Transitional Separation Bubble Research Articles

Research on the influence of spanwise cross-flow on the boundary layer transition of compressor cascade

The cross-flow perpendicular to the inviscid main flow in the boundary layer has potential instability, causing the transition from laminar flow to turbulent flow. In order to explore the mechanism of cross-flow in the blade boundary layer on transition, this paper studies the rectangular cascade of a certain compressor stator blade. Large eddy simulation calculations and flow display experiments for six attack angles with end wall cascades were carried out. It is found that the disturbance is dominated by the two-dimensional Kelvin–Helmholtz (K–H) instability. The transition begins at the position where the separation bubble begins to fall off into a two-dimensional K–H vortex and is completed where the K–H vortex breaks. The closer to the blade root, the later the transition occurs and the smaller the total pressure loss. The cross-flow velocity develops alternately between positive and negative, showing severe instability with more than 4 inflection points. The study on variable angles of attack shows that there is a superposition of two mechanisms, namely, separation bubble transition and cross-flow transition, at an angle of attack from −4° to 10°. In summary, although the separation bubble transition is dominated by K–H vortices, the occurrence of cross-flow instability is closely related to the transition position.

The triple-deck stage of marginal separation

The method of matched asymptotic expansions is applied to the investigation of transitional separation bubbles. The problem-specific Reynolds number is assumed to be large and acts as the primary perturbation parameter. Four subsequent stages can be identified as playing key roles in the characterization of the incipient laminar–turbulent transition process: due to the action of an adverse pressure gradient, a classical laminar boundary layer is forced to separate marginally (I). Taking into account viscous–inviscid interaction then enables the description of localized, predominantly steady, reverse flow regions (II). However, certain conditions (e.g. imposed perturbations) may lead to a finite-time breakdown of the underlying reduced set of equations. The ensuing consideration of even shorter spatio-temporal scales results in the flow being governed by another triple-deck interaction. This model is capable of both resolving the finite-time singularity and reproducing the spike formation (III) that, as known from experimental observations and direct numerical simulations, sets in prior to vortex shedding at the rear of the bubble. Usually, the triple-deck stage again terminates in the form of a finite-time blow-up. The study of this event gives rise to a noninteracting Euler–Prandtl stage (IV) associated with unsteady separation, where the vortex wind-up and shedding process takes place. The focus of the present paper lies on the triple-deck stage III and is twofold: firstly, a comprehensive numerical investigation based on a Chebyshev collocation method is presented. Secondly, a composite asymptotic model for the regularization of the ill-posed Cauchy problem is developed.

Modeling of Wake Effects in Steady State Mixing Plane Simulations of a High Lift Turbine Cascade with Different Combinations of Wake Passing Frequency and Wake Orientation

Due to operation at low Reynolds numbers, low pressure turbines of aircraft engines mostly show large laminar boundary layers and transitional separation bubbles which considerably change their viscous losses when interacting with impinging wakes. The change of loss depends on several wake parameters, among others on wake passing frequency and wake orientation. In the present work, these parameters are expressed in terms of Strouhal number and flow coefficient and their influence is investigated by means of unsteady Reynolds-averaged Navier-Stokes (RANS) simulations. Different combinations of both wake parameters which are typical of aircraft engine conditions, are prescribed upstream of a high lift turbine cascade, while the Reynolds number and Mach number are kept constant. The solver TRACE by DLR and MTU Aero Engines together with the γ − Re Θ transition model by Langtry and Menter has been used. Further, the wake profile is representative for upstream turbine profiles and is prescribed by a correlation framework which has been calibrated in previous work. A newly developed quasi-unsteady wake model (QUWM) is applied in order to model the effects of periodically passing wakes in steady state simulations involving mixing plane interfaces. It is shown that the gap between unsteady and steady state simulations is narrowed significantly by the QUWM while still maintaining quick turnaround times that are crucial in industrial flow solver applications.

On secondary instability of a transitional separation bubble

It is well established in the natural transition of an attached boundary layer that the transition process starts with a two–dimensional primary instability (Tollmien–Schlichting wave, denoted as TS wave), followed by usually a three-dimensional secondary instability (fundamental mode or subharmonic mode) leading to the breakdown to turbulence. However, the transition process of a separation bubble (laminar flow or laminar boundary layer at separation and transition occurs downstream of the separation, leading to turbulence at reattachment) is less well understood, especially on the nature of secondary instability.The focus of this paper is on trying to advance our understanding of secondary instability of a transitional separation bubble on a flat plate with a blunt leading edge (separation is induced geometrically at the leading edge) under a very low free-stream turbulence level (< 0.1%). Large-Eddy Simulation (LES) is employed in the current study with a dynamic sub-grid-scale model. The numerical flow visualisation together with the spectral analysis has indicated that a three dimensional secondary instability, the elliptical instability, which occurs for fundamental frequency is the main mechanism at work whereas the subharmonic mode in the form of vortex-pairing is hardly active. There is no evidence for the existence of hyperbolic instability in the braid region either.

Noise Generation of a Bionic Airfoil Based on Owl Wings

A bionic airfoil is used to investigate a preliminary understanding of the noise mechanism generated by the flow around the owl wing. The flow indicates a transitional separation bubble on the surface and the turbulent boundary layer reattaches at the downstream end of the bubble. This causes turbulent boundary layer trailing-edge scattering noise corresponding to the broadband noise of owl wings at low Reynolds numbers. Furthermore, a large-scale vortex detaches from the bubble and then drifts downstream. Thus, a tone will be generated by the vortex shedding. However, the computations of the acoustic field for both cases, where the on-body data surface and the off-body data surface are used respectively, predominantly verify the broadband nature of the noise that well agrees with the noise scattering caused by the turbulent boundary layer passing by the sharp trailing edge. Furthermore, the significant decrease of the spectra around 2k Hz is consistent with that of silent owl wings. This fact suggests that the numerical simulations are capturing the basic physical mechanism responsible for the noise radiated by the natural owl wing. This might be able to provide a reference for engineering applications of the owl technology.

On the initial phase of the triple deck stage in marginally separated flows

AbstractThe method of matched asymptotic expansions is used to investigate marginally separated boundary layer flows (laminar or alternatively transitional separation bubbles) at high Reynolds numbers. Typical examples include, among others, the flow past slender airfoils at small to moderate angels of attack and channel flows with suction. As is well‐known, classical (hierarchical) boundary layer computations usually break down under the action of an adverse pressure gradient on the flow, a scenario associated with the appearance of the Goldstein separation singularity. If, however, the parameter controlling the strength of the pressure gradient (the angle of attack or the relative suction rate in the examples mentioned above) is adjusted accordingly, the application of a local viscous‐inviscid interaction strategy is capable of describing localized boundary layer separation. Moreover, taking into account unsteady effects and flow control devices allows the investigation of the conditions leading to forced or self‐sustained vortex generation and the subsequent evolution process culminating in bubble bursting. Within the asymptotic formulation of this stage bubble bursting is associated with the formation of finite time singularities in the solution of the underlying equations and a corresponding break down. The distinct blow‐up structure gives rise to a fully non‐linear triple deck interaction stage featuring shorter spatio‐temporal scales characteristic of the successive vortex evolution process. The paper will focus on the numerical treatment of the initial phase of the latter stage. (© 2016 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

DNS of unsteady effects on the control of laminar separated boundary layers

The main factor that determines the efficiency of a high-lift low-pressure-turbine operating at low Reynolds numbers is the size of the laminar separation bubble that forms on the suction side of the turbine blade. In this study, the suction side of a low-pressure gas-turbine blade is modeled as a flat plate with a streamwise pressure distribution. The combined effects of discrete surface roughness and periodic large-scale wake forcing on separation bubble transition and control are investigated numerically by direct numerical simulation. The laminar separation bubble is controlled by positioning the roughness element upstream of the separation bubble and introducing a low-frequency large-scale wake forcing. The three-dimensional discrete roughness with varying roughness height in the spanwise direction is modeled using immersed boundary method. The wake effect is numerically modeled as the mean wake deficit profile created by a linear row of cylinders moving in a direction perpendicular to the flat plate. Results indicate that the location of transition and hence the shape and extent of the separation bubble, largely depend on which of the above-noted passive control mechanisms dominates the unsteady transition process. It is shown that considering the mean flow properties, the roughness effect is found to be negligible compared to the individual wake effect.

Experiments on Natural Transition in Separation Bubbles

An experimental work on transitional separation bubbles is presented. The bubbles are generated on a flat plate by imposing, at some distance from the plate's leading edge, a region with a constant inviscid flow deceleration. Wall pressure, pitot-static probes, hot-wire, PIV, and LDV anemometry measurements are conducted to characterize the flow evolution. The different regions of the separation bubbles are studied and scaling laws are proposed to quantify the laminar shear layer length, its angle with the wall, the characteristic most amplified frequency, and the amplification rate during the linear stages of the transitional phenomena. The reattachment of the flow is found to be related to the evolution of the large scale structure after the shear layer rolls up. Downstream from reattachment, the velocity profile at the turbulent boundary layer seems to scale to a self-similar form.

On the bursting condition for transitional separation bubbles

The reattachment region in a transitional, separated boundary layer has been experimentally investigated using non-intrusive, laser based flow diagnostics. The separated flow is generated over a flat plate that is subject to an externally imposed adverse pressure gradient. After boundary layer separation, the resulting shear layer undergoes transition and it may reattach to form a closed recirculation bubble. Particle Image Velocimetry measurements are used to obtain a detailed description of the separated flow region. Subcritical and supercritical reattachment regimes, respectively characterized by short and long recirculation bubbles, are found to depend on the Reynolds number based on the maximum edge velocity and on the pressure gradient characteristic length. Previously reported criteria are explored to describe the value of the critical Reynolds number limiting the two flow configurations. Detailed measurements are conducted to describe phenomenological differences between the two flow regimes. Based on these descriptions, a simplified model is proposed to estimate the critical Reynolds number, showing that it is able to provide appropriate scaling of this parameter.

On the laminar region and the initial stages of transition in transitional separation bubbles

Separated transitional boundary layer flows exhibit a laminar region after separation. The momentum thickness and the distance to the wall of the separated shear layer are the key parameters controlling the instability process that promotes transition and the reattachment of the flow. This work proposes scaling laws for the defining parameters of this shear layer: its angle with the wall, its length, and the momentum thickness evolution. The laws are supported by experimental measurements performed in a boundary layer that develops over a flat plate, subject to an adverse pressure gradient such that in the inviscid limit the velocity over the plate decreases linearly along its length. The flow Reynolds number based on the characteristic boundary layer edge velocity and deceleration length takes values in the 105–106 range. The edge velocity and the momentum thickness along the separated shear layer are found to be almost constant. Furthermore, the layer is seen to separate from the wall with the appropriate angle to compensate the externally imposed adverse pressure gradient, and a relationship between its length and angle is found. Additionally, a comparison between Linear Stability Theory for parallel flows and hot-wire velocity spectral measurements performed in the separated shear layer is presented. A good agreement between the most unstable frequencies and amplification rates predicted by this theory and the ones experimentally measured is found. The hypothesis of a Kelvin–Helmholtz like instability (inviscid or inflectional instability) triggering the instability process is also reinforced as a result.

The final stages of transition and the reattachment region in transitional separation bubbles

The final stages of transitional phenomena in laminar separation bubbles play a key role in their reattachment process, and they condition the boundary layer properties and flow structure after reattachment. In this experimental study, the evolution of the perturbation velocity spectra found in this zone is first presented, showing the nonlinear growth of instabilities in their path to develop fully turbulent spectra. The study of the average flow field allows the scaling of the reattachment region, both in its extension and in the characterization of the integral boundary layer magnitudes. Experimental laws are proposed for the evolution of the momentum thickness and of the shape factor. In addition, a universal, wake-like mean velocity profile is found shortly after the reattachment station. The phase-locked characterization technique allows measurements conditioned to the presence of a fluid event. This technique is used to track the evolution of large-scale structures, whose dynamics is seen to dominate the fluid behavior in the reattachment zone. The simultaneous existence of two vortex blobs is found to characterize this flow region, with the longest lived one being convected toward the wall and stretched. This process results in the fast breakdown of the large-scale vorticity structure and the sudden formation of 3-D, small scales that promote the rapid flow evolution toward a fully developed turbulent state.

Direct Numerical Simulations of Transitional Separation-Bubble Development in Swept-Blade Flow Conditions

This paper describes numerical simulations of the instability mechanisms in a separation bubble subjected to a three-dimensional freestream pressure distribution. Two direct numerical simulations are performed of a separation bubble with laminar separation and turbulent reattachment under low freestream turbulence at flow Reynolds numbers and streamwise pressure distributions that approximate the conditions encountered on the suction side of typical low-pressure gas-turbine blades with blade sweep angles of 0 deg and 45 deg. The three-dimensional (3D) pressure field in the swept configuration produces a crossflow-velocity component in the laminar boundary layer upstream of the separation point that is unstable to a crossflow instability mode. The simulation results show that crossflow instability does not play a role in the development of the boundary layer upstream of separation. An increase in the amplification rate and the most amplified disturbance frequency is observed in the separated-flow region of the swept configuration and is attributed to boundary-layer conditions at the point of separation that are modified by the spanwise pressure gradient. This results in a slight upstream movement of the location where the shear layer breaks down to small-scale turbulence and modifies the turbulent mixing of the separated shear layer to yield a downstream shift in the time-averaged reattachment location. The results demonstrate that although crossflow instability does not appear to have a noticeable effect on the development of the transitional separation bubble, the 3D pressure field does indirectly alter the separation-bubble development by modifying the flow conditions at separation.

Temperature-Sensitive Paint Visualization of the Transitional Separation Bubble over Wings at Reynolds Numbers of Several Ten Thousand

Flow fields characterized by chord-based Reynolds numbers of several ten thousand over wings of conventional cross sections are analyzed below. Utilizing temperature-sensitive paint visualization and constant-temperature anemometry the results depict a laminar-to-turbulent transition process that develops over the wings. The visualizations were utilized in order to obtain the proper length scales which characterized the transition process and to allow effective use of the constant-temperature anemometry. Not only did the constant-temperature anemometry yielded a quantitative velocity measurement in the volume over the wings, it also complemented the low spectral resolution which characterized the visualization technique. Both experimental techniques depicted the evolution of stationary cellular flow structures over the wings along the transition process. These cellular flow structures were reported in recent publications and are associated with closed separation bubbles which are subjected to flow disturbances of finite amplitude. The volumetric time-accurate velocity measurements showed that the number of cellular flow structures was function of the wing aspect ratio; moreover, it allowed proper interpretation of the temperature-sensitive paint visualizations in regions of high velocity standard deviation.

Sensitivity of linear stability analysis of measured separated shear layers

Linear stability analysis is commonly performed on measured mean velocity profiles in experimental studies on transitional separation bubbles; however, the results of such an analysis are sensitive to both the analysis approach and to experimental data scatter. In this investigation, the sensitivity of linear stability analysis of measured separated shear layer profiles is examined in order to identify reliable analysis approaches and to quantify the uncertainty in the results due to experimental data scatter and the method of analysis. Analysis approaches are compared based on their predictions for a simulated velocity profile without data scatter, profiles with simulated data scatter, and several published experimental separated shear layer profiles. Both viscous and inviscid analyses are considered. The predicted maximum disturbance amplification rates between the viscous and inviscid solutions are found to agree to within 15% for several measured separated shear layer profiles. It is shown that, for the level of data scatter typical of hot-wire measurements over flat plates and airfoils, the measured mean velocity profile should not be used directly in the stability equation, and therefore curve fitting the base velocity profile is necessary. Three curve fits are identified that provide stability predictions with relatively low sensitivity to mean profile data scatter. Stability predictions obtained using these fits are found to be more sensitive to the type of curve fit used in the analysis than to experimental data scatter, with the predicted maximum disturbance growth rate and corresponding frequency varying by approximately 35% between fits. The results of this investigation provide a means of estimating the uncertainty in linear stability predictions for measured separated shear layer profiles.

Separated shear layer transition over an airfoil at a low Reynolds number

Shear layer development over a NACA 0018 airfoil at a chord Reynolds number of 100 000 was investigated using a combination of flow visualization, velocity field mapping, surface pressure fluctuation measurements, and stability analysis. The results provide a detailed description of shear layer transition on an airfoil at low Reynolds numbers. An extensive comparison of measured surface pressure and velocity fluctuations demonstrated that time-resolved surface pressure sensor arrays can be used to identify the presence of flow separation, estimate the extent of the separated flow region, and measure disturbance growth rate spectra in significantly less time than is required by conventional techniques. Surface pressure sensor measurements of disturbance growth rate, wave number, and convection speed are found to compare well with predictions of linear stability theory, supporting the claim that convection speeds measured in separation bubbles over low Reynolds number airfoils are associated with wave packets of growing disturbances propagating through the shear layer. Through a comparison of measured convection speeds in this investigation and prior low Reynolds number airfoil experiments, it is shown that disturbance convection speeds of between 30% and 50% of the edge velocity are typical for this type of flow, consistent with phase speed estimates from previous analytical studies on transitional separation bubbles. Modal RMS velocity profiles were measured and found to be reasonably predicted by stability theory. The results suggest that, even for the relatively thick NACA 0018 airfoil profile, disturbance development over the majority of the laminar separated shear layer is primarily governed by a linear inviscid mechanism.

Transverse instability and low-frequency flapping in incompressible separated boundary layer flows: an experimental study

AbstractThe unstable dynamics of a transitional laminar separation bubble behind a two-dimensional bump geometry is investigated experimentally using dye visualizations and particle image velocimetry measurements. For Reynolds numbers above a critical value, the initially two-dimensional recirculation bubble is subject to modulations in the spanwise direction which can trigger vortex shedding. Increasing the Reynolds number further, the unstable behaviour is dominated by a low-frequency flapping motion, well known in transonic flows, and here investigated for the first time experimentally in an incompressible flow regime. These phenomena are characterized by non-intrusive measurements of the spatial structure and the frequencies of the unsteady motion. The results are in excellent agreement with previous numerical and theoretical predictions for the same geometry.

Interaction of viscous and inviscid instability modes in separation–bubble transition

This paper describes numerical simulations that are used to examine the interaction of viscous and inviscid instability modes in laminar-to-turbulent transition in a separation bubble. The results of a direct numerical simulation are presented in which separation of a laminar boundary-layer occurs in the presence of an adverse streamwise pressure gradient. The simulation is performed at low freestream-turbulence levels and at a flow Reynolds number and pressure distribution approximating those typically encountered on the suction side of low-pressure turbine blades in a gas-turbine engine. The simulation results reveal the development of a viscous instability upstream of the point of separation which produces streamwise-oriented vortices in the attached laminar boundary layer. These vortices remain embedded in the flow downstream of separation and are carried into the separated shear layer, where they are amplified by the local adverse pressure-gradient and contribute to the formation of coherent hairpin-like vortices. A strong interaction is observed between these vortices and the inviscid instability that typically dominates the shear layer in the separated zone. The interaction is noted to determine the spanwise extent of the vortical flow structures that periodically shed from the downstream end of the separated shear layer. The structure of the shed vortical flow structures is examined and compared with the coherent structures typically observed within turbulent boundary layers.

DNS database of a transitional separation bubble on a flat plate and application to RANS modeling validation

The present study consists in an analysis of the DNS database of a flow overcoming a transitional separation induced by an adverse pressure gradient on a flat plate under a curved upper wall. This study takes place in the context of improving RANS models for the simulation of the stall phenomenon for rotor blades applications. To mimic the real flow mechanisms, the flow characteristics are chosen to be typical of the leading edge of the OA209 airfoil at an incidence just below stall occurence: 15° of incidence, Rc∞=1.8×106 and M∞=0.16. The budgets of the turbulent kinetic energy transport equations have been computed by the DNS. Their evolution is analysed from the separation up to the downstream turbulent flow. Comparisons with a URANS k–ω Wilcox computation are presented to illustrate the application of the DNS simulation.

Large Eddy Simulation of Transitional Separated Flow over a Flat Plate and a Compressor Blade

The ability of Large-Eddy Simulation (LES) to predict transitional separation bubbles is investigated, with particular emphasis being placed on the response to free-stream-turbulence. The principal objective is to quantify the penalties, relative to Direct Numerical Simulations (DNS), that arise from the coarser resolution and the use of subgrid-scale models. Two flow configurations are considered: a flat-plate boundary layer, subjected to different free-stream-turbulence levels, ranging from 0 to 2% (at the point of separation), and the flow over a compressor blade at 0 and 3.25% turbulence levels. For both cases, results are compared with DNS data. A number of challenges associated with the use of LES in transitional flows are addressed, including the representation of the decay of free-stream turbulence and the mesh resolution needed for a correct description of the growth of instability waves in the early stage of transition.

Transition Mechanisms in Separation Bubbles Under Low- and Elevated-Freestream Turbulence

Through numerical simulations, this paper examines the nature of instability mechanisms leading to transition in separation bubbles. The results of two direct numerical simulations are presented in which separation of a laminar boundary layer occurs over a flat surface in the presence of an adverse pressure gradient. The primary difference in the flow conditions between the two simulations is the level of freestream turbulence with intensities of 0.1% and 1.45% at separation. In the first part of the paper, transition under a low-disturbance environment is examined, and the development of the Kelvin–Helmholtz instability in the separated shear layer is compared to the well-established instability characteristics of free shear layers. The study examines the role of the velocity-profile shape on the instability characteristics and the nature of the large-scale vortical structures shed downstream of the bubble. The second part of the paper examines transition in a high-disturbance environment, where the above-mentioned mechanism is bypassed as a result of elevated-freestream turbulence. Filtering of the freestream turbulence into the laminar boundary layer results in streamwise streaks, which provide conditions under which turbulent spots are produced in the separated shear layer, grow, and then merge to form a turbulent boundary layer. The results allow identification of the structure of the instability mechanism and the characteristic structure of the resultant turbulent spots. Recovery of the reattached turbulent boundary layer is then examined for both cases. The large-scale flow structures associated with transition are noted to remain coherent far downstream of reattachment, delaying recovery of the turbulent boundary layer to an equilibrium state.