On the dynamics in a transitional boundary layer

IntroductionIll 1883 Professor Osborne Reynolds published in Philosopl1ical Transactions of the RoyalSociety the outcomes of his flow visua1ization at Manchester. These had shown that whetherthe flow in a pipe was direct to sinuous (or, as nowadays we would say, laminar to turbulent)depended on its Reynolds number. Transition from Iaminar to turbuIent flow becomes animportant probIem i1l fluid mechanics, which has attracted the interest of investigators fOrmore than l00 years. The partic…     

Occurrence of Taylor vortices in the flow between two rotating conical cylinders

The behavior of the flow between two coaxial conical cylinders with the inner one rotating and the outer one stationary is studied numerically. Special attention is paid to the occurrence of Taylor vortices in basic flow and unsteady helical vortices. It is found that, in basic flow, the vortices occur in the direction toward smaller radius, while toward bigger radius in unsteady helical vortices; moreover, the unsteady helical vortices can coexist with unstable steady Taylor vortices. The results suggest that the behavior of conical flow is dominated by a competition between the meridional flow and radial flow. The effect of meridional flow is most significant at small apex angle or in basic flow and helical vortices, while the radial flow dominates the structure at larger apex angle or in steady vortical flow. In order to get better understanding the competition and the transition of Taylor–Couette flow to conical flow, a velocity angle related to velocity components is defined, and the pattern evolution of velocity, streamlines and the velocity angle are examined with respect to apex angle, as well as Reynolds number. Finally, the statistical properties of turbulent conical flow are investigated.     

Multidimensional turbulence spectra – Statistical analysis of turbulent vortices

Strong nonlinear or very fast phenomena such as mixing, coalescence and breakup in chemical engineering processes, are not correctly described using average turbulence properties. Since these phenomena are modeled by the interaction of fluid particles with single or paired vortices, distribution of the properties of individual turbulent vortices should be studied and understood. In this paper, statistical analysis of turbulent vortices was performed using a novel vortex tracking algorithm. The vortices were identified using the normalized Q-criterion with extended volumes calculated using the Biot–Savart law in order to capture most of the coherent structure related to each vortex. This new and fast algorithm makes it possible to estimate the volume of all resolved vortices. Turbulence was modeled using large-eddy simulation with the dynamic Smagorinsky–Lilly subgrid scale model for different Reynolds numbers. Number density of turbulent vortices were quantified and compared with different models. It is concluded that the calculated number densities for vortices in the inertial subrange and also for the larger scales are in very good agreement with the models proposed by Batchelor and Martinez-Bazán. Moreover, the associated enstrophy within the same size of coherent structures is quantified and its distribution is compared to models for distribution of turbulent kinetic energy. The associated enstrophy within the same size of coherent structures has a wide distribution that is normal distributed in the logarithmic scale.     

Vortex breakdown in turbulent pipe flows

In many technical applications turbulent flows with embedded slender vortices exist. Depending on the boundary conditions vortex breakdown can occur. The purpose of this work is to develop and implement a solution scheme for large‐eddy simulations of vortex breakdown in turbulent pipe flows. One of the main problems in this simulation is the formulation of the inflow boundary condition for a fully developed turbulent flow with an embedded vortex. For that purpose a rescaling technique is developed in which a solution at a downstream location is inserted at the inflow boundary after an appropriate rescaling. To determine rescaling laws for pipe flows with an embedded vortex, analytical velocity profiles of swirling flows are first prescribed in a laminar flow. From the spatial development of the vortex a scaling law is deduced. In a next step this procedure is to be transferred to turbulent flows.     

Wavelet filtering to study mixing in 2D isotropic turbulence

This paper presents the application of coherent vortex simulation (CVS) filtering, based on an orthogonal wavelet decomposition of vorticity, to study mixing in 2D homogeneous isotropic turbulent flows. The Eulerian and Lagrangian dynamics of the flow are studied by comparing the evolution of a passive scalar and of particles advected by the coherent and incoherent velocity fields, respectively. The former is responsible for strong mixing and produces the same anomalous diffusion as the total flow, due to transport by the coherent vortices, while mixing in the latter is much weaker and corresponds to classical diffusion.     

A numerical study on statistical temporal scales in inertia particle dispersion

The statistical temporal scales involved in inertia particle dispersion are analyzed numerically. The numerical method of large eddy simulation, solving a filtered Navier-Stokes equation, is utilized to calculate fully developed turbulent channel flows with Reynolds numbers of 180 and 640, and the particle Lagrangian trajectory method is employed to track inertia particles released into the flow fields. The Lagrangian and Eulerian temporal scales are obtained statistically for fluid tracer particles and three different inertia particles with Stokes numbers of 1, 10 and 100. The Eulerian temporal scales, decreasing with the velocity of advection from the wall to the channel central plane, are smaller than the Lagrangian ones. The Lagrangian temporal scales of inertia particles increase with the particle Stokes number. The Lagrangian temporal scales of the fluid phase ‘seen’ by inertia particles are separate from those of the fluid phase, where inertia particles travel in turbulent vortices, due to the particle inertia and particle trajectory crossing effects. The effects of the Reynolds number on the integral temporal scales are also discussed. The results are worthy of use in examining and developing engineering prediction models of particle dispersion.     

Turbulent Flow with Embedded Vortical Structures Induced by Vortex Generators in a Cascade

Presented work is the next step after several experimental examinations of vortex generator influence on a flow separation occurring on a model of the NACA 63A421 airfoil with deflected simple flap. In this stage of research the vortices produced by vortex generators (VGs) were studied using Particle Image Velocimetry technique (PIV) and numerical simulations. Vane type VGs with two spacings among VGs pairs in straight channel with turbulent flow were tested. The average velocity flow field, peak of vorticity and circulation decay downstream of VGs were evaluated. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Investigation of physiological pulsatile flow in a model arterial stenosis using large-eddy and direct numerical simulations

Physiological pulsatile flow in a 3D model of arterial stenosis is investigated by using large eddy simulation (LES) technique. The computational domain chosen is a simple channel with a biological type stenosis formed eccentrically on the top wall. The physiological pulsation is generated at the inlet using the first harmonic of the Fourier series of pressure pulse. In LES, the large scale flows are resolved fully while the unresolved subgrid scale (SGS) motions are modelled using a localized dynamic model. Due to the narrowing of artery the pulsatile flow becomes transition-to-turbulent in the downstream region of the stenosis, where a high level of turbulent fluctuations is achieved, and some detailed information about the nature of these fluctuations are revealed through the investigation of the turbulent energy spectra. Transition-to-turbulent of the pulsatile flow in the post stenosis is examined through the various numerical results such as velocity, streamlines, velocity vectors, vortices, wall pressure and shear stresses, turbulent kinetic energy, and pressure gradient. A comparison of the LES results with the coarse DNS are given for the Reynolds number of 2000 in terms of the mean pressure, wall shear stress as well as the turbulent characteristics. The results show that the shear stress at the upper wall is low just prior to the centre of the stenosis, while it is maximum in the throat of the stenosis. But, at the immediate post stenotic region, the wall shear stress takes the oscillating form which is quite harmful to the blood cells and vessels. In addition, the pressure drops at the throat of the stenosis where the re-circulated flow region is created due to the adverse pressure gradient. The maximum turbulent kinetic energy is located at the post stenosis with the presence of the inertial sub-range region of slope −5/3.     

Computational fluid dynamics simulation of fluid particle fragmentation in turbulent flows

A simulation methodology is presented that allows detailed studies of the breakup mechanism of fluid particles in turbulent flows. The simulations, based on large eddy and volume of fluid simulations, agree very well with high-speed measurements of the breakup dynamics with respect to deformation time and length scales, and also the resulting size of the daughter fragments. The simulations reveal the size of the turbulent vortices that contribute to the breakup and how fast the interaction and energy transfer occurs. It is concluded that the axis of the deformed particle and the vortex core axis are aligned perpendicular to each other, and that breakup sometimes occurs due to interaction with two vortices at the same time. Analysis of the energy transfer from the continuous phase turbulence to the fluid particles reveals that the deformed particle attains it maximum in interfacial energy before the breakup is finalized. Similar to transition state theory in chemistry this implies that an activation barrier exists. Consequently, by considering the dynamics of the phenomenon, more energy than required at the final stage needs to be transferred from the turbulent vortices for breakup to occur. This knowledge helps developing new, more physical sound models for the breakup phenomenon required to solve scale separation problems in computational fluid dynamics simulations.     

Large eddy simulation and PIV experiments of air–water mixing tanks

The simulations and experiments of a turbulent bubbly flow are carried out in a cylindrical mixing vessel. Dynamics of the turbulent bubbly flow is visualized using a novel two-phase particle image velocimetry (PIV) with a combination of back lighting, digital masking and fluorescent tracer particles. Using an advanced technique, Mie’s scattering at surfaces of bubbles is totally filtered out and, henceforth, images of tracer particles and of bubbles are obtained with high quality. In parallel to the comprehensive experimental studies, numerical results are obtained from large eddy simulations (LES) of the two-phase air–water mixer. The impeller-induced flow at the blade tip radius is modeled by using sliding mesh method. The results demonstrate the existence of large structures such as tip-vortex tips, and also some finer details. In addition, the stability of the jet is found to be connected with the fluctuations of the tip vortices whose dynamics are affected by the presence of bubbles. Numerical results are used to interpret the measurement data and to guide the refinement of consistent theoretical analyses. Such information is invaluable in the development of advanced theories capable of describing bubbly flows in the presence of complex liquid flow. This detailed information is of real significance in facilitating the design and scale-up of practical stirred tanks.     

Incorporating dust lift-off into a CFD model of a blast furnace gravity dust-catcher

A gravity dust-catcher separates a mixture of dusts from the spent top gas flow of a blast furnace. These dusts are predominantly made up of limestone, iron ore and coke/coal. As a result of the turbulent gas flow patterns within a dust-catcher, modelling of the flow pattern can be very complex, attributed to the turbulent vortices that can be formed within the main body of the structure. Using data from an experimental prototype test rig, a simple model to capture the lift-off characteristics of particle lift-off from dust pile surfaces is created and incorporated into a computational fluid dynamics (CFD) model of the dust-catcher.The variation of particle separation performance over a typical blast furnace (BF) operational cycle is analysed. An attempt is made to explain the observed phenomena in terms of particle–fluid interaction. It is found that particle separation efficiency is largely unaffected by dust lift-off at low dust-catcher hopper fullness levels, but is significant at higher levels. It is found that the topography of the dust surface is important when predicting particle lift-off trends. It is concluded that this is due to the exposure experienced by a given particle when subjected to a surface velocity.     

细长体截面绕流的稳定性及扰动的影响

应用拓扑结构的稳定性理论,分析了细长旋成体截面绕流的结构稳定性．在分析时取极限流线作为流场的内边界,并证明极限流线的鞍点-鞍点连接是拓扑结构稳定的A·D2通过分析发现,由于旋成体背涡的发展,导致截面流场拓扑结构变化,由稳定对称旋涡流态变成不稳定对称旋涡流态．此时流场中存在空间的鞍点-鞍点连接的不稳定拓扑结构,在小扰动下出现分叉,变成稳定非对称旋涡流态,形成非对称背涡．并应用开折理论分析了扰动对流场结构的影响．     

Large eddy simulation of coherent structures in rectangular methane non-premixed flame

Large eddy simulation of a three-dimensional spatially developing transitional free methane non-premixed flame is performed. The solver of the governing equations is based upon a projection method. The Smagorinsky model is utilized for the turbulent subgrid scale terms. A global reaction mechanism is applied for the simulation of methane/air combustion. Simulation results clearly illustrate the coherent structure of the rectangular non-premixed flame, consisting of three distinct zones in the near field. Periodic characteristics of the coherent structures in the rectangular non-premixed flame are discussed. The predicted structure of the flame is in good agreement with the experimental results. Distributions of species concentrations across the flame surfaces are illustrated and typical flame structures in the far field are analyzed. Local mass fraction analysis and flow visualization indicate that the black spots of the flames are due to strong entrainment of oxygen into the central jet by streamwise vortices, and breaking up of the flame is caused by an enormous amount of entrainment of streamwise vortices as well as stretching of spanwise vortices at the bottom of the flame.     

The Motion of a Vortex Pair in a Stratified Atmosphere

The movement of a horizontal vortex pair through an inhomogeneous fluid is considered. The problem is formulated first for the case when the ambient fluid is uniform, the fluid moving with the vortex pair has a different density, and the motion is supposed laminar and inviscid. An approximate solution is obtained, which predicts that the distance between the vortices stays constant and the vortices accelerate at a constant rate. This solution is then applied to motion in a stratified atmosphere and it is found that the vortices oscillate vertically with a frequency and amplitude depending on the initial conditions and the stratification. Finally, approximate equations are constructed to describe the effects of turbulent entrainment into the fluid moving with the vortex pair, and an estimate of the damping is obtained.     

Trajectory statistics and turbulence evolution

The aim of this paper is to understand the tendency to organization of the turbulence in two-dimensional ideal fluids. A different perspective on vorticity separation and on the inverse cascade of energy yields from this study. Trajectory trapping or eddying appears to be strongly connected to these nonlinear processes. The statistics of the trajectories of the vorticity elements in a turbulent state is studied using a semi-analytic method. We show that the separation of the positive and negative vorticities is due to the attraction produced by a large scale vortex on the small scale vortices of the same sign. More precisely, a large scale velocity is shown to determine average transverse drifts, which have opposite orientations for positive and negative vorticity. They appear only in the presence of trapping and lead to energy flow to large scales due to the increase of the circulation of the large vortex. Recent results on drift turbulence evolution in magnetically confined plasmas are discussed in order to underline the idea that there is a link between the inverse cascade and trajectory trapping. The physical mechanisms are different in fluids and plasmas due to the different types of nonlinearities of the two systems, but trajectory trapping has the main role in both cases.     

Large eddy simulation of an ethylene-air turbulent premixed V-flame

Large eddy simulation (LES) using a dynamic eddy viscosity subgrid scale stress model and a fast-chemistry combustion model without accounting for the finite-rate chemical kinetics is applied to study the ignition and propagation of a turbulent premixed V-flame. A progress variable c-equation is applied to describe the flame front propagation. The equations are solved two dimensionally by a projection-based fractional step method for low Mach number flows. The flow field with a stabilizing rod without reaction is first obtained as the initial field and ignition happens just upstream of the stabilizing rod. The shape of the flame is affected by the velocity field, and following the flame propagation, the vortices fade and move to locations along the flame front. The LES computed time-averaged velocity agrees well with data obtained from experiments.     

Quasimolecular modelling of turbulent and nonturbulent vortices

A quasimolecular, particle model is developed for simulating both turbulent and nonturbulent vortices. The approach uses n-body modeling with molecular-type force interactions. Large systems of second-order, ordinary differential equations are generated and solved numerically. Serial and vector computer examples are described and discussed.     

On the dynamics of the vortex structures generated by plasma DBD actuator

The plasma actuator is used to generate pseudo-periodical vortices moving almost parallel to the wall under various settings of high-voltage high-frequency power AC. Low-frequency amplitude modulation is desired to generate vortices, otherwise wall-jet-like flow is present. It will be shown how the dynamics of generated coherent vortices alternates depending on generator setting, frequency spectrum will be introduced in dependency on frequency of amplitude modulation and duty cycle. Measurements will be performed using TR-PIV technique or HW anemometry across wall-jet flow. The generated flow patterns are to be applied for control of boundary layers. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)