Crossflow Instability Research Articles

Miniaturization and Model-Integration of the Optical Measurement System for Temperature-Sensitive Paint Investigations.

The temperature-sensitive paint (TSP) method, an optical measurement technique, is used for qualitative skin friction visualizations in a wide variety of aerodynamic applications. One such application is the visualization of the laminar-turbulent boundary-layer transition. Optical access to the surface of interest is mandatory for the measurement system, which consists of scientific cameras and LEDs. But the optical access to the area of interest is often impeded by the available windows of the wind tunnel and the wind tunnel model itself, reducing the field of view and the spatial resolution. In some cases, it is of interest to increase the flexibility of the installation of the optical measurement system by reducing its physical dimensions and placing the installation inside the plenum. The DLR Swept flat PlatE Cross-flow TRAnsition (SPECTRA-A) configuration was selected to investigate the influence of two-dimensional steps on the cross-flow-induced boundary layer transition by means of TSP, as part of the EU project Clean Sky 2. The SPECTRA-A configuration consists of two main elements: a flat plate and a displacement body mounted within a very close distance of each other, creating a narrow gap between the two elements. The surface of interest is the area on the flat plate facing the displacement body. The narrow gap limits the utilization of an external camera setup due to poor optical access. A new optical setup consisting of four miniature CMOS machine-vision cameras and five miniature high-power LEDs was integrated into the displacement body. The characteristics of the camera system were analyzed in laboratory tests, establishing that the miniature CMOS machine-vision cameras are suitable for qualitative TSP skin friction visualizations. This was confirmed by successfully measuring the laminar-turbulent boundary-layer transition on the SPECTRA-A configuration. The integrated TSP system is capable of resolving even small variations of the transition location caused by changing the amplitude of the stationary cross-flow instability. The quality of the TSP visualization with the integrated optical system allows for the measurement of the transition location and the wavelength of the stationary cross-flow instability. Overall, a cost-effective TSP visualization system with small space requirements was developed and tested for future applications in wind tunnel models, model support, or side walls of wind tunnels.

Effect of slip on the linear stability of the rotating disk boundary layer

The linear stability of the rotating disk boundary layer with surface roughness is investigated. Surface roughness is modeled using slip boundary conditions [M. Miklavčič and C. Y. Wang, Z. Angew. Math. Phys. 55, 235–246 (2004)], which establish concentric grooves, radial grooves, and isotropic roughness. The effect on the stationary crossflow and Coriolis instabilities is analyzed by applying slip conditions to the undisturbed flow and linear disturbances. This analysis builds on the work of Cooper et al. [Phys. Fluids 27, 014107 (2015)], who modeled slip effects on the base flow but applied the no-slip condition to the linear perturbations. Neutral stability curves and critical parameter settings for linearly unstable behavior are computed for several radial and azimuthal slip length settings. The application of slip on the linear disturbances has a significant impact on the flow stability. In particular, the Coriolis instability undergoes considerable destabilization in the instance of concentric grooves (i.e., radial slip) and radial grooves with sufficiently large azimuthal slip lengths. In addition, concentric grooves destabilize the crossflow instability when the radial slip length is small. Moreover, in the instance of isotropic roughness, the stabilizing effect is markedly less than the observations of Cooper et al. [Phys. Fluids 27, 014107 (2015)]. Finally, an energy analysis is undertaken to ascertain the physical mechanisms brought about by surface roughness.

Comparative performance of nonlinear energy harvesters through strongly coupled fluid-structure-electrical interactive models

Micro power generators (MPGs) can harvest electrical power from ambient energy resources in natural environments to operate small-scale electronic devices. Such systems exploit structural vibrations due to cross-flow instabilities through fluid–structure interactions (FSI). Due to attractive features of piezoelectric transducers, we utilize them for vibration-to-electricity conversion in this work. We develop strongly coupled FSI-based computational models to handle large-amplitude structural motions in which unsteady forces exerted by fluid flows on structures, their dynamical responses, and harvested power are directly computed. Our mathematical model for incompressible flows over moving bodies relies on arbitrary Lagrangian–Eulerian (ALE) formulation. Our in-house FSI solver primarily works using radial basis interpolation technique for grid morphing. Using broad ranges of fluidic, structural, and electrical parameters, we investigate the power generation performance of two types of MPGs, working through vortex-induced vibrations of a circular cylinder and a fluttering NACA-0012 airfoil, under different excitation conditions. Optimum values of load resistance are found to maximize the harvested power. Furthermore, our findings support the linear analysis, which provides insights into the possible instabilities in the electro-mechanical system. Another salient feature of this research work is the inclusion of cubic nonlinear stiffness in the energy harvesting models.

Resonance Impact of a Periodic Sequence of Plasma Actuators in Flow Control in a Swept-Wing Boundary Layer

The process of flow control in the swept-wing boundary layer using a number of plasma actuators mounted at an angle to the leading edge is theoretically studied. The resonance response of the controlled flow is investigated when the angle of inclination of the actuators is close to the angle of inclination of the stationary vortices of cross-flow instability. The calculation of the controlled flow is carried out within the framework of the parabolic system of Navier–Stokes equations. The stability characteristics of periodic flows formed by the action of a control bulk force are calculated.

Improved Amplification Factor Transport Transition Model for Transonic Boundary Layers

Linear-stability-theory-based method plays an important role in boundary-layer transition prediction of aeronautical flows. Based on the simplification of linear stability theory (Drela and Giles, AIAA J, 1987), the amplification factor transport (AFT) equation for Tollmien–Schlichting waves using local variables was first proposed in 2013 (Coder and Maughmer, AIAA J, 2014). However, in transonic high-Reynolds-number flows, the AFT model seriously overestimates the value of . To fix this problem, we have conducted many linear stability analyses to rebuild the formulations of AFT model. Compressibility effect, which has a significant impact on the prediction of value, has been considered in the improved version. Coupled with the model for crossflow instabilities (Xu et al., CJA, 2020), the improved AFT model is established for transonic boundary layers. Several classic test cases are successfully employed to validate present AFT model, including a flat plate, an airfoil, an infinite swept wing, a sickled-shape wing, a 6:1 inclined prolate spheroid, the NASA Common Research Model, and ARA Transonic Swept Wing. Our prediction results show that both Tollmien–Schlichting instabilities and stationary crossflow instabilities can be captured and predicted well by the improved model in subsonic and transonic boundary layers.

Effect of Small Angles of Attack on Turbulence Generation in Supersonic Boundary Layers on Swept Wings

We present the new (for Mach numbers М = 3 and 3.5) and generalizing (for Mach numbers from 2 to 4) results of experimental investigations on the effect of small angles of attack on laminar-turbulent transition in the supersonic boundary layer on a swept wing with the leading-edge slip angle of 72°. The angle-of-attack variation has a strong effect on the transition Reynolds number. The transition Reynolds number decreases with increase in the Mach number. The measurements were carried out by means of a constant-temperature hot-wire anemometer using the proven procedure of determining the transition location. The eN method is used for the first time for numerically estimating the transition Reynolds numbers in the supersonic boundary layer on a swept wing with the leading-edge slip angle of 72°. The growth of the amplitudes of the steady and unsteady modes of the boundary layer crossflow are calculated in accordance with the linear stability theory, within the framework of the Lees–Lin system of equations. The numerical results indicate that, in accordance with the experimental results, laminar-turbulent transition in the boundary layer on the model swept wing is governed by the growth of stationary modes of the crossflow instability.

Effect of Small Angles of Attack on Turbulence Generation in Supersonic Boundary Layers on Swept Wings

We present the new (for Mach numbers М = 3 and 3.5) and generalizing (for Mach numbers from 2 to 4) results of experimental investigations on the effect of small angles of attack on laminar-turbulent transition in the supersonic boundary layer on a swept wing with the leading-edge slip angle of 72°. The angle-of-attack variation has a strong effect on the transition Reynolds number. The transition Reynolds number decreases with increase in the Mach number. The measurements were carried out by means of a constant-temperature hot-wire anemometer using the proven procedure of determining the transition location. The eN method is used for the first time for numerically estimating the transition Reynolds numbers in the supersonic boundary layer on a swept wing with the leading-edge slip angle of 72°. The growth of the amplitudes of the steady and unsteady modes of the boundary layer crossflow are calculated in accordance with the linear stability theory, within the framework of the Lees–Lin system of equations. The numerical results indicate that, in accordance with the experimental results, laminar-turbulent transition in the boundary layer on the model swept wing is governed by the growth of stationary modes of the crossflow instability.

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)).

Measurement and Identification of Supersonic Stationary Crossflow Waves Based on Sublimation Method

Aiming at the crossflow transition problem of supersonic swept wings, an experimental study on the measurement and identification of boundary-layer stationary crossflow waves was carried out at Mach number 2.0. A 65 deg straight-swept-wing model with simple airfoil geometry was designed to capture the crossflow transition phenomenon. The sublimation method for a large-scale cold supersonic wind tunnel was developed to acquire a transition pattern. The stationary crossflow wave identification technology is based on image processing, a vertical and horizontal decomposition method is established, and the quantitative characteristic information (such as the vortex axis spacing and direction) can be identified from high-resolution sublimation images. The experimental results show that the transition position caused by crossflow instability is closed to the leading edge for supersonic wings with large sweep angles at high Reynolds numbers, and the transition position moves upstream with the increase of the unit Reynolds number. The identified vortex axis spacing and direction are basically consistent with the linear stability theory. The stationary disturbance wave information at different Reynolds numbers is compared and analyzed. It is found that the unit Reynolds number plays an important role in the selection and amplification of the unstable stationary modes with different wavelengths in the transition process.

The near wake of discrete roughness elements on swept wings

This work presents the first experimental characterization of the flow field in the vicinity of periodically spaced discrete roughness elements (DRE) in a swept wing boundary layer. The time-averaged velocity fields are acquired in a volumetric domain by high-resolution dual-pulse tomographic particle tracking velocimetry. Investigation of the stationary flow topology indicates that the near-element flow region is dominated by high- and low-speed streaks. The boundary layer spectral content is inferred by spatial fast Fourier transform (FFT) analysis of the spanwise velocity signal, characterizing the chordwise behaviour of individual disturbance modes. The two signature features of transient growth, namely algebraic growth and exponential decay, are identified in the chordwise evolution of the disturbance energy associated with higher harmonics of the primary stationary mode. A transient decay process is instead identified in the near-wake region just aft of each DRE, similar to the wake relaxation effect previously observed in two-dimensional boundary layer flows. The transient decay regime is found to condition the onset and initial amplitude of modal crossflow instabilities. Within the critical DRE amplitude range (i.e. affecting boundary layer transition without causing flow tripping) the transient disturbances are strongly receptive to the spanwise spacing and diameter of the elements, which drive the modal energy distribution within the spatial spectra. In the super-critical amplitude forcing (i.e. causing flow tripping) the near-element stationary flow topology is dominated by the development of a high-speed and strongly fluctuating region closely aligned with the DRE wake. Therefore, elevated shears and unsteady disturbances affect the near-element flow development. Combined with the harmonic modes transient growth these instabilities initiate a laminar streak structure breakdown and a bypass transition process.

Adjoint-based robust optimization design of laminar flow wing under flight condition uncertainties

It is an inherent uncertainty problem that the application of laminar flow technology to the wing of large passenger aircraft is affected by flight conditions. In order to seek a more robust natural laminar flow control effect, it is necessary to develop an effective optimization design method. Meanwhile, attention must be given to the impact of crossflow (CF) instability brought on by the sweep angle. This paper constructs a robust optimization design framework based on discrete adjoint methods and non-intrusive polynomial chaos. Transition prediction is implemented by coupled Reynolds-Averaged Navier-Stokes (RANS) and simplified eN method, which can consider both Tollmien-Schlichting (TS) wave and crossflow vortex instability. We have performed gradient enhancement processing on the general Polynomial Chaos Expansion (PCE), which is advantageous to reduce the computational cost of single uncertainty propagation. This processing takes advantage of the gradient information obtained by solving the coupled adjoint equations considering transition. The statistical moment gradient solution used for the robust optimization design also uses the derivatives of coupled adjoint equations. The framework is applied to the robust design of a 25° swept wing with infinite span in transonic flow. The uncertainty quantification and sensitivity analysis on the baseline wing shows that the uncertainty quantification method in this paper has high accuracy, and qualitatively reveals the factors that dominate in different flow field regions. By the robust optimization design, the mean and standard deviation of the drag coefficient can be reduced by 29% and 45%, respectively, and compared with the deterministic optimization design results, there is less possibility of forming shock waves under flight condition uncertainties. Robust optimization results illustrate the trade-off between the transition delay and the wave drag reduction.

Design Exploration of Transonic Airfoils for Natural and Hybrid Laminar Flow Control Applications

Designing transonic laminar swept wing at high Reynolds numbers is challenging due to the premature flow transition from the prominent crossflow instabilities (CFIs). Hence, natural laminar flow (NLF) wings are limited to lower sweep angles. In this study, hybrid laminar flow control (HLFC) is used to extend this limit to design low-drag transonic infinite wing. A multi-objective genetic algorithm with competing drag components as objectives is used to design NLF and HLFC airfoils. Optimal design is a tradeoff between the drag reduction from skin friction drag, pressure drag, and suction drag, and does not resemble initial airfoils. Airfoil shape and suction distribution are coupled and optimized simultaneously. Euler flow solver with integral boundary-layer method is coupled with a higher-fidelity Linear Stability Analysis using 2.5D approximation for transition prediction. At wing sweep of 22.5°, Mach number of 0.78, and Reynolds number of 30 million, optimum NLF airfoil has 27% lower drag than an optimum turbulent airfoil. The optimum HLFC airfoil showed a 25% lower total drag than the NLF airfoil. A higher optimum sweep angle was observed for low-drag HLFC airfoil (20.5°) in comparison to the NLF airfoil (16.8°) and both favored an undercut on the lower surface to dampen CFI.

Compressibility corrections to extend a smooth local correlation-based transition model to transonic flows

AbstractThis paper presents progress towards a transition modelling capability for use in the numerical solution of the Reynolds-averaged Navier-Stokes equations that provides accurate predictions for transonic flows and is thus suitable for use in the design of wings for aircraft flying at transonic speeds. To this end, compressibility corrections are developed and investigated to extend commonly used empirical correlations to transonic flight conditions while retaining their accuracy at low speeds. A compressibility correction for Tollmien-Schlichting instabilities is developed and applied to a smooth local correlation-based transition model and a stationary crossflow instability compressibility correction is included by adding a new crossflow source term function. Two- and three-dimensional transonic transition test cases demonstrate that the Tollmien-Schlichting compressibility correction produces substantially improved agreement with the experimental transition locations, particularly for higher Reynolds number applications where the effects of flow compressibility are expected to be more significant, such as the NASA CRM-NLF wing-body configuration, while the crossflow compressibility correction prevents an inaccurate, upstream transition front. The compressibility corrections and modifications do not significantly affect the numerical behaviour of the model, which provides an efficient alternative to non-local and higher-fidelity approaches, and can be applied to other transport-equation-based transition models with low-speed empirical correlations without affecting their predictive capability in the incompressible regime.

Attachment-line, crossflow and Tollmien-Schlichting instabilities on swept ONERA-D and Joukowski airfoils.

Linear stability analyses are performed to investigate the boundary layer instabilities developing in an incompressible flow around the whole leading-edge of swept ONERA-D and Joukowski airfoils of infinite span. The stability analyses conducted in our study are global in the chordwise direction and local in the spanwise direction. A neutral curve is drawn at a given leading-edge Reynolds number ReR and several overlapping regions, called "lobes", are identified on a physical basis. A detailed study of the marginal modes reveals the presence of attachment-line and crossflow instabilities, as well as modes whose features do not fall within the standards of a specific type. Connected crossflow/Tollmien-Schlichting modes, that show a dominant spatial structure reminiscent of Tollmien-Schlichting waves but whose destabilization is linked to a crossflow mechanism, have been identified. The comparison of several neutral curves at different ReR values reveals the greater stabilizing effect of the increase of ReR on the crossflow instability compared to the attachment-line instability. The influence of the airfoil shape is also studied by comparing the neutral curves of the ONERA-D with the neutral curves of the Joukowski airfoil. These curves reveal similar characteristics with the presence of distinct lobes and their comparison at constant sweep angle shows that, under the conditions studied, the ONERA-D airfoil is more stable than the Joukowski airfoil, even for crossflow instabilities. The absolutely or convectively unstable nature of the flow in the spanwise direction is also tackled and our results suggest that the flow is only convectively unstable.

Effect of environmental disturbances on crossflow instability

Wind tunnel experiments on the receptivity of three-dimensional boundary layers were performed in a range of freestream turbulence intensities, Tu, from 0.01%—the lowest level ever achieved in this type of work—up to 0.41%. This work confirms that for Tu=0.01%, and presumably below this level, the transition process is dominated by stationary modes. These are receptive to surface roughness and generate Type-I and Type-II secondary instabilities that eventually cause the transition to turbulence. The saturation amplitude of these stationary waves is highly sensitive to the level of environmental disturbances; the former is here recorded to be the highest in the literature, with the latter being the lowest. Travelling modes are still present; however, their influence on the transition process is marginal. At matched surface roughness levels, when the level of environmental disturbance is enhanced to Tuge 0.33%, the travelling modes acquire more importance, strongly influencing the laminar/turbulent transition process, whilst the initial amplitude and growth of the stationary modes are hindered. For this level of Tu, is the interaction of steady and unsteady disturbances that produces highly amplified waves (Type-III), that quickly lead to nonlinear growth and anticipated turbulence. Finally, a simple rule of thumb is proposed, where the transition front was found to move forward by roughly 10% chord for an increase in one order of magnitude in the Tu levels.Graphical abstract

On the identification of cross-flow mode in three-dimensional boundary layers

Parametric zones are obtained where the cross-flow instability can be identified as a mode in the three-dimensional boundary layers with the Mach number ranging from 0 to 10. Although the term cross-flow mode is widely used in the investigations on boundary-layer instability, the previous work [Z. Liu, Phys. Fluids 34, 094110 (2022)] has demonstrated that a cross-flow mode cannot be designated in certain circumstances. The identification of the cross-flow mode is significant not only in the justifiable use of the term but also in judging whether a disturbance is more inclined to a cross-flow type or not. In this work, a criterion is built to identify the cross-flow mode based on the growth-rate peak and disturbance shape. By means of extensive calculations and identifications, parametric zones are presented for the unstable cross-flow mode. It is found that the cross-flow mode cannot be identified at large local sweep or at Mach numbers larger than 1.6. In parametric zones, the cross-flow mode can be distinguished from the Tollmien–Schlichting mode, or identified as the solely dominant mode. Based on the identifications, the maximum growth rates of the cross-flow mode, the Tollmien–Schlichting mode, and the Mack modes in the three-dimensional boundary layers are provided. The dominant mode can be determined at different Mach numbers. The cross-flow mode is revealed to dominate the boundary-layer instability at low Mach numbers. Under large cross-flow strengths, the second mode could not be the dominant mode in the hypersonic boundary layers, which contrasts sharply with the two-dimensional case.

Cancellation of crossflow instabilities through multiple discrete roughness elements forcing

The presented work introduces a novel cancelation technique, based on the linear superposition of stationary crossflow instabilities (CFI) through the application of a streamwise series of optimally positioned discrete roughness elements (DRE) arrays on a swept wing surface. The DRE arrays are designed and arranged with suitable amplitude and phase shift to induce velocity disturbance systems that destructively interact, ultimately damping the developing CFI. This results in the suppression of monochromatic CFI, reducing their amplitude and growth and delaying the boundary layer transition to turbulence.

Investigation and Design of the Transonic Laminar Flow Characteristics in a Laminar Aircraft

Reducing drag is critical to aircraft design. In recent years, laminar technology has become one of the most important feasible technologies for civil aircraft drag reduction design under many design constraints. However, various factors have a certain impact on the laminar flow characteristics in the state of transonic flight. Therefore, it is necessary to deeply understand the specific effects of various flight parameters on the characteristics of laminar flow. In this paper, a parameter sensitivity analysis for a central experimental wing in a special layout aircraft was carried out to investigate its transonic laminar characteristics. Then, the airfoil of the central experimental wing of the aircraft was designed for real flight. The RANS (Reynold-averaged Navier–Stokes) method combined with the γ−Reθ transition model based on local variables was used. The computational approach was validated by the wind tunnel tests and analyzed by the grid independence analysis. The sensitivity mainly focuses on the transition location and the length of the laminar flow zone of the central experiment under different boundary conditions. The transonic transition was affected by a variety of interacting factors that include FSTI (free stream turbulence intensity), pressure gradient, Re (Reynolds number), Ma (Mach number) and α (angle of attack, degree). The essence of the transition is the disruption of flow stability caused by the increase in flow entropy. Among these factors, FSTI directly affects global flow stability, and the pressure gradient affects local flow stability. Ma and α can indirectly affect the flow stability by changing the pressure gradient. Re can control the boundary layer properties to change the flow stability, whereas its effect is easily determined by the pressure gradient. Finally, the improved design of the airfoil with the central experimental wing was conducted. The design of weak shock wave and aerodynamic load on the rear part of the airfoil can improve the aerodynamic characteristics (CL, lift coefficient, increases by 0.28) of the airfoil, which can reduce the load burden on the outboard wing without affecting the laminar flow characteristics of the airfoil. In the next step, cross-flow instability will be considered.

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.