Free Shear Layer Research Articles

On the mass exchange mode controlled by high-speed compressive mainstream/cavity interaction in a laboratory dual-mode scramjet combustor

Stable and efficient mass exchange is crucial to the combustion stability of a dual-mode scramjet. In subsonic mode, the progression of mass exchange between the cavity fluid and the mainstream, which is controlled by the cavity shear layer, is different from the scramjet mode due to the weak compressibility effects. However, mass exchange mode studies in the subsonic mode are rare. In this study, experimental research has been conducted to obtain the flow structure of Mach 0.3 and 0.5 inflow over a rectangular cavity and reveal the properties of mass exchange using particle image velocimetry technology. The results reveal the weak compressibility effects and geometry effects on the mass exchange by analyzing the growth rate and turbulence characteristics of the cavity shear layer. The mass exchange between the cavity fluid and mainstream is determined based on the vertical velocity along the cavity lip line. When the flow Mach number increased from 0.3 to 0.5, the growth rate of the cavity shear layer decreases due to the weak compressibility effects. Also, the growth rate of the cavity shear layer is smaller than that of the compressible free shear layer due to the effects of recirculation within the cavity. For length-to-depth (L/D) ratios ranging from 0.8 to 1.2, the cavity shear-layer growth rate decreases with increasing L/D. However, at an L/D of 1.5, the shear-layer growth rate increases, which changes the mass exchange mode. Finally, the effects of increasing the Mach number (Mach = 0.3 versus 0.5) show that the L/D ratio at the “crossover” point of the mass exchange mode transition is reduced (L/D = 1.5 versus 1.2) due to the weak compressibility at a higher Mach number.

Aspect ratio and the dynamic wake of the Ahmed body

The dynamic structures in the wake of the Ahmed body with a 25° slant angle were investigated. It is well established that the wake is dominated by two, counter rotating, streamwise vortex structures (C-pillar vortices). The influence these vortices have on the flow over the slant back was altered by modifying the width of the body between 60% to 120% of the standard width. The wake was measured using time-resolved particle-image velocimetry in several streamwise and spanwise planes for a height-based Reynolds number of 2.6×104. The wake measurements were decomposed with a spectral proper orthogonal decomposition technique, revealing two oscillatory modes. Firstly, the C-pillar vortical structures alternately contract and expand with a Strouhal number of 0.24, mildly dependent on the width. Secondly, the boundary layers on the sides of the body separate at the end of the body, forming shear layers with a dominant frequency of St = 2.30. Reducing the width of the body to 60% rotates the symmetry axis of the shedding mode. Furthermore, changing the spacing between the C-pillar vortices, by changing the width of the body, alters the nature of the spanwise vortical structures that form behind the base of the model. Intermediate width bodies produce two stable spanwise vortices. For wide bodies, the flow remains separated over the entire slant, and the top spanwise vortex does not form. Rather, the flow over the slant resembles a free shear layer with a Kelvin–Helmholtz-like instability leading to periodic shedding of small-scale vortex structures. Conversely, for narrow bodies, this phenomenon is observed at the bottom of the body and the lower spanwise vortex no longer forms while the flow over the slant remains attached.

Electrically driven cylindrical free shear flows under an axial uniform magnetic field

We consider a mathematical model of two-dimensional electrically driven laminar axisymmetric circular free shear flows in a cylindrical vessel under the action of an applied axial uniform magnetic field. The mathematical approach is based on the studies by J.C.R. Hunt and W.E. Williams (J. Fluid. Mech., 31, 705, 1968). We solve a system of stationary partial differential equations with two unknown functions of velocity and induced magnetic field. The flows are generated as a result of the interaction of the electric current injected into the liquid and the applied field using one or two pairs of concentric annular electrodes located apart on the end walls. Two lateral free shear layers and two Hartmann layers on the end walls and a quasi-potential flow core between them emerge when the Hartmann number Ha >> 1. As a result, almost all injected current passes through these layers. Depending on the direction of the current injection, coinciding or two counter flows between the end walls are realized. The Hartmann number varies in a range from 2 to 300. When a moderate magnetic field (Ha = 50) is reached, the flow rate and the induced magnetic field flux cease to depend on the magnitude of the applied field but depend on the injected electric current value. Increasing magnetic field leads only to inner restructuring of the flows. Redistributions of velocities and induced magnetic fields, electric current density versus Hartmann number are analyzed. Figs 18, Refs 21.

Far Wake and Its Relation to Aerodynamic Efficiency

Correlations were found between the aerodynamic efficiency and the mean and fluctuating quantities in the far wake of a wall-to-wall SD7003 model and an AR 4 flat plate. This correlation was described algebraically by modeling the wake signature as a function of wing geometry and initial conditions. The model was benchmarked against experimental results to elicit the wing performance as a function of angle of attack by interrogating the wake. In these algebraic models, the drag coefficient along with other initial conditions of the turbulent generator (either airfoil or wing) were used to reconstruct the Reynolds Stress distribution and the momentum deficit distribution in the turbulent wake. Experiments were undertaken at the United States Air Force Research Labs Horizontal Free Surface Water Tunnel (AFRL/HFWT). These experiments build on previous results obtained at the University of Dayton Low Speed Wind Tunnel (UD-LSWT) on a cylinder, an AR 7 SD7062 wing, and a small remote control twin motor aircraft. The Reynolds stress and the momentum deficit of the turbulent generators were experimentally determined using Particle Image Velocimetry (PIV) with a minimum of 1000 image pairs averaged at each condition. The variation of an empirical factor (γ) used to match the Reynolds stress and momentum deficit distributions showed striking correlation to the variation of drag and aerodynamic efficiency of the turbulent generator. This correlation suggests that the wing performance information is preserved in the free shear layer 10 chord lengths downstream of the trailing edge (TE) of the wing irrespective of the dimensionality of the flow.

Shock and shear layer interactions in a confined supersonic cavity flow

The impinging shock of varying strengths on the free shear layer in a confined supersonic cavity flow is studied numerically using the detached eddy simulation. The resulting spatiotemporal variations are analyzed between the different cases using unsteady statistics, x–t diagrams, spectral analysis, and modal decomposition. A cavity of length to depth ratio [L/D]=2 at a freestream Mach number of M∞=1.71 is considered to be in a confined passage. Impinging shock strength is controlled by changing the ramp angle (θ) on the top wall. The static-pressure ratio across the impinging shock (p2/p1) is used to quantify the impinging shock strength. Five different impinging shock strengths are studied by changing the pressure ratio: 1.0,1.2,1.5,1.7, and 2.0. As the pressure ratio increases from 1.0 to 2.0, the cavity wall experiences a maximum pressure of 25% due to shock loading. At [p2/p1]=1.5, fundamental fluidic mode or Rossiter's frequency corresponding to n = 1 mode vanishes whereas frequencies correspond to higher modes (n = 2 and 4) resonate. Wavefronts interaction from the longitudinal reflections inside the cavity with the transverse disturbances from the shock-shear layer interactions is identified to drive the strong resonant behavior. Due to Mach reflections inside the confined passage at [p2/p1]=2.0, shock-cavity resonance is lost. Based on the present findings, an idea to use a shock-laden confined cavity flow in an enclosed supersonic wall-jet configuration as passive flow control or a fluidic device is also demonstrated.

Numerical investigation of cavitation instability characteristics under the interference effects

The cavitation instability between two side-by-side cylinders at a constant Reynolds number of 64,000 and four typical cavitation numbers, σ = 1.5, 2.0, 2.5, and 3.0, are investigated in this study. Large eddy simulation (LES) method and Zwart-Gerber-Belamri cavitation model are used to capture the dynamic and unsteady cavitation behaviors. The results show that cavities around circular cylinders mainly originate in the free shear layers and can roughly be divided into band-like cavities and clump-like cavities. When cavitation occurs, the transition of shear layers is brought forward and the bi-stable regime is no longer existing. Based on the vorticity equation, the vortex dilatation is mainly concentrated in the shear layers of the two cylinders while the vortex stretching is concentrated in both shear layers and wakes. The Reynolds shear stress in spanwise for the down cylinder is significantly suppressed due to the interference effects while it is free from this suppression when cavitation occurs. It follows that the interference effects of the two side-by-side cylinders could be weakened when cavitation occurs. Besides, the mean drag coefficients will increase dramatically when cavitation occurs while the mean lift coefficients are little influenced.

Direct numerical simulation of a turbulent boundary layer over a bump with strong pressure gradients

Abstract

Fluid Dynamics of a Bistable Diverter Under Ultrasonic Excitation—Part I: Performance Characteristic

Abstract This paper investigates an ultrasonically driven bistable fluidic diverter at inlet nozzle Mach numbers of up to Mn = 0.3 and operating pressure ratios of up to Pr = 1.1. Part I examines the switching characteristics with respect to nondimensional parameters of excitation amplitude, frequency, required energy, switching time and inlet total pressure. It is shown that to promote switching at turbulent jet Mach numbers of up to Mn = 0.3 it is necessary to excite a jet preferred mode of St = 0.45 which differs from previously reported laminar jet operation of the similar device. For the reference case the switching time amounts to 1.2 ms suggesting oscillation frequencies of up to 500 Hz. Part II is a combined experimental and numerical study that examines the triggered instability modes in the free shear layer using large eddy simulations (LES) and visualizes the flow field using Particle Image Velocimetry (PIV).

Application of Omega vortex identification method in cavity buffeting noise

The cavity buffeting noise is related to the free shear layer oscillation and the periodic vortex shedding, where weak vortices coexist with strong vortices and the strong shear phenomenon also exists at the opening of the cavity. Therefore, it is of great significance to accurately capture vortices at the opening for the control of the cavity buffeting noise. This paper first compares the Omega vortex identification method with the Q and λ2 criteria based on the large eddy simulation (LES) of the backward-facing step flow, and it is found that the Omega method enjoys the following advantages: it is not sensitive to a moderate threshold change and Ω = 0.52 can be used as a fixed threshold, it can capture both the strong and weak vortices at the same time; and it will not be contaminated by the shear. Then the Omega (Ω) method is applied to the LES of the cavity buffeting noise: the mechanism of the cavity buffeting noise is studied based on a simple cavity model firstly, and then the effects of the incoming boundary layer thicknesses and the incoming boundary layer shapes on the cavity buffeting noise are analyzed. The results show that: the Ω method clearly captures the processes of the vortex generation, development, collision and fragmentation, verifying that the generation of the cavity buffeting noise is related to the free shear layer oscillation and the periodic vortex shedding; as the thickness of the incoming boundary layer increases, the free shear layer becomes more stable and the Helmholtz resonance is avoided effectively, thereby the cavity buffeting noise is reduced effectively, adding a convexity upstream of the cavity opening to interfere the shape of the incoming boundary layer to reduce the acoustic feedback effect can reduce the cavity buffeting noise effectively.

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.

Shock-related unsteadiness of axisymmetric spiked bodies in supersonic flow

Shock-related unsteadiness over axisymmetric spiked body configurations is experimentally investigated at a freestream supersonic Mach number of 2.0 at 0 $$^\circ $$ angle of attack. Three different forebody configurations mounted with a sharp spike-tip ranging from blunt to streamlined (flat-face, hemispherical, and elliptical) are considered. Steady and unsteady pressure measurements, short-exposure high-speed shadowgraphy, shock footprint analysis from $$x-t$$ plots, and identification of dominant spatiotemporal modes through modal analysis are carried out to explain the unsteady flow physics. The present investigation tools are validated against the well-known events of ‘pulsation’ corresponding to the flat-face case. The hemispherical case is characterized by the formation of a separated free shear layer and associated localized shock oscillations. The cycle of charging and ejection of fluid mass from the recirculation zone is identified to drive the flow unsteadiness. Such an event triggers the movement of the separated and reattachment shocks in the opposite direction with respect to each other (out-of-phase shocks motion). In the elliptical case, the overall flow field resembles that of the hemispherical case, except with dampened unsteadiness. The value of the cone angle ( $$\lambda $$ ) associated with the recirculation region is found responsible for the fluctuations caused by the charging and ejection of fluid mass. Thereby, it controls the extent of out-of-phase shocks motion. In the elliptical case, shock unsteadiness is reduced as $$\lambda $$ is observed to be smaller. Based on the gathered results and understanding, the reduction in unsteadiness associated with the aerodisk mounted on the hemispherical forebody is demonstrated and explained via the almost complete elimination of the out-of-phase shocks motion.

Modeling of destructive interaction of hot jet and solid plate

Based upon the results of a literature review, a set of physical parameters suitable for quantitative comparison in experimental and numerical studies is determined. The review showed the feasibility of modeling the process of the outflow of an immersed jet of inert gas into the surrounding space and the evolution of a free shear layer formed by hot and cold gases to analyze the process of convective and diffusion transport of various types of particles. In the model formulation we consider the problem of solid destruction by a melt of the same substance, as well as by a nitrogen stream at high temperature. The test simulation of the problems of two-phase interaction of a immersed jet of molten liquid and hot gas, on the whole, qualitatively showed the reproduction of the main characteristics of the flow: the generation of large-scale vortices around the jet in the induction zone, the oscillations of the jet when it collides with an obstacle, and the shape of the cavity formed.

Stationary cross-flow breakdown in a high-speed swept-wing boundary layer

A new type-II secondary instability mode was recently identified in high-speed cross-flows using stability analysis, but its role in the transition process is not yet clear. Here, the breakdown of stationary cross-flow vortices at high speeds is examined using direct numerical simulation to determine differences from the low-speed case. The transition is achieved by disturbing stationary cross-flow vortices with unsteady blowing/suction in a swept-wing boundary layer with swept angle 45°, free-stream Mach number 6, and unit Reynolds number 8 ×106. The results reveal that, as in low-speed cases, the type-I secondary instability mode (with frequency ≈190 kHz) is crucial to the breakdown, but neither the traditional nor the new type-II secondary instability play a role. The vortical structure induced by the type-I secondary instability mode has two counter-rotating tubes stretched along the spanwise direction and a footprint aligned normal to the mean flow direction. The composite vortex structures are similar to rolls/braids in plane free-shear layers arising from Kelvin–Helmholtz instability and they evolve into hairpins in the late stage of the transition. Some preliminary statistics from a three-dimensional turbulent boundary layer are provided as a comparison to the two-dimensional ones. The fluctuating cross-flow velocity does not contribute to the momentum and heat transfer on average, probably due to the very weak mean cross-flow profile. Thus, the obtained three-dimensional turbulent boundary layer is the same as the two-dimensional one but inclined by a swept angle. To the authors’ knowledge, this is the first in-depth analysis of the high-speed cross-flow transition to full turbulence.

Compressibility effects on energy exchange mechanisms in a spatially developing plane free shear layer

Abstract

Reacting Flow Simulations of a Dual Throat-Dual Fuel Thruster

Numerical simulation of the supersonic turbulent reacting flow field in a dual throat- dual fuel rocket thrust chamber is presented. Future single stage to orbit and high lift space transportation missions aspire a reliable, efficient, and cost-effective propulsion systems. The dual throat-dual fuel concept is a simple altitude compensating propulsion alternative with reusable possibilities. Turbulent reacting supersonic flow field emanating from independent thrust chambers needs to be resolved for a better understanding of the flow structures and design modifications for the performance improvement. The operation of a dual throat nozzle brings about a unique shock train in reacting supersonic flow. Two-dimensional axis-symmetric compressible reacting flow field has been solved using HLLC (Harten, Lax, van Leer, with Contact wave) scheme based finite volume Riemann solver with multi-step finite rate chemistry model for hydrocarbon/hydrogen-oxygen combustion. The computational procedure has been validated with experimental data for species distribution of a coaxial supersonic combustor. Chemical species distribution in the supersonic free shear layer is analyzed in detail to explore the nature of active reaction zones in the flow field.

Effects of different droplet dispersion modeling methods on diesel spray simulation in Eulerian-Lagrangian framework

The realistic prediction of spray dynamics and dispersion is one of the main tasks of the combustion simulations in diesel engines. Usually, droplet dispersion modeling accuracy can be improved by the development of turbulence models and stochastic dispersion models. Although droplet dispersion due to turbulence is an important phenomenon in high-velocity fuel sprays, studies on the effect of these models are relatively few. Among these studies, the influence of a common used stochastic dispersion model on spray dynamics is not well understood and the application of hybrid turbulence models to fuel spray simulation in the Eulerian-Lagrangian framework with two-way coupling is still at starting stage. In the present study, a better understanding of the effect of the stochastic model on spray dynamics can be obtained by using a statistical analysis of stochastic dispersion time and velocity of dispersed droplets. In order to assess the ability of the hybrid model to improve the radial spread and the inhomogenous distribution of small droplets produced by a high-pressure injector, a partially averaged Navier-Stokes (PANS) model is implemented in an open-source code OpenFOAM and is compared with an unsteady Reynolds averaged Navier-Stokes (RANS) model and a large eddy simulation (LES) model. The results show the importance of resolving large-scale turbulent structures on droplet dispersion modeling in high-velocity fuel spray simulation. The common stochastic dispersion model used in RANS developed for homogenous, isotropic turbulent flows leads to the non-physical dynamics and distribution of droplets and hence is not applicable to the droplet dispersion which is dominated by the non-stochastic motion of large-scale structures in free shear layers. Using PANS instead of RANS should improve the droplet dispersion modeling accuracy of high-velocity fuel sprays in the development of diesel engines with an advanced injection system.

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.

Investigation of the acoustic particle velocity using synchronized non-invasive measurements in the near and far field of a turbulent flow

The sound generation of an aeroacoustic source with dominating tonal components and the propagation into the acoustic far field is investigated based on measurements of the flow around a square rod - mounted horizontally in an open-jet closed-circuit anechoic wind-tunnel - at a Reynolds number of 6×104. Pressure time series are measured with microphones in the far field while velocity field measurements are performed simultaneously with the non-invasive particle image velocimetry (PIV) technique in the flow field. It is shown that the propagation of acoustic waves from the source region to the far field can be resolved analyzing additionally flow fields recorded in vertically shifted fields of view, if the time evolution is synchronized properly with the far-field pressure signal. Furthermore, a comparison with two analytical solutions shows that the cross-correlation function of far-field pressure and near-field velocity fluctuations, normalized by the standard deviation of the pressure signal, corresponds to the acoustic particle velocity. However, this only applies to areas where the acoustic fluctuations dominate, i.e. not in the wake or in the free shear layer between the wind tunnel flow and the quiescent air where acoustic fluctuations are superimposed by hydrodynamic ones.

STABILITY CHARACTERISTICS OF COMPRESSIBLE BINARY PLANAR JETS

The present work investigates the stability of compressible binary planar jets. Different from a homogeneous jet, where a single chemical species is present, the binary jet may have strong density gradients due to the choice of the chemical species considered in each stream. The goal is to identify the possible instability modes for simple and co-flowing jets and investigate the effect of density gradients on the flow structure, growth rates, unstable frequency range and disturbance phase speed for each mode. The effect of species concentration on free shear layer stability has been reported previously in the literature, but detailed comparisons between stability modes and characteristics for a range of density ratios typical of oxygen and hydrogen mixtures as well as the identification of inner and outer sinuous and varicose modes are new. Linear stability theory is used to determine the stability characteristics of the different configurations. For the co-flowing jet four different modes are found, the inner and outer shear layers both have sinuous and varicose modes. Both for the sinuous and varicose modes the simple jet is more unstable when the fluid with the highest density is at the inner jet, with amplification rates twice as high as the lowest density ratio considered, but the range of unstable frequencies can be four times lower. The sinuous mode is less dispersive than the varicose and the disturbance speeds may vary by one order of magnitude with density ratio. For co-flowing jets the external mode is up to seven times more unstable, but this is due to the choice of the velocity ratio considered. For the inner mode the density gradient has a stabilizing effect regardless of which species is at the center. The co-flowing jet is more dispersive, except for the varicose inner mode. The variation of phase speed with density gradient is not as strong as in the simple jet. The ratio of larges to lower phase speeds are of the order of 2 for the co-flowing jet and 4 for the simple jet.

LES study of contrasting behavior of pulsating plane impinging jets for heating and cooling applications

Forced turbulent plane impinging jets at a frequency of 600 Hz, are studied using LES. The jets impinge on a curved surface for cooling and heating applications. The jets generate two free-shear layers releasing primary vortices moving with a sweeping effect above the target wall. The sweeping motion affects the convex wall boundary layer by generating secondary vortices and entraining air from both the jet and the surroundings. In both situations the fluid drawn in by the jet from the free entrainment boundary is cold, a condition considered realistic. The trajectories of the primary vortices exhibit a cyclic trend within a certain distance, in the streamwise direction. Forcing the jets leads to a decrease of the Nusselt number at the impingement region and away beyond four jet widths from the impingement point. The cooling jet is more efficient compared to the heating jet beyond four jet widths from the impingement point because it entrains cold surrounding air towards the wall which is desirable for cooling but undesirable for heating. The complex behavior of the cyclic groups of vortices cause the flow dynamics and heat transfer to be de-correlated intermittently.