The structure of organized vortices in a free shear layer

1981 ◽  
Vol 102 ◽  
pp. 301-313 ◽  
Author(s):  
R. T. Pierrehumbert ◽  
S. E. Widnall
Keyword(s):  
Shear Layer ◽  
Finite Thickness ◽  
Major Axis ◽  
Vortex Sheet ◽  
Layer Growth ◽  
Approximate Theory ◽  
Free Shear Layer ◽  
Mathematical Basis ◽  
Energetic Properties ◽  
New Family

A new family of solutions to the steady Euler equations corresponding to spatially periodic states of a free shear layer is reported. This family bifurcates from a parallel shear layer of finite thickness and uniform vorticity, and extends continuously to a shear layer consisting of a row of concentrated pointlike vortices. The energetic properties of the family are considered, and it is concluded that a vortex in a row of uniform vortices produced by periodic roll-up of a vortex sheet must have a major axis of length approximately 50% or more of the distance between vortex centres; it is also concluded that vortex amalgamation events tend to reduce vortex size relative to spacing. The geometric and energetic properties of the solutions confirm the mathematical basis of the tearing mechanism of shear-layer growth first proposed in an approximate theory of Moore & Saffman (1975).

Crossflow past a prolate spheroid at Reynolds number of 10000

2010 ◽  
Vol 659 ◽  
pp. 365-374 ◽  
Author(s):  
GEORGE K. EL KHOURY ◽  
HELGE I. ANDERSSON ◽  
BJØRNAR PETTERSEN
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Large Scale ◽  
Major Axis ◽  
Vortex Sheet ◽  
Prolate Spheroid ◽  
Minor Axis ◽  
Oncoming Flow ◽  
Near Wake ◽  
Frontal Side

The flow field around a 6:1 prolate spheroid has been investigated by means of direct numerical simulations. Contrary to earlier studies the major axis of the spheroid was oriented perpendicular to the oncoming flow. At the subcritical Reynolds number 10 000 the laminar boundary layer separated from the frontal side of the spheroid and formed an elliptical vortex sheet. The detached shear layer was unstable from its very inception and even the near-wake turned out to be turbulent. The Strouhal number associated with the large-scale shedding was 0.156, significantly below that of the wake of a sphere. A higher-frequency mode was associated with Kelvin–Helmholtz instabilities in the detached shear layer. The shape of the near-wake mirrored the shape of the spheroid. Some 10 minor diameters downstream, the major axis of the wake became aligned with the minor axis of the spheroid.

On the reflection and transmission of sound in a thick shear layer

2000 ◽  
Vol 424 ◽  
pp. 303-326 ◽  
Author(s):  
L. M. B. C. CAMPOS ◽  
M. H. KOBAYASHI
Keyword(s):  
Wave Equation ◽  
Mach Number ◽  
Shear Flow ◽  
Shear Layer ◽  
Acoustic Field ◽  
Free Stream ◽  
Finite Thickness ◽  
Vortex Sheet ◽  
Angle Of Incidence ◽  
Reflection And Transmission

The propagation of sound across a shear layer of finite thickness is studied using exact solutions of the acoustic wave equation for a shear flow with hyperbolic-tangent velocity profile. The wave equation has up to four regular singularities: two corresponding to the upper and lower free streams; one corresponding to a critical layer, where the Doppler-shifted frequency vanishes if the free streams are supersonic; and a fourth singularity which is always outside the physical region of interest. In the absence of a critical layer the matching of the two solutions, around the upper and lower free streams, specifies exactly the acoustic field across the shear layer. For example, for a sound wave incident from below (i.e. upward propagation in the lower free stream), the reflected wave (i.e. downward propagating in the lower free stream) and the transmitted wave (i.e. upward propagating in upper free stream) are specified by the continuity of acoustic pressure and vertical displacement. Thus the reflection and transmission coefficients, which are generally complex, i.e. involve amplitude and phase changes, are plotted versus angle of incidence for several values of free stream Mach number, and ratio of thickness of the shear layer to the wavelength; the vortex sheet is the particular case when the latter parameter is zero. The modulus and phase of the total acoustic field are also plotted versus the coordinate transverse to the shear flow, for several values of angle of incidence, Mach number and shear layer thickness. The analysis and plots in the present paper demonstrate significant differences between sound scattering by a shear layer of finite thickness, and the limiting case of the vortex sheet.

scholarly journals Laminar free shear layer modification using localized periodic heating

2017 ◽  
Vol 822 ◽  
pp. 561-589 ◽  
Author(s):  
Chi-An Yeh ◽  
Phillip M. Munday ◽  
Kunihiko Taira
Keyword(s):  
Heat Flux ◽  
Shear Layer ◽  
Stokes Equations ◽  
Finite Thickness ◽  
Control Input ◽  
Free Shear Layer ◽  
Periodic Heating ◽  
Trailing Edge ◽  
Thermal Forcing ◽  
Flux Boundary Condition

The application of local periodic heating for control of a spatially developing shear layer downstream of a finite-thickness splitter plate is examined by numerically solving the two-dimensional Navier–Stokes equations. At the trailing edge of the plate, an oscillatory heat flux boundary condition is prescribed as the thermal forcing input to the shear layer. The thermal forcing introduces a low level of oscillatory surface vorticity flux and baroclinic vorticity at the actuation frequency in the vicinity of the trailing edge. The vortical perturbations produced can independently excite the fundamental instability that accounts for shear layer roll-up as well as the subharmonic instability that encourages the vortex pairing process farther downstream. We demonstrate that the nonlinear dynamics of a spatially developing shear layer can be modified by local oscillatory heat flux as a control input. We believe that this study provides a basic foundation for flow control using thermal-energy-deposition-based actuators such as thermophones and plasma actuators.

Numerical Study of the Particle Dispersion on a Supersonic Shear Layer

2015 ◽  
Vol 798 ◽  
pp. 536-540
Author(s):  
Altyn Makasheva ◽  
Altynshash Naimanova ◽  
Yerzhan Belyayev
Keyword(s):  
Boundary Condition ◽  
Shear Layer ◽  
Large Scale ◽  
Stokes Equations ◽  
Numerical Study ◽  
Turbulence Models ◽  
Euler Method ◽  
Particle Dispersion ◽  
Layer Growth ◽  
Free Shear Layer

The numerical study of the two-dimensional supersonic hydrogen-air mixing in the free shear layer is performed. The system of the Favre-Averaged Navier-Stokes equations for multispecies flow is solved using the ENO scheme of the third order accuracy. The k-ε two-equation turbulence models with compressibility correction are applied to calculate the eddy viscosity coefficient. The dispersion of the particles is studied by following their trajectories in the shear layer by Euler method. In order to produce the roll-up and pairing vortex rings, an unsteady boundary condition is applied at the inlet plane. At the outflow, the non-reflecting boundary condition is taken. The influence of different Mach numbers on the formation of vorticity structures and shear layer growth rate are studied. The obtained results are compared with the available experimental data and the numerical results of other authors. The numerical simulation of the particle dispersion in the shear layer with large scale vortical structure is conducted.

The flow over a backward-facing step under controlled perturbation: laminar separation

1992 ◽  
Vol 238 ◽  
pp. 73-96 ◽  
Author(s):  
M. A. Z. Hasan
Keyword(s):  
Shear Layer ◽  
Low Frequency ◽  
Layer Growth ◽  
Stream Velocity ◽  
Backward Facing Step ◽  
Laminar Separation ◽  
Vortex Merging ◽  
Layer Growth Rate ◽  
Merging Process ◽  
Layer Flow

The flow over a backward-facing step with laminar separation was investigated experimentally under controlled perturbation for a Reynolds number of 11000, based on a step height h and a free-stream velocity UO. The reattaching shear layer was found to have two distinct modes of instability: the ‘shear layer mode’ of instability at Stθ ≈ 0.012 (Stθ ≡ fθ/UO, θ being the momentum thickness at separation and f the natural roll-up frequency of the shear layer); and the ‘step mode’ of instability at Sth ≈ 0.185 (Sth ≡ fh/U0). The shear layer instability frequency reduced to the step mode one via one or more stages of a vortex merging process. The perturbation increased the shear layer growth rate and the turbulence intensity and decreased the reattachment length compared to the unperturbed flow. Cross-stream measurements of the amplitudes of the perturbed frequency and its harmonics suggested the splitting of the shear layer. Flow visualization confirmed the shear layer splitting and showed the existence of a low-frequency flapping of the shear layer.

Deformable bubbles in a free shear layer

1997 ◽  
Vol 23 (5) ◽  
pp. 977-1001 ◽  
Author(s):  
E. Loth ◽  
M. Taeibi-Rahni ◽  
G. Tryggvason
Keyword(s):  
Shear Layer ◽  
Free Shear Layer

Assessment of turbulence models using DNS data of compressible plane free shear layer flow

2021 ◽  
Vol 931 ◽  
Author(s):  
D. Li ◽  
J. Komperda ◽  
A. Peyvan ◽  
Z. Ghiasi ◽  
F. Mashayek
Keyword(s):  
Shear Layer ◽  
Compressible Flows ◽  
Eddy Viscosity ◽  
Turbulence Models ◽  
Correlation Coefficients ◽  
Free Shear Layer ◽  
Smagorinsky Model ◽  
Reynolds Analogy ◽  
Velocity Fluctuations ◽  
Scale Similarity

The present paper uses the detailed flow data produced by direct numerical simulation (DNS) of a three-dimensional, spatially developing plane free shear layer to assess several commonly used turbulence models in compressible flows. The free shear layer is generated by two parallel streams separated by a splitter plate, with a naturally developing inflow condition. The DNS is conducted using a high-order discontinuous spectral element method (DSEM) for various convective Mach numbers. The DNS results are employed to provide insights into turbulence modelling. The analyses show that with the knowledge of the Reynolds velocity fluctuations and averages, the considered strong Reynolds analogy models can accurately predict temperature fluctuations and Favre velocity averages, while the extended strong Reynolds analogy models can correctly estimate the Favre velocity fluctuations and the Favre shear stress. The pressure–dilatation correlation and dilatational dissipation models overestimate the corresponding DNS results, especially with high compressibility. The pressure–strain correlation models perform excellently for most pressure–strain correlation components, while the compressibility modification model gives poor predictions. The results of an a priori test for subgrid-scale (SGS) models are also reported. The scale similarity and gradient models, which are non-eddy viscosity models, can accurately reproduce SGS stresses in terms of structure and magnitude. The dynamic Smagorinsky model, an eddy viscosity model but based on the scale similarity concept, shows acceptable correlation coefficients between the DNS and modelled SGS stresses. Finally, the Smagorinsky model, a purely dissipative model, yields low correlation coefficients and unacceptable accumulated errors.

CFD analysis of free shear layer approximations for a pulsed air jet

2014 ◽  
Vol 43 ◽  
pp. 49-58
Author(s):  
Nawel Khaldi ◽  
Salwa Marzouk ◽  
Hatem Mhiri ◽  
Philippe Bournot
Keyword(s):  
Shear Layer ◽  
Cfd Analysis ◽  
Free Shear Layer ◽  
Air Jet
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