Cross-stream Plane Research Articles

Instabilities and turbulence in a forced turbulent convex wall jet

The outer part of a turbulent wall jet streaming over a convex surface satisfies the centrifugal instability criterion. This gives rise to streamwise vortices that convect and grow with the wall jet. These vortices are highly unsteady, which causes the turbulence characteristics of a convex wall jet to be much stronger than that of a plane wall jet. Particle image velocimetry based investigations have been carried out in this work to understand the source of this unsteadiness. A cylinder with steady spanwise heterogeneities at the nozzle lip has been used to restrict the unsteadiness of the naturally occurring streamwise vortices such that ensemble averaging techniques can be applied. The analysis reveals that the turbulent stresses are spanwise periodic; radial and azimuthal fluctuations are highest in the upwash regions, and spanwise fluctuations are highest in the downwash regions between the counter-rotating vortices. The spanwise wavelength of the vortices increases by merging, but the merging process does not restore the spanwise uniformity of the Reynolds stresses. A Proper Orthogonal Decomposition (POD) analysis in the cross-stream plane suggests the existence of instabilities that extract energy from the mean flow to sustain these fluctuations. Secondary flows produced by steadier streamwise vortices generate inflection points in the spanwise and radial directions that trigger such secondary instabilities. POD analysis in the streamwise plane reveals the presence of a traveling wave that gives rise to the spanwise meandering of the vortices. The local Strouhal number of this traveling wave, defined using the local spanwise wavelength and jet maximum velocity, is a constant value of 1. Instability waves with similar characteristics have also been observed in other centrifugally unstable flows.

Secondary flow in a laminar boundary layer developing over convergent-divergent riblets

Convergent-divergent (C-D) riblets are a type of bio-inspired surface pattern. They are known to induce secondary flow in a boundary layer that may point to their potential for surface friction drag reduction and flow separation control. In this paper, a systematic investigation of the effect of riblet height, wavelength and yaw angle on the secondary flow in a flat-plate laminar boundary layer developing over a C-D riblet section is undertaken. The large-scale secondary flow in the cross-stream plane belongs to Prandtl’s first kind, and is induced by the spanwise velocity generated by the yawed riblet passages. The exact structure of this secondary flow depends on the relative size of riblet height and wavelength to the local boundary layer thickness, and three different patterns are observed within the range of parameters examined. As the wavelength increases, the strength of the secondary flow increases firstly and then levels off at large wavelengths, whereas the average strength per unit area exhibits a peak around a ratio between wavelength and local boundary layer thickness of 1. As the yaw angle increases from 20o to 70o, the strength of the secondary flow exhibits a parabolic trend and achieves a maximum around a yaw angle of 45o. The findings from this work can be used to inform the choice of riblet geometry for maximizing the strength of the secondary flow in a given boundary layer flow.

Experimental study on secondary flow in turbulent boundary layer over spanwise heterogeneous microgrooves

Convergent–divergent riblets (C–D riblets) are a type of grooved surface pattern with directionality and spanwise heterogeneity. In the cross-stream plane, we apply stereoscopic particle image velocimetry to study the characteristics of the secondary flow over C–D riblets. Three different heights of h+ = 8, 14, and 20 are applied in the turbulent boundary layers at Reθ = 723 to reveal the effect of riblet height on the flow field. In the cross-stream plane, increasing the riblet height intensifies the heterogeneity of turbulent properties, i.e., a wider downwelling region, a stronger spanwise flow, a narrower upwelling region, and a stronger deceleration effect. Compared with the smooth-wall case, the magnitude of spanwise velocity fluctuations is larger over the converging region. The dispersive momentum transfer is primarily contributed by the secondary-flow-induced stress compared with the roughness-induced stress, and it becomes more intense as the riblet height increases. Compared with the smooth-wall case, the near-wall streamwise turbulent events are slightly wider over the diverging region and much narrower over the converging region. Overall, the higher C–D riblets generate a more intense secondary flow, and the mechanism of an increasing riblet height is attributed to the greater capability of deeper yawed microgrooves. In light of the results from our study, we propose a different way of categorizing the surface patterns with spanwise heterogeneity from the perspectives of surface geometry, roll mode, and secondary flow generation mechanisms.

Analysis of heat and fluid flow between parallel plates by inserting triangular cross-section rods in the cross-stream plane

In the present research, heat and fluid flow between the parallel plates has been investigated in the presence of the forward triangular cross-section rods. The rods are located at different non-dimensional axial distances such as S/Lh = 1/3, 1/4, and 1/5. In addition, the rods are distributed at two rows having vertical non-dimensional gap spaces of G/H = 0, 0.1, and 0.2. Computations have been performed numerically by means of the finite volume approach at various Reynolds numbers in the range from 400 to 1000 based on the channel mean velocity and its hydraulic diameter. Several quantitative and qualitative results are presented in the present study. It is found that all parameters under consideration such as S/Lh, G/H, and Re have considerable effects on the flow behavior and heat transfer rate of the advanced channel. In other words, decreasing S/Lh (or increasing the number of rods) as well as increasing the Reynolds number upgrades the channel heat transfer performance, generally. However, the maximum heat transfer enhancements occur in the case of G/H = 0.1 at each S/Lh and Re. The maximum heat transfer enhancement of the advanced channel with respect to the conventional parallel plate is obtained with 64.8% under Re = 1000, G/H = 0.1, and S/Lh = 1/5. Moreover, values of the pressure drop penalty and goodness factor have been presented accordingly for all cases under consideration.

The near wake of a sinusoidal wavy cylinder with a large spanwise wavelength using time-resolved particle image velocimetry

The near wake of a sinusoidal wavy cylinder is investigated using time-resolved particle image velocimetry (TR-PIV). The wavy cylinder has a large spanwise wavelength of six mean diameters. TR-PIV measurements are taken in three orthogonal planes in the near wake at a Reynolds number Re = 3.0 × 103. Flow structures are documented in detail, in terms of time-mean flows, Reynolds stresses, and dominant structures. A substantially long recirculation bubble is observed downstream of the saddle and node planes, corroborating the fact that fluid forces are largely reduced. Furthermore, different frequencies of vortex shedding at the saddle and node are observed for the first time, that is, vortical structures shed from the saddle and node at higher and lower frequencies, respectively. In the cross-stream plane, time-mean streamwise vorticities concentrate between the saddle and node and show an alternating pattern along the spanwise direction. Moreover, results from proper orthogonal decomposition (POD) analyses reveal distinct characteristics in the lower POD modes for the saddle and node planes; meanwhile, upwash/downwash flows downstream of the saddle, together with streamwise vortices, are associated with the lower POD modes in the cross-stream plane. Comparison is made between the present results and that for a wavy cylinder with a relatively small wavelength at similar Reynolds numbers.

A technique for measuring ensemble-averaged, three-component liquid velocity fields in two-phase, gas–liquid, intermittent pipe flows

Gas–liquid intermittent flows can be found in many engineering applications, nevertheless a detailed knowledge of this flow pattern is still not fully available. In the present work, an experimental study was conducted with the objective of developing a measurement procedure capable of providing ensemble-averaged three-component velocity fields in the liquid phase of a gas–liquid, intermittent, horizontal flow in a pipe. To this end, a high-frequency stereoscopic particle image velocimetry system (SPIV) was employed, combined with the laser induced fluorescence (LIF) technique to separate the light scattered by the liquid–gas interfaces from that emitted by the fluorescent tracer particles. A set of photogates was used to trigger the SPIV system, allowing for the measurement of velocity fields in the liquid plug, downstream of the elongated bubble, and in the liquid film, upstream of the elongated bubble nose position. The triggered measurements allowed the determination of ensemble-averaged three-component velocity fields at different positions in relation to the bubble nose, obtained from the replication of a sufficiently large number of bubble passage events. Contours of the liquid flow streamwise vorticity component in cross-stream planes upstream and downstream of the bubble nose tip were also obtained from the SPIV measurements. The photogate system was also employed to measure the bubble velocity. This information was used to transform time-based into space-based velocity field data. This allowed the construction of a three-dimensional representation of the ensemble-averaged structure of the gas bubble nose and the associated vortical structures induced in the liquid flow. The three-component velocity information obtained revealed the influence of the gas bubble motion on the liquid flow in the plug and liquid film regions.

Seismic Improvement of Gravity Dams Using Isolation Layer in Contact Area of Dam–Reservoir in Smeared Crack Approach

This study has been conducted to evaluate the effect of the isolation layer on the seismic improvement of concrete gravity dams considering dam–reservoir interaction. Koyna dam in India, due to both horizontal and vertical components of Koyna earthquake, is modeled as a case study to show the effect of the upstream isolation layer on the seismic response of concrete gravity dams, and also the interaction effect is considered in models. The water is taken as a compressible, inviscid fluid and the foundation as rigid. Gravity dams are considered as 2D structures due to long dimension in cross-stream direction and plane strain assumptions. ANSYS software was used for analysis so that the fixed smeared crack model is used to consider the nonlinear behavior of mass concrete. A flexible layer which is attached to the upstream face of the dam under different thickness and material properties is considered. The response of unisolated and isolated dams is compared under various conditions. Finally, the effect of unisolated and isolated layers in the reduction of the seismic response of the concrete is evaluated under various thicknesses comparatively. Considering obtained results revealed that the layer can have the reducing effect on responses and crack propagation process of dam model because of damping the induced hydrodynamic pressure due to the earthquake.

Partially filled pipes: experiments in laminar and turbulent flow

Pressure-driven laminar and turbulent flow in a horizontal partially filled pipe was investigated using stereoscopic particle imaging velocimetry (S-PIV) in the cross-stream plane. Laminar flow velocity measurements are in excellent agreement with a recent theoretical solution in the literature. For turbulent flow, the flow depth was varied independently of a nominally constant Reynolds number (based on hydraulic diameter, $D_{H}$; bulk velocity, $U_{b}$ and kinematic viscosity $\unicode[STIX]{x1D708}$) of $Re_{H}=U_{b}D_{H}/\unicode[STIX]{x1D708}\approx 30\,000\pm 5\,\%$. When running partially full, the inferred friction factor is no longer a simple function of Reynolds number, but also depends on the Froude number $Fr=U_{b}/\sqrt{gD_{m}}$ where $g$ is gravitational acceleration and $D_{m}$ is hydraulic mean depth. S-PIV measurements in turbulent flow reveal the presence of secondary currents which causes the maximum streamwise velocity to occur below the free surface consistent with results reported in the literature for rectangular cross-section open channel flows. Unlike square duct and rectangular open channel flow the mean secondary motion observed here manifests only as a single pair of vortices mirrored about the vertical bisector and these rollers, which fill the half-width of the pipe, remain at a constant distance from the free surface even with decreasing flow depth for the range of depths tested. Spatial distributions of streamwise Reynolds normal stress and turbulent kinetic energy exhibit preferential arrangement rather than having the same profile around the azimuth of the pipe as in a full pipe flow. Instantaneous fields reveal the signatures of elements of canonical wall-bounded turbulent flows near the pipe wall such as large-scale and very-large-scale motions and associated hairpin packets whilst near the free surface, the signatures of free surface turbulence in the absence of imposed mean shear such as ‘upwellings’, ‘downdrafts’ and ‘whirlpools’ are present. Two-point spatio-temporal correlations of streamwise velocity fluctuation suggest that the large-scale coherent motions present in full pipe flow persist in partially filled pipes but are compressed and distorted by the presence of the free surface and mean secondary motion.

Turbulence modifications in a turbulent boundary layer over a rough wall with spanwise-alternating roughness strips

Turbulence modifications over a rough wall with spanwise-varying roughness are investigated at a moderate Reynolds number Reτ ≈ 2000 (or Reθ ≈ 6400), using particle image velocimetry (PIV) and hotwire anemometry. The rough wall is comprised of spanwise-alternating longitudinal sandpaper strips of two different roughness heights. The ratio of high- and low-roughness heights is 8, and the ratio of high- and low-roughness strip width is 0.5. PIV measurements are conducted in a wall-parallel plane located in the logarithmic region, while hotwire measurements are made throughout the entire boundary layer in a cross-stream plane. In a time-average sense, large-scale counter-rotating roll-modes are observed in the cross-stream plane over the rough wall, with downwash and upwash common-flows displayed over the high- and low-roughness strips, respectively. Meanwhile, elevated and reduced streamwise velocities occur over the high- and low-roughness strips, respectively. Significant modifications in the distributions of mean vorticities and Reynolds stresses are observed, exhibiting features of spatial preference. Furthermore, spatial correlations and conditional average analyses are performed to examine the alterations of turbulence structures over the rough wall, revealing that the time-invariant structures observed are resultant from the time-average process of instantaneous turbulent events that occur mostly and preferentially in space.

Vortical structures and development of laminar flow over convergent-divergent riblets

In this work, the development of a laminar boundary layer over a rectangular convergent-divergent riblet section with a finite streamwise length is studied experimentally using dye visualization and particle image velocimetry in a water flume. The flow topology over this highly directional spanwise roughness is established from this study. It is shown that convergent-divergent riblets generate a spanwise flow above the riblets from the diverging line toward the adjacent converging line. This consequently leads to the formation of a weak recirculating secondary flow in cross-stream planes across the boundary layer that creates a downwash motion over the diverging line and an upwash motion over the converging line. It is found that the fluid inside the riblet valley follows a helicoidal path and it also interacts with the crossflow boundary layer hence playing a key role in determining the structure of the secondary flow across the boundary layer. The impact of riblet wavelength on vortical structures is also revealed for the first time. A larger riblet wavelength is seen to produce a stronger upwash/downwash and hence a more intense secondary flow as well as a stronger deceleration effect on the crossflow. Furthermore, the streamwise development of the flow over the riblet section can be divided into a developing stage followed by a developed stage. In the developing stage, the magnitude of induced streamwise velocity and vorticity over the converging line continues to increase, whereas in the developed stage the values of these parameters remain essentially unchanged.

Flow over a flat surface behind delta winglets of varying aspect ratios

The effect of winglet aspect ratio on the generated vortical flow over a flat surface was experimentally scrutinized in a wind tunnel using a triple sensor hot-wire. Aspect ratios of 1, 2 and 4 were considered at a Reynolds number based on winglet height of 6000 and an angle of attack of 30 degrees. A large longitudinal vortex structure was observed in the cross-stream plane. The streamwise velocity deficit at the main vortex core lessened, while that at the Upwash Region remained unaltered, with increasing aspect ratio. Moreover, the vortex moved downward and inward and its intensity decreased. The turbulence level decreased with a corresponding increase in Taylor microscale. The integral length was found to be independent of the aspect ratio but scaled with the winglet height.

Influence of optimally amplified streamwise streaks on the Kelvin–Helmholtz instability

The optimal energy amplifications of streamwise-uniform and spanwise-periodic perturbations of the hyperbolic-tangent mixing layer are computed and found to be very large, with maximum amplifications increasing with the Reynolds number and with the spanwise wavelength of the perturbations. The optimal initial conditions are streamwise vortices and the most amplified structures are streamwise streaks with sinuous symmetry in the cross-stream plane. The leading suboptimal perturbations have opposite (varicose) symmetry. When forced with finite amplitudes these perturbations modify the characteristics of the Kelvin–Helmholtz instability. Maximum temporal growth rates are reduced by optimal sinuous perturbations and are slightly increased by varicose suboptimal ones. In contrast, the onset of absolute instability is delayed by varicose suboptimal perturbations and is slightly promoted by sinuous optimal ones. We show that if, instead of the computed fully nonlinear basic-flow distortions, the stability analysis is based on a shape assumption for the flow distortions, then opposite effects on the flow stability are predicted in most of the considered cases. These strong differences are attributed to the spanwise-uniform component of the nonlinear basic-flow distortion which, we conclude, should be systematically included in sensitivity analyses of the stability of two-dimensional basic flows to three-dimensional basic-flow perturbations. We finally show that the leading-order quadratic sensitivity of the eigenvalues to the amplitude of the streaks is preserved if the effects of the mean flow distortion are included in the sensitivity analysis.

Effect of Rectangular Winglet Pair in Common Flow Down Configuration on Heat Transfer from an Isothermally Heated Plate

ABSTRACTPresent three-dimensional numerical study aims to investigate the effect of mounting rectangular winglet pair (RWP) on heat transfer enhancement in flow over a flat plate. Computations for incompressible flow of air have been carried out using commercial software ANSYS Fluent. Flow of air has been considered over the surface of an isothermally heated horizontal plate in presence of RWP in the range of Reynolds number from 400 to 2000. Common flow down configuration of RWP has been considered to study the effect of various geometric parameters, such as length of RWP, spacing between leading edges of the winglets and angle of attack of RWP, on flow characteristics and enhancement in heat transfer. Flow and temperature field characteristics have been presented using streamlines and temperature contours near the plate surface and streamlines in cross-stream planes. Enhancement in heat transfer in presence of RWP has been quantified using cross-stream variation of local Nusselt number, streamwise variation of span-averaged Nusselt number and surface-averaged overall Nusselt number.

Interaction between plasma synthetic jet and subsonic turbulent boundary layer

This paper experimentally investigates the interaction between a plasma synthetic jet (PSJ) and a subsonic turbulent boundary layer (TBL) using a hotwire anemometer and phase-locked particle imaging velocimetry. The PSJ is interacting with a fully developed turbulent boundary layer developing on the flat wall of a square wind tunnel section of 1.7 m length. The Reynolds number based on the freestream velocity (U∞ = 20 m/s) and the boundary layer thickness (δ99 = 34.5 mm) at the location of interaction is 44 400. A large-volume (1696 mm3) three-electrode plasma synthetic jet actuator (PSJA) with a round exit orifice (D = 2 mm) is adopted to produce high-speed (92 m/s) and short-duration (Tjet = 1 ms) pulsed jets. The exit velocity variation of the adopted PSJA in a crossflow is shown to remain almost identical to that in quiescent conditions. However, the flow structures emanating from the interaction between the PSJ and the TBL are significantly different from what were observed in quiescent conditions. In the midspan xy plane (z = 0 mm), the erupted jet body initially follows a wall-normal trajectory accompanied by the formation of a distinctive front vortex ring. After three convective time scales the jet bends to the crossflow, thus limiting the peak penetration depth to approximately 0.58δ99. Comparison of the normalized jet trajectories indicates that the penetration ability of the PSJ is less than steady jets with the same momentum flow velocity. Prior to the jet diminishing, a recirculation region is observed in the leeward side of the jet body, experiencing first an expansion and then a contraction in the area. In the cross-stream yz plane, the signature structure of jets in a crossflow, the counter-rotating vortex pair (CVP), transports high-momentum flow from the outer layer to the near-wall region, leading to a fuller velocity profile and a drop in the boundary layer shape factor (1.3 to 1.2). In contrast to steady jets, the CVP produced by the PSJ exhibits a prominent spatiotemporal behaviour. The residence time of the CVP is estimated as the jet duration time, while the maximum extent of the affected flow in the three coordinate directions (x, y, and z) is approximately 32D, 8.5D, and 10D, respectively. An extremely high level of turbulent kinetic energy production is shown in the jet shear-layer, front vortex ring, and CVP, of which the contribution of the streamwise Reynolds normal stress is dominant. Finally, a conceptual model of the interaction between the PSJ and the TBL is proposed.

Near-field dynamics of parallel twin jets in cross-flow

The present study examines the near-field flow developments and dynamics of parallel twin jets in cross-flow (TJICF) configured with jet-to-jet separation distances of 1.5 to 3 jet diameters (D) and velocity ratios of 2, 4, and 6. Both laser-induced fluorescence and particle-image velocimetry measurements were made along the streamwise and cross-stream planes in order to investigate the effects of the separation distance and velocity ratio upon the deflected jet and the formation of counter-rotating vortex-pairs (CVPs) within the near-field region. Results show that each jet in the parallel TJICF configuration attains higher cross-flow entrainment and produces greater jet half-widths than a single jet in cross-flow (SJICF). Moreover, as the separation distance decreases to 1.5D, the twin jets interact closer to the jet exit such that organized leading-edge and lee-side vortices are present along the symmetry plane. Cross-stream results indicate that the pair of inner vortices associated with the two resulting CVPs is being induced to move towards each other along the symmetry plane, where their opposite-signed vorticities annihilate with each other eventually. As such, the vorticity transition from two CVPs into a resulting single CVP takes place quickly within the near-field region when the separation distance is sufficiently small. Streamwise circulation decays determined for parallel TJICF show that their circulations increase moderately when the two CVPs begin to interact with each other. Further examination into the Reynolds shear stresses indicates that there exists substantial flow shear stress as the pair of inner vortices interacts, which yields higher entrainment level of the cross-flow fluid in regions adjacent to the symmetry plane. As a result, the near-field jet trajectories for each jet in the parallel TJICF are always lower than that of the corresponding SJICF when the separation distance is small, regardless of the velocity ratios.

Cross-stream stereoscopic particle image velocimetry of a modified turbulent boundary layer over directional surface pattern

A turbulent boundary layer developed over a herringbone patterned riblet surface is investigated using stereoscopic particle image velocimetry in the cross-stream plane at$Re_{\unicode[STIX]{x1D70F}}\approx 3900$. The three velocity components resulting from this experiment reveal a pronounced spanwise periodicity in all single-point velocity statistics. Consistent with previous hot-wire studies over similar-type riblets, we observe a weak time-average secondary flow in the form of$\unicode[STIX]{x1D6FF}$-filling streamwise vortices. The observed differences in the surface and secondary flow characteristics, compared to other heterogeneous-roughness studies, may suggest that different mechanisms are responsible for the flow modifications in this case. Observations of instantaneous velocity fields reveal modified and rearranged turbulence structures. The instantaneous snapshots also suggest that the time-average secondary flow may be an artefact arising from superpositions of much stronger instantaneous turbulent events enhanced by the surface texture. In addition, the observed instantaneous secondary motions seem to have promoted a free-stream-engulfing behaviour in the outer layer, which would indicate an increase turbulent/non-turbulent flow mixing. It is overall demonstrated that the presence of large-scale directionality in transitional surface roughness can cause a modification throughout the entire boundary layer, even when the roughness height is 0.5 % of the layer thickness.

Turbulence investigation of the NASA common research model wing tip vortex

The paper presents high-speed stereo particle image velocimetry investigation of the NASA Common Research Model wing tip vortex. A three-percent scaled semi?span model, without nacelle and pylon, was tested in the 32- by 48-inch Indraft tunnel, at the Fluid Mechanics Laboratory at the NASA Ames Research Center. Turbulence investigation of the wing tip vortex is presented. Measurements of the wing-tip vortex were performed in a vertical cross-stream plane three tip-chords downstream of the wing tip trailing edge with a 2 kHz sampling rate. Experimental data are analyzed in the invariant anisotropy maps for three various angles of attack (0?, 2?, and 4?) and the same speed generated in the tunnel (V? = 50 m/s). This corresponds to a chord Reynolds number 2.68x105, where the chord length of 3? is considered the characteristic length. The region of interest was x = 220 mm and y = 90 mm. The 20 000 particle image velocimetry samples were acquired at each condition. Velocity fields and turbulence statistics are given for all cases, as well as turbulence structure in the light of the invariant theory. Prediction of the wing tip vortices is still a challenge for the computational fluid dynamics codes due to significant pressure and velocity gradients.

Shock wave–boundary layer interaction in supersonic flow over a forward-facing step

We study in the present work a Mach 2.5 flow over a forward-facing step. The focus of the work is the flow ahead of the step, in particular, the unsteady interactions between the shock, the boundary layer and the separation bubble. The primary geometrical parameter in the problem is the ratio of the step height to the incoming boundary layer thickness,$h/\unicode[STIX]{x1D6FF}$, which is kept fixed at 2. Results are presented from detailed particle image velocimetry (PIV) measurements in two orthogonal planes to obtain a reasonable picture of the whole flow field. The mean velocity field in the central cross-stream or wall-normal ($x$–$y$) plane shows that the incoming boundary layer separates upstream of the step forming a large separation bubble ahead of the step, which can be relatively well resolved in PIV measurements compared to the compression ramp cases. Wall pressure fluctuation spectra close to the separation location show a dominant frequency ($f$) that is two orders of magnitude smaller than the characteristic frequency of the incoming boundary layer ($U_{\infty }/\unicode[STIX]{x1D6FF}$), consistent with low-frequency motions of the shock that have received a lot of recent attention ($U_{\infty }$ $=$ free-stream velocity,$\unicode[STIX]{x1D6FF}$ $=$ boundary layer thickness). PIV measurements in the wall-normal plane show large variations in shock position with time. The shock position measured from velocity data outside the boundary layer is found to be well correlated with the reverse flow area ahead of the step, and weakly correlated to structures in the incoming boundary layer. In contrast, the shock foot, determined from velocity data within the boundary layer, is found to be well correlated to the low- and high-speed streaks in the incoming boundary layer, in addition to the reverse flow area ahead of the step. Instantaneous velocity fields in the spanwise ($x$–$z$) plane parallel to the lower wall show that the shock is broadly two-dimensional with small spanwise ripples, while the recirculation region has very large spanwise variations. The spanwise-averaged shock location is found to be well correlated to the most upstream location of the recirculation region over a spanwise length ($x_{r,min}^{sp}$). Instantaneous velocity fields show that when some part of the recirculation region is far upstream, the corresponding nearly two-dimensional shock is also far upstream. On the other hand, when$x_{r,min}^{sp}$is relatively downstream, the resulting shock is also found to be downstream. Hence, the present results suggest that for the forward-facing step configuration, the large-scale streamwise motions of the shock are mainly correlated to the most upstream point of the recirculation region, which has large spanwise variations.

An experimental investigation of resonant interaction of a rectangular jet with a flat plate

The interaction between an 8:1 aspect ratio rectangular jet and a flat plate, placed parallel to the jet, is addressed in this study. At high subsonic conditions and for certain relative locations of the plate, a resonance takes place with accompanying audible tones. Even when the tone is not audible the sound pressure level spectra are often marked by conspicuous peaks. The frequencies of these peaks, as functions of the plate’s length, its location relative to the jet as well as jet Mach number, are studied in an effort to understand the flow mechanism. It is demonstrated that the tones are not due to a simple feedback between the nozzle exit and the plate’s trailing edge; the leading edge also comes into play in determining the frequency. With parametric variation, it is found that there is an order in the most energetic spectral peaks; their frequencies cluster in distinct bands. The lowest frequency band is explained by an acoustic feedback involving diffraction at the plate’s leading edge. Under the resonant condition, a periodic flapping motion of the jet column is seen when viewed in a direction parallel to the plate. Phase-averaged Mach number data on a cross-stream plane near the plate’s trailing edge illustrate that the jet cross-section goes through large contortions within the period of the tone. Farther downstream a clear ‘axis switching’ takes place for the time-averaged cross-section of the jet that does not occur otherwise for a non-resonant condition.

The evolution of large-scale motions in turbulent pipe flow

A dual-plane snapshot proper orthogonal decomposition (POD) analysis of turbulent pipe flow at a Reynolds number of 104 000 is presented. The high-speed particle image velocimetry data were simultaneously acquired in two planes, a cross-stream plane (2D–3C) and a streamwise plane (2D–2C) on the pipe centreline. The cross-stream plane analysis revealed large structures with a spatio-temporal extent of $1{-}2R$, where $R$ is the pipe radius. The temporal evolution of these large-scale structures is examined using the time-shifted correlation of the cross-stream snapshot POD coefficients, identifying the low-energy intermediate modes responsible for the transition between the large-scale modes. By conditionally averaging based on the occurrence/intensity of a given cross-stream snapshot POD mode, a complex structure consisting of wall-attached and -detached large-scale structures is shown to be associated with the most energetic modes. There is a pseudo-alignment of these large structures, which together create structures with a spatio-temporal extent of approximately $6R$, which appears to explain the formation of the very-large-scale motions previously observed in pipe flow.