Structure Of Shear Layer Research Articles

Transient acoustic processes in a low-Mach-number shear flow

A systematic perturbation procedure, based on a small mean flow Mach number and large duct Reynolds number, is employed to formulate and solve an initial-boundary-value problem for acoustic processes in a shear flow contained within a rigid-walled parallel duct. The results describe the general transient evolution of acoustic waves driven by a plane source located at a given duct cross-section. Forced bulk oscillations near the source and oblique wave generation are shown to result from refraction of the basic planar axial disturbance by the shear flow. Refraction also causes the axial waves to exhibit higher-order amplitude variations in the transverse direction. As the source frequency approaches certain critical values, specific refraction-induced oblique waves evolve into amplifying purely transverse waves. As a result, the magnitude of the refraction effect increases with time, and quasi-steady solutions do not exist. The analysis is extended to the thin acoustic boundary layer adjacent to the solid walls to examine the shear-layer structure induced by the variety of acoustic waves in the core flow. Nonlinear effects and acoustic streaming are shown to be negligibly small on the scale of a few axial wavelengths.

Numerical simulations of the structure of supersonic shear layers

Time-dependent two-dimensional numerical calculations were performed to study the mixing characteristics of unforced, planar, confined shear layers formed by two parallel streams of air that come into contact after passing over a splitter plate. The evolution of the shear layer was examined by systematically varying the velocities, densities, and the static pressures of the two streams that come into contact at the trailing edge of the plate. At least one of the streams was always supersonic. For the range of the parameters studied, the supersonic shear layers show some organization, albeit less coherent than their subsonic counterparts. The most amplified frequency, obtained by Fourier analysis of the velocity and pressure fluctuations, depends on the effective inlet momentum thickness. Convective Mach numbers of the streams corresponding to each side of the shear layer were found to be quite different. The simulations indicate that the single convective Mach number as derived from an isentropic model is not sufficient to characterize the mixing behavior when the velocity, pressure, and density ratios are changed independently.

Structure of the Compressible Turbulent Shear Layer

The large-scale structure of the turbulent compressible shear layer is investigated in a two-stream supersonic wind tunnel. Double-exposure schlieren photography reveals that the two convective Mach numbers, corresponding to each side of the shear layer, are very different: one is sonic or supersonic and the other is low subsonic. This contradicts the current isentropic large-scale-structure model, which predicts the convective Mach numbers to be equal or very close. It is speculated that effects of shock waves are responsible for these asymmetries.

Near acoustic field and shock structure of rectangular supersonic jets

An underexpanded supersonic rectangular jet is studied experimentally at a pressure ratio range of 1-15. The shock-cell and shear-layer structure variation with the pressure ratio is shown to be related to the near-field pressure fluctuations. Near the sonic, fully adapted velocity, the jet is fully symmetric. An abrupt change to a flapping mode occurs at a low Mach number, causing a large increase in the spreading rate, which is also related to the appearance of an upstream propagating screech component

An experimental investigation of turbulent shear flow cavitation

Cavitation inception in a turbulent shear layer was studied at Reynolds numbers up to 2 × 106. Flash photography, high-speed motion pictures and holography were used to study the relation of cavitation inception to the shear-layer turbulent structure. Both spanwise and streamwise vortices were clearly visualized by the cavitation. Cavitation inception consistently occurred in the streamwise vortices and more fully developed cavitation was visible in both structures, with the streamwise cavities typically confined to the braid regions between adjacent spanwise vortices. The strength of the streamwise vortices was estimated using a Rankine vortex model, which showed that their strength was always less than 10% of that of the spanwise vortices. Measurements of fluctuating pressures were made by holographically monitoring the size of air bubbles injected into the non-cavitating shear flow. The measured pressure fluctuations had positive and negative peaks as high as 3 times the free-stream dynamic pressure, sufficient to explain cavitation inception at high values of the inception index. The occurrence of inception in the streamwise vortices of the shear layer, combined with previous reports of velocity dependence of the streamwise vortex strength, may explain the commonly observed Reynolds-number scaling of the cavitation inception index in shear flows.

Vortex dynamics in a plane, moderate-Reynolds-number shear layer

A completely non-intrusive technique, utilizing synchronized flow visualization and one-point, two-component laser-Doppler velocimetry, has been developed to examine the vortical structure of a homogeneous plane shear layer at a moderate Reynolds number. Results include ensemble-averaged velocity and vorticity maps and, derived from these data, zone-averaged statistics of the basic structure, at 6.2 initial wavelengths downstream of the splitter-plate trailing edge. The velocity field data paint a clear picture of the processes involved in the engulfment or entrainment of free-stream irrotational fluid by the vortices, and the evolution of the material interface separating fluid from the two free streams. The ensemble-averaged vorticity distribution is seen to be of an elliptical cross-section, closely resembling that of the Stuart vortex for a vorticity distribution parameter of 0.4. The effect of jitter which, in the case of zone averages is effectively removed, is assessed by comparison to conventional mean flow properties. It is found that vortex jitter greatly influences u′ and Ruu and, in confirmation of previous results, that a passive vortex does not contribute to the production of large-scale Reynolds stress.

Pressure and force fluctuations on isolated circular cylinders of finite height in boundary layer flows

Abstract This paper presents spatio-temporal measurements of a fluctuating pressure field acting on isolated roughened cylinders of finite height in simulated turbulent boundary layer flows at subcritical Reynolds numbers. The cylinder surface is roughened by placing discrete roughness elements along the height at four circumferential locations. The resulting surface roughness configuration helps to modify the flow over the cylinder, which leads to the pressure field that exhibits characteristics similar to the transcritical Reynolds numbers. The space-time measurements of the random pressure field allowed computations of the mean and r.m.s. pressure coefficients, power spectral density, spanwise and circumferential correlations, and their eigenfunction expansions. A manifold-pneumatic averaging technique was utilized to evaluate time varying area-averaged loads at various levels along the model height. The spatially averaged measurements of the pressure field over the roughened cylinder facilitated the estimation of local and mode-generalized alongwind and acrosswind aerodynamic force coefficients, their spectral descriptions and multi-level force correlations. An increase in the turbulence level influences the fluctuating pressure field through modifications which take place in the structure of the boundary layer over the cylinder and the structure of the separated shear layers.

Rotating stratified flow past a steep-sided obstacle: incipient separation

Many of the most interesting phenomena observed to occur in the flow of rotating and stratified fluids past obstacles, for example eddy shedding and wake unsteadiness, are due to separation of the boundary layer on the obstacle or its Taylor column. If the Rossby number of the flow lies between E½ and E (E is the Ekman number) and the Burger number is small, the structure of a viscous shear layer of width E⅙ on the circumscribing cylinder of an axisymmetric obstacle controls the inviscid flow. The surface boundary layer is not an Ekman layer, but a Prandtl layer, even at small Rossby numbers. As the slope of the obstacle at its base increases, the nature of the inviscid motion is altered substantially, in the rotation-dominated regime. We show that, for sufficiently large slopes, the flow develops a small region of non-uniqueness external to the column, simultaneously with the separation of the narrow band of fluid flowing round the base of the object.

The structure of a shear layer bounding a separation region. Part 2. Effects of free-stream turbulence

Detailed measurements throughout the separated region behind a flat plate placed normal to a turbulent stream are reported. A long, central, downstream splitter plate prevented vortex shedding and led to a relatively extensive reversed flow region. Mean flow and turbulence data are compared with results obtained in the (nominal) absence of free-stream turbulence, and attention is concentrated on the changes in the shear-layer structure resulting from the different nature of the upstream flow.Many aspects of the results confirm those obtained recently by other workers. Free-stream turbulence enhances shear-layer entrainment rates, reduces the distance to reattachment and modifies the relatively low-frequency ‘flapping’ motion of the shear layer. In addition, however, extensive use of pulsed wire anemometry has allowed detailed measurements of the turbulence structure throughout the flow and it is shown that this is also modified significantly by the stream turbulence.

Effects of the separating shear layer on the reattachment flow structure part 2: Reattachment length and wall shear stress

Measurements of reattachment length of a separated flow behind a backward-facing step for a range of Reynolds numbers (8000 < ReH < 40,000) and initial boundary-layer thickness (0 < δ/H < 2) were performed with the purpose of explaining the scatter in existing (high quality) data sets and to understand the effect of the initial shear-layer structure on the reattachment zone. The reattachment length for the case of laminar boundary layers upstream of the step were 30% smaller than when the boundary layer upstream of the step was turbulent. Measured values of the mean wall shear stress in the reattachment zone were also measurably affected by the upstream boundary-layer state. The (rms) levels of fluctuating wall stress were not sensitive to boundary-layer state, but rather to δ/H, as was the case for the pressure profiles in part 1 (Adams and Johnston 1988).

The structure of a turbulent shear layer bounding a separation region

Detailed measurements within the separated shear layer behind a flat plate normal to an airflow are reported. A long, central splitter plate in the wake prevented vortex shedding and led to an extensive region of separated flow with mean reattachment some ten plate heights downstream. The Reynolds number based on plate height was in excess of 2 × 1044.Extensive use of pulsed-wire anemometry allowed measurements of all the Reynolds stresses throughout the flow, along with some velocity autocorrelations and integral timescale data. The latter help to substantiate the results of other workers obtained in separated flows of related geometry, particularly in the identification of a very low-frequency motion with a timescale much longer than that associated with the large eddies in the shear layer. Wall-skin-friction measurements are consistent with the few similar data previously published and indicate that the thin boundary layer developing beneath the separated region has some ‘laminar-like’ features.The Reynolds-stress measurements demonstrate that the turbulence structure of the separated shear layer differs from that of a plane mixing layer between two streams in a number of ways. In particular, the normal stresses all rise monotonically as reattachment is approached, are always considerably higher than the plane layer values and develop in quite different ways. Flow similarity is not a useful concept. A major conclusion is that any effects of stabilizing streamline curvature are weak compared with the effects of the re-entrainment at the low-velocity edge of the shear layer of turbulent fluid returned around reattachment. It is argued that the general features of the flow are likely to be similar to those that occur in a wide range of complex turbulent flows dominated by a shear layer bounding a large-scale recirculating region.

Turbulent mass diffusion through the side opening of a circular pipe.

The turbulent mass exchange through an opening of a circular pipe is studied experimentally. The mass is transported exclusively by the turbulence generated in the shear layer between pipe flow and the surroundings. To make precise measurements of the total amount of diffused tracer gas across the opening, a new method using a closed loop conduit with an opening is developed. As dimensionless parameters which represent the intensity of turbulent diffusion, the diffusion factor, the interference factor and the breathing rate are newly defined, and the influence of opening length and shape on these parameters is quantitatively clarified. Velocity and concentration distributions are also obtained to examine the structure of the turbulent shear layer in the opening.

Pressure distributions behind a rearward facing segmented step

Effects of 3-D disturbances on a separating flow past a rearward facing step have been studied with emphasis on pressure distributions in the separation and reattachment regions. The results show that the 3-D disturbances to a separating shear layer diminish rapidly and the flow downstream of reattachment appears to have a 2-D global shearlayer structure.

Rectangular Cylinders in Flows with Harmonic Perturbations

The effects of small amplitude harmonic perturbations on the pressure coefficients and wake development behind rectangular cylinders are examined. Two body configurations with slenderness ratios (streamwise body dimension/transverse body dimension) of B/D=0.5 and 2.0 are used. For the B/D=0.5 body, with the pulsation frequency equal to twice or four times the natural shedding frequency, and with amplitudes of the order of 1% of the freestream velocity, the mean base pressure shows a decrease of up to 18% when compared with its value in steady flow. Flow visualization shows this decrease in mean base pressure to be associated with increased vortex strength, decreased vortex formation length, and the corresponding increase in shear layer curvature. When the perturbation amplitude exceeds an undetermined threshold value at a frequency corresponding to four times the natural shedding frequency, two vortices are shed simultaneously and symmetrically with respect to the body centerline. For the B/D=2.0 body, the primary effect of the pulsations is to enhance the orderly structure of the separated shear layers.

A turbulent mixing layer constrained by a solid surface. Part 2. Measurements in the wall-bounded flow

The single- and two-point measurements made in a high-Reynolds-number single-stream mixing layer growing to encounter a wind-tunnel floor on its high-velocity side that were described by Wood &amp; Bradshaw (1982) have been extended to the wall-bounded flow. It is shown that the expected large amplification of the normal-stress components in the plane of the wall does not occur until after the mixing layer reaches the surface. There is some evidence that the double-roller component of the large-eddy structure of the original free shear layer is being re-established in the wall-bounded flow after having been stretched and weakened by the initial effect of the wall. The triple-product terms appearing in the turbulent-energy and shear-stress equations are altered in a way that cannot be reproduced by models used in current calculation methods. It appears that all the pressure-fluctuation terms in the individual normal-stress and shear-stress transport equations respond in a non-monotonic manner to the imposition of the wall. The implications for calculation methods suitable for predicting the change from an initially unaffected free shear layer to a wall-bounded flow are discussed.

Pressure fluctuations on a square building model in boundary-layer flows

Spatio-temporal measurements of a fluctuating pressure field acting on the side faces of a square prism of finite height in boundary-layer flows are presented for 0° angle of attack. Two typical neutral atmospheric flow conditions were simulated in the wind tunnel to represent open country and urban flow environments. The fluctuating pressure field data allowed computations of the mean and r.m.s. (root mean square) pressure coefficients, power spectral density, autocorrelations, co-spectra, cross-correlations, orthogonal eigenfunction expansions and statistical dependence. Increased levels of turbulence in the incident flow have a marked influence on the fluctuating pressure field, through modifications which take place in the structure of the separated shear layers. The periodic vortex-shedding process is vitiated in the presence of high levels of turbulence intensity in the incident flow, resulting in redistribution of the energy associated with pressure fluctuations over a wider frequency range.

Correlation of flight effects on centerline velocity decay for cold‐flow acoustically excited jets

Acoustic excitation can influence the large‐scale shear layer structure of jet flow, thereby causing the jet centerline velocity to decay more rapidly. This phenomena has numerous practical applications, such as the reduction of jet/flap impingement velocity in order to reduce flap structural loads for under‐the‐wing STOL aircraft concepts. In the present paper, cold‐flow centerline velocity decay data obtained with acoustic excitation of the jet exhaust flow are correlated with and without flight effects. Initially, static data are correlated in terms of a new acoustic parameter involving the threshold sound level needed to initiate acoustic excitation of the jet plume. It is shown that for a given flight speed, the same acoustic excitation parameter is valid as that developed for the static condition. Finally, an aerodynamic flight effects parameter is included to correlate the static and flight centerline velocity decay data with and without acoustic excitation.

The shear-layer structure in a rotating fluid near a differentially rotating sidewall

This paper describes the flow of a homogeneous fluid contained in a rapidly rotating cylinder. The upper part of the cylinder rotates slightly faster, giving rise to a discontinuity in the sidewall velocity. The Stewartson-layer structure arising at the sidewall is essentially affected by this discontinuity. In contrast with previously studied problems, the E¼ layer (E is the Ekman number) is unable to perform the matching of the interior flow to the sidewall. It is shown that this matching is carried out partially by the E¼ layer and partially by the E1/3 layer, the latter accounting for the jump discontinuity. This paper also presents an analytical description of the flow in the singularity region near the sidewall discontinuity.

Turbulence suppression in free shear flows by controlled excitation

Turbulence suppression in the near field of a free shear flow under controlled excitation is investigated in four circular jets, a plane jet, and a plane mixing layer. The suppression is a consequence of an excitation-induced modification of the shear layer structure and occurs at the excitation frequency corresponding to the maximally unstable disturbance frequency of the initial free shear layer. The most pronounced suppression occurs when the shear layer is excited at a frequency 40% higher than the natural roll-up frequency. Excitation at a Strouhal number of about 0.017 produces a rapid roll-up and early breakdown of the shear layer, and thus inhibits the formation of the energetic large-scale vortices which otherwise survive farther downstream, grow to larger sizes, and undergo successive pairings in the corresponding unexcited flow.

The effect of mean compression or dilatation on the turbulence structure of supersonic boundary layers

It is now well known that the turbulence structure of thin shear layers can be strongly affected by the application of extra rates of strain in addition to the shear velocity gradient. Examples of such extra strain rates include lateral divergence or convergence, and streamline curvature in the plane of the mean shear. The changes in Reynolds stress are an order of magnitude larger than would be expected from the explicit extra terms in the Reynolds-stress transport equations, and therefore an order of magnitude larger than predicted by conventional calculation methods. In the present paper, one of a series on ‘complex’ turbulent flows, we show that bulk compression or dilatation (i.e. an extra strain rate div U) also appears to affect turbulent shear layers, typical values of Reynolds stress being increased by compression and decreased by dilatation. The fractional change in Reynolds stress is an order of magnitude larger than the fractional change in volume of a fluid element. The physical mechanism is probably analogous to that responsible for the large effects of divergence or convergence in incompressible flow. Because the phenomenon seems to be of great practical importance we discuss it in the context of engineering calculation methods. An empirical correction formula, analogous to those used to allow for divergence or curvature effects, greatly reduces the large discrepancies found between recent experiments on supersonic boundary layers and calculations by conventional extensions of successful incompressible-flow methods.