Vortex Growth Research Articles

Spatio-temporal and modal analysis of unsteady fluctuations in a high-subsonic base flow

The high-subsonic flow over an axisymmetric backward facing step is investigated at a Mach number of 0.7, with high-speed particle image velocimetry operating at acquisition frequency up to 20 kHz to resolve the time dependent behavior of the separated flow in the longitudinal plane. The statistical flow properties such as the approaching boundary layer thickness, mean and fluctuating velocity field and shear layer growth are quantified. It is found that the shear layer growth is nearly linear up to x/D = 0.6; downstream this location, the reattachment surface influences the shear layer growth rate, causing it to decrease. The visualization of the high-speed measurements shows a quasi-cyclic behavior of the separated region characterized by a fluctuation of the flow reattachment location. The growing and shrinking of the separated region is accompanied by large-scale fluctuations that dominate the flow motions and the momentum exchange across the shear layer. The analysis of the large-scale fluctuations based on proper orthogonal decomposition (POD) of the velocity field indicates that the separated region exhibits pulsating behaviour as associated to the highest energy mode. The second and third modes are approximately in phase quadrature and can be associated to the growth of large azimuthal vortices that undulate the shear layer approaching the mean reattachment location. Conditional averaging of the data indicates that the second/third mode is associated to either the entrainment of high momentum fluid or ejection of low momentum fluid from the separated region depending on the phase. The high-speed measurements enable the spectral analysis of the velocity; the power spectral density of the POD time coefficients for the first three modes is evaluated. The first mode associated to pulsatile growth and collapse of the separated region yields a dominant frequency at StrD = 0.13 (f = 585 Hz) while the second mode features a broader frequency distribution in the range from 1 to 3 kHz (0.22 < StrD < 0.67) with a distinguishable peak at StrD = 0.4. The dynamical correlation between these two modes shows that time derivative of the first mode temporal coefficient and second mode coefficient are strongly correlated. This suggests that the entrainment of high momentum fluid into the separated region is responsible for the wake growth phenomenon.

PIV-based load investigation in dynamic stall for different reduced frequencies

Measuring the aerodynamic loads on dynamic objects in small wind tunnels is often challenging. In this regard, fast-response particle image velocimetry (PIV) data are post-processed using advanced tools to calculate aerodynamic loads based on the control-volume approach. For dynamic stall phenomena, due to the existence of dynamic stall vortices and significant load changes over a short time interval, applying the control-volume technique is difficult in particular for drag estimation. In this study, an examination of the dynamic stall phenomena of an oscillating SD7037 airfoil is reported for a reduced frequency range of \(0.05\le k \le 0.12\) when \(Re=4\times 10^{4}\). A numerical simulation is utilized as an alternative method for comparison and agrees well with the experimental results. The results suggest that loads can be determined accurately if the spatial resolution satisfies the reduced frequency increment. Minimizing the control-volume works best for lift determination. For the drag calculation, it was found that the location of the downstream boundary should be placed where it was not disturbed with wake vortices. The high-velocity gradients of the wake vortices increase the error level along the downstream boundary for the drag calculation but not for the lift estimation. Beside the load calculation, high-resolution PIV velocity fields also reveal insights into the effects of reduced frequency on dynamic flow behavior including the pitch angle range for vortex growth (between vortex generation and pinch-off), phase delay and number of vortices. These observations agree well with the load curve behavior.

A study of the transient dynamics of perturbations in Keplerian discs using a variational approach

We study linear transient dynamics in a thin Keplerian disc employing a method based on variational formulation of optimisation problem. It is shown that in a shearing sheet approximation due to a prominent excitation of density waves by vortices the most rapidly growing shearing harmonic has azimuthal wavelength, $\lambda_y$, of order of the disc thickness, $H$, and its initial shape is always nearly identical to a vortex having the same potential vorticity. Also, in the limit $\lambda_y\gg H$ the optimal growth $G\propto (\Omega/\kappa)^4$, where $\Omega$ and $\kappa$ stand for local rotational and epicyclic frequencies, respectively, what suggests that transient growth of large scale vortices can be much stronger in areas with non-Keplerian rotation, e.g. in the inner parts of relativistic discs around the black holes. We estimate that if disc is already in a turbulent state with effective viscosity given by the Shakura parameter $\alpha<1$, the considered large scale vortices with wavelengths $H/\alpha>\lambda_y>H$ have the most favourable conditions to be transiently amplified before they are damped. At the same time, turbulence is a natural source of the potential vorticity for this transient activity. We extend our study to a global spatial scale showing that global perturbations with azimuthal wavelengths more than an order of magnitude greater than the disc thickness still are able to attain the growth of dozens of times in a few Keplerian periods at the inner boundary of disc.

Time–Weissenberg number superposition in planar contraction microchannel flows

The flow of viscoelastic fluids in a micro-fabricated 4:1 planar contraction channel was studied through flow visualization. As the Weissenberg number (Wi) increased, the flow developed from a Newtonian-like to vortex growth, and the transient start-up flow at high Wi was found to experience all the steady patterns at lower Wi flows. The flow sequence was different depending on the fluids and channel dimensions, however, in all the cases we could reach, the steady patterns at a low Wi flow could be matched 1:1 with the transient patterns at a high Wi flow. The plot of Wi and time when the two sets (transient and steady) were matched showed a clear functional relationship, from which the time–Weissenberg number superposition could be confirmed.

Vorticity amplification near the stagnation point of landing gear wheels

The vicinity near the forward stagnation point of landing-gear wheels has been found to support a mechanism for oncoming streams of weak vorticity to collect, grow, and amplify into discrete large-scale vortical structures that then shed with a distinct periodicity. To the authors’ knowledge, such a flow phenomenon has never been reported before for landing gear wheels, which are in essence finite (three-dimensional) cylinders. To gain further insight into this phenomenon, a detailed experimental study has been undertaken employing the hydrogen bubble visualization and Particle Image Velocimetry techniques. A very thin platinum wire, similar to those used in hydrogen bubble visualization applications, was placed upstream of the wheel model to produce two streams of weak vorticity (with opposite sign) that convected toward the model. As the vorticity streams enter the stagnation region of the wheels, significant flow deceleration and vorticity stretching act to collect, grow, and amplify the incoming vorticity streams into large-scale vortical structures. Experiments were performed at a fixed Reynolds number, with a value of 32 500 when defined based on the diameter of the wheel and a value of 21 based on the diameter of the vorticity-generating upstream wire. First, to establish a baseline, the natural flow field (without the presence of an upstream wire) was characterized, where experimentally determined values for the stagnation boundary-layer thickness and the velocity profile along the stagnation streamline were both found to agree with the values provided in the literature for two-dimensional cylinders. Subsequently, the dynamics of vorticity collection, growth, amplification, and shedding were studied. The size, stand-off distance and the shedding frequency of the vortical structures forming near the stagnation region were all found to strongly depend on the impingement location of the inbound vorticity on the wheel. A simple relationship between the non-dimensional characteristic size and the non-dimensional shedding frequency was found to hold over the entire range of locations where vorticity amplification and shedding were observed. Penetration of the vortical structures into the stagnation boundary layer was observed for specific locations of inbound vorticity impingement.

On the laminar–turbulent transition of the rotating-disk flow: the role of absolute instability

AbstractThis paper describes a detailed experimental study using hot-wire anemometry of the laminar–turbulent transition region of a rotating-disk boundary-layer flow without any imposed excitation of the boundary layer. The measured data are separated into stationary and unsteady disturbance fields in order to elaborate on the roles that the stationary and the travelling modes have in the transition process. We show the onset of nonlinearity consistently at Reynolds numbers, $R$, of $\sim $510, i.e. at the onset of Lingwood’s (J. Fluid Mech., vol. 299, 1995, pp. 17–33) local absolute instability, and the growth of stationary vortices saturates at a Reynolds number of $\sim $550. The nonlinear saturation and subsequent turbulent breakdown of individual stationary vortices independently of their amplitudes, which vary azimuthally, seem to be determined by well-defined Reynolds numbers. We identify unstable travelling disturbances in our power spectra, which continue to grow, saturating at around $R=585$, whereupon turbulent breakdown of the boundary layer ensues. The nonlinear saturation amplitude of the total disturbance field is approximately constant for all considered cases, i.e. different rotation rates and edge Reynolds numbers. We also identify a travelling secondary instability. Our results suggest that it is the travelling disturbances that are fundamentally important to the transition to turbulence for a clean disk, rather than the stationary vortices. Here, the results appear to show a primary nonlinear steep-fronted (travelling) global mode at the boundary between the local convectively and absolutely unstable regions, which develops nonlinearly interacting with the stationary vortices and which saturates and is unstable to a secondary instability. This leads to a rapid transition to turbulence outward of the primary front from approximately $R=565$ to 590 and to a fully turbulent boundary layer above 650.

Impact of Shear Flow Instabilities on the Magnitude and Saturation of the Flame Response

Amplitude-dependent flame transfer functions, also denoted as flame describing functions, are valuable tools for the prediction of limit-cycle amplitudes of thermoacoustic instabilities. However, the effects that govern the transfer function magnitude at low and high amplitudes are not yet fully understood. It is shown in the present work that the flame response at perfectly premixed conditions is strongly influenced by the growth rate of vortical structures in the shear layers. An experimental study in a generic swirl-stabilized combustor was conducted in order to measure the amplitude-dependent flame transfer function and the corresponding flow fields subjected to acoustic forcing. The applied measurement techniques included the multi-microphone-method, high-speed OH*-chemiluminescence measurements, and high-speed particle image velocimetry. The flame response and the corresponding flow fields are assessed for three different swirl numbers at 196 Hz forcing frequency. The results show that forcing leads to significant changes in the time-averaged reacting flow fields and flame shapes. A triple decomposition is applied to the time-resolved data, which reveals that coherent velocity fluctuations at the forcing frequency are amplified considerably stronger in the shear layers at low forcing amplitudes than at high amplitudes, which is an indicator for a nonlinear saturation process. The strongest saturation is found for the lowest swirl number, where the forcing additionally detached the flame. For the highest swirl number, the saturation of the vortex amplitude is weaker. Overall, the amplitude-dependent vortex amplification resembles the characteristics of the flame response very well. An application of a linear stability analysis to the time-averaged flow fields at increasing forcing amplitudes yields the decreasing growth rates of shear flow instabilities at the forcing frequency. It therefore successfully predicts a saturation at high forcing amplitudes and demonstrates that the mean flow field and its modifications are of utmost importance for the growth of vortices in the shear layers. Moreover, the results clearly show that the amplification of vortices in the shear layers is an important driver for heat release fluctuations and their saturation.

Unsteady pulsating characteristics of the fluid flow through a sudden expansion microvalve

This paper investigates the unsteady characteristics of flow in a specific type of microvalve with sudden expansion shape. The resultant vortex structures cause different flow resistance in forward and backward flow directions. This may be used in applications such as a microvalve in micropump system and MEMS-based devices. A time-varying sinusoidal pressure was set at the inlet of the microchannel to produce unsteadiness and simulate the pumping action. The existence of block obstacle and expansion shoulders leads to various sizes of vortex structures in each flow direction. All simulation results are based on the numerical simulation of two-dimensional, unsteady, incompressible and laminar Navier–Stokes equations. Two fundamental parameters were varied to investigate the vortex growth throughout the time: the frequency of the inlet actuating mechanism (1 Hz ≤ f ≤ 1,000 Hz) and the amplitude of the inlet pressure. In this way, one can see the effect of actuation mechanism on the onset of separation and follow the size and duration of the vortex growth. In order to better understand the effect of geometry and frequency on flow field, the pressure and velocity distributions are studied through one cycle. Strouhal number is calculated for frequency, and a critical value of f = 250 Hz is found for St = 1. The obtained results provide a deep insight into the physics of unsteady flow in valveless micropumps and leads to better use of current design as a part of microfluidic system.

Effects of nonuniform incident velocity on a dynamic wind turbine airfoil

AbstractFor further insight into the performance of a horizontal axis wind turbine blade section under yaw loads, a 2D numerical simulation of a pitching S809 airfoil under dynamic stall with an unsteady incident velocity is presented. The streamwise incident velocity and pitch angle of incidence oscillated with the same frequency but with a range of phase differences, − π ≤ Φ ≤ π. Changing Φ caused variation of the results, which can be highlighted as significantly augmented and dramatically damped dynamic stall loads, both increasing and decreasing trends for vortex growth time during Φ increase, a shifted location of the maximum loads and a change in the order of the vortex pair circulation in each cycle. The results showed strong dependency on the velocity and acceleration of the freestream during dynamic stall, which categorized the results in four individual subdomains with different behaviors. Copyright © 2014 John Wiley &amp; Sons, Ltd.

Characteristic length scales for vortex detachment on plunging profiles with varying leading-edge geometry

Experiments on leading-edge vortex (LEV) growth and detachment from a plunging profile have been conducted in a free-surface water tunnel. Direct-force and velocity-field measurements have been performed at a Reynolds number of Re = 10,000, a reduced frequency of k = 0.25, and a Strouhal number of St = 0.16, for three varying leading-edge geometries. The leading-edge shape is shown to influence the shear layer feeding the LEV, and thus to some extent the development of the LEV and associated flow topology. This effect in turn influences the arrival time of the rear (LEV) stagnation point at the trailing edge, which, once breached, constitutes a detachment of the LEV. It is found that despite minor phase changes in LEV detachment through leading-edge shape, the position of the trailing edge (chord length) should be chosen as the characteristic length scale for the vortex separation process.

Flow and heat transfer characteristics of finned tube with internal and external fins in air cooler for waste heat recovery of gas-fired boiler system

In this present study, attempts were made to investigate the flow and heat transfer characteristics of finned tube with internal fins and external fins by experiment and numerical simulation. The test finned tube was installed in a single smooth tube and formed a shell-and-tube heat exchanger. The experiments were conducted in heat transfer test system with hot air in the tube side and cold air in the shell side. Overall heat transfer coefficients were calculated and heat transfer coefficients in the tube side were determined. Three-dimension computation was performed to predict the flow and heat transfer performance in the finned tube. The effects of external fin height and pitch of the finned tube on shell-side flow and heat transfer were studied by numerical simulation. The numerical results agree well with the measurements. The maximum differences between the present numerical results and the experimental data are approximately 6.9% for heat transfer coefficient and 4.7% for friction factor, respectively. The velocity and temperature fields are obtained to discern the mechanisms of heat transfer enhancement. Numerical results indicate that the steady and spatially periodic growth and disruption of vortices occur in external fin to fin region.

An investigation into vortex growth and stabilization for two-dimensional plunging and flapping plates with varying sweep

A simple analytical model for leading-edge vortex (LEV) growth is proposed and tested, based on the transport of vorticity-containing mass through the shear-layer. The two-dimensional case is validated using time-resolved Particle Image Velocimetry. As a precursor to developing a model for finite wings, the effect of varying spanwise flow on a nominally two-dimensional profile is investigated by imposing plunging and flapping motions on high aspect-ratio flat-plate profiles of sweep angles Λ=+45°,−45° and 0°. By varying sweep angle, both coinciding and opposing gradients of spanwise vorticity stretching and convection were tested. It was shown that nominally two-dimensional spanwise flow has no effect on vortex strength and thus force history for plunging kinematics. However, force histories for flapping kinematics were dependent on sweep angle suggesting that spanwise flow regulates vortex strength when coupled with gradients in effective incidence.

Dynamical-systems analysis and unstable periodic orbits in reacting flows behind symmetric bluff bodies

Dynamical systems analysis is performed for reacting flows stabilized behind four symmetric bluff bodies to determine the effects of shape on the nature of flame stability, acoustic coupling, and vortex shedding. The task requires separation of regular, repeatable aspects of the flow from experimental noise and highly irregular, nonrepeatable small-scale structures caused primarily by viscous-mediated energy cascading. The experimental systems are invariant under a reflection, and symmetric vortex shedding is observed throughout the parameter range. As the equivalence ratio-and, hence, acoustic coupling-is reduced, a symmetry-breaking transition to von Karman vortices is initiated. Combining principal-components analysis with a symmetry-based filtering, we construct bifurcation diagrams for the onset and growth of von Karman vortices. We also compute Lyapunov exponents for each flame holder to help quantify the transitions. Furthermore, we outline changes in the phase-space orbits that accompany the onset of von Karman vortex shedding and compute unstable periodic orbits (UPOs) embedded in the complex flows prior to and following the bifurcation. For each flame holder, we find a single UPO in flows without von Karman vortices and a pair of UPOs in flows with von Karman vortices. These periodic orbits organize the dynamics of the flow and can be used to reduce or control flow irregularities. By subtracting them from the overall flow, we are able to deduce the nature of irregular facets of the flows.

Vortex dynamics in 3D shock-bubble interaction

The dynamics of shock-bubble interaction involve an interplay of vortex stretching, dilation, and baroclinic vorticity generation. Here, we quantify the interplay of these contributions through high resolution 3D simulations for several Mach and Atwood numbers. We present a volume rendering of density and vorticity magnitude fields of shock-bubble interaction at M = 3 and air/helium density ratio η = 7.25 to elucidate the evolution of the flow structures. We distinguish the vorticity growth rates due to baroclinicity, stretching, and dilatation at low and high Mach numbers as well as the late time evolution of the circulation. The results demonstrate that a number of analytical models need to be revised in order to predict the late time circulation of shock-bubble interactions at high Mach numbers. To this effect, we propose a simple model for the dependence of the circulation to Mach number and ambient to bubble density ratio for air/helium shock-bubble interactions.

Dynamic stall simulation of a pitching airfoil under unsteady freestream velocity

Effects of horizontal oscillations of the freestream velocity superimposed on a pitch oscillating NACA0012 airfoil were investigated using Computational Fluid Dynamics (CFD). The SST k−ω model coupled with a low-Reynolds number correction was applied for Re ≈105, when the airfoil was undergoing dynamic stall. The main parameter Φ, the phase difference between the freestream oscillation and the airfoil oscillation, was varied from 0 to π. The Φ variation resulted in several times amplitude dynamic loads when Φ≤π/2 to several times damping dynamic loads for Φ>π/2 where some dynamic stall loads were damped even below static stall load values. It was found that Φ variation was divided into two main ranges based on the values of the unsteady freestream velocity at dynamic stall. The load variation also appeared with some differences including the shape of the trailing edge vortex sheet before stall, the circulation of the dynamic stall vortex pairs, the critical angles, vortex growth time and the secondary lift peak location that are discussed in detail.

Universal mechanism for saturation of vorticity growth in fully developed fluid turbulence

AbstractNumerical results from large-scale, long-time, simulations of decaying homogeneous turbulence are reported, which indicate that blow-up of inviscid flows is tamed by the emergence of collective dynamics of coherent structures. The simulations also suggest that this collective dynamics might lead to universal behaviour during the transient evolution of turbulence. In particular, simulations with three different initial conditions show evidence of a ${k}^{- 3} \log k$ spectrum in the transient stage, before the Kolmogorov ${k}^{- 5/ 3} $ asymptotic regime is attained. Such a universal transient might serve as a spectral funnel to the time-asymptotic Kolmogorov spectrum, which is invariably observed in the late stage of all three simulations presented in this work. The present work is entirely based on simulation evidence. However, the statistical analysis of the coherent structures suggests an analogy with population dynamics, which might be conducive to new mathematical models of transient decaying turbulence.

Experimental investigation on transverse jet penetration into a supersonic turbulent crossflow

The paper evaluates the evolvement of coherent structures and penetration height of gaseous transverse jet penetration into a supersonic turbulent flow. The high spatiotemporal resolution coherent structures of the jet plume are obtained by utilizing the nanoparticle-based planar laser scattering technique (NPLS). The evolving pattern of the coherent structures generated on the upwind surface of the transverse jet is analyzed based on the NPLS images. The shedding eddies from the jet near-field have lower convection velocity along freestream direction, while vortex growth rate is apparently higher than the far-field. Farther downstream, the large-scale eddies have less deformation and translate at velocities near the freestream velocity. Thus the near-field determines the scale of eddies in the far-field and affects the whole mixing process. The effect of injection stagnation pressure on the coherent structures is discussed and a modified penetration correlation is proposed based on an edge approximation definition and least square method with various injection pressures.

Elongational flow effects on the vortex growth out of Couette flow in ferrofluids

The growth behavior of stationary axisymmetric vortices and of oscillatory, nonaxisymmetric spiral vortices in Taylor-Couette flow of a ferrofluid in between differentially rotating cylinders is analyzed using a numerical linear stability analysis. The investigation is done as a function of the inner and outer cylinder's rotation rates, the axial wave number of the vortex flows, and the magnitude of an applied homogeneous axial magnetic field. In particular, the consequences of incorporating elongational flow effects in the magnetization balance equation on the marginal control parameters that separate growth from decay behavior are determined. That is done for several values of the transport coefficient that measures the strength of these effects.

Rayleigh convective instability in the presence of phase transitions of water vapor. The formation of large-scale eddies and cloud structures

Convective motions in moist saturated air are accompanied by the release of latent heat of condensation. Taking this effect into account, we consider the problem of convective instability of a moist saturated air layer, generalizing the formulation of the classical Rayleigh problem. An analytic solution demonstrating the fundamental difference between moist convection and Rayleigh convection is obtained. Upon losing stability in the two-dimensional case, localized convective rolls or spatially periodic chains of rollers with localized areas of upward motion evolve. In the case of axial symmetry, the growth of localized convective vortices with circulation characteristic of tropical cyclones (hurricanes) is possible at the early stages of development and on the scale of tornados to tropical cyclones.

Numerical study of laminar-turbulent transition in particle-laden channel flow

We present direct numerical simulations of subcritical transition to turbulence in a particle-laden channel flow, with particles assumed rigid, spherical, and heavier than the fluid. The equations describing the fluid flow are solved with an Eulerian mesh, whereas those describing the particle dynamics are solved by Lagrangian tracking. Two-way coupling between fluid and particles is modeled with Stokes drag. The numerical code is first validated against previous results from linear stability: the nonmodal growth of streamwise vortices resulting in streamwise streaks is still the most efficient mechanism for linear disturbance amplification at subcritical conditions as for the case of a single phase fluid. To analyze the full nonlinear transition, we examine two scenarios well studied in the literature: (1) transition initiated by streamwise independent counter-rotating streamwise vortices and one three-dimensional mode and (2) oblique transition, initiated by the nonlinear interaction of two symmetric oblique waves. The threshold energy for transition is computed, and it is demonstrated that for both scenarios the transition may be facilitated by the presence of particles at low number density. This is due to the fact that particles may introduce in the system detrimental disturbances of length scales not initially present. At higher concentrations, conversely, we note an increase of the disturbance energy needed for transition. The threshold energy for the oblique scenario shows a more significant increase in the presence of particles, by a factor about four. Interestingly, for the streamwise-vortex scenario the time at which transition occurs increases with the particle volume fraction when considering disturbances of equal initial energy. These results are explained by considering the reduced amplification of oblique modes in the two-phase flow. The results from these two classical scenarios indicate that, although linear stability analysis shows hardly any effect on optimal growth, particles do influence secondary instabilities and streak breakdown. These effects can be responsible of the reduced drag observed in turbulent channel flow laden with heavy particles.