Disturbances In Boundary Layer Research Articles

Probing horizontal convection instability via perturbation of the forcing boundary layer using a synthetic jet

Horizontal convection driven by a linear temperature profile along the bottom of a two-dimensional rectangular enclosure is perturbed by a small tuned synthetic (zero-net-mass-flux/ZNMF) jet. The jet permits instability in the horizontal convection boundary layer to be investigated in a controlled manner. At a Prandtl number Pr = 6.14 and Rayleigh number Ra = 2.5 × 108, slightly below the natural onset of instability, the boundary layer is found to be convectively unstable, exhibiting a disturbance pattern consistent with a Rayleigh–Bénard mechanism. Advection of the boundary layer disturbance gives rise to unsteadiness in the vertical end-wall plume. Nusselt number is enhanced across a range of frequencies for all perturbation amplitudes, with the response dominated by two frequencies differing by approximately a factor of two: each invokes the periodic shedding of vorticity into the vertical end-wall plume at the higher frequency. This suggests that there exists a natural sensitivity in this flow to disturbances convecting in the upstream boundary layer. That is, a convective instability in the horizontal convection boundary layer serves as a disturbance amplifier, with the end-wall plume controlling the frequency of the resulting instability mode. The increase in Nusselt number achieved by a jet with peak speed of the same order as the horizontal convective velocity in the unperturbed flow is consistent with a greater than two-fold increase in Rayleigh number.

Boundary-layer disturbances subjected to free-stream turbulence and simulation on bypass transition

The phenomena associated with the entrainment of free-stream turbulence (FST) into boundary-layer flows are relevant for a number of subjects. It has been believed that the continuous spectra of the Orr-Sommerfeld (O-S)/Squire equations describe the entrainment process, and thus they are used to specify the inlet condition in simulation of bypass transition. However, Dong and Wu (Dong, M. and Wu, X. On continuous spectra of the Orr-Sommerfeld/Squire equations and entrainment of free-stream vortical disturbances. Journal of Fluid Mechanics, 732, 616–659 (2013)) pointed out that continuous spectra exhibit several non-physical features due to neglecting the non-parallelism. They further proposed a large-Reynolds-number asymptotic approach, and showed that the non-parallelism is a leading-order effect even for the short-wavelength disturbance, for which the response concentrates in the edge layer. In this paper, the asymptotic solution is verified numerically by studying its evolution in incompressible boundary layers. It is found that the numerical results can be accurately predicted by the asymptotic solution, implying that the latter is adequate for moderate Reynolds numbers. By introducing a series of such solutions as the inflow perturbations, the bypass transition is investigated via the direct numerical simulation (DNS). The transition processes, including the evolution of streaks, the amplification of secondary-instability modes, and the emergence of turbulent spots, agree with the experimental observations.

Linear development of controlled disturbances in the supersonic boundary layer on a swept wing at Mach 2

Experimental results are presented on the linear development of a wave train in a three-dimensional supersonic boundary layer on a swept wing with 45°-sweep angle at Mach number M = 2.0. Artificial disturbances in the boundary layer were excited by periodical glow discharge mainly at frequencies 10 and 20 kHz. The maximum of the controlled pulsation amplitude was localized in the boundary layer in normal to the swept-wing surface direction for spatial amplitude distributions as well as for the amplitude wave spectra. The asymmetry of the wave characteristics of the unstable disturbances in the boundary layer of a swept wing caused by the presence of crossflow is confirmed. The stability characteristics, including dispersion relations and amplification rates over a wide range of wave inclination angles, are obtained for disturbances with prescribed frequencies 10 and 20 kHz.

Entrainment of short-wavelength free-stream vortical disturbances in compressible and incompressible boundary layers

The fundamental difference between continuous modes of the Orr–Sommerfeld/Squire equations and the entrainment of free-stream vortical disturbances (FSVD) into the boundary layer has been investigated in a recent paper (Dong & Wu, J. Fluid Mech., vol. 732, 2013, pp. 616–659). It was shown there that the non-parallel-flow effect plays a leading-order role in the entrainment, and neglecting it at the outset, as is done in the continuous-mode formulation, leads to non-physical features of ‘Fourier entanglement’ and abnormal anisotropy. The analysis, which was for incompressible boundary layers and for FSVD with a characteristic wavelength of the order of the local boundary-layer thickness, is extended in this paper to compressible boundary layers and FSVD with even shorter wavelengths, which are comparable with the width of the so-called edge layer. Non-parallelism remains a leading-order effect in the present scaling, which turns out to be more general in that the equations and solutions in the previous paper are recovered in the appropriate limit. Appropriate asymptotic solutions in the main and edge layers are obtained to characterize the entrainment. It is found that when the Prandtl number $\mathit{Pr}<1$, free-stream vortical disturbances of relatively low frequency generate very strong temperature fluctuations within the edge layer, leading to formation of thermal streaks. A composite solution, uniformly valid across the entire boundary layer, is constructed, and it can be used in receptivity studies and as inlet conditions for direct numerical simulations of bypass transition. For compressible boundary layers, continuous spectra of the disturbance equations linearized about a parallel base flow exhibit entanglement between vortical and entropy modes, namely, a vortical mode necessarily induces an entropy disturbance in the free stream and vice versa, and this amounts to a further non-physical behaviour. High Reynolds number asymptotic analysis yields the relations between the amplitudes of entangled modes.

Growth and Characterization of Pencil-Like ZnO Nanowires in the Presence of a Disturbance in Boundary Layer

Pencil-like zinc oxide (ZnO) nanowire was synthesized on Si (111) substrate through a simple vapor phase method using a mixture of zinc oxide and graphite as the source material. The source inside a quartz tube created a Zn-rich vapor that facilitated the formation and growth of ZnO nanowires. Field emission scanning electron microscopic studies indicated that pencil-like ZnO nanowires had a size of the range from 50 to 150 nm in diameter and several microns in length. X-ray diffraction was used to investigate the crystal structure of ZnO nanowires. Raman scattering and photoluminescence were applied to characterize the optical properties of the pencils. The growth mechanism of the nanopencils was discussed based on the growth conditions.

Numerical studies of heat transfer enhancement by cross-cut flow control in wavy fin heat exchangers

Heat transfer enhancement by cross-cut induced flow control in a wavy fin heat exchanger was studied numerically. The concept of cross-cut is cutting fin in a direction perpendicular to the flow direction. A two-dimensional five-waved wavy fin with corrugation angle 20° was used as the geometry for simulation and the cross-cut was applied at the 3rd wave only. The simulation was performed using non dimensional governing equations for a steady laminar flow. The parametric study was conducted to find the optimum position and length of the cross-cut. The results showed that the heat transfer performance of optimized cross-cut wavy fin was enhanced by a maximum of 23.81% greater than a typical wavy fin. The pressure drop also increased by a maximum 7.04% in optimized case. Generally, the heat transfer performance of cross-cut applied plain fin has an enhanced heat transfer performance because of the thermal boundary layer disturbance and block of longitudinal heat transfer. In the case of the cross-cut applied wavy fin, additional heat transfer enhancement can be found because the cross-cut induced flow control makes a relatively low temperature fluid at the middle of internal flow attached to the fin wall after the cross-cut region.

Spreading of Linear Disturbances in Boundary Layers at Mach Number Five and the Effect of Wall Cooling

AbstractWe determine inviscid eigensolutions in zero pressure gradient flat plate boundary layers at Mach number five and evaluate the eigensolutions with the method of steepest descent. The resulting wave packets show that with wall cooling the tail of the packets becomes slower. Although the boundary layers investigated are all convectively unstable we interpret the slow tail of the wave packets as a trend towards an absolute instability. From a comparison of the wave packets with turbulent spot transition, we conclude that for wall cooling the general transition properties are close to those of an absolutely unstable flow. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Numerical investigation of transition in a boundary layer subjected to favourable and adverse streamwise pressure gradients and elevated free stream turbulence

Laminar-to-turbulent transition of a boundary layer subjected to streamwise pressure gradients and elevated free stream turbulence is computed through direct numerical simulation. The streamwise pressure distribution and elevated free stream turbulence levels mimic the conditions present on the suction side of highly-cambered airfoils. Longitudinal streamwise streaks form in the laminar boundary layer through the selective inclusion of low-frequency disturbances from the free stream turbulence. The spanwise spacing normalized by local inner variables indicates stabilization of the streaks occurs by the favourable pressure gradient and prevents the development of secondary streak instability modes until downstream of the suction peak. Two distinct processes are found to trigger transition to turbulence in the adverse pressure gradient region of the flow. One involves the development of varicose secondary instability of individual low-speed streaks that results in their breakdown and the formation and growth of discrete turbulent spots. The other involves a rapid amplification of free stream disturbances in the inflectional boundary layer in the adverse pressure gradient region that results in a largely homogeneous breakdown to turbulence across the span. The effect of high-frequency free stream disturbances on the streak secondary instability and on the nonlinear processes within the growing turbulent spot are analysed through the inviscid transport of instantaneous vorticity. The results suggest that free stream turbulence contributes to the growth of the turbulent spot by generating large strain rates that activate vortex-stretching and tilting processes within the spot.

Nonlinear Response of a Compressible Boundary Layer to Free-stream Vortical Disturbances

The nonlinear response of a compressible boundary layer to unsteady free-stream vortical fluctuations of the convected-gust type is investigated. The amplitude of the disturbances is strong enough for nonlinear interactions to be induced within the boundary layer. Attention is focused on the induced low-frequency streamwise-stretched components of the boundary-layer disturbances, known as streaks or Klebanoff modes, which may become unstable and break down to fully developed turbulence. The streaks are described using the mathematical framework of the so-called boundary-region equations, i.e. the asymptotic limit of the Navier-Stokes equations for low-frequency disturbance, developed by Leib et al.1 and extended by Ricco & Wu 2 and Ricco et al.3 to linear perturbations in compressible boundary layers, and nonlinear disturbances in incompressible boundary layers, respectively. In the present work, compressibility is taken into account through aerodynamic heating effects due to the mean-flow velocity being comparable with the speed of sound. Both velocity and thermal (temperature) streaks are generated as well as are a new mean flow and fluctuations of higher frequencies. Nonlinearity attenuates the fluctuations of the streamwise velocity and a similar stabilizing effect is observed on the temperature.This represents the preliminary study which is necessary to carry out the secondary instability analysis on the new unsteady compressible three-dimensional flow generated by the nonlinear interactions.

Influence of boundary-layer disturbances on the instability of a roughness wake in a high-speed boundary layer

AbstractThe excitation of instability modes in the wake generated behind a discrete roughness element in a boundary layer at Mach 6 is analysed through numerical simulations of the compressible Navier–Stokes equations. Recent experimental observations show that transition to turbulence in high-speed boundary layers during re-entry flight is dominated by wall roughness effects. Therefore, understanding the roughness-induced transition to turbulence in this flow regime is of primary importance. Our results show that a discrete roughness element with a height of about half the local boundary-layer thickness generates an unstable wake able to sustain the growth of a number of modes. The most unstable of these modes are a sinuous mode (mode SL) and two varicose modes (modes VL and VC). The varicose modes grow approximately 17 % faster than the most unstable Mack mode and their growth persists over a longer streamwise distance, thereby leading to a notable acceleration of the laminar–turbulent transition process. Two main mechanisms are identified for the excitation of wake modes: the first is based on the interaction between the external disturbances and the reverse flow regions induced by the roughness element and the second is due to the interaction between the boundary-layer modes (first modes and Mack modes) and the non-parallel roughness wake. An important finding of the present study is that, while being less unstable, mode SL is the preferred instability for the first of the above excitation mechanisms, which drives the wake modes excitation in the absence of boundary-layer modes. Modes VL and VC are excited through the second mechanism and, hence, become important when first modes and Mack modes come into interaction with the roughness wake. The new mode VC presents similarities with the Mack mode instability, including the tuning between its most unstable wavelength and the local boundary-layer thickness, and it is believed to play a fundamental role in the roughness-induced transition of high-speed boundary layers. In contrast to the smooth-wall case, wall cooling is stabilising for all the roughness-wake modes.

Experimental investigation on the steady and unsteady disturbances in a flat plate boundary layer

Recent experiments have shown that miniature vortex generators (MVGs) are coveted devices to stabilize unsteady disturbances in flat plate boundary layers and to delay the onset of turbulence by modulating the base flow in the spanwise direction. The spanwise modulation is a result from the non-modal transient growth of steady and spanwise periodic streamwise vortices being generated by the MVGs. The present experimental investigation aims at studying the transient growth of non-modal disturbances induced by a spanwise periodic array of MVGs and its stabilizing effect on non-linear unsteady disturbances in the boundary layer originating from planar Tollmien-Schlichting (TS) waves. Measurements consist of cross-stream planes at different downstream locations in the boundary layer and a spatio-temporal analysis of different modes of the disturbances is carried out. In the streaky boundary layer generated by the MVGs the fundamental spanwise mode, with the same wavelength as the MVG pairs in the array, and its first harmonic, both undergo transient growth whereas the higher harmonics decay immediately downstream of the array. In the unstable region formed in the wake of the MVG blades, i.e., just downstream of the array, a wide range of spanwise modes contributes to an initial growth in the energy of unsteady disturbances. Similar behavior is observed upstream of branch II position of the neutral stability curve where the unsteady disturbances undergo a second energy growth in the unstable region. It is shown that the spatial gradients of the base flow in the wall-normal and spanwise directions are contributing to the amplification and attenuation of the TS wave disturbances, respectively, in the streaky boundary layer.

Numerical Study of Hypersonic Boundary-Layer Receptivity with Freestream Hotspot Perturbations

This paper presents a numerical-simulation study of transient flow over a blunt compression cone under the effect of freestream hotspot perturbations. This study is motivated by concurrent wind-tunnel laser-spot experiments carried out at Purdue University. The flow conditions used in the simulation are based on the experimental conditions. The simulation is performed using a high-order shock-fitting finite-difference scheme. The simulation results show that the hotspot is able to excite second-mode instability, where the instability growth is found to be dominant in the boundary layer. The receptivity mechanism is investigated by comparing the simulated results with linear-stability theory. Fast acoustic waves generated by hotspot–shock interaction excite the boundary-layer disturbances. Also, the synchronization of mode F and mode S leads to the dominance of boundary-layer disturbances by the growing second mode.

Nonlinear interaction mechanisms of disturbances in supersonic flat-plate boundary layers

Due to the complexity of compressible flows, nonlinear hydrodynamic stability theories in supersonic boundary layers are not sufficient. In order to reveal the nonlinear interaction mechanisms of the rapidly amplified 3-D disturbances in supersonic boundary layers at high Mach numbers, the nonlinear evolutions of different disturbances in flat-plate boundary layers at Mach number 4.5, 6 and 8 are analyzed by numerical simulations. It can be concluded that the 3-D disturbances are amplified rapidly when the amplitude of the 2-D disturbance reaches a certain level. The most rapidly amplified 3-D disturbances are Klebanoff type (K-type) disturbances which have the same frequency as the 2-D disturbance. Among these K-type 3-D disturbances, the disturbances located at the junction of upper branch and lower branch of the neutral curve are amplified higher. Through analyzing the relationship between the amplification rate and the spanwise wavenumber of the 3-D disturbances at different evolution stages, the mechanism of the spanwise wavenumber selectivity of K-type 3-D disturbances in the presence of a finite amplitude 2-D disturbance is explained.

Tollmien–Schlichting wave growth over spanwise-periodic surface patterns

AbstractA novel type of surface roughness is deployed in a zero-pressure-gradient boundary layer with the goal of delaying the onset of laminar-to-turbulent transition for drag reduction purposes. This proof-of-concept experiment relies on forcing phase-triggered Tollmien–Schlichting (TS) waves across a range of initial amplitudes to produce amplified boundary-layer disturbances in a controlled and repeatable manner. Building on earlier work demonstrating attenuation of forced disturbances and delay of transition with spanwise arrays of discrete roughness and miniature vortex generators (MVGs), the present work seeks a roughness shape which might find success in a wider range of flows. Toward that end, streamwise-elongated humps are regularly spaced in the spanwise direction to form a wavy wall. By direct modulation of the mean flow, growth rates of the forced disturbances are increased or decreased, depending on the roughness configuration. Boundary-layer velocity measurements with hot-wire probes have been performed in a parametric study of the effects of roughness-field geometry and forcing amplitude on TS-wave growth and transition. The roughness field proves detrimental to passive flow control efforts in some configurations, while a reduction in the TS-wave amplitudes compared with the smooth-wall reference case is observed at other conditions. Substantial delays in the onset of transition are demonstrated when TS waves are forced with large amplitudes.

Free-stream coherent structures in parallel boundary-layer flows

AbstractOur concern in this paper is with high-Reynolds-number nonlinear equilibrium solutions of the Navier–Stokes equations for boundary-layer flows. Here we consider the asymptotic suction boundary layer (ASBL) which we take as a prototype parallel boundary layer. Solutions of the equations of motion are obtained using a homotopy continuation from two known types of solutions for plane Couette flow. At high Reynolds numbers, it is shown that the first type of solution takes the form of a vortex–wave interaction (VWI) state, see Hall & Smith (J. Fluid Mech., vol. 227, 1991, pp. 641–666), and is located in the main part of the boundary layer. On the other hand, here the second type is found to support an equilibrium solution of the unit-Reynolds-number Navier–Stokes equations in a layer located a distance of $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}O(\ln \mathit{Re})$ from the wall. Here $\mathit{Re}$ is the Reynolds number based on the free-stream speed and the unperturbed boundary-layer thickness. The streaky field produced by the interaction grows exponentially below the layer and takes its maximum size within the unperturbed boundary layer. The results suggest the possibility of two distinct types of streaky coherent structures existing, possibly simultaneously, in disturbed boundary layers.

Active Noise Control in a Closed-Circuit Wind Tunnel

Experiments on boundary-layer receptivity to freestream sound use downstream-traveling planar sound that interacts with a model to create boundary-layer disturbances. These experiments are complicated by the wind-tunnel geometry downstream of the test section that creates upstream-traveling reflections. In this work, active noise control is implemented in a closed-circuit wind tunnel to eliminate these reflections. The control system filters an input signal to drive two speakers downstream of the test section. These speakers create upstream-traveling sound that destructively interferes with the reflections. Without the controller activated, the average downstream- and upstream-traveling waves are 98 and 85 dB, respectively. With the controller activated, the upstream-traveling reflections are reduced up to 31 dB at , and 29 dB at . The performance of the controller decreases as the frequency approaches the planar-wave-cutoff frequency of the test section due to nonplanar waves created by the control speakers. Active noise control is also used to reduce upstream-traveling tonal background noise up to 12 dB. The adaptive control system allows greater experimental control during sound-receptivity experiments.

Quantitative Study of Excitation of Unsteady Görtler Instability Modes in Concave-Wall Boundary Layer by Free-Stream Turbulence

The paper is devoted to the first experimental study of distributed excitation of Görtler instability modes due the distributed mechanism of receptivity of a concave-wall boundary layer to streamwise freestream vortices. Experiments are carried out in the following range of problem parameters: Görtler numbers G* = 7,4÷21,3, frequencies f = 15, 20, and 26 Hz (nondimensional frequency parameters are F = 17,04; 22,72 and 29,54), and a broad range of spanwise scales of disturbances z = 8÷24 мм (nondimensional scales are Λ = 149÷774). It is found that this receptivity mechanism is quite efficient and can lead to amplification of unsteady Görtler vortices even in regimes where the boundary layer is linearly stable to these boundary-layer disturbances. Estimations of quantitative characteristics of the investigated physical phenomenon: the complex values of the distributed vortex receptivity coefficients are obtained in the present study for the first time. It is found that examined receptivity mechanism is especially effective for vortices with spanwise wavelengths close to the most dangerous in terms of the linear stability theory. The amplitudes of the receptivity coefficients are found to decrease with the streamwise coordinate

Linear evolution of controlled disturbances in the supersonic boundary layer on a swept wing

The linear development of controlled disturbances in the three-dimensional supersonic boundary layer on a swept model wing with a sharp leading edge is experimentally investigated at the Mach number 2. The spatial-temporal and spectral-wave characteristics of the wave train of unstable disturbances are obtained. The asymmetry of these characteristics, due to the secondary flow in the three-dimensional boundary layer, is confirmed.

Nonlinear evolution of Klebanoff type second mode disturbances in supersonic flat-plate boundary layer

Studying the evolution of 3D disturbances is of crucial theoretical importance for understanding the transition process. The present study concerns the nonlinear evolution of second mode unstable disturbances in a supersonic boundary layer by the numerical simulation, and discusses the selectivity of 3D disturbances and possibility to transition. The results indicate that a Klebanoff type nonlinear interaction between 2D and 3D disturbances with the same frequency may amplify a band of 3D disturbances centered at a finite spanwise wavenumber. That is, certain 3D disturbances can be selectively and rapidly amplified by the unstable 2D disturbances, and certain small-scale 3D structures will appear.

Schlieren visualization for high-speed flows based on laser-induced fluorescence

The use of a short-duration laser as a light source for Schlieren flow visualization is described. The coherent nature of this light source has been removed using the laser-induced fluorescence principle. The quality of the speckle-free pictures obtained competes with the one achieved using conventional illumination techniques. Flow features are frozen in space thanks to the short duration of the laser flashes. The applicability of the technique is demonstrated with the characterization of hypersonic conical boundary layers at Mach 11. Pairs of images have been obtained using successive laser flashes with a separation time down to 2 μs. Instantaneous convection velocities and spectral properties of the dominant boundary layer disturbances have been determined. These characteristics compare favorably with the values determined from synchronized time-resolved wall pressure measurements.