Scale-to-scale anisotropy in homogeneous turbulence

2017 ◽  
Vol 827 ◽  
pp. 250-284 ◽  
Author(s):  
Douglas W. Carter ◽  
Filippo Coletti
Keyword(s):  
Large Scale ◽  
Velocity Structure ◽  
Longitudinal Velocity ◽  
Reynolds Numbers ◽  
Homogeneous Turbulence ◽  
Mean Flow ◽  
Spatially Correlated ◽  
Air Jets ◽  
Image Velocimetry ◽  
Definition Of

We experimentally investigate scale-to-scale anisotropy from the integral to the dissipative scales in homogeneous turbulence. We employ an apparatus in which two facing arrays of randomly actuated air jets generate turbulence with negligible mean flow and shear, over a volume several times larger than the energy-containing eddy size. The Reynolds number based on the Taylor microscale is varied in the range$Re_{\unicode[STIX]{x1D706}}\approx 300{-}500$, while the axial-to-radial ratio of the root mean square velocity fluctuations ranges between 1.38 and 1.72. Two velocity components are measured by particle image velocimetry at varying resolutions, capturing from the integral to the Kolmogorov scales and yielding statistics up to sixth order. Over the inertial range, the scaling exponents of the velocity structure functions are found to differ not only between the longitudinal and transverse components, but also between the axial and radial directions of separation. At the dissipative scales, the moments of the velocity gradients indicate that departure from isotropy is, at the present Reynolds numbers, significant and more pronounced for stronger large-scale anisotropy. The generalized flatness factors of the longitudinal velocity differences tend towards isotropy as the separation is reduced from the inertial to the near-dissipative scales (down to about$10\unicode[STIX]{x1D702}$,$\unicode[STIX]{x1D702}$being the Kolmogorov length), but become more anisotropic for even smaller scales which are characterized by high intermittency. At the large scales, the direction of turbulence forcing is associated with a larger integral length, defined as the distance over which the velocity component in a given direction is spatially correlated. Because of anisotropy, the definition of the integral length is not trivial and may lead to dissimilar conclusions on the qualitative behaviour of the large scales and on the quantitative values of the normalized dissipation. Alternative definitions of these quantities are proposed to account for the anisotropy. Overall, these results highlight the importance of evaluating both the different velocity components and the different spatial directions across all scales of the flow.

Turbulent flow between counter-rotating concentric cylinders: a direct numerical simulation study

2008 ◽  
Vol 615 ◽  
pp. 371-399 ◽  
Author(s):  
S. DONG
Keyword(s):  
Turbulent Flow ◽  
Large Scale ◽  
Outer Cylinder ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Taylor Vortex ◽  
Small Scale ◽  
Mean Flow ◽  
Concentric Cylinders ◽  
High Reynolds

We report three-dimensional direct numerical simulations of the turbulent flow between counter-rotating concentric cylinders with a radius ratio 0.5. The inner- and outer-cylinder Reynolds numbers have the same magnitude, which ranges from 500 to 4000 in the simulations. We show that with the increase of Reynolds number, the prevailing structures in the flow are azimuthal vortices with scales much smaller than the cylinder gap. At high Reynolds numbers, while the instantaneous small-scale vortices permeate the entire domain, the large-scale Taylor vortex motions manifested by the time-averaged field do not penetrate a layer of fluid near the outer cylinder. Comparisons between the standard Taylor–Couette system (rotating inner cylinder, fixed outer cylinder) and the counter-rotating system demonstrate the profound effects of the Coriolis force on the mean flow and other statistical quantities. The dynamical and statistical features of the flow have been investigated in detail.

scholarly journals Comparison of Large Eddy Simulations and κ-ε Modelling of Fluid Velocity and Tracer Concentration in Impinging Jet Mixers

2015 ◽  
Vol 36 (2) ◽  
pp. 251-262 ◽  
Author(s):  
Krzysztof Wojtas ◽  
Wojciech Orciuch ◽  
Łukasz Makowski
Keyword(s):  
Large Scale ◽  
Fluid Velocity ◽  
Reynolds Numbers ◽  
Tracer Concentration ◽  
Eddy Simulation ◽  
Cfd Models ◽  
Image Velocimetry ◽  
Large Eddy ◽  
Planar Laser ◽  
Scale Inhomogeneity

Abstract Simulations of turbulent mixing in two types of jet mixers were carried out using two CFD models, large eddy simulation and κ-ε model. Modelling approaches were compared with experimental data obtained by the application of particle image velocimetry and planar laser-induced fluorescence methods. Measured local microstructures of fluid velocity and inert tracer concentration can be used for direct validation of numerical simulations. Presented results show that for higher tested values of jet Reynolds number both models are in good agreement with the experiments. Differences between models were observed for lower Reynolds numbers when the effects of large scale inhomogeneity are important.

scholarly journals Structure and Motion of Severe-Wind-Producing Mesoscale Convective Systems and Derechos in Relation to the Mean Wind

2017 ◽  
Vol 32 (2) ◽  
pp. 423-439 ◽  
Author(s):  
Matthew A. Campbell ◽  
Ariel E. Cohen ◽  
Michael C. Coniglio ◽  
Andrew R. Dean ◽  
Stephen F. Corfidi ◽  
...  
Keyword(s):  
Large Scale ◽  
Mean Flow ◽  
Convective Systems ◽  
Structure And Motion ◽  
Mesoscale Convective ◽  
The Mean ◽  
Wind Events ◽  
Motion Characteristics ◽  
Definition Of ◽  
Convective Vortices

Abstract The goal of this study is to document differences in the convective structure and motion of long-track, severe-wind-producing MCSs from short-track severe-wind-producing MCSs in relation to the mean wind. An ancillary goal is to determine if these differences are large enough that some criterion for MCS motion relative to the mean wind could be used in future definitions of “derechos.” Results confirm past investigations that well-organized MCSs, including those that produce derechos, tend to move faster than the mean wind, exhibiting a significantly larger degree of propagation (component of MCS motion in addition to the component contributed by the mean flow). Furthermore, well-organized systems that produce shorter-track swaths of damaging winds likewise tend to move faster than the mean wind with a significant propagation component along the mean wind. Therefore, propagation in the direction of the mean wind is not necessarily a characteristic that can be used to distinguish derechos from nonderechos. However, there is some indication that long-track damaging wind events that occur without large-scale or persistent bow echoes and mesoscale convective vortices (MCVs) require a strong propagation component along the mean wind direction to become long lived. Overall, however, there does not appear to be enough separation in the motion characteristics among the MCS types to warrant the inclusion of a mean-wind criterion into the definition of a derecho at this time.

scholarly journals Experimental investigations on the sharp leading-edge separation over a flat plate at zero incidence using particle image velocimetry

2020 ◽  
Vol 61 (9) ◽  
Author(s):  
K. Fujiwara ◽  
R. Sriram ◽  
K. Kontis
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Particle Image ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Reattachment Length ◽  
Large Scale Structures ◽  
Image Velocimetry ◽  
Scale Structures ◽  
Sharp Leading Edge

Abstract Leading-edge separated flow field over a sharp flat plate is experimentally investigated in Reynolds numbers ranging from 6.2 × 103 to 4.1 × 104, using particle image velocimetry (PIV) and its statistics. It was observed that the average reattachment length is nearly independent of Reynolds number and the small secondary bubble observed near the leading edge was found to shrink with increasing Reynolds number. The wall-normal profiles of the statistical values of kinematic quantities such as the velocity components and their fluctuations scaled well with average reattachment length lR and freestream velocity U∞. Their magnitudes compare well with previous investigations even though the current triangular shaped sharp leading edge is different from previous flat-faced or semi-circular ones. The shear layer was observed to exhibit 2 different linear growth rates over 2 distinct regions. Instantaneous PIV realizations demonstrate unsteady nature of the separation bubble, whose origins in the upstream portion of the bubble are analysed. Bimodal nature of the probability density function (PDF) of fluctuating streamwise velocity at around x/lR = 0.08–0.15 indicates successive generation and passage of vortices in the region, which subsequently interact and evolve into multiscale turbulent field exhibiting nearly Gaussian PDF. Shedding of vortices with wide range of scales are apparent in most of the instantaneous realizations. Proper Orthogonal Decomposition (POD) of the velocity fluctuation magnitude field revealed that the flow structures of the dominant modes and their relative energies are independent of Reynolds number. In each of the dominant modes (first 3 modes), the length scales corresponding to the large scale structures and their spacing are the same for all Reynolds numbers, suggesting that their Strouhal number (observed to be ~ 0.09–0.2 at Reynolds number of 6.2 × 103) of unsteadiness should also be independent of Reynolds number. A single large structure- comparable in size to lR—was apparent well before reattachment in a few instantaneous realizations, as compared to multiple small-scale structures visible in most realizations; at Reynolds number of 6.2 × 103, realizations with such large-scale structures occurred approximately after every 20–30 realizations, corresponding to non-dimensional frequency of 0.4–0.6, which is identified to be the “regular shedding”. It was possible to reconstruct the large-scale structure during the instances from just the first 3 POD modes, indicating that the Strouhal number of regular shedding too is independent of Reynolds number. Graphic abstract

Universality of the energy-containing structures in wall-bounded turbulence

2017 ◽  
Vol 823 ◽  
pp. 498-510 ◽  
Author(s):  
Charitha M. de Silva ◽  
Dominik Krug ◽  
Detlef Lohse ◽  
Ivan Marusic
Keyword(s):  
Turbulent Flows ◽  
Friction Velocity ◽  
Velocity Structure ◽  
Longitudinal Velocity ◽  
Reynolds Numbers ◽  
Structure Functions ◽  
Self Similarity ◽  
Logarithmic Region ◽  
High Reynolds ◽  
Wall Bounded Turbulence

The scaling behaviour of the longitudinal velocity structure functions $\langle (\unicode[STIX]{x1D6E5}_{r}u)^{2p}\rangle ^{1/p}$ (where $2p$ represents the order) is studied for various wall-bounded turbulent flows. It has been known that for very large Reynolds numbers within the logarithmic region, the structure functions can be described by $\langle (\unicode[STIX]{x1D6E5}_{r}u)^{2p}\rangle ^{1/p}/U_{\unicode[STIX]{x1D70F}}^{2}\approx D_{p}\ln (r/z)+E_{p}$ (where $r$ is the longitudinal distance, $z$ the distance from the wall, $U_{\unicode[STIX]{x1D70F}}$ the friction velocity and $D_{p}$, $E_{p}$ are constants) in accordance with Townsend’s attached eddy hypothesis. Here we show that the ratios $D_{p}/D_{1}$ extracted from plots between structure functions – in the spirit of the extended self-similarity hypothesis – have further reaching universality for the energy containing range of scales. Specifically, we confirm that this description is universal across wall-bounded flows with different flow geometries, and also for both the longitudinal and transversal structure functions, where previously the scaling has been either difficult to discern or differences have been reported when examining the direct representation of $\langle (\unicode[STIX]{x1D6E5}_{r}u)^{2p}\rangle ^{1/p}$. In addition, we present evidence of this universality at much lower Reynolds numbers, which opens up avenues to examine structure functions that are not readily available from high Reynolds number databases.

Finite Reynolds number effect on the scaling range behaviour of turbulent longitudinal velocity structure functions

2017 ◽  
Vol 820 ◽  
pp. 341-369 ◽  
Author(s):  
S. L. Tang ◽  
R. A. Antonia ◽  
L. Djenidi ◽  
L. Danaila ◽  
Y. Zhou
Keyword(s):  
Reynolds Number ◽  
Structure Function ◽  
Large Scale ◽  
Velocity Structure ◽  
Longitudinal Velocity ◽  
Structure Functions ◽  
Third Order ◽  
Reynolds Number Effect ◽  
Rate Of Increase ◽  
Velocity Structure Function

The effect of large-scale forcing on the second- and third-order longitudinal velocity structure functions, evaluated at the Taylor microscale $r=\unicode[STIX]{x1D706}$, is assessed in various turbulent flows at small to moderate values of the Taylor microscale Reynolds number $R_{\unicode[STIX]{x1D706}}$. It is found that the contribution of the large-scale terms to the scale by scale energy budget differs from flow to flow. For a fixed $R_{\unicode[STIX]{x1D706}}$, this contribution is largest on the centreline of a fully developed channel flow but smallest for stationary forced periodic box turbulence. For decaying-type flows, the contribution lies between the previous two cases. Because of the difference in the large-scale term between flows, the third-order longitudinal velocity structure function at $r=\unicode[STIX]{x1D706}$ differs from flow to flow at small to moderate $R_{\unicode[STIX]{x1D706}}$. The effect on the second-order velocity structure functions appears to be negligible. More importantly, the effect of $R_{\unicode[STIX]{x1D706}}$ on the scaling range exponent of the longitudinal velocity structure function is assessed using measurements of the streamwise velocity fluctuation $u$, with $R_{\unicode[STIX]{x1D706}}$ in the range 500–1100, on the axis of a plane jet. It is found that the magnitude of the exponent increases as $R_{\unicode[STIX]{x1D706}}$ increases and the rate of increase depends on the order $n$. The trend of published structure function data on the axes of an axisymmetric jet and a two-dimensional wake confirms this dependence. For a fixed $R_{\unicode[STIX]{x1D706}}$, the exponent can vary from flow to flow and for a given flow, the larger $R_{\unicode[STIX]{x1D706}}$ is, the closer the exponent is to the value predicted by Kolmogorov (Dokl. Akad. Nauk SSSR, vol. 30, 1941a, pp. 299–303) (hereafter K41). The major conclusion is that the finite Reynolds number effect, which depends on the flow, needs to be properly accounted for before determining whether corrections to K41, arising from the intermittency of the energy dissipation rate, are needed. We further point out that it is imprudent, if not incorrect, to associate the finite Reynolds number effect with a consequence of the modified similarity hypothesis introduced by Kolmogorov (J. Fluid Mech., vol. 13, 1962, pp. 82–85) (K62); we contend that this association has misled the vast majority of post K62 investigations of the consequences of K62.

Unsteady numerical investigation of two different corrugated airfoils

2016 ◽  
Vol 231 (13) ◽  
pp. 2423-2437 ◽  
Author(s):  
WH Ho ◽  
TH New
Keyword(s):  
Large Scale ◽  
Numerical Study ◽  
Flow Characteristics ◽  
Reynolds Numbers ◽  
Mean Flow ◽  
Airfoil Surface ◽  
Low Reynolds Numbers ◽  
Corrugated Surfaces ◽  
Large Scale Flow ◽  
Lift And Drag

An unsteady, two-dimensional numerical study was conducted to investigate the aerodynamic and flow characteristics of two bio-inspired corrugated airfoils at Re = 14,000 and compared with those of a smooth NACA0010 airfoil. Mean aerodynamic results reveal that the corrugated airfoils have better lift performance compared to the NACA0010 airfoil but incur slightly higher drag penalty. Mean flow streamlines indicate that this favourable performance is due to the ability of the corrugated airfoils in mitigating large-scale flow separations and stall. Unsteady flow field results show persistent formations of small recirculating vortices that remain within the corrugations at 10° angle-of-attack or less for one of the corrugated airfoil and below 15° for the other. In contrast, the flow behaviour can be highly turbulent with regular pairings of large-scale flow separation vortices along the upper surface at higher angles-of-attack. This not only disrupts the small recirculating vortices and causes them to detach from the corrugated surfaces, but it gets increasingly dominant at higher angles-of-attack resulting in regular lift and drag oscillations. At the end of each cycle, there is a sudden ejection of flow perpendicular to the airfoil surface and these disruptions manifest themselves as “kinks” in the instantaneous lift and drag of the corrugated airfoils. Therefore instead of regular fluctuations, the lift and drag curves have additional undulations. Despite that, the corrugations are able to produce larger pressure differentials between the upper and lower surfaces than the smooth airfoil. The current study demonstrates the intricate relationships between different sharp surface corrugations and favourable aerodynamic performance. In particular, results from this paper supports earlier investigations that corrugated airfoils may be used to good effects even at low Reynolds numbers, where flow separations are more likely.

scholarly journals Properties of the turbulent/non-turbulent interface in boundary layers

2016 ◽  
Vol 801 ◽  
pp. 554-596 ◽  
Author(s):  
Guillem Borrell ◽  
Javier Jiménez
Keyword(s):  
Boundary Layer ◽  
Large Scale ◽  
Free Stream ◽  
Strain Tensor ◽  
Reynolds Numbers ◽  
Web Page ◽  
Number Range ◽  
Self Similar ◽  
Definition Of ◽  
Flow Variables

The turbulent/non-turbulent interface is analysed in a direct numerical simulation of a boundary layer in the Reynolds number range$Re_{{\it\theta}}=2800{-}6600$, with emphasis on the behaviour of the relatively large-scale fractal intermittent region. This requires the introduction of a new definition of the distance between a point and a general surface, which is compared with the more usual vertical distance to the top of the layer. Interfaces are obtained by thresholding the enstrophy field and the magnitude of the rate-of-strain tensor, and it is concluded that, while the former are physically relevant features, the latter are not. By varying the threshold, a topological transition is identified as the interface moves from the free stream into the turbulent core. A vorticity scale is defined which collapses that transition for different Reynolds numbers, roughly equivalent to the root-mean-squared vorticity at the edge of the boundary layer. Conditionally averaged flow variables are analysed as functions of the new distance, both within and outside the interface. It is found that the interface contains a non-equilibrium layer whose thickness scales well with the Taylor microscale, enveloping a self-similar layer spanning a fixed fraction of the boundary-layer thickness. Interestingly, the straining structure of the flow is similar in both regions. Irrotational pockets within the turbulent core are also studied. They form a self-similar set whose size decreases with increasing depth, presumably due to breakup by the turbulence, but the rate of viscous diffusion is independent of the pocket size. The raw data used in the analysis are freely available from our web page (http://torroja.dmt.upm.es).

scholarly journals Effects of initial conditions in decaying turbulence generated by passive grids

2007 ◽  
Vol 585 ◽  
pp. 395-420 ◽  
Author(s):  
P. LAVOIE ◽  
L. DJENIDI ◽  
R. A. ANTONIA
Keyword(s):  
Power Law ◽  
Large Scale ◽  
Velocity Structure ◽  
Isotropic Turbulence ◽  
Initial Conditions ◽  
Reynolds Numbers ◽  
Recent Analysis ◽  
Grid Turbulence ◽  
Power Law Exponent ◽  
Decaying Turbulence

The effects of initial conditions on grid turbulence are investigated for low to moderate Reynolds numbers. Four grid geometries are used to yield variations in initial conditions and a secondary contraction is introduced to improve the isotropy of the turbulence. The hot-wire measurements, believed to be the most detailed to date for this flow, indicate that initial conditions have a persistent impact on the large-scale organization of the flow over the length of the tunnel. The power-law coefficients, determined via an improved method, also depend on the initial conditions. For example, the power-law exponent m is affected by the various levels of large-scale organization and anisotropy generated by the different grids and the shape of the energy spectrum at low wavenumbers. However, the results show that these effects are primarily related to deviations between the turbulence produced in the wind tunnel and true decaying homogenous isotropic turbulence (HIT). Indeed, when isotropy is improved and the intensity of the large-scale periodicity, which is primarily associated with round-rod grids, is decreased, the importance of initial conditions on both the character of the turbulence and m is diminished. However, even in the case where the turbulence is nearly perfectly isotropic, m is not equal to −1, nor does it show an asymptotic trend in x towards this value, as suggested by recent analysis. Furthermore, the evolution of the second- and third-order velocity structure functions satisfies equilibrium similarity only approximately.

Flow Field and Turbulence Characterization of a Counter Impinging Jet Reactor Using Particle Image Velocimetry

2013 ◽  
Vol 135 (9) ◽  
Author(s):  
Victor A. Miller ◽  
Mirko Gamba
Keyword(s):  
Particle Image Velocimetry ◽  
Flow Field ◽  
Reynolds Stress ◽  
Particle Image ◽  
Impinging Jet ◽  
Reynolds Numbers ◽  
Inlet Section ◽  
Turbulent Stress ◽  
Mean Flow ◽  
Image Velocimetry

We characterize the three dimensional structure and quantify turbulence quantities in a counter-impinging jet reactor with trapezoidal cross-section to test the feasibility of achieving stratified mixing. Dye flow-visualization and particle image velocimetry (PIV) velocity field measurements are made in the inlet section of the reactor. Two-component velocity measurements are made on three sets of orthogonal planes for Rej = 1000, 1800, 2600, and 3700; the overall structure of the flow field is found to be qualitatively similar for the Reynolds numbers studied, but the precise trajectory of the mean flow is found to be sensitive to inflow boundary conditions. Reynolds stresses and anisotropic invariants are calculated; the turbulent kinetic energy decreases linearly with increasing distance downstream in the reactor and it decreases at the same relative rate for all Reynolds numbers studied; anisotropic invariants and Reynolds stress maps indicate a turbulent stress state that tends toward isotropy downstream of the inlets. Turbulent stress maps indicate that the Reynolds stress components are stratified in the reactor channel, becoming uniform as a function of z by y/Dh = 4.

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