Crossflow Instability Research Articles

Receptivity to Freestream Acoustic Noise in Hypersonic Flow over a Generic Forebody

Direct numerical simulations of the Navier–Stokes equations have been performed to investigate the receptivity and breakdown mechanisms in a Mach 6 flow over a generic forebody geometry with freestream acoustic disturbances. The simulations are based on transition experiments carried out in April 2015 in the Boeing/U.S. Air Force Office of Scientific Research Mach 6 facility at Purdue University. A three-dimensional model for both fast and slow freestream acoustic waves with multiple frequencies and spanwise wave numbers has been adopted in the numerical simulations, for which high-amplitude disturbances have been considered in order to simulate noisy wind-tunnel conditions. The numerical results revealed similarities in comparison to the experimental observations, especially when slow acoustic waves were considered as freestream disturbances. In particular, slow acoustic waves have been found to induce the breakdown process via crossflow instabilities located in the off-centerline region, with formation of streamwise streaks. Fast acoustic waves, in contrast, appeared more efficient in inducing earlier nonlinear growth through destabilization of the boundary layer along the symmetry plane of the body.

Quantitative study of localized mechanisms of excitation of cross-flow instability modes in a swept-wing boundary layer

An experimental study of two efficient receptivity mechanisms of excitation of cross-flow (CF) instability modes is carried out in a boundary layer of a real airfoil section of a swept wing due to: (i) action of localized surface vibrations, and (ii) scattering of 2D freestream vortices on them. It is found that the two mechanisms lead to rather efficient excitation of CF-modes both at surface vibration frequency and at combination ‘vortex-vibration’ frequencies. First estimations of the corresponding localized receptivity coefficients are obtained. Direct comparison of the experimental amplification curves of the excited CF-modes with those calculated based on the linear stability theory (LST) has shown that the experimental data obtained at vibration frequency are in excellent agreement with the LST. At the same time, growth rates of the CF-modes excited at combination frequencies are found to be completely inconsistent with the LST. A possible explanation of this phenomenon via action of a new efficient distributed receptivity mechanism is suggested. This mechanism is associated with scattering of freestream vortices on rather high-amplitude CF-modes excited by surface vibrations.

Parabolized Stability Equation Analysis of Crossflow Instability on HIFiRE-5b Flight Test

Basic state calculations were performed for the Hypersonic International Flight Research Experiment 5 geometry for both flight and wind-tunnel conditions using the US3D flow solver. Linear parabolized stability equation calculations were performed for the crossflow instabilities, and linear stability theory calculations were performed for the second-mode instabilities using the LASTRAC3d (the three-dimensional Langley stability and transition analysis code) stability suite. Conditions were chosen to represent the flight conditions at a time when a three-lobed transitional front was observed experimentally. Preliminary N-factor thresholds of for the second mode and for stationary crossflow provided a lower bound for the transitional N factor for the observed transitional front during flight conditions over much of the acreage of the vehicle. Applying the same criterion to conditions of recent wind-tunnel tests also reasonably reproduced observed transitional behavior, indicating that the relative physics were accurately captured.

Hypersonic Crossflow Instability

Under the auspices of NATO STO AVT-240: “Hypersonic Boundary-Layer Transition Prediction”, this paper describes the results of close collaborations among the authors toward the fundamental understanding and modeling of the instabilities associated with three-dimensional boundary layers in hypersonic flight. Specifically, the focus is directed toward the crossflow instability. A common straight circular cone geometry is analyzed for and from both a computational and experimental perspective using methods that are unique to each facility and methodology. Disturbance wavelength and trajectory, surface roughness, and the use of quiet wind tunnels are just a few items found to be key factors in the investigation of the crossflow instability. Quiet tunnels allow experiments to be performed in a disturbance environment comparable to that expected from flight, and the combination of different facilities and computations displays a comprehensive analysis that would be unobtainable from any individual approach alone.

Control of stationary cross-flow modes in a Mach 6 boundary layer using patterned roughness

Experiments were performed to investigate passive discrete roughness for transition control on a sharp right-circular cone at an angle of attack at Mach 6.0. A cone angle of attack of $6^{\circ }$ was set to produce a mean cross-flow velocity component in the boundary layer over the cone by which the cross-flow instability was the dominant mechanism of turbulent transition. The approach to transition control is based on exciting less-amplified (subcritical) stationary cross-flow modes through the addition of discrete roughness that suppresses the growth of the more-amplified (critical) cross-flow modes, and thereby delays transition. The passive roughness consisted of indentations (dimples) that were evenly spaced around the cone at an axial location that was just upstream of the first linear stability neutral growth branch for cross-flow modes. The experiments were performed in the air force academy (AFA) Mach 6.0 Ludwieg Tube Facility. The cone model was equipped with a motorized three-dimensional traversing mechanism that mounted on the support sting. The traversing mechanism held a closely spaced pair of fast-response total pressure Pitot probes. The measurements consisted of surface oil flow visualization and off-wall azimuthal profiles of mean and fluctuating total pressure at different axial locations. These documented an 25 % increase in the transition Reynolds number with the subcritical roughness. In addition, the experiments revealed evidence of a nonlinear, sum and difference interaction between stationary and travelling cross-flow modes that might indicate a mechanism of early transition in conventional (noisy) hypersonic wind tunnels.

Plasma virtual roughness elements for cross-flow instability control

Recent experiments and numerical simulations demonstrated that discrete roughness elements can be used to control cross-flow instability over a swept wing. Here, the application of this passive technique requires a row of thin cylindrical elements of a few microns high immediately downstream of the leading edge to excite the subcritical modes of cross-flow instability. By properly choosing the spanwise spacing of these roughness elements, one can suppress the growth of most unstable modes, thereby delay transition. However, this passive technique of controlling cross-flow instability is very sensitive to the size (diameter and height), shape and location of discrete roughness. To mimic the discrete roughness elements and to be able to adjust the roughness parameters dynamically, virtual roughness elements based on dielectric-barrier-discharge plasma actuators have been developed and tested. In this paper, we show the plasma-induced flow field of several different prototype virtual roughness elements for cross-flow instability control, by describing the mechanisms of vortex generation from the virtual roughness elements through an interaction with the incoming laminar boundary layer.Graphical abstract

Control of crossflow instability over a swept wing using dielectric-barrier-discharge plasma actuators

This paper investigates the potential use of dielectric-barrier-discharge (DBD) plasma actuators to control the crossflow instability of the boundary layer on a 45° swept NLF-0415 airfoil at −4∘ angle of attack.The disturbance evolution is resolved using nonlinear parabolized stability equations (NPSEs). Actuators are mounted near the leading edge and generate an electric wind perpendicular to the crossflow vortex axes. The spanwise distance between neighboring actuators is first set to be the fundamental wavelength of the unstable mode. This harmonic actuation reduces the disturbance energy only when the induced body force and the disturbance velocity have reverse sign. At certain different locations, the actuators can actually increase the disturbance energy. The robustness in laminar flow control is improved when two actuators per fundamental wavelength are used. This subharmonic actuation leads to reduction in the energy of the primary unstable mode independent of the actuator locations. Finally, the simulation without baseflow forcing reveals that harmonic modes play important roles in this subharmonic control.

Stability and receptivity of boundary layers in a swirl flow channel

The analysis of the disturbances on a spiraling base flow is relevant for the design, operation, and control of technological devices such as parallel-disk turbines and swirl flow channel heat sinks. Spiraling inflow inside an annular cavity closed at the top and bottom is analyzed in the framework of modal and nonmodal stability theories. Local and parallel flow approximations are applied, and the inhomogeneous direction is discretized using the Chebyshev collocation method. The optimal growth of initial disturbances and the optimal response to external harmonic forcing are characterized by the exponential and the resolvent of the dynamics matrix. As opposed to plane Poiseuille flow, transient growth is small, and consequently, it does not play a role in the transition mechanism. The transition is attributed to a crossflow instability that occurs because of the change in the shape of the velocity profile due to rotational effects. Agreement is found between the critical Reynolds number predicted in this work and the deviation of laminar behavior observed in the experiments conducted by Ruiz and Carey (J Heat Transfer 137(7):071702, 2015). For the harmonically driven problem, an energy amplification of $$\textit{O}(100)$$ is observed for spiral crossflow waves. Transition to turbulence should be avoided to ensure the safe operation of a parallel-disk turbine, whereas large forcing amplification may be sought to promote mixing in a swirl flow channel heat sink. The analysis presented predicts and provides insight into the transition mechanisms. Due to its easy implementation and low computational cost, it is particularly useful for the early stages of engineering design.

A Method for Approximate Prediction of Laminar–Turbulent Transition on Helicopter Rotors

An approximate method is presented to predict the laminar-turbulent transition onset within the unsteady Reynolds-averaged Navier-Stokes (URANS) simulations of helicopter rotors. Based on the presented method, the influence of laminar flow on the required rotor power and generated rotor thrust is investigated and compared to fully turbulent results. To compute the laminar boundary layer, an integral method according to Schlichting/Walz and a set of rotating velocity profiles according to Blaser and Velkoff are used. The laminar-turbulent transition onset is predicted by empirical criteria with respect to Tollmien-Schlichting and crossflow instabilities, bypass mechanisms, and attachment line contamination. The method presented accounts for the turbulence-level variation of the simulated rotor wake. A detection of the boundary layer edge within the URANS solution is not required. The approximate method is validated using the experimental onset positions of representative transition test cases. This includes a laminar flow airfoil and a swept wing. To cover a rotor in forward flight, the onset positions on the model rotor of a Mach-scaled helicopter configuration are computed and compared to available hot-film measurements. In general, the predicted laminar flow lengths on the rotor blades reduce the required rotor power by 4-5%. The rotor thrust remains practically unaffected.

Transport Modeling for the Prediction of Crossflow Transition

Two fully local model variants of a correlation-based transport model that predicts transition due to crossflow instability as well as two-dimensional transition mechanisms are introduced. Whereas the application of one model variant is restricted to wing-like geometries where the flow fulfills certain requirements, the second model variant is applicable to arbitrarily shaped geometries. The derivation and complete formulation of the two model variants is described in detail. An extensive validation study is presented using experimental data from infinite swept wing flows and three-dimensional configurations with different geometries. The capability of both model variants to predict transition due to crossflow instability is demonstrated and discussed.

Aerodynamic Shape Optimization of Natural-Laminar-Flow Wing Using Surrogate-Based Approach

Aerodynamic shape optimization of a swept natural-laminar-flow wing in the transonic regime is still challenging. The difficulty is associated with reliable prediction of laminar–turbulence transition and reasonable compromise of viscous and wave drags. This paper proposes to use efficient global optimization based on surrogate models to address this problem. The Reynolds-averaged Navier–Stokes flow solver features automatic transition prediction via a full method, in which dual factors are used for Tollmien–Schlichting and crossflow instabilities, respectively. The optimizer is based on the kriging surrogate model and parallel infill-sampling method. The baseline natural-laminar-flow wing for short- and medium-range transport aircraft is designed at a cruise Mach number 0.75. Then, drag minimization with up to 42 design variables is carried out, and significant drag reduction (8.79%) has been achieved. A close examination of the optimal wing shows that the drag reduction mainly comes from shock-wave weakening on the upper surface and laminar flow extending via suppression of crossflow instability on the lower surface. Robustness of the optimal wing is investigated, and multipoint optimization is further exercised to improve the robustness to the Mach number variation. It is demonstrated that surrogate-based optimization is feasible and effective for aerodynamic shape optimization of transonic natural-laminar-flow wings.

Secondary crossflow instability through global analysis of measured base flows

A combined experimental and numerical approach to the analysis of the secondary stability of realistic swept-wing boundary layers is presented. Global linear stability theory is applied to experimentally measured base flows. These base flows are three-dimensional laminar boundary layers subject to spanwise distortion due to the presence of primary stationary crossflow vortices. A full three-dimensional description of these flows is accessed through the use of tomographic particle image velocimetry (PIV). The stability analysis solves for the secondary high-frequency modes of type I and type II, ultimately responsible for turbulent breakdown. Several pertinent parameters arising from the application of the proposed methodology are investigated, including the mean flow ensemble size and the measurement domain extent. Extensive use is made of the decomposition of the eigensolutions into the terms of the Reynolds–Orr equation, allowing insight into the production and/or destruction of perturbations from various base flow features. Stability results demonstrate satisfactory convergence with respect to the mean flow ensemble size and are independent of the handling of the exterior of the measurement domain. The Reynolds–Orr analysis reveals a close relationship between the type I and type II instability modes with spanwise and wall-normal gradients of the base flow, respectively. The structural role of the in-plane velocity components in the perturbation growth, topology and sensitivity is identified. Using the developed framework, further insight is gained into the linear growth mechanisms and later stages of transition via the primary and secondary crossflow instabilities. Furthermore, the proposed methodology enables the extension and enhancement of the experimental measurement data to the pertinent instability eigenmodes. The present work is the first demonstration of the use of a measured base flow for stability analysis applied to the swept-wing boundary layer, directly avoiding the modelling of the primary vortices receptivity processes.

Conditioning of unsteady cross-flow instability modes using dielectric barrier discharge plasma actuators

In this study, experiments are performed towards the identification and measurement of unsteady modes occurring in a transitional swept wing boundary layer. These modes are generated by the interaction between the primary stationary and travelling cross-flow instabilities or by secondary instability mechanisms of the stationary cross-flow vortices and have a crucial role in the laminar-to-turbulent breakdown process. Detailed hot-wire measurements were performed at the location of stationary instability amplitude-saturation. In order to deterministically capture the spatio-temporal evolution of the unsteady modes, measurements were phase- and frequency-conditioned using concurrent forcing by means of a dielectric barrier discharge plasma actuator mounted upstream of the measurement domain. The actuator effect, when positioned sufficiently upstream the secondary modes onset, was tuned such to successfully condition the high-frequency type-I and the low-frequency type-III modes without modifying the transition evolution. Two primary stationary cross-flow vortices of different amplitude were measured, revealing the effect of base-flow variations on the growth of travelling instabilities. The response of these two stationary waves to the naturally occurring and forced fluctuations was captured at different chordwise positions. Additionally, the deterministic conditioning of the instability phase to the phase of the actuation allowed phase-averaged reconstruction of the spatio-temporal evolution of the unsteady structures providing valuable insight on their topology. Finally, the effect of locating the actuator at a more downstream position, closer to the type-I mode branch-I, resulted in laminar-to turbulent breakdown for the high-frequency actuation while the low-frequency forcing showed milder effects on the transition evolution.

A combined criteria-based method for hypersonic three-dimensional boundary layer transition prediction

In this paper, a new method for predicting hypersonic three-dimensional (3D) boundary layer transition is developed. It is based on the Reθ/Me criterion for streamwise instability and on the Recf,new criterion for crossflow instability. An intermittency function is also formulated and applied to combine laminar and turbulent flows. Additionally, a computational grid pretreating method, compatible with modern computational fluid dynamics (CFD) techniques based on parallel execution is adopted in order to obtain the boundary layer parameters. Four criteria are compared to define the boundary layer edge. A HIFiRE-5 elliptic cone at different Reynolds numbers is adopted to validate the performance of the criteria-based transition model and the effectiveness of the four criteria for boundary layer edge definition. The results show that the boundary layer edge of complex hypersonic 3D flows could be obtained properly with the computational grid pretreating method and the combination of h0/h0,∞=0.995 and (du/dH)/(du/dH)w=0.1 criteria. Moreover, the computed Reθ/Me and Recf,new distributions in the region between the leading edge and the centerline are similar to the N-factor for streamwise and crossflow instabilities from linear parabolized stability equation (PSE) methods. The shape and trend of the transition onsets predicted by the criteria-based transition model between the centerline and leading edge of HIFiRE-5 agree well with the experiment. However, as for the transition on the centerline, which is dominated by the inflection point in streamwise velocity profiles, using the criteria-based transition model related to boundary layer thickness would predict the transition onset prematurely.

Conditioning of cross-flow instability modes using dielectric barrier discharge plasma actuators

In the current study, selective forcing of cross-flow instability modes evolving on a $45^{\circ }$ swept wing at $Re=2.17\times 10^{6}$ is achieved by means of spanwise-modulated plasma actuators, positioned near the leading edge. In the perspective of laminar flow control, the followed methodology holds on the discrete roughness elements/upstream flow deformation (DRE/UFD) approach, thoroughly investigated by e.g. Saric et al. (AIAA Paper 1998-781, 1998), Malik et al. (J. Fluid Mech., vol. 399, 1999, pp. 85–115) and Wassermann & Kloker (J. Fluid Mech., vol. 456, 2002, pp. 49–84). The possibility of using active devices for UFD provides several advantages over passive means, allowing for a wider range of operating $Re$ numbers and pressure distributions. In the present work, customised alternating current dielectric barrier discharge plasma actuators have been designed, manufactured and characterised. The authority of the actuators in forcing monochromatic stationary cross-flow modes at different spanwise wavelengths is assessed by means of infrared thermography. Moreover, quantitative spatio-temporal measurements of the boundary layer velocity field are performed using time-resolved particle image velocimetry. The results reveal distinct steady and unsteady forcing contributions of the plasma actuator on the boundary layer. It is shown that the actuators introduce unsteady fluctuations in the boundary layer, amplifying at frequencies significantly lower than the actuation frequency. In line with the DRE/UFD strategy, forcing a sub-critical stationary mode, with a shorter wavelength compared to the naturally selected mode, results in less amplified primary vortices and related fluctuations, compared to the critical forcing case. The effect of the forcing on the flow stability is further inspected by combining the measured actuators body force with the numerical solution of the laminar boundary layer and linear stability theory. The simplified methodology yields fast and computationally cheap estimates on the effect of steady forcing (magnitude and direction) on the boundary layer stability.

Interaction of a Backward-Facing Step and Crossflow Instabilities in Boundary-Layer Transition

A swept flat plate model with an imposed pressure gradient was experimentally investigated in a low-speed flow to determine the effect of a backward-facing step on transition in a stationary crossflow–dominated flow. Detailed hotwire measurements of boundary-layer flow were performed to investigate the upstream shift in transition due to a step height of 49% of the local unperturbed boundary-layer thickness. Increasing the initial stationary crossflow amplitude caused an upstream movement of the transition front for the backward-facing step case. The step caused a local increase in the growth of the stationary crossflow instabilities, but the stationary crossflow amplitude at transition was sufficiently low () so that stationary crossflow was not solely responsible for transition. The unsteady velocity spectra downstream of the step were rich with unsteady disturbances in the 80- to 1500-Hz range. Three distinct families of disturbances were identified based on phase speed and wave angle, namely, a highly oblique disturbance (possibly traveling-crossflow-like), a Tollmien–Schlichting-wave-like disturbance, and a shear-layer instability. The stationary crossflow disturbances caused a modulation of the unsteady disturbances, resulting in spatially concentrated peaks in unsteady disturbance amplitude. This modulation of the unsteady disturbances is believed to be the reason for the upstream movement of the transition front with increasing stationary crossflow amplitude.

Effect of transition on the aerodynamic characteristics of a spinning cone

In order to study the effect of transition on the aerodynamic characteristics of a pointed cone at small angles of attack in supersonic flows, the [Formula: see text] transition model, γ transition model, and a trip wire applied with [Formula: see text] transition model coupled with the Reynolds-averaged Navier–Stokes equations were used to simulate the flow over the spinning cone. The γ transition model, including the effects of crossflow instability, is better than other models in the transition and Magnus force prediction. The numerical calculations are in certain agreement with the experimental data. The results indicate that the positions of the maximum boundary layer thickness remain unchanged using different turbulence models, while the results obtained by the transition model shift towards spin direction, intensifying the difference of the boundary layer thickness between the right and the left side bodies; the contribution of the skin friction on the Magnus force increases due to the shift in the transition position; the contribution of pressure on the Magnus force also changes with the distortion of the boundary layer.

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.

Direct Simulation of Hypersonic Crossflow Instability on an Elliptic Cone

Direct numerical simulation is performed on a 38.1% scale Hypersonic International Flight Research Experimentation Program Flight 5 forebody to study stationary crossflow instability. Computations use the US3D Navier–Stokes solver to simulate Mach 6 flow at Reynolds numbers of and , which are conditions used by quiet-tunnel experiments at Purdue University. Distributed roughness with point-to-point height variation on the computational grid and maximum heights of is used with the intent to emulate smooth-body transition and excite the naturally occurring most unstable disturbance wavenumber. Cases at the low-Reynolds number condition use three grid sizes, and hence three different roughness patterns, and demonstrate that the exact flow solution is dependent on the particular roughness pattern. The same roughness pattern is interpolated onto each grid, which yields similar solutions, indicating grid convergence. A steady physical mechanism is introduced for the sharp increase in wall heat flux seen in both computations and experiment at the high-Reynolds number condition. Evolution of disturbance spanwise wavelength is computed, and is found to be more sensitive to Reynolds number than roughness, indicating that the disturbance wavelength is primarily the naturally occurring, flow-selected wavelength for these cases.

Instability analysis and drag coefficient prediction on a swept RAE2822 wing with constant lift coefficient

Swept wing is widely used in civil aircraft, whose airfoil is chosen, designed and optimized to increase the cruise speed and decrease the drag coefficient. The parameters of swept wing, such as sweep angle and angle of attack, are determined according to the cruise lift coefficient requirement, and the drag coefficient is expected to be predicted accurately, which involves the instability characteristics and transition position of the flow. The pressure coefficient of the RAE2822 wing with given constant lift coefficient is obtained by solving the three-dimensional Navier-Stokes equation numerically, and then the mean flow is calculated by solving the boundary layer (BL) equation with spectral method. The cross-flow instability characteristic of boundary layer of swept wing in the windward and leeward is analyzed by linear stability theory (LST), and the transition position is predicted by eN method. The drag coefficient is numerically predicted by introducing a laminar/turbulent indicator. A simple approach to calculate the lift coefficient of swept wing is proposed. It is found that there is a quantitative relationship between the angle of attack and sweep angle when the lift coefficient keeps constant; when the angle of attack is small, the flow on the leeward of the wing is stable. when the angle of attack is larger than 3°, the flow becomes unstable quickly; with the increase of sweep angle or angle of attack the disturbance on the windward becomes more unstable, leading to the moving forward of the transition position to the leading edge of the wing; the drag coefficient has two significant jumping growth due to the successive occurrence of transition in the windward and the leeward; the optimal range of sweep angle for civil aircraft is suggested.