Turbulent Shear Layer Research Articles

Detecting vortical structures in time-resolved volumetric flow fields

The detection of three-dimensional coherent vortical structures that get advected as well as deformed with time is a challenge. However, it is critical for the statistical analysis of these vortices, for example, the quasi-streamwise vortices (QSVs) in the near field of a turbulent shear layer, where cavitation inception typically occurs. These structures exhibit underlying correlations among different properties that can be derived from the velocity gradients. Exploiting these correlations, a pseudo-Lagrangian vortex detection method is proposed that uses k-means clustering based on vorticity magnitude and direction, values of λ2, strain rate structure, axial stretching, and location. The method facilitates the finding that QSVs have pressure minima that are lower than those in the surrounding flow, including the primary spanwise vortices. These minima typically appear after a period of axial stretching and before contraction events.

Effects of the spanwise heterogeneity of a three-dimensional wavy wall on momentum and scalar transport

We numerically investigate turbulent flow and scalar transport over a three-dimensional wavy wall using a large eddy simulation. The results show that the spanwise heterogeneity of the three-dimensional wall affects the characteristics of turbulent flow as well as momentum and scalar transport. The 3D wavy wall induces alternating distributed secondary flows along the spanwise direction, which weakens the intensity of the streamwise turbulent shear layer and Reynolds stress. The double-averaged streamwise velocity profile displays an obviously upward shift relative to the two-dimensional case. The magnitude of the dispersive stress is modulated in the spanwise direction, suggesting the formation of low- and high-momentum pathways. The peak convection intensity is independent of the wall topography, albeit with shifts along the spanwise direction due to the strong shear layer between the inflow and reversed flow. The profiles of the vertical turbulent scalar flux show positive–negative variance in the viscous sublayer in both the streamwise and spanwise directions. This is also induced by the secondary flow. Vortices around a hill have a spanwise-bend feature, which strongly affects the turbulent scalar flux. The spanwise heterogeneity modulates the mean flow fields through the formation of a secondary flow ahead of the hill and a reversed vortex pair after the crest develops downstream. Both the secondary flow and reversed vortex pair have an orderly and alternating distribution near the wall.

Turbulent shear layers in a uniformly stratified background: DNS at high Reynolds number

Abstract

The scales of the leading-edge separation bubble

The leading-edge separation bubble is a flow feature occurring on the suction side of thin foils as a result of separation at the sharp leading-edge followed by reattachment downstream along the chord. For a flat plate at zero angle of attack, the reattachment length of the bubble depends on the plate thickness t. At a nonzero incidence, instead, the underlying scale governing bubble length is not clear. To investigate, we undertake a critical review of experimental and theoretical studies and develop an analytical formulation to predict the reattachment length of plates both at zero and at small incidences. We focus on conditions where the bubble is turbulent, i.e., when transition occurs at a negligible distance from the point of separation. This occurs at thickness- and chord-based Reynolds numbers Ret≳104, Rec≳105. At angle of attack α = 0, we find that the reattachment length is xR≈4.8t when the chord-to-thickness ratio is c/t>12. At α>0, we find that xR/c=πσα2, where σ≈7.9 is the inverse of the growth rate of a turbulent free shear layer. These results allow estimating xR on the thin wings of, for example, aerial vehicles and yacht sails.

Influence of low-level blocking and turbulence on the microphysics of a mixed-phase cloud in an inner-Alpine valley

Abstract. Previous studies that investigated orographic precipitation have primarily focused on isolated mountain barriers. Here we investigate the influence of low-level blocking and shear-induced turbulence on the cloud microphysics and precipitation formation in a complex inner-Alpine valley. The analysis focuses on a mid-level cloud in a post-frontal environment and a low-level feeder cloud induced by an in-valley circulation. Observations were obtained from an extensive set of instruments including ground-based remote sensing instrumentation, in situ instrumentation on a tethered-balloon system and ground-based precipitation measurements. During this event, the boundary layer was characterized by a blocked low-level flow and enhanced turbulence in the region of strong vertical wind shear at the boundary between the blocked layer in the valley and the stronger cross-barrier flow aloft. Cloud radar observations indicated changes in the microphysical cloud properties within the turbulent shear layer including enhanced linear depolarization ratio (i.e., change in particle shape or density) and increased radar reflectivity (i.e., enhanced ice growth). Based on the ice particle habits observed at the surface, we suggest that riming, aggregation and needle growth occurred within the turbulent layer. Collisions of fragile ice crystals (e.g., dendrites, needles) and the Hallett–Mossop process might have contributed to secondary ice production. Additionally, in situ instrumentation on the tethered-balloon system observed the presence of a low-level feeder cloud above a small-scale topographic feature, which dissipated when the low-level flow turned from a blocked to an unblocked state. Our observations indicate that the low-level blocking (due to the downstream mountain barrier) created an in-valley circulation, which led to the production of local updrafts and the formation of a low-level feeder cloud. Although the feeder cloud did not enhance precipitation in this particular case (since the majority of the precipitation sublimated when falling through a subsaturated layer above), we propose that local flow effects such as low-level blocking can induce the formation of feeder clouds in mountain valleys and on the leeward slope of foothills upstream of the main mountain barrier, where they can act to enhance orographic precipitation through the seeder–feeder mechanism.

Turbulent Flow Structure in a Confluence: Influence of Tributaries Width and Discharge Ratios

River channel confluences are rather important interfaces where intense changes in physical, mixing and sediment transport processes occur. Following an experimental campaign, the main flow mechanisms in confluences and the development of the shear layer formed between the two tributary flows are presented. As the experimental flow cases comprised changes in the flow discharge and channel widths of the tributaries, the influence of width and discharge ratios on the turbulent flow structure and shear layer is also evaluated. Main findings indicate that changes in the difference between momentum ratio in the tributaries have a significant effect on the magnitude and location of flow mechanisms.

Unsteadiness characterization of shock wave/turbulent boundary layer interaction controlled by high-frequency arc plasma energy deposition

We carried out an experimental study of Mach 2.5 airflow over a semicircular column with 15 kHz arc plasma energy deposition (APED). The APED was pulsed at microsecond time scales, and it rapidly added high-repetition-frequency thermal bubbles that propagated downstream. Time-resolved schlieren imaging with a frame rate of 30 kHz was utilized to record the dynamic flow fields. This study was aimed at investigating the effects of these thermal bubbles on the unsteadiness characterization of a shock wave/turbulent boundary layer interaction (STBLI) by some statistical methods based on the spatial gray value extracted from a sequence of time-resolved schlieren images. The results showed that APED pulsed at 15 kHz was highly effective in weakening both the separation shock and the attached shock continuously and in narrowing the low frequency component of the oscillatory separation shock. A stronger oscillation of the attached shock under APED was found. The thermal bubbles increased the characteristic scales of vortex in the incoming turbulent boundary layer and shear layer, enhancing the fluctuation of the shear layer with large numbers of high-frequency components. The continuous transforming of the enlarged eddies along the shear layer was regarded as the main cause of shock weakening and frequency modulation of the STBLI in this study.

Whistling of deep cavities subject to turbulent grazing flow: intermittently unstable aeroacoustic feedback

Abstract

On the generation of turbulent inflow for hybrid RANS/LES jet flow simulations

The present work is devoted to the assessment of a low-noise turbulence generation methodology used to produce boundary layer with three-dimensional resolved turbulence at the exit of a jet nozzle to reproduce experimental conditions. The method relies on the use of roughness elements introduced in the computational domain with Immersed Boundary Conditions and ZDES mode 3 (Wall Modelled LES branch of ZDES). The simulation of a round jet at M = 0.9 and Reynold number 106 with turbulence generation is compared to a simulation with no resolved turbulence in the nozzle boundary layer using ZDES mode 2. The behaviour of the boundary layer downstream of the roughness elements inside the nozzle is scrutinized using two grids. The turbulence generation method combined with ZDES mode 3 produces satisfying levels of resolved turbulence at the nozzle exit. The early stages of the shear layer development are modified by the ZDES mode 3 simulations providing an initially turbulent shear layer. On the other hand, the ZDES mode 2 simulations, with a turbulent mean exit velocity profile but no resolved turbulence, display a short area of strong shear layer instabilities leading to the quick development of three-dimensional turbulence in the mixing layer. The present results give insights on the level of turbulent modelling of the nozzle boundary layer needed depending on the purposes of the jet flow simulations considered.

Study on Dynamic Stall Control of Rotor Airfoil Based on Coflow Jet

In this study, a dynamic stall control strategy, called the co-flow jet (CFJ), is applied to the rotor airfoil. The effect of the CFJ on the unsteady dynamic stall characteristics of the rotor airfoil is numerically investigated via numerical simulations of the unsteady Reynolds-averaged Navier-Stokes (URANS) equations coupled with the Spalart-Allmaras (S-A) turbulence model. The numerical methods are validated by a NACA0012 pitching airfoil case and a NACA6415 airfoil case based on the CFJ, and good agreement with experiments is found. Via the study of the typical conditions of CFJ control to suppress the dynamic stall of the OA212 rotor airfoil, it is verified that this method has a good effect on dynamic stall suppression. The diffusion and blending of the turbulent shear layer between the CFJ injection jet and the main flow excite the main flow and enhance its ability to resist the reverse pressure gradient; this suppresses the generation and development of the separation vortex, thereby enhancing the aerodynamic characteristics, improving the hysteresis effect, and increasing the system stability. On this basis, the control parameters of the CFJ are further studied, including the influences of the jet momentum coefficient and the positions and sizes of the injection and suction slots on suppressing the dynamic stall of the rotor airfoil. It is found that there is a jet momentum coefficient that optimizes the suppression effect of the dynamic stall of the rotor airfoil. Moreover, the position of the injection slot is found to have a greater effect on the dynamic stall suppression, while the size of the injection slot and the position and size of the suction slot have little effect.

Internal regulation in compressible turbulent shear layers

Abstract

The role of the “monopole” instability in the evolution of two-dimensional turbulent free shear layers

The role of instability in the growth of a two-dimensional, temporally evolving, “turbulent” free shear layer is analyzed using vortex-gas simulations that condense all dynamics into the kinematics of the Biot–Savart relation. The initial evolution of perturbations in a constant vorticity layer is found to be in accurate agreement with the linear stability theory of Rayleigh. There is then a stage of non-universal evolution of coherent structures that is closely approximated not by Rayleigh stability theory, but by the Karman–Rubach–Lamb linear instability of monopoles, until the neighboring coherent structures merge. After several mergers, the layer evolves eventually to a self-preserving reverse cascade, characterized by a universal spread rate found by Suryanarayanan, Narasimha, and Hari Dass [“Free turbulent shear layer in a point vortex gas as a problem in nonequilibrium statistical mechanics,” Phys. Rev. E 89, 013009 (2014)] and a universal value of the ratio of dominant spacing of structures (Λf) to the layer thickness (δω). In this universal, self-preserving state, the local amplification of perturbation amplitudes is accurately predicted by Rayleigh theory for the locally existing “base” flow. The model of Morris, Giridharan, and Lilley [“On the turbulent mixing of compressible free shear layers,” Proc. R. Soc. London, Ser. A 431, 219–243 (1990)], which computes the growth of the layer by balancing the energy lost by the mean flow with the energy gain of the perturbation modes (computed from an application of Rayleigh theory), is shown, however, to provide a non-universal asymptotic state with initial condition dependent spread rate and spectra. The reason is that the predictions of the Rayleigh instability, for a flow regime with coherent structures, are valid only at the special value of Λf/δω achieved in the universal self-preserving state.

On the statistical evolution of viscous vortex-gas free shear layers

The temporal vortex-gas free shear layer is a Hamiltonian system of N-point vortices in a singly-periodic domain relevant to the (large-scale) development of plane (3D Navier–Stokes) turbulent shear layers. It has been shown (Suryanarayanan et al., 2014) that there are three distinct temporal regimes in its evolution, including an intermediate self-similar regime (RII) with a universal constant spreading rate, and a final state of relative equilibrium. Here, we study the evolution of vortex-gas free shear layers affected by viscosity as simulated by the addition of a random walk component to the motion of the vortices (Chorin, 1973). We show that while the momentum thickness of the layer, θ, scales as t1∕2 in the first and final regimes for the viscous system, it grows as t1 in the intermediate Regime II (observed here for momentum thickness Reynolds numbers Reθ from 50 to over 5000 across different simulations), with the same universal growth rate dθ∕dtΔU=0.0166±0.0002 as in the inviscid case. This suggests that the non-equilibrium universality of Regime II is robust to small perturbations of the Hamiltonian, and that this result could have general consequences for systems with long-range interactions. We further find that, even under conditions where the viscous shear stress is not negligible, the Reynolds shear stress adjusts itself in such a way that their sum is a constant in Regime II and equal to the value of the latter in the inviscid case. The implications of this observation on the dynamics of turbulent shear flows are elaborated.

Measurements of freestream density fluctuations in a hypersonic wind tunnel

Density disturbances in the freestream of the University of Southern Queensland’s Mach 6 wind tunnel ( $$\rho _{\infty } \approx {34\, \hbox {gm}^{-3}}$$ ) have been measured using a focused laser differential interferometer (FLDI). The direct contribution of the turbulent shear layer from the Mach 6 nozzle to the FLDI signal was largely eliminated by mechanically shielding the FLDI beams from these effects. This improvement significantly enhanced the low wavenumber FLDI spectra which allowed a von Kármán spectrum fit and demonstrated a $$-5/3$$ roll-off in the inertial subrange and enabled the identification of the integral length scale (28–29 mm). The normalised root-mean-square density fluctuations were found to change over the flow duration (typically between 0.4 and $$0.6\%$$ ) for the 1–250 kHz frequency range which corresponds to the wavenumber range of 6– 1600 $${\mathrm{m}}^{-1}$$ in this Mach 6 flow. Previous disturbance measurements using intrusive methods have identified a narrowband 3–4 kHz disturbance that is first measured in the core flow about 65 ms after the flow begins and remains until the flow terminates. The onset of this narrowband disturbance was previously correlated with transition-to-turbulence in the subsonic test gas supply to the nozzle. This correlation was investigated further herein, and the 3–4 kHz feature was inferred to be entropy mode disturbances by showing the departure of the FLDI measurements from Pitot pressure measurements. Through the comparison of FLDI and Pitot pressure data, Pitot pressure probes were demonstrated to produce a poor estimate of the static pressure fluctuations when non-isentropic disturbances are non-negligible.

On the manipulation of flow and acoustic fields of a blunt trailing edge aerofoil by serrated leading edges.

This paper employs serrated leading edges to inject streamwise vorticity to the downstream boundary layer and wake to manipulate the flow field and noise sources near the blunt trailing edge of an asymmetric aerofoil. The use of a large serration amplitude is found to be effective to suppress the first noise source-bluntness-induced vortex shedding tonal noise-through the destruction of the coherent eigenmodes in the wake. The second noise source is the instability noise, which is produced by the interaction between the boundary layer instability and separation bubble near the blunt edge. The main criterion needed to suppress this noise source is related to a small serration wavelength because, through the generation of more streamwise vortices, it would facilitate a greater level of destructive interaction with the separation bubble. If the leading edge has both a large serration amplitude and wavelength, the interaction between the counter-rotating vortices themselves would trigger a turbulent shear layer through an inviscid mechanism. The turbulent shear layer will produce strong hydrodynamic pressure fluctuations to the trailing edge, which then scatter into broadband noise and transform into a trailing edge noise mechanism. This would become the third noise source that can be identified in several serrated leading edge configurations. Overall, a leading edge with a large serration amplitude and small serration wavelength appears to be the optimum choice to suppress the first and second noise sources and, at the same time, avoid the generation of the third noise source.

Singular air entrapment at vertical and horizontal supported jets: plunging jets versus hydraulic jumps

In plunging jets and at hydraulic jumps, large amounts of air bubbles are entrained at the impingement of the liquid jet into the receiving body. Air is entrapped and advected into a turbulent shear layer with strong interactions between the air bubble advection process and momentum shear flow. In this new physical study, air-water flow measurements were systematically repeated with identical inflow length, inflow depth and inflow velocity in a vertical supported jet (PJ) and a horizontal hydraulic jump (HJ). Detailed measurements were conducted with the same instrumentation. Both similarities and differences were observed between the two multiphase gas-liquid shear flows. Visual observations showed a key difference in the outer region, with a buoyancy-driven flow in the plunging jet with negligible void fraction, versus a strong recirculation motion with uncontrolled interfacial aeration in the hydraulic jump. Differences were also observed at the impingement perimeter, in terms of fluctuation frequencies and amplitudes, for identical inflow conditions. Both flow conditions yielded intense local singular air entrainment and close results were observed in terms of void fraction, bubble count rate, bubble chord sizes and interfacial area in the shear layer, in both the plunging jet and hydraulic jump. The transfer of momentum between impinging jet and receiving water, as well as the effect of buoyancy, were however affected by the flow geometry.

Effect of the Reynolds number on the aeroacoustic fields of a transitional supersonic jet

The Reynolds number effect on the aeroacoustic fields of a supersonic jet was experimentally investigated via particle image velocimetry (PIV), schlieren visualization, and near-field acoustic measurements. Cold supersonic jets under ideally expanded conditions at a Mach number of 2.0 were produced with the Reynolds number, based on the diameter of the nozzle exit, ranging from 105 to 106. This study focuses on the laminar-to-turbulent transition of a supersonic jet, including a transitional condition (Re ≈ 105). The PIV results of the high-Reynolds-number jet (Re = 106), which exhibited a fully turbulent shear layer at the nozzle exit, show a linear growth of the shear layer width. Conversely, a significant increase in the turbulent fluctuations and a drastic change in the shear-layer-growth rate were observed near the transition region in the case of the low-Reynolds-number jet (Re = 105). The schlieren visualization and acoustic measurements imply that the turbulent fluctuations of the transition generated strong Mach waves. The effect of disturbing the nozzle flow was also investigated because the laminar-to-turbulent transition is sensitive to the initial disturbance. A physical disturbance added in the inlet of the low-Reynolds-number jet (Re = 105) can promote an earlier transition and suppress a significant increase in the turbulence fluctuations outside the nozzle. The changes in the flow fields due to the disturbance result in a decrease in the sound pressure level. Therefore, the aeroacoustic fields of the low-Reynolds-number jet with the disturbance show similar trends to those of the high-Reynolds-number jet (Re = 106), which already exhibited a fully turbulent shear layer at the nozzle exit.

Experimental study of a lenticular jet.

Non-circular jets, particularly elongated jets and jets with sharp corners, are of interest due to their enhanced large- and small-scale mixing and combustion stability. Non-circular jet geometries such as elliptic, triangular, rectangular, and square have been extensively studied. The non-uniform curvature and elongated design of elliptic and rectangular jets has been shown to facilitate axis switching. Additionally, jets with sharp corners have been shown to facilitate small-scale mixing and further vortex ring deformation, as has been observed in triangular, square, and rectangular jets. There are, however, currently no data on the flow characteristics of a jet that combines these two features, i.e., it enhances both large- and small-scale mixing. The jet is issuing from a nozzle shape defined by two arcs of a circle connecting at sharp corners in the shape of an eye (hereafter termed 'lenticular'). The current study uses experimental techniques to characterize the lenticular jet and compare its behavior to previously studied circular and non-circular jets. Additionally, snapshot POD analysis was used to identify coherent structures and their dynamic features. The lenticular jet was found to have higher entrainment and stronger mixing than a traditional round jet, and comparable mixing and entrainment characteristics as previously studied non-circular jet geometries. It is particularly interesting to compare the jet behavior of the lenticular jet to an elliptic jet. The geometry of these two jets is extremely similar, the difference being sharp corners along the major axis of the lenticular jet. By comparing the lenticular jet and the elliptic jet, the effect of sharp corners, which have been shown to increase small-scale mixing and vortex ring deformation, can be observed. It was found that along the minor axis, where geometry was similar, shear layer turbulence intensity and spreading rate of the jets were also similar. Along the major axis, however, introducing corner features in the lenticular jet lowered the spread rate, resulted in a faster breakdown of turbulence in the shear layer, increased exit turbulence, and resulted in anisotropic centerline turbulence.

Investigation on spatial distribution of acoustic resonance in annular cavity: Frequency and intensity

This paper studies the acoustic behavior inside the deep annular and cylindrical cavity at low Mach number. The turbulent shear layer above the cavity acts as a broadband noise source and drives resonant standing waves inside the cavity for various modes. According to previous investigation, those resonant standing waves inside the cavity play an important role in the aeroacoustic resonance of cavity noise, which gives perfect prediction of tonal frequency from the solution of wave equation. From the perspective of engineering application, it is more important to predict the spatial distribution of tonal intensity. It is needed to point out that the solution of the linear wave equation also provides the relative spatial distribution tonal intensity and the absolute value of tonal intensity can be determined from the acoustic experiments that is measured only at some locations. Based on this idea, a scheme is setup and validated to predict the amplitude spatial distribution of tonal intensity of aeroacoustic resonance. For example, an analytical model is established to provide the relative mode shape of aeroacoustic resonance in a simple geometry of cavity, which is realized by solving the wave equation with boundary conditions in a semi-closed space. This model considers the freestream velocity scaling and the depth correction factor varying with the Helmholtz number. The experimental aeroacoustic result is acquired by measuring the pressure fluctuation at some locations of cavity internal wall with the use of surface microphones. The experimental results are used to supplement and validate this analytical model. The amplitude spatial distribution at any freestream velocity (low Mach number) can be acquired by measuring the pressure fluctuation once at the leading edge or trailing edge of cavity bottom at an arbitrary Mach number, as the amplitude of most modes reaches its maximum here.

Error propagation from the PIV-based pressure gradient to the integrated pressure by the omnidirectional integration method

This paper reports a theoretical analysis and the corresponding numerical and experimental validation results of the error propagation characteristics of the omnidirectional integration method used for pressure reconstruction from the PIV measured pressure gradient. The analysis shows that the omnidirectional integration provides an effective mechanism in reducing the sensitivity of the reconstructed pressure to the random noise embedded in the measured pressure gradient. Accurate determination of the boundary pressure values is the first step in ensuring the accuracy of the reconstructed pressure. The boundary pressure error consists of two parts, with one part decreasing exponentially in magnitude and eventually vanishing, and the other remaining as a constant with small magnitude through iteration. These results are verified by using a direct numerical simulation database of isotropic turbulence flow superimposed with noise at various noise levels and spatial distribution schemes to simulate noise embedded data. The nondimensionalized average error of the reconstructed pressure based on 1000 statistically independent pressure gradient field realizations with a 40% added noise level is 0.854 ± 0.406 for the pressure Poisson equation with Neumann boundary condition, 0.154 ± 0.015 for the circular virtual boundary omnidirectional integration and 0.149 ± 0.015 for the rotating parallel ray omnidirectional integration. If the converged boundary pressure values obtained by the rotating parallel ray are used as Dirichlet boundary conditions, the average pressure error by Poisson is reduced to 0.151 ± 0.015. Of the different variations of the omnidirectional methods, the parallel ray method shows the best performance and therefore is the method of choice. Comparisons of the performance of these pressure reconstruction methods using an experimentally obtained turbulent shear layer flow over an open cavity are in agreement with the conclusions obtained with the DNS simulation data. With the noise added DNS data, limitations regarding the pressure reconstruction methods in determining pressure fluctuation statistics are also identified and quantified.