Intrinsic and extrinsic vortex nucleation mechanisms in the flow

We propose very general vortex nucleation mechanisms[1] analogous to a hydrodynamic instability and calculate associated critical velocity in agreement with experiments. The creation of vortices via extrinsic mechanism is driven by a formation of the surface vorticity sheet created by the flow, which reaches a critical size. Such a sheet screens an attraction of a half-vortex ring to the wall, the barrier for the vortex nucleation disappears and the vortex nucleation is started. In the intrinsic mechanism the creation of a big vortex ring, which transforms into the vortex, is driven by a fluctuative generation of small vortex rings.     

Intrinsic and extrinsic vortex nucleation mechanisms in the flow

We propose very general vortex nucleation mechanisms[1] analogous to a hydrodynamic instability and calculate associated critical velocity in agreement with experiments. The creation of vortices via extrinsic mechanism is driven by a formation of the surface vorticity sheet created by the flow, which reaches a critical size. Such a sheet screens an attraction of a half-vortex ring to the wall, the barrier for the vortex nucleation disappears and the vortex nucleation is started. In the intrinsic mechanism the creation of a big vortex ring, which transforms into the vortex, is driven by a fluctuative generation of small vortex rings. Work supported by NORDITA and Landau Institute     

矩形通道内层流对流换热的最优速度场

针对矩形通道内的层流对流换热问题,通过数值求解速度场协同方程,得到了给定黏性耗散条件下通道内的最优速度场为多纵向涡的流动结构,表明多纵向涡流型可在流阻增加不多的情况下使换热显著强化.通过在通道壁面布置不连续双斜肋,在通道内产生了接近于最优速度场的多纵向涡流动,数值计算结果表明,在Re=1000时,与光滑通道相比,不连续...     

The generation of wind waves on clean water and in the presence of an oil film

The conditions of the resonant excitation of waves on a liquid surface by a horizontal air flow that has a decreasing velocity in the direction of motion were established, such that steady waves occurred when the period of the escape of a chain of eddies that is generated in a viscous layer of an air flow coincided with the period of natural oscillations, which is determined by the dispersion relationship for a group of waves. The dependence of the lengths of steady waves on the air-flow velocity over the surface of clean water and water with a light oil film was obtained. The resulting model was tested experimentally.     

Stable periodic vortex shedding studied using computational fluid dynamics, laser sheet flow visualization, and MR imaging

Recirculating and detached flow patterns close to the carotid bifurcation are thought to play an important role in the development of carotid stenoses by promoting atherosclerosis. The aim of this study was to investigate a flow regime with strong transient characteristics, including vortex shedding and transport to develop methodologies appropriate to the analysis of carotid stenoses. The existence of a regular periodic vortex street behind a cylindrical flow obstruction was predicted and analysed in detail by Theodore van Karman in the early 20th century. This model was chosen in our study for both ease of phantom construction and of theoretical modelling using finite element computational fluid dynamics (CFD). The results of the theoretical calculations have been compared with two methods of flow visualization-laser sheet imaging and real-time echo planar magnitude MR imaging. Flow was investigated over a range of Reynold's number from 40 through 400 through which vortex shedding is predicted. Good overall agreement was obtained between the theoretical (16 mm-CFD) and experimental (16+/-2 mm-Laser, 17+/-2 mm-MRI) estimates of the Karman Vortex street wavelength for a Reynolds number of 200.     

Three-dimensional mixed convection flow with variable thermal conductivity and frictional heating

In this article,three-dimensional mixed convection flow over an exponentially stretching sheet is investigated.Energy equation is modelled in the presence of viscous dissipation and variable thermal conductivity.Temperature of the sheet is varying exponentially and is chosen in a form that facilitates the similarity transformations to obtain self-similar equations.Resulting nonlinear ordinary differential equations are solved numerically employing the Runge-Kutta shooting method.In order to check the accuracy of the method,these equations are also solved using bvp4c built-in routine in Matlab.Both solutions are in excellent agreement.The effects of physical parameters on the dimensionless velocity field and temperature are demonstrated through various graphs.The novelty of this analysis is the self-similar solution of the threedimensional boundary layer flow in the presence of mixed convection,viscous dissipation and variable thermal conductivity.     

Nonlinear development of instabilities in supersonic vortex sheets: I. The basic kink modes

Classical linearized stability analysis predicts (neutral) stability of supersonic vortex sheets for compressible flow with normalized Mach numbers, M > √2, while recent detailed numerical simulations by Woodward indicate the nonlinear development of instabilities for M > √2 through the development and interaction of propagating kink modes in the slip-stream. These kink modes are discontinuities in the slip-stream bracked by shock waves and rarefaction waves which grow self-similarly in time. In this paper, the apparent paradox is resolved by developing appropriate small amplitude high frequency nonlinear time-dependent asymptotic perturbed solutions which yield the response to a very small amplitude nonlinear planar sound wave incident on the vortex sheet. The analysis leads to three specific angles of incidence depending on M > √2 where nonlinear resonance occurs. For these three special resonant angles of incidence the perturbation expansions automatically yield simplified equations. These equations involve an appropriate Hamilton-Jacobi equation for the perturbed vortex sheet location; the derivative of the solution of this Hamilton-Jacobi equation provides boundary data for two nonlinear Burgers transport equations for the sound wave emanating from the two sides of the vortex sheet. These equations are readily solved exactly and lead to the quantitative time-dependent nonlinear development of three different types of kink modes with a structure similar to that observed by Woodward.     

Scattering and absorption of sound at flow duct expansions

The scattering of plane acoustic waves at area expansions in flow ducts is analysed using the vortex sheet model where the flow at the expansion is modelled as a jet, with a vortex sheet emanating from the edge. Of particular interest is the influence of the flow field on acoustic scattering and absorption.First, it is demonstrated that the stability properties of the shear layer can be simulated by modifying the edge condition within the vortex sheet model. To this end the accuracy for the region where the shear layer is changing from unstable to stable is improved by introducing a gradually relaxed Kutta edge condition with empirically derived coefficients. For low Strouhal numbers the vortex sheet model applies and for higher Strouhal numbers the two models converge.Second, it is demonstrated that the acoustic transmission through the jet expansion region can be determined by neglecting the scattering there. Incorporating this assumption, the vortex sheet model reproduces well the experimental results on transmission and absorption for an area expansion. This result supports the assumption that the main part of the scattering occurs at the area expansion at least for the low-frequency range. Furthermore, the influence of the flow field is particularly strong for small Strouhal numbers.     

Sound scattering by a Karman street consisting of large-scale vortices

The scattering of acoustic waves by a vortex street formed behind a cylinder in an air flow is studied both theoretically and experimentally for the case of the sound wavelength being much less than the vortex size. The theoretical calculations show that, at flow velocities well below the sound velocity, the vortex street can be considered as a moving phase screen. The spectrum of scattered sound in the far zone is shown to consist of harmonics whose frequencies differ by a multiple of the vortex rate. The computational results agree well with the experimental data obtained for the diffraction of ultrasound of the wavelength λ=3 mm by the Karman street formed behind a circular cylinder with an 8 mm diameter at a flow velocity of 7 m/s.     

Helicity generation in uniform helical flows

Helicity generation conditions are derived for helical flows of Joukowski type with allowance for effects due to viscosity, buoyancy, temperature nonuniformity, and solid-body rotation. The upper and lower limits are determined for the rotation-frequency interval in which helicity can be generated by viscous forces. These conditions correspond to the regime of an isolated tornado-like vortex. An exact solution to the time-independent equations of motion for inviscid incompressible flow is obtained. The solution describes a generalized Kelvin-Helmholtz vortex having the form of a localized cylindrical vortex with nontrivial stable topological vortex-core structure determined by a finite value of helicity. For linear traveling inertia waves, which must have uniform helical structure, a general representation is found that characterizes helical structures of different origin.     

Cherenkov radiation emitted by a vortex into an anisotropic dielectric

The fields produced by a Josephson vortex moving in a sandwich placed into an anisotropic dielectric are investigated. When the vortex velocity exceeds the velocity of light in the direction of the normal to the sandwich surface, Cherenkov emission of electromagnetic waves propagating from the sandwich to the bulk of the dielectric takes place. The Poynting vector of outgoing waves is determined. It is shown that the radiation directivity considerably depends on the degree of anisotropy in the permittivity. The radiation loss power of the vortex is determined, and the relation between the transport current and the vortex velocity is established.     

A fast resurrected core-spreading vortex method with no-slip boundary conditions

To simulate two-dimensional viscous incompressible flows based on a scheme of blob splitting and merging, we developed a vortex method and employed a fast multipole method to speed the computation of velocities. The diffusion of the vortex sheet induced at a solid wall by the no-slip boundary conditions is first modeled according to the analytical solution of Koumoutsakos and then converted into discrete blobs in the vicinity of the wall. To prevent the vorticity from entering the solid body, we introduce a concept residual circulation in a sense that only a partial circulation of the vortex sheet is diffused into the flow field; the rest remains at the wall. Blobs near the wall are thus avoided. Blobs near the wall that might cause large fluctuations in the strength of the vortex sheet are handled similarly. The solver thus developed requires no grid-based remeshing. We applied this solver to simulate the flow induced with an impulsively initiated circular cylinder; the results agree satisfactorily with those of previous experimental and numerical investigations.     

Visualisation and analysis of large-scale vortex structures in three-dimensional turbulent lid-driven cavity flow

In this paper, large eddy simulation (LES) of a three-dimensional turbulent lid-driven cavity (LDC) flow at Re = 10,000 has been performed using the multiple relaxation time lattice Boltzmann method. A Smagorinsky eddy viscosity model was used to represent the sub-grid scale stresses with appropriate wall damping. The prediction for the flow field was first validated by comparing the velocity profiles with previous experimental and LES studies, and then subsequently used to investigate the large-scale three-dimensional vortical structures in the LDC flow. The instantaneous three-dimensional coherent structures inside the cavity were visualised using the second invariant (Q), Δ criterion, λ₂ criterion, swirling strength (λ_ci) and streamwise vorticity. The vortex structures obtained using the different criteria in general agree well with each other. However, a cleaner visualisation of the large vortex structures was achieved with the λ_ci criterion and also when the visualisation is based on the vortex identification criteria expressed in terms of the swirling strength parameters. A major objective of the study was to perform a three-dimensional proper orthogonal decomposition (POD) on the fluctuating velocity fields. The higher energy POD modes efficiently extracted the large-scale vortical structures within the flow which were then visualised with the swirling strength criterion. Reconstruction of the instantaneous fluctuating velocity field using a finite number of POD modes indicated that the large-scale vortex structures did effectively approximate the large-scale motion. However, such a reduced order reconstruction of the flow based on the large-scale vortical structures was clearly not as effective in predicting the small-scale details of the fluctuating velocity field which relate to the turbulent transport.     

Simulating the dynamics of flexible bodies and vortex sheets

We present a numerical method for the dynamics of a flexible body in an inviscid flow with a free vortex sheet. The formulation is implicit with respect to body variables and explicit with respect to the free vortex sheet. We apply the method to a flexible foil driven periodically in a steady stream. We give numerical evidence that the method is stable and accurate for a relatively small computational cost. A continuous form of the vortex sheet regularization permits continuity of the flow across the body’s trailing edge. Nonlinear behavior arises gradually with respect to driving amplitude, and is attributed to the rolling-up of the vortex sheet. Flow quantities move across the body in traveling waves, and show large gradients at the body edges. We find that in the small-amplitude regime, the phase difference between heaving and pitching which maximizes trailing edge deflection also maximizes power output; the phase difference which minimizes trailing edge deflection maximizes efficiency.     

On calculation of the rate of mass transfer by periodic waves propagating over the surface of a viscous liquid

A generalization of the Stokes classical drift model describing mass transfer by periodic waves propagating over the surface of an infinitely deep incompressible liquid to the case of a viscous liquid is constructed. An analytic expression is proposed for the velocity of an additional flow into which the liquid is involved by horizontal viscous shear stresses emerging between adjacent horizontal layers of the liquid participating in the drift.     

Dissipation in the dynamics of a moving contact line: effect of the substrate disorder

We investigate the time-dependent flow of water around a solid triangular profile oscillating horizontally in a narrow rectangular container. The flow is quasi two-dimensional and using particle image velocimetry we measure 20 snapshots of the entire velocity field during a period of oscillation. From the velocity measurements we obtain the circulation of the vortices and study the vortex dynamics. The time-dependence of the flow gives rise to the formation of a jet-like flow structure which enhances the vorticity production compared to the time-independent case. We introduce a simple phenomenological model to describe the important dynamical parameters of the flow, i.e., the vortex circulation and the jet velocity. We solve the model analytically without viscous damping and find good agreement between the model predictions and our measurements. Our work adds to the recent effort to understand more complicated flows past sand-ripples and insect wings.Received: 6 January 2004, Published online: 20 April 2004PACS: 47.32.Cc Vortex dynamics - 47.32.Ff Separated flows     

Sound generated by a vortex convected past an elastic sheet

We study the motion and sound generated when a line vortex is convected in a uniform low-Mach flow parallel to a thin elastic sheet. The linearized sheet motion is analyzed under conditions where the unforced sheet (in the absence of the line vortex) is stationary. The vortex passage above the sheet excites a resonance mode of motion, where the sheet oscillates at its least stable eigenmode. The sources of sound in the acoustic problem include the sheet velocity and fluid vorticity. It is shown that the release of trailing-edge vortices, resulting from the satisfaction of the Kutta condition, has two opposite effects on sound radiation: while trailing-edge vortices act to reduce the pressure fluctuations occurring owing to the direct interaction of the line vortex with the unperturbed sheet, they extend and amplify the acoustic signal produced by the motion of the sheet. The sheet motion radiates higher sound levels as the system approaches its critical conditions for instability, where the effect of resonance becomes more pronounced. It is argued that the present theory describes the essential mechanism by which sound is generated as a turbulent eddy is convected in a mean flow past a thin elastic airfoil.     

New thermodynamics of entropy generation minimization with nonlinear thermal radiation and nanomaterials

This research addressed entropy generation for MHD stagnation point flow of viscous nanofluid over a stretching surface. Characteristics of heat transport are analyzed through nonlinear radiation and heat generation/absorption. Nanoliquid features for Brownian moment and thermophoresis have been considered. Fluid in the presence of constant applied inclined magnetic field is considered. Flow problem is mathematically modeled and governing expressions are changed into nonlinear ordinary ones by utilizing appropriate transformations. The effects of pertinent variables on velocity, nanoparticle concentration and temperature are discussed graphically. Furthermore Brownian motion and thermophoresis effects on entropy generation and Bejan number have been examined. Total entropy generation is inspected through various flow variables. Consideration is mainly given to the convergence process. Velocity, temperature and mass gradients at the surface of sheet are calculated numerically.     

A reliable treatment of the homotopy analysis method for viscous flow over a non-linearly stretching sheet in presence of a chemical reaction and under influence of a magnetic field

The similarity solution for the steady two-dimensional flow of an incompressible viscous and electrically conducting fluid over a non-linearly semi-infinite stretching sheet in the presence of a chemical reaction and under the influence of a magnetic field gives a system of non-linear ordinary differential equations. These non-linear differential equations are analytically solved by applying a newly developed method, namely the Homotopy Analysis Method (HAM). The analytic solutions of the system of non-linear differential equations are constructed in the series form. The convergence of the obtained series solutions is carefully analyzed. Graphical results are presented to investigate the influence of the Schmidt number, magnetic parameter and chemical reaction parameter on the velocity and concentration fields. It is noted that the behavior of the HAM solution for concentration profiles is in good agreement with the numerical solution given in reference [A. Raptis, C. Perdikis, Int. J. Nonlinear Mech. 41, 527 (2006)].