Large-Scale Streamwise Vortices in Turbulent Channel Flow Induced by Active Wall Actuations

Direct numerical simulations of turbulent flow in a plane channel using spanwise alternatively distributed strips (SADS) are performed to investigate the characteristics of large-scale streamwise vortices (LSSVs) induced by small-scale active wall actuations, and their role in suppressing flow separation. SADS control is obtained by alternatively applying out-of-phase control (OPC) and in-phase control (IPC) to the wall-normal velocity component of the lower channel wall, in the spanwise direction. Besides the non-controlled channel flow simulated as a reference, four controlled cases with 1, 2, 3 and 4 pairs of OPC/IPC strips are studied at M =?0.2 and R e =?6,000, based on the bulk velocity and the channel half height. The case with 2 pairs of strips, whose width is Δz ⁺ =?264 based on the friction velocity of the non-controlled case, is the most effective in terms of generating large-scale motions. It is also found that the OPC (resp. IPC) strips suppress (resp. enhance) the coherent structures and that leads to the creation of a vertical shear layer, which is responsible for the LSSVs presence. They are in a statistically steady state and their cores are located between two neighbouring OPC and IPC strips. These motions contribute significantly to the momentum transport in the wall-normal and spanwise directions showing potential for flow separation suppression.     

Multisensor Hot Wire Vorticity Probe Measurements of the Formation Field of Two Corotating Vortices

Experimental evidence is reported, regarding the formation of a pair of co-rotating tip vortices by a split wing configuration, consisting of two half wings at equal and opposite angles of attack. Simultaneous measurements of the three-dimensional vector fields of velocity and vorticity were conducted on a cross plane at a downstream distance corresponding to 0.3 cord lengths (near wake), using an in-house constructed 12-sensor hot wire anemometry vorticity probe. The probe consists of three closely separated orthogonal 4-wire velocity sensor arrays, measuring simultaneously the three-dimensional velocity vector at three closely spaced locations on a cross plane of the flow filed. This configuration makes possible the estimation of spatial velocity derivatives by means of a forward difference scheme of first order accuracy. Velocity measurements obtained with an X-wire are also presented for comparison. In this near wake location, the flow field is dictated by the pressure distribution established by the flow around the wings, mobilizing large masses of air and leading to the roll up of fluid sheets. Fluid streams penetrating between the wings collide, creating on the cross plane flow a stagnation point and an “impermeable” line joining the two vortex centres. Along this line fluid is directed towards the two vortices, expanding their cores and increasing their separation distance. This feeding process generates a dipole of opposite sign streamwise mean vorticity within each vortex. The rotational flow within the vortices obligates an adverse streamwise pressure gradient leading to a significant streamwise velocity deficit characterizing the vortices. The turbulent flow field is the result of temporal changes in the intensity of the vortex formation and changes in the position of the cores (wandering).     

Streamwise Vortices and Velocity Streaks in a Locally Drag-Reduced Turbulent Boundary Layer

This work aims to understand the changes associated with the near-wall streaky structures in a turbulent boundary layer (TBL) where the local skin-friction drag is substantially reduced. The Reynolds number is R e _?? = 1000 based on the momentum thickness or R e _τ = 440 based on the friction velocity of the uncontrolled flow. The TBL is perturbed via a local surface oscillation produced by an array of spanwise-aligned piezo-ceramic (PZT) actuators and measurements are made in two orthogonal planes using particle image velocimetry (PIV). Data analyses are conducted using the vortex detection, streaky structure identification, spatial correlation and proper orthogonal decomposition (POD) techniques. It is found that the streaky structures are greatly modified in the near-wall region. Firstly, the near-wall streamwise vortices are increased in number and swirling strength but decreased in size, and are associated with greatly altered velocity correlations. Secondly, the velocity streaks grow in number and strength but contract in width and spacing, exhibiting a regular spatial arrangement. Other aspects of the streaky structures are also characterized; they include the spanwise gradient of the longitudinal fluctuating velocity and both streamwise and spanwise integral length scales. The POD analysis indicates that the turbulent kinetic energy of the streaky structures is reduced. When possible, our results are compared with those obtained by other control techniques such as a spanwise-wall oscillation, a spanwise oscillatory Lorentz force and a transverse traveling wave.     

Large-Scale Streamwise Vortices in the Supersonic Part of a Permeable Nozzle

Large-scale streamwise vortices in the vicinity of a perforated wall in the supersonic part of the nozzle are studied. The governing effect of gas inflow through a perforated wall on origination and parameters of streamwise vortices is experimentally established.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 68–75, September–October, 2005.     

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.     

Singularities in Three-Dimensional Compressible Euler Flows with Vorticity

It is known from earlier work that three-dimensional incompressible Euler flows with vorticity can develop a singularity in a finite time, at least if the initial conditions are of a certain class. Here we discuss corresponding possibilities for flows with compressibility. Naturally, it is known that the shock-wave phenomenon represents an important singular field in compressible fluid dynamics especially in the irrotational case. However, here we are concerned not with that phenomenon but rather with compressible flows where any singularity is associated with the presence of vorticity. In particular we expose the role played by the ratio of specific heats in an adiabatic flow field. Received 9 December 1996 and accepted 4 April 1997     

Unsteady Viscous Flows about Bodies: Vorticity Release and Forces

The force (drag and lift) exerted on a body moving in a viscous fluid is expressed via the free and bound vorticity moments, and the role of vortex shedding is discussed. The formulation encompasses classical, inviscid flows, and leads to efficient computational methods. Numerical results for a few prototype flows are presented.     

Effect of Streamline Curvature on Intensity of Streamwise Vortices in the Mixing Layer of Supersonic Jets

The structure of supersonic nonisobaric jets with Mach numbers M_a = 1 and 2 is considered experimentally to find the effect of streamline curvature on the evolution of streamwise vortices in the mixing layer. The spatial development of steady streamwise vortices in the mixing layer of supersonic jets is considered. A method for generation of steady streamwise vortices by applying microroughness elements of controlled size onto the inner surface of the nozzle is developed. Radial profiles and azimuthal variations of total pressure are obtained; the mixinglayer thickness and the curvature of streamlines in supersonic jets are determined. A significant effect of microroughness elements of prescribed shape located on the nozzle surface on the behavior of total pressure in the mixing layer of supersonic jets, as compared to natural disturbances, is obtained.     

New Answers on the Interaction Between Polymers and Vortices in Turbulent Flows

Numerical data of polymer drag reduced flows is interpreted in terms of modification of near-wall coherent structures. The originality of the method is based on numerical experiments in which boundary conditions or the governing equations are modified in a controlled manner to isolate certain features of the interaction between polymers and turbulence. As a result, polymers are shown to reduce drag by damping near-wall vortices and sustain turbulence by injecting energy onto the streamwise velocity component in the very near-wall region.     

Spatial Stationary Long Waves in Shear Flows

The system of integrodifferential equations describing the spatial stationary freeboundary shear flows of an ideal fluid in the shallowwater approximation is considered. The generalized characteristics of the model are found and the hyperbolicity conditions are formulated. A new class of exact solutions of the governing equations is obtained which is characterized by a special dependence of the desired functions on the vertical coordinate. The system of equations describing this class of solutions in the hyperbolic case is reduced to Riemann invariants. New exact solutions of the equations of motion are found.     

Existence and Uniqueness for Stochastic 2D Euler Flows with Bounded Vorticity

The strong existence and the pathwise uniqueness of solutions with \({L^{\infty}}\)-vorticity of the 2D stochastic Euler equations are proved. The noise is multiplicative and it involves the first derivatives. A Lagrangian approach is implemented, where a stochastic flow solving a nonlinear flow equation is constructed. The stability under regularizations is also proved.     

Anisotropy Invariant Reynolds Stress Model of Turbulence (AIRSM) and its Application to Attached and Separated Wall-Bounded Flows

Numerical predictions with a differential Reynolds stress closure, which in its original formulation explicitly takes into account possible states of turbulence on the anisotropy-invariant map, are presented. Thus the influence of anisotropy of turbulence on the modeled terms in the governing equations for the Reynolds stresses is accounted for directly. The anisotropy invariant Reynolds stress model (AIRSM) is implemented and validated in different finite-volume codes. The standard wall-function approach is employed as initial step in order to predict simple and complex wall-bounded flows undergoing large separation. Despite the use of simple wall functions, the model performed satisfactory in predicting these flows. The predictions of the AIRSM were also compared with existing Reynolds stress models and it was found that the present model results in improved convergence compared with other models. Numerical issues involved in the implementation and application of the model are also addressed.     

Symmetries, Invariance and Scaling-Laws in Inhomogeneous Turbulent Shear Flows

An approach to derive turbulent scaling laws based on symmetry analysis is presented. It unifies a large set of scaling laws for the mean velocity of stationary parallel turbulent shear flows. The approach is derived from the Reynolds averaged Navier–Stokes equations, the fluctuation equations, and the velocity product equations, which are the dyad product of the velocity fluctuations with the equations for the velocity fluctuations. For the plane case the results include the logarithmic law of the wall, an algebraic law, the viscous sublayer, the linear region in the centre of a Couette flow and in the centre of a rotating channel flow, and a new exponential mean velocity profile that is found in the mid-wake region of high Reynolds number flat-plate boundary layers. The algebraic scaling law is confirmed in both the centre and the near wall regions in both experimental and DNS data of turbulent channel flows. For a non-rotating and a moderately rotating pipe about its axis an algebraic law was found for the axial and the azimuthal velocity near the pipe-axis with both laws having equal scaling exponents. In case of a rapidly rotating pipe, a new logarithmic scaling law for the axial velocity is developed. The key elements of the entire analysis are two scaling symmetries and Galilean invariance. Combining the scaling symmetries leads to the variety of different scaling laws. Galilean invariance is crucial for all of them. It has been demonstrated that two-equation models such as the k– model are not consistent with most of the new turbulent scaling laws.     

Dispersion Equation for Water Waves with Vorticity and Stokes Waves on Flows with Counter-Currents

The two-dimensional free-boundary problem of steady periodic waves with vorticity is considered for water of finite depth. We investigate how flows with small-amplitude Stokes waves on the free surface bifurcate from a horizontal parallel shear flow in which counter-currents may be present. Two bifurcation mechanisms are described: one for waves with fixed Bernoulli’s constant, and the other for waves with fixed wavelength. In both cases the corresponding dispersion equations serve for defining wavelengths from which Stokes waves bifurcate. Necessary and sufficient conditions for the existence of roots of these equations are obtained. Two particular vorticity distributions are considered in order to illustrate the general results.     

Thermocapillary Vortices Induced by a Light Beam near a Bubble Surface in a Hele-Shaw Cell

This paper studies thermocapillary vortices induced by local heating of a bubble surface in a Hele-Shaw cell by a light beam. It is found that the vortex rotation frequency and its depth depend on the distance from the light-beam projection onto the layer to the bubble boundary. The surface velocity of the thermocapillary flow is calculated using the balance of the near-surface and return flows of the thermocapillary vortex and the equality of capillary and dynamic pressures. It is shown that a decrease in the surface velocity and the vortex rotation frequency with increase in the distance from the light beam to the bubble surface is due to a decrease in the temperature gradient between the illuminated and cold poles of the bubble.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 93–99, September–October, 2005.     

Stationary Flows of Shear Thickening Fluids in 2D

We investigate the steady flow of a shear thickening generalized Newtonian fluid under homogeneous boundary conditions on a domain in \mathbbR²{\mathbb{R}^{2}}. We assume that the stress tensor is generated by a potential of the form H = h (|e(u)|){H = h (|\varepsilon (u)|)}, e(u){\varepsilon (u)} denoting the symmetric part of the velocity gradient. We prove the existence of strong solutions for a large class of functions h having the property that h′ (t)/t increases (shear thickening case).     

Effect of the Streamwise Component of the Vorticity Formed in a Turbulent Jet Source on the Acoustic Characteristics of the Jet

The results of an experimental study of the effects of different nozzle heads on turbulent jet noise are analyzed. A configuration of four cylindrical heads, tabbed heads, and chevron nozzles are considered and the decreases in the acoustic-mechanical efficiency of the jet (acoustic power reduction) for jets exposed to different modes of action are compared.It is shown that the effects of tabbed and cylindrical heads, as well as of chevrons, share a common property which is associated with the occurrence of vorticity in the jet source and can be described on the basis of a unified criterion characterizing the action on both the jet flow structure and the jet noise.     

Effects of Compressibility and Shock-Wave Interactions on Turbulent Shear Flows

Compressibility effects are present in many practical turbulent flows, ranging from shock-wave/boundary-layer interactions on the wings of aircraft operating in the transonic flight regime to supersonic and hypersonic engine intake flows. Besides shock wave interactions, compressible flows have additional dilatational effects and, due to the finite sound speed, pressure fluctuations are localized and modified relative to incompressible turbulent flows. Such changes can be highly significant, for example the growth rates of mixing layers and turbulent spots are reduced by factors of more than three at high Mach number. The present contribution contains a combination of review and original material. We first review some of the basic effects of compressibility on canonical turbulent flows and attempt to rationalise the differing effects of Mach number in different flows using a flow instability concept. We then turn our attention to shock-wave/boundary-layer interactions, reviewing recent progress for cases where strong interactions lead to separated flow zones and where a simplified spanwise-homogeneous problem is amenable to numerical simulation. This has led to improved understanding, in particular of the origin of low-frequency behaviour of the shock wave and shown how this is coupled to the separation bubble. Finally, we consider a class of problems including side walls that is becoming amenable to simulation. Direct effects of shock waves, due to their penetration into the outer part of the boundary layer, are observed, as well as indirect effects due to the high convective Mach number of the shock-induced separation zone. It is noted in particular how shock-induced turning of the detached shear layer results in strong localized damping of turbulence kinetic energy.     

Linear Dynamics of Perturbations in Flows with Constant Horizontal Shear

The dynamics of perturbations in shallow water and incompressible stratified fluid flows with constant horizontal shear are described using the nonmodal analysis. It is shown that the shear flow perturbations can be divided into two classes on the basis of the potential vorticity: rapidly oscillating wave perturbations with zero potential vorticity and slow vortex perturbations with nonzero potential vorticity. In the cases of weak and strong shear the main features of the dynamics of wave and vortex perturbations are studied analytically (using the WKBG method) and numerically. It is shown that for large times the wave perturbation energy increases linearly, i.e., the shear flow is algebraically unstable due to the growth of rapid wave perturbations. This instability can be of importance in processes of turbulence development and surface and internal wave generation.