Shear Layer Width Research Articles

Influence of submergence ratio on flow and drag forces generated by a long rectangular array of rigid cylinders at the sidewall of an open channel

This paper discusses how the submergence ratio, defined as the ratio between the flow depth, D, and the height, h, of the solid rigid cylinders forming the array affects flow and turbulence structure inside and around a rectangular array of cylinders placed adjacent to one of the channel sidewalls. As the array becomes submerged, a vertical shear layer develops in between the top face of the array and the free surface, which strongly increases flow three-dimensionality and modifies how the momentum exchange between the array and the surrounding open water regions occurs with respect to the case of an emerged array where only a horizontal shear layer forms as part of the incoming flow approaching the array is deflected laterally. Eddy-resolving simulations are conducted for several values of the solid volume fraction, ϕ, and of the submergence ratio, 1.0 ≤ D/h ≤ 4.0. Similar to the limiting case of an emerged array (D/h = 1.0), the width- and depth-averaged streamwise velocity inside the array reaches a constant value after an initial adjustment region in the submerged-array cases. For D/h ≥ 1.33, the mean normal velocities through the top and side faces of the array do not become equal to zero downstream of the initial adjustment region. The flow inside the array reaches an equilibrium regime where the local flux of fluid leaving the array through its side face is balanced by the local flux of fluid entering the array through its top face. This regime is observed until close to the end of the array. For D/h ≥ 2.0, the horizontal shear layer vortices do not generate successive regions of high and low streamwise velocity and bed friction velocity inside the array, as is observed in the emerged cases. With respect to the emerged case, the size of the shear layer vortices and the shear layer width increase for low submergence ratios before decreasing rapidly for D/h ≥ 1.33. Significant three-dimensional effects are present inside the array and the horizontal shear layer for cases with both emerged and submerged arrays. In the ϕ = 0.08 cases, strong upwelling and downwelling motions are observed inside the array for D/h ≥ 1.33, while the circulation of the streamwise-oriented cell of secondary flow forming close to the lateral face of the array peaks when the submergence ratio is close to 1.33. For constant ϕ, the total streamwise drag force normalized with the height and width of the array increases with increasing submergence ratio. As the array submergence increases, the cylinders near the front of the array contribute less to the total force acting on the cylinders forming the array. For constant D/h, the total streamwise drag force acting on the array increases with ϕ for the submerged and emerged cases.

Flow structure and parameter evaluation of conical convergent–divergent nozzle supersonic jet flows

Supersonic gas jets in conical convergent–divergent nozzles are studied numerically using the OpenFOAM rhoCentralFoam solver. The spatiotemporal evolution of the jet flow field is analyzed. The influence of the operating conditions on the flow field is studied parametrically, including the nozzle pressure ratio (NPR), area ratio, and throat position. The behaviors and mechanisms of the double-diamond structure, throat wave, and exit wave are interpreted in detail. The results show that a conical convergent–divergent nozzle always generates shock waves. The throat shock reaches its maximum length during the initial stage, then becomes slightly shorter before becoming stationary, dominated by the exit velocity. Furthermore, it is shown that the jet flow changes from overexpansion to underexpansion with increasing NPR. With an increasing area ratio, the trend is the opposite. The throat position affects the jet divergence angle at the nozzle exit, consequently causing a variation in the core radius of the jet. It is further shown that the double-diamond structure does not always appear. The throat shock angle, exit wave angle, and shear layer width directly affect the shape of the double-diamond structure. The favorable pressure gradient of the nozzle ultimately dominates the changes in the length of the throat wave and exit wave.

Evaluation of a random displacement model for scalar mixing in ecological channels partially covered with vegetation.

The flow structure in natural rivers may change due to the disturbance of vegetation, further affecting the transport of pollutants and sediment (Liu et al. 2020). In this paper, the random displacement model (RDM) is presented to study the material transport in the emergent vegetated flow by predicting the longitudinal dispersion coefficient (LDC), which plays an important role in the longitudinal transport of pollutants in natural rivers covered by emergent vegetation. RDM can be applied for the analysis of the vegetated flow provided that the velocity distribution and the turbulent diffusion coefficient distribution remain known. According to the experimental data on velocity and Reynolds stress, the flow field was divided into four sub-zones along the cross-sectional area where the transverse distribution of the longitudinal velocity and also transverse turbulent diffusion coefficient were determined. Moreover, the simulated results of the longitudinal dispersion coefficient were verified by using the previously measured data. In addition, the sensitivity analysis of RDM parameters was carried out. In comparison with the shear layer width and the velocity difference, the impact of vegetation zone width on the longitudinal dispersion coefficient was greater, but the model was fundamentally stable, further confirming that the analytical model can be reliable for predicting the longitudinal dispersion coefficient in the vegetated open-channel flow. Accurately estimating the longitudinal dispersion coefficient is useful for understanding the transport and fate of pollutants in river channels and, thereby, for exploring the sustainable development of the river ecological environment, as well as optimizing the planning and design of river course.

On the interplay between interchange turbulence and sheared flows

The presence and the position of an X-point, namely, if the ion diamagnetic drift points toward it or not, strongly impact the edge plasma rotation in tokamaks. In the absence of kinetic effects such as magnetic ripple or ion orbit loss, the shape of the velocity profile results from the balance between neoclassical predictions and turbulent flow generation. In this contribution, we derive a reduced model of turbulence plunged in a shear flow. This model is based on (1) a description of the impact of a sheared flow on the interchange turbulence and (2) a prediction of the poloidal momentum generated by the turbulence. It includes the effects of both the magnetic topology and the finite shear layer width. The model is verified against 2D non-linear flux-driven simulations. Finally, the model predictions of the edge rotation resulting from the equilibrium between the neoclassical prediction and the poloidal momentum generation by the turbulence are invoked to describe the observations from experiment managed in the WEST tokamak. It points out the important role of the magnetic shear in the turbulence tilting and in the flow generation.

Noncirculatory Force on a Finite Thickness Body Encountering a Gust

The origin of the noncirculatory force arising during a cylinder sharp-edged gust encounter is investigated experimentally at a Reynolds number of 6000. Planar particle image velocimetry and force balance measurements are employed simultaneously to assess the response of a translating cylinder encountering nominal gust ratios of 0.5, 1, and 1.5. Although the vortex sheet distribution, which represents the boundary-layer vorticity, agrees with that calculated following Küssner’s potential flow approach for a sharp-edged transverse gust, it was found that the sheet can also be determined from the vorticity distribution in the shear layers forming the gust edges. Furthermore, it is found that the noncirculatory force calculated using Küssner’s model is an overestimate because the implicit assumption of rigid gust shear layers leads to an unphysical additional momentum change as a body of volume enters the gust regime. A volume correction is therefore proposed. In addition, it is found that the gust shear layer width and deformation have a noticeable effect on the unsteady noncirculatory force development, which reduces the applicability of Küssner’s method for large gust ratios and objects with considerable volume.

Nonuniform Flows in a Compound Open‐Channel: Assessment of a Hybrid RANS‐LES Approach

AbstractOverbank flows in rivers, also termed compound open‐channel flows, are rarely uniform in the streamwise direction. Flow nonuniformity involves transverse currents directed from the river main channel (MC) to adjacent floodplains (FPs) or vice versa. Depending on their direction and magnitude, the transverse currents can laterally displace the planform shear layer that forms at the interface between MC and FP. They can also modify the cross‐sectional distribution of the helical secondary currents (SCs). This paper reports a numerical study that focuses on assessing the ability of a hybrid RANS (Reynolds Averaged Navier‐Stokes) ‐ LES (Large Eddy Simulation) approach, namely, the Scale Adaptive Simulation (SAS), to capture the evolving structure of both depth‐uniform and nonuniform flows in a straight compound open‐channel. The simulated flows have recently been studied in an 18 m long and 3 m wide laboratory flume by Proust and Nikora (2020, https://doi.org/10.1017/jfm.2019.973). The originality of the study lies in the modeling of flows over the entire flume length and in the estimate of the length‐scales of the large Kelvin‐Helmholtz‐type coherent structures (KHCSs). The SAS approach can accurately predict the longitudinal evolution of: (i) the streamwise time‐averaged flow, including the planform shear layer width, (ii) the SC patterns, and (iii) the turbulence statistics. The emergence and development of the KHCSs are qualitatively retrieved and are confirmed to be controlled by dimensionless velocity shear irrespective of flow depth. The simulations also show that SC patterns depend on the magnitude and direction of the transverse currents and also on the development of KHCSs.

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.

Pressure gradient tailoring effects on the mechanisms of bluff-body flame extinction

The mechanisms of flame blowout under pressure gradient effects are explored for a bluff-body stabilized flame. The blowout process is induced through equivalence ratio reduction from a lean stabilized flame to complete blowout. Simultaneous high-speed particle image velocimetry (PIV) and C2*/CH* chemiluminescence imaging diagnostics are used to obtain the instantaneous flame structure, vorticity field, equivalence ratio, and local strain rate during the extinction process. The goal is to elucidate the effect of flame-generated vorticity on lean flame extinction. Three test-sections configured as a nozzle, a rectangular duct, and a diffuser, are used to alter the downstream pressure gradient yielding high, nominal, and low magnitudes of flame-generated baroclinic torque. For all three configurations, the flame brush narrows and the shear layer vorticity expands in the transverse direction resulting in flame-shear interactions and extinction. The flame-shear layer interaction increases the strain rate along the flame; however, the strong flame-generated vorticity for the nozzle case delayed the strain rate increase by keeping the flame away from the shear layer the longest. The sharp increase in the Karlovitz number above unity caused by the sudden increase in the strain rate corresponds to the time of flame brush contraction and shear layer width expansion. It is shown that the downstream pressure gradient can either augment or attenuate the time required for the Karlovitz number to reach a critical value of unity, which is associated with local extinctions along the flame. In all of the test-section configurations, the flame-generated vorticity has a weak influence on the Bénard von Kármán (BVK) instability mode and its harmonics. The Strouhal number during blow-out remained relatively constant in all of the cases showing greater sensitivity to the shear layer length than to the BVK frequency.

Derivation of the physical parameters of the jet in S5 0836+710 from stability analysis

Context. A number of extragalactic jets show periodic structures at different scales that can be associated with growing instabilities. The wavelengths of the developing instability modes and their ratios depend on the flow parameters, so the study of those structures can shed light on jet physics at the scales involved. Aims. In this work, we use the fits to the jet ridgeline obtained from different observations of S5 B0836+710 and apply stability analysis of relativistic, sheared flows to derive an estimate of the physical parameters of the jet. Methods. Based on the assumption that the observed structures are generated by growing Kelvin–Helmholtz (KH) instability modes, we ran numerical calculations of stability of a relativistic, sheared jet over a range of different jet parameters. We spanned several orders of magnitude in jet-to-ambient medium density ratio, and jet internal energy, and checked different values of the Lorentz factor and shear layer width. This represents an independent method to obtain estimates of the physical parameters of a jet. Results. By comparing the fastest growing wavelengths of each relevant mode given by the calculations with the observed wavelengths reported in the literature, we have derived independent estimates of the jet Lorentz factor, specific internal energy, jet-to-ambient medium density ratio, and Mach number. We obtain a jet Lorentz factor γ ≃ 12, specific internal energy of ε ≃ 10−2 c2, jet-to-ambient medium density ratio of η ∼ 10−3, and an internal (classical) jet Mach number of Mj ∼ 12. We also find that the wavelength ratios are better recovered by a transversal structure with a width of ≃10% of the jet radius. Conclusions. This method represents a powerful tool to derive the jet parameters in all jets showing helical patterns with different wavelengths.

Amplification and structure of streamwise-velocity fluctuations in compression-corner shock-wave/turbulent boundary-layer interactions

In this work, we study the effect of the compression-corner angle on the streamwise turbulent kinetic energy (sTKE) and structure in Mach 2.8 flow. Krypton tagging velocimetry (KTV) is used to investigate the incoming turbulent boundary layer and flow over$8^{\circ }$,$16^{\circ }$,$24^{\circ }$and$32^{\circ }$compression corners. The experiments were performed in a 99 %$\text{N}_{2}$and 1 % Kr gas mixture in the Arnold Engineering Development Complex (AEDC) Mach 3 Calibration Tunnel (M3CT) at$Re_{\unicode[STIX]{x1D6E9}}=1750$. A figure of merit is defined as the wall-normal integrated sTKE ($\overline{\text{sTKE}}$), which is designed to identify turbulence amplification by accounting for the root-mean-squared (r.m.s.) velocity fluctuations and shear-layer width for the different geometries. We observe that the$\overline{\text{sTKE}}$increases as an exponential with the compression-corner angle near the root when normalized by the boundary-layer value. Additionally, snapshot proper orthogonal decomposition (POD) is applied to the KTV results to investigate the structure of the flow. From the POD results, we extract the dominant flow structures and compare each case by presenting mean-velocity maps that correspond to the largest positive and negative POD mode coefficients. Finally, the POD spectrum reveals an inertial range common to the boundary-layer and each compression-corner flow that is present after the first${\approx}10$dominant POD modes.

On the flow organization of a chevron synthetic jet

In the present study, the flow fields generated by two synthetic jets with a chevron and a conventional circular nozzle exits are studied and compared. For both configurations, the devices are operated at the same input electrical power, thus leading to Reynolds and Strouhal numbers equal to 5600 and 0.115 (for the circular exit) and 6000 and 0.106 (for the chevron exit). Phase-locked stereoscopic particle image velocimetry measurements are used to reconstruct the three-dimensional coherent vortex structures. Time-averaged and phase-averaged mean and turbulent statistics are analysed and discussed. The flow field strongly depends on the exit geometry. In presence of the chevron exit, the conventional vortex ring issued through the circular nozzle exit, is replaced by a non-circular vortex ring with additional streamwise vortices. The mutual interaction between these structures prevents the axis-switching of the non-circular vortex ring during its convection. These streamwise vortices disappear convecting downstream and the vortex ring assumes a circular shape. Comparing the two configurations, the chevron exit generates a larger time-averaged streamwise velocity along the centreline but with lower turbulent kinetic energy intensity. Differences are also present between the notch and the apex planes of the chevron exit. In the notch plane, both the time-averaged axial velocity component profile in the spanwise direction and the shearlayer width are wider than in the apex plane. Furthermore, the presence of the streamwise vortices causes a flow motion towards the jet axis in the apex plane and an opposite motion in the notch plane.

Prediction of depth averaged velocity and boundary shear distribution of a compound channel based on the mixing layer theory

The complexity of transfer of momentum between the main channel and flood plain in a compound channel can be tackled through the analytical solution of Shiono and Knight Method. Solution of this approach counts on the calibration of three indispensable parameters i.e., secondary currents, eddy viscosity coefficient and bottom friction. Due to uniqueness of these parameters, the boundary friction factor changes unevenly throughout the lateral direction especially at the shear layer region. In this paper, the analytical solution eventuating in the Shiono Knight Method is solved considering a new panel of shear layer width at the junction. Reliable experimental measurements are employed for quantification of shear layer width and to procure the new calibrating coefficients for secondary flow and friction factor for the proposed panels. The model is found to provide satisfactory results when applied to experimental, FCF channels and natural river data sets.

Non-linear response of geocell reinforced dense granular layer over weak soil under circular loading

A modified Pasternak model has been proposed to predict the behavior of a circular footing resting on a geocell reinforced granular layer overlying soft soil. In this model, the geocell reinforced granular layer was considered as a Pasternak shear layer and the soft soil as a series of Winkler springs to predict the overall behavior. Both linear and non-linear responses of the geocell reinforced bed were considered in the analysis, which correspond to low- (≤1% of footing width) and high-footing settlements (>1% of footing diameter), respectively. An iterative finite difference scheme is employed for obtaining the solution for the governing differential equations and the results presented in non-dimensional form. Results from the present model were validated with independent experimental test data by comparing the load-deformation responses. The model parameters, inverse of normalized shear stiffness of the geocell (α2) and the inverse of normalized ultimate bearing capacity (μ), were varied for the parametric study. It was found that the shear stiffness of the reinforced granular bed, i.e. the product of shear modulus and height of the geocell in a granular bed, plays an important role in improving the performance of the reinforced bed. Design charts were presented in the form of improvement factors for practical range of shear layer width, shear stiffness of the geocell reinforcement, and ultimate bearing capacity of the soft soil.

Numerical modelling of strip footing on geocell-reinforced beds

Geosynthetics in the form of three-dimensional geocells has been in use for some time to improve the performance of foundations. A mathematical formulation was developed to predict the behaviour of a rigid strip footing resting on a geocell-reinforced granular layer overlying soft soil. The combined geocell-reinforced granular layer and the soft soil were considered as Pasternak shear layer and a series of Winkler springs, respectively. Both linear and non-linear responses of the reinforced bed were considered in the analysis, which corresponded to low (< 1% of footing width) and high footing settlements (> 1% of footing width), respectively. An iterative finite-difference scheme was employed to obtain the solution for the governing differential equations and the results are presented in non-dimensional form. The present model was validated with two independent experimental test data by comparing the load–deformation patterns which indicated good agreement. Combined soil–geocell properties were varied to obtain the improved load-carrying capacity of the reinforced ground. It was found that the shear stiffness of the reinforced granular bed, namely the product of shear modulus and height of the geocell in a granular bed, plays an important role in improving the performance of the reinforced bed. The effect of shear layer width, shear stiffness of the geocell-reinforced ground and ultimate bearing capacity of the soft soil that brings in variation in improvement of the ground were analysed and the results are presented in terms of design charts.

FULLY DEVELOPED STAGE OF PERTURBATIONS IN PARALLEL TRANSVERSE SHEAR FLOWS

A predictive theory to study the nonlinear development of the perturbations in a channel with a lateral gradient in the streamwise velocity due to the presence of bank vegetation is presented. The ratio between the undisturbed parallel velocities in the vegetated and non-vegetated zones is taken as the expanded parameter at the weakly nonlinear stability analysis, along with its corresponding wavenumber at a critical condition where the perturbations nor grow nor decay. In most cases evaluated herein, we have supercritical bifurcation, where the amplitude of the perturbations is found to reach an upper bound as time tends to infinity. We find reasonable agreement between predicted and experimental results for the time-averaged velocity profile, kinematic eddy viscosity, shear layer width and maximum friction velocity.

SHEAR LAYER AND WAVE STRUCTURE OVER PARTIALLY SPANNING CAVITIES

Study of the wave structure and shear layer in the vicinity of a wall mounted cavity is done by time averaged colour schlieren and time resolved instantaneous shadowgraph technique in an M=1.7 flowfield. Effect of change of cavity width on flow structure is investigated by using constant length to depth (L/D) ratio cavity models with varying length to width (L/W) ratio of 0.83 to 4. The time averaged shock wave structure was observed to change with change in cavity width. Dependence of the shock angle at the leading edge on the shear layer width is also evident from the images obtained. Unsteadiness in the flow field in terms of shear layer dynamics and quasi steady nature of shock waves was evident from the images obtained during instantaneous shadowgraph experiments. Apart from the leading and trailing edge shocks, several other waves and flow features were observed. These flow features and the associated physical phenomena are discussed in details and presented in the paper.

Macroscopic parameters of three-dimensional flows in free shear turbulence

The initial stage of the onset of turbulence in a three-dimensional compressible inviscid shear flow is studied. An initial deterministic velocity perturbation in the form of one or several Fourier modes leads to the development of a cascade of instabilities, which is numerically simulated. The influence exerted on the formation of the cascade of instabilities and the transition to turbulence by the size of the computational domain, the shear layer width, and the initial conditions is analyzed. It is shown that the mechanism of turbulence onset is essentially three-dimensional. The influence of various flow parameters and initial conditions on the formation of the turbulence cascade is studied numerically.

Measurements of mean and fluctuating temperature in an underexpanded jet using electrostrictive laser-induced gratings

Instantaneous temperature measurements were obtained in an underexpanded jet using electrostrictive laser-induced gratings. Evaluation of the technique under static, low-pressure conditions provided a baseline uncertainty or precision for single-shot temperature measurements of 4.4% of the local mean temperature, which represents the minimum detectable temperature fluctuation. The underexpanded jet was operated at a nozzle pressure ratio of 2.39 and a fully expanded jet Mach number of 1.19. Data were acquired along the centerline and over two radial traverses through the shear layer. Mean temperature data agree well with expectations, describing the shock-cell structure and the compressible shear layer. The growth in shear-layer width with downstream distance can be identified in the mean and fluctuating temperature measurements. Temperature fluctuations are near the baseline detection limit in the jet core and surrounding ambient air, and reach a maximum in the shear layer. The temperature fluctuation measurements compare well with previous computational and experimental work, confirming the application of the technique to a turbulent, supersonic flow.

Low-dimensional characteristics of a transonic jet. Part 1. Proper orthogonal decomposition

An experimental investigation concerning the most energetic turbulent features of the flow exiting from an axisymmetric converging nozzle at Mach 0.85 and ambient temperature is discussed using planar optical measurement techniques. The arrangement of the particle image velocimetry (PIV) system allows for all three components of the velocity field to be captured along the (r, θ)-plane of the jet at discrete streamwise locations betweenx/D=3.0 and 8.0 in 0.25 diameter increments. The ensemble-averaged (time-suppressed) two-point full Reynolds stress matrix is constructed from which the integral eigenvalue problem of the proper orthogonal decomposition (POD) is applied using both scalar and vector forms of the technique. A grid sensitivity study indicates that the POD eigenvalues converge safely to within 1% of their expected value when the discretization of the spatial grid is less than 30% of the integral length scale or 10% of the shear-layer width. The first POD eigenvalue from the scalar decomposition of the streamwise component is shown to agree with previous investigations for a range of Reynolds numbers and Mach numbers with a peak in azimuthal mode 5 atx/D=3.0, and a gradual shift to azimuthal mode 2 byx/D=8.0. The eigenvalues from the scalar POD of the radial and azimuthal components are shown to be much lower-dimensional with most of their energy residing in the first few azimuthal modes, that is modes 0, 1 and 2, with little change in the relative energies along the streamwise direction. From the vector decomposition, the azimuthal eigenspectra of the first two POD modes shift from a peak in azimuthal mode 5 atx/D=3.0, followed by a gradual decay to azimuthal mode 2 atx/D=8.0, the differences in the peak energies being very subtle. The conclusion from these findings is that when the Mach number is subsonic and the Reynolds number sufficiently large, the structure of the turbulent jet behaves independently of these factors.

Decay of MHD-scale Kelvin-Helmholtz vortices mediated by parasitic electron dynamics.

We have simulated nonlinear development of MHD-scale Kelvin-Helmholtz (KH) vortices by a two-dimensional two-fluid system including finite electron inertial effects. In the presence of moderate density jump across a shear layer, in striking contrast to MHD results, MHD KH vortices are found to decay by the time one eddy turnover is completed. The decay is mediated by smaller vortices that appear within the parent vortex and stays effective even when the shear layer width is made larger. It is shown that the smaller vortices are basically of MHD nature while the seeding for these is achieved by the electron inertial effect. Application of the results to the magnetotail boundary layer is discussed.