Vortex Shedding Process Research Articles

Vortex Shedding and Periodic Combustion Processes in a Rijke Type Pulse Combustor

Abstract This paper presents the initial results of an investigation of the mechanism that controls the operation of a Rijke type pulse combustor with tangential reactant injection. The study is focused on the role played by reacting vortices, generated in the initial section of the shear layers of the injected reactant flow, upon the driving of the pulsations. Detailed spatial distributions of the reaction rates were obtained by an intensified imaging system. They reveal that reacting, vortex-like, structures are formed near the region where the reactants enter the injection duel when the combustor pressure is near its minimum. Subsequently, these reacting structures grow in size and merge with each other. The merging process is accompanied by a dramatic increase in the reaction intensity that occurs when the combustor pressure reaches its maximum. This satisfies Rayleigh's criterion for driving pulsations by a heat addition process. In contrast, images obtained when the combustor is operated in a steady...

Acoustically Induced Periodic Vortex Shedding At Sharp Edged Open Channel Ends: Simple Vortex Models

Simple flow models proposed by Howe [1975 Journal of Fluid Mechanics 71 , 625-673] and Disselhorst and van Wijngaarden [1980 Journal of Fluid Mechanics 99, 293-319] are used to describe the periodic vortex shedding induced at a two-dimensional channel end with infinitely thin, sharp edges by a harmonically varying acoustic flow with zero mean flow. For low Strouhal numbers a quasi-stationary theory can be used, while for high Strouhal numbers the problem can be simplified to that of vortex shedding at a semi-infinite plate. Our experiments show fair agreement with both limiting theories. A single vortex theory will be shown to be useful in the high Strouhal number limit, although a correction for the pressure force acting at a connecting line between the edge and the vortex is necessary when the vortex is increasing in strength. A correction in terms of a Magnus force applied to the single vortex does, however, influence the acoustic energy balance. A correction to the theoretical formula derived for a continuous distribution of vorticity due to the action of external forces is proposed. For intermediate Strouhal numbers, both the quasi-stationary and single vortex models fail to describe the flow at the channel end accurately. A single panel method proposed in this paper is a compromise between the single vortex description and the much more accurate but time-consuming panel method. The vortex shedding process described by the single panel method is compared with flow visualization experiments performed by Diselhorst and van Wijngaarden. Fair agreement between the single panel theory and experiments is obtained.

Vortex Formation with Free Surface Variation in Shear Layer of Open Channel Flows near Abrupt Expansion

The vortex formation with the free surface variation in the shear layer of open channel flows is investigated by means of the plane-2D-shallow water equations. The invisid instability analysis of the tanhtype velocity profile is firstly shown in order to make sure the applicability of the equations for the vortex formation in a free boundary layer. Then, the numerical simulation is made for the plane 2D-flow domain of open-channels with an abrupt expansion. Some numerical results conserning the vortex formation (velocity vectors, contour lines of depth etc.) are shown indicating the relation between the temporal velocity variations and the vortex shedding processes.

Mitigation of pressure oscillations induced by supersonic flow over slender cavities

Supersonic flow over a slender cavity excited high-frequency and high-g vibrational forces inside the cavity. The excitation of the whistle is caused by vortex shedding at the upstream end of the cavity and vortex interaction with the downstream end of the cavity associated with sound generation. The sound is fed back upstream and drives the vortex-shedding process. To suppress the acoustic whistle, an experimental test program was undertaken to characterize the acoustic cavity oscillations in a deep and narrow cavity, using microphones and flow visualization, and reduce the coherence of the vortices by geometric changes of the upstream end of the cavity. The changes that included multisteps and pins extending into the supersonic approach flow were selected to break up the orderly development of coherent vortices under acoustic excitation. With these passive shearflow control devices, acoustic amplitude reductions by a maximum factor of 5 were obtained, essentially eliminating acoustic pressure oscillation in the cavity over the entire range of Mach numbers tested. In this article, the detailed geometric and flow parameter variation and its effect on the cavity pressure oscillations are described. I. Introduction A COUSTIC oscillations inside cavities, induced by flow over the cavity, were studied extensively in the last two decades.16 This phenomenon is important in subsonic and supersonic flight of airframes with cavities such as wheel wells and weapons bays, due to the excitation of structural vibrations. The oscillations are usually characterized by broadband and pure-tone components. The broadband components are primarily associated with shallow cavities, whereas deep cavities usually excite pure periodic oscillations similar to those excited by the edge-tone phenomenon. Earlier investigations1 were aimed to quantify the sound emissions caused by cavity resonance. Later investigations attempted to develop analytical predictions for the phenomenon.2'3 Plumbee et al. 2 developed a mathematical model that was able to predict the resonant modes by relating the cavity oscillation to resonance induced by turbulent noise from the shear-layer flowing over the open end. This model was particularly successful in predicting the noise produced by deep cavities. East3 showed that some of the acoustic modes can be excited even at low subsonic Mach numbers. Over the years, different investigations proposed various theories for the excitation of the cavity pressure oscillations. Basically, most works relate these oscillations to interaction between the separated shear layer that spans across the open end of the cavities and the acoustic response of the cavity. Rossiter5 studied the problem experimentally in the Mach number range of 0.4-1.2 and cavity length to depth (L/D) ratios of 1-10 and concluded that an acoustic feedback is driving the oscillations. Rossiter proposed that the vortices in the shear layer that is separated from the upstream lip of the cavity, interact with the downstream lip generating acoustic pulses. These pulses propagate upstream, inside the cavity, exciting the shear layer at the upstream lip and thus enhancing the shedding of new vortices in the shear-layer. Using these arguments he devised an empirical equation for the tone frequencies /

A proposal of a ring-type vortex flowmeter

A configuration of a ring-type bluff body situated in a circular pipe is suggested as a design of a vortex flowmeter. Experiments were carried out to test a series of ring-type bluff models, whose geometrical parameters are expressed in terms of the gap ratio G/W and the slenderness ratio D̄/W, where G denotes the gap width between the outer edge of the ring and the pipe wall, W denotes the width of the ring, and D̄ denotes the mean diameter of the ring. Major efforts are focused upon a group of the ring-type vortex shedders whose vortex shedding process is strongly influenced by the presence of the wall. Results obtained suggest the appropriate sizes of rings for which the vortex shedding frequency can be clearly measured either on the pipe wall or at the center of the pipe.

Flow past two tandem circular cylinders of unequal diameter

SummaryThe present work investigates the structure associated with flow past two tandem circular cylinders with a diameter ratio of 0·33. The smaller cylinder is always upstream. The two parameters varied in the present work are the spacing between the cylinders denoted by l/d2where l is the centre to centre spacing and d2 is the diameter of the downstream cylinder, and the Reynolds number Re based on d2 Just like the case of flow past two equal size cylinders, a critical spacing was found to exist. For spacing less than the critical value, shear layers that separate from the upstream cylinder reattach onto the downstream cylinder (reattached flow regime) whereas for spacing larger than the critical value both cylinders shed vortices (co-shedding flow regime). For diameter ratio dl/d2 of 0·33 and at Re ≈ 6·27 × 104, the critical spacing is at l/d2 ≈ 1·8 to 2·2. In 1·8 ≤ l/d2 ≤ 2·2, bi-stable flow situation where the flow structure changes intermittently between the reattached and the co-shedding types was observed and the probability that the flow is co-shedding within the bi-stable regime is found to follow a normal distribution.It was also found that the reattached flow regime can be sub-divided into two sub-regimes. In 0·66 ≤ l/d2 ≤ 1·2 (sub-regime 1), the vortex formation length, lf, of vortices shed by the downstream cylinder appears to be shorter, resulting in larger drag force on the downstream cylinder and larger r.m.s. pressure around it. In 1·4 ≤ l/d2 ≤ 1·18 (subregime 2), lf appears to be larger which results in a smaller drag force and smaller r.m.s. pressure distribution when compared with sub-regime 1. Only the downstream cylinder has a Strouhal number S2 associated with it in the reattached flow regime. The general trend is that of a slight reduction in S2 with increasing l/d2 which is consistent with the relation of larger lf at larger l/d2 in the reattached flow regime. In the coshedding regime, the Strouhal numbers of both cylinders are similar.The Reynolds number was varied in the range 3·15 × 104 ≤ Re ≤ 8·81 × 104. It was observed that both the mean drag and the r.m.s. lift and drag forces reduce in magnitude when Re was increased. From the spectra of the lift force, reduction in C'L was found to be due to a reduction in the regularity of the vortex shedding process. From the pressure distribution of the downstream cylinder at constant l/d2, it was found that the reduction in mean drag with increasing Re is caused by an increase in base pressure which in turn is likely to be the consequence of an increase in vortex formation length. The upper and lower limits of the range in the lldi at which bistable flow was detected were found to decrease with increasing Re. At l/d2 = 2·0, the flow was of the reattached type at Re = 3·15 × 104 and 4·75 × 104 but became bi-stable at Re ≥ 6·27 × 104.

Vortex Shedding From a Bluff Body Adjacent to a Plane Sliding Wall

The characteristics of the flow around a bluff body of square cross-section in contact with a solid-wall boundary are investigated numerically using a finite difference procedure. Previous studies (Taneda, 1965; Kamemoto et al., 1984) have shown qualitatively the strong influence of solid-wall boundaries on the vortex-shedding process and the formation of the vortex street downstream. In the present study three cases are investigated which correspond to flow past a square rib in a freestream, flow past a rib on a fixed wall and flow past a rib on a sliding wall. Values of the Reynolds number studied ranged from 100 to 2000, where the Reynolds number is based on the rib height, H, and bulk stream velocity, Ub. Comparisons between the sliding-wall and fixed-wall cases show that the sliding wall has a significant destabilizing effect on the recirculation region behind the rib. Results show the onset of unsteadiness at a lower Reynolds number for the sliding-wall case (50 ≤ Recrit ≤100) than for the fixed-wall case (Recrit≥100). A careful examination of the vortex-shedding process reveals similarities between the sliding-wall case and both the freestream and fixed-wall cases. At moderate Reynolds numbers (Re≥250) the sliding-wall results show that the rib periodically sheds vortices of alternating circulation in much the same manner as the rib in a freestream; as in, for example, Davis and Moore [1982]. The vortices are distributed asymmetrically downstream of the rib and are not of equal strength as in the freestream case. However, the sliding-wall case shows no tendency to develop cycle-to-cycle variations at higher Reynolds numbers, as observed in the freestream and fixed-wall cases. Thus, while the moving wall causes the flow past the rib to become unsteady at a lower Reynolds number than in the fixed-wall case, it also acts to stabilize or “lock-in” the vortex-shedding frequency. This is attributed to the additional source of positive vorticity immediately downstream of the rib on the sliding wall.

Dynamics of fluid mixing in separated flows

The dynamics of the flow in the separated region and near wake of a vertical flat plate was analyzed with the phase-locked laser-Doppler technique at Reynolds number Re=2.8×104. The flow exhibits an intense quasiperiodic component at a Strouhal frequency of St=0.14. The vortex shedding process was resolved into six phases, resulting in a time difference between consecutive phases of Δt=0.02 sec. Interactions between the free shear layers, emanating from the model edges, lead to nonlinear dynamics of the flow. The distributions of the Reynolds stresses indicate that maximal amplitudes in the normal stresses 〈u′2〉 and 〈v′2〉 as well as in the shear stress term 〈u′v′〉 are provoked by positive pressure gradients in the shear layer flows upstream of saddle points. Saddles are quasiperiodically formed by interactions between the two free shear layers. Regions with enhanced Reynolds stresses and saddles are convectively transported within the flow field.

MECHANISMS OF VORTEX FORMATION, SHEDDING AND ATTENUATION IN THE NEAR. WAKE OF A BLUNT TRAILING EDGE

The unsteady wake from a blunt trailing-edge has been investigated experimentally. Moth c0SeS of fully turbulent and laminar boundary layer aL separation have been studied. Intensive flow visualization by hydrogen bubble technique, velocity measurements in the near--wake region and pressure measurements along the surface trailing-edge reveal. 'several . new aspects of this class of flow_th; highly organized oscillations occur in the wake region. irrespective of the boundary layer at separation whether it is fully turbulent or laminar. A well defiped meehapism for vortex formation and shedding process has been introduced by the aid of topological concepts. Subsequently, a new technique -is elaborated for attenuation of the coherent vertical structural, by interference of a splitter plate, in the near Wake region. These findings assists the existence of a powerful mechanism or absolute instability in the near-wake region as suggested in previous Investigations.

Effects of controlling vortex dynamics on the performance of a dump combustor

The use of flow control methods to improve the performance of air-breathing combustors, specifically with respect to controlling both energy release and combustion instability, is investigated. The flow control techniques were chosen for their ability to alter the vortex dynamics associated with the shear layer and recirculating flow regions in the combustor. Deltawing vortex generators and vortex generator jets were used to introduce streamwise vorticity into the flow. Periodic spanwise forcing of the inlet boundary layer was used to control the spanwise vortex shedding process in the combustor. These control strategies were applied separately and together to a laboratory-scale dump combustor, and the effects on combustor performance were determined. The introduction of streamwise vorticity into the inlet flow of the combustor causes the shear layer to become corrugated and results in a three-dimensional flame structure. The modification of flame structure is accompanied by increases in volumetric energy release of up to 75%. When vortex generator jets are used to create streamwise vorticity the increases in volumetric energy release are dependent on the jet-to-crossflow velocity ratio, R. The magnitude of the combustion pressure fluctuations is not significantly altered when using fixed vortex generators to create streamwise vorticity; however, pressure fluctuation levels were found to increase with increasing R when using vortex generator jets. Spanwise forcing of the inlet boundary layer creates a periodic two-dimensional structure in the flame, resulting in modest increases in volumetric energy release. The periodic nature of the flame structure with spanwise forcing gives rise to a dominant frequency of unsteady heat release which may be adjusted to reduce flame driving of longitudinal acoustic modes of the combustor, resulting in a reduction of combustion instability. By combining the vortex generators with spanwise forcing, it was possible to produce significant increases in volumetric energy release while achieving modest reductions in pressure fluctuations.

Determination of drag of a circular cylinder

the incident vortex has its maximum tangential velocity at the radius of the core. At this instant, the incident vortex not only distorts but also splits into upper and lower vortices. The pair of shed vortices roll up into a strong vortex of circular shape. At t = 1.5, the split incident vortices interact with the flow in the boundary layer and are convected at different local velocities. The shed vortex is convected at a local velocity, which is much slower than that of the lower split incident vortex as shown in the figure. This occurs because the rotation of the shed vortex is opposite to that of the incident vortex. No additional vortex is shed near the leading edge as seen in the figure. This is because the local angle of attack becomes small. The vortex shedding process at t = 0.6 and t =0.9 is shown in detail in Fig. 2 , which clearly indicates that the vortex pair rolls up into a single circular vortex at / =0.9. Comparisions between the experimental results of Ref. 2 and the present computed ones are not included here because of the different structures and strengths of the incident vortices studied in the experiment and the present analysis. Nevertheless, the predicted distortion and splitting of the incident vortex, and vortex shedding near the leading edge have behaviors similar to those observed in the experiment.2 Conclusions Vortex-wedge interaction is investigated using the hybrid, vortex sheet-random vortex method, including viscous effects, and a fast vortex method, involving a large number of vorticity particles. The Schwarz-Christoffel transformation is applied to generate the grid system around the wedge. The shed vortex is formed by the vorticity particles generated all along the surface. Distortion of the incident vortex during the interaction and the appearance of a secondary shed vortex near the leading edge are clearly presented. A pair of vortices are shed and they roll up into a single circular vortex. It is presumed that a variety of shed vortex patterns may prevail depending upon the incident vortex size, strength, and initial position.

Reduction of tall building motion by aerodynamic treatments

In recent years the subject of tall building motion and its reduction has received considerable attention. With present trends towards taller, lighter, and more flexible structures, the importance of this topic is ever-increasing. Of particular interest are methods to reduce the potentially severe across-wind motion due to vortex shedding excitation. One such method presently under investigation at the Boundary Layer Wind Tunnel Laboratory (BLWTL) is the aerodynamic modification of the building shape to disrupt the vortex shedding process. This paper reports on a wind tunnel model study of a slender tall building of square cross-section. The aerodynamics are modified by introducing openings or “gaps” in the upper half of the building. These gaps extend through the entire building. Different gap widths are examined and two types of data are presented. First, information is presented on the effects of these gaps on overall forces and responses of a 9:1 aspect ratio building, tested on a high frequency force balance. Second, the effects on the time-varying pressures are examined with a 2-dimensional model tested in uniform flow. This study is ongoing and further findings will be reported elsewhere.

Aerodynamic sources of acoustic resonance in a duct with baffles

Experimental and numerical investigations of the generation of resonant sound by flow in a duct containing two sets of baffles and the “feedback” of the sound on the vortex shedding process are reported. The experiments are conducted in a wind tunnel and the numerical simulations are used to predict the sources of resonant sound in the flow. The resonant sound field, which is principally longitudinal, is calculated by the finite element method and a discrete-vortex model is used to predict the observed separated flow. Analysis of the passage of a single point vortex past a baffle indicates that the amount of acoustic energy generated is a function of the phase of the acoustic cycle at which the vortex passes the baffle. A more elaborate model simulates the growth of vortex clouds through the clustering of elemental vortices shed from an upstream baffle, tracks the passage of these vortex clouds past a downstream baffle, predicts the generation of acoustic energy using Howe's theory of aerodynamic sound, and accounts for the feedback of sound on the vortex shedding. Comparison is made between the predicted time-dependent structures and the observed flow structures using smoke visualization. The vortex cloud model predicts the flow conditions under which net acoustic energy is generated by the flow and therefore when resonance can be sustained; the results are consistent with the occurrence of peaks in the observed resonant sound pressure levels.

Occurrence of anticyclonic eddies on the Prince Edward Plateau (Southern Ocean): effects on phytoplankton biomass and production

Dimensional analysis suggests that mesoscale eddies observed at the Prince Edward Islands (47°S, 38°E) are unlikely to be the result of an island wake vortex shedding process. The analysis shows that appropriate conditions can exist for the formation of closed streamline, anticyclonic eddies (Taylor columns) over the plateau. Hydrographic observations on six surveys in the area show the repeated presence of anticyclonic eddies in the vicinity of the islands. These eddies appear to have some characteristics that are consistent with Taylor column phenomena, but the spatial resolution of the hydrographic data is not sufficient to draw conclusive results. Dense phytoplankton blooms are repeatedly found between the islands. A mechanism explaining these blooms in terms of the stability of the surface mixed layer and the availability of reduced forms of nitrogen is proposed. It is suggested that both water-column stability and available nutrient concentrations are locally enhanced by run-off retained by the eddy field.

Direct simulation of vortex shedding in dilute gas flows past an inclined flat plate

The vortex shedding in dilute gas flows past an inclined flat plate is studied using the null-collision direct-simulation Monte Carlo (DSMC) method. It is shown that the DSMC method is capable of generating large-scale vortices even for the collision-cell size considerably greater than the mean free path, provided that an average molecular number per cell is sufficiently large. There exists the cell-size effect that the vortex structure becomes more obscure and the decay length of large-scale vortices becomes shorter with an increase in the collision-cell size. The Strouhal number evaluated from the vortex shedding process for the free-stream Mach number M∞=0.7 and Knudsen number Kn∞= (1)/(60) and (1)/(200) , for which the Reynolds number Re∞=69.2 and 231, respectively, is about 0.2. It is found that large-scale vortices disappear at a rather small Mach (M∞≳2 for Kn∞= (1)/(60) ) or Knudsen (Kn∞≳0.1 for M∞=0.7) number.

Reduction of tall building motion by aerodynamic treatments

In recent years the subject of tall building motion and its reduction has received considerable attention. With present trends towards taller, lighter, and more flexible structures, the importance of this topic is ever-increasing. Of particular interest are methods to reduce the potentially severe across-wind motion due to vortex shedding excitation. One such method presently under investigation at the Boundary Layer Wind Tunnel Laboratory (BLWTL) is the aerodynamic modification of the building shape to disrupt the vortex shedding process. This paper reports on a wind tunnel model study of a slender tall building of square cross-section. The aerodynamics are modified by introducing openings or “gaps” in the upper half of the building. These gaps extend through the entire building. Different gap widths are examined and two types of data are presented. First, information is presented on the effects of these gaps on overall forces and responses of a 9:1 aspect ratio building, tested on a high frequency force balance. Second, the effects on the time-varying pressures are examined with a 2-dimensional model tested in uniform flow. This study is ongoing and further findings will be reported elsewhere.

Vortex shedding mechanism from a triangular prism in a subsonic flow

Alternate periodic vortices shed from a triangular prism arranged as either a wedge or a reversed wedge are studied experimentally at a Mach number of 0.377 and at a Reynolds number of 1.73 × 105 (based on the prism height). It is found that the flow around the triangular prism arranged as a wedge (referred to as prism 1) separates at the sharp trailing edges, and the main vortices are generated immediately after the separation. No secondary vortex is generated around prism 1 ; however the flow around the other triangular prism arranged as a reversed wedge (prism 2) separates at the sharp leading edges. The main vortices are not formed immediately after the separation; rather their formation is finished either over or under the trailing edge. In this case, strong secondary vortices on and beneath the trailing edge are generated by the upper and lower main vortices, respectively. The vortices behind prism 1 are weaker than those behind prism 2, but the rate of the vortex shedding process behind prism 1 is higher than that behind prism 2. That is, the weaker the vortices are, the higher the rate of the vortex shedding process (or the Strouhal number) is, and vice versa. The vertical spacing between the loci of the upper and lower main vortices behind prism 1 is wider than that behind prism 2, but the width of the wake behind prism 1 is narrower than that behind prism 2. It is suggested that the Strouhal number for a wedge is sensitive to the front shape (i.e. the wedge angle), but that for a reversed wedge is not sensitive to the rear shape. Finally, the vortex shedding mechanism from a triangular prism arranged as either a wedge or reversed wedge has been proposed. It is concluded that, irrespective of the arrangement, vortex shedding is maintained by the unstable system of three vortices generated in the vortex formation region, but the effect of the downstream oscillating wake on vortex shedding is not critical.

Effects of an airfoil and shock waves on vortex shedding process behind a square cylinder

Effects of an airfoil and shock waves on vortex shedding process behind a square cylinder have been examined experimentally at a Mach number of about 0.91 and at a Reynolds number (based on the side lengthD of the square cylinder) of about 4.2×105. The main experimental parameter is the spacing ratioL/D, and is varied from 1.125 to 5.5, whereL is the spacing between the square cylinder and the airfoil.

Recirculation structure of the coannular swirling jets in a combustor

edge, and the flow picture would be distorted. Figure 2 shows the strengths of the wake vortices plotted against the time. In Fig. 3, the unsteady lift components induced by the three vortical regions are plotted separately. These curves show that the most important factor in this blade-vortex interaction is the vortex shedding process. Figure 4 shows the total vortex-induced unsteady lift as compared to the viscous flow solutions given by McCroskey and Goorjian and by Sankar and Tang. The good agreement between the present results and those of others from viscous flow solvers indicates that the present vortex flow model simulates high-Reynolds number attached unsteady flows very accurately.

Mach number effects on vortex shedding of a square cylinder and thick symmetrical airfoil arranged in tandem

An experimental study was done to elucidate the Mach number effects on vortex shedding of a square cylinder (side length D = 20 mm) and thick symmetrical airfoil (NACA 0018, chord length 20 mm) arranged in tandem , at free stream Mach numbers between 0.1526 and 0.9081, and at free stream Reynolds numbers (based on the side length D ) between 0.702 x 10 5 and 4.188 x 10 5 . The spacing ratio of the central distance, L , between the square cylinder and the airfoil to the side length, D , of the square cylinder was varied from 1.125 to 5.5. It was found that the regular vortex shedding is not suppressed by steady shock waves in the local supersonic flow regions; the periodic vortex shedding is still present, irrespective of the appearance of the shock waves. When the spacing ratio is fixed, the Strouhal number behind the square cylinder is almost constant up to the critical Mach number of about 0.70, but it increases rapidly with further increase of the Mach number. However, once the shock waves are formed on both sides of the vortex formation region, various frequency components, other than the vortex shedding frequency appear; the spectral peaks lower than those of the vortex shedding frequency were identified as frequencies of an acoustic-feedback oscillation and the resonance of the wind tunnel structural system. With increasing the Mach number, the formation region becomes small and asymmetric, and the separating shear layers become wavy. These changes result in an increase of the scale and strength of the vortices and thus enhance the vortex shedding process. However, when the Mach number exceeds the critical value, the streamwise length of the formation region increases suddenly and becomes long enough to enclose the downstream airfoil. Under this circumstance, the formation region is almost symmetrical with respect to the wake axis, and shock waves are formed on the upper and lower separating shear layers. The shock waves are almost normal to the wake axis at M = 0.7512 and 0.8215, but incline to the downstream direction at M = 0.9081. Acoustic waves travelling upstream have been observed most clearly when the vortex shed from the square cylinder hits the leading edge of the airfoil at a Mach number of about 0.63, which is close to, but slightly smaller than the critical value. The mean pressure and the amplitude of the pressure fluctuations in the test section decreases and increases, respectively, with increasing the Mach number. However, the amplitude of the pressure fluctuations decreases suddenly when the steady shock waves are formed on the upper and lower separating shear layers.