Cross-flow Instability Modes Research Articles

Measurement and analysis of crossflow instability modes on a 7-degree yawed cone at Mach 6

In this work, the crossflow instability modes on a 7° half-angle cone with 6° angle of attack at Mach 6 have been experimentally studied. To begin with, the complete laminar-to-turbulence transition process is acquired by infrared thermography, and the heat flux streaks caused by the stationary crossflow vortices are distinct over the areas of leeward side. Further wavelet analysis reveals a dominant wavenumber of the stationary crossflow vortices, which is centered at about k = 50. Subsequently, the spatial distribution characteristics of the traveling crossflow instability (f = 20–50 kHz) and high-frequency instabilities (f = 100–500 kHz) are acquired between the azimuthal angle Φ = 90°–150° (windside to leeside) through wall mounted pressure sensors. The results of spectral and wavelet analysis indicate that the two types of instability are the traveling crossflow instability and its secondary instability, respectively. Further bispectral analysis is used to show that these high-frequency waves undergo several quadratic phase-coupled interactions with themselves to produce harmonics, as well interact with low-frequency waves that results in spectral broadening.

Excitation of crossflow modes in a swept-airfoil boundary layer, Part 2: Surface-vortex receptivity

An extensive experimental investigation of two receptivity mechanisms of localized excitation of unsteady (in general) Cross-Flow (CF) instability modes in a three-dimensional (3D) swept-airfoil boundary layer has been carried out within one extended set of measurements. Two mechanisms of the boundary-layer receptivity have been investigated: (i) to surface nonuniformities (vibrations, in general) and (ii) to scattering of freestream vortices on surface nonuniformities. All obtained results are deeply processed and analyzed. Part 1 of the present study (Borodulin et al., 2023), was devoted to description of the results obtained for problem (i). Meanwhile, results of detailed investigation of problem (ii) are presented in Part 2 of this study (the present paper).

Excitation of crossflow modes in a swept-airfoil boundary layer. Part 1. Surface receptivity

An extensive experimental investigation of two receptivity mechanisms of localized excitation of unsteady (in general) Cross-Flow (CF) instability modes in a three-dimensional (3D) swept-airfoil boundary layer has been carried out within one extended set of measurements. Two mechanisms of the boundary-layer receptivity have been investigated: (i) to surface nonuniformities (vibrations, in general) and (ii) to scattering of freestream vortices on surface nonuniformities. All obtained results are deeply processed and analyzed. Part 1 of the present study (this paper) is devoted to description of the results obtained for problem (i). Meanwhile, results of detailed investigation of problem (ii) are presented in Part 2 of this study (the next paper Borodulin et al. (2023)).

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.

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.

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.

Hypersonic boundary layer transitions over a yawed, blunt cone

The boundary layer transition process for a straight circular cone with angle of attack (AoA) of 6° at Mach 6 was studied via high-resolution direct numerical simulations and stability analyses. A pair of strong streamwise vortices simultaneously induced a low-speed mushroom structure to emerge near the leeward plane. This structure was subject to low-frequency sinuous and high-frequency varicose instabilities. The transition between windward and leeward rays likely occurred due to the interactions between low-frequency traveling and stationary crossflow vortices. The lower-amplitude high-frequency secondary crossflow instability mode could be traced back to the upstream Mack mode. Although the axial and crossflow vortices were fundamentally different, there was a striking similarity between them since both high-frequency perturbations were driven by azimuthal shear and resulted in staggered positive and negative axial vortices along the streamwise direction.

Comparison of amplitude method of roughness-induced swept-wing transition prediction with experiment

An amplitude method of laminar-turbulent transition prediction in the boundary layer on a swept wing has been developed and tested. The method computes the amplitudes and spectra of steady cross-flow instability modes generated by surface roughness. The transition criterion is based on the crucial, threshold values of maximal or local amplitudes of these perturbations found from experiments. Statistical methods describing the intermittency in the transition zone based on this criterion are proposed.

Distributed vortex receptivity of a swept-wing boundary layer. Part 2. Receptivity characteristics

Abstract

Distributed vortex receptivity of a swept-wing boundary layer. Part 1. Efficient excitation of CF modes

Abstract

Thermal imaging of laminar-turbulent transition on experimental model of swept wing. Creating database of experimental data

The paper is devoted to the problem of creation of experimental database obtained due to systematic extended series of experiments aimed at registering the laminar-turbulent transition in boundary layers on a swept wing model. The experiments were carried out in a low-turbulence wind tunnel in boundary layers developed on ‘suction’ and ‘pressure’ sides of experimental model of an airfoil in a broad range of problem parameters (angle of attack, free-stream velocity, free-stream turbulence etc.). The main feature of performed experiments is using of a new panoramic experimental technique based on application of sensitive infrared camera. Digital postprocessing of obtained thermograms that gave a possibility to detect the position of transition occurred due to amplification of cross-flow instability modes, TS-waves or both of them. The article includes description of the approaches used and the first preliminary results.

Transition control in a three-dimensional boundary layer at elevated free stream turbulence using dielectric barrier discharge

The results of an experimental study of the effect of dielectric barrier discharge (DBR) actuator on laminar-turbulent transition in a three-dimensional boundary layer under influence of elevated free-stream turbulence are presented. The travelling cross-flow instability modes are dominated in transition in a base configuration. Their characteristics do not depend on a spanwise position. The DBD-actuator that generated stationary cross-flow vortices with the predefined spanwise wavelength when turned on was capable to reduce a turbulent spots production rate in comparison to the base regime.

Experimental and theoretical study of swept-wing boundary-layer instabilities. Unsteady crossflow instability

Extensive combined experimental and theoretical investigations of the linear evolution of unsteady (in general) Cross-Flow (CF) and three-dimensional (3D) Tollmien-Schlichting (TS) instability modes of 3D boundary layers developing on a swept airfoil section have been carried out. CF-instability characteristics are investigated in detail at an angle of attack of −5° when this kind of instability dominates in the laminar-turbulent transition process, while the 3D TS-instability characteristics are studied at an angle of attack of +1.5° when this kind of instability is predominant in the transition process. All experimental results are deeply processed and compared with results of calculations based on several theoretical approaches. For the first time, very good quantitative agreement of all measured and calculated stability characteristics of swept-wing boundary layers is achieved both for unsteady CF- and 3D TS-instability modes for the case of a boundary layer developing on a real swept airfoil. The first part of the present study (this paper) is devoted to the description of the case of CF-dominated transition, while the TS-dominated case will be described in detail in a subsequent second part of this investigation.

Control of the Laminar-Turbulent Transition in a Three-Dimensional Boundary Layer under Elevated External Turbulence Using Dielectric Barrier Discharge

The results of experimental study of the effect the dielectric barrier discharge (DBR) actuator on the laminar-turbulent transition in a three-dimensional boundary layer under the influence of elevated free-stream turbulence are presented. Traveling cross-flow instability modes dominate in the transition to turbulence in the base boundary layer. Their characteristics are independent of the spanwise position. The DBR actuator that generates stationary longitudinal vortices with a predefined spanwise wavelength when turned on is able to lower the production rate of turbulent spots in comparison with the base regime.

Assessment of laminar-turbulent transition models for Hypersonic Inflatable Aerodynamic Decelerator aeroshell in convection heat transfer

Hypersonic Inflatable Aerodynamic Decelerator (HIAD) has shown its great potential for future planetary explorations. However, the HIAD surface deflections could both promote boundary-layer transition early and augment heating levels sharply, which poses challenges for survivability of a Thermal Protection System (TPS). The goal of this work is to assess different transition models for the prediction of hypersonic transitional flows over scalloping deformed HIAD surface and to seek the critical factor for their capabilities to provide a reference for the application and advancement. Three representative transition models are considered: γ-Reθ, k-ω-γ and kT-kL-ω. The results show that the undulating surface causes flow separations and reattachments in valleys and strong crossflow along the leeward. k-ω-γ model can correctly predict both the shapes and locations of the transition onsets. The transition zone predicted by γ-Reθ model is much small, while kT-kL-ω is incapable of transition prediction for such a complex and irregular configuration. Moreover, this study reveals that the crossflow instability plays a dominant role in the transition. The crossflow Reynolds number Recf, whose distributions are approximately consistent with the transition zone, could be a feasible crossflow strength indicator for the transition onsets on the undulating surface. Once k-ω-γ model excludes effects of crossflow instability, it predicts incorrect transition results for the deformed surface of HIAD. Besides, a detailed analysis shows that both the crossflow instability mode and the first disturbance mode in valleys are the major contributors to the transition on the leeward surface. Near the leeward ray, the transition is mainly determined by the first disturbance mode.

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.

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.

Excitation of controllable perturbations in the three-dimensional boundary layer using plasma actuators

Two versions of the structure of a multi-discharge plasma actuator intended to excite boundary layer perturbations in the neighborhood of the leading swept-wing edge are suggested. The actuator must prevent from appearance and development of the crossflow instability modes leading to laminarturbulent transition under the normal conditions. In the case of flow past a swept wing, excitation of controllable perturbations by the plasma actuator is simulated numerically in the steady-state approximation under the typical conditions of cruising flight of a subsonic aircraft. The local body force and thermal impact on the boundary layer flow which is periodic along the leading wing edge is considered. The calculations are carried out for the physical impact parameters realizable in the near-surface dielectric barrier discharge.

Receptivity mechanism of cross-flow instablity modes induced in three-dimensional boundary layer

Boundary-layer receptivity is the initial stage of the laminar-turbulent transition process, which plays a key role in the transition, especially for the case of three-dimensional boundary-layer flow. The research of the three-dimensional boundary-layer receptivity is theoretically significant for further understanding of the mechanisms of laminar-turbulent transition and turbulence formation. A numerical method is used to study the three-dimensional boundary-layer receptivity under the interaction of the free-stream turbulence and the three-dimensional localized wall roughness. Then whether a new cross-flow instability mode can be found in the three-dimensional boundary layer is studied. Subsequently, investigated are the conditions under which the steady or unsteady cross-flow instability mode can be induced in the three-dimensional boundary layer, the influences of the intensity, spanwise wave number and normal wave number of the free-stream turbulence, and the size and structure of the three-dimensional roughness on the three-dimensional boundary-layer receptivity under the free-stream turbulence interacting with the three-dimensional localized wall roughness, and the instability mode that can be induced and its role in the three-dimensional boundary-layer receptivity. The numerical results show that when the turbulence intensity is low, the steady cross-flow vortex excited by the three-dimensional localized wall roughness dominates the three-dimensional boundary-layer receptivity; on the contrary, when the turbulence intensity is high, the unsteady cross-flow vortex excited by the free-stream turbulence dominates the receptivity; additionally, when the interaction between the three-dimensional localized wall roughness and the free-stream turbulence is existent, three kinds of instability modes are all produced at the same time, namely, the steady cross-flow vortex, the unsteady cross-flow vortex and the new unsteady cross-flow vortex whose dispersion relation is equal to the linear combination of the positive and negative spanwise wave numbers of the first steady cross-flow vortex and the second unsteady cross-flow vortex. The in-depth research on the three-dimensional boundary-layer receptivity under the interaction of the free-stream turbulence and the three-dimensional localized wall roughness is of benefit to accomplishing the hydrodynamic instability theory and the turbulence theory, and providing the theoretical foundation for the prediction and control of the laminar-turbulent transition.

An energy analysis of convective instabilities of the Bödewadt and Ekman boundary layers over rough surfaces

▪ An energy balance equation for the three-dimensional Bödewadt and Ekman layers of the so called “BEK family” of rotating boundary-layer flows is derived. A Chebyshev discretization method is used to solve the equations and investigate the effect of surface roughness on the physical mechanisms of transition. All roughness types lead to a stabilization of the Type I (cross-flow) instability mode for both flows, with the exception of azimuthally-anisotropic roughness (radial grooves) within the Bödewadt layer which is destabilizing. In the case of the viscous Type II instability mode, the results predict a destabilization effect of radially-anisotropic roughness (concentric grooves) on both flows, whereas both azimuthally-anisotropic roughness and isotropic roughness have a stabilization effect. The results presented here confirm the results of our prior linear stability analyses.