Stationary Crossflow Vortices Research Articles

Breakdown mechanisms induced by stationary crossflow vortices in hypersonic three-dimensional boundary layers

This study investigates the crossflow breakdown of a Mach 6 flow over a swept flat plate by direct numerical simulation (DNS) considering three cases with different spanwise wavenumbers of stationary vortices. Transition in these cases is initiated by the linear and nonlinear evolution of these vortices, followed by secondary instabilities and breakdown due to type-I, type-II modes, and wall blowing/suction perturbations, respectively. The results showed that amplified secondary instabilities significantly distort the mean flow, causing a steep rise in the wall friction coefficient. Fourier analysis shows that, in this fast-varying flow region, the low-frequency disturbances undergo significantly greater amplifications than high-frequency disturbances. Moreover, the stability characteristics of the time- and spanwise-averaged mean flow were examined to elucidate the breakdown mechanisms. It was found that the unstable region initially contracts to a lower frequency band and then expands significantly in the spanwise wavenumber range at low frequencies. This suggests the significant amplifications of low-frequency disturbances, consistent with the observations from DNS. These amplified low-frequency disturbances, in turn, modify the mean flow, leading to the final breakdown. The presented mechanisms, highlighting the critical role of low-frequency disturbances in the breakdown process, are likely to be universally relevant across various parameter regimes.

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.

Receptivity and Stability Theory Analysis of a Transonic Swept Wing Experiment

Surface suction provides an efficient way to delay boundary layer transitions. In order to verify the suction effects and determine the mechanism of suction control in transonic swept wing boundary layers, wind tunnel transition measurements in a hybrid laminar flow control (HLFC) wind tunnel model uses an infrared thermography technique in the Aircraft Research Association (ARA) 2.74 m × 2.44 m low turbulence level transonic wind tunnel. Based on the experimental data of stationary crossflow dominant transitions without and with surface suction in transonic swept wing boundary layers, in this paper, the effects on the receptivity and linear and nonlinear evolution of stationary crossflow vortices have been analyzed with the consideration of curvature. Theoretical analysis agreed with the experimental observations in regard to the transition delay caused by boundary layer suction near the leading-edge region.

Flows Over Rotating Disks and Cones

Rotating-disk flows were first considered by von Kármán in a seminal paper in 1921, where boundary layers in general were discussed and, in two of the nine sections, results for the laminar and turbulent boundary layers over a rotating disk were presented. It was not until in 1955 that flow visualization discovered the existence of stationary cross-flow vortices on the disk prior to the transition to turbulence. The rotating disk can be seen as a special case of rotating cones, and recent research has shown that broad cones behave similarly to disks, whereas sharp cones are susceptible to a different type of instability. Here, we provide a review of the major developments since von Kármán's work from 100 years ago, regarding instability, transition, and turbulence in the boundary layers, and we include some analysis not previously published.

On the Possibility of Cross-Flow Vortex Cancellation by Plasma Actuators

Cancellation of the cross-flow vortices in a swept-wing boundary layer is attempted by plasma actuator array in numerical simulation. The response of the boundary layer to the stationary excitation by a single actuator section is measured experimentally and compared to the response obtained from the solution to the parabolized stability equations. A linear approach is shown to be held within the peak-to-peak magnitude of the stationary cross-flow vortices below 10% of the local potential flow velocity. Within the linear model, an optimal control strategy and a faster suboptimal one are developed to calculate voltage amplitude distribution across the electrodes, taking into account the forcing constraints. Simulation of the cancellation process is performed, showing up to a 20 dB reduction in the initial spanwise velocity modulation in the boundary layer. The minimal actuator resolution required for the successive implementation of the control is shown to be in the order of a quarter of the most amplified wavelength, or 3–4 displacement thickness of the boundary layer. Linear estimates predict up to a 150 mm (22% of flow acceleration region length) transition delay for an actuator momentum coefficient of 0.005%.

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.

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.

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.

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

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

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.

Validation of a laminar-turbulent transition prediction technique for a swept-wing boundary-layer flow

The laminar-turbulent transition in the boundary layer of a 45° swept wing model installed at zero attack angle in the test section of a subsonic wind-tunnel was detected with the help of an infrared camera. The camera recorded sequences of frames, the evolution of the preheated model surface temperature acquired and used for differentiating between the laminar and turbulent regions. The transition onset was evaluated at both sides of the model. Corresponding main flow computations in the virtual wind tunnel test section were performed at the same flow conditions with ANSYS Fluent. The computed main-flow velocity profiles along inviscid streamlines were used for analysis of hydrodynamic stability of the boundary layer with respect to Tollmien-Schlichting waves and stationary cross-flow vortices to obtain N-factor distributions along the model chord. A comparison of the experimental and the computed transition onsets was performed.

An adjoint approach for computing the receptivity of the rotating disc boundary layer to surface roughness

An adjoint approach is developed to compute the receptivity of the rotating disc boundary layer to surface roughness. The adjoint linearised Navier–Stokes equations, in cylindrical coordinates, are derived and receptivity characteristics are computed for a broad range of azimuthal mode numbers using a fully equivalent velocity–vorticity formulation. For each set of flow conditions (i.e. azimuthal mode number), the adjoint method only requires that the linear and adjoint solutions be computed once. Thus, the adjoint approach offers significant computational and time advantages over alternative receptivity schemes (i.e. direct linearised Navier–Stokes) as they can be used to instantaneously compute the receptivity of boundary layer disturbances to many environmental mechanisms. Stationary cross-flow disturbances are established by randomly distributed surface roughness that is periodic in the azimuthal direction and modelled via a linearisation of the no-slip condition on the disc surface. Each roughness distribution is scaled on its respective root-mean-square. A Monte-Carlo type uncertainty quantification analysis is performed, whereby mean receptivity amplitudes are computed by averaging over many thousands of roughness realisations with variable length and wavelength filters. The amplitude of the cross-flow instability is significantly larger for roughness distributions near the conditions for neutral linear instability, while roughness elements radially outboard have a negligible effect on the receptivity process. Furthermore, receptivity increases sharply for roughness distributions that encompass wavelength scales equivalent to that associated with the cross-flow instability. Finally, mean receptivity characteristics are used to predict the radial range that stationary cross-flow vortices achieve amplitudes sufficient to invalidate the linear stability assumptions.

Roughness-Induced Instabilities and Transition on a Generic Hypersonic Forebody at Mach 6

In hypersonic flows, it is often necessary to be able to trip the transition to turbulence, upstream of air intakes, for example. Direct numerical simulations have been performed to identify the roughness-induced transition mechanisms on a wedgelike forebody at Mach 6 and unit Reynolds number million (/m). Good agreement with the experiments performed in the Boeing/Air Force Office of Scientific Research Mach-6 Quiet Tunnel at Purdue University was obtained in terms of wall heat-flux and wall-pressure fluctuations. First, an isolated roughness was considered. The presence of the roughness in the span-inhomogeneous base flow leads to the formation of a crossflowlike vortex. High-frequency secondary instabilities of the stationary crossflow vortex are observed in the wake and are found to be responsible for the breakdown to turbulence. Spatial linear modal instability analysis of this flow has been performed at selected streamwise locations. The linear stability approach is found to give accurate predictions in terms of mode shapes, most-amplified disturbance frequencies, and growth rates, as it only underpredicts the N-factor of the most unstable mode by 10% compared to the direct numerical simulations. Unsteady simulations were then carried out for a trip array configuration and showed that it does not change the transition mechanisms, but the frequencies of the most unstable secondary instabilities were found to be higher.

Identification of traveling crossflow waves under real hypersonic flight conditions

Understanding crossflow instabilities in three-dimensional boundary layers triggered by either traveling crossflow waves or stationary crossflow vortices is of great importance for modeling, predicting, and controlling hypersonic laminar-turbulent transition. However, due to very limited available flight experiment data, the crossflow instability under real flight conditions is still far from fully understood. To gain further insight, the raw data of a recent model flight experiment conducted by China Aerodynamics Research and Development Center have been thoroughly analyzed in the present study. The instrumented model is an inclined blunt cone mounted with several pressure sensors. Distinct low-frequency signals detected by these pressure sensors are peaked at about 10 kHz, which are in good agreement with the traveling-crossflow-wave frequencies with the largest N factors predicted by the eN method. Moreover, propagation velocities and wave angles of these signals obtained from correlation analysis also agree with the results from linear stability theory. The present study confirms that the detected low-frequency signals are traveling crossflow waves and provides the first evidence of traveling crossflow waves under real flight conditions.

Stationary cross-flow breakdown in a high-speed swept-wing boundary layer

A new type-II secondary instability mode was recently identified in high-speed cross-flows using stability analysis, but its role in the transition process is not yet clear. Here, the breakdown of stationary cross-flow vortices at high speeds is examined using direct numerical simulation to determine differences from the low-speed case. The transition is achieved by disturbing stationary cross-flow vortices with unsteady blowing/suction in a swept-wing boundary layer with swept angle 45°, free-stream Mach number 6, and unit Reynolds number 8 ×106. The results reveal that, as in low-speed cases, the type-I secondary instability mode (with frequency ≈190 kHz) is crucial to the breakdown, but neither the traditional nor the new type-II secondary instability play a role. The vortical structure induced by the type-I secondary instability mode has two counter-rotating tubes stretched along the spanwise direction and a footprint aligned normal to the mean flow direction. The composite vortex structures are similar to rolls/braids in plane free-shear layers arising from Kelvin–Helmholtz instability and they evolve into hairpins in the late stage of the transition. Some preliminary statistics from a three-dimensional turbulent boundary layer are provided as a comparison to the two-dimensional ones. The fluctuating cross-flow velocity does not contribute to the momentum and heat transfer on average, probably due to the very weak mean cross-flow profile. Thus, the obtained three-dimensional turbulent boundary layer is the same as the two-dimensional one but inclined by a swept angle. To the authors’ knowledge, this is the first in-depth analysis of the high-speed cross-flow transition to full turbulence.

Wall pressure beneath a transitional hypersonic boundary layer over an inclined straight circular cone

Properties of wall pressure beneath a transitional hypersonic boundary layer over a 7∘ half-angle blunt cone at angle of attack 6∘ are studied by Direct Numerical Simulation. The wall pressure has two distinct frequency peaks. The low-frequency peak with f≈10−50 kHz is very likely the unsteady crossflow mode based on its convection direction, i.e. along the axial direction and towards the windward symmetry ray. High-frequency peaks are roughly proportional to the local boundary layer thickness. Along the trajectories of stationary crossflow vortices, the location of intense high-frequency wall pressure moves from the bottom of trough where the boundary layer is thin to the bottom of shoulder where the boundary layer is thick. By comparing the pressure field with that inside a high-speed transitional swept-wing boundary layer dominated by the z-type secondary crossflow mode, we found that the high-frequency signal originates from the Mack mode and evolves into the secondary crossflow instability.

Experimental investigation of nose-tip bluntness effects on the hypersonic crossflow instability over a cone

The nose-tip bluntness effects on the hypersonic crossflow instability were experimentally investigated over a 7∘ half-angle straight cone at 6∘ angle of attack. The experiments were conducted in a Mach 6 wind tunnel at Reynolds number of 7.94×106 m−1 using temperature-sensitive paint (TSP) and fast-response pressure transducers. The wavelet transform was applied to obtain the most amplified wavenumber of the stationary crossflow vortices. The stationary crossflow vortices with wavenumber of 40–60 and the traveling crossflow waves with characteristic frequencies of 9–20 kHz have been detected. TSP results indicate that the bluntness has little influence on the boundary layer transition location with a small nose-tip radius (smaller than 1.5 mm), while the transition front moves backward obviously with a larger nose-tip radius (larger than 2.5 mm). The developments of two types of crossflow instability, the stationary mode and the traveling mode, are both not sensitive to the bluntness when the nose-tip radius is below 1.5 mm. And the growth and saturation of the two types crossflow mode are both inhibited under larger bluntness. Besides, possible explanations for how the bluntness affects the transition location and crossflow instability is discussed.

Plasma-Actuated Flow Control of Hypersonic Crossflow-Induced Boundary-Layer Transition

The purpose of this research was to design, fabricate, and test a plasma-based active flow-control system to accelerate and delay crossflow-induced boundary-layer transition on a cone at an angle of attack at Mach 6 under quiet-flow conditions. A model with interchangeable nosetips was designed and fabricated from stainless steel, polyether ether ketone (PEEK), and Macor®. Transition on the model was characterized using infrared thermography and Kulite pressure transducers in the Boeing/U.S. Air Force Office of Scientific Research Mach 6 Quiet Tunnel at Purdue University. The flow controllers were assessed by their impact on the transition location and wave number of the largest-amplitude hot streaks. The transition location was accelerated by critical forcing (actuator wave number equals wave number of naturally largest-amplitude waves) and delayed by subcritical forcing (actuator wave number larger than natural waves). The disturbance wave number input of the plasma actuators was observed downstream on the model for many of the plasma-on runs, demonstrating that the plasma actuators introduced discrete forcing into the flow. The precise locations of the hot streaks arising from stationary crossflow vortices varied for different nosetips, presumably due to differences in their microscale roughness.

Analysis of the hypersonic cross-flow instability with experimental wavenumber distributions

Stationary cross-flow vortex N-factors were calculated over the surface of a yawed circular cone using computationally predicted and experimentally observed wavenumber distributions. Surface heat-flux data were obtained on a half-angle circular cone to investigate the behaviour of the stationary waves at different angles of attack and Reynolds numbers at Mach 6 under quiet-flow conditions in the Boeing/AFOSR Mach-6 Quiet Tunnel at Purdue University. A wavelet analysis was conducted on the experimental surface heat-flux data to construct a spatial mapping of the local largest amplitude wavenumbers of the stationary cross-flow waves, which were between 40 and 80 per circumference. Significant axial and azimuthal variation was observed. The results from the wavelet analysis were used to inform the stability analysis. The computed integration marching directions demonstrated very good agreement with the experimentally observed paths. N-factors were first calculated by integrating the local amplification rate corresponding to the most amplified experimental wavenumbers. The calculations were repeated based on non-dimensional computationally varying wavenumber ratios, which were dimensionalized by the experimental data. The computed N-factors showed good agreement between the two techniques. N-factors were also computed using the computationally predicted most unstable wavenumbers. The results showed decreased agreement with the other two cases, suggesting that this assumption does not properly model the cross-flow transition process.

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

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