Showing papers in "European Journal of Mechanics B-fluids in 1998"

Local and global instability properties of separation bubbles

Abstract: A family of velocity profiles with reversed flow, typical of those found in separated flows, are examined for their linear instability properties. Specifically, a family of modified Falkner-Skan profiles are analyzed for the onset of absolute instability as the magnitude of the reversed flow increases. The mode of instability associated with the inflection point in the vicinity of the dividing streamline is found to become absolutely unstable as the peak reversed flow approaches about thirty percent of the free stream value. The family of profiles were used to construct generic models of separation bubbles and study the possible onset of global instability in the representative spatially-developing flows.

Three-dimensional instabilities in wake transition

Abstract: It is now well-known that the wake transition regime for a circular cylinder involves two modes of small-scale three-dimensional instability, modes “A” and “B”, occurring in different Reynolds number ranges. These modes are quite distinct in spanwise lengthscale and in symmetry, and they are found to scale on different physical features of the flow. Mode A has a large spanwise wavelength of around 3–4 cylinder diameters, and scales on the larger physical structure in the flow, namely the core of the primary Karman vortices. The feedback from one vortex to the next gives an out-of-phase streamwise vortex pattern for this mode. In contrast, the mode B instability has a distinctly smaller spanwise wevelength (1 diameter) which scales on the smaller physical structure in the flow, namely the braid shear layer. The symmetry of mode B is determined by the reverse flow behind the bluff cylinder, leading to a system of streamwise vortices which are in phase between successive half cycles. The symmetries of both modes are the same as the ones found in the vortex system evolving from perturbed plane wakes studied by Meiburg and Lasheras (1988) and Lasheras and Meiburg (1990). Furthermore, the question of the physical origin of these three-dimensional instabilities is addressed. We present evidence that they are linked to general instability mechanisms found in two-dimensional linear flows. In particular, mode A seems to be a result of an elliptic instability of the near-wake vortex cores; predictions based on elliptic instability theory concerning the initial perturbation shape and the spanwise wevelength are in good agreement with experimental observations. For the mode B instability, it is suggested that it is a manifestation of a hyperbolic instability of the stagnation point flow found in the braid shear layer linking the primary vortices.

Identification and analysis of vortical structures

Abstract: Various identification and visualization methods of vortical structures, especially of slender vortices, are critically reviewed with a special attention to their objectivity. The sectional-swirl-and-pressure-minimum scheme is presented as a new identification method and applied to homogeneous turbulence. Since the physical quantities associated with an individual vortex can be analyzed separately, this new scheme enables us to investigate quantitatively various physical characteristics related to vortices, such as the variations of the core shape, the circulation and the vorticity vector along a vortex and the temporal evolution of arbitrarily selected vortices.

Streamwise vortices in Large-Eddy simulations of mixing layers

Abstract: The formation of three-dimensional vortices in spatially-growing incompressible mixing layers is investigated in Large-Eddy Simulation at zero molecular viscosity, with the aid of the Filtered Structure Function subgrid-scale model proposed in Ducros et al. (1996, J. Fluid Mech., 326, pp. 1–36). Up to the second pairing at least, strong sensitivity to the nature of the random upstream perturbations and the spanwise size of the domain is observed. In addition to ‘unequal’ pairings between Kelvin-Helmholtz billows having undergone a different number of pairings and destructive ‘translative-pairing-and-tearing’ events, the two types of flow patterns obtained in the temporal Direct Numerical Simulations of Comte et al. (1992, Phys. Fluids A, 4, 2761–2778), are recovered, namely, highly three-dimensional vortex lattices undergoing local or helical pairings, as in the experiments of Chandrsuda et al. (1978, J. Fluid Mech., 85), or quasi-two-dimensional billows undergoing successive pairings while stretching streamwise vortices in between each other, as observed by Bernal and Roshko (1986, J. Fluid Mech., 170, 499–525). These streamwise vortices form in a succession of stages involving local roll-up and pairing, as conjectured by Lin and Corcos (1984, J. Fluid Mech., 141). Streamwise vortices are also found in a mixing layer formed within a solid-propellant rocket engine. At the wall of the outlet nozzle, they interact and possibly merge with Dean-Gortler-type vortices.

Experiments on localized disturbances in a flat plate boundary layer. Part 1. The receptivity and evolution of a localized free stream disturbance

Abstract: The receptivity of a laminar boundary layer to free stream disturbances has been experimentally investigated through the introduction of deterministic localized disturbances upstream of a flat plate mounted in a wind tunnel. Hot-wire measurements indicate that the spanwise gradient of the normal velocity component (and hence the streamwise vorticity) plays an essential role in the transfer of disturbance energy into the boundary layer. Inside the laminar boundary layer the disturbances were found to give rise to the formation of longitudinal structures of alternating high and low streamwise velocity. Similar streaky structures exist in laminar boundary layers exposed to free stream turbulence, in which the disturbance amplitude increases in linear proportion to the displacement thickness. In the present study the perturbation amplitude of the streaks was always decaying for the initial amplitudes used, in contrast to the growing fluctuations that are observed in the presence of free stream turbulence. This points out the importance of the continuous influence from the free stream turbulence along the boundary layer edge.

Is concentrated vorticity that important

Abstract: The main purpose of this paper is to bring about a better balance between views of the exaggerated importance of concentrated vorticity, on one hand, and the underestimated role of three kinds of regions other than concentrated vorticity: i — ‘structureless’ background, ii — regions of strong vorticity/strain (self) interaction and strong enstrophy generation, and iii — regions with negative enstrophy production, on the other hand, with the emphasis on the latter. Results of experiments on turbulent grid flow and DNS of decaying turbulent flow in a periodic ‘box’ at the same Reynolds number (Reλ ≈ 75) are used in order to demonstrate that all these regions are strongly non-Gaussian, dynamically significant and possess structure. It is argued that due to the strong nonlocality of turbulence in physical space all the four regions are in continuous interaction and are strongly correlated. Thus the answer to the question posed in the title is that — though important — regions of concentrated vorticity are not as important as is commonly believed.

Experimental and theoretical stability investigations of plane liquid jets

Abstract: The present investigation has been undertaken in order to better understand the development of free, plane liquid jets. Both the development of the basic laminar flow as well as its stability have ...

Numerical and experimental investigation of thermal convection for a thermodependent Herschel-Bulkley fluid in an annular duct with rotating inner cylinder

Abstract: This paper presents an experimental and numerical investigation of the thermal convection for a Herschel-Bulkley fluid, in an annular duct, with rotating inner cylinder. The outer cylinder is heated at constant heat flux density (φ) p and the inner one is adiabatic. This work has two main motivations. First, it seeks to determine the angular velocity Ω c for which the plug zone is reduced to zero. Second, to arrive at a better comprehension and better description of the effect of the variation of the consistency K with temperature T on heat transfer. In the case of slot approximation, Bittleston and Hassager (1992) presented for a Bingham fluid an analytical expression of Ω c .

Elliptic instability in two-sided lid-driven cavity flow

Abstract: The recently discovered concentration of vorticity in slender vortex tubes in turbulent flow fields has motivated the investigation of a class of vortices with elliptical streamlines. As a prototype of this flow, long vortices confined in a rectangular cavity and driven by tangentially moting walls are studied. These vortices are characterized by a large rate of plane strain at the core. The quasi-two-dimensional flow is found to be unstable at small Reynolds numbers, if the eccentricity of the streamlines, i.e. the strain rate, is sufficiently large. The three-dimensional supercritical flow is found to be steady with a wavelength of the order of the vortex core diameter. The flow pattern appears in the form of rectangular cells that are very robust. Good agreement between experiment and numerical calculations is obtained. It is argued that the instability found is due to the elliptic instability mechanism.

Mathematical Topics in Fluid Mechanics, Volume 1, Incompressible Models

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Absolute instability conditions for variable density, swirling jet flows

Abstract: Two different vortex sheet models are used to study the transition from absolute to convective instability in variable-density, swirling jet flows. It is found that swirl enhances the tendency for absolute instability in a jet issuing into a non-swirling medium when the vortical core of the swirling flow is small compared to the jet radius. When the size of the vortical core approximates the size of the jet, the effect of swirl on promoting absolute instability is quite weak. The trend toward absolute instability is accentuated when the jet is heated relative to the ambient. If the flow external to the jet also possesses swirl, the tendency toward absolute instability is increased when the jet shear layer is centrifugally unstable according to Rayleigh's criterion (i.e., the circulation decreases with increasing radius) and is decreased when the shear layer is centrifugally stable.

Three-dimensional solitary waves in the presence of additional surface effects

Abstract: Bifurcations from the quiescent state of three dimensional water wave solutions of a sixth order model equation are analysed. The equation in question is a generalization of the Kadomtsev-Petviashvili equation, and is obtained due to the presence of certain surface effects. These effects are caused either by a surface tension with Bond number close to 1 3 , or by an elastic ice-sheet floating on the water surface. The equation describing travelling waves is reduced to a system of ordinary differential equations on a center manifold. Solutions having the form of a solitary wave with damped oscillations, propagating in a channel, are obtained. In the direction transverse to the propagation they satisfy boundary conditions which are either periodic or of Dirichlet type. In the periodic case we find both asymmetric and symmetric waves. In particular, some of these solutions fill a gap in the speeds of the travelling waves where no two-dimensional solitary waves exist. We show that the critical spectra of the linear operators of the model equation and of the full water wave problem are identical.

Oblique two-fluid stagnation-point flow

Abstract: Exact similarity solutions for the impingement of two viscous, immiscible oblique stagnation flows forming a flat interface are given. The problem is governed by three parameters: the ratios of density ρ = ρ1ρ2 and of viscosity μ = μ1μ2 of the two fluids and R = tanθ1tanθ2 where θ1 and θ2 are the asymptotic angles of the incident streamlines in each fluid layer. For given values of ρ, μ, and θ2, the compatible flows in the lower fluid, as measured by the strain rate ratio β = β1β2 of the two fluids and the asymptotic angle of incidence θ1, are found such that the interface remains horizontal in a uniform gravitational field. For ρ = 1, explicit solutions show that a family of co-current and counter-current shears supporting a flat interface exist for all finite, nonzero values of R. For ρ ≠ 1, the normal stress interfacial boundary conditions restricts the flow to a unique combination of asymptotic far-field shear and Hiemenz stagnation-point flow in each fluid layer. The displacement thicknesses in each layer are always positive when the fluid densities are not equal, but vanish simultaneously as ρ → 1. At each value of ρ the interfacial velocities increase with increasing viscosity ratio μ. As a generalization of the present oblique two-fluid stagnation-point flow problem, we discuss how the flat interface may be inclined with respect to the horizontal in a uniform gravitational field.

Unsteady gaseous flows in rectangular microchannels: frequency response of one or two pneumatic lines connected in series

Abstract: This paper represents an initial analysis of unsteady gaseous flows in a rectangular microchannel under usual pressure and temperature conditions. The effect of depth and aspect ratios of the cross-section is investigated. With most fluid-based mechanical microsystems of small internal dimensions and subject to normal pressure and temperature conditions, flow is rarefied with slip at the walls. This flow is then modeled by the Navier-Stokes equations combined with slip and temperature jump conditions at the walls. These conditions are represented by Maxwell-Smoluchowski first order equations. By concentrating essentially on the pulsed sinusoidal regime, it is shown that the instantaneous flow rate amplitude, as well as the band pass of the microchannel are underestimated when slip at the walls is not taken into account. The frequency response of two microchannels connected in series with different cross-sectional areas is also studied. Finally, the proposed model can serve as a tool giving information about the current feasibilities of pressure sensors for the measurement of the dynamic characteristics of gaseous flows in microchannels.

Analytical study of transonic flows of a gas condensing onto its plane condensed phase on the basis of kinetic theory

Abstract: A uniform flow of a gas condensing onto its plane condensed phase (commonly known as the half-space problem of condensation) is considered. The problem is studied analytically on the basis of the Boltzmann equation when the flow is in a transonic region. The paper clarifies the analytical structure of the solution, especially the mechanism by which the range of the parameters (the flow speed, pressure, and temperature of the uniform flow blowing from infinity) where a steady solution exists changes abruptly (from a surface to a domain in the parameter space) when the flow speed passes the sonic speed, the correspondence of a family of supersonic solutions to a subsonic solution, etc. The solutions constructed analytically are compared with new numerical solutions near the sonic point.

Wetting prevention by thermal marangoni effect. Experimental and numerical simulation

Abstract: The behaviour of small liquid drops, hanging from a circular disk and approaching a flat wall at a different temperature is studied experimentally and numerically. If the pendant drop and the solid surface are at the same temperature and if the liquid wets the solid, the drop spreads over the surface forming a liquid bridge in times of the order of milliseconds. If the upper disk is heated and/or the solid surface is cooled, then the drop does not wet the wall, even if pressed against the surface, but it is deformed in a completely reversible way, similarly to an elastic material (e.g. like a rubber balloon). To investigate this unusual and intriguing phenomenon, a systematic experimental programme has been carried out on silicone oils (with different viscosities) and on diesel oils. At the same time the problem was studied numerically under the assumption that a thin air film exists between the drop and the solid surface. This film is formed by the entrainment of the surrounding air caused by the Marangoni flow directed, along the liquid surface, from the upper disk towards the contact zone. If suitable conditions are established, the pressure in the air film balances the pressure necessary to deform the liquid drop, preventing the wetting of the solid surface. The experimental results agree with the proposed numerical model. In particular the computed equilibrium air film thicknesses are compared with the thicknesses measured with a background illumination system and with an interferometric technique; a good agreement is found between numerical and experimental results, for different liquids and different geometrical configurations.

Radial inflow between a rotating and a stationary disc

Abstract: The asymptotic behaviour of the motion of an incompressible fluid between a stationary and a rotating disc with a low aspect ratio and a radial inflow is analyzed assuming a small Ekman number. Two distinct solutions are obtained for the central core flow behaviour, depending on whether or not there is a superposed inflow, and general integral relations are presented. An experimental study is performed in air. Detailed measurements provide data for the radial and circumferential mean velocity components, Reynolds stress components and static pressure on the stator, for several values of the significant dimensionless parameters. This experimental investigation shows that it is relevant to consider the dimensionless inflow rate as a significant parameter. Comparisons between the analytical solutions and the experimental data are in agreement with the features of the asymptotic model and are used to provide a better physical understanding of the flow.

Experiments on localized disturbances in a flat plate boundary layer. Part 2. Interaction between localized disturbances and TS-waves

Abstract: Previous studies on boundary layer transition at moderate levels of free stream turbulence (FST) have shown that the transition process can be promoted by the introduction of Tollmien-Schlichting (TS) waves. In the present work the interaction between localized boundary layer disturbances and controlled TS-waves is studied experimentally. The localized disturbances are generated either from a controlled free stream perturbation, or by means of suction or injection through a slot in the flat plate surface. Both methods result in boundary layer disturbances dominated by elongated streamwise streaks of high and low velocity in the streamwise component. A strong interaction is observed preferably for high frequency TS-waves, which are damped when generated separately, and the interaction starts as a local amplification of a wide band of low-frequency oblique waves. The later stages of the transition process can be identified as a non-linear interaction between the oblique structures, leading to regeneration of new and stronger streamwise streaks.

Small scale intermittency in turbulence

Abstract: The present theoretical and experimental knowledge of the intense intermittent events in high Reynolds number turbulence is reviewed. An attempt is made to relate the two main streams of research in this area: the multifractal description and the coherent filaments identified in numerical simulations. It is concluded that, although both approaches can be expressed in a common language, they are inconsistent in detail and both are incomplete. While the multifractal approach is a kinematic description without dynamics, the present understanding of the scaling and dynamics of the coherent vortices requires the existence of stable laminar structures of arbitrarily large Reynolds numbers, and probably represents only one of a hierarchy of intermittent objects. It is suggested that the vortices may not survive at very high values of Re λ , and that the problem extends to all the intermittent structures of turbulence. It is shown that the filaments should dominate the structure functions in a range of scales that goes from beyond the Kolmogorov scale for p < 4 to the whole inertial range if the scaling exponent ζ p → ∞ (usually expected as p → ∞.)

Benjamin-feir and eckhaus instabilities with galilean invariance: the case of interfacial waves in viscous shear flows

Abstract: We consider the stability of interfacial waves in a two-layer viscous shear flow. The weakly nonlinear dynamics are governed by a set of two coupled amplitude equations (Renardy and Renardy, 1993): a complex Ginzburg-Landau equation for the travelling wave with finite wavenumber kc, and a Burgers-type equation for the neutral mode with wavenumber k = 0. We study here the linear stability, against long wavelength disturbances, of the travelling wave solutions of these equations. For the travelling wave with k = kc, the Lange & Newell criterion for the Benjamin-Feir instability is modified by the coupling, and a new kind of instability may arise from the neutral mode k = 0. For travelling waves with k ≠ kc, several wavenumber bands may be Eckhaus-unstable, with growth rate much larger than for the classical Eckhaus instability. A physical mechanism for this instability is proposed. Beyond the case of interfacial waves in viscous shear flows, the results apply for physical systems with translational and galilean invariances, and no-space-reflection symmetry.

Boundary layer over a slotted plate

Abstract: In order to investigate the boundary layer over a slotted plate, we first set up a hydrodynamic boundary condition for a parallel flow from a numerical study, performed on a periodic perforated medium at the local scale of the perforations. This boundary condition links the shear stress at the wall and the slip velocity along the plate by a partial slip coefficient. Then, a parametric study is conducted to analyse this partial slip coefficient versus the surface porosity of the plate and the Reynolds number of the flow. Afterwards, we introduce this partial slip boundary condition in the Blasius formalism and express the dynamic boundary layer thickness, the reduced slip velocity and the shear stress at the wall as functions of the slip coefficient, the Reynolds number and the reduced abscissa on the plate. Finally, we compare these latter laws with direct simulation results of the boundary layer flow over a slotted plate, considered as a very thin homogeneous permeable flat wall.

Effect of a rotating magnetic field of arbitrary frequency on a liquid metal column

Abstract: We consider the influence of a rotating magnetic field on an infinitely long cylindrical liquid metal column. A solution for the flow field and magnetic field distribution is obtained for any value of the Hartmann number, Ha, and of the shielding parameter, Rω. When Ha ⪢ 1, it has been shown that, as long as R ω Ha √2 , the flow consists of a core rotating with the same angular velocity as that of the magnetic field and of a Hartmann boundary layer at the wall. The flow also contains recirculating eddies which are aligned with the magnetic field in the cylinder core. It is noted that the magnetic field is swept by the convective effect of the flow in the wall boundary layer whereas it satisfies a pure diffusion regime in the core. A simplified ring model permits a simple explanation of the critical value R ω = Ha √2 .

Experimental and numerical investigations of low-temperature superfluid turbulence

Abstract: Low-temperature superfluid turbulence is studied experimentally in a Helium swirling flow and numerically with the Gross-Pitaevskii equation in the geometry of the Taylor-Green (TG) vortex flow. Numerically, it was found in Nore et al. (1997a, b) that the kinetic energy transfer in the superfluid TG vortex is comparable to that of the viscous TG vortex and that the energy spectrum of the superflow is compatible with Kolmogorov's scaling. The vorticity dynamics of the superflow are similar to that of the viscous flow. In both cases, many vortex reconnection events happen throughout the flow. Experimentally, power measurements and pressure fluctuation spectra show very little difference above and far below the superfluid transition temperature, where the normal-fluid component of Helium is negligible (less than 5% in mass at T = 1.2 K).

Kelvin twist waves in the transition to turbulence

Abstract: We present evidence for Kelvin twist waves on vortex tubes in a numerical simulation of the transition to turbulence in a breaking internal gravity wave. Specifically, m = 0, m = 1, and m = 2 twist waves are found and are compared to analytic versions of the waves. The observed twist waves are of a sufficiently large amplitude to break up the vortex tubes on which they reside, with the m = 0 waves fragmenting the vortex tubes along their length and the m = 2 waves unraveling the vortex tubes into pairs of helical tubes. Under the influence of these waves, the flow evolves from an organized collection of horseshoe vortices to a disorganized collection of vortex fragments.

A contribution to the physical analysis of separated flows past three-dimensional humps

Abstract: The aim of this article is to present a few improvements in the understanding of both mathematical and physical aspects of three-dimensional separated flows past a protuberance on a flat plate. Only steady laminar incompressible flows are considered here. The asymptotic structure of boundary-layer flows with strong viscous-inviscid interaction has been extensively studied by several authors, mainly with the triple-deck theory. The first part of this paper presents the results of a systematic analysis of the asymptotic structure when the obstacle's dimensions vary. This work explains why the triple-deck properties are so much characteristic. The three-dimensional boundary-layer equations are then solved with a quasi-simultaneous interacting technique, and the results are examined in order to describe the three-dimensional topology of the flow. Two types of flows are described, corresponding to a dent and a hump, that exhibit completely different behaviours.

Intermittency in the closed flow between coaxial corotating disks

Abstract: We report an experimental study of the swirling flow generated in the gap between two coaxial corotating disks in an enclosed geometry, i.e. when the flow is enclosed in a cylindrical vessel. In this situation the angular momentum generated by the disk rotation tends to concentrate in a strong axial vortex. In the range of high Reynolds numbers explored, we show that two regimes exist, depending on the disk angular velocities. When they rotate at quite different speeds, we observe very intermittent fluctuations of the axial vorticity associated with quasi-periodic vortex bursting, whereas at comparable rotation rates a more stable vorticity structure is observed. We describe these regimes using global measurements; we also show, using local velocimetry, how the structure of the flow affects the small scale turbulence.

Experimental evidence for a new type of stretched vortex

Abstract: Experimental measurements performed under conditions which reproduce most of the dynamical characteristics of the natural evolution of vorticity filaments in turbulent flows are presented here. Strong deviations from the Burgers vortex (which is a non-confined stretched vortex model) are observed and analyzed.