Swept-wing Flows Research Articles

Mechanisms of instability growth, interaction and breakdown induced by a backward-facing step in a swept-wing flow

Time-resolved particle image velocimetry measurements were performed downstream of a swept backward-facing step. The measurements allow detailed analysis of the interactions between the unsteady instabilities and the stationary crossflow vortices. Different mechanisms are identified that lead to the modulation of the different families of unsteady instabilities that occur downstream of the step. For the low-frequency spanwise-travelling mode, the modulation occurs due to a redistribution of momentum when the instability encounters regions of large spanwise shear of the wall-normal and streamwise velocity. However, the higher-frequency streamwise-travelling instabilities undergo the familiar ‘lift-up’ mechanism when they encounter the regions of large vertical velocity due to the presence of the stationary crossflow vortices. The process leading to large velocity spikes, and ultimately to a laminar breakdown to turbulence, is identified as a constructive interaction between the different unsteady instabilities, coupled with an interaction with the stationary crossflow vortices when the phases align properly.

Stability and Receptivity of the Swept-Wing Boundary-Layer Flow Controlled by a Periodic Sequence of Plasma Actuators

Stability and Receptivity of the Swept-Wing Boundary-Layer Flow Controlled by a Periodic Sequence of Plasma Actuators

The secondary instabilities of stationary cross-flow vortices in a Mach 6 swept wing flow

The secondary instabilities of stationary cross-flow vortices in a Mach 6 swept wing flow are studied using Floquet theory. High-frequency secondary instability modes of ‘y’ mode on top of stationary cross-flow vortices, and ‘z’ mode concentrating on the shoulder of the stationary cross-flow vortex are found. The most unstable secondary instability mode is always the ‘z’ mode as in incompressible swept wing flows. A new secondary instability mode concentrating on the trough of the stationary cross-flow vortex is found. The balance analysis of disturbance kinetic energy shows that the new mode belongs to the class of ‘y’ mode. The growth rate of the new ‘y’ mode located on the trough of the stationary cross-flow vortex is significantly larger than that of the ‘y’ mode on top of the stationary cross-flow vortex, and is comparable with the growth rate of the ‘z’ mode. It is also found that the new ‘y’ mode with higher frequency can evolve into the ‘z’ mode further downstream. The role of the pressure fluctuation term, including the pressure diffusion and pressure dilatation, in the energy production of secondary instability modes, is also investigated. It is shown that the pressure diffusion will only enhance the growth rate of the ‘z’ mode with higher frequency, but has little influence on other types of secondary instability mode. However, the pressure dilatation term arising from non-vanishing velocity divergence will reduce the growth rates of all secondary instability modes.

Transition to turbulence in the rotating-disk boundary-layer flow with stationary vortices

This paper proposes a resolution to the conundrum of the roles of convective and absolute instability in transition of the rotating-disk boundary layer. It also draws some comparison with swept-wing flows. Direct numerical simulations based on the incompressible Navier–Stokes equations of the flow over the surface of a rotating disk with modelled roughness elements are presented. The rotating-disk flow has been of particular interest for stability and transition research since the work by Lingwood (J. Fluid Mech., vol. 299, 1995, pp. 17–33) where an absolute instability was found. Here stationary disturbances develop from roughness elements on the disk and are followed from the linear stage, growing to saturation and finally transitioning to turbulence. Several simulations are presented with varying disturbance amplitudes. The lowest amplitude corresponds approximately to the experiment by Imayama et al. (J. Fluid Mech., vol. 745, 2014a, pp. 132–163). For all cases, the primary instability was found to be convectively unstable, and secondary modes were found to be triggered spontaneously while the flow was developing. The secondary modes further stayed within the domain, and an explanation for this is a proposed globally unstable secondary instability. For the low-amplitude roughness cases, the disturbances propagate beyond the threshold for secondary global instability before becoming turbulent, and for the high-amplitude roughness cases the transition scenario gives a turbulent flow directly at the critical Reynolds number for the secondary global instability. These results correspond to the theory of Pier (J. Engng Maths, vol. 57, 2007, pp. 237–251) predicting a secondary absolute instability. In our simulations, high temporal frequencies were found to grow with a large amplification rate where the secondary global instability occurred. For smaller radial positions, low-frequency secondary instabilities were observed, tripped by the global instability.

Applications of EPSE method for predicting crossflow instability in swept-wing boundary layers

The nth-order expansion of the parabolized stability equation (EPSEn) is obtained from the Taylor expansion of the linear parabolized stability equation (LPSE) in the streamwise direction. The EPSE together with the homogeneous boundary conditions forms a local eigenvalue problem, in which the streamwise variations of the mean flow and the disturbance shape function are considered. The first-order EPSE (EPSE1) and the second-order EPSE (EPSE2) are used to study the crossflow instability in the swept NLF(2)-0415 wing boundary layer. The non-parallelism degree of the boundary layer is strong. Compared with the growth rates predicted by the linear stability theory (LST), the results given by the EPSE1 and EPSE2 agree well with those given by the LPSE. In particular, the results given by the EPSE2 are almost the same as those given by the LPSE. The prediction of the EPSE1 is more accurate than the prediction of the LST, and is more efficient than the predictions of the EPSE2 and LPSE. Therefore, the EPSE1 is an efficient e N prediction tool for the crossflow instability in swept-wing boundary-layer flows.

Computational Investigation of Step Excrescence Sensitivity in a Swept-Wing Boundary Layer

The interaction between an existing stationary crossflow instability and a two-dimensional step excrescence placed into a swept boundary layer on a lifting surface has been investigated computationally. Backward-facing steps were found to not amplify the stationary modes. The existence of an additional local traveling instability was found in the recirculation region following the step. Further time-resolved calculations were recommended to confirm this mode as the cause of breakdown. Forward-facing steps were found to affect the transition location only once a critical step height was exceeded. This height was associated with sudden amplification of stationary crossflow modes and transition moving forward to the step. A physics-based correlation based on linear stability theory and associated with the height of the core of the stationary crossflow vortex was proposed for that critical height, which agreed well with results for the geometry and Reynolds numbers tested experimentally. Critical forward-facing step heights were in the majority of cases higher than those associated with backward-facing steps for the same conditions. Moreover, the physics associated with two-dimensional excrescences in swept-wing flow was fundamentally different from that associated with other types of roughness, as well as all roughnesses in two-dimensional flowfields. Upon further validation, the proposed correlation for forward-facing steps would provide a reasonable manufacturing criteria available to airframe designers that would prove less restrictive and more accurate than existing empirical criteria.

Mechanisms of flow tripping by discrete roughness elements in a swept-wing boundary layer

The effects of a spanwise row of finite-size cylindrical roughness elements in a laminar, compressible, three-dimensional boundary layer on a wing profile are investigated by direct numerical simulations (DNS). Large elements are capable of immediately tripping turbulent flow by either a strong, purely convective or an absolute/global instability in the near wake. First we focus on an understanding of the steady near-field past a finite-size roughness element in the swept-wing flow, comparing it to a respective case in unswept flow. Then, the mechanisms leading to immediate turbulence tripping are elaborated by gradually increasing the roughness height and varying the disturbance background level. The quasi-critical roughness Reynolds number above which turbulence sets in rapidly is found to be $Re_{kk,qcrit}\approx 560$ and global instability is found only for values well above 600 using nonlinear DNS; therefore the values do not differ significantly from two-dimensional boundary layers if the full velocity vector at the roughness height is taken to build $Re_{kk}$. A detailed simulation study of elements in the critical range indicates a changeover from a purely convective to a global instability near the critical height. Finally, we perform a three-dimensional global stability analysis of the flow field to gain insight into the early stages of the temporal disturbance growth in the quasi-critical and over-critical cases, starting from a steady state enforced by damping of unsteady disturbances.

The Mach number effect on the nonlinear instability of swept-wing flows

The Mach number effect on the nonlinear instability of swept-wing flows

Secondary instability control of compressible flow by suction for a swept wing

The crossflow instability of a three-dimensional boundary layer is a main factor affecting the transition around the swept-wing. The three-dimensional boundary layer flow affected by the saturated crossflow vortex is very sensitive to the high frequency disturbances, which foreshadows that the swept wing flow transition will happen. The primary instability of the compressible flow over a swept wing is investigated with nonlinear parabolized stability equations (NPSE). The Floquet theory is then applied to the analysis of the influence of localized steady suction on the secondary instability of crossflow vortex. The results show that suction can significantly suppress the growth of the crossflow mode as well as the secondary instability modes.

Secondary instability of a swept-wing boundary layer disturbed by controlled roughness elements

Wind-tunnel data on velocity perturbations evolving in a laminar swept-wing flow under low subsonic conditions are reported. The focus of the present experiments are secondary disturbances of the boundary layer which is modulated by stationary streamwise vortices. Both the stationary vortices and the secondary oscillations of interest are generated in a controlled manner. The experimental data are obtained through hot-wire measurements. Thus, evolution of the vortices, either isolated or interacting with each other, is reconstructed in detail. As is found, the secondary disturbances, initiating the laminar-flow breakdown, are strongly affected by configuration of the stationary boundary-layer perturbation that may have an implication to laminar-turbulent transition control.

Transition to turbulence in the boundary layer over a smooth and rough swept plate exposed to free-stream turbulence

Receptivity, disturbance growth and transition to turbulence of the three-dimensional boundary layer developing on a swept flat plate are studied by means of numerical simulations. The flow is subject to a favourable pressure gradient and represents a model for swept-wing flow downstream of the leading edge and upstream of the pressure minimum of the wing. The boundary layer is perturbed by free-stream turbulence and localized surface roughness with random distribution in the spanwise direction. The intensity of the turbulent free-stream fluctuations ranges from conditions typical for free flight to higher levels usually encountered in turbo-machinery applications. The free-stream turbulence initially excites non-modal streak-like disturbances as in two-dimensional boundary layers, soon evolving into modal instabilities in the form of unsteady crossflow modes. The crossflow modes grow faster than the streaks and dominate the downstream disturbance environment in the layer. The results show that the receptivity mechanism is linear for the disturbance amplitudes under consideration, while the subsequent growth of the primary disturbances rapidly becomes affected by nonlinear saturation in particular for free-stream fluctuations with high intensity. Transition to turbulence occurs in the form of localized turbulent spots randomly appearing in the flow. The main features of the breakdown are presented for the case of travelling crossflow vortices induced by free-stream turbulence. The flow is also receptive to localized roughness strips, exciting stationary crossflow modes. The mode with most efficient receptivity dominates the downstream disturbance environment. When both free-stream fluctuations and wall roughness act on the boundary layer at the same time, transition is dominated by steady crossflow waves unless the incoming turbulence intensity is larger than about 0.5% for roughness amplitudes of about one tenth of the boundary-layer displacement thickness. The results show that a correct prediction of the disturbance behaviour can be obtained considering the receptivity and evolution of individual modes. In addition, we provide an estimate for the amplitudes of the external disturbance sources above which a fully nonlinear receptivity analysis is necessary.

Experiments on Streamline-Curvature Instability in Boundary Layers on a Yawed Cylinder

Instability of the three-dimensional boundary layer on a yawed circular cylinder placed in a uniform flow is investigated experimentally by introducing acoustic disturbances from a point near the attachment line. To exemplify the flow dominated by streamline-curvature instability rather than crossflow instability, which has been often observed in many swept-wing flows, is the aim here. In upstream regions of the disturbance wedge originating from the point source, both streamline-curvature and crossflow disturbances are superposed on each other and yield complicated amplitude distributions. A newly proposed method enables the decomposition of the distorted amplitude distribution into contributions from the two instability modes. Detailed observations, however, show that the crossflow mode decays with the distance from the source much faster than the streamline-curvature mode and allows the latter to be dominant in a region further downstream. A fundamental characteristic of the streamline-curvature instability wave is confirmed by examining its phase distribution in the spanwise and normal directions.

Secondary instability of crossflow vortices and swept-wing boundary-layer transition

Crossflow instability of a three-dimensional boundary layer is a common cause of transition in swept-wing flows. The boundary-layer flow modified by the presence of finite-amplitude crossflow modes is susceptible to high-frequency secondary instabilities, which are believed to harbinger the onset of transition. The role of secondary instability in transition prediction is theoretically examined for the recent swept-wing experimental data by Reibert et al. (1996). Exploiting the experimental observation that the underlying three-dimensional boundary layer is convectively unstable, non-linear parabolized stability equations are used to compute a new basic state for the secondary instability analysis based on a two-dimensional eigenvalue approach. The predicted evolution of stationary crossflow vortices is in close agreement with the experimental data. The suppression of naturally dominant crossflow modes by artificial roughness distribution at a subcritical spacing is also confirmed. The analysis reveals a number of secondary instability modes belonging to two basic families which, in some sense, are akin to the ‘horseshoe’ and ‘sinuous’ modes of the Görtler vortex problem. The frequency range of the secondary instability is consistent with that measured in earlier experiments by Kohama et al. (1991), as is the overall growth of the secondary instability mode prior to the onset of transition (e.g. Kohama et al. 1996). Results indicate that the N-factor correlation based on secondary instability growth rates may yield a more robust criterion for transition onset prediction in comparison with an absolute amplitude criterion that is based on primary instability alone.

Effect of Isolated Micron-Sized Roughness on Transition in Swept-Wing Flows

Boundary-layer transition-to-turbulence studies are conducted in the Arizona State University Unsteady Wind Tunnel on a 45-deg swept airfoil. The pressure gradient is designed so that the initial stability characteristics are purely crossflow dominated. Flow-visualization and hot-wire measurements show that the development of the crossflow vortices is influenced by roughness near the attachment line. Comparisons of transition location are made between a painted surface (distributed 9-μm peaks and valleys on the surface), a machine-polished surface (0.5-μm rms finish), and a hand-polished surface (0.25-μm rms finish). Then isolated 6-μm roughness elements are placed near the attachment line on the airfoil surface under conditions of the final polish (0.25-μm rms). These elements create an enhanced packet of stationary crossflow waves, which results in localized early transition. The diameter, height, and location of these roughness elements are varied in a systematic manner. Spanwise hot-wire measurements are taken behind the roughness element to document the enhanced vortices. These scans are made at several different chord locations to examine vortex growth

Effect of isolated micron-sized roughness on transition in swept-wing flows

Effect of isolated micron-sized roughness on transition in swept-wing flows

Active Control of Wave Instabilities in Three-Dimensional Compressible Flows

In many fluid flows of practical importance transition is caused by the linear growth of wave instabilities, such as Tollmien–Schlichting waves, which eventually grow to a finite size at which stage secondary instabilities come into play. If transition is to be delayed or even avoided in such flows, then the linear growth of the disturbances must be prevented since control in the nonlinear regime would be a considerably more difficult task. Here a strategy for active control of two-dimensional incompressible and compressible Tollmien–Schlichting waves and its use in controlling the more practically relevant problem of crossflow instability which arises in swept-wing flows is discussed. The control is through an active suction/blowing distribution at the wall though the same result could be achieved by variable wall heating. In order to control the instability it is assumed that the wall shear stress and pressure are known from measurements. It is shown that, certainly at finite Reynolds numbers, it is sufficient to know the flow properties at a finite number of points along the wall. The cases of high and finite Reynolds numbers are discussed using asymptotic and numerical methods respectively. It is shown that a control strategy can be developed to stop the growth of all two-dimensional Tollmien–Schlichting waves at finite and large Reynolds numbers. Some discussion of nonlinear effects in the presence of active control is given and the possible control of other instability mechanisms investigated.

What makes the difference between shock boundary-layer interaction on an airfoil and on a swept wing?

Swept wing flows are characterized by the curvature of the streamlines in the projection to the wing plan and by the skewing of the velocity profile in the boundary layer. The aerodynamic performance of supercritical wings at transonic speeds is trongly influenced by the interaction between a weak shock front and a turbulent boundary layer. The characteristic elements of this interaction are the precompression, the post-shock expansion, and the shock diffusion. The differences between the interactive flow over an airfoil and over a swept wing are elaborated by the comparison between the two-dimensional case and the flow with superposed tangential velocity.

Laminar-Turbulent Transition on a Swept Wing.

Three-dimensional boundary-layer transition experiments are currently being conducted on a 45° swept wing in the Arizona State University Unsteady Wind Tunnel. Crossflow-dominated transition is produced via a model with contoured end liners to simulate infinite swept-wing flow. Fixed-wavelength, stationary and traveling crossflow vortices are observed. The frequencies of the most amplified traveling waves are in agreement with linear-stability theory; however, traveling waves at frequencies an order of magnitude higher than predicted are also observed near transition. Boundary-layer profiles measured at several spanwise locations show streamwise disturbance profiles characteristic of the crossflow instability. Near the transition location, severe distortions of the steady boundary-layer profiles are observed in the form of multiple inflection points. This distorted boundary layer is due to the stationary crossflow vortex and is subject to a Rayleigh-type instability in the stream direction. As a result, a high-frequency secondary instability is detected in the transition region, and spatial relations of the process are well documented by the coupled use of flow visualization and hot-wire measuremests. In all cases, we observe a transition due to this high-frequency Rayleigh instability induced by the stationary crossflow vortex.

Vortex instabilities in three-dimensional boundary layers: the relationship between Görtler and crossflow vortices

The inviscid and viscous stability problems are addressed for a boundary layer which can support both Görtler and crossflow vortices. The change in structure of Görtler vortices is found when the parameter representing the degree of three-dimensionality of the basic boundary-layer flow under consideration is increased. It is shown that crossflow vortices emerge naturally as this parameter is increased and ultimately become the only possible vortex instability of the flow. It is shown conclusively that at sufficiently large values of the crossflow there are no unstable Görtler vortices present in a boundary layer which, in the zero-crossflow case, is centrifugally unstable. The results suggest that in many practical applications Görtler vortices cannot be a cause of transition because they are destroyed by the three-dimensional nature of the basic state. In swept-wing flows the Görtler mechanism is probably not present for typical angles of sweep of about 20°.Some discussion of the receptivity problem for vortex instabilities in weakly three-dimensional boundary layers is given; it is shown that inviscid modes have a coupling coefficient marginally smaller than those of the fastest growing viscous modes discussed recently by Denier, Hall & Seddougui (1991). However, the fact that the growth rates of the inviscid modes are the larger in most situations means that they are probably the more likely source of transition.

Wave interactions in swept-wing flows

The leading-edge region of swept wings is dominated by the crossflow instability, resulting in vortices that all rotate in the same sense. The effect of these vortices on the behavior of other disturbances is examined and an interaction between these and disturbances of half the dominating crossflow wavelength is predicted. According to theory, the interaction is of crossflow–crossflow type. The effect explains the anomalies found in the experimental observations of Saric and Yeates [Laminar-Turbulent Transition (Springer, Berlin, 1985), p. 429]. Visually Saric and Yeates observe vortices at the wavelength predicted by linear theory; however, in their hot-wire measurements they find that the second harmonic dominates disturbance growth, with eventually three times the amplitude of the primary wave. In this case, the usual transition–prediction methods would fail, clearly indicating the importance of studying interactions of this sort.