coriolis force on the mean flow and other statistical quantities. The dynamical and statistical features of the flow have been investigated in detail.

scholarly journals Near-Wake Observations behind Azimuthally Perforated Disks With Varying Hole Layout and Porosity in Smooth Airstreams at High Reynolds Numbers

2018 ◽  
Vol 141 (5) ◽  
Author(s):  
Raf Theunissen ◽  
Robert Worboys
Keyword(s):  
Drag Coefficient ◽  
Experimental Studies ◽  
Reynolds Numbers ◽  
Wake Flow ◽  
Mean Flow ◽  
Flow Topology ◽  
Near Wake ◽  
Two Component ◽  
High Reynolds ◽  
Component Particle

Porous disks are commonly encountered in experimental studies dealing with flow through objects such as wind turbines, parachutes, and fluidic devices to regulate pressure and/or downstream turbulence. Perforations are typically staggered and only porosity is altered to attain the required disk drag coefficient, despite a documented influence of topology. Few works have reported, however, to which extent the spatial distribution of the circular perforations affect the mean flow pertaining freestanding disks, and for this reason, this work presents a first, more systematic study focused on the effect of azimuthally varying hole topology and porosity on disk drag and near-wake characteristics. An experimental study performed in airflows of negligible freestream turbulence at Reynolds numbers in the order of 105 is reported and related to the existing literature to ensure reliability. Complementary to drag measurements, near-wake surveys have been performed on a variety of perforation layouts using two-component laser Doppler velocimetry and two-component particle image velocimetry. It is shown that minor changes in perforations can cause drastic changes in near-wake flow topology and no perforation layout can be consistently associated with highest drag. Explicit empirical expressions for drag coefficient linked with the simplified topologies considered have been derived.

Airfoil Trailing Edge Noise Reduction Using a Boundary-Layer Bump

2019 ◽  
Vol 105 (5) ◽  
pp. 814-826 ◽  
Author(s):  
Yuejun Shi ◽  
Seongkyu Lee
Keyword(s):  
Boundary Layer ◽  
Noise Reduction ◽  
Suction Side ◽  
Reynolds Numbers ◽  
Numerical Approach ◽  
Trailing Edge ◽  
Velocity Deficit ◽  
Trailing Edge Noise ◽  
Field Noise ◽  
High Reynolds

This paper presents a new idea of reducing airfoil trailing edge noise using a small bump in the turbulent boundary layer. First, we develop and validate a new computational approach to predict airfoil trailing edge noise using steady RANS CFD, an empirical wall pressure spectrum model, and Howe's diff raction theory. This numerical approach enables fast and accurate predictions of trailing edge noise, which is used to study the noise reduction from the bump for various airfoil geometries and flow conditions at high Reynolds numbers. Three types of bumps, the suction-side bump, pressure-side bump, and both-side bumps, are studied. The results show that all types of bumps are able to reduce far-field noise up to 10 dB compared to clean airfoils, but their impacts are diff erent in terms of the eff ective frequency range. Also, bumps with four diff erent heights are compared with each other to investigate the eff ect of the height of bumps on noise reduction. It is demonstrated that a bump causes velocity deficit within the boundary layer near the wall. This velocity deficit results in reduced turbulence kinetic energy near the wall, which is responsible for trailing edge noise reduction. Overall, this paper demonstrates the potential of a boundary-layer bump in trailing edge noise reduction and sheds light on the physical mechanism of noise reduction with boundary-layer bumps.

Temperature Control of Blow-Down, Supersonic Tunnels

1956 ◽  
Vol 60 (541) ◽  
pp. 67-70
Author(s):  
T. A. Thomson
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Mach Number ◽  
Reynolds Numbers ◽  
Stagnation Temperature ◽  
Blow Down ◽  
High Reynolds Numbers ◽  
Experimental Errors ◽  
High Reynolds

The blow-down type of intermittent, supersonic tunnel is attractive because of its simplicity and because relatively high Reynolds numbers can be obtained for a given size of test section. An adverse characteristic, however, is the fall of stagnation temperature during runs, which can affect experiments in several ways. The Reynolds number varies and the absolute velocity is not constant, even if the Mach number and pressure are; heat-transfer cannot be studied under controlled conditions and the experimental errors arising from the effect of heat-transfer on the boundary layer vary in time. These effects can become significant in quantitative experiments if the tunnel is large and the variation of temperature very rapid; the expense required to eliminate them might then be justified.

scholarly journals Assessment of inner–outer interactions in the urban boundary layer using a predictive model

2019 ◽  
Vol 875 ◽  
pp. 44-70 ◽  
Author(s):  
Karin Blackman ◽  
Laurent Perret ◽  
Romain Mathis
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Predictive Model ◽  
Boundary Layers ◽  
Large Scale ◽  
Reynolds Numbers ◽  
Limited Range ◽  
Rough Wall ◽  
Wall Boundary ◽  
Layer Flow

Urban-type rough-wall boundary layers developing over staggered cube arrays with plan area packing density, $\unicode[STIX]{x1D706}_{p}$, of 6.25 %, 25 % or 44.4 % have been studied at two Reynolds numbers within a wind tunnel using hot-wire anemometry (HWA). A fixed HWA probe is used to capture the outer-layer flow while a second moving probe is used to capture the inner-layer flow at 13 wall-normal positions between $1.25h$ and $4h$ where $h$ is the height of the roughness elements. The synchronized two-point HWA measurements are used to extract the near-canopy large-scale signal using spectral linear stochastic estimation and a predictive model is calibrated in each of the six measurement configurations. Analysis of the predictive model coefficients demonstrates that the canopy geometry has a significant influence on both the superposition and amplitude modulation. The universal signal, the signal that exists in the absence of any large-scale influence, is also modified as a result of local canopy geometry suggesting that although the nonlinear interactions within urban-type rough-wall boundary layers can be modelled using the predictive model as proposed by Mathis et al. (J. Fluid Mech., vol. 681, 2011, pp. 537–566), the model must be however calibrated for each type of canopy flow regime. The Reynolds number does not significantly affect any of the model coefficients, at least over the limited range of Reynolds numbers studied here. Finally, the predictive model is validated using a prediction of the near-canopy signal at a higher Reynolds number and a prediction using reference signals measured in different canopy geometries to run the model. Statistics up to the fourth order and spectra are accurately reproduced demonstrating the capability of the predictive model in an urban-type rough-wall boundary layer.

Sign in / Sign up

Export Citation Format

Share Document