Effects of Heating on Two-Dimensional Mixing Layers

1997 ◽  
Vol 119 (3) ◽  
pp. 180-183
Author(s):  
N. Butuk ◽  
S. R. Gollahalli
Keyword(s):  
Velocity Field ◽  
Shear Layer ◽  
Room Temperature ◽  
Shear Layers ◽  
Mixing Layers ◽  
Two Dimensional ◽  
Horizontal Shear ◽  
Streamwise Direction ◽  
The Mean

Transverse profiles of temperature and the mean velocities in the streamwise direction in a horizontal shear layer are presented. The variation of vorticity thickness along the streamwise coordinate is examined for the cases when both streams were at room temperature and when the top stream was heated to 360 K. The similarity of the velocity field is observed only near the plane of the interface of the two streams in both cases. The vorticity thickness-velocity ration correlation agrees well with the data available for the isothermal shear layers. The heating of one stream was not found to significantly influence the vorticity thickness, which is explained by the counteracting influences of viscosity and density changes.

The anatomy of the mixing transition in homogeneous and stratified free shear layers

2000 ◽  
Vol 413 ◽  
pp. 1-47 ◽  
Author(s):  
C. P. CAULFIELD ◽  
W. R. PELTIER
Keyword(s):  
Shear Layer ◽  
Three Dimensional ◽  
Streamwise Vortex ◽  
Shear Layers ◽  
Finite Amplitude ◽  
Small Scale ◽  
Two Dimensional ◽  
Streamwise Vortices ◽  
Free Shear Layers ◽  
Nonlinear Amplification

We investigate the detailed nature of the ‘mixing transition’ through which turbulence may develop in both homogeneous and stratified free shear layers. Our focus is upon the fundamental role in transition, and in particular the associated ‘mixing’ (i.e. small-scale motions which lead to an irreversible increase in the total potential energy of the flow) that is played by streamwise vortex streaks, which develop once the primary and typically two-dimensional Kelvin–Helmholtz (KH) billow saturates at finite amplitude.Saturated KH billows are susceptible to a family of three-dimensional secondary instabilities. In homogeneous fluid, secondary stability analyses predict that the stream-wise vortex streaks originate through a ‘hyperbolic’ instability that is localized in the vorticity braids that develop between billow cores. In sufficiently strongly stratified fluid, the secondary instability mechanism is fundamentally different, and is associated with convective destabilization of the statically unstable sublayers that are created as the KH billows roll up.We test the validity of these theoretical predictions by performing a sequence of three-dimensional direct numerical simulations of shear layer evolution, with the flow Reynolds number (defined on the basis of shear layer half-depth and half the velocity difference) Re = 750, the Prandtl number of the fluid Pr = 1, and the minimum gradient Richardson number Ri(0) varying between 0 and 0.1. These simulations quantitatively verify the predictions of our stability analysis, both as to the spanwise wavelength and the spatial localization of the streamwise vortex streaks. We track the nonlinear amplification of these secondary coherent structures, and investigate the nature of the process which actually triggers mixing. Both in stratified and unstratified shear layers, the subsequent nonlinear amplification of the initially localized streamwise vortex streaks is driven by the vertical shear in the evolving mean flow. The two-dimensional flow associated with the primary KH billow plays an essentially catalytic role. Vortex stretching causes the streamwise vortices to extend beyond their initially localized regions, and leads eventually to a streamwise-aligned collision between the streamwise vortices that are initially associated with adjacent cores.It is through this collision of neighbouring streamwise vortex streaks that a final and violent finite-amplitude subcritical transition occurs in both stratified and unstratified shear layers, which drives the mixing process. In a stratified flow with appropriate initial characteristics, the irreversible small-scale mixing of the density which is triggered by this transition leads to the development of a third layer within the flow of relatively well-mixed fluid that is of an intermediate density, bounded by narrow regions of strong density gradient.

The Shear Layer above and in Urban Canopies

2007 ◽  
Vol 46 (3) ◽  
pp. 368-376 ◽  
Author(s):  
Pablo Huq ◽  
Louis A. White ◽  
Alejandro Carrillo ◽  
Jose Redondo ◽  
Seshu Dharmavaram ◽  
...  
Keyword(s):  
New York ◽  
New York City ◽  
Los Angeles ◽  
Shear Layer ◽  
Urban Canopy ◽  
Ground Level ◽  
Shear Layers ◽  
Mean Velocity ◽  
Building Height ◽  
The Mean

Abstract The nature and role of the shear layer, which occurs at the level of the average building height in urban canopies, are poorly understood. Velocity data are analyzed to determine the characteristics of the shear layer of the urban canopy, defined as the broad, linear segment of the mean velocity profile in a region of high shear. Particle image velocimetry measurements in a water tunnel were undertaken to resolve velocity profiles for urban canopies of two geometries typical of Los Angeles, California, and New York City, New York, for which the aspect ratios (average building height-to-width ratio) H/wb are 1 and 3, respectively. The shear layers evolve with distance differently: For H/wb = 1 the urban canopy shear layer extends quickly from above the building height to ground level, whereas for H/wb = 3 the urban canopy shear layer remains elevated at the vicinity of the building height, only reaching to a depth of z/H ∼ 0.5 far downstream. Profiles of the mean velocity gradient also differ from each other for urban canopies associated with H/wb of 1 or 3. Values of shear dU/dz increase toward ground level for an urban canopy associated with H/wb = 1. For an urban canopy associated with H/wb = 3, localized peaks of shear dU/dz exist at the building height and at ground level, with values of shear decreasing to zero at building midheight and far above the building height. A consequence of the different forms of the shear layers of the two urban canopies is that the ground-level dispersion coefficient is likely to be greater for urban canopies associated with H/wb = 1 than for those associated with H/wb = 3 because of an increased ventilation and exchange mechanism for cities such as Los Angeles relative to cities such as New York City that possess urban canyons.

Turbulent Flow Past a Surface-Mounted Two-Dimensional Rib

1994 ◽  
Vol 116 (2) ◽  
pp. 238-246 ◽  
Author(s):  
S. Acharya ◽  
S. Dutta ◽  
T. A. Myrum ◽  
R. S. Baker
Keyword(s):  
Kinetic Energy ◽  
Shear Layer ◽  
High Speed ◽  
Two Dimensional ◽  
Duct Flow ◽  
Core Flow ◽  
The Core ◽  
Separated Shear Layer ◽  
Flow Past ◽  
The Mean

The ability of the nonlinear k–ε turbulence model to predict the flow in a separated duct flow past a wall-mounted, two-dimensional rib was assessed through comparisons with the standard k–ε model and experimental results. Improved predictions of the streamwise turbulence intensity and the mean streamwise velocities near the high-speed edge of the separated shear layer and in the flow downstream of reattachment were obtained with the nonlinear model. More realistic predictions of the production and dissipation of the turbulent kinetic energy near reattachment were also obtained. Otherwise, the performance of the two models was comparable, with both models performing quite well in the core flow regions and close to reattachment and both models performing poorly in the separated and shear-layer regions close to the rib.

The vortex line in steady, incompressible Oseen flow

2005 ◽  
Vol 462 (2066) ◽  
pp. 391-401 ◽  
Author(s):  
Edmund Chadwick
Keyword(s):  
Velocity Field ◽  
Vortex Line ◽  
Horseshoe Vortex ◽  
Transverse Plane ◽  
Far Field ◽  
Two Dimensional ◽  
Streamwise Direction ◽  
Oseen Flow ◽  
Laminar Wake ◽  
Oseen Vortex

The horseshoe vortex is given in Oseen flow as a constant spanwise distribution of lift Oseenlets. From this, the vortex line is represented in steady, incompressible Oseen flow. The velocity near to the vortex line is determined, as well as near to and far from the far field wake. The velocity field in the transverse plane near to the vortex line is shown to approximate to the two-dimensional Lamb–Oseen vortex, and the velocity field in the streamwise direction is generated by the bound vortex line of the horseshoe vortex giving a streamwise decay much faster than that of the Batchelor vortex. The far field wake description is shown to be consistent with laminar wake theory.

The Shear Layers of a Two-Dimensional Jet Excited by Flexible Wires

2003 ◽  
Vol 125 (3) ◽  
pp. 597-599
Author(s):  
Ming-huei Yu ◽  
Yi-chun Liao ◽  
Chung-ho Tseng
Keyword(s):  
Spectral Analysis ◽  
Shear Layer ◽  
Density Ratio ◽  
Jet Flow ◽  
Shear Layers ◽  
Spanwise Direction ◽  
External Forcing ◽  
Two Dimensional ◽  
Air Jet ◽  
Plane Jet

A two-dimensional air jet, heated at a density ratio of 0.8, under external forcing by flexible wires is investigated experimentally. In each shear layer of the hot jet flow, a wire of diameter 0.23 mm (0.015 jet width) is flexibly mounted along the spanwise direction. By flow visualization, temperature measurements, and spectral analysis, the study demonstrates that the wires have quite different effects on the jet flow depending on that the wires are motionless or vibrating in the flow, and the shear layers of the heated plane jet can be manipulated by means of flexible wires.

Effect of enclosure height on the structure and stability of shear layers induced by differential rotation

2015 ◽  
Vol 765 ◽  
pp. 45-81 ◽  
Author(s):  
Tony Vo ◽  
Luca Montabone ◽  
Gregory J. Sheard
Keyword(s):  
Stability Analysis ◽  
Shear Layer ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Differential Rotation ◽  
Shear Layers ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Axisymmetric Model ◽  
Two Dimensional Model

AbstractThe structure and stability of Stewartson shear layers with different heights are investigated numerically via axisymmetric simulation and linear stability analysis, and a validation of the quasi-two-dimensional model is performed. The shear layers are generated in a rotating cylindrical tank with circular disks located at the lid and base imposing a differential rotation. The axisymmetric model captures both the thick and thin nested Stewartson layers, which are scaled by the Ekman number ($\mathit{E}\,$) as $\mathit{E}\,^{1/4}$ and $\mathit{E}\,^{1/3}$ respectively. In contrast, the quasi-two-dimensional model only captures the $\mathit{E}\,^{1/4}$ layer as the axial velocity required to invoke the $\mathit{E}\,^{1/3}$ layer is excluded. A direct comparison between the axisymmetric base flows and their linear stability in these two models is examined here for the first time. The base flows of the two models exhibit similar flow features at low Rossby numbers ($\mathit{Ro}$), with differences evident at larger $\mathit{Ro}$ where depth-dependent features are revealed by the axisymmetric model. Despite this, the quasi-two-dimensional model demonstrates excellent agreement with the axisymmetric model in terms of the shear-layer thickness and predicted stability. A study of various aspect ratios reveals that a Reynolds number based on the theoretical Ekman layer thickness is able to describe the transition of a base flow that is reflectively symmetric about the mid-plane to a symmetry-broken state. Additionally, the shear-layer thicknesses scale closely to the expected ${\it\delta}_{vel}\propto A\mathit{E}\,^{1/4}$ and ${\it\delta}_{vort}\propto A\mathit{E}\,^{1/3}$ for shear layers that are not affected by the confinement ($A\mathit{E}\,^{1/4}\lesssim 0.34$ in this system, the ratio of tank height to shear-layer radius). The linear stability analysis reveals that the ratio of Stewartson layer radius to thickness should be greater than $45$ for the stability of the flow to be independent of aspect ratio. Thus, for sufficiently small $A\mathit{E}\,^{1/4}$ and $A\mathit{E}\,^{1/3}$, the flow characteristics remain similar and the linear stability of the flow can be described universally when the azimuthal wavelength is scaled against $A$. The analysis also recovers an asymptotic scaling for the normalized azimuthal wavelength which suggests that ${\it\lambda}_{{\it\theta},c}^{\ast }\propto (|\mathit{Ro}|/\mathit{E}\,^{2})^{-1/5}$ for geometry-independent shear layers at marginal stability.

Effect of initial conditions on two-dimensional free shear layers

1985 ◽  
Vol 152 ◽  
pp. 419-442 ◽  
Author(s):  
B. Dziomba ◽  
H. E. Fiedler
Keyword(s):  
Wind Tunnel ◽  
Shear Layer ◽  
Initial Conditions ◽  
Shear Layers ◽  
Splitter Plate ◽  
Two Dimensional ◽  
Trailing Edge ◽  
Periodic Perturbations ◽  
Displacement Thickness ◽  
Free Shear Layers

The influence of periodic perturbations on the development of two-dimensional free shear layers generated by a splitter plate was investigated in cases where the ratios of the two velocities u1 and u2 either side of the splitter plate were such that 0 < u1/u2 < 1. Investigations were carried out in both a suction and a blower wind tunnel. Results show that even very weak periodic perturbations caused by the wind tunnel may cause significant nonlinear spreading in the downstream development of the shear layer, a behaviour which is also observed when the shear layer is deliberately excited. Other things being equal, the effect of the disturbance is greater when flow separation at the splitter plate is turbulent than when it is laminar.No self-induced feedback frequencies were measured in the test section. All tonal components that were detected in the flow could be traced to external sources.The influence of trailing-edge thickness on the shear-layer development is found to become significant when it exceeds 50% of the sum of boundary-layer displacement thickness at the point of separation. As the trailing edge becomes thicker, the range over which the shear layer is self-similar is shifted farther downstream. This behaviour may be crucial for predicting the evolution of shear layers in high-speed flows having thin boundary layers at separation.The momentum thickness criterion for estimating the development length of the flow as suggested by Bradshaw is shown to be insufficient for two-stream layers, where additional parameters, e.g. the trailing-edge geometry, have to be taken into account. Discrepancies between previously published observations of shear layers, as well as the considerable scatter in reported measurements, may therefore, to a large extent, be attributable to contamination of the experimental facility.

scholarly journals Shear flow instabilities in shallow-water magnetohydrodynamics

2016 ◽  
Vol 788 ◽  
pp. 767-796 ◽  
Author(s):  
J. Mak ◽  
S. D. Griffiths ◽  
D. W. Hughes
Keyword(s):  
Magnetic Field ◽  
Shear Layer ◽  
Shallow Water ◽  
Froude Number ◽  
Water System ◽  
Shear Layers ◽  
Linear Instability ◽  
Horizontal Shear ◽  
Shallow Water Magnetohydrodynamics ◽  
The Magnetic Field

Within the framework of shallow-water magnetohydrodynamics, we investigate the linear instability of horizontal shear flows, influenced by an aligned magnetic field and stratification. Various classical instability results, such as Høiland’s growth-rate bound and Howard’s semi-circle theorem, are extended to this shallow-water system for quite general flow and field profiles. In the limit of long-wavelength disturbances, a generalisation of the asymptotic analysis of Drazin & Howard (J. Fluid Mech., vol. 14, 1962, pp. 257–283) is performed, establishing that flows can be distinguished as either shear layers or jets. These possess contrasting instabilities, which are shown to be analogous to those of certain piecewise-constant velocity profiles (the vortex sheet and the rectangular jet). In both cases it is found that the magnetic field and stratification (as measured by the Froude number) are generally each stabilising, but weak instabilities can be found at arbitrarily large Froude number. With this distinction between shear layers and jets in mind, the results are extended numerically to finite wavenumber for two particular flows: the hyperbolic-tangent shear layer and the Bickley jet. For the shear layer, the instability mechanism is interpreted in terms of counter-propagating Rossby waves, thereby allowing an explication of the stabilising effects of the magnetic field and stratification. For the jet, the competition between even and odd modes is discussed, together with the existence at large Froude number of multiple modes of instability.

Large-eddy simulation of boundary-layer separation and transition at a change of surface curvature

2001 ◽  
Vol 439 ◽  
pp. 305-333 ◽  
Author(s):  
ZHIYIN YANG ◽  
PETER R. VOKE
Keyword(s):  
Boundary Layer ◽  
Shear Layer ◽  
Three Dimensional ◽  
Leading Edge ◽  
Boundary Layer Transition ◽  
Two Dimensional ◽  
Layer Transition ◽  
Transition Mechanism ◽  
The Mean ◽  
Dimensional Instability

Transition arising from a separated region of flow is quite common and plays an important role in engineering. It is difficult to predict using conventional models and the transition mechanism is still not fully understood. We report the results of a numerical simulation to study the physics of separated boundary-layer transition induced by a change of curvature of the surface. The geometry is a flat plate with a semicircular leading edge. The Reynolds number based on the uniform inlet velocity and the leading-edge diameter is 3450. The simulated mean and turbulence quantities compare well with the available experimental data.The numerical data have been comprehensively analysed to elucidate the entire transition process leading to breakdown to turbulence. It is evident from the simulation that the primary two-dimensional instability originates from the free shear in the bubble as the free shear layer is inviscidly unstable via the Kelvin–Helmholtz mechanism. These initial two-dimensional instability waves grow downstream with a amplification rate usually larger than that of Tollmien–Schlichting waves. Three-dimensional motions start to develop slowly under any small spanwise disturbance via a secondary instability mechanism associated with distortion of two-dimensional spanwise vortices and the formation of a spanwise peak–valley wave structure. Further downstream the distorted spanwise two-dimensional vortices roll up, leading to streamwise vorticity formation. Significant growth of three-dimensional motions occurs at about half the mean bubble length with hairpin vortices appearing at this stage, leading eventually to full breakdown to turbulence around the mean reattachment point. Vortex shedding from the separated shear layer is also observed and the ‘instantaneous reattachment’ position moves over a distance up to 50% of the mean reattachment length. Following reattachment, a turbulent boundary layer is established very quickly, but it is different from an equilibrium boundary layer.

scholarly journals On the boundary layer structure on suction side of an airfoil

2019 ◽  
Vol 213 ◽  
pp. 02088
Author(s):  
Václav Uruba ◽  
Pavel Procházka ◽  
Vladislav Skála
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Velocity Field ◽  
Layer Structure ◽  
Suction Side ◽  
Streamwise Direction ◽  
Mean Velocity ◽  
Time Resolved ◽  
Piv Technique ◽  
The Mean

The structure of boundary layer on an airfoil suction side was studied using stereo time resolved PIV technique experimentally in low Reynolds number, about 33 thousands. The mean velocity field is close to the 2D case, however the instantaneous structure is highly dynamical and 3D. Dynamics of the vortices in the boundary layer has been analysed using POD method. The results show lag of coherence in the streamwise direction, oblique patterns are detected instead.

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