Transition mechanisms in laminar separation bubbles with and without incoming wakes and synthetic jet effects

Laminar separation and transition processes of the boundary layer developing under a strong adverse pressure gradient, typical of Ultra-High-Lift turbine profiles, have been experimentally investigated for a low Reynolds number case. The boundary layer development has been surveyed for different conditions: with steady inflow, with incoming wakes and with the synchronized forcing effects due to both incoming wakes and synthetic jet (zero net mass flow rate jet). In this latter case, the jet Strouhal number has been set equal to half the wake-reduced frequency to synchronize the unsteady forcing effects on the boundary layer. Measurements have been taken by means of a single-sensor hot-wire anemometer. For the steady inflow case, particle image velocimetry has been employed to visualize the large-scale vortical structures shed as a consequence of the Kelvin?CHelmholtz instability mechanism. For the unsteady inflow cases, a phase-locked ensemble averaging technique, synchronized with the wake and the synthetic jet frequencies, has been adopted to reconstruct the boundary layer space-time evolution. Results have been represented as color plots, for several time instants of the forcing effect period, in order to provide an overall view of the time-dependent transition and separation processes in terms of ensemble-averaged velocity and unresolved unsteadiness distributions. The phase-locked distributions of the unresolved unsteadiness allowed the identification of the instability mechanisms driving transition as well as the Kelvin?CHelmholtz structures that grow within the separated shear layer during the incoming wake interval and the synthetic jet operating period. Incoming wakes and synthetic jet effects in reducing and/or suppressing flow separation are investigated in depth.     

Loss Production Mechanisms in a Laminar Separation Bubble

The present paper reports the results of a detailed experimental study, carried out by means of a two-component Laser Doppler Velocimeter, aimed at investigating the loss generation mechanisms induced by laminar separation bubble and transition process. Measurements have been performed along a flat plate installed within a double contoured test section, designed to produce an adverse pressure gradient typical of Ultra-High-Lift turbine blade profiles, which induces the formation of a laminar separation bubble. Results were detailed enough to allow calculating laminar and turbulent deformation works in the separated flow region. Normal and shear contributions of both viscous and turbulent deformation works have been analyzed and employed to explain the generation of total pressure losses in the separated flow region, where the generation and amplification of Kelvin–Helmholtz instability induces the separated shear layer roll-up, thus the bubble reattachment. Results obtained for different Reynolds number conditions have been employed for the formulation of a loss scaling procedure involving the separated shear layer thickness, which is directly correlated to the dynamics of Kelvin–Helmholtz roll-up vortices.     

Instability of the interface in two-layer flows with large viscosity contrast at small Reynolds numbers

The Kelvin–Helmholtz instability is believed to be the dominant instability mechanism for free shear flows at large Reynolds numbers. At small Reynolds numbers, a new instability mode is identified when the temporal instability of parallel viscous two fluid mixing layers is extended to current-fluid mud systems by considering a composite error function velocity profile. The new mode is caused by the large viscosity difference between the two fluids. This interfacial mode exists when the fluid mud boundary layer is sufficiently thin. Its performance is different from that of the Kelvin–Helmholtz mode. This mode has not yet been reported for interface instability problems with large viscosity contrasts.These results are essential for further stability analysis of flows relevant to the breaking up of this type of interface.     

Characteristic Regimes of Transitional Separation Bubbles in Unsteady Flow

This experimental investigation deals with transition phenomena of a separated boundary layer under unsteady inlet flow conditions. The main purpose of this investigation is to understand the influence of the rotor-stator interaction in turbomachinery on the subsequent, highly loaded boundary layer. The research project is divided into two phases. In the first phase, which has been completed recently, only the variation of mean velocity caused by upstream blades was simulated in the experiments while the free-stream turbulence intensity was retained at a constant low level. The experiments are carried out in an Eifel-type wind tunnel to investigate the laminar separated boundary layer of a flat plate under oscillating inlet conditions. The adverse pressure gradient, similar to that of turbomachines, is generated by the contoured upper wall. The unsteadiness is produced by a rotating flap located downstream of the test section. The reduced frequency, the amplitude and the mean Reynolds number are varied to simulate the conditions prevailing in turbomachines. In addition to the Kelvin–Helmholtz instability of the separated shear layer, a lower frequency instability was observed. This is frequently referred to as `free shear layer flapping' and results in two distinctly different ways of re-attachment, depending primarily on the Reynolds number. For low momentum thickness Reynolds numbers at the separation point, large-scale vortices locked to the frequency of the unsteady main flow are identified. They originate nearly at the top of the separation bubble and are ejected downstream. A fully turbulent boundary layer develops after these vortices mix out. For higher Reynolds numbers, transition is completed within a short length of the free shear layer and there-attachment region. The characteristic momentum thickness Reynolds number separating these two regimes in unsteady flow is about 125. The Strouhal number (reduced frequency) does not appear to have any significant effect. Based on the experimental results, this behaviour is discussed in some detail. This revised version was published online in July 2006 with corrections to the Cover Date.     

Large-eddy simulation study of upstream boundary conditions influence upon a backward-facing step flowÉtude par simulation des grandes échelles de l'influence des conditions aux limites amont sur l'écoulement derrière une marche descendante

We use Large Eddy Simulation to investigate the influence of upstream boundary conditions on the development of a backward facing step flow. The first inlet condition consists of a mean turbulent boundary layer velocity profile perturbed by a white noise. The second relies upon a precursor calculation where the development of a quasi-temporal turbulent boundary layer is simulated. In this case, the quasi-longitudinal vortices in the upstream turbulent boundary-layer trigger the destabilization of the shear layer just behind the step, resulting in a shortening of the recirculation length and an increase of the characteristic frequency associated to the Kelvin–Helmholtz vortices. The mean flow and the characteristic frequencies of pressure fluctuations are strongly dependent of the upstream flow. It demonstrates the importance of realistic boundary conditions for the simulation of complex 3D flows or for flow control simulations. To cite this article: J.-L. Aider, A. Danet, C. R. Mecanique 334 (2006).     

Shock-vortex shear-layer interaction in the transonic flow around a supercritical airfoil at high Reynolds number in buffet conditions

This paper provides a conceptual analysis and a computational model for how the unsteady ‘buffeting’ phenomenon develops in transonic, low incidence flow around a supercritical aerofoil, the OAT15A, at Reynolds number of 3.3 million. It is shown how a low-frequency buffet mode is amplified in the shock-wave region and then develops upstream and downstream interaction with the alternating von Kármán eddies in the wake past the trailing-edge as well as with the shear-layer, Kelvin–Helmholtz vortices. These interactions are tracked by wavelet analysis, autoregressive (AR) modelling and by Proper Orthogonal Decomposition. The frequency modulation of the trailing-edge instability modes is shown in the spectra and in the wall-pressure fluctuations. The amplitude modulation of the buffet and von Kármán modes has been also quantified by POD analysis. The thinning of the shear layers, both at the outer edge of the turbulent boundary layers and the wake, caused by an ‘eddy-blocking’ mechanism is modelled by stochastic forcing of the turbulent kinetic energy and dissipation, by small-scale straining of the higher-order POD modes. The benefits from thinning the shear-layers by taking into account the interfacial dynamics are clearly shown in the velocity profiles, and wall pressure distribution in comparison with the experimental data.     

Vortex dynamics mechanisms of separated boundary layer in a highly loaded low pressure turbine cascade

This paper investigates the vortex dynamics in the suction-side boundary layer on an aero-engine low pressure turbine blade at two different Reynolds numbers at which short and long laminar separation bubbles occur. Different vortical patterns are observed and investigated through large eddy simulation (LES). The results show that at the higher Reynolds number, streamwise streaks exist upstream of separation line. These streaks initiate spanwise undulation in the form of vortex tubes, which roll-up and shed from the shear layer due to the Kelvin–Helmholtz instability. The vortex tubes alternately pair together and eventually distort and break down to small-scale turbulence structures near the mean reattachment location and convect into a fully turbulent boundary layer. At the lower Reynolds number, streamwise streaks are strong and the separated flow is unable to reattach to the blade surface immediately after transition to turbulence. Therefore, bursting of short bubbles into long bubbles can occur, and vortex tubes have larger diameters and cover a part of the blade span. In this case vortex pairing does not occur and vortex shedding process is promoted mainly by flapping phenomenon. Moreover, the results of dynamic mode decomposition (DMD) analysis show a breathing motion as a source of unsteadiness in the separation location, which is accompanied by the flapping phenomenon.     

The near wake structure of a square cylinder

The near wake structure of a square cross section cylinder in flow perpendicular to its length was investigated experimentally over a Reynolds number (based on cylinder width) range of 6700–43,000. The wake structure and the characteristics of the instability wave, scaling on θ at separation, were strongly dependent on the incidence angle () of the freestream velocity. The nondimensional frequency (St_θ) of the instability wave varied within the range predicted for laminar instability frequencies for flat plate wakes, jets and shear layers. For = 22.5°, the freestream velocity was accelerated over the side walls and the deflection of the streamlines (from both sides of the cylinder) towards the center line was higher compared to the streamlines for = 0°. This caused the vortices from both sides of the cylinder to merge by x/d 2, giving the mean velocity distribution typical of a wake profile. For = 0°, the vortices shed from both sides of the cylinder did not merge until x/d 4.5. The separation boundary layer for all cases was either transitional or turbulent, yet the results showed good qualitative, and for some cases even quantitative, agreement with linearized stability results for small amplitude disturbances waves in laminar separation layers.     

Bifurcation mechanism of interfacial electrohydrodynamic gravity-capillary waves near the minimum phase speed under a horizontal electric field

We investigate the evolution of interfacial gravity-capillary waves propagating along the interface between two dielectric fluids under the action of a horizontal electric field. There is a uniform background flow in each layer, and the relative motion tends to induce Kelvin–Helmholtz(KH) instability. The combined effects of gravity, surface tension and electrically induced forces are all taken into account. Under the short-wave assumption, the expansion and truncation method of Dirichlet-Neumann(DN) operators is applied to derive a reduced dynamical model. When KH instability is suppressed linearly by a considerably large electric field, our numerical results reveal that in certain regions of parameter space, nonlinear symmetric traveling wave solutions can be found near the minimum phase speed. Additionally, the detailed bifurcation structures are presented together with typical wave profiles.     

Numerical study on the turbulent mixing of planar shock-accelerated triangular heavy gases interface

The interaction of a planar shock wave with a triangle-shaped sulfur hexafluoride (\(\mathrm{SF_6}\)) cylinder surrounded by air is numerically studied using a high resolution finite volume method with minimum dispersion and controllable dissipation reconstruction. The vortex dynamics of the Richtmyer–Meshkov instability and the turbulent mixing induced by the Kelvin–Helmholtz instability are discussed. A modified reconstruction model is proposed to predict the circulation for the shock triangular gas–cylinder interaction flow. Several typical stages leading the shock-driven inhomogeneity flow to turbulent mixing transition are demonstrated. Both the decoupled length scales and the broadened inertial range of the turbulent kinetic energy spectrum in late time manifest the turbulent mixing transition for the present case. The analysis of variable-density energy transfer indicates that the flow structures with high wavenumbers inside the Kelvin–Helmholtz vortices can gain energy from the mean flow in total. Consequently, small scale flow structures are generated therein by means of nonlinear interactions. Furthermore, the occasional “pairing” between a vortex and its neighboring vortex will trigger the merging process of vortices and, finally, create a large turbulent mixing zone.     

Study on the instability in separating–reattaching flow over a surface-mounted rib

A numerical study on the flow structure and instability in the separated–reattached flow over a surface-mounted rib at Re = 1000 is performed using large eddy simulation. It is found that the phenomenon of vortex pairing, which has been extensively observed in similar flows, exists in the separation zone. Based on the spectral analysis, the Kelvin–Helmholtz (K-H) instability of shear layer at St ≈ 0.361 (St ≡ fh/U₀) and its subharmonic at St ≈ 0.18 are found. It is assumed that the K-H instability reduces to its subharmonic through the vortex pairing. This process is further confirmed by the flow visualisation. The two-dimensional (2D) structures are subjected to sinusoidal undulation along the spanwise and observed to undergo helical pairing process, which is attributed to the transformation of 2D structures into 3D. However, the low frequency due to flapping of the shear layer is not found.     

Application of a Synthetic Jet to Control Boundary Layer Separation under Ultra-High-Lift Turbine Pressure Distribution

The transition and separation processes of the boundary layer developing on a flat plate under a prescribed adverse pressure gradient typical of Ultra-High-Lift low-pressure turbine profiles have been investigated, with and without the application of a synthetic jet (zero net mass flow rate jet). A mechanical piston has been adopted to produce an intermittent flow with zero net mass flow rate. The capability of the device to suppress or reduce the large laminar separation bubble occurring under steady inflow condition at low Reynolds numbers has been experimentally investigated by means of hot-wire measurements. Wall static pressure measurements complement the hot-wire time-resolved velocity results. The paper reports the investigations performed for both steady and controlled conditions. The active device is able to control the laminar separation bubble induced at low Reynolds number conditions by the strong adverse pressure gradient. An overall view of the time-dependent evolution of the controlled boundary layer is provided by the phase-locked ensemble averaging technique, triggered at the synthetic jet frequency. The separated flow transition process, which is detected for the uncontrolled condition, is modified by the synthetic jet in different ways during the blowing and suction phases. Overall, the phase-locked velocity distributions show a reduced separated flow region for the whole jet cycle as compared to the uncontrolled condition. The phase-locked distributions of the random unsteadiness allow the identification of vortical structures growing along the shear layer mainly during the blowing phase.     

Numerical studies of the instability and breakdown of a boundary-layer low-speed streak

The experimental configuration in [M. Asai, M. Minagawa, M. Nishioka, The instability and breakdown of a near-wall low-speed streak, J. Fluid Mech. 455 (2002) 289–314] is numerically reproduced in order to examine the instability of a single low-speed streak in a laminar boundary layer and to investigate the resulting generation of coherent structures. Such a configuration is chosen since the experimental data show that the two instability modes, varicose and sinuous, are of comparable strength. The instability characteristics are retrieved from the simulation of the flow impulse response. The varicose instability is associated to higher frequencies and lower group velocities than those of the sinuous modes. The latter are less affected by the diffusion of the streak mean shear and are amplified for a longer streamwise distance. Analysis of the perturbation kinetic energy production reveals that both the varicose and the sinuous instability are driven by the work of the Reynolds stress against the wall-normal shear of the streak. The base flow considered here therefore presents an exception to the common knowledge, supported by several previous studies, that the sinuous instability is associated to the streak spanwise shear. The vortical structures at the late stage of the varicose breakdown are identified from the numerical data. By comparing them with those pertaining to other transition scenarios, it is confirmed that streaks and streamwise vortices are universal features of boundary layer transition.     

Large eddy simulation of boundary layer flow under cnoidal waves

Water waves in coastal areas are generally nonlinear, exhibiting asymmetric velocity profiles with different amplitudes of crest and trough. The behaviors of the boundary layer under asymmetric waves are of great significance for sediment transport in natural circumstances. While previous studies have mainly focused on linear or symmetric waves, asymmetric wave-induced flows remain unclear, particularly in the flow regime with high Reynolds numbers.Taking cnoidal wave as a typical example of asymmetric waves, we propose to use an infinite immersed plate oscillating cnoidally in its own plane in quiescent water to simulate asymmetric wave boundary layer. A large eddy simulation approach with Smagorinsky subgrid model is adopted to investigate the flow characteristics of the boundary layer. It is verified that the model well reproduces experimental and theoretical results. Then a series of numerical experiments are carried out to study the boundary layer beneath cnoidal waves from laminar to fully developed turbulent regimes at high Reynolds numbers, larger than ever studied before.Results of velocity profile, wall shear stress, friction coefficient, phase lead between velocity and wall shear stress, and the boundary layer thickness are obtained. The dependencies of these boundary layer properties on the asymmetric degree and Reynolds number are discussed in detail.     

Recognition of coherent structures in the boundary layer of a low-pressure-turbine blade for different free-stream turbulence intensity levels

Particle Image Velocimetry (PIV) has been adopted to analyze the instantaneous flow field developing on a high-lift turbine blade profile operating under low and elevated free-stream turbulence conditions (FSTI). Results reported in the paper allow us to analyze the dynamics leading to transition and separation of the suction side boundary layer, looking to generation, propagation and breakdown of coherent structures observed in the two different FSTI cases. To this end, measurements have been performed in two orthogonal planes. Results obtained in the blade-to-blade plane allow the detailed characterization of the propagation of Kelvin–Helmholtz (KH) rolls generating, at low FSTI condition, as a consequence of a non-reattaching separation. Otherwise, data in the wall-parallel plane allow recognizing the presence of three-dimensional disuniformities induced at high FSTI by low and high speed streaks (Klebanoff mode). The sinuous breakdown of boundary layer streaks generates other complex three-dimensional coherent structures such as hairpin or cane-like vortices that induce transition. Proper Orthogonal Decomposition (POD) has been adopted to in depth characterize these structures, thus further explaining the mechanisms through which the free-stream turbulence intensity modify the transition/separation processes of the suction side boundary layer of an highly loaded low pressure turbine blade.     

Three-dimensional instability analysis of boundary layers perturbed by streamwise vortices

A parametric study is presented for the incompressible, zero-pressure-gradient flat-plate boundary layer perturbed by streamwise vortices. The vortices are placed near the leading edge and model the vortices induced by miniature vortex generators (MVGs), which consist in a spanwise-periodic array of small winglet pairs. The introduction of MVGs has been experimentally proved to be a successful passive flow control strategy for delaying laminar-turbulent transition caused by Tollmien–Schlichting (TS) waves. The counter-rotating vortex pairs induce non-modal, transient growth that leads to a streaky boundary layer flow. The initial intensity of the vortices and their wall-normal distances to the plate wall are varied with the aim of finding the most effective location for streak generation and the effect on the instability characteristics of the perturbed flow. The study includes the solution of the three-dimensional, stationary, streaky boundary layer flows by using the boundary region equations, and the three-dimensional instability analysis of the resulting basic flows by using the plane-marching parabolized stability equations. Depending on the initial circulation and positioning of the vortices, planar TS waves are stabilized by the presence of the streaks, resulting in a reduction in the region of instability and shrink of the neutral stability curve. For a fixed maximum streak amplitude below the threshold for secondary instability (SI), the most effective wall-normal distance for the formation of the streaks is found to also offer the most stabilization of TS waves. By setting a maximum streak amplitude above the threshold for SI, sinuous shear layer modes become unstable, as well as another instability mode that is amplified in a narrow region near the vortex inlet position.     

Attenuating the large-scale turbulent oscillations sustained by shallow cavities with a perforated lid

Marine engineers face a challenging problem when designing recessed cavities that require perforated covers. Under certain geometric and kinematic conditions, the separated shear layers directly above the perforations support the spatial maturity of periodic large-scale structures. Intermittent spoilers attenuate the structure's maturity by interrupting communication between the shear layer and the adjacent inner cavity, but this success fails during transient flow conditions. In the far-field, the corresponding noise pulse is easily detectable. Evolutionary growth of the streamwise structures originates from small Kelvin–Helmholtz (K–H) waves within the shear layers just after separation and are sustained by a pressure feedback mechanism that occurs within the cavity itself. Herein, the resolved physics from large-eddy simulations along with the previous experimental evidence show analogous fundamental characteristics between the open and perforated covered cavities regardless of whether upstream separation is laminar or turbulent. These quantitative analogies are equally similar for lids perforated by staggered circular holes or slots that are tightly spaced in the streamwise direction. An alternative measure permits formation of the K–H waves, then successfully mitigates their streamwise growth by elongating the distance between perforations. This latter corrective measure reverses the mean resultant lid force to the preferred outboard direction.     

A Stability Criterion for Two-Fluid Interfaces and Applications

We derive a new stability criterion for two-fluid interfaces that ensures the existence of “stable” local solutions that do not break down too fast due to Kelvin–Helmholtz instabilities. It can be seen both as a two-fluid generalization of the Rayleigh–Taylor criterion and as a nonlinear version of the Kelvin stability condition. We show that gravity can control the inertial effects of the shear up to frequencies that are high enough for the surface tension to play a relevant role. This explains why surface tension is a necessary condition for well-posedness while the (low frequency) main dynamics of interfacial waves are unaffected by it. In order to derive a practical version of this criterion, we work with a nondimensionalized version of the equations and allow for the possibility of various asymptotic regimes, such as the shallow water limit. This limit being singular, we have to derive a new symbolic analysis of the Dirichlet–Neumann operator that includes an infinitely smoothing “tail” accounting for the contribution of the bottom. We then validate our criterion by comparison with experimental data in two important settings: air–water interfaces and internal waves. The good agreement we observe allows us to discuss the scenario of wave breaking and the behavior of water-brine interfaces, and to propose a formula for the maximal amplitude of interfacial waves. We also show how to rigorously justify two-fluid asymptotic models used for applications and how to relate some of their properties to Kelvin–Helmholtz instabilities.     

Design for a high energy density Kelvin–Helmholtz experiment

While many high energy density physics (HEDP) Rayleigh–Taylor and Richtmyer–Meshkov instability experiments have been fielded as part of basic HEDP and astrophysics studies, not one HEDP Kelvin–Helmholtz (KH) experiment has been successfully performed. Herein, a design for a novel HEDP X-ray driven KH experiment is presented along with supporting radiation-hydrodynamic simulation and theory.     

Frontal collision of internal solitary waves of first mode

The dynamics and energetics of a frontal collision of internal solitary waves (ISW) of first mode in a fluid with two homogeneous layers separated by a thin interfacial layer are studied numerically within the framework of the Navier–Stokes equations for stratified fluid. It was shown that the head-on collision of internal solitary waves of small and moderate amplitude results in a small phase shift and in the generation of dispersive wave train travelling behind the transmitted solitary wave. The phase shift grows as amplitudes of the interacting waves increase. The maximum run-up amplitude during the wave collision reaches a value larger than the sum of the amplitudes of the incident solitary waves. The excess of the maximum run-up amplitude over the sum of the amplitudes of the colliding waves grows with the increasing amplitude of interacting waves of small and moderate amplitudes whereas it decreases for colliding waves of large amplitude. Unlike the waves of small and moderate amplitudes collision of ISWs of large amplitude was accompanied by shear instability and the formation of Kelvin–Helmholtz (KH) vortices in the interface layer, however, subsequently waves again become stable. The loss of energy due to the KH instability does not exceed 5%–6%. An interaction of large amplitude ISW with even small amplitude ISW can trigger instability of larger wave and development of KH billows in larger wave. When smaller wave amplitude increases the wave interaction was accompanied by KH instability of both waves.