Reynolds number effect on velocity field and on coherent structures behind a cylinder

2019 ◽  
Author(s):  
Pavel Procházka ◽  
Václav Uruba
Keyword(s):  
Reynolds Number ◽  
Velocity Field ◽  
Coherent Structures ◽  
Reynolds Number Effect

scholarly journals Three-dimensional vortex organization in a high-Reynolds-number supersonic turbulent boundary layer

2010 ◽  
Vol 644 ◽  
pp. 35-60 ◽  
Author(s):  
G. E. ELSINGA ◽  
R. J. ADRIAN ◽  
B. W. VAN OUDHEUSDEN ◽  
F. SCARANO
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Velocity Field ◽  
Turbulent Boundary Layer ◽  
Coherent Structures ◽  
Large Scale ◽  
Three Dimensional ◽  
Velocity Fields ◽  
Hairpin Structure ◽  
Streamwise Direction

Tomographic particle image velocimetry was used to quantitatively visualize the three-dimensional coherent structures in a supersonic (Mach 2) turbulent boundary layer in the region between y/δ = 0.15 and 0.89. The Reynolds number based on momentum thickness Reθ = 34000. The instantaneous velocity fields give evidence of hairpin vortices aligned in the streamwise direction forming very long zones of low-speed fluid, consistent with Tomkins & Adrian (J. Fluid Mech., vol. 490, 2003, p. 37). The observed hairpin structure is also a statistically relevant structure as is shown by the conditional average flow field associated to spanwise swirling motion. Spatial low-pass filtering of the velocity field reveals streamwise vortices and signatures of large-scale hairpins (height > 0.5δ), which are weaker than the smaller scale hairpins in the unfiltered velocity field. The large-scale hairpin structures in the instantaneous velocity fields are observed to be aligned in the streamwise direction and spanwise organized along diagonal lines. Additionally the autocorrelation function of the wall-normal swirling motion representing the large-scale hairpin structure returns positive correlation peaks in the streamwise direction (at 1.5δ distance from the DC peak) and along the 45° diagonals, which also suggest a periodic arrangement in those directions. This is evidence for the existence of a spanwise–streamwise organization of the coherent structures in a fully turbulent boundary layer.

Evolution of clusters of sedimenting low-Reynolds-number particles with Oseen interactions

2008 ◽  
Vol 603 ◽  
pp. 63-100 ◽  
Author(s):  
G. SUBRAMANIAN ◽  
DONALD L. KOCH
Keyword(s):  
Reynolds Number ◽  
Velocity Field ◽  
Aspect Ratio ◽  
Evolution Equation ◽  
Similarity Solution ◽  
Initial Conditions ◽  
Radial Distance ◽  
Two Dimensions ◽  
Number Density ◽  
Cluster Radius

A theoretical framework is developed to describe, in the limit of small but finite Re, the evolution of dilute clusters of sedimenting particles. Here, Re =aU/ν is the particle Reynolds number, where a is the radius of the spherical particle, U its settling velocity, and ν the kinematic viscosity of the suspending fluid. The theory assumes the disturbance velocity field at sufficiently large distances from a sedimenting particle, even at small Re, to possess the familiar source--sink character; that is, the momentum defect brought in via a narrow wake behind the particle is convected radially outwards in the remaining directions. It is then argued that for spherical clusters with sufficiently many particles, specifically with N much greater than O(R0U/ν), the initial evolution is strongly influenced by wake-mediated interactions; here, N is the total number of particles, and R0 is the initial cluster radius. As a result, the cluster first evolves into a nearly planar configuration with an asymptotically small aspect ratio of O(R0U/N ν), the plane of the cluster being perpendicular to the direction of gravity; subsequent expansion occurs with an unchanged aspect ratio. For relatively sparse clusters with N smaller than O(R0U/ν), the probability of wake interactions remains negligible, and the cluster expands while retaining its spherical shape. The long-time expansion in the former case, and that for all times in the latter case, is driven by disturbance velocity fields produced by the particles outside their wakes. The resulting interactions between particles are therefore mutually repulsive with forces that obey an inverse-square law. The analysis presented describes cluster evolution in this regime. A continuum representation is adopted with the clusters being characterized by a number density field (n(r, t)), and a corresponding induced velocity field (u (r, t)) arising on account of interactions. For both planar axisymmetric clusters and spherical clusters with radial symmetry, the evolution equation admits a similarity solution; either cluster expands self-similarly for long times. The number density profiles at different times are functions of a similarity variable η = (r/t1/3), r being the radial distance away from the cluster centre, and t the time. The radius of the expanding cluster is found to be of the form Rcl (t) = A (ν a)1/3N1/3t1/3, where the constant of proportionality, A, is determined from an analytical solution of the evolution equation; one finds A = 1.743 and 1.651 for planar and spherical clusters, respectively. The number density profile in a planar axisymmetric cluster is also obtained numerically as a solution of the initial value problem for a canonical (Gaussian) initial condition. The numerical results compare well with theoretical predictions, and demonstrate the asymptotic stability of the similarity solution in two dimensions for long times, at least for axisymmetric initial conditions.

scholarly journals Global energy fluxes in turbulent channels with flow control

2018 ◽  
Vol 857 ◽  
pp. 345-373 ◽  
Author(s):  
Davide Gatti ◽  
Andrea Cimarelli ◽  
Yosuke Hasegawa ◽  
Bettina Frohnapfel ◽  
Maurizio Quadrio
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Energy Dissipation ◽  
Velocity Field ◽  
Flow Control ◽  
Reynolds Shear Stress ◽  
Power Input ◽  
Energy Fluxes ◽  
Mean Velocity ◽  
The Mean

This paper addresses the integral energy fluxes in natural and controlled turbulent channel flows, where active skin-friction drag reduction techniques allow a more efficient use of the available power. We study whether the increased efficiency shows any general trend in how energy is dissipated by the mean velocity field (mean dissipation) and by the fluctuating velocity field (turbulent dissipation). Direct numerical simulations (DNS) of different control strategies are performed at constant power input (CPI), so that at statistical equilibrium, each flow (either uncontrolled or controlled by different means) has the same power input, hence the same global energy flux and, by definition, the same total energy dissipation rate. The simulations reveal that changes in mean and turbulent energy dissipation rates can be of either sign in a successfully controlled flow. A quantitative description of these changes is made possible by a new decomposition of the total dissipation, stemming from an extended Reynolds decomposition, where the mean velocity is split into a laminar component and a deviation from it. Thanks to the analytical expressions of the laminar quantities, exact relationships are derived that link the achieved flow rate increase and all energy fluxes in the flow system with two wall-normal integrals of the Reynolds shear stress and the Reynolds number. The dependence of the energy fluxes on the Reynolds number is elucidated with a simple model in which the control-dependent changes of the Reynolds shear stress are accounted for via a modification of the mean velocity profile. The physical meaning of the energy fluxes stemming from the new decomposition unveils their inter-relations and connection to flow control, so that a clear target for flow control can be identified.

Free-stream coherent structures in parallel boundary-layer flows

2014 ◽  
Vol 752 ◽  
pp. 602-625 ◽  
Author(s):  
Kengo Deguchi ◽  
Philip Hall
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Coherent Structures ◽  
Free Stream ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Homotopy Continuation ◽  
Boundary Layer Flows ◽  
Navier Stokes Equations ◽  
High Reynolds

AbstractOur concern in this paper is with high-Reynolds-number nonlinear equilibrium solutions of the Navier–Stokes equations for boundary-layer flows. Here we consider the asymptotic suction boundary layer (ASBL) which we take as a prototype parallel boundary layer. Solutions of the equations of motion are obtained using a homotopy continuation from two known types of solutions for plane Couette flow. At high Reynolds numbers, it is shown that the first type of solution takes the form of a vortex–wave interaction (VWI) state, see Hall & Smith (J. Fluid Mech., vol. 227, 1991, pp. 641–666), and is located in the main part of the boundary layer. On the other hand, here the second type is found to support an equilibrium solution of the unit-Reynolds-number Navier–Stokes equations in a layer located a distance of $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}O(\ln \mathit{Re})$ from the wall. Here $\mathit{Re}$ is the Reynolds number based on the free-stream speed and the unperturbed boundary-layer thickness. The streaky field produced by the interaction grows exponentially below the layer and takes its maximum size within the unperturbed boundary layer. The results suggest the possibility of two distinct types of streaky coherent structures existing, possibly simultaneously, in disturbed boundary layers.

scholarly journals Examination of Reynolds number effect on the development of round jet flow

2021 ◽  
pp. 39-47
Author(s):  
Olanrewaju Miracle Oyewola ◽  
Adebunmi Okediji ◽  
Olusegun Olufemi Ajide ◽  
Muyiwa Samuel Adaramola
Keyword(s):  
Reynolds Number ◽  
Reynolds Numbers ◽  
Jet Flow ◽  
Exit Section ◽  
Ambient Fluid ◽  
Potential Core ◽  
Round Jet ◽  
Reynolds Number Effect ◽  
Downstream Distance ◽  
Low Reynolds

In this study, the Reynolds number effect on the development of round jet flow is presented. The jet is produced from a smoothly contracting round nozzle and the flow structure is controlled by varying the air blower speed in order to obtain various Reynolds numbers (Re). The flow Reynolds number considered varies between 1140 and 9117. Mean velocity measurements were taken using hot-wire probe at different axial and lateral distances (0≤x/d≤50, where x is the downstream distance and d is the nozzle diameter) for the jet flow and at for 0≤x/d≤30 in long pipe attached to the nozzle. Measurements reveal that Reynolds number dictate the potential core length such that the higher the Reynolds number, the lower the potential core which is a measure of mixing of jet and ambient fluid. It shows that further away from the jet exit section, potential core decreases as Reynolds number increases, the velocity profile has a top hat shape very close to the nozzle exit and the shape is independent of Reynolds number. It is found that potential core extends up to x/d=8 for Reynolds number of 1140 as against conventional near field 0≤x/d≤6. This may suggest effect of very low Reynolds number. However, further investigation is required to ascertain this at extremely low Reynolds numbers. It is also observed that further away from the jet exit section, the higher the downstream distance, the higher the jet half-width (R1/2). Furthermore, the flow in the pipe shows almost constant value of normalised axial centerline velocity for a longer distance and this clearly indicates that there is mass redistribution rather than entrainment of ambient fluid. Overall, the Reynolds number controls the magnitude rather than the wavelength of the oscillation

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