Crossflow Instability Research Articles

Instabilities in three-dimensional boundary-layer flows with a highly non-ideal fluid

The present work investigates the linear instability of three-dimensional boundary layers in thermodynamically non-ideal regimes. As a representative fluid, we consider carbon dioxide at supercritical pressure (80 bar). The flow set-up is matched to the redesigned DLR (German Aerospace Center) experiment on cross-flow instability, with identical pressure-coefficient distribution (accelerating the flow), sweep angle and Reynolds number, at a low Mach number. The flow temperature relative to the Widom line – also known as the pseudocritical line – thus characterises the non-ideality of the flow. We consider supercritical (gas-like), subcritical (liquid-like) and transcritical (pseudoboiling) regimes, where the flow temperature remains above, below or crosses the Widom line. The stability analyses of the parabolised Navier–Stokes baseflows indicate that wall heating destabilises the flow in the supercritical regime while wall cooling stabilises both effects similar to the ideal-fluid situation but being stronger. On the contrary, wall heating/cooling exhibits reversed effects in the subcritical regime, like for an ideal liquid. In the transcritical regime, with its sharp gradients of the thermodynamic and transport properties, wall heating stabilises the flow. Most substantially, however, wall cooling provokes a changeover of the leading instability mechanism: the accelerated streamwise flow attains inflectional wall-normal profiles, and the invoked inviscid Tollmien–Schlichting instability prevails with growth rates up to one order of magnitude larger than those of the cross-flow mode. We establish a two-fold mathematical relation from the momentum equation that explains the consequence of non-ideality and wall heating/cooling. The streamwise perturbation patterns of the flows in their linear instability regime are shown by mimicking wave trains emanating from virtual point-disturbance sources. From the viewpoint of keeping laminar flows, the transcritical thermodynamic state with a cooling wall must be avoided.

Optimizing control of stationary cross-flow vortices excited by surface roughness

Stationary cross-flow vortices are excited within the swept Hiemenz boundary layer via surface roughness and actively controlled using an optimally configured control device. Control is modeled using localized wall motion, but in practice the optimization strategy could be applied to other laminar flow control technologies. A sensor-control iterative procedure, based on solutions of the forward and adjoint linearized Navier–Stokes equations, is applied to both feedforward and feedback loop systems. The former strategy only allows the control settings to be configured once, while the latter approach permits the repeated reoptimization of the control device. Surface roughness establishes a stationary cross-flow disturbance with a predefined set of flow conditions, but an unknown amplitude and phase. A sensor measures the local amplitude of the perturbation and relays the information to the control mechanism. Solutions of the adjoint linearized Navier–Stokes equations are coupled with the sensor measurements to configure and optimize the control mechanism, and establish an anti-phase wave that brings about destructive wave interference. The amplitude of the stationary cross-flow instability is reduced by an order 103 for the feedforward system, while amplitude reductions of the order 103 per iteration and 108 overall are realizable for the feedback modeling approach. Similar levels of flow control are realizable for a multiple controller configuration. However, stationary cross-flow disturbances could not be eliminated indefinitely. Inevitably, the cross-flow instability started to grow again, albeit at a considerably lower magnitude. The analysis is extended to include the effects of systematic error in the sensors measuring capability.

Unsteady disturbances in a swept wing boundary layer due to plasma forcing

This work investigates the response of a transitional boundary layer to spanwise-invariant dielectric barrier discharge plasma actuator (PA) forcing on a 45° swept wing at a chord Reynolds number of 2.17×106. Two important parameters of the PA operation are scrutinized, namely, the forcing frequency and the streamwise location of forcing. An array of passive discrete roughness elements is installed near the leading edge to promote and condition a set of critical stationary crossflow (CF) instability modes. Numerical solutions of the boundary layer equations and linear stability theory are used in combination with the experimental pressure distribution to provide predictions of critical stationary and traveling CF instabilities. The laminar–turbulent transition front is visualized and quantified by means of infrared thermography. Measurements of velocity fields are performed using hotwire anemometry scans at specific chordwise locations. The results demonstrate the inherent introduction of unsteady velocity disturbances by the plasma forcing. It is shown that, depending on actuator frequency and location, these disturbances can evolve into typical CF instabilities. Positive traveling low-frequency type III modes are generally amplified by PA in all tested cases, while the occurrence of negative traveling high-frequency type I secondary modes is favored when PA is operating at high frequency and at relatively downstream locations, with respect to the leading edge.

Instability and Transition of Hypersonic Boundary Layer on a Blunted Delta Wing

The instability and transition of hypersonic boundary layer on a blunted delta wing is performed by numerical simulation of experiments conducted in the quiet wind tunnel. Disturbances are calculated using linear stability theory to obtain the integrated disturbance growth rates and amplification factors from laminar steady base flows. Comparisons are made between the results of the stability analysis and the experimentally measured transition characteristics. The results show that the generalized inflections existing in velocity profiles reveal both the streamwise instability and crossflow instability of the boundary layer on the delta wing. In the parameter spaces of frequency and wave number, there is only one unstable region in which the first-mode and second-mode waves are integrated with each other at angle of attack, whereas the unstable regions of the first-mode and second-mode waves are separately distributed at angle of attack of . The numerically predicted factor distribution is in good agreement with the measured transition front, and the factor is about 3 when boundary-layer transition occurs. The low-frequency unstable waves with about 25–30 kHz play a key role in dominating the boundary-layer transition of the delta wing.

Experimental base flow modification on a swept wing using plasma forcing

This work experimentally investigates plasma actuator (PA) forcing effects on the base flow and developing crossflow (CF) instabilities in a swept wing boundary layer. Spanwise-invariant plasma forcing near the leading edge is configured according to the base flow modification (BFM) strategy. A simplified predictive model is constructed by coupling an experimentally derived plasma body force and a linear stability theory and is used to infer the stability characteristics of the boundary layer subject to BFM. The base flow velocity is measured by stereo particle image velocimetry (PIV) at various PA operating conditions. Similarly, the developing CF instabilities, triggered through discrete roughness elements, are quantified by planar-PIV. The results demonstrate that a PA can reduce the boundary layer CF component, whereas the control authority shows a high dependence on the momentum coefficient. The dissimilar reduction between the streamline-aligned velocity and CF component leads to a local re-orientation of the base flow. Spanwise spectral analysis of the time-averaged flow indicates that stationary CF instabilities can be favorably manipulated whereas the BFM reduction effects depend on the corresponding initial amplitudes of stationary instabilities. An evident spanwise shift in the trajectory of stationary CF vortices is observed, which appears to result from the local alteration of the boundary layer stability due to the PA forcing. Despite the overall reduction in the amplitude of stationary CF instabilities, unsteady disturbances are found to be enhanced by the PA forcing. The current results shed light on the underlying principles of BFM-based PA operation in the context of laminar flow control.

Competing roughness effects on the non-stationary crossflow instability of the boundary-layer over a rotating broad cone

There are two primary aims of this paper: the first aim is to investigate the effects of the roughness types of the Miklavčič and Wang model on stationary disturbances of the boundary-layer flow over a broad rotating cone in still fluid. The second aim is to examine similar effects of surface roughness, but on non-stationary modes of crossflow instability. This study begins with the formulations of the mean-flow system based on the cone geometry. These equations are solved using a spectral numerical method based on Chebyshev polynomials and then used to formulate the linear stability system, which are computed for obtaining neutral curves of the unsteady flows. For the stationary modes, our results indicate that the inviscid instability (type I mode) is more stable, while the viscous instability (type II mode) entirely eliminates, as concentric grooves or isotropic roughness and the cone half-angle increase. In contrast, streamwise grooves have a slight stabilizing effect on the type I mode and a significant destabilizing effect on the viscous instability. Another finding indicates that decreasing the half-angle leads to a greater stabilizing effect of isotropic roughness on the type I modes. Our outcomes are also confirmed by the growth rate and the energy analysis, which shows a large reduction of the total energy balance as a result of increasing concentric grooves or isotropic roughness for the crossflow mode. For non-stationary modes, similar effects are observed in that increasing all levels of roughness stabilizes the type I branch (with concentric grooves and isotropic roughness having a much stronger effect than streamwise grooves), and although increasing concentric grooves and isotropic roughness stabilizes the type II branch, increasing streamwise grooves destabilizes this branch. For modes traveling slower than the rotation of the cone, concentric grooves generally have a stronger stabilization effect for the type I branch, whereas for modes traveling faster than the cone, isotropic grooves have a stronger stabilization effect on the type I branch for all broad half angles. Importantly, increasing concentric grooves and isotropic roughness increases the frequency at which the most dangerous modes occur, whereas increasing the streamwise grooves reduces the frequency at which the most dangerous modes occur.

Linear impulse response in three-dimensional oscillatory boundary layers formed by periodic modulation of a rotating disk

A numerical investigation is undertaken on the development of linear disturbances in the rotating disk boundary layer, in which a time-periodic modulation is applied to the disk rotation rate. The model gives a prototypical example of a three-dimensional oscillatory boundary layer, by adding a Stokes layer to the von Kármán flow that develops on a steady disk. The study extends the Floquet analysis of Morgan et al. (J. Fluid Mech., vol. 925, 2021, A20), who showed that disk modulation stabilises the stationary convective instabilities found on the steady rotating disk. Using a radial homogeneous flow approximation, whereby the radial dependence of the basic state is ignored, disturbance development is simulated for several modulation settings, with flow conditions matched to both convective and absolute forms of linear instability. Disturbances excited via a stationary periodic wall forcing display behaviour consistent with that found using Floquet theory; time-periodic modulation stabilises the cross-flow instability by reducing the radial growth rate. In addition, convective and absolute instabilities, generated by an impulsive wall forcing, are both stabilised by the introduction of modulation to the disk rotation rate. Modulation establishes a significant reduction in both the temporal growth rate and the disturbance amplitude as it propagates away from the impulse origin. Moreover, greater stabilising control benefits are realised as the modulation amplitude increases.

Cross-flow linear instability in compressible boundary layers over a flat plate

The linear instability of compressible boundary layers over a flat plate in the presence of parameterized crossflow has been investigated by means of linear stability theory. A family of boundary layer with crossflow is obtained as the base flow from the compressible Falkner–Skan–Cooke (FSC) flow model. Two factors, that is, the local swept angle and the pressure-gradient parameter, are designed to create the crossflow with different directions and magnitudes, which further results in the variation of the cross-flow instability. Modal properties related to the cross-flow instability are emphasized. The association between the cross-flow mode and the Mack's mode is clarified by extending the base flow from two dimension to three dimension. The cross-flow instability is discovered to be integrated with the slow-mode instability, that is, the instability related to the Tollmien–Schlichting (T–S) mode or the first mode, and it can hardly be distinguished as an individual mode in most cases. The effects of Mach number, pressure gradient, local sweep, and wall temperature are studied. The behaviors of the cross-flow instability under such effects resemble those of the slow-mode instability in the two-dimensional boundary layers. It is found that the unstable modes in the three-dimensional boundary layers are mainly affected by the streamwise pressure gradient and the crossflow per se. Specifically, the first mode is much more sensitive to the crossflow than the second mode. As a result, more marked variations are commonly observed for the first mode in the boundary layers with crossflow.

Cross-flow vortices and their secondary instabilities in hypersonic and high-enthalpy boundary layers

Compared to the streamwise instability, the cross-flow instability in high-enthalpy flows has received relatively less attention, but the latter is of vital importance in the flow transition for practical configurations. This work aims to investigate the cross-flow primary and secondary instabilities in hypersonic and high-enthalpy boundary layers, considering thermochemical non-equilibrium (TCNE) effects. The numerical tools adopted include a high-order shock-fitting solver, nonlinear parabolized stability equations and secondary instability theory (SIT). The flow over a swept parabola is calculated at a free-stream Mach number of 16. It is found that TCNE has a destabilizing effect on the cross-flow mode with a non-catalytic wall. Two important non-dimensional parameters are summarized to explain this effect. One is the ratio between the wall and boundary-layer edge temperatures, and the other is the cross-flow Mach number. Due to nonlinear effects, the stationary cross-flow vortices evolve and exhibit the classic rollover structures as in lower-speed flows. Two different disturbance energy norms are used in the energy budget analysis to classify the secondary cross-flow instability modes. The results from SIT highlight the importance of type-IV modes in TCNE flows at the downwash region of the vortex. The type-IV modes arise with the combined contribution from the wall-normal (on top and trough of the vortex) and spanwise (in the downwash region) production terms. The type-I mode is dominant in the calorically perfect gas case with an adiabatic wall, whereas the type-IV mode has the largest growth rate in the TCNE cases irrespective of wall temperature variation.

Transport-Based Transition Prediction for the Common Research Model Natural Laminar Flow Configuration

This paper presents the application of a new -based one-equation transition transport model to the Common Research Model Natural Laminar Flow Configuration (CRM-NLF), which was the central test case of the 1st AIAA CFD Transition Modeling and Prediction Workshop. The new model uses a simplified formulation of the Arnal, Habiballah, and Delcourt transition criterion that is stability based. The model is formulated in a grid-point-local manner and is coupled to the Menter shear stress transport eddy-viscosity turbulence model. The flow conditions applied are exactly those that were reported from the National Transonic Facility wind tunnel test campaign. The comparisons of the results yielded by the new model in terms of the transition fronts along the wing span show a very good match with the transition fronts derived from the temperature-sensitive paint images taken during the wind tunnel test and with computational result from an -based Two--factor strategy using critical -factors for Tollmien–Schlichting and crossflow instabilities and applying a local linear stability code.

Linear modal global instabilities of hypersonic flow over an inclined cone

A systematic parametric study is presented on the modal global linear instability of Mach 6 boundary-layer flow over an inclined cone at a 6° angle of attack under typical wind tunnel conditions. The analysis is performed using the spatial BiGlobal theory. Results reveal two classes of global instabilities in the outboard region away from the leeward plane: high-frequency (hundreds of kHz) second mode instabilities and low-frequency (tens of kHz) crossflow instabilities. In the global eigenvalue spectra of the second mode instability, two distinct branches of significantly unstable modes are identified, namely, an approximately continuous spectrum (branch S) and a few discrete points (branch D). The branch D modes peak at the windward centerline, while branch S modes lie at a certain distance away from the windward meridian. The global stability characteristics of the crossflow instability over a conical configuration are uncovered for the first time. In the global eigenvalue spectra of the crossflow instability, many unstable modes emerge and form a complex pattern, with the most amplified frequency of around 30 kHz. The unstable crossflow modes are mainly distributed on the leeward side and wave angles obviously increase toward the leeward centerline. The peak growth rates are slightly smaller than those of second modes, and yet the most amplified frequency varies rather mildly along the streamwise direction so that they may achieve larger integrated growth rates than second modes do.

On the near-wall instability of oblique flow over a wavy wall

The instability of a shear flow passing over a wavy wall with wave crests not perpendicular to the flow direction is investigated. The friction Reynolds number for the flow is large and the wave amplitude scaled on the wavelength is small compared with the viscous wall layer. The instability takes the form of a streamwise vortex of wavelength comparable to the viscous wall layer in which the basic flow adjusts to the presence of the wall. For a given wall amplitude, the instability considered is the first one to arise as the Reynolds number is increased and modes of wavelength comparable to the viscous layer grow much faster than modes of wavelength comparable to the wall wavelength. The instability is not driven by centrifugal or viscous effects but is a novel kind of cross-flow vortex instability associated with a spatially periodic flow; the existence of the instability is associated with the orientation of the wave crests. The instability is investigated for wavelengths comparable to the depth of the viscous wall layer; the limiting cases of large and small wavelengths are investigated asymptotically. At small wavenumbers and roughness heights the instability connects with disturbances of wavelength comparable to the wall wavelength. At high wavenumbers and roughness heights a new structure emerges and the disturbance moves away from the wall, that structure takes on a self-similar form with progressively faster variations in the streamwise and spanwise directions as the roughness height increases.

Improved crossflow transition predictions for the one-equation [formula omitted] transition model

A variant of the local correlation-based transition model (LCTM) γ is presented to account for the prediction of transition due to stationary crossflow instabilities. The presented Tc1 crossflow criterion is a local approximation of the well-known C1 criterion by Arnal (1984), evaluated locally through auxiliary functions expressed by the solution of the Falkner–Skan–Cooke (FSC) equations. The criterion, originally proposed by Menter and Smirnov (2014), uses the wall-normal directional change of the normalized vorticity as indicator of the crossflow strength. Hereafter, an original calibration FSC-based of Menter & Smirnov criterion is proposed. A local approximation of the sweep angle is included in order to achieve better results on non-wing-like geometries. The capability of this model variant to predict stationary crossflow transition is therefore discussed. A validation study is presented using experimental data on the 6:1 prolate spheroid and the sickle wing.

Influence of Nose Bluntness on Crossflow Instability

Much work has been focused on the initiation of crossflow instability due to roughness-induced mode excitation. Here we emphasize another aspect of the problem; how changes in nose bluntness (possibly due to ablation or other effects) may also alter the dynamics of crossflow instability via entropy layer modification. The effect of nose bluntness on crossflow instability for a Mach 6 yawed cone is considered at two different angles of attack. Linear parabolized stability equations investigation is performed on crossflow vortices along vortex lines calculated by the inflection point method. It is found that small changes in nose bluntness significantly alter the trajectory of crossflow vortices, the strength of the crossflow instability, and the most unstable wavenumber of the crossflow vortices. These results may be of particular importance to experimentalists studying the effect of ablation on crossflow instability.

Direct numerical simulation of interaction between a stationary crossflow instability and forward-facing steps

The interaction between forward-facing steps of several heights and a pre-existing critical stationary crossflow instability of a swept-wing boundary layer is analysed. Direct numerical simulations (DNS) are performed of the incompressible three-dimensional laminar base flow and the stationary distorted flow that arise from the interaction between an imposed primary stationary crossflow perturbation and the steps. These DNS are complemented with solutions of the linear and the nonlinear parabolised stability equations, used towards identifying the influence of linearity and non-parallelism near the step. A fully stationary solution of the Navier–Stokes equations is enforced numerically, in order to isolate the mechanisms pertaining to the interaction of the stationary disturbance with the step. Results provide insight into the salient modifications of the base laminar boundary layer due to the step, and the response of the incoming crossflow instability to these changes. The fundamental spanwise Fourier mode of the disturbance field gradually lifts up as it approaches the step and passes over it. The flow environment around the step is characterised by a sudden spanwise modulation of the base-flow streamlines. Additional stationary perturbation structures are induced at the step, which manifest in the form of spanwise-aligned velocity streaks near the wall. Shortly downstream of the step, the fundamental component of the crossflow perturbation maintains a rather constant amplification for the smallest steps studied. For the largest step, however, the fundamental crossflow perturbation is stabilised significantly shortly downstream of the largest step. This surprising result is ascribed to a modulation of the kinetic energy transfer between the base flow and the fundamental perturbation field, which is brought forward as a new step interaction mechanism. Possible non-modal growth effects at the step are discussed. Furthermore, the results from DNS indicate significant amplification of the high-order harmonic crossflow components downstream of the step.

Receptivity of crossflow instability to discrete roughness amplitude and location

The effect of discrete roughness elements on the development and breakdown of stationary crossflow instability on a swept wing is explored. Receptivity to various element heights and chordwise locations is explored using a combination of experimental and theoretical tools. Forcing configurations, determined based on linear stability predictions, are manufactured and applied on the wing in a low turbulence facility. Measurements are performed using infrared thermography, quantifying the transition front location, and planar particle image velocimetry, providing a reconstruction of stationary crossflow instabilities and their associated growth. Measurements are corroborated with simulations based on nonlinear parabolised stability equations. Results confirm the efficacy of discrete roughness elements in introducing and conditioning stationary crossflow instabilities. Primary instability amplitudes and resulting laminar-turbulent transition location are found to strongly depend on both roughness amplitude and chordwise location. The Reynolds number based on element height is found to satisfactorily approximate the initial forcing amplitude, revealing the importance of local velocity effects in non-zero-pressure gradient flows. Direct estimation of initial perturbation amplitudes from nonlinear simulations suggests the existence of pertinent flow mechanisms in the element vicinity, active in conditioning the onset of modal instabilities. Dedicated velocimetry planes, elucidate the development of a momentum deficit wake which rapidly decays downstream of the element followed by mild growth, representing the first experimental evidence of transient behaviour in swept wing boundary layers. The outcome of this work identifies a strong scalability of the transition dynamics to roughness amplitude and location, warranting the upscaling of roughness elements to more accessible, measurable and spatially resolved configurations in future experiments.

Unsteady interaction of crossflow instability with a forward-facing step

Experiments have been conducted on a swept wing model in a low-turbulence wind tunnel at chord Reynolds number of $2.17 \times 10^{6}$ to investigate the unsteady interaction of a forward-facing step (FFS) with incoming stationary crossflow (CF) vortices. The impact of varying the FFS height on the development and growth of primary and secondary CF disturbances and the ensuing laminar–turbulent transition is quantified through detailed hot-wire anemometry and infrared thermography measurements. The presence of the FFS results in either a critical (i.e. moderate transition advancement) or a supercritical behaviour (i.e. transition advancing abruptly to the FFS location). The arrival of the forced stationary CF vortices at the step is accompanied by their amplification. Unsteady analysis for the critical cases indicates temporal velocity fluctuations following closely the development of the baseline configuration (i.e. agreeing with the development of secondary instabilities). Consequently, laminar breakdown originates from the outer side of the upwelling region of the CF vortices. In contrast, for the supercritical FFS, the laminar breakdown unexpectedly originates from the inner side of the upwelling region. Evidence points to an unsteady mechanism possibly supported by locally enhanced spanwise-modulated shears and the recirculation region downstream of the FFS edge. This mechanism appears to govern the abrupt tripping of the flow in supercritical step cases. The findings in this work provide insight into the unsteady FFS–CF vortex interaction, which is pivotal to understanding the influence of an FFS on the laminar–turbulent boundary-layer transition in swept aerodynamic surfaces.

Boundary layer transition and linear modal instabilities of hypersonic flow over a lifting body

Boundary layer transition over a lifting body of 1.6 m length at $2^\circ$ angle of attack has been simulated at Mach 6 and a unit Reynolds number $1.0 \times 10^7$ m$^{-1}$. The model geometry is the same as the Hypersonic Transition Research Vehicle designed by the China Aerodynamics Research and Development Center. Four distinct transitional regions are identified, i.e. windward vortex region, shoulder vortex region, windward cross-flow region and shoulder cross-flow region. Multi-dimensional linear stability analyses by solving the two-dimensional eigenvalue problem (spatial BiGlobal approach) and the plane-marching parabolized stability equations (PSE3D approach) are further carried out to uncover the dominant instabilities in the last three regions as well as the shoulder attachment-line region. The shoulder vortex is conducive to both inner and outer modes of shear-layer instability, of which the latter most likely trigger the vortex breakdown. A novel method is presented to substantially reduce the computational cost of BiGlobal and PSE3D in resolving the cross-flow instabilities in cross-flow regions. The peak frequencies of cross-flow modes lie between 15 and 45 kHz. Whereas oblique second Mack modes are marginally unstable in the windward cross-flow region, they could be strong enough to compete with the cross-flow modes in the shoulder cross-flow region. In the shoulder attachment-line region, there exists only one unstable mode of Mack instability, differing from previous studies that show a hierarchy of modes in the context of symmetrical attachment-line flows. Results of the numerical simulation and multi-dimensional stability analyses are compared when possible, showing a fair agreement between the two approaches and highlighting the necessity of considering non-parallel effects.

An improved physics-informed transition-turbulence model for asymmetric transition over supersonic rotating projectiles

On the surface of a rotating projectile flying with a supersonic speed, due to the rotational motion, an asymmetric boundary layer transition will occur. This boundary layer distortion caused by the rotation has a significant contribution to the Magnus effect, which will produce a large instability moment and cause flight instability. Therefore, it is of great significance to conduct in-depth research and flow mechanism analysis on the asymmetric boundary layer transition phenomenon on the surface of high-speed rotating projectiles. On the one hand, in supersonic boundary layers, the steamwise flow instability modes are mainly the first mode and the laminar flow separation mode; on the other hand, strong crossflow velocity shear will be generated in the self-rotating state of the projectile and the compressible crossflow instability plays an extremely important role. This paper proposes a physics-informed transition-turbulence model suitable for supersonic/hypersonic boundary layers, which contains physical instability mechanisms and all variables can be solved locally. New time scales for the first mode and crossflow mode are developed. Furthermore, compressibility corrections and cooled wall modifications are performed on the model. Based on this model, we conducted the unsteady simulations of the high-speed rotating straight cone, and carefully compared the mesh sensitivity. In detail, the boundary layer transition characteristics under different Mach numbers, angles of attack, Reynolds numbers and rotational speeds are analyzed through the present transition-turbulence model. Decent agreement with the experiment data verifies that the transition-turbulence model developed by the authors can be applied to predict the asymmetric transition phenomenon on the supersonic flying rotating projectiles with high accuracy.

Surface-Roughness Effects on Crossflow Instability of Swept-Wing Boundary Layers Through Generalized Resonances

It is known that crossflow instability and transition can be influenced significantly by micrometer-sized surface roughness. A recent study sought to explain such a sensitive effect from the standpoint of a generalized resonant-triad interaction between crossflow instability modes and distributed roughness-induced perturbations. The mechanism was demonstrated for Falkner–Skan–Cooke similarity velocity profiles. In the present paper, we examine its role in destabilizing stationary and travelling crossflow vortices in the boundary layers over the NLF(2)-0415 swept wing, for which experiments found that micrometer-sized roughness caused earlier transition. Our analysis shows that the generalized resonance mechanism operates in a swept-wing boundary layer. Under the assumption that roughness consists of all spectral components, a crossflow mode with a fixed-dimensional frequency and wavelength resonates at each chordwise location with one or more other modes. We derive the amplitude equations for the interacting modes. The calculations show that the resonance is highly effective, especially when the roughness elements are near the leading edge. Importantly, it is found that the wave numbers of the roughness spectra participating in the most effective resonant interactions are very close to those of the right-branch neutral stationary eigenmode. As a result, micrometer-sized distributed roughness generates a perturbation of much larger amplitude, which alters, through the resonant interactions, the local growth rates of the crossflow vortices by an amount for both stationary and travelling vortices. We also traced the chordwise development of crossflow vortices with fixed-dimensional frequencies and spanwise wave numbers by integrating the local growth rate, or by solving the initial-value problem of the amplitude equations, for roughness without and with chordwise modulation. For roughness with a height of , the accumulated effect of the dominant resonances, whether acting alone or simultaneously, leads to a significant correction to the amplification factor of stationary and travelling vortices.