Generation mechanism of a hierarchy of vortices in a turbulent boundary layer

2019 ◽  
Vol 865 ◽  
pp. 1085-1109 ◽  
Author(s):  
Yutaro Motoori ◽  
Susumu Goto
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Energy Spectrum ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Generation Mechanism ◽  
Small Scale ◽  
Generation Process ◽  
Mean Flow ◽  
The Mean

To understand the generation mechanism of a hierarchy of multiscale vortices in a high-Reynolds-number turbulent boundary layer, we conduct direct numerical simulations and educe the hierarchy of vortices by applying a coarse-graining method to the simulated turbulent velocity field. When the Reynolds number is high enough for the premultiplied energy spectrum of the streamwise velocity component to show the second peak and for the energy spectrum to obey the$-5/3$power law, small-scale vortices, that is, vortices sufficiently smaller than the height from the wall, in the log layer are generated predominantly by the stretching in strain-rate fields at larger scales rather than by the mean-flow stretching. In such a case, the twice-larger scale contributes most to the stretching of smaller-scale vortices. This generation mechanism of small-scale vortices is similar to the one observed in fully developed turbulence in a periodic cube and consistent with the picture of the energy cascade. On the other hand, large-scale vortices, that is, vortices as large as the height, are stretched and amplified directly by the mean flow. We show quantitative evidence of these scale-dependent generation mechanisms of vortices on the basis of numerical analyses of the scale-dependent enstrophy production rate. We also demonstrate concrete examples of the generation process of the hierarchy of multiscale vortices.

Further space-time correlations of velocity in a turbulent boundary layer

1958 ◽  
Vol 3 (4) ◽  
pp. 344-356 ◽  
Author(s):  
A. J. Favre ◽  
J. J. Gaviglio ◽  
R. J. Dumas
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Flow Direction ◽  
Space Time ◽  
Mean Flow ◽  
Taylor’S Hypothesis ◽  
Time Correlations ◽  
The Mean ◽  
Hot Wires

This paper describes the results of further experimental investigation of the turbulent boundary layer with zero pressure gradient. Measurements of autocorrelation and of space-time double correlation have been made respectively with single hot-wires and with two hot-wires with the separation vector in any direction. Space-time correlations reach a maximum for some optimum delay. In the case of two points set on a line orthogonal to the plate, the optimum delay Ti is not zero. In the general case it is equal to the corresponding delay Ti, increased by compensating delay for translation with the mean flow. Taylor's hypothesis may be applied to the boundary layer at distances from the wall greater than 3% of the layer thickness. Space-time isocorrelation surfaces obtained with optimum delay have a large aspect ratio in the mean flow direction, even if they are relative to a point close to the wall (0·03δ); the correlations along the mean flow then retain high values on account of the large scale of the turbulence.

scholarly journals The amplification of large-scale motion in a supersonic concave turbulent boundary layer and its impact on the mean and statistical properties

2019 ◽  
Vol 863 ◽  
pp. 454-493 ◽  
Author(s):  
Qian-Cheng Wang ◽  
Zhen-Guo Wang ◽  
Ming-Bo Sun ◽  
Rui Yang ◽  
Yu-Xin Zhao ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Strain Rate ◽  
Turbulence Intensity ◽  
Large Scale ◽  
Principal Strain ◽  
Mean Flow ◽  
Turbulence Statistics ◽  
Concave Boundary ◽  
The Mean

Direct numerical simulation is conducted to uncover the response of a supersonic turbulent boundary layer to streamwise concave curvature and the related physical mechanisms at a Mach number of 2.95. Streamwise variations of mean flow properties, turbulence statistics and turbulent structures are analysed. A method to define the boundary layer thickness based on the principal strain rate is proposed, which is applicable for boundary layers subjected to wall-normal pressure and velocity gradients. While the wall friction grows with the wall turning, the friction velocity decreases. A logarithmic region with constant slope exists in the concave boundary layer. However, with smaller slope, it is located lower than that of the flat boundary layer. Streamwise varying trends of the velocity and the principal strain rate within different wall-normal regions are different. The turbulence level is promoted by the concave curvature. Due to the increased turbulence generation in the outer layer, secondary bumps are noted in the profiles of streamwise and spanwise turbulence intensity. Peak positions in profiles of wall-normal turbulence intensity and Reynolds shear stress are pushed outward because of the same reason. Attributed to the Görtler instability, the streamwise extended vortices within the hairpin packets are intensified and more vortices are generated. Through accumulations of these vortices with a similar sense of rotation, large-scale streamwise roll cells are formed. Originated from the very large-scale motions and by promoting the ejection, sweep and spanwise events, the formation of large-scale streamwise roll cells is the physical cause of the alterations of the mean properties and turbulence statistics. The roll cells further give rise to the vortex generation. The large number of hairpin vortices formed in the near-wall region lead to the improved wall-normal correlation of turbulence in the concave boundary layer.

Reynolds-number scaling of the flat-plate turbulent boundary layer

2000 ◽  
Vol 422 ◽  
pp. 319-346 ◽  
Author(s):  
DAVID B. DE GRAAFF ◽  
JOHN K. EATON
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Flat Plate ◽  
Extensive Study ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
The Mean

Despite extensive study, there remain significant questions about the Reynolds-number scaling of the zero-pressure-gradient flat-plate turbulent boundary layer. While the mean flow is generally accepted to follow the law of the wall, there is little consensus about the scaling of the Reynolds normal stresses, except that there are Reynolds-number effects even very close to the wall. Using a low-speed, high-Reynolds-number facility and a high-resolution laser-Doppler anemometer, we have measured Reynolds stresses for a flat-plate turbulent boundary layer from Reθ = 1430 to 31 000. Profiles of u′2, v′2, and u′v′ show reasonably good collapse with Reynolds number: u′2 in a new scaling, and v′2 and u′v′ in classic inner scaling. The log law provides a reasonably accurate universal profile for the mean velocity in the inner region.

Turbulent boundary layer relaxation from convex curvature

1990 ◽  
Vol 211 ◽  
pp. 529-556 ◽  
Author(s):  
Amy E. Alving ◽  
Alexander J. Smits ◽  
Jonathan H. Watmuff
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Stable State ◽  
Relaxation Behaviour ◽  
Mean Flow ◽  
Mean Velocity ◽  
Measuring Station ◽  
The Mean ◽  
Convex Curvature

A study was undertaken to examine the flat plate relaxation behaviour of a turbulent boundary layer recovering from 90° of strong convex curvature (δ0/R = 0.08), for a length of ≈ 90δ0 after the end of curvature, where δ0 is the boundary layer thickness at the start of the curvature. The results show that the relaxation behaviour of the mean flow and the turbulence are quite different. The mean velocity profile and skin friction coefficient asymptotically approach the unperturbed state and at the last measuring station appear to be fully recovered. The turbulence relaxation, however, occurs in several stages over a much longer distance. In the first stage, a stress ‘bore’ (a region of elevated stress) is generated near the wall, and the bore thickens with distance downstream. Eventually it fills the whole boundary layer, but the stress levels continue to rise beyond their self-preserving values. Finally the stresses begin a gradual decline, but at the last measuring station they are still well above the unperturbed levels, and the ratios of the Reynolds stresses are distorted. These results imply a reorganization of the large-scale structure into a new quasi-stable state. The long-lasting effects of curvature highlight the sensitivity of a boundary layer to its condition of formation.

Investigation of the influence of miniature vortex generators on the large-scale motions of a turbulent boundary layer

2021 ◽  
Vol 932 ◽  
Author(s):  
C.I. Chan ◽  
R.C. Chin
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Turbulent Boundary Layer ◽  
Velocity Fluctuation ◽  
High Speed ◽  
Large Scale ◽  
Vortex Generators ◽  
Mean Flow ◽  
Low Speed ◽  
The Mean

Well resolved large-eddy simulation data are used to study the physical modulation effects of miniature vortex generators (MVGs) in a moderate Reynolds number zero pressure gradient turbulent boundary layer. Large-scale counter-rotating primary vortex pairs (PVPs) imposed by the MVG contribute to the formation of streamwise streaks by transporting high momentum fluids from the outer regions of the boundary layer towards the wall, giving rise to high-speed regions centred at the PVP. Consequently, low-speed regions are formed along the outer flank of the PVP, resulting in a pronounced alternating high- and low-speed flow pattern. The PVP also relates to regions with skin friction modification, where a local skin friction reduction of up to 15 % is obtained at the low-speed region, but the opposite situation is observed over the high-speed region. The MVG-induced flow feature is further investigated by spectral analysis of the triple decomposition velocity fluctuation. Pre-multiplied energy spectra of the streamwise MVG-induced velocity fluctuation reveal that the large-scale induced modes scale with the spanwise wavelength and the length of the MVG, but the energy peak is eventually repositioned to the size of the near-wall streaks in the streamwise direction. Analysis of the triple decomposition of the kinetic energy transport equations revealed the significance of the mean flow gradient in generating kinetic energy which sustains the secondary motion. There is also an energy transfer between the turbulent and MVG-induced kinetic energy independent of the mean flow.

On the formation of longitudinal vortices in a turbulent boundary layer over wavy terrain

1996 ◽  
Vol 326 ◽  
pp. 321-341 ◽  
Author(s):  
W. R. C. Phillips ◽  
Z. Wu ◽  
J. L. Lumley
Keyword(s):  
Boundary Layer ◽  
Growth Rate ◽  
Turbulent Boundary Layer ◽  
Rayleigh Waves ◽  
Longitudinal Vortex ◽  
Small Scale ◽  
Instability Mechanism ◽  
Mean Flow ◽  
Longitudinal Vortices ◽  
The Mean

Parallel inviscid O(1) shear interacting with O(ε) spanwise-independent neutral rotational Rayleigh waves are used to model turbulent boundary layer flow over small-amplitude rigid wavy terrain. Of specific interest is the instability of the flow to spanwise-periodic initially exponentially growing longitudinal vortex modes via the Craik–Leibovich CL2-O(1) instability mechanism and whether it is this instability mechanism that gives rise to longitudinal vortices evident in the recent experiments of Gong et al. (1996). In modelling the flow, wave and turbulence length scales are assumed sufficiently disparate to cause minimal interaction. This allows the primary mean velocity profile to be specified. Two profiles were chosen: a power law and the logarithmic law of the wall. Important in wave–mean interactions of this class are the effect of wave-induced fluctuations upon the mean state and the influence of the developing mean flow on the fluctuating part of the motion. The former is described by a generalized Lagrangian-mean formulation; the latter by a modified Rayleigh equation. Together they comprise an eigenvalue problem for the growth rate appropriate to the initial stages of the instability. Both primary mean flows are unstable to longitudinal vortex form in the presence of Rayleigh waves whose amplitudes diminish with altitude. Moreover the interaction is most unstable for streamwise wavenumbers α = O(1), the growth rate increasing with increased spanwise wavenumber. In comparing the results with experiment, it is first shown that spanwise-independent waves excited in Gong et al.'s experiment depict velocity fluctuations whose amplitudes diminish with altitude in accord with those for appropriate Rayleigh waves. Concordantly, the longitudinal vortices depict transverse velocity components that are weaker by a factor of ε than the axial perturbation and are observed to grow at a rate consistent with exponential growth. All are key features of CL2-O(1), although the observed growth rate is not in accord with the maximal suggested by inviscid instability theory. Rather it appears that the spanwise wavenumber takes a value at which energy is extracted from the mean motion in an optimal volume-averaged sense while minimizing energy loss to both viscous dissipation and small-scale turbulence. It is concluded that the CL2-O(1) instability mechanism is physically realizable and that the data of Gong et al. represent the first documented observations thereof.

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.

Pressure gradient effects on the large-scale structure of turbulent boundary layers

2013 ◽  
Vol 715 ◽  
pp. 477-498 ◽  
Author(s):  
Zambri Harun ◽  
Jason P. Monty ◽  
Romain Mathis ◽  
Ivan Marusic
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Amplitude Modulation ◽  
Large Scale ◽  
Outer Region ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Small Scale

AbstractResearch into high-Reynolds-number turbulent boundary layers in recent years has brought about a renewed interest in the larger-scale structures. It is now known that these structures emerge more prominently in the outer region not only due to increased Reynolds number (Metzger & Klewicki, Phys. Fluids, vol. 13(3), 2001, pp. 692–701; Hutchins & Marusic, J. Fluid Mech., vol. 579, 2007, pp. 1–28), but also when a boundary layer is exposed to an adverse pressure gradient (Bradshaw, J. Fluid Mech., vol. 29, 1967, pp. 625–645; Lee & Sung, J. Fluid Mech., vol. 639, 2009, pp. 101–131). The latter case has not received as much attention in the literature. As such, this work investigates the modification of the large-scale features of boundary layers subjected to zero, adverse and favourable pressure gradients. It is first shown that the mean velocities, turbulence intensities and turbulence production are significantly different in the outer region across the three cases. Spectral and scale decomposition analyses confirm that the large scales are more energized throughout the entire adverse pressure gradient boundary layer, especially in the outer region. Although more energetic, there is a similar spectral distribution of energy in the wake region, implying the geometrical structure of the outer layer remains universal in all cases. Comparisons are also made of the amplitude modulation of small scales by the large-scale motions for the three pressure gradient cases. The wall-normal location of the zero-crossing of small-scale amplitude modulation is found to increase with increasing pressure gradient, yet this location continues to coincide with the large-scale energetic peak wall-normal location (as has been observed in zero pressure gradient boundary layers). The amplitude modulation effect is found to increase as pressure gradient is increased from favourable to adverse.

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