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The paper presented the results on the generation and development of the wave train in spanwise modulated supersonic boundary layer at Mach 2 and 2.5, which obtained experimentally in the same conditions of controlled experiment. In experiments on the flat plate with roughness it was obtained that at the Mach number M = 2.5 both a subharmonic and fundamental wave packet develops almost linearly, whereas at the Mach number M = 2.0 there is competition between the two mechanisms of unstable waves interaction. It was obtained that in the boundary layer on swept wing the roughness presence can leads to the stabilization of the wave packet development at fundamental and subharmonic frequency in the downstream direction.

The evolution of the artificial wave packet in laminar flat-plate boundary layer was experimentally studied by hot-wire measurements at M=2. The localized disturbances were generated by pulse glow discharge. The wave analysis of evolution of wave packet was provided. It was found, that the most unstable waves are oblique, that consistent with results of linear theory.

The paper is devoted to an experimental study of laminar-turbulent transition in a three-dimensional supersonic boundary layer. The experiments were conducted at the low nose supersonic wind tunnel T-325 of ITAM at Mach numbers M=2 - 4. Model is a symmetrical wing with a 45° sweep angle, a 3 percent-thick circular-arc airfoil. The influence of flow parameters, such as the Mach number, unit Reynolds number, angle of attack, level of perturbations on the transitions to turbulence are on the consideration. Transition Reynolds numbers are obtained. Analysis of all obtained data allow to determine reliable value of Retr of swept wing supersonic boundary layer, that especially important at consideration of experiments fulfilled at different flow conditions in different wind tunnels.

An experiment on a swept cylinder with 68°-sweep angle at Mach number M = 2.5 is described. The flow attachment line was disturbed by two weak shock waves. Shock waves were generated by a two-dimensional surface inhomogeneity on the wall of the test section of wind tunnel. It was found that the laminar-turbulent transition on the attachment-line of the cylinder is accompanied by an uneven growth of pulsations. Influence of Mach waves on the transition when their fall on the cylinder far away from domain of measuring is not observed. The laminar-turbulent transition occurs at a much lower unit Reynolds numbers in the case when a pair of waves falling on the attachment-line near the measurement field.

Joint theoretical and experimental investigation on the influence of surface permeability and roughness on stability of a supersonic flat-plate boundary layer at free-stream Mach number M=2 has been performed. Artificial disturbances have been introduced in the model’s boundary layer by means of a harmonic point glow discharge disturbance generator.

Experimental data on the nonlinear wave train development in 3D supersonic boundary layer over a 45° swept-wing at Mach number 2 are presented. Travelling artificial disturbances were introduced in the boundary layer by periodical glow discharge at frequencies 10 and 20 kHz. It is shown that the additional peaks in β′-spectra arise for both subharmonic and fundamental frequencies. The experiments indicate the presence of oblique breakdown mechanism in 3D supersonic boundary layer. The three-wave triad consisting of two primary travelling waves and one steady wave is discussed. The linear stability theory results demonstrate the possibility of the existence for such triads.Experimental data on the nonlinear wave train development in 3D supersonic boundary layer over a 45° swept-wing at Mach number 2 are presented. Travelling artificial disturbances were introduced in the boundary layer by periodical glow discharge at frequencies 10 and 20 kHz. It is shown that the additional peaks in β′-spectra arise for both subharmonic and fundamental frequencies. The experiments indicate the presence of oblique breakdown mechanism in 3D supersonic boundary layer. The three-wave triad consisting of two primary travelling waves and one steady wave is discussed. The linear stability theory results demonstrate the possibility of the existence for such triads.

In the present study, we examined, both experimentally and theoretically, the influence of porouscoating thickness on the stability and laminar-turbulent transition of flat-plate supersonic boundary layer at free-stream Mach number M∞ = 2. A qualitative agreement between the data calculated by the linear theory of stability and the experimental data on the transition obtained for models with different porous-coating thicknesses was established. We show that with decreasing (within a certain interval) the porouscoating thickness the boundary layer becomes more stable to perturbations, and the laminar-turbulent transition, more delayed.

Results of experimental study of influence of spanwise flow nonuniformity on the wave train evolution in supersonic boundary layer at Mach number M = 2 are presented. Spanwise modulation of mean flow in a boundary layer was created by means of labels from scotch tape by thickness of 60 and 110 microns. Downstream evolution of controlled disturbances was investigated. The wave characteristics of traveling disturbances were obtained. It was found that the wave trains development depends from size and location of the roughness. It is shown that the wave packet evolution qualitatively has the similar development in both cases as for the smooth surfaces. At the same time, the spanwise modulation of the mean flow leads to the fundamental wave excitation with high inclination angle. The phase spectra indicate that excitation of these waves takes place in the center of the wave packet. It was shown, that mean flow modulation can lead to stabilization of disturbance development in supersonic boundary layer on a flat plate.

In the present study, we examined, both experimentally and theoretically, the influence of surface permeability on the stability and laminar-turbulent transition of supersonic boundary layer at free-stream Mach number M∞ = 2. A satisfactory agreement was obtained between the data calculated by the linear theory of stability and the data obtained in experiments with natural disturbances performed on models with different porous inserts.

The results of an experimental study of weakly nonlinear interaction mechanisms of the instability waves in a supersonic boundary layer on flat plate at Mach number М = 2 are presented in the paper. The downstream evolution of artificial disturbances of small amplitude was studied experimentally. The wave characteristics of traveling disturbances were determined. Obtained, that disturbances evolution at basic frequency was happen in according to the linear theory of hydrodynamical stability. Confirmed, that subharmonical resonance on asymmetrical wave triplet was the reason of amplification of the high inclined subharmonic pulsations. The role of high-frequency disturbances was not significant in the region of weakly nonlinear interactions. The initial stage of a parametrical resonance was characterized by appearance of a stationary wave, jumps of a phase on 180° on frequency of a subharmonic in a cross-section direction, and also not symmetry in amplitude β-spectra.

Theoretical and an experimental research results of the disturbances development in a swept wing boundary layer are presented at Mach number М = 2. In experiments development of natural and small amplitude controllable disturbances downstream was studied. Experiments were carried out on a swept wing model with a lenticular profile at a zero attack angle. The swept angle of a leading edge was 40°. Wave parameters of moving disturbances were determined. In frames of the linear theory and an approach of the local self-similar mean flow the stability of a compressible three-dimensional boundary layer is studied. Good agreement of the theory with experimental results for transversal scales of unstable vertices of the secondary flow was obtained. However the calculated amplification rates differ from measured values considerably. This disagreement is explained by the nonlinear processes observed in experiment

Experimental data on stability of a three-dimensional supersonic boundary layer on a swept wing are presented. The experiments are performed on a swept wing model with a lenticular profile with a 40° sweep angle of the leading edge at a zero angle of attack. The supersonic boundary layer on the swept wing was laminarized with the use of distributed roughness. A pioneering study of interaction of traveling and stationary disturbances is performed. Some specific features of this interaction are identified. The main reason for turbulence emergence in a supersonic boundary layer on a swept wing is demonstrated to be secondary crossflow instability.

A passive control method for supersonic boundary-layer transition on a swept wing using longitudinal roughness is proposed. Tests were carried out to examine the effect of distributed roughness on the development of flow peturbations and on the laminar-turbulent transition. The method makes it possible to manipulate the transition in a wide range, bringing it either closer to the leading edge of the wing by 30 % or delaying it by 40%.

Experiments on the influence of flat isolated square and diamond shaped roughness elements on the mean and pulsation characteristics of the boundary layer on a flat plate and a swept wing of comparable size are conducted. The shape of stickers has almost no effect on the mass flow pulsation amplitude in the trace of roughness. The relative “receptivity” of the three-dimensional (3D) boundary layer to stationary perturbations is approximately 1.5 times greater than the “receptivity” of the twodimensional (2D) boundary layer. The presence of roughness on the disturbance source line changes the pulsation spectra in 2D/3D boundary layer compared to the spectra in boundary layer on smooth surface.

An experimental study of the controlled disturbance field, introduced into the free stream with the help of the local source of disturbances, was carried out. The controlled disturbances were excited in the supersonic boundary layer by using a local disturbance generator designed based on the amount of discharge in the chamber in the plate. This process was accompanied by radiation of controlled disturbances into the free stream. This radiation from the system “discharge-boundary layer” was used as controlled disturbances in the free stream. The acoustic nature of the radiation was obtained. The levels, wave characteristics and modes of the artificial fluctuations have been obtained by hot-wire measurements in the free stream of the supersonic wind tunnel at a Mach number of 2.

Results of experimental investigations of the evolution of natural disturbances and laminar–turbulent transition in a supersonic boundary layer on the attachment line of a circular cylinder with a sweep angle of 68° and a free‐stream Mach number M = 2 are presented. The experimental studies are supplemented by calculations of the mean flow and stability characteristics. Flow regimes in the boundary layer on the attachment line are determined by a hot‐wire technique as functions of the Reynolds number and height of two‐dimensional roughness elements. The results are compared with NASA (Ames) experiments.

Experimental data on the evolution of controlled stationary and travelling disturbances in a 3D supersonic boundary layer, over a 45° swept-wing at Mach number 2.0, is presented. Travelling artificial disturbances were introduced in the boundary layer by periodical glow discharge, at a frequency of 20 kHz. Stationary disturbances were acquired by setting the roughness elements on the surface of the model. Spatial-temporal and spectral-wave characteristics of the wave train at the frequency 20 kHz, in the linear region of development, were obtained. It was found that the periodic modulation of mean flow can lead to the stabilization of unstable travelling disturbances in the supersonic boundary layer of a swept wing. These experiments have investigated the viability of using roughness elements to control laminar-turbulent transition.

Experimental data on stability of a three-dimensional supersonic boundary layer on a swept wing are presented. Evolution of artificial wave trains was studied. The experiments were conducted for Mach numberM=2.0 and unit Reynolds numberRe 1=6.6·106m−1 on a swept-wing model with a lenticular profile and a40° sweep angle of the leading edge at zero incidence. Excitation of high-frequency disturbances caused by secondary-flow instability at a high initial amplitude was observed. It is shown that the evolution of disturbances at frequencies of10, 20, and30 kHz is similar to the development of travelling waves for the case of subsonic velocities.

Nonlinear evolution of high-amplitude periodic disturbances in a boundary layer on a flat plate for Mach numberM=2 is studied. An anomalous downstream evolution of the disturbances is found, quasi-two-dimensional disturbances being most unstable. The obtained phase velocities of the waves are 30–40% greater than the phase velocities of the Tollmien-Schlichting waves. The nonlinear evolution of vortex waves is accompanied by an increase in steady disturbances from the source of controlled vibrations. High-frequency disturbances decay, and a periodic wave train degenerates downstream into a quasiharmonic wave train.

The paper is devoted to an experimental study of the laminar€ turbulenttransitionandtheinstabilitydisturbancesevolutioninathreedimensional(3D)supersonicboundarylayeronasweptwingwithsharp and blunted leading edges at M=2€4. The detailed data of the natural disturbances development are obtained. Characteristic zones of disturbances evolution are determined. It is found that for Mach numbers 2 and2.5measurementscanbe performedinthe regionofthelinearstage of disturbances evolution, and the experimental data can be compared with the results of the calculations on the linear stability theory. The

Results of the controlled disturbance experiments in the supersonic boundary layer on a swept wing are considered. The high-frequency glow discharge technique is used for the disturbance generation. The linear development of wave trains is tested in smooth and rough surface conditions of the models. The relative receptivity of a three-dimensional (3D) boundary layer to stationary and nonstationary disturbances is estimated. Obtained that by using microroughness elements located in a swept wing boundary layer, it is possible to get a damping effect on the linear development of a spatial wave packet in the near field of the disturbances source.

Experimental data on the linear and nonlinear wave train development in 3D supersonic boundary layer over a 45° swept-wing at Mach number 2.5 are presented. Travelling artificial disturbances were introduced in the boundary layer by periodical glow discharge at frequencies 10 and 20 kHz. The spatial-temporal and spectral-wave characteristics of the wave train of unstable disturbances in the linear region are obtained. It is shown that the additional peaks in β'-spectra arise for both subharmonic and fundamental frequencies. The experiments indicate the presence of subharmonic resonance mechanism in 3D boundary layer at Mach number 2.5.

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.

The paper is devoted to an experimental study of laminar-turbulent transition and instability disturbances evolution in a three-dimensional supersonic boundary layer on swept wing with sharp leading edge. The detailed data of natural disturbances development are obtained for the first time. Characteristic zones of disturbances evolution are determined. A position of instability region of secondary flow is experimentally defined. Some features of disturbances evolution, characteristic only for a supersonic boundary layer are revealed. It was shown experimentally that secondary cross-flow instability plays the main role in laminar-turbulent transition in 3-D supersonic boundary layers.

The experimental investigation of wave train development in the spanwise modulated flow of the supersonic flat plate boundary layer are conducted in comparison with smooth plate. It was found that the spanwise flow modulation can increase the receptivity features of supersonic boundary layer to the surface excited controlled pulsations.

The development of three-dimensional wave packets artificially introduced into a boundary layer has been experimentally investigated. The measurements were made by the hot-wire anemometer method in the boundary layer on a flat plate at a Mach number M = 4. The artificial disturbances were introduced into the boundary layer by means of an electric discharge. A Fourier analysis of the data made it possible to obtain the wave characteristics of the plane waves. The composition of the disturbances was analyzed and those most dangerous from the instability standpoint were identified. The data obtained are compared with the results of experiments carried out at M = 2. The differences in the data are discussed.

The paper is devoted to an experimental study of controlled disturbances evolution in supersonic boundary layer of swept wing. We obtained, that the evolution of disturbances at frequencies of 10, 20, and 30 kHz are similar to the development of traveling waves for subsonic velocities. We shown, that mechanism of secondary cross-flow instability play main role in laminar- turbulent transition in 3-D supersonic boundary layer. On the basis of the obtained data the technique of laminar-turbulent transition control with the help of the distributed roughness was developed. Usage of this technique, has allowed as to bring transition upstream by 30 % to delay downstream by 40 %.

A study was conducted to enhance the analytical modeling of the laminar-to-turbulent transition initiated by trip disks placed on a wind tunnel model at transonic speeds. Trip disks are the standard technique used in the Boeing Transonic Wind Tunnel for tripping the laminar boundary layer. The study consisted of wind tunnel testing and CFD analyses aimed at predicting the drag increment resulting from the trip disks. The experiments were conducted in the low speed wind tunnel at the Institute of Theoretical and Applied Mechanics in Novosibirsk, Russia. In the experiments, the laminar boundary layer profiles were measured at the trip location and turbulent profiles were measured at a series of downstream locations. These profiles were used to develop a trip model, describing the change in profile characteristics behind the row of trip disks. The trip model describes the turbulent boundary layer as a function of the laminar profile characteristics and the trip height. This trip model was then used in the CFD code TRANAIR to determine the trip drag increments on a transonic airplane model. The standard integral boundary layer model in TRANAIR was modified to enable the imposition of a step change in trip conditions generated using the trip model. Transonic wind tunnel data was used to calibrate the TRANAIR transition modeling. The CFD code was used to analyze a wide range of flow conditions, where wind tunnel data was also available. The overall agreement between the wind tunnel results and the CFD is shown to be excellent.

Freestream and boundary layer measurements are made at a freestream Mach number of 2.54 using both constant temperature (CTA) and constant voltage (CVA) anemometry. The performance of both anemometers is systematically made by operating the same hot-wire under identical conditions and applying post-test software corrections to the fluctuating measurements. In the case of the CTA the bridge frequency response is measured to take into account the change in the dynamic behavior of the bridge at different wire temperatures. In the case of the CVA the in situ time constant of the hot wire is measured to compensate the measured CVA output. The measurements show that when the signal-to-noise Research Assistant, Institut fur Aerodynamik und Gasdynamik. Currently Development Engineer, ALSTOM (Switzerland) Ltd., Baden, Switzerland. Head of Gas Dynamics, Institut fur Aerodynamik und Gasdynamik. Member AIAA. Professor, Institut fur Aerodynamik und Gasdynamik. Member AIAA. Professor, Mechanical and Aerospace Engineering Department. Associate Fellow AIAA. Emeritus Professor, Laboratoire de Mecanique des Fluides et Acoustique. Senior Member AIAA. Senior Researcher, Institute of Theoretical and Applied Mechanics. Copyright © 2003 by Ndaona Chokani, Genevieve Comte-Bellot and Julien Weiss. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. ratio is greater than one for both systems, the results are in very good agreement. The measurements of turbulence intensities are in good agreement with previous studies. This confirms the need to apply a correction for the bridge frequency response if accurate large bandwidth CTA measurements are desired. However the frequency at which noise dominates is lower for the CTA. Thus the CVA bandwidth is very much larger than that of the CTA. The amplitude roll-off at high frequencies is as theoretically expected. Thus it is desirable to obtain new quantitative turbulence measurements with larger bandwidth using the CVA.

At present it is generally accepted that laminar-turbulent transition in boundary layer is connected with the loss of stability of the initially laminar flow and the receptivity phenomena. The problem of receptivity mechanisms for supersonic boundary layers still needs a serious consideration. The first attempt of theoretical investigation of the interaction of acoustic waves and the supersonic boundary layer was made in [6] on the basis of stability theory. Some theoretical papers appeared recently which studied the role of the leading edge in receptivity of supersonic boundary layer to external acoustic waves [1-3]. The generation of unstable waves in the boundary layer was found to depend on the inclination angle of acoustic wave. We note, that conclusions of [2, 3] need experimental verification.

The development of the artificial disturbances in the system “boundary layer on a flat plate — boundary layer on an opposite wedge (model stern) behind a fan of expansion waves — wake” at supersonic freeflow velocities was investigated.

The nonlinear evolution of modulated wave train with large amplitude have been investigated. Strong amplification of two-dimensional disturbances in supersonic boundary layer has been found which cannot be explained within the framework of existing theoretical models and have no analogues in other experiments.

In the paper two methods of transition control of supersonic boundary layer on flat plate are considered. First one is a technique of an artificial turbulization of the supersonic boundary layer on the basis of the periodic electrical discharge, allowing smoothly to change a transition Reynolds number Re tr . A dependency of value of Re tr from artificial disturbance frequency is found. Second method is inhomogeneous heating of the model surface. Influence of the heating of a leading edge region on development of disturbances in the supersonic boundary layer is investigated. A gradient of temperatures on the leading part of the model allowed as to stabilize as to destabilize the supersonic boundary layer.

Instability of three-dimensional boundary layers was studied intensively both theoretically and experimentally last decade [1, 2]. Such boundary layers take place, in particularly, on swept wings of airplanes in the regions of negative and positive pressure gradients. Practically, all investigations were conducted for subsonic speeds. This problem is not solved till now in spite of a large number of the investigations. There is a qualitative difference in calculations and experimental data and in experimental results of different research groups. The complication of the problem lies in the fact that additional instability waves connected with cross-flows are developing in three-dimensional case side by side with well-known Tollmien-Schlichting waves, development of which leads to the laminar-turbulent transition in two-dimensional boundary layers. They are steady vortexes with axis directed approximately in the directions of outer flow streamlines and some traveling (not Tollmien-Schlichting waves). The development of all of these waves and their relative role in the transition process depends strongly on outer conditions.

Due to significant efforts to prove of linear stability theory by experimentally [1–8] it became possible to make progress at studying of nonlinear stability of supersonic boundary layer. Experiments shown that subharmonic resonance takes place in supersonic boundary layer [9]. A transformation of wave spectra from three- to two-dimensional disturbances at increasing Reynolds number was found later [10]. Up to now experiments and nonlinear theory have developed independently. Recently theoretic model of subharmonic resonance relevant to experiments [9] was developed by Tumin [11]. However, streamwise vortex growth still was not tested in experiments as predicted by theory [12]. More detail review of nonlinear results obtained for boundary layer is presented in [11]. In the paper, we discuss an initial amplitude influence of artificial disturbances on nonlinear development of wave trains and origin of sound radiation by supersonic boundary layer.

Experimental investigations of the laminar-turbulent transition in the low-speed boundary layers [1] – [6] have shown the possibilities of various scenarios for a nonlinear stage in the transition zone. The physical features of the nonlinear mechanisms are discussed in the review [7]. The nonlinear stage of the transition in supersonic boundary layers has not been understood yet, because of difficulties in experimental research.

In the paper theoretical and experimental results of investigation of the linear and nonlinear development of waves in the supersonic boundary layer are given.

The present paper reports an experimental study of the nonlinear development of spatial wave packets in the boundary layer on a flat plate at Mach 2. It is shown that subharmonic resonance phenomena may take place in the supersonic boundary layer. The resonance occurs for nonsymmetrical wave triplets.

The paper is devoted to an experimental study of natural disturbances evolution and laminar-turbulent transition in a three-dimensional supersonic boundary layer on swept wing at different Mach numbers. Characteristic zones of disturbances evolution are determined. It is found that for Mach numbers 2 and 2.5 measurements were performed in the region of linear stage of disturbances evolution, and the experimental data can be compared with the results of the calculations on linear stability theory. Oscillograms, amplitude-frequency spectra, pulsation profiles and statistical diagrams of natural fluctuations are obtained. Secondary instability of supersonic boundary layer on swept wing is under consideration

Experimental investigation has been carried out of the development of perturbations in separation zone of supersonic boundary layer with laminar flow-around of the model of the cones with varying angle of taper: α/2=5° and 10°. The Mach number of the incident flow equals 2.0. Frequency-wave characteristics of disturbances and mean flow parameters in separation zone have been determined.

The present paper describes the carried out experimental studies of the supersonic laminar boundary layer stability on the cone-cylinder model. The method of introducing the artificial disturbances into the supersonic flow is used. The wave characteristics of unstable plane waves in zero pressure gradient boundary layer of conical part of the model are obtained. The comparison of these characteristics with the results of the hydrodynamic stability theory and the experimental data for a flat plate is made. The development of the disturbances in the zone of interaction of boundary layer and expansion fan area are investigated. It is shown that the disturbances consisting of a vortical and compressible modes are engendered in a supersonic boundary layer by a local source of artificial disturbances. A portion of the compressible mode in the gradient pressure flow is essentially higher than in the zero-gradient one. A strong stabilizing influence of the negative pressure gradient on the disturbances has been found. The three dimensional disturbances of the vortical mode with angles of the wave vector to the flow being χ = 40–60° are found to be the most unstable in the supersonic boundary layer of the cone.