Showing papers in "European Journal of Mechanics B-fluids in 2004"

On Tollmien–Schlichting-like waves in streaky boundary layers

Abstract: The linear stability of the boundary layer developing on a flat pl ate in the presence of finite-a mplitude, steady and spanwise periodic streamwise streaks is investigated. The streak amplitudes considered here are below the threshold for onset of the inviscid inflectional instability of sinuous perturbations. It is found that , as the amplitude of the streaks is increased, the most unstable viscous waves evolve from two-dimensional Tollmien–Schlichting waves into three-dimensional varicose fundamental modes which compare well with early experimental findings. The analysis of the growth rates of these modes confirms the stabilising effect of the streaks on the viscous instability and that this stabilising effect increases with the streak amplitude. Varicose subharmonic modes are also found to be unstable but they have growth rates which typically are an order of magnitude lower than those of fundamental modes. The perturbation kinetic energy production associated with the spanwise shear of the streaky flow is found to play an essential rol e in the observed stabilisation. The possibl e relevance of the streak stabilising role for applications in boundary layer transition delay is discussed.  2004 Elsevier SAS. All rights reserved.

Experimental studies of passive control of vortex-induced vibration

Abstract: Measurements of vortex-induced vibration of a plain circular cylinder and cylinders fitted with strakes and bumps are presented. Experiments were carried out in water with mass ratios in a range from about 1.5 to 5.5 and combined mass and damping values between about 2×10−3 and 7×10−3. Reynolds numbers were within the range 103 to 104. Although the wakes of fixed cylinders with strakes or bumps show little or no evidence of regular vortex shedding it was found to establish itself across a range of reduced velocity when the mass and damping parameters are sufficiently small. However, the amplitudes of vibration were less than those for a plain cylinder. It is observed that the modes of shedding found for an oscillating plain cylinder are also present for a responding cylinder fitted with vortex suppression devices.

Three-dimensional stationary flow over a backward-facing step

Abstract: Three-dimensional stationary structure of the flow over a backward-facing step is studied experimentally. Visualizations and Particle Image Velocimetry (PIV) measurements are investigated. It is shown that the recirculation length is periodically modulated in the spanwise direction with a well-defined wavelength. Visualizations also reveal the presence of longitudinal vortices. In order to understand the origin of this instability, a generalized Rayleigh discriminant is computed from a two-dimensional numerical simulation of the basic flow in the same geometry. This study reveals that actually three regions of the two-dimensional flow are potentially unstable through the centrifugal instability. However both the experiment and the computation of a local Gortler number suggest that only one of these regions is unstable. It is localized in the vicinity of the reattached flow and outside the recirculation bubble.

Propulsive efficiency of oscillating foils

Abstract: The dynamics of the vortex structures generated by a foil in steady forward motion, plus a combination of harmonic heaving and pitching oscillations, is determined by means of the numerical solution of the vorticity equation. The force and the torque acting on the foil are also computed. The investigation extends a previous study of the phenomenon (J. Fluid Mech. 410 (2000) 323–341), where only heaving oscillations were considered. The pitching motion turns out to be the only means to produce thrust when the forward motion of the foil vanishes, i.e., for foils operating in the hovering mode. Moreover pitching oscillations added to the heaving motion of the foil produce much larger values of the thrust and better efficiencies. Results are obtained for many combinations of the parameters characterizing the phenomenon and the investigation allows us to identify the range of the parameters providing high propulsive efficiency. The numerical results agree well with previous experimental measurements and, in addition, allow access to the velocity and vorticity fields as functions of space and time, which in turn allows us to identify the underlying thrust production mechanisms more easily.

A high-amplitude 2T mode of vortex-induced vibration for a light body in XY motion

Abstract: Although there are a great many papers dedicated to the problem of a cylinder vibrating transverse to a fluid flow (Y-motion), there are almost no papers studying the more practical case of vortex-induced vibration in two degrees of freedom (XY-motion) where the mass and natural frequencies are precisely the same in both X and Y directions. We have designed the present pendulum apparatus to achieve both of these criteria. Even down to the low mass ratios, where m ∗ =6 , it is remarkable that the freedom to oscillate in-line with the flow, affects the transverse vibration surprisingly little. There is, however, a dramatic change in the fluid–structure interactions when mass ratios are reduced below m ∗ =6 . A new amplitude response branch with significant streamwise motion appears, in what we call the “super-upper” branch, yielding massive amplitudes of 3 diameters peak-to-peak ( A ∗ Y ∼1.5 ). We discover a corresponding periodic vortex wake mode, comprising a triplet of vortices being formed in each half cycle, in what we define as a “2T” mode. The extensive studies of VIV for Y-only body motions, built up over the last 35 years, remain of strong relevance, for m ∗ >6 . It is only for “light” bodies, m ∗ , that one observes a rather marked departure from previous results.

Multi-modal Vortex-Induced Vibrations of a vertical riser pipe subject to a uniform current profile

Abstract: The transverse Vortex-Induced Vibrations of a long (length to diameter ratio, L/D=1544), flexible pipe, that was subjected to a uniform current profile (Reynolds number, Re=2.84×105) have been simulated using a strip theory Computational Fluid Dynamics model. The pipe's mass ratio (the ratio of the pipe's mass to the mass of fluid displaced by it) was varied between 1.0 and 3.0 in order to study its effect upon the vibrational behaviour of the pipe. Despite the inflow current being uniform the pipe was observed to vibrate multi-modally. Furthermore, all of the excited modes vibrated at the excitation (Strouhal) frequency. The fluid, via its added mass, was found to be able to excite modes whose natural frequencies differed from the excitation frequency. This ability was observed to decrease with increasing mass ratio.

Vortex-induced travelling waves along a cable

Abstract: We investigate the vortex-induced vibrations (VIV) of a very slender cable subjected to a stationary uniform cross-flow, using a travelling wave approach. A phenomenological model of the near wake based on van der Pol oscillators is developed and tested in comparison with numerical simulations and experimental data. A selection criterion for vortex-induced waves (VIW) is established: the fluid selects the frequency, according to Strouhal's law, and the structure fixes the wavenumber, as dictated by its dispersion relation.

Sound generation by turbulence

Abstract: Sound is a weak by-product of a subsonic turbulent flow. The main convective elements of the turbulence are silent and it is only spectral components with supersonic phase speeds that couple to the far-field sound. This paper reviews recent work on sound generation by turbulence. Just as there is a hierarchy of numerical models for turbulence (scaling, RANS, LES and DNS), there are different approaches for relating the near-field turbulence to the far-field sound. Kirchhoff approaches give the far-field sound in a straightforward way, but provide little insight into the sources of sound. Acoustic analogies can be used with different base flows to describe the propagation effects and to highlight the major noise producing regions.

Critical mass in vortex-induced vibration of a cylinder

Abstract: In this paper, we study the transverse vortex-induced vibrations of a cylinder at low mass-damping values. The response in this case consists of three distinct branches; namely the initial, upper and lower branches. For an elastically-mounted cylinder, the oscillation frequency can,be shown to be primarily dependent on the mass ratio (m* = mass/displaced fluid mass). For large mass ratios, m* = O(100), the vibration frequency for synchronization lies close to the natural frequency (f* = f/f(N) similar to 1.0), but as mass is reduced to m* = O(1), f* can reach remarkably large values. We deduce an expression for the frequency of the lower-branch vibration, at small mass-damping values, as follows:

Numerical simulations of VIV on long flexible cylinders immersed in complex flow fields

Abstract: The main purpose of this paper is to investigate the hydroelastic interactions that take place between long oscillating flexible cylinders and fluid forces. The cylinders are subjected to currents and shear flow emulating complex flow fields, which are present in oceanographic conditions in deep waters. In our calculations, the hydrodynamic forces are estimated by a computationally efficient discrete vortex method (DVM). The calculations are compared with results obtained employing the quasi-steady theory. The reduced velocity vs. non-dimensional amplitude curve obtained in the calculations is compared with experiments. Visualizations of the wake indicate a hybrid mode of vortex shedding along the span. Employing the terminology suggested by Williamson and Roshko [J. Fluids Struct. 2 (1988) 355], a 2 S mode is found in regions of low amplitudes, changing to a 2 P mode in regions of larger amplitudes. The position of the transition of modes varies with the reduced velocity.

Interactions of the wakes of two spheres placed side by side

Abstract: The periodic coupled wakes of two spheres, placed side by side in a uniform stream at low Reynolds numbers, are studied experimentally and by Direct Numerical Simulations. Distinctly different regimes of interaction are observed, depending on the separation distance between the spheres. For touching spheres, a single wake is found. At very small separations, it is shown through numerical simulations that the wakes interact strongly and the combined wake is offset with respect to the centreplane between the spheres. The wake is presumably metastable, probably resulting in the strong structural vibrations of the spheres observed in the present experiments for this regime. At slightly larger separations, the two wakes still interact strongly, and out-of-phase shedding occurs predominantly. In-phase shedding is observed experimentally for intermediate gap sizes, whereas DNS does not reveal a preferred phase difference between the two wakes. At distances above three sphere diameters, shedding is uncorrelated. Variations of the critical Reynolds number and shedding frequencies with separation distance are shown.

Predicted low frequency structures in the wake of elliptical cylinders

Abstract: The vortex structures in the wake of 2D elliptical cylinders at low Reynolds numbers are investigated for a Reynolds numbers range of 75 to 175 using direct numerical simulation. By varying the aspect ratio of an elliptical cylinder, the geometry is varied between the extremes of a circular cylinder and a flat plate normal to the flow. The power spectrum analysis of the vertical velocity along the horizontal centreline shows the presence of secondary and tertiary frequencies in the far region of the wake. As the Reynolds number is increased and/or the aspect ratio is decreased, the lower frequencies in the far wake become more dominant and their inception point occurs closer to the elliptical cylinder. This research suggests that the low frequency unsteadiness behind normal flat plates does not need to be due to the vortex interaction, but, rather, can result from the presence of a two-dimensional instability of the mean wake.  2003 Elsevier SAS. All rights reserved.

Control of separated flows by time periodic Lorentz forces

Abstract: Electromagnetic, i.e. Lorentz forces, may be used to influence the flow of electrically conducting fluids. The present paper investigates the application of time periodic Lorentz forces to the control of the suction side flow on a NACA 0015 hydrofoil. Experimental results, consisting of flow visualizations and force measurements, characterizing the control effect in the low Reynolds number range of 104≲Re≲105, are presented. A comparison of the forcing effect with stationary Lorentz forces on one hand and conventional oscillatory blowing on the other hand is given as well.

Numerical simulation of 3-D incompressible, multi-phase flows over cavitating projectiles

Abstract: The hydrodynamic cavitation over axisymmetric projectiles is computed using the unsteady incompressible Navier–Stokes equations for multi-fluid elements. The governing equations are discretized on a structured grid using an upwind difference scheme with flux limits. A preconditioning dual-time stepping method is used for the unsteady computations. The eigensystem is derived for the Jacobian matrices. This eigensystem is suitable for high-density ratio multi-fluid flows and it provides high numerical stability and fast convergence. This method can be used to compute single- as well as multi-phase flows. Cavitating flows over projectiles with different geometries are computed and the results are in good agreement with available experimental data and other published computations.

Flow-induced in-line oscillation of a circular cylinder

Abstract: Flow-induced in-line oscillation of a circular cylinder either spring-mounted (two-dimensional rigid cylinder) or cantilevered was experimentally studied in free-oscillation tests in a water tunnel. In the free-oscillation tests of a two-dimensional cylinder, two different types of excitations appear at approximately half of the resonance flow velocity. The response amplitudes are sensitive to the reduced mass-damping parameter for the in-line oscillation in the first excitation region with a symmetric vortex street, while the alternate vortices are locked-in with the vibration of the cylinder in the second excitation region. For a cantilevered circular cylinder with a finite span-length, it is found that cylinders with aspect ratios of 5 and 10 have a single excitation region, and cylinders with aspect ratios of 14 and 21 have two excitation regions. The mechanism of vibration was also investigated using a splitter plate in the wake to prevent alternate vortices. It is noted that the amplitude of oscillation with the splitter plate is greater than that without the splitter plate, especially at Vr=2.3 to 3.0, where a cylinder with an end plate shows the second excitation region. In other words, the alternate vortices suppress the excitation amplitude in this range. The results of this study are providing important supporting data for the recent Standard JSME S012-1998, “Guideline for Evaluation of Flow-Induced Vibration of a Cylindrical Structure in a Pipe”, by the Japan Society of Mechanical Engineers.

Wake states and response branches of forced and freely oscillating cylinders

Abstract: A freely-oscillating, elastically-mounted cylinder has two or three different response branches, where the third response branch is characterised by high amplitude oscillations and occurs at low values of the mass-damping parameter. Similarly, a cylinder undergoing forced transverse oscillations in a free stream flow exhibits two different wake states, with an additional third state at high oscillation amplitudes. In this paper the characteristic lift properties and patterns of near wake vorticity for the forced wake states are compared with those of the free response branches. The forced oscillations are shown to replicate many features of the freely oscillating case. However, these results also show that there are some important aspects to be resolved before forced oscillations can be used to predict flow-induced motion.

Three-dimensionality of mode transition in vortex-induced vibrations of a circular cylinder

Abstract: End lift forces and hot-wire anemometry in the wake of a flexibly-mounted rigid cylinder, undergoing vortex-induced vibrations within a uniform flow, show that the spanwise correlation undergoes a sharp reduction near conditions of maximum amplitude. Peak lift force and motion amplitudes occur on the low-velocity side of this low-correlation region; the region is bounded above by the advent of frequency lock-in. Certain aspects of this correlation loss are interpreted in the context of other free- and forced-vibration tests, and highlight the sensitivity of three-dimensional effects to the physical parameters.

Numerical study of viscoelastic mixtures through a Cahn–Hilliard flow model

Abstract: In this paper we are concerned with the numerical study of viscoelastic diphasic flows. We first propose a complete model and give some formal justifications including the case where both or one phase is a non-Newtonian one. Then, we have implemented a numerical method taking into account the lagrangian transport in the resolution of the extra-stress equation of Oldroyd type. We describe this fully-practical method and prove its stability so that one can perform long-time numerical simulations. Several significant tests (channel under shear, filling of tanks, breakup of jets...) illustrate the pertinency of the model and of the numerical method. We show that the results are in accordance with the various qualitative behaviors observed in physical experiments.

Plane Couette flow of binary gaseous mixture in the whole range of the Knudsen number

Abstract: The Couette flow of binary gaseous mixtures is studied on the basis of the McCormack model of the Boltzmann equation, which was solved numerically by the discrete velocity method. The calculations were carried out for three mixtures of noble gases: neon–argon, helium–argon, and helium–xenon. The stress tensor and bulk velocity of both species were calculated for several values of the gas rarefaction in the range from 0.01 to 40 for three values of the molar concentrations: 0.1,0.5 and 0.9. The numerical solution together with an analytical solution based on the slip boundary condition cover the whole range of the gas rarefaction. It was showed that the Couette flow is weakly affected by the intermolecular interaction law.

The Stuart-Landau model applied to wake transition revisited

Abstract: Following previous experimental and computational studies, this article further investigates the applicability of the Stuart–Landau equation to describe the Hopf bifurcation occurring for flow past a circular cylinder. It is shown that when the amplitude variable is taken as the transverse velocity component at a point in the wake, the so-called Landau constant varies considerably with position and importantly is generally far from constant during the saturation phase of wake development. The variation with downstream distance is quantified. However, it is found that the Landau constant at saturation is indeed a position-independent constant and this value is close to that generally measured previously both experimentally and numerically. It is shown that if the amplitude variable is taken as the lift coefficient of the cylinder (a global variable) then the same Landau constant is measured at saturation and the zero amplitude Landau constant corresponds to that for the transverse velocity at the back of the cylinder. These findings are used to interpret the wake behaviour of a transversely oscillating circular at subcritical Reynolds numbers.

The algebraically decaying wall jet

Abstract: The possible existence of a self-similar wall jet over a permeable plane surface in the presence of a (suitable) lateral suction of the fluid is proved. In contrast to its well known exponentially decaying counterpart (the Glauert-jet) formed over an impermeable wall, the suction-controlled wall jet decays algebraically with increasing distance from the wall. However, as the suction becomes vanishingly small, it approaches the profile of the Glauert-jet gradually.

Secondary instability mechanisms in the wake of a flat plate

Abstract: We extend the work of Sutherland and Peltier (Phys. Fluids 6 (1994) 1267) and investigate numerically the three-dimensional (3D) secondary stability of a wake forming behind a thin flat plate. The primary flow is a Karman vortex street numerically computed from the two-dimensional (2D) even instability of a parallel wake based on the Bickley velocity profile. Considering the symmetries of the von Karman Street, the 3D modes are classified into two families, whether symmetric or antisymmetric. For each family, we determine the leading eigenmodes using a Krylov method. The growth rate curves show that both the most unstable symmetric and antisymmetric modes are stationary and present a maximum of amplification for a wavelength of the order of the primary vortex spacing. The maximum growth rate, corresponding wavelength and cutoff wavelength are well predicted by the elliptic instability of the vortex core. The eigenmode structure of the most unstable wavenumber is centered in the core and is typical of the elliptic instability. The hyperbolic instability of the braid region gives a growth rate five times larger and a cutoff two times higher than the ones computed. As recently discussed for mixing layers by Caulfield and Kerswell (Phys. Fluids 12 (5) (2000) 1032), this is not surprising since the hyperbolic instability applies for an unbounded hyperbolic flow. When the region of hyperbolic flow is bounded, intense transient growth is generated, but when time goes to infinity, the instability becomes small or even dies out. Finally, good qualitative and quantitative agreement is found with the experiments previously done by Julien, Lasheras and Chomaz (J. Fluid Mech. 479 (2003) 155) on the secondary instability in the wake of a flat plate for the symmetry selection, the most amplified wavenumber and growth rate.  2003 Elsevier SAS. All rights reserved.

Two-dimensional Floquet stability analysis of the flow produced by an oscillating circular cylinder in quiescent fluid

Abstract: We study the two-dimensional symmetry breaking transitions in the time-periodic flow generated in quiescent fluid by a rigid cylinder with simple harmonic rectilinear translation in a direction normal to its axis. The base flow possesses two symmetries: a spatio-temporal symmetry and a spatial reflection symmetry about the axis of oscillation. Two distinct regimes of marginal stability are identified through two-dimensional Floquet analysis. These correspond to (I) a pair of real Floquet multipliers simultaneously crossing the unit circle at µ =+ 1 and (II) a pair of complex-conjugate multipliers crossing the unit circle, µ = e ±iθ (a Neimark–Sacker bifurcation). In both transitions the spatial reflection symmetry of the base flow is broken, but for type I transitions, the spatio–temporal symmetry of the base flow is retained.  2003 Elsevier SAS. All rights reserved.

Concise and accurate solutions to half-space binary-gas flow problems defined by the McCormack model and specular-diffuse wall conditions

Abstract: An analytical version of the discrete-ordinates method (the ADO method) is used to establish concise and particularly accurate solutions to the viscous-slip and the half-space thermal-creep problems for a binary gas mixture. The kinetic equations used to describe the flow are based on the McCormack model for mixtures. In addition to a computation of the viscous-slip and thermal-slip coefficients, for the case of Maxwell boundary conditions for each of the two species, the velocity, heat-flow and shear-stress profiles are established for both types of particles. Numerical results are reported for three binary mixtures (Ne–Ar, He–Ar and He–Xe) with various molar concentrations. The complete solution requires only a (matrix) eigenvalue/eigenvector routine and the solution of a system of linear algebraic equations, and thus the algorithm is considered especially easy to use. The developed (FORTRAN) code requires typically less than 0.1 seconds on a 1.2 GHz Pentium-based PC to solve both problems.

Skin friction and turbulence measurements in a boundary layer with zero-pressure-gradient under the influence of high intensity free-stream turbulence

Abstract: This experimental investigation deals with the influence of turbulence intensities Tuδ⩽13% and a ratio of integral length scale Λ11 to boundary layer thickness δ99.5 smaller than two on an axisymmetric turbulent boundary layer with zero pressure gradient. The free-stream turbulence was generated by jets injected normal to the flow upstream of the test section. The boundary layer had a Reynolds number range 1000⩽Reδ2⩽2700. Skin-friction measurements were performed using oil-film interferometry, Preston tubes and wall hot-wire probes. Mean and fluctuating velocities were measured by hot-wire anemometry and Reynolds stresses, triple correlations and spectra were evaluated. The free-stream turbulence increases the skin friction by up to 34% and considerably changes both mean and fluctuating velocity distributions in the outer region of the boundary layer.

Mesoscale plasma dynamics, transport barriers and zonal flows: simulations and paradigms

Abstract: Tokamaks are magnetic confinement fusion devices which seek to produce power from fusion reactions between the isotopes of hydrogen (deuterium and tritium). The understanding of turbulent transport processes which govern the energy, momentum and current distributions in tokamak plasmas is important to optimising the economically viable design of future power plants based on the tokamak concept. With the advent of powerful modern computers it has become possible to model the plasma dynamics on the so-called “mesoscale” which consists of electromagnetic turbulence with wavelengths intermediate to the ion gyro radius and the system size of typical tokamaks. This paper attempts to describe one such approach which evolves the two-fluid model of a tokamak plasma globally (i.e., both on the macroscale and the mesoscale), using a nonlinear, electromagnetic, three-dimensional code CUTIE. Recent researches, both theoretical and experimental, on tokamaks indicate the spontaneous (or, externally induced) generation of so-called “zonal flows”, which, under well-defined conditions, can lead to substantial reduction of turbulent transport in localized regions known as transport barriers. This type of confinement enhancement is of great importance in the design and construction of practical fusion power plants and has been the subject of intensive study. In addition to the computational approach based on CUTIE simulations, we also describe some simpler paradigmatic models which are designed to illustrate the genesis of zonal flows by characteristic drift wave fluctuations and the effects of such highly sheared advective flows on the system dynamics. These models help one to understand in a much clearer fashion the rather complex processes simulated by CUTIE.

Temporal statistics in high Rayleigh number convective turbulence

Abstract: Temporal statistics of temperature and velocity fluctuations are studied in a highly turbulent convective flow developed within a cylindrical cell of aspect ratio Γ=1/2. Numerical data are analyzed for Ra up to 2×1011 at fixed Prandtl number (Pr=0.7). Temperature and velocity time series are collected from numerical probes placed within the fluid volume in the bulk and close to the boundaries. It is shown that the effects of the boundaries and of the large scale recirculation are reflected in the temporal statistics of the analyzed quantities. Spectra and structure functions show that the temperature statistics follow the Bolgiano scaling while the velocity fluctuations exhibit scaling laws which are surprisingly very close to those of the temperature. These results are in contrast with the Bolgiano or Kolmogorov behaviors expected for the velocity statistics and a possible theoretical explanation is presented.

The McCormack model: channel flow of a binary gas mixture driven by temperature, pressure and density gradients

Abstract: An analytical version of the discrete-ordinates method (the ADO method) is used to establish concise and particularly accurate solutions to the problems of Poiseuille flow, thermal-creep flow and diffusion flow for a binary gas mixture confined between parallel walls. The kinetic equations used to describe the flow are based on the McCormack model for mixtures. The analysis yields, for the general (specular-diff use) case of Maxwell boundary conditions for each of the two species, the velocity, heatflow and shear-stress profiles for both types of particles. Numerical results are reported for two binary mixtures (Ne–Ar and He–Xe) with various molar concentrations. The complete solution requires only a (matrix) eigenvalue/eigenvector routine and a solver of a system of linear algebraic equations, and thus the algorithm is considered especially easy to use. The developed (FORTRAN) code requires typically less than a second on a 2.2 GHz Pentium IV machine to solve all three problems.  2004 Elsevier SAS. All rights reserved.

Characterization of low-speed streaks in the near-wall region of a turbulent boundary layer

Abstract: The low-speed streaks occurring in the near wall region of a turbulent boundary layer have been studied by means of two nonintrusive experimental techniques: the electrochemical method for the wall shear stress measurements, and the Laser Doppler Anemometer (LDA) for the velocity measurements. Correlations between the wall shear stress simultaneously measured at several points in the spanwise direction, and the correlations between the velocity and the wall shear stress simultaneously measured, indicate that in the near-wall region y+ 10. These correlations also show the presence of a double-peak in the correlation curves indicating the existence of structures ±6° tilted in (x,z) plane.