A Simplified Model Predicting the Kelvin–Helmholtz Instability Frequency for Laminar Separated Flows

2015 ◽  
Vol 138 (4) ◽  
Author(s):  
Daniele Simoni ◽  
Marina Ubaldi ◽  
Pietro Zunino
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Shear Layer ◽  
Layer Thickness ◽  
Active Flow Control ◽  
Linear Stability Theory ◽  
Aerodynamic Loading ◽  
Gradient Parameter ◽  
Semi Empirical ◽  
Instability Frequency

A semi-empirical model for the estimation of the Kelvin–Helmholtz (KH) instability frequency, in the case of short laminar separation bubbles over airfoils, has been developed. To this end, the Thwaites's pressure gradient parameter has been adopted to account for the effects induced by the aerodynamic loading distribution as well as by the Reynolds number on the separated shear layer thickness at separation. The most amplified frequency predicted by linear stability theory (LST) for a piecewise linear profile, which can be considered as the KH instability frequency, has been related to the shear layer thickness at separation, hence to the Reynolds number and the aerodynamic loading distribution through the Thwaites's pressure gradient parameter. This procedure allows the formulation of a functional dependency between the Strouhal number of the shedding frequency based on exit conditions and the dimensionless parameters. Experimental results obtained in different test cases, characterized by different Reynolds numbers and aerodynamic loading distributions, have been used to validate the model, as well as to identify the regression curve best fitting the data. The semi-empirical correlation here derived can be useful to set the activation frequency of active flow control devices for the optimization of boundary layer separation control strategies.

The structure of a highly decelerated axisymmetric turbulent boundary layer

2021 ◽  
Vol 929 ◽  
Author(s):  
N. Agastya Balantrapu ◽  
Christopher Hickling ◽  
W. Nathan Alexander ◽  
William Devenport
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Shear Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Large Scale ◽  
Convection Velocity ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean

Experiments were performed over a body of revolution at a length-based Reynolds number of 1.9 million. While the lateral curvature parameters are moderate ( $\delta /r_s < 2, r_s^+>500$ , where $\delta$ is the boundary layer thickness and r s is the radius of curvature), the pressure gradient is increasingly adverse ( $\beta _{C} \in [5 \text {--} 18]$ where $\beta_{C}$ is Clauser’s pressure gradient parameter), representative of vehicle-relevant conditions. The mean flow in the outer regions of this fully attached boundary layer displays some properties of a free-shear layer, with the mean-velocity and turbulence intensity profiles attaining self-similarity with the ‘embedded shear layer’ scaling (Schatzman & Thomas, J. Fluid Mech., vol. 815, 2017, pp. 592–642). Spectral analysis of the streamwise turbulence revealed that, as the mean flow decelerates, the large-scale motions energize across the boundary layer, growing proportionally with the boundary layer thickness. When scaled with the shear layer parameters, the distribution of the energy in the low-frequency region is approximately self-similar, emphasizing the role of the embedded shear layer in the large-scale motions. The correlation structure of the boundary layer is discussed at length to supply information towards the development of turbulence and aeroacoustic models. One major finding is that the estimation of integral turbulence length scales from single-point measurements, via Taylor's hypothesis, requires significant corrections to the convection velocity in the inner 50 % of the boundary layer. The apparent convection velocity (estimated from the ratio of integral length scale to the time scale), is approximately 40 % greater than the local mean velocity, suggesting the turbulence is convected much faster than previously thought. Closer to the wall even higher corrections are required.

Mitigating Blockage Effects on Flow Over a Circular Cylinder in an Adaptive-Wall Wind Tunnel

2011 ◽  
Vol 133 (8) ◽  
Author(s):  
Michael Bishop ◽  
Serhiy Yarusevych
Keyword(s):  
Reynolds Number ◽  
Wind Tunnel ◽  
Circular Cylinder ◽  
Shear Layer ◽  
Cylinder Surface ◽  
Blockage Ratio ◽  
Shear Layer Instability ◽  
Frequency Increase ◽  
Pressure Distributions ◽  
Instability Frequency

The effect of wall streamlining on flow development over a circular cylinder was investigated experimentally in an adaptive-wall wind tunnel. Experiments were carried out for a Reynolds number of 57,000 and three blockage ratios of 5%, 8%, and 17%. Three test section wall configurations were investigated, namely, geometrically straight walls (GSW), aerodynamically straight walls (ASW), and streamlined walls (SLW). The results show that solid blockage effects are evident in cylinder surface pressure distributions for the GSW and ASW configurations, manifested by an increased peak suction and base suction. Upon streamlining the walls, pressure distributions for each blockage ratio investigated closely match distributions expected for low blockage ratios. Wake blockage limits wake growth in the GSW configuration at 7.75 and 15 diameters downstream of the cylinder for blockages of 17% and 8%, respectively. This adverse effect can be rectified by streamlining the walls, with the resulting wake width development matching that expected for low blockage ratios. Wake vortex shedding frequency and shear layer instability frequency increase in the GSW and ASW configurations with increasing blockage ratio. The observed invariance of the near wake width with wall configuration suggests that the frequency increase is caused by the increased velocity due to solid blockage effects. For all the blockage ratios investigated, this increase is rectified in the SLW configuration, with the resulting Strouhal numbers of about 0.19 matching that expected for low blockage ratios at the corresponding Reynolds number. Blockage effects on the shear layer instability frequency are also successfully mitigated by streamlining the walls.

Governing Parameters of Adverse Pressure Gradient Turbulent Boundary Layers

2018 ◽  
Author(s):  
Yvan Maciel ◽  
Tie Wei ◽  
Ayse G. Gungor ◽  
Mark P. Simens
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Outer Region ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Inertial Parameter ◽  
Velocity Scale ◽  
Gradient Parameter

We perform a careful nondimensional analysis of the turbulent boundary layer equations in order to bring out, without assuming any self-similar behaviour, a consistent set of nondimensional parameters characterizing the outer region of turbulent boundary layers with arbitrary pressure gradients. These nondimensional parameters are a pressure gradient parameter, a Reynolds number (different from commonly used ones) and an inertial parameter. They are obtained without assuming a priori the outer length and velocity scales. They represent the ratio of the magnitudes of two types of forces in the outer region, using the Reynolds shear stress gradient (apparent turbulent force) as the reference force: inertia to apparent turbulent forces for the inertial parameter, pressure to apparent turbulent forces for the pressure gradient parameter and apparent turbulent to viscous forces for the Reynolds number. We determine under what conditions they retain their meaning, depending on the outer velocity scale that is considered, with the help of seven boundary layer databases. We find the impressive result that if the Zagarola-Smits velocity is used as the outer velocity scale, the streamwise evolution of the three ratios of forces in the outer region can be accurately followed with these non-dimensional parameters in all these flows — not just the order of magnitude of these ratios. This cannot be achieved with three other outer velocity scales commonly used for pressure gradient turbulent boundary layers. Consequently, the three new nondimensional parameters, when expressed with the Zagarola-Smits velocity, can be used to follow — in a global sense — the streamwise evolution of the stream-wise mean momentum balance in the outer region. This study provides a clear and consistent framework for the analysis of the outer region of adverse-pressure-gradient turbulent boundary layers.

Mitigating Blockage Effects on Flow Over a Circular Cylinder in an Adaptive-Wall Wind Tunnel

2010 ◽  
Author(s):  
Michael Bishop ◽  
Serhiy Yarusevych
Keyword(s):  
Reynolds Number ◽  
Wind Tunnel ◽  
Circular Cylinder ◽  
Shear Layer ◽  
Cylinder Surface ◽  
Blockage Ratio ◽  
Shear Layer Instability ◽  
Frequency Increase ◽  
Pressure Distributions ◽  
Instability Frequency

The effect of wall streamlining on flow development over a circular cylinder was investigated experimentally in an adaptive-wall wind tunnel. Experiments were carried out for a Reynolds number of 57,000 and three blockage ratios of 5%, 8%, and 17%. Three test section wall configurations were investigated, namely, geometrically straight walls (GSW), aerodynamically straight walls (ASW), and streamlined walls (SLW). The results show that solid blockage effects are clearly evident in cylinder surface pressure distributions for the GSW and ASW configurations, manifested by an increased peak suction and base suction. Upon streamlining the walls, pressure distributions for each blockage ratio investigated closely match distributions expected for low blockage ratios. Wake blockage limits wake growth in the GSW configuration at 7.75 and 15 diameters downstream of the cylinder for blockages of 17% and 8%, respectively. This adverse effect can be rectified by streamlining the walls, with the resulting wake width development matching that expected for low blockage ratios. Wake vortex shedding frequency and shear layer instability frequency increase in the GSW and ASW configurations with increasing blockage ratio. The observed invariance of the near wake width with wall configuration suggests that the frequency increase is caused by the increased velocity due to solid blockage effects. For all the blockage ratios investigated, this increase is rectified in the SLW configuration, with the resulting Strouhal numbers of about 0.19 matching that expected for low blockage ratios at the corresponding Reynolds number. Blockage effects on the shear layer instability frequency are also successfully mitigated by streamlining the walls.

History effects and near equilibrium in adverse-pressure-gradient turbulent boundary layers

2017 ◽  
Vol 820 ◽  
pp. 667-692 ◽  
Author(s):  
A. Bobke ◽  
R. Vinuesa ◽  
R. Örlü ◽  
P. Schlatter
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Mean Velocity ◽  
History Effects ◽  
Displacement Thickness ◽  
Gradient Parameter

Turbulent boundary layers under adverse pressure gradients are studied using well-resolved large-eddy simulations (LES) with the goal of assessing the influence of the streamwise pressure-gradient development. Near-equilibrium boundary layers were characterized through the Clauser pressure-gradient parameter $\unicode[STIX]{x1D6FD}$. In order to fulfil the near-equilibrium conditions, the free stream velocity was prescribed such that it followed a power-law distribution. The turbulence statistics pertaining to cases with a constant value of $\unicode[STIX]{x1D6FD}$ (extending up to approximately 40 boundary-layer thicknesses) were compared with cases with non-constant $\unicode[STIX]{x1D6FD}$ distributions at matched values of $\unicode[STIX]{x1D6FD}$ and friction Reynolds number $Re_{\unicode[STIX]{x1D70F}}$. An additional case at matched Reynolds number based on displacement thickness $Re_{\unicode[STIX]{x1D6FF}^{\ast }}$ was also considered. It was noticed that non-constant $\unicode[STIX]{x1D6FD}$ cases appear to approach the conditions of equivalent constant $\unicode[STIX]{x1D6FD}$ cases after long streamwise distances (approximately 7 boundary-layer thicknesses). The relevance of the constant $\unicode[STIX]{x1D6FD}$ cases lies in the fact that they define a ‘canonical’ state of the boundary layer, uniquely characterized by $\unicode[STIX]{x1D6FD}$ and $Re$. The investigations on the flat plate were extended to the flow around a wing section overlapping in terms of $\unicode[STIX]{x1D6FD}$ and $Re$. Comparisons with the flat-plate cases at matched values of $\unicode[STIX]{x1D6FD}$ and $Re$ revealed that the different development history of the turbulent boundary layer on the wing section leads to a less pronounced wake in the mean velocity as well as a weaker second peak in the Reynolds stresses. This is due to the weaker accumulated effect of the $\unicode[STIX]{x1D6FD}$ history. Furthermore, a scaling law suggested by Kitsios et al. (Intl J. Heat Fluid Flow, vol. 61, 2016, pp. 129–136), proposing the edge velocity and the displacement thickness as scaling parameters, was tested on two constant-pressure-gradient parameter cases. The mean velocity and Reynolds-stress profiles were found to be dependent on the downstream development. The present work is the first step towards assessing history effects in adverse-pressure-gradient turbulent boundary layers and highlights the fact that the values of the Clauser pressure-gradient parameter and the Reynolds number are not sufficient to characterize the state of the boundary layer.

The effect of confinement on the stability of viscous planar jets and wakes

2010 ◽  
Vol 656 ◽  
pp. 309-336 ◽  
Author(s):  
S. J. REES ◽  
M. P. JUNIPER
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Layer Thickness ◽  
Finite Thickness ◽  
Temporal Analysis ◽  
Velocity Profiles ◽  
Shear Layers ◽  
Channel Width ◽  
Planar Jet ◽  
Spatio Temporal

This theoretical study examines confined viscous planar jet/wake flows with continuous velocity profiles. These flows are characterized by the shear, confinement, Reynolds number and shear-layer thickness. The primary aim of this paper is to determine the effect of confinement on viscous jets and wakes and to compare these results with corresponding inviscid results. The secondary aim is to consider the effect of viscosity and shear-layer thickness. A spatio-temporal analysis is performed in order to determine absolute/convective instability criteria. This analysis is carried out numerically by solving the Orr–Sommerfeld equation using a Chebyshev collocation method. Results are produced over a large range of parameter space, including both co-flow and counter-flow domains and confinements corresponding to 0.1 < h2/h1 < 10, where the subscripts 1 and 2 refer to the inner and outer streams, respectively. The Reynolds number, which is defined using the channel width, takes values between 10 and 1000. Different velocity profiles are used so that the shear layers occupy between 1/2 and 1/24 of the channel width. Results indicate that confinement has a destabilizing effect on both inviscid and viscous flows. Viscosity is found always to be stabilizing, although its effect can safely be neglected above Re = 1000. Thick shear layers are found to have a stabilizing effect on the flow, but infinitely thin shear layers are not the most unstable; having shear layers of a small, but finite, thickness gives rise to the strongest instability.

Impingement Cooling Flow and Heat Transfer Under Acoustic Excitations

1997 ◽  
Vol 119 (4) ◽  
pp. 810-817 ◽  
Author(s):  
C. Gau ◽  
W. Y. Sheu ◽  
C. H. Shen
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Shear Layer ◽  
Turbulence Intensity ◽  
Pressure Level ◽  
Unstable Wave ◽  
Impingement Cooling ◽  
Cooling Flow ◽  
Acoustic Excitations ◽  
Excitation Pressure

Experiments are performed to study (a) slot air jet impingement cooling flow and (b) the heat transfer under acoustic excitations. Both flow visualization and spectral energy evolution measurements along the shear layer are made. The acoustic excitation at either inherent or noninherent frequencies can make the upstream shift for both the most unstable waves and the resulting vortex formation and its subsequent pairing processes. At inherent frequencies the most unstable wave can be amplified, which increases the turbulence intensity in both the shear layer and the core and enhances the heat transfer. Both the turbulence intensity and the heat transfer increase with increasing excitation pressure levels Spl until partial breakdown of the vortex occurs. At noninherent frequencies, however, the most unstable wave can be suppressed, which reduces the turbulence intensity and decreases the heat transfer. Both the turbulence intensity and the heat transfer decreases with increasing Spl, but increases with increasing Spl when the excitation frequency becomes dominant. For excitation at high Reynolds number with either inherent or noninherent frequency, a greater excitation pressure level is needed to cause the enhancement or the reduction in heat transfer. During the experiments, the inherent frequencies selected for excitation are Fo/2 and Fo/4, the noninherent frequencies are 0.71 Fo, 0.75 Fo, and 0.8 Fo, the acoustic pressure level varies from 70 dB to 100 dB, and the Reynolds number varies from 5500 to 22,000.

scholarly journals A frictional Cosserat model for the slow shearing of granular materials

2002 ◽  
Vol 457 ◽  
pp. 377-409 ◽  
Author(s):  
L. SRINIVASA MOHAN ◽  
K. KESAVA RAO ◽  
PRABHU R. NOTT
Keyword(s):  
Angular Velocity ◽  
Granular Material ◽  
Shear Layer ◽  
Granular Materials ◽  
Layer Thickness ◽  
Couette Flow ◽  
Velocity Fields ◽  
Cosserat Continuum ◽  
Cosserat Model ◽  
Cylindrical Couette Flow

A rigid-plastic Cosserat model for slow frictional flow of granular materials, proposed by us in an earlier paper, has been used to analyse plane and cylindrical Couette flow. In this model, the hydrodynamic fields of a classical continuum are supplemented by the couple stress and the intrinsic angular velocity fields. The balance of angular momentum, which is satisfied implicitly in a classical continuum, must be enforced in a Cosserat continuum. As a result, the stress tensor could be asymmetric, and the angular velocity of a material point may differ from half the local vorticity. An important consequence of treating the granular medium as a Cosserat continuum is that it incorporates a material length scale in the model, which is absent in frictional models based on a classical continuum. Further, the Cosserat model allows determination of the velocity fields uniquely in viscometric flows, in contrast to classical frictional models. Experiments on viscometric flows of dense, slowly deforming granular materials indicate that shear is confined to a narrow region, usually a few grain diameters thick, while the remaining material is largely undeformed. This feature is captured by the present model, and the velocity profile predicted for cylindrical Couette flow is in good agreement with reported data. When the walls of the Couette cell are smoother than the granular material, the model predicts that the shear layer thickness is independent of the Couette gap H when the latter is large compared to the grain diameter dp. When the walls are of the same roughness as the granular material, the model predicts that the shear layer thickness varies as (H/dp)1/3 (in the limit H/dp [Gt ] 1) for plane shear under gravity and cylindrical Couette flow.

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