Instability Of Boundary Layer Research Articles

Hybrid forced-buoyancy convection in a channel with a backward facing step

The present work integrates and expands the line of inquiry started in Inam and Lappa (2021), Int. J. of Heat and Mass Transfer, 173, 121267 for unsteady mixed forced-buoyancy convection in a channel with a forward facing step by addressing the mirror case where the fluid flowing in a duct undergoes a sudden expansion (i.e., a channel with a backward facing step). By alternatively setting some portions of the lower boundary of the system as isothermal (heated) or adiabatic surfaces, the interplay of forced and buoyancy convection is investigated numerically for a fixed expansion ratio (ER = 2) and a variety of conditions corresponding to extended intervals of the Rayleigh number Ra and several values of the Richardson number Ri (Ra≥O(104) and Ri≥O(1)). It is shown that the emerging dynamics involve a variety of concurrent mechanisms, which range from the standard hydrodynamic phenomena typical of isothermal fluids, to specific effects of buoyant nature (driven by the instability of thermal boundary layers and the ensuing emergence of thermal plumes in various parts of the domain). Comparison with the equivalent forward facing step configuration indicates that, besides the differences, these two systems display interesting analogies.

Double Acceleration Effects of Closely Spaced Pairs of Ocean Fronts on High‐Wind Occurrence Frequency During Boreal Winter

AbstractPrevious studies have found that sea surface temperature (SST) fronts have significant impacts on high‐wind frequency. Strong winds over the mid‐latitude North Pacific and North Atlantic Oceans occur frequently downstream of SST fronts in boreal winter. An SST front can significantly increase the instability of the marine atmospheric boundary layer, which accelerates the wind on the warmer flank. This study uses satellite observations to examine the “double acceleration” effects of closely spaced paired fronts (with interfrontal distances of 300–1,000 km) on high‐wind occurrence frequency in the Pacific subarctic frontal zone east of Japan and over the Atlantic Ocean east of Newfoundland. During boreal winter each year, mean westerly winds frequently cross two or more closely spaced SST fronts, with probabilities of 85% over the North Pacific and 87% over the North Atlantic. Over the warmer flank of the first front, the average high‐wind occurrence frequency (wind speed) increases due to the vertical‐mixing mechanism. Downstream of the second front, average high‐wind occurrence frequency (wind speed) reaches maxima of ∼9% (11.5 m s−1) over the Pacific and ∼11.5% (12 m s−1) over the Atlantic. Stronger westerly winds lead to greater high‐wind frequency. The first front contributes to the observed high winds downstream of the second front due to little friction and suppression of upward vertical momentum transfer between paired fronts.

Effects of spanwise-periodic surface heating on supersonic boundary-layer instability

The effects of streamwise-elongated, spanwise-periodic surface heating on a supersonic boundary-layer instability are investigated under the assumption of high Reynolds number. Our focus is on the lower-branch viscous instability and so the spanwise spacing of the elements is chosen to be of $O({\textit {Re}}^{-3/8}L)$ , the wavelength of the latter, where ${\textit {Re}}$ is the Reynolds number based on $L$ , the distance from the leading edge to the centre of the elements. The streamwise length is assumed to be much longer in order to simplify the mathematical description. Starting with classical triple-deck theory, the equations governing the heating-induced streaky flow are derived by appropriate rescaling. When Chapman's viscosity law is adopted, a similarity solution is found. The stability of the streaky flow, which is of a bi-global nature, is shown to be governed by a novel triple-deck structure characterised by fully compressible dynamics in the lower deck. Through asymptotic analysis, the bi-global stability is reduced to a one-dimensional eigenvalue problem, which involves only the spanwise-dependent wall temperature and wall shear. The instability modes may be viewed as a continuation of oncoming first Mack modes, but might also be considered as a new kind since they exhibit two distinctive features: strong temperature perturbation near the wall and spontaneous radiation of an acoustic wave to the far field, neither of which is shared by first Mack modes. Numerical calculations, performed for two simple patterns of spanwise-periodic heating elements, demonstrate their stabilising/destabiling effects on modes with different frequencies and spanwise wavelengths.

Transition Prediction of Boundary Layers in the Presence of Backward-Facing Steps

A set of available engineering models for the prediction of transition to turbulence is evaluated via comparisons with a high-quality experiment involving a backward-facing step (BFS) on a flat plate at subsonic freestream conditions. The streamwise shift in the transition location is monitored as the step height and flow speed are varied across step-height-to-local-displacement-thickness ratios of . We apply the -factor method based on the linear amplification of boundary-layer instabilities to laminar two-dimensional basic states. -factor correlations that rely on quasi-parallel linear stability theory (LST), the parabolized stability equations, and the harmonic linearized Navier–Stokes equations (HLNSE) yield good agreement with the experimental data, except if the onset of transition occurs slightly downstream of the BFS. For LST, the neglect of nonparallel flow effects results in transition locations that are further upstream compared to HLNSE. In contrast, models that use auxiliary transport equations and transition correlations based on local parameters fail to capture the physics associated with a BFS for moderate step heights. Specifically, the results obtained with the model indicate that it is unable to account for the flow history effects. Results show the amplification-factor-transport model also fails to capture the BFS effects in spite of accounting for the basic-state distortion near the step.

Impact of COVID-19 lockdown on the atmospheric boundary layer and instability process over Indian region

The abrupt reduction in the human activities during the first lockdown of the COVID-19 pandemic created unprecedented changes in the background atmospheric conditions. Several studies reported the anthropogenic and air quality changes observed during the lockdown. However, no attempts are made to investigate the lockdown effects on the Atmospheric Boundary Layer (ABL) and background instability processes. In this study, we assess the lockdown impacts on the ABL altitude and instability parameters (Convective Available Potential Energy (CAPE) and Convective Inhibition Energy (CINE)) using WRF model simulations. Results showed a unique footprint of COVID-19 lockdown in all these parameters. Increase in the visibility, surface temperature and wind speed and decrease in relative humidity during the lockdown is noticed. However, these responses are not uniform throughout India and are significant in the inland compared to the coastal regions. The spatial variation of temperature (wind speed) and relative humidity shows an increase and decrease over the Indo Gangetic Plain (IGP) and central parts of India by 20% (100%) and 40%, respectively. Increase (80%) in the ABL altitude is larger over the IGP and central parts of India during lockdown of 2020 compared to similar time period in 2015–2019. This increase is attributed to the stronger insolation due to absence of anthropogenic activity and other background conditions. At the same time, CAPE decreased by 98% in the IGP and central parts of India, where it shows an increase in other parts of India. A prominent strengthening of CINE in the IGP and a weakening elsewhere is also noticed. These changes in CAPE and CINE are mainly attributed to the dearth of saturation in lower troposphere levels, which prevented the development of strong adiabatic ascent during the lockdown. These results provide a comprehensive observation and model-based insight for lockdown induced changes in the meteorological and thermo-dynamical parameters.

Wall-cooling effects on secondary instabilities of Mack mode disturbances at Mach 6

In hypersonic boundary layers, Mack modes play a crucial role in flow instability, whose secondary instability is a hot research topic. Since hypersonic flight vehicles will probably work under high-stagnation temperature conditions, which significantly affect the aerodynamic heating calculation and aero-thermal protection design of hypersonic vehicles, it is necessary to compare the primary and secondary instabilities in high-stagnation temperature boundary layers and that in the Boeing/AFOSR Mach 6 quiet tunnel (BAM6QT). Herein, wall-cooling is adopted in order not to consider chemical reactions. With the same freestream temperature of 100 K, two Mach 6 boundary layers with the wall temperature of 20 and 600 K, corresponding to the cooled wall condition and the quiet wind tunnel condition, respectively, are chosen to conduct the linear/non-linear stability and the secondary instability analysis. Our results show that the most dangerous Mack mode originates from a fast discrete mode in the present cooled-wall flow and the most dangerous Mack mode is born from the slow discrete modes in BAM6QT boundary layers. Furthermore, when the primary amplitude of Mack mode disturbances is large, the fundamental resonance always dominates the secondary instability, resulting in steady streaky structures that have the largest amplitude in the spectrum. In addition, the present results point out that the distribution of the eigenfunctions of the fundamental modes and subharmonic modes are significantly different under various wall-temperatures. What is more, different ratios of wall temperature to incoming flow temperature have changed the spanwise wave-angle of the secondary disturbances.

Instabilities of buoyancy-induced flow along vertical cylinder in thermally stratified medium

In this paper, the instability of the buoyancy-driven boundary layer on a vertical cylinder is considered. We provide a mathematical description of a vertical cylinder immersed in a stably stratified fluid, and the analytical solutions of the basic flow are derived. Based on linear stability analysis, the effects of Prandtl number and transversal curvature have been investigated. It is found that the most unstable mode for Pr = 0.7 is three-dimensional for the cylindrical radii between 0.03 and 46, while the critical modes are axisymmetric for Pr = 7 and 100. All the results for different Pr are consistent with those of the vertical plate when the radius is large enough. Additionally, for absolute instability analysis, there exists absolute instability in the present model when the dimensionless radius is less than 0.31, which is quite different from the results obtained in the vertical plate. These encouraging results revealed in this paper should be helpful for understanding such a buoyancy-driven flow system.

Experimental Measurements of Hypersonic Instabilities over Ogive-Cylinders at Mach 6

Hypersonic boundary-layer instability disturbance and transition experiments were performed in the Air Force Research Laboratory Mach-6 Ludwieg Tube on a 1-m-long ogive-cylinder model with interchangeable nose-tip geometries of varying ogive radii and nose bluntnesses. Boundary-layer disturbances were measured via focused laser differential interferometry, surface-mounted pressure sensors, and high-speed schlieren videography at unit Reynolds numbers ranging from to . Three primary disturbance structures were observed that were dependent on ogive radius and nose bluntness. Each disturbance structure exhibits unique characteristics that are closely tied to the leading-edge geometry of the model. The addition of nose bluntness is shown to have an overall delay in transition onset, and a possible blunt nose transition reversal is observed as bluntness is further increased. It is also shown that the effects of the ogive radius in addition to nose bluntness alter the flow instability disturbance and transition behaviors and are likely tied to a modification of the entropy layer structure. A novel curvature-based Reynolds number is proposed that successfully correlates the effects of multiple leading-edge radii of curvature to dominant downstream boundary-layer disturbances and transition onset locations.

Energy transfer of hypersonic and high-enthalpy boundary layer instabilities and transition

Flow instability of hypersonic and high-enthalpy boundary layers with thermal-chemical nonequilibrium (TCNE) effects is studied for Mach numbers of up to 15. It is quantitatively illustrated that the TCNE effects change the disturbance characteristics predominantly through mean flow modification. In the oblique-mode breakdown case, the intensive energy transfer between the selected modes and their harmonic waves is found to occur where they interact strongly with the mean flow. (L${}_{\mathrm{\ensuremath{\Gamma}}}$ and N${}_{\mathrm{\ensuremath{\Gamma}}}$ in the figure are separately the energy transfer through the linear and nonlinear terms in the disturbance energy-norm equation.)

Spiral instability modes on rotating cones in high-Reynolds number axial flow

This work shows the behavior of an unstable boundary-layer on rotating cones in high-speed flow conditions: high Reynolds number Rel>106, low rotational speed ratio S<1–1.5, and inflow Mach number M = 0.5. These conditions are most-commonly encountered on rotating aeroengine nose cones of transonic cruise aircraft. Although it has been addressed in several past studies, the boundary-layer instability on rotating cones remains to be explored in high-speed inflow regimes. This work uses infrared-thermography with a proper orthogonal decomposition approach to detect instability-induced flow structures by measuring their thermal footprints on rotating cones in high-speed inflow. The observed surface temperature patterns show that the boundary-layer instability induces spiral modes on rotating cones, which closely resemble the thermal footprints of the spiral vortices observed in past studies at low-speed flow conditions: Rel<105, S > 1, and M≈0. Three cones with half-cone angles ψ=15°, 30°, and 40° are tested. For a given cone, the Reynolds number relating to the maximum amplification of the spiral vortices is found to follow an exponential relation with the rotational speed ratio S, extending from the low- to high-speed regime. At a given rotational speed ratio S, the spiral vortex angle appears to be as expected from the low-speed studies, irrespective of the half-cone angle.

Global stability and resolvent analyses of laminar boundary-layer flow interacting with viscoelastic patches

The attenuation of two-dimensional boundary-layer instabilities by a finite-length, viscoelastic patch is investigated by means of global linear stability theory. First, the modal stability properties of the coupled problem are assessed, revealing unstable fluid-elastic travelling-wave flutter modes. Second, the Tollmien–Schlichting instabilities over a rigid wall are characterised via the analysis of the fluid resolvent operator in order to determine a baseline for the fluid-structural analysis. To investigate the effect of the elastic patch on the growth of these flow instabilities, we first consider the linear frequency response of the coupled fluid-elastic system to the dominant rigid-wall forcing modes. In the frequency range of Tollmien–Schlichting waves, the energetic flow amplification is clearly reduced. However, an amplification is observed for higher frequencies, associated with travelling-wave flutter. This increased complexity requires the analysis of the coupled fluid-structural resolvent operator; the optimal, coupled, resolvent modes confirm the attenuation of the Tollmien–Schlichting instabilities, while also being able to capture the amplification at the higher frequencies. Finally, a decomposition of the fluid-structural response is proposed to reveal the wave cancellation mechanism responsible for the attenuation of the Tollmien–Schlichting waves. The viscoelastic patch, excited by the incoming rigid-wall wave, provokes a fluid-elastic wave that is out-of-phase with the former, thus reducing its amplitude.

Coupled structural resonance of elastic panels for suppression of airfoil tonal noise

In this paper the aeroacoustic characteristics of coupled flow-induced vibration of elastic panels mounted on an airfoil is numerically studied to uncover its potential for suppression of airfoil tonal noise. The proposed approach utilizes the inter-dynamical structural coupling between two elastic panels which maintain a synchronized flow-induced vibration pattern to weaken the flow fluctuations responsible for tonal noise generation. In the study, a NACA0012 airfoil at a low Reynolds number of 5×104 and an angle of attack of 5° is taken as the basic structure on which various panel configurations are attempted. The results of preliminary analysis of aeroacoustic-structural interactions of various panel configurations, using a reduced-order modeling approach, reveal that an airfoil-panel configuration with two elastic panels separated by approximately one convective wavelength and mounted in a region exposed to high boundary layer flow instabilities yields optimal noise suppression. Comprehensive aerodynamic and acoustic analyzes of airfoil-panel configurations, using the results of high fidelity direct aeroacoustic simulation, reveal that an average and maximum noise suppression up to 7.6 dB and 7.9 dB respectively can be achieved with negligible sacrifice on overall airfoil aerodynamics when strongly coupled structural resonance between the panels prevails. The magnitude of noise suppression is higher than twice of that from the configuration mounted with a single panel. This fact firmly illustrates the synergy of coupled flow-induced structural resonance of the panels prevailing in noise suppression. Nonlinear fluid–structure interactions of coupled resonant panels in airfoil-panel configuration are characterized by extensive spectral analyzes in frequency and wavenumber domains as well as correlation analyzes. The panels exhibit highly synchronized dynamic behaviors and run into limit cycle oscillations. Their strongly coherent structural responses are proven able to provide a more effective suppression of the boundary layer instabilities to be scattered at airfoil trailing edge as noise. The upstream propagating component of the generated noise does not interfere the coupled structural resonance of the panels as revealed from their weak correlations. Key characteristics required for the design of strongly coupled structural resonant panels for effective absorption of flow fluctuation energy are discerned and discussed.

Active control of the instability of a dynamic laminar boundary layer on a flat impermeable plate subjected to a magnetic field

Active control of the instability of a dynamic laminar boundary layer on a flat impermeable plate subjected to a magnetic field

Experimental study of hypersonic traveling crossflow instability over a yawed cone

Boundary layer transition is an important factor in the design process of hypersonic vehicles, and crossflow instability is a critical mode. In this paper, the traveling crossflow instability in a laminar boundary layer at Mach 6 is experimentally investigated. Experiments were performed over a 7∘ half-angle cone at 6∘ angle of attack, with the unit Reynolds number of Re∞=5.75×106 m−1. Flush-mounted fast-response pressure transducers and time-averaging temperature-sensitive paint were used to capture the traveling crossflow instability and the stationary crossflow instability, respectively. The traveling crossflow waves with characteristic frequencies between 10 and 25 kHz are detected in the planes with the azimuthal angle between 23∘ and 143∘ away from the leeward ray. The three-dimensional amplitude growth was obtained. In general, the amplitude growth of the traveling crossflow instability is roughly leeside-forward and windside-aft. Although the traveling crossflow instability grows earlier on the leeward side, it has a larger amplitude on the windward side. Compared with the stationary mode, the traveling mode grows faster and reaches the highest amplitude earlier. In addition, a high-frequency instability with characteristic frequencies between 100 and 200 kHz is observed. It may be the secondary instability of the traveling crossflow waves, but whether it is true or not needs further experimental and numerical studies.

Oblique instability of a stratified oscillatory boundary layer

The instability and dynamics of a vertical oscillatory boundary layer in a container filled with a stratified fluid are addressed. Past experiments have shown that when the boundary oscillation frequency is of the same order as the buoyancy frequency, the system is unstable to a herringbone pattern of oblique waves. Prior studies assuming the basic state to be a unidirectional oscillatory shear flow were unable to account for the oblique waves. By accounting for confinement effects present in the experiments, and the ensuing three-dimensional structure of the basic state, we are able to numerically reproduce the experimental observations, opening the door to fully analysing the impacts of stratification on such boundary layers.

Instability of the attachment line boundary layer in a supersonic swept flow

Theoretical analysis of attachment-line instabilities is performed for supersonic swept flows using the compressible Hiemenz approximation for the mean flow and the successive approximation procedures for disturbances. The theoretical model captures the dominant attachment-line modes in wide ranges of the sweep Mach number ${M_e}$ and the wall temperature ratio. It is shown that these modes behave similar to the first and second Mack modes in the boundary layer flow. This similarity allows us to extrapolate the knowledge gained for Mack modes to the attachment-line instabilities. In particular, we find that at sufficiently large ${M_e}$ , the dominant attachment-line instability is associated with the synchronisation of slow and fast modes of acoustic nature. Point-by-point comparisons of the theoretical predictions with the experiments of Gaillard et al. (Exp. Fluids, vol. 26, 1999, pp. 169–176) demonstrate that at ${M_e} > 4$ , the theory captures a significant drop of the transition onset Reynolds number, which is below the contamination criterion of Poll $({R_\mathrm{\ast }} = 250)$ at ${M_e} > 6$ . This contradicts the generally accepted assumption that the attachment-line flow is stable for ${R_\mathrm{\ast }} \le 250$ . The theoretical critical Reynolds numbers lie well below the experimental transition-onset Reynolds numbers. Stability computations using the Navier–Stokes mean flow and accounting for the leading-edge curvature effect do not eliminate this discrepancy. Most likely, in the experiments of Gaillard et al., we face with an unknown effect that does not fit to the concept of transition arising from linear instability.

Experimental investigation of aerofoil tonal noise at low Mach number

This paper presents an experimental investigation of aerofoil tones emitted by a controlled-diffusion aerofoil at low Mach number ( $0.05$ ), moderate Reynolds number based on the chord length ( $1.4 \times 10^{5}$ ) and moderate incidence ( $5^{\circ }$ angle of attack). Wall-pressure measurements have been performed along the suction side of the aerofoil to reveal the acoustic source mechanisms. In particular, a feedback loop is found to extend from the aerofoil trailing edge to the regions near the leading edge where the flow encounters a mean favourable pressure gradient, and consists of acoustic disturbances travelling upstream. Simultaneous wall-pressure, velocity and far-field acoustic measurements have been performed to identify the boundary-layer instability responsible for tonal noise generation. Causality correlation between far-field acoustic pressure and wall-normal velocity fluctuations has been performed, which reveals the presence of a Kelvin–Helmholtz-type modal shape within the velocity disturbance field. Tomographic particle image velocimetry measurements have been performed to understand the three-dimensional aspects of this flow instability. These measurements confirm the presence of large two-dimensional rollers that undergo three-dimensional breakdown just upstream of the trailing edge. Finally, modal decomposition of the flow has been carried out using proper orthogonal decomposition, which demonstrates that the normal modes are responsible for aerofoil tonal noise. The higher normal modes are found to undergo regular modulations in the spanwise direction. Based on the observed modal shape, an explanation of aerofoil tonal noise amplitude reduction is given, which has been previously reported in modular or serrated trailing-edge aerofoils.

Inviscid Modes within the Boundary-Layer Flow of a Rotating Disk with Wall Suction and in an External Free-Stream

The purpose of this paper is to investigate the linear stability analysis for the laminar-turbulent transition region of the high-Reynolds-number instabilities for the boundary layer flow on a rotating disk. This investigation considers axial flow along the surface-normal direction, by studying analytical expressions for the steady solution, laminar, incompressible and inviscid fluid of the boundary layer flow due to a rotating disk in the presence of a uniform injection and suction. Essentially, the physical problem represents flow entrainment into the boundary layer from the axial flow, which is transferred by the spinning disk surface into flow in the azimuthal and radial directions. In addition, through the formation of spiral vortices, the boundary layer instability is visualised which develops along the surface in spiral nature. To this end, this study illustrates that combining axial flow and suction together may act to stabilize the boundary layer flow for inviscid modes.

Boundary-layer instability measurements on a cone at freestream Mach 3.5

An experimental study was conducted in the NASA (National Aeronautics and Space Administration) Langley Supersonic Low-Disturbance Tunnel to investigate naturally occurring instabilities in a supersonic boundary layer on a 7° half-angle cone at nominal freestream conditions: Mach 3.5, total temperature of 299.8 K, and unit Reynolds numbers (millions per m) of 9.89, 13.85, 21.77, and 25.73. Instability measurements were acquired under noisy-flow and quiet-flow conditions. Pitot-pressure and calibrated hot-wire measurements were obtained using a model-integrated traverse system to document the model flow field. In noisy-flow conditions, growth rates and mode shapes achieved good agreement between the measured results and linear stability theory (LST). The corresponding N factor at transition from LST is N≈3.9. Under quiet-flow conditions, the most unstable first-mode instabilities as predicted by LST were measured, but this mode was not the dominant instability measured in the boundary layer. Instead, the dominant instabilities were less-amplified, low-frequency disturbances predicted by LST, and grew according to linear theory. These low-frequency unstable disturbances were initiated by freestream acoustic disturbances through a receptivity process believed to occur near the branch I location of the cone. Under quiet-flow conditions, the boundary layer remained laminar up to the last measurement station for the largest unit Reynolds number, implying a transition N factor of N > 8.5.

Extremum Seeking Control Applied to Airfoil Trailing-Edge Noise Suppression

Extremum seeking control (ESC) and its slope seeking generalization are applied in a high-fidelity flow simulation framework for reduction of acoustic noise generated by a NACA0012 airfoil. Two Reynolds numbers are studied for which different noise generation mechanisms are excited. For a low Reynolds number flow, the scattering of vortex shedding at the airfoil trailing edge produces tonal noise, while for a moderate Reynolds number case, boundary-layer instabilities scatter at the trailing edge, leading to noise emission at multiple tones superimposed on a broadband hump. Different control setups are investigated, and they are configured to either find an optimal steady actuator intensity or an optimal position for a blowing/suction device. Implementation details are discussed regarding the control modules and design of digital filters. Analyses of physical phenomena as well as of relevant behavior of the actuated plant are conducted to understand how the extremum seeking loop leverages the flow physics to control noise. Depending on the flow configuration studied and the control setup, results demonstrate that the ESC can provide considerable airfoil noise reductions.