Two-dimensional Wake Research Articles

Phase identification of quasi-periodic flow measured by particle image velocimetry with a low sampling rate

This work mainly deals with the proper orthogonal decomposition (POD) time coefficient method used for extracting phase information from quasi-periodic flow. The mathematical equivalence between this method and the traditional cross-correlation method is firstly proved. A two-dimensional circular cylinder wake flow measured by time-resolved particle image velocimetry within a range of Reynolds numbers is then used to evaluate the reliability of this method. The effect of both the sampling rate and Reynolds number on the identification accuracy is finally discussed. It is found that the POD time coefficient method provides a convenient alternative for phase identification, whose feasibility in low-sampling-rate measurement has additional advantages for experimentalists.

Experimental Investigation of Wake-Induced Bypass Transition Control by Surface Roughness

Surface roughness is experimentally used to control the flat-plate boundary layer bypass transition induced by an upstream convected two-dimensional (2D) circular cylinder wake. It is shown that the later stage of this bypass transition is successfully postponed, at the price of accelerating the earlier transition stage. A regularisation process of the hairpin vortices, which are the dominant coherent structures to promote the transition process, are observed under the influence of roughness elements. Significant scale reduction and localisation of these hairpins are achieved, which enhances the possibility of a hairpin self-annihilation process. Therefore, the cascade to large-scale structures in the later transition stage might be impeded/weakened.

Vehicle queue effect on the characteristics of air flow, and exhaust scalar dispersion and distribution fields in the vehicle wake

The characteristics of air flow, and vehicular exhaust scalar (i.e., pollutant) dispersion and distribution fields in the near-wake region of a scale-model vehicle which was placed alone or behind the preceding one(s) in a closed-circuit wind tunnel facility were experimentally investigated for typical urban driving conditions. The wake structure behind a queue of studied vehicles is mainly dominated by the last one, while the preceding vehicle(s) will lead to a stronger downwash flow in the wake. For the vehicle with rear slant angle (α<30°) which has a pair of trailing vortices in the wake flow, the vehicular exhaust jet plume will be mainly trapped inside these two trailing vortices and fills an “m-shaped” scalar distribution region behind the vehicle. Half of the m-shaped region which is on the vehicular tailpipe exit side shares a larger portion of scalar distribution than the other half. This unbalanced scalar distribution is enhanced by the preceding vehicle(s). For the vehicle with rear slant angle (α>30°) which has a two-dimensional wake flow, the vehicular exhaust jet plume will be carried by such a wake flow to form an “n-shaped” scalar distribution region behind the vehicle with a peak scalar region at its center. The preceding vehicle(s) will further enlarge the n-shaped scalar distribution region and push the peak scalar region closer to the ground. It is clearly shown that the two- or three-dimensional flow behind the studied vehicle can provide different shapes of exhaust scalar dispersion and distribution fields in the vehicle wake.

Three-dimensional wake transition behind an inclined flat plate

Transition phenomena in the wake of a flat plate at 25° angle of attack are investigated by means of three-dimensional computer simulations. The Strouhal number versus Reynolds number relationship was determined for Re from 275 to 800. The Strouhal number turned out to be independent of the Reynolds number for Re &amp;gt; 400 and distinctly lower than that reported from recent two-dimensional simulations. A first subharmonic frequency was detected already at Re = 300, at which the originally two-dimensional wake also became three-dimensional. The spanwise wavelength of the most energetic three-dimensional mode turned out to be about two times the projected width of the plate and almost independent of Re. The complexities of the vortex shedding increased gradually with increasing Reynolds number until a turbulent-like state with a continuous spectrum of spanwise scales was found. However, while a strict spanwise periodicity was observed for Re = 350, a more irregular wake topology occurred at Re = 325 with two distinctly different spanwise wavelengths along the span of the plate. The spectral energy of the subharmonic frequency of the longer of these wavelengths was the dominating one.

Uncertainty Quantification of Two-Dimensional Wake Vortices Near the Ground

Uncertainty Quantification of Two-Dimensional Wake Vortices Near the Ground

On least-order flow representations for aerodynamics and aeroacoustics

AbstractWe propose a generalization of proper orthogonal decomposition (POD) for optimal flow resolution of linearly related observables. This Galerkin expansion, termed ‘observable inferred decomposition’ (OID), addresses a need in aerodynamic and aeroacoustic applications by identifying the modes contributing most to these observables. Thus, OID constitutes a building block for physical understanding, least-biased conditional sampling, state estimation and control design. From a continuum of OID versions, two variants are tailored for purposes of observer and control design, respectively. Firstly, the most probable flow state consistent with the observable is constructed by a ‘least-residual’ variant. This version constitutes a simple, easily generalizable reconstruction of the most probable hydrodynamic state to preprocess efficient observer design. Secondly, the ‘least-energetic’ variant identifies modes with the largest gain for the observable. This version is a building block for Lyapunov control design. The efficient dimension reduction of OID as compared to POD is demonstrated for several shear flows. In particular, three aerodynamic and aeroacoustic goal functionals are studied: (i) lift and drag fluctuation of a two-dimensional cylinder wake flow; (ii) aeroacoustic density fluctuations measured by a sensor array and emitted from a two-dimensional compressible mixing layer; and (iii) aeroacoustic pressure monitored by a sensor array and emitted from a three-dimensional compressible jet. The most ‘drag-related’, ‘lift-related’ and ‘loud’ structures are distilled and interpreted in terms of known physical processes.

Experimental sensitivity analysis of the global properties of a two-dimensional turbulent wake

AbstractThe sensitivity of the global properties of a two-dimensional turbulent wake produced by the separated flow of a ‘D’-shaped cylinder at$\mathit{Re}= 13\hspace{0.167em} 000$is investigated experimentally using a small circular control cylinder as a local disturbance. The height of the main cylinder is$D= 25~\mathrm{mm} $and control cylinders are of diameters$d= 0. 04D$and$d= 0. 12D$, the former being smaller than the shear layer thickness detaching from the main cylinder, while the latter is larger. In both cases, the control cylinder is able to modify the global frequency, base pressure and spanwise velocity correlation. The results are presented as sensitivity maps. Reynolds stresses spatial structure and the recirculation bubble length are examined in detail when the control cylinder is displaced vertically across the wake at a fixed downstream location. It is found that the increase of the recirculation bubble length is accompanied by a damping of Reynolds stresses with a downstream shift of their spatial structures together with the base pressure increase. The global frequency can be either decreased or increased independently of the bubble length modification. The sensitivity of these global properties is interpreted on the basis of the ability of the control cylinder to change the size of the formation region of the Kármán vortex street by interacting with the primary detached shear layers. The corresponding physical mechanisms are discussed. The impact of a two-dimensional control cylinder on the three-dimensional properties of the wake is examined through spanwise correlation. This is found to be improved whenever the control cylinder is placed inside the recirculation region of the main cylinder wake.

Influence of confinement on a two-dimensional wake

AbstractThe spatio-temporal development of an incompressible two-dimensional viscous wake flow confined by two flat slipping plates is investigated by means of direct numerical simulation (DNS), using a spectral Chebyshev multi-domain method. The limit between unstable and stable configurations is determined with respect to several non-dimensional parameters: the confinement, the velocity ratio and two different Reynolds numbers, $100$ and $500$. The comparison of such limit curves with theoretical results obtained by Juniper (J. Fluid Mech., vol. 565, 2006, pp. 171–195) confirms the existence of a region at moderate confinement where the instability is maximal. Moreover, instabilities are also observed under sustained co-flow, in the form of a vacillating front. Using a direct computation of the two-dimensional base flow, we perform a local linear stability analysis for several velocity profiles prevailing at different spatial locations, so as to determine the local spatio-temporal nature of the flow: convectively unstable or absolutely unstable. Comparisons of the DNS and local stability analysis results are provided and discussed.

Exact self-similar solutions for axisymmetric wakes

This Note presents an analytical solution of two-dimensional axisymmetric wakes valid in the development region, before the ultimate equilibrium state. Based on the boundary layer equations in polar coordinates, assuming a small velocity defect, the problem reduces to a linear diffusive equation and can be expressed as an eigenvalue problem. Then a complete set of eigenfunctions is analytically obtained, which are damped and evolve self-similarly in space. The first mode corresponds to the Schlichtingʼs solution, in agreement with the downstream asymptotic behavior.

Simulation of two-dimensional high reynolds number wake flows with the use of filtered lagrangian navier-stokes equations

This work presents a method for numerical simulation of viscous fluid flows based on the use of filtered Lagrangian Navier-Stokes equations. It is based on the hypothesis that the small scale motions are responsible for the homogenization of the physical properties in infinitesimal fluid parcels through a mixing process, mathematically expressed as a spatial filter, which implicitly works as an averaging operator. When the filter was applied to the Navier-Stokes equations for incompressible flows, in the Lagrangian frame of reference, the functional form of the resulting equations was preserved, and the number of unknowns remained the same as the number of available equations, therefore circumventing the need of an explicit subgrid scale model. The method was validated by performing two-dimensional simulations of high Reynolds number wake flows. It was verified that the main large scale characteristics of the flows were properly replicated.

The influence of shear layer thickness on the stability of confined two-dimensional wakes

The influence of confinement onto the inviscid and incompressible linear stability of the family of wakes introduced by Monkewitz [Phys. Fluids 31, 999 (1988)] is examined. The nondimensional parameters of the model, the velocity ratio Λ, defined as ratio of the velocity gap to the mean velocity, the profile shape parameter, which controls the shear layer thickness δw, and the confinement parameter, are varied and their effect onto temporal and spatiotemporal stability properties is considered. Particularly, the limit between absolute (A) and convective (C) instability is investigated as a function of the different parameters. For a given confinement, there exists an optimal value of the shear layer thickness for which the absolute instability is maximal. The absolute frequency and complex wavenumber of the mode at the C/A transition are discussed. Furthermore, the continuous profiles are approximated by means of piecewise broken-line profile, with similar spatiotemporal properties. As a typical application, a few nonparallel base flows, computed by direct numerical simulation at Re=500, are analyzed on a weakly nonparallel basis by plotting the locus of the local velocity profile in the (δw,Λ) plane. The absolute frequency at the C/A transition point is seen to predict accurately the frequency prevailing in the nonlinear direct numerical simulations. These results further help interpreting the influence of confinement on the Strouhal number measured experimentally in the wake of confined cylinders.

Modulated waves in a periodically driven annular cavity

Time-periodic flows with spatio-temporal symmetry Z2 × O(2) – invariance in the spanwise direction generating the O(2) symmetry group and a half-period-reflection symmetry in the streamwise direction generating a spatio-temporal Z2 symmetry group – are of interest largely because this is the symmetry group of periodic laminar two-dimensional wakes of symmetric bodies. Such flows are the base states for various three-dimensional instabilities; the periodically shedding two-dimensional circular cylinder wake with three-dimensional modes A and B being the generic example. However, it is not easy to physically realize the ideal flows owing to the presence of end effects and finite spanwise geometries. Flows past rings are sometimes advanced as providing a relevant idealization, but in fact these have symmetry group O(2) and only approach Z2 × O(2) symmetry in the infinite aspect ratio limit. The present work examines physically realizable periodically driven annular cavity flows that possess Z2 × O(2) spatio-temporal symmetry. The flows have three distinct codimension-1 instabilities: two synchronous modes (A and B), and two manifestations of a quasi-periodic (QP) mode, either as modulated standing waves or modulated travelling waves. It is found that the curvature of the system can determine which of these modes is the first to become unstable with increasing Reynolds number, and that even in the nonlinear regime near onset of three-dimensional instabilities the dynamics are dominated by mixed modes with complicated spatio-temporal structure. Supplementary movies illustrating the spatio-temporal dynamics are available at journals.cambridge.org/flm.

Efficient simulation of electron trapping in laser and plasma wakefield acceleration

The two-dimensional quasistatic simulation code WAKE [P. Mora and T. Antonsen, Phys. Plasmas 4, 217 (1997)] used to model laser pulse propagation in tenuous plasma is modified to describe the dynamics of energetic particles. In the original code, all particles were assumed to satisfy the quasistatic approximation, which assumes that the driver and its wakefields are undisturbed during the transit time of plasma electrons through the pulse. Here, WAKE is modified to include the effects of electron trapping and beam loading by introducing a population of beam electrons, which are no longer subject to the quasistatic approximation. Algorithms for populating the group of beam particles are considered and are benchmarked to the full particle-in-cell simulations and experimental results. These modifications to WAKE provide a tool for simulating GeV laser or plasma wakefield acceleration on desktop computers.

Comparison between Measurements and Predictions of Fan Broadband Noise on a Low Speed Fan Rig

This paper presents a comparison between measurements and predictions of the fan broadband noise in a low speed fan rig. It is assumed here that the broadband noise is due to the interaction between turbulence generated in the wake of the rotor and the downstream stator vanes. The contribution due to the background turbulence level is also included in the analysis. The stator vanes are assumed to be unloaded flat plates and the wakes are assumed to satisfy two-dimensional plane wake theory. The wake turbulence velocity correlation function is assumed to be periodic in the blade pitch direction (i.e., cyclo-stationary). Aerodynamic input data to the model, both steady and unsteady, is taken directly from hot wire velocity measurements. Comparisons between predicted and measured sound power spectra are in reasonable agreement with spectral shape being particularly well captured by the model. We first review the details of the broadband noise prediction model. Hot wire velocity data will then presented by way of validating the model simplifying assumptions, and to provide the input data to the model. Finally, comparisons between the measured and predicted sound power spectrum will be presented. The work reported here was undertaken as part of the European project, PROBAND.

Conditional averaging of TR-PIV measurements of wake behind square cylinder using an improved cross-correlation approach

An improved phase averaging method based on cross-correlation of the instantaneous velocity field determined by TR-PIV measurements is proposed in this article. A Time-Resolved Particle Image Velocimetry (TR-PIV) is used to measure the two-dimensional wake behind the square cylinder. The phase signals associated with the deterministic appearance of the Karman vortex street are obtained by calculating the correlation matrix of the low-pass filtered velocity field, and can provide the complete information of the phase-averaged wake flow. The results show the advantages of the enhanced methodology in extracting the quasi-periodic flow patterns related to the shedding coherent structures without using additional reference signals.

Real-time three-color reflection holographic interferometer

A compact real-time three-color reflection holographic interferometer (RCRHI) was developed by Office National d'Etudes et de Recherches Aérospatiales for analyzing high-speed flows. As a classical in-line Lippmann-Denisyuk holographic setup, a reflection panchromatic silver-halide holographic plate is used to simultaneously record three reference holograms. The best results are obtained when the diffraction efficiency of the holographic plate reaches 50% for the three wavelengths used (red-green-blue). For that, problems in gelatin shrinkage due to the hologram treatment had to be solved for the two types of holographic plates used (Slavich and Gentet). This new optical setup was applied to analyze the two-dimensional unsteady wake flow around a circular cylinder at Mach 0.45. Interferograms recorded at a high framing rate exhibit very well saturated colors and high contrast, which eases the quasi-automated interferogram analysis. Finally, the evolution in time of the instantaneous gas density field has been obtained from the analysis of several interferograms covering one period of the phenomenon. In the future, the analysis of three-dimensional flows should be investigated using an optical bench based on RCRHI multidirectional tomography.

Influence of slip on the dynamics of two-dimensional wakes

We study numerically the two-dimensional flow past a circular cylinder as a prototypical transitional flow, and investigate the influence of a generic slip boundary condition on the wake dynamics. We show that slip significantly delays the onset of recirculation and shedding in the wake behind the cylinder. As expected, the drag on the cylinder decreases with slip, with an increased drag sensitivity for large Reynolds numbers. We also show that past the critical shedding Reynolds number, slip decreases the vorticity intensity in the wake, as well as the lift forces on the cylinder, but increases the shedding frequency. We further provide evidence that the shedding transition can be interpreted as a critical accumulation of surface vorticity, similarly to related studies on wake instability of axisymmetric bodies. Finally, we propose that our results could be used as a passive method to infer the effective friction properties of slipping surfaces.

An Exploratory Analysis of the Transient and Long-Term Behavior of Small Three-Dimensional Perturbations in the Circular Cylinder Wake

An initial-value problem (IVP) for arbitrary small three-dimensional vorticity perturbations imposed on a free shear flow is considered. The viscous perturbation equations are then combined in terms of the vorticity and velocity, and are solved by means of a combined Laplace‐Fourier transform in the plane normal to the basic flow. The perturbations can be uniform or damped along the mean flow direction. This treatment allows for a simplification of the governing equations such that it is possible to observe long transients, which can last hundreds time scales. This result would not be possible over an acceptable lapse of time by carrying out a direct numerical integration of the linearized Navier‐Stokes equations. The exploration is done with respect to physical inputs as the angle of obliquity, the symmetry of the perturbation, and the streamwise damping rate. The base flow is an intermediate section of the growing two-dimensional circular cylinder wake where the entrainment process is still active. Two Reynolds numbers of the order of the critical value for the onset of the first instability are considered. The early transient evolution offers very different scenarios for which we present a summary for particular cases. For example, for amplified perturbations, we have observed two kinds of transients, namely (1) a monotone amplification and (2) a sequence of growth‐decrease‐final growth. In the latter case, if the initial condition is an asymmetric oblique or longitudinal perturbation, the transient clearly

Suppression of the unsteady vortex wakes of a circular cylinder pair by a doublet‐like counter‐rotation

AbstractThe present investigation examines the suppression of unsteady, two‐dimensional wake instabilities of a pair of identical circular cylinders, placed side‐by‐side normal to freestream at a low Reynolds number of 150. It is found that when the cylinders are counter‐rotated, unsteady vortex wakes can be completely suppressed. At fast enough rotational speeds, a virtual elliptic body is produced by a closed streamline, strongly resembling a doublet potential flow. Copyright © 2009 John Wiley &amp; Sons, Ltd.

Drag and momentum in a two-dimensional vortex wake

The average drag on a body due to a vortex wake in two-dimensional flow was first calculated by Kármán, using pairs of point vortices to approximate the wake. An inviscid wake model with finite-area vortices was used by Saffman and Schatzman to find an analogous drag formula, one component of which is an integral along a path transverse to the wake. In this paper, the integral is found explicitly, in two forms, and corresponding formulae for the average drag are derived.