Columnar vortices in isotropic turbulence

The structure of the intense vorticity regions is studied in numerically simulated homogeneous, isotropic, equilibrium turbulent flow fields at four different Reynolds numbers, in the rangeRe =35–170, and is found to be organized in coherent, cylindrical or ribbon-like, vortices (worms). At the Reynolds numbers studied, they are responsible for much of the extreme intermittent tails observed in the statistics of the velocity gradients, but their importance seems to decrease at higherRe . Their radii scale with the Kolmogorov microscale and their lengths with the integral scale of the flow, while their circulation increases monotonically withRe . An explanation is offered for this latter scaling, based in the assumed presence of axial inertial waves along their cores, excited by a random background strain of the order of the root mean square vorticity. This explanation is consistent with the presence of comparable amounts of stretching and compression along the vortex cores.

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Sommario La struttura di regioni ad intensa vorticità in campi di flusso turbolento omogenei, isotropi ed in equilibrio, simulati numericamente, viene studiata per quattro differenti numeri di Reynolds nell'intervalloRe =35÷170, e si trova che tali regioni si organizzano in vortici coerenti, cilindrici o a forma di nastro (vermi). Con rifermento ai numeri di Reynolds studiati, si vede che tali vortici sono responsabili per gran parte delle code estreme ed intermittenti, osservate nelle statistiche dei gradienti di velocità, ma la loro importanza sembra decrescere a più altiRe . I loro raggi scalano con la microscala di Kolmogorov e le loro lunghezze con la scala integrale del flusso, mentre la loro circolazione cresce monotonicamente conRe . Per quest'ultimo riscalamento viene offerta una spiegazione basata sull'assunzione della presenza di onde inerziali assiali lungo i loro nuclei, eccitate da una deformazione di fondo casuale dell'ordine della radice quadrata della velocità media. Questa spiegazione è consistente con la presenza di incrementi paragonabili di allungamenti e compressioni lungo i nuclei dei vortici.

     

On the refracted patterns produced by liquid vortices

A theoretical analysis of the refracted shadows produced by steady and time-decaying liquid vortices under uniform illumination from above is given in this article. An expression for the induced shadow intensity is derived and found to be a function of the vortex’s free surface profile, i.e., function of the static pressure distribution. The patterns for different focusing depth are given and compared with previous visualization results from the literature. The phenomenon is examined and illustrated as a bench mark case by using both steady and time-decaying algebraic vortex models. However, this study can be extended to check the feasibility of recovering the main flow properties by analyzing the luminous image intensity of the refracted patterns. The present analysis is valid only when the swirl velocity is order of magnitude higher than the meridional flow components and the vorticity is concentrated within the core region and of intense conditions.     

Vortices,Complex Flows and Inertial Particles

The properties of vortical structures at high Reynolds number in uniform flows and near rigid boundaries are reviewed. New properties are derived by analysing the dynamics of the main flow features and the related integral constraints, including the relations between mean swirl and bulk speed, the relative level of internal fluctuations to bulk properties, and connections between the steadiness and topology of the structures. A crucial property that determines energy dissipation and the transport of inertial particles (with finite fall speed) is the variation across the structure of the ratio of the mean strain rate (Σ) to the mean vorticity (Ω). It is shown how, once such particles are entrained into the vortical regions of a coherent structure, they can be transported over significant distances even as the vortices grow and their internal structure is distorted by internal turbulence, swirling motions and the presence of rigid boundaries. However if the vortex is strongly distorted by a straining motion so that Σ is greater than Ω, the entrained particles are ejected quite rapidly. These mechanisms are consistent with previous studies of entrained and sedimenting particles in disperse two phase flows over flat surfaces, and over bluff obstacles and dunes. They are also tested in more detail here through laboratory observations and measurements of 50–200-μm particles entrained into circular and non-circular vortices moving first into still air and then onto rigid surfaces placed parallel and perpendicular to the direction of motion of the vortices.     

Dynamics of trailing vortices in the wake of a generic high-speed train

The three-dimensional dynamics of a pair of counter-rotating streamwise vortices that are present in the wake of an ICE3 high-speed train typical of modern, streamlined vehicles in operation, is investigated in a 1/10th-scale wind-tunnel experiment. Velocity mapping, frequency analysis, phase-averaging and proper orthogonal decomposition of data from high-frequency multi-hole dynamic pressure probes, two-dimensional total pressure arrays and one-dimensional multi-hole arrays was performed. Sinusoidal, antisymmetric motion of the pair of counter-rotating streamwise vortices in the wake is observed. These unsteady characteristics are proposed to be representative of full-scale operational high-speed trains, in spite of the experimental limitations: static floor, reduced model length and reduced Reynolds number. This conclusion is drawn from favourable comparisons with numerical literature, and the ability of the identified characteristics to explain phenomena established in full-scale and scaled moving-model experiments.     

On the development of Taylor vortices in a vertical annulus with a heated rotating inner cylinder

A numerical study has been conducted to determine the heat transfer characteristics and flow patterns which develop around a rotating, heated vertical cylinder enclosed within a stationary concentric cylinder. A tall annulus (aspect ratio of 10) with fixed, adiabatic horizontal end-plates and a radius ratio of 0·5 has been considered. Furthermore, the effect that the introduction of buoyancy forces by heating the inner cylinder has on the development of the Taylor vortex flow is examined. It is observed that the formation of the Taylor vortices is delayed until the rotational parameter σ = Gr/Re² has a value below unity for any given Reynolds number Re which is above the critical value Re_crit for the formation of Taylor vortices in an isothermal flow. Also, the Taylor cells first appear at the top of the annulus. As σ is gradually decreased below unity, bifurcations to other states are observed. The final structure of the secondary flow is noticeably distorted in the mixed-convection mode, with the size of the Taylor cells varying greatly along the height of the annulus. This distortion diminishes as σ is further decreased, until the isothermal flow pattern is nearly recovered below σ = 0·01.     

A review of research on cylindrical particulate flows

The study of cylindrical particulate flows has wide industrial applicability hence received much attention. The purpose of the present paper is to provide a review on our research over the last few years. The research is related to the motion of cylindrical particles in mixing layer, pipe flow, channel flow, converging channel flow; the sedimentation of cylindrical particles in a Newtonian fluid; the structural feature and rheological property of cylindrical particulate suspensions; and the hydrodynamic instability of cylindrical particulate suspensions.     

Granular vortices: Identification,characterization and conditions for the localization of deformation

We relate the micromechanics of vortex evolution to that of force chain buckling and, on this basis, formulate the conditions for strain localization in a continuum model of dense granular media. Using the traditional bifurcation analysis of shear bands, we show that kinematic vortex fields are in fact solutions to the boundary value problem satisfying null boundary conditions. To establish an empirical basis for our study, we first develop a method to identify the location of the core and boundary of each vortex from a given displacement field in two dimensions. We then employ this method to characterize the residual deformation field (i.e., the deviation of particle motions from the continuum deformation) in a physical experiment and a discrete element simulation of dense granular samples submitted to biaxial compression. Vortices in the failure regime are essentially confined to the shear band. Primary vortices, the clear majority, rotate in the same direction as the shear band; secondary vortices, the so-called wakes, rotate in the opposite direction. Primary vortices align in spatial succession along the central axis of the band; wakes form next to the band boundaries, in between and beside two adjacent primary vortices. Force chain buckling, the governing mechanism for shear bands, is responsible for vortex formation in the failure regime. Vortex dynamics are consistent with stick-slip dynamics. From quiescent conditions of jamming or stick, vortical motions arise from force chain buckling and associated relative particle rotations and sliding; these in turn precipitate intermittent periods of unjamming or slip, evident in the attendant drops in stress ratio and bursts in both kinetic energy and local nonaffine deformation. A kinematic vortex field inside shear bands is proposed that is consistent with the equations of continuum mechanics and the underlying instability of force chain buckling: such a field is periodic with a repeating unit cell comprising a primary vortex at the center of the band, with two trailing wakes close next to the band boundaries.     

Mixing and coherent vortices in turbulent coaxial jets

Direct numerical simulations associated with mixing in constant-density round coaxial jets are performed. They are validated by comparison against laboratory experiments. The mixing process is studied by seeding a passive tracer first in the outer annular jet, then in the inner jet. We demonstrate the important role played by coherent vortices in the mixing mechanisms. The turbulent mixing exhibits an intermittent character as a consequence of fluid ejections caused by the counter-rotating streamwise vortices. We quantify also the domination of the outer jet and show that the fluid issuing from the central jet remains confined. To cite this article: G. Balarac, M. Si-Ameur, C. R. Mecanique 333 (2005).     

On the numerical solution of the turbulence energy equations for wave and tidal flows

This paper deals with the numerical solution, using finite difference methods, of the hydrodynamic and turbulence energy equations which describe wind wave and tidally induced flow. Calculations are performed using staggered and non-staggered finite difference grids in the vertical, with various time discretizations of the production and dissipation terms in the turbulence energy equations. It is shown that the time discretization of these terms can significantly influence the stability of the solution. The effect of time filtering on the numerical stability of the solution is also considered. The form of the mixing length is shown to significantly influence the bed stress in wind wave problems. A no-slip condition is applied at the sea bed, and the associated high-shear bottom boundary layer is resolved by transforming the equations onto a logarithmic or log-linear co-ordinate system before applying the finite difference scheme. A computationally economic method is developed which remains stable even when a very fine vertical grid (over 200 points) is used with a time step of up to 30 min.     

Effect of trailing edge shape on hydrodynamic damping for a hydrofoil

Flow induced vibration on a hydrofoil may be significantly reduced with a slight modification of the trailing edge without alteration of the hydrodynamic performance. Particularly, the so called Donaldson trailing edge shape gave remarkable results and is being used in a variety of industrial applications. Nevertheless, the physics behind vibration reduction is still not understood. In the present study, we have investigated the hydrodynamic damping of a 2D hydrofoil with Donaldson trailing edge shape. The results are compared with the same hydrofoil with blunt trailing edge. The tests are carried out in EPFL high speed cavitation tunnel and two piezoelectric patches are used for the hydrofoil excitation in non-intrusive way. It was found that the hydrodynamic damping is significantly increased with the Donaldson cut. Besides, as the flow velocity is increased, the hydrodynamic damping is found to remain almost constant up to the hydrofoil resonance and then increases linearly, for both tested trailing edge shapes and for both first bending and torsion modes.     

Linear stability of channel entrance flow

The spatial stability of two dimensional, steady channel flow is investigated in the downstream entry zone for both exponentially and algebraically growing disturbances. A model based on previous work is presented for the base flow which represents a small deformation of plane Poiseuille flow. The base flow evolution towards the fully developed state comes from the experimental and theoretical study of M. Asai and J.M. Floryan [M. Asai, J.M. Floryan, Certain aspects of channel entrance flow, Phys. Fluids 16 (2004) 1160–1163]. This flow is found to be more stable than the parabolic Poiseuille flow. The most destabilizing base flow defect is then calculated using a variational method. The compromise between the destabilizing effect of the defect, which diffuses downstream, and the instability growth is found to be insufficient to provoke transition in the downstream laminar flow.     

The calculation of incompressible separated turbulent boundary layers

The algebraic turbulent model of Baldwin and Lomax was incorporated into the incompressible full Navier–Stokes code FIDAP. This model was extensively tested in the past in finite difference codes. We believe that the incorporation of the model also into the finite element code has resulted in a practical method to compute a variety of separated turbulent 2D flows. Firstly, we use the model to compute the attached flow about an aerofoil. Next, the application of the model to separated flows is presented by computing the flows at high angles of attack up to maximum lift. It is shown that the model is capable of predicting separation, steady stall and C_Lmax. As a difficult test of the model we compute the laminar separation bubble development directly using the full Navier–Stokes finite element code. As far as we know, this approach has not yet been reported. The importance of using an appropriate upwinding is discussed. When possible, comparison of computed results with experiments is presented and the agreement is good.     

The Onset and Nonlinear Development of Vortex Instabilities in a Horizontal Forced Convection Boundary Layer With Uniform Surface Suction

We consider the flow and heat transfer caused by a strong external flow passing over a hot surface with uniform surface suction. When the Péclet number based on the external velocity is sufficiently large, the resulting thermal boundary layer develops in a nonsimilar manner until it attains an asymptotic state which is independent of the streamwise coordinate, x, when it is dominated by the surface suction. For sufficiently large, but moderate, values of the Darcy–Rayleigh number this boundary layer becomes unstable to streamwise vortex disturbances. We employ a parabolic solver to determine how such disturbances, when placed very close to the leading edge, evolve with distance downstream. Neutral stability is then defined to be when a suitable energy functional ceases to decay/grow as x increases. Thus a neutral curve may be mapped out based upon the behaviour of this functional. Given that the uniform asymptotic state is well known to admit subcritical instabilities, our linearised analysis is extended into the nonlinear domain and the effect of different magnitudes of disturbance is ascertained. It is found that a surprisingly rich variety of vortex pattern emerges which is sometimes sensitively dependent on the values of the governing parameters. These patterns include wavy vortices and abrupt changes in perceived wavelength.     

Interfacial instability in turbulent flow over a liquid film in a channel

We revisit the stability of a deformable interface that separates a fully-developed turbulent gas flow from a thin layer of laminar liquid. Although this problem has received considerable attention previously, a model that requires no fitting parameters and that uses a base-state profile that has been validated against experiments is, as yet, unavailable. Furthermore, the significance of wave-induced perturbations in turbulent stresses remains unclear. To address these outstanding issues, we investigate this problem and introduce a turbulent base-state velocity that requires specification of a flow rate or a pressure drop only; no adjustable parameters are necessary. This base state is validated extensively against available experimental data as well as the results of direct numerical simulations. In addition, the effect of perturbations in the turbulent stress distributions is investigated, and demonstrated to be small for cases wherein the liquid layer is thin. The detailed modelling of the liquid layer also elicits two unstable modes, ‘interfacial’ and ‘internal’, with the former being the more dominant of the two. We show that it is possible for interfacial roughness to reduce the growth rate of the interfacial mode in relation to that of the internal one, promoting the latter, to the status of most dangerous mode. Additionally, we introduce an approximate measure to distinguish between ‘slow’ and ‘fast’ waves, the latter being the case for ‘critical-layer’-induced instabilities; we demonstrate that for the parameter ranges studied, the large majority of the waves are ‘slow’. Finally, comparisons of our linear stability predictions are made with experimental data in terms of critical parameters for onset of wave-formation, wave speeds and wavelengths; these yield agreement within the bounds of experimental error.     

Instability analysis of modulated Taylor vortices

This study investigates the instability analysis of modulated Taylor vortices flow by utilising a numerical method. Based on the consideration that the outer cylinder is fixed and the inner cylinder rotates at a non-zero averaged speed under varying modulated amplitudes and frequencies, the flow is converted from one-dimension Couette flow to Taylor vortices. When the modulated amplitude is greater than 1 and the rotation speed of the inner cylinder exceeds the threshold value for one-dimensional flow, the flow will be more stable at intermediate and high frequencies. When the modulated amplitude is sufficiently large and the inner cylinder rotates at medium frequency, subharmonic flow arises.     

A design of a two-dimensional,supersonic KH experiment on OMEGA-EP

An experiment meant to investigate the evolution of single mode Kelvin–Helmholtz (KH) instability in the supersonic regime is presented and theoretically analyzed. This experiment is intended to provide a direct measurement of the two-dimensional vortex evolution so that the high-Mach-number effects can be measured. The proposed design takes advantage of the ability of OMEGA-EP to drive experiments for up to 30 ns to produce steady conditions for KH that endure long enough to observe substantial growth. KH growth for the proposed design has been analyzed using two-dimensional numerical simulations. The results were compared to synthetic temporal KH numerical simulations using non-dimensional scaling in the low and high Mach number regime. The comparisons show that the growth in the high Mach number regime is expected to be suppressed by up to a factor of two. The effects of two-dimensional rarefactions from the lateral boundaries of the experimental system were also investigated. It was found that they introduce no major uncertainties or hazards to the experiment. We produced simulated radiographs, which show that the proposed experimental system will enable observation of the KH structures. An experiment of this kind has not yet been performed, and therefore would serve to validate numerical results and analytical models presented here and in the literature.     

Centrifugal instability and the rib vortices in the cylinder wake

The physical mechanism for generation of streamwise vortices (or rib vortices) in the cylinder wake is numerically investigated with a finite-difference scheme. Rayleigh's theory of centrifugal instability for inviscid axisymmetric flow is extended to analyze the 2-D primary flows. Accordingly, an analytical dimensionless groupRay=−(r/v _θ)∂v _θ/∂r−1 is derived, wherev _θ represents the velocity of a fluid element relative to the oncoming flow,r is the local curvature radius of the element pathline. Centrifugal instability occurs whenRay>0. Stability analyses are carried out with this discriminant for primary flows at different time levels in a half shedding period of the von Kármán (or vK) vortices. Unstable areas are identified and the locations of rib vortices are coincident well with the unstable areas within the first wavelength of vK vortices behind the cylinder. The numerical results also show that rib vortices experience amplification in this region. It is apparent that centrifugal instability plays an important role in the generation of rib vortices in the cylinder wake. The project spported by the National Natural Science Foundation of China