Phase Averaging by Wavelet Transformation and the Application to Periodically Fluctuated Separation Flow

The vortex structures in a separated region are generated by the motion of the separated shear layer caused by the introduction of periodic fluctuation. The main cause of the motion of the separated shear layer is the external fluctuation with the characteristic frequency. In order to investigate the principal motion of the velocity field, phase averaging was conducted to the velocity signals obtained by single hot-wire measurement. In phase averaging, wavelet analysis was applied to obtain the dominant frequency and the characteristic phase in the fluctuation. The profiles and the contours of the phase-averaged velocity could be found and discussed. The profiles vary dynamically at each phase and show the periodic motion of the shear layer. The separated shear layer flutters with the external fluctuation in the mean flow. If the suitable frequency is selected in the external fluctuation, the separated region disappears in almost all each phases owing to the depression of the shear layer near the wall.

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The structure of a highly decelerated axisymmetric turbulent boundary layer

Journal of Fluid Mechanics ◽

10.1017/jfm.2021.845 ◽

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.

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Measurements and Characterization of Turbulence in the Tip Region of an Axial Compressor Rotor

Journal of Turbomachinery ◽

10.1115/1.4037773 ◽

2017 ◽

Vol 139 (12) ◽

Cited By ~ 4

Author(s):

Yuanchao Li ◽

Huang Chen ◽

Joseph Katz

Keyword(s):

Strain Rate ◽

Shear Layer ◽

Turbulent Flows ◽

Reynolds Stress ◽

Suction Side ◽

Stress And Strain ◽

Spatial And Temporal Variability ◽

Mean Flow ◽

The Mean ◽

Stress And Strain Rate

Modeling of turbulent flows in axial turbomachines is challenging due to the high spatial and temporal variability in the distribution of the strain rate components, especially in the tip region of rotor blades. High-resolution stereo-particle image velocimetry (SPIV) measurements performed in a refractive index-matched facility in a series of closely spaced planes provide a comprehensive database for determining all the terms in the Reynolds stress and strain rate tensors. Results are also used for calculating the turbulent kinetic energy (TKE) production rate and transport terms by mean flow and turbulence. They elucidate some but not all of the observed phenomena, such as the high anisotropy, high turbulence levels in the vicinity of the tip leakage vortex (TLV) center, and in the shear layer connecting it to the blade suction side (SS) tip corner. The applicability of popular Reynolds stress models based on eddy viscosity is also evaluated by calculating it from the ratio between stress and strain rate components. Results vary substantially, depending on which components are involved, ranging from very large positive to negative values. In some areas, e.g., in the tip gap and around the TLV, the local stresses and strain rates do not appear to be correlated at all. In terms of effect on the mean flow, for most of the tip region, the mean advection terms are much higher than the Reynolds stress spatial gradients, i.e., the flow dynamics is dominated by pressure-driven transport. However, they are of similar magnitude in the shear layer, where modeling would be particularly challenging.

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On the stability of an inviscid shear layer which is periodic in space and time

Journal of Fluid Mechanics ◽

10.1017/s0022112067002538 ◽

1967 ◽

Vol 27 (4) ◽

pp. 657-689 ◽

Cited By ~ 137

Author(s):

R. E. Kelly

Keyword(s):

Growth Rate ◽

Shear Layer ◽

Finite Amplitude ◽

Periodic Component ◽

Periodic Flow ◽

Flow Profile ◽

Mean Flow ◽

Mean Velocity ◽

The Mean ◽

The Stability

In experiments concerning the instability of free shear layers, oscillations have been observed in the downstream flow which have a frequency exactly half that of the dominant oscillation closer to the origin of the layer. The present analysis indicates that the phenomenon is due to a secondary instability associated with the nearly periodic flow which arises from the finite-amplitude growth of the fundamental disturbance.At first, however, the stability of inviscid shear flows, consisting of a non-zero mean component, together with a component periodic in the direction of flow and with time, is investigated fairly generally. It is found that the periodic component can serve as a means by which waves with twice the wavelength of the periodic component can be reinforced. The dependence of the growth rate of the subharmonic wave upon the amplitude of the periodic component is found for the case when the mean flow profile is of the hyperbolic-tangent type. In order that the subharmonic growth rate may exceed that of the most unstable disturbance associated with the mean flow, the amplitude of the streamwise component of the periodic flow is required to be about 12 % of the mean velocity difference across the shear layer. This represents order-of-magnitude agreement with experiment.Other possibilities of interaction between disturbances and the periodic flow are discussed, and the concluding section contains a discussion of the interactions on the basis of the energy equation.

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SPILLING BREAKERS, BORES, AND HYDRAULIC JUMPS

Coastal Engineering Proceedings ◽

10.9753/icce.v16.30 ◽

1978 ◽

Vol 1 (16) ◽

pp. 30 ◽

Cited By ~ 8

Author(s):

D.H. Peregrine ◽

I.A. Svendsen

Keyword(s):

Water Waves ◽

Mean Flow ◽

The Mean ◽

White Water ◽

Pass Through ◽

Definition Of ◽

Spilling Breakers ◽

Almost All ◽

Plunging Breaker ◽

Spilling Breaker

On gently sloping beaches, almost all water waves break. After the initial breaking the water motion usually appears quite chaotic. However, for a moderate time, for example two or three times the descent time of the "plunge" in a plunging breaker, the flow can be relatively well organised despite the superficial view which is largely of spray and bubbles. If waves continue to break the breaking motion, or "white water" soon becomes fully turbulent and the mean motions become quasisteady. A reasonable definition of a quasi-steady wave is one which changes little during the time a water particle takes to pass through it. We exclude water particles which may become trapped in a surface roller and surf along with the wave. At this stage in its development a wave on a beach may be described as a spilling breaker or as a bore. In fact, there is a range of these waves from those with a little white water at the crest to examples where the whole front of the wave is fully turbulent. In investigating the properties of such waves it is desirable to start by looking at the whole range of related motions. The most obvious extension is to the hydraulic jump; since, in the simplest view, it is equivalent to a bore but in a frame of reference moving with the wave. It is also an example where the mean flow is steady rather than quasisteady.

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On the interactions between large-scale structure and fine-grained turbulence in a free shear flow I. The development of temporal interactions in the mean

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1976.0172 ◽

1976 ◽

Vol 352 (1669) ◽

pp. 213-247 ◽

Cited By ~ 21

Keyword(s):

Energy Transfer ◽

Kinetic Energy ◽

Shear Layer ◽

Turbulent Kinetic Energy ◽

Viscous Dissipation ◽

Mean Flow ◽

Fine Grained ◽

Large Eddy ◽

The Mean ◽

Three Components

In this problem a mean turbulent shear layer originally exists, homogeneous in the streamwise direction, formed perhaps by previous instabilities, but in equilibrium with the fine-grained turbulence. At a given time, a large eddy of a fixed horizontal wavenumber is initiated. We study the subsequent time development of the non-equilibrium interactions between the three components of flow as they adjust towards ultimate simultaneous equilibrium, using the integrated energy-balance conservation equations to derive the amplitude equations. This necessarily involves the usual averaging procedure and a conditional or phase-averaging procedure by which the large structure motion is educed from the total fluctuations. In general, the mean flow growth is due to the energy transfer to both fluctuating components, the large eddy gains energy from the mean motion and exchanges energy with the fine-grained turbulence, while the fine-grained turbulence gains energy from the mean flow and exchanges with the large eddy and converts its energy to heat through viscous dissipation of the smallest scales. The closure problem is obtained via the shape assumptions which enter into the interaction integrals. The situation in which the fine-grained turbulent kinetic energy production and viscous dissipation are in local balance is considered, the displacement from equilibrium being due only to the energy transfer from the large eddy. The large eddy shape is taken to be two-dimensional, instability-wavelike, with its vorticity axis perpendicular to the direction of the mean outer stream. Prior to averaging, detailed but approximate calculations of the wave-induced turbulent Reynolds stresses are obtained; the product of these stresses with the appropriate large-eddy rates of strain give the energy transfer mechanism between the two disparate scales of fluctuations. Coupled, nonlinear amplitude or energy density equations for the three components of motion are obtained, the coefficients of which are the interaction integrals guided by the shape assumptions. It is found that for the special case of parallel flow, the energy of the large eddy first undergoes a hydrodynamic-instability type of amplification but eventually decays due to the energy transfer to the fine-grained turbulence, while the turbulent kinetic energy is displaced from an original level of equilibrium to a new one because of the ability of the large eddy to negotiate an indirect energy transfer from the mean flow. For the growing shear layer, approximate considerations show that if the mechanism of energy transfer from the large to the small scale is eventually weakened by the shear layer growth compared to the large-eddy production mechanism so that the amplification and decay process repeats, ‘bursts’ of the remnant of the same large eddy will occur repeatedly until an ultimate equilibrium is reached among the three interacting components of motion. However, for the large eddy whose wavenumber corresponds to that of the initially most amplified case, the ‘bursting’ phenomenon is much less pronounced and equilibrium is very nearly reached at the end of the very first ‘burst’.

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Direct numerical simulations of roughness-induced transition in supersonic boundary layers

Journal of Fluid Mechanics ◽

10.1017/jfm.2011.417 ◽

2012 ◽

Vol 693 ◽

pp. 28-56 ◽

Cited By ~ 27

Author(s):

Suman Muppidi ◽

Krishnan Mahesh

Keyword(s):

Numerical Simulations ◽

Shear Layer ◽

Boundary Layers ◽

Plate Boundary ◽

Direct Numerical Simulations ◽

Transition To Turbulence ◽

Streamwise Vortices ◽

Mean Flow ◽

The Mean ◽

Near Wall

AbstractDirect numerical simulations are used to study the laminar to turbulent transition of a Mach 2.9 supersonic flat plate boundary layer flow due to distributed surface roughness. Roughness causes the near-wall fluid to slow down and generates a strong shear layer over the roughness elements. Examination of the mean wall pressure indicates that the roughness surface exerts an upward impulse on the fluid, generating counter-rotating pairs of streamwise vortices underneath the shear layer. These vortices transport near-wall low-momentum fluid away from the wall. Along the roughness region, the vortices grow stronger, longer and closer to each other, and result in periodic shedding. The vortices rise towards the shear layer as they advect downstream, and the resulting interaction causes the shear layer to break up, followed quickly by a transition to turbulence. The mean flow in the turbulent region shows a good agreement with available data for fully developed turbulent boundary layers. Simulations under varying conditions show that, where the shear is not as strong and the streamwise vortices are not as coherent, the flow remains laminar.

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Turbulent Flow Past a Surface-Mounted Two-Dimensional Rib

Journal of Fluids Engineering ◽

10.1115/1.2910261 ◽

1994 ◽

Vol 116 (2) ◽

pp. 238-246 ◽

Cited By ~ 46

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.

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Flow Past a Permeable Manipulator Ring Placed in a Turbulent Pipe Flow

ASME-JSME-KSME 2011 Joint Fluids Engineering Conference: Volume 1, Symposia – Parts A, B, C, and D ◽

10.1115/ajk2011-25004 ◽

2011 ◽

Author(s):

Koji Utsunomiya ◽

Suketsugu Nakanishi ◽

Hideo Osaka

Keyword(s):

Turbulent Flow ◽

Shear Layer ◽

Pipe Flow ◽

Area Ratio ◽

Turbulent Pipe Flow ◽

Wall Region ◽

Open Area ◽

Mean Flow ◽

Flow Past ◽

The Mean

Turbulent pipe flow past a ring-type permeable manipulator was investigated by measuring the mean flow and turbulent flow fields. The permeable manipulator ring had a rectangular cross section and a height 0.14 times the pipe radius. The experiments were performed under four conditions of the open area ratio β of the permeable ring (β = 0.1, 0.2, 0.3 and 0.4) for Reynolds number of 6.2×104. The results indicate that as the open-area ratio increased, the separated shear layer arising from the permeable ring top became weaker and the pressure loss was reduced by increasing fluid flow through the permeable ring. When β was less than 0.2, the velocity gradient was steeper over the permeable ring and in the shear layer near the reattachment region. When β was greater than 0.3, the width of the shear layer showed a relatively large augmentation and the back pressure in the separating region increases. Further, the response of the turbulent flow field to the permeable ring was delayed compared with that of the mean velocity field, and these differences increased with β. The turbulence intensities and Reynolds shear stress profiles near the reattachment point increased near the wall region as β increased, while those peak values that were taken at the locus of the manipulator ring height decreased as β increased.

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