Turbulent Shear Layer Research Articles

Development of a Dual-PIV system for high-speed flow applications

A new Dual-particle image velocimetry (Dual-PIV) system for application in supersonic flows was developed. The system was designed for shock wave/turbulent boundary layer interactions with separation. This type of flow places demanding requirements on the system, from the large range of characteristic frequencies O(100 Hz–100 kHz) to spatial and temporal resolutions necessary for the measurement of turbulent quantities (Dolling in AIAA J 39(8):1517–1531, 2001; Dupont et al. in J Fluid Mech 559:255–277, 2006; Smits and Dussauge in Turbulent shear layers in supersonic flow, 2nd edn. Springer, New York, 2006). While classic PIV systems using high-resolution CCD sensors allow high spatial resolution, these systems cannot provide the required temporal resolution. Existing high-speed PIV systems provide temporal and CMOS sensor resolutions, and even laser pulse energies, that are not adapted to our needs. The only obvious solution allowing sufficiently high spatial resolution, access to high frequencies, and a high laser pulse energy is a multi-frame system: a Dual-PIV system, consisting of two synchronized PIV systems observing the same field of view, will give access to temporal characteristics of the flow. The key technology of our system is frequency-based image separation: two lasers of different wavelengths illuminate the field of view. The cross-pollution with laser light from the respective other branches was quantified during system validation. The overall system noise was quantified, and the prevailing error of only 2 % reflects the good spatial and temporal alignment. The quality of the measurement system is demonstrated with some results on a subsonic jet flow including the spatio-temporal inter-correlation functions between the systems. First measurements in a turbulent flat-plate boundary layer at Mach 2 show the same satisfactory data quality and are also presented and discussed.

Entropy Filtered Density Function for Large Eddy Simulation of Turbulent Flows

A methodology termed entropy filtered density function (En-FDF) is developed to account for entropy transport in large eddy simulation of turbulent flows. The filtered entropy transport equation includes several unclosed terms which are the subgrid scale entropy flux and the filtered entropy generation resulting from irreversibilities in heat conduction, mass diffusion, chemical reaction and viscous dissipation. The En-FDF contains the complete statistical information about entropy, velocity, scalar and turbulent frequency fields and thus, provides closure for all the unclosed terms in the filtered transport equations. An exact transport equation is derived for the En-FDF which contains the effects of convection along with chemical reaction and its associated entropy generation in closed forms. The En-FDF transport is modeled by a set of stochastic differential equations. The numerical solution procedure is based on a hybrid finite difference/Monte Carlo method in which the large eddy simulation filtered transport equations are solved by the finite difference, and the stochastic differential equations are solved by a Lagrangian Monte Carlo procedure. This methodology is applied for large eddy simulation of a turbulent shear layer involving transport of passive scalars and predictions are compared against the data generated by direct numerical simulation. The En-FDF predictions show favorable agreement with the direct numerical simulation data.

Very near-nozzle shear-layer turbulence and jet noise

One of the principal challenges in the prediction and design of low-noise nozzles is accounting for the near-nozzle turbulent mixing layers at the high Reynolds numbers of engineering conditions. Even large-eddy simulation is a challenge because the locally largest scales are so small relative to the nozzle diameter. Model-scale experiments likewise typically have relatively thick near-nozzle shear layers, which potentially hampers their applicability to high-Reynolds-number design. To quantify the sensitivity of the far-field sound to nozzle turbulent-shear-layer conditions, a family of diameter $D$ nozzles is studied in which the exit turbulent boundary layer momentum thickness is varied from $0.0042D$ up to $0.021D$ for otherwise identical flow conditions. Measurements include particle image velocimetry (PIV) to within $0.04D$ of the exit plane and far-field acoustic spectra. The influence of the initial turbulent-shear-layer thickness is pronounced, though it is less significant than the well-known sensitivity of the far-field sound to laminar versus turbulent shear-layer exit conditions. For thicker shear layers, the nominally missing region, where the corresponding thinner shear layer would develop, leads to the noise difference. The nozzle-exit momentum thickness successfully scales the high-frequency radiated sound for nozzles of different sizes and exhaust conditions. Yet, despite this success, the detailed turbulence statistics show distinct signatures of the different nozzle boundary layers from the different nozzles. Still, the different nozzle shear-layer thicknesses and shapes have a similar downstream development, which is consistent with a linear stability analysis of the measured velocity profiles.

Dielectric barrier discharge plasma actuator to control turbulent flow downstream of a backward-facing step

The objective of these experiments was to determine the optimal forcing location and unsteady forcing actuation produced by a single dielectric barrier discharge plasma actuator for controlling the flow downstream of a backward-facing step. The investigated configuration is a 30-mm-height step mounted in a closed-loop wind tunnel. The flow velocity is fixed at 15 m/s, corresponding to a Reynolds number based on the step height equal to 3 × 104 (Re θ = 1400). The control authority of the plasma discharge is highlighted by the time-averaged modification of the reattachment point and by the effects obtained on the turbulent dynamics of the reattached shear layer. Several locations of the device actuator are considered, and a parametric study of the input signal is investigated for each location. This procedure leads to the definition of an optimal control configuration regarding the minimization of the reattachment length. When the actuator—that produces an electrohydrodynamic force resulting in an electric wind jet—is located upstream the separation point, it can manipulate the first stages of the formation of the turbulent free shear layer and consequently to modify the flow dynamics. Maximum effects have been observed when the high voltage is burst modulated at a frequency f BM = 125 Hz with a duty-cycle of 50 %. This forcing corresponds to a Strouhal number based on the momentum thickness equal to 0.011, a value corresponding to the convective instability or Kelvin–Helmholtz instability of the separated shear layer.

Simulating air entrainment and vortex dynamics in a hydraulic jump

The air entrainment characteristics of three separate Froude number hydraulic jumps are investigated numerically using an unsteady RANS, realizable k–ε turbulence model, with a Volume of Fluid treatment for the free surface. Mean velocity profiles, average void fraction, and Sauter mean diameter compare favorably with experimental data reported in literature. In all simulations, time-averaged void fraction profiles show good agreement with experimental values in the turbulent shear layer and an accurate representation of interfacial aeration at the free surface. Sauter mean diameter is well represented in the shear layer, and free surface entrainment results indicate bubble size remains relatively unchanged throughout the depth of the jump. Several different grid resolutions are tested in the simulations. Significant improvements in void fraction and bubble size comparison are seen when the diameter to grid size ratio of the largest bubbles in the shear layer surpasses eight. A three-dimensional simulation is carried out for one Froude number jump, showing an improvement in the prediction of entrained air and bubble size compared with two-dimensional results at a substantial increase in computation time. An analysis of three-dimensional vorticity shows a complex interaction between spanwise and streamwise vortical structures and entrained air bubbles. The jump is similar to a turbulent mixing layer, constrained by the free surface, with vortex pairing and subsequent fluctuations in free surface elevation. Downstream fluctuations of the toe are associated with a roll up of the primary spanwise vortex, fluctuations of the free surface, and counter-rotating streamwise vortex pairs. The action of these flow structures is likely responsible for the improvement in three-dimensional results.

Investigation of coherent structures generated by acoustic tube in turbulent flow separation control

An acoustic tube was designed in order to control the turbulent flow separation downstream of a backward-facing step. The Reynolds number based on the free-stream velocity and the step height was Reh = 2.0 × 104. As an active flow control device, the acoustic tube generated periodic pressure perturbations at a frequency of fa = 100 Hz, which was close to the most amplified frequency of the shedding instability of the turbulent shear layer. Spanwise vortices rolled up due to the perturbations. 2D–2C particle image velocimetry was used to measure separated shear layer and the reattachment area downstream of the BFS. The flow control results show that the acoustic tube can suppress recirculation regions behind the step and reduce the reattachment length by 43.7 %. The roll-up and pairing processes of the vortices lead to an increase in the total Reynolds shear stress. The coherent structures are extracted by proper orthogonal decomposition and represented by two pairs of modes, of which the coherence is analyzed by the corresponding coefficients. Both the primary and secondary series of vortices are reconstructed as traveling waves with the fundamental frequency fa and the overtone frequency 2fa, respectively.

Analysis of pressure perturbation sources on a generic space launcher after-body in supersonic flow using zonal turbulence modeling and dynamic mode decomposition

A sparsity promoting dynamic mode decomposition (DMD) combined with a classical data-based statistical analysis is applied to the turbulent wake of a generic axisymmetric configuration of an Ariane 5-like launcher at Ma∞ = 6.0 computed via a zonal Reynolds-averaged Navier-Stokes/large-eddy simulation (RANS/LES) method. The objective of this work is to gain a better understanding of the wake flow dynamics of the generic launcher by clarification and visualization of initially unknown pressure perturbation sources on its after-body in coherent flow patterns. The investigated wake topology is characterized by a subsonic cavity region around the cylindrical nozzle extension which is formed due to the displacement effect of the afterexpanding jet plume emanating from the rocket nozzle (Mae = 2.52, pe/p∞ = 100) and the shear layer shedding from the main body. The cavity region contains two toroidal counter-rotating large-scale vortices which extensively interact with the turbulent shear layer, jet plume, and rocket walls, leading to the shear layer instability process to be amplified. The induced velocity fluctuations in the wake and the ultimately resulting pressure perturbations on the after-body feature three global characteristic frequency ranges, depending on the streamwise position inside the cavity. The most dominant peaks are detected at SrD r3 = 0.85 ± 0.075 near the nozzle exit, while the lower frequency peaks, in the range of SrD r2 = 0.55 ± 0.05 and SrD r1 = 0.25 ± 0.05, are found to be dominant closer to the rocket’s base. A sparse promoting DMD algorithm is applied to the time-resolved velocity field to clarify the origin of the detected peaks. This analysis extracts three low-frequency spatial modes at SrD = 0.27, 0.56, and 0.85. From the three-dimensional shape of the DMD modes and the reconstructed modulation of the mean flow in time, it is deduced that the detected most dominant peaks of SrD r3 ≈ 0.85 are caused by the radial flapping motion of the shear layer, while the middle-frequency range of SrD r2 ≈ 0.55 is found to be associated with its swinging motion. The less intensive peaks of SrD r1 ≈ 0.25 pronounced on the base wall are caused by the low-frequency longitudinal pumping of the two toroidal large-scale vortices inside the cavity.

Radiated Sound from a Circular Cylinder in a Turbulent Shear Layer

The effect of turbulent approach flow on the radiated sound from a circular cylinder was studied experimentally. The approach flow turbulence was provided by a single stream shear layer produced by an open jet anechoic tunnel facility. An instrumented cylinder was used to measure steady and unsteady surface pressure. The sound radiated from the cylinder placed in both an irrotational approach flow and the highly turbulent approach flow of the shear-layer was measured and compared. The cylinders located within the shear layer produced a less tonal sound with a higher broadband amplitude when compared to that of the free-stream approach flow. Secondly, the radiated sound from cylinders of different diameters was investigated to assess the effect of the ratio of cylinder diameter to approach flow length scale. It was found that as this ratio decreased, the broadband sound levels decreased as well. A simple theoretical model was then used to provide a prediction of the radiated sound for the cylinder within the shear layer. The theoretical model used statistics of the velocity field of the approach shear layer and the radiated sound spectrum the cylinder placed in a free stream. It was found that this method provided a similar spectral shape to the measured radiated sound.

The Influence of Orifice Insertion for Low Noxious Emissions from Combustion System

This paper presents the effect of inserting swirler outlet orifice plate of different sizes at the exit plane of the radial air swirler in liquid fuel burner system. Tests were carried out with three different orifice plates with area ratios (orifice area to swirler exit area ratio) between 0.7 and 1.0 using 280 mm inside diameter combustor of 1000 mm length. Several tests were conducted using the commercial diesel as fuel. The fuel was injected at the back plate of the 45o vane angle swirler outlet using a central fuel injector with a single fuel nozzle pointing axially outwards. The aim of the insertion of orifice plates is to create the swirler pressure loss at the swirler outlet phase in order to maximise the swirler outlet shear layer turbulence to assist the fuel/air mixing. In the present work, the orifice plate with smaller area ratios exhibited very low NOX emissions for the whole operating equivalence ratios. The NOX reduction of more than 20 percent is achieved for orifice with 0.7 area ratio compared to 1.0 area ratio. Other emission such as carbon monoxide is increased with the decrease in the orifice area ratios. The results from this experiment show that good combustion is achieved by using smallest area ratios of orifice plate.

Large eddy simulation of highly turbulent under-expanded hydrogen and methane jets for gaseous-fuelled internal combustion engines

Burning hydrogen in conventional internal combustion (IC) engines is associated with zero carbon-based tailpipe exhaust emissions. In order to obtain high volumetric efficiency and eliminate abnormal combustion modes such as preignition and backfire, in-cylinder direct injection (DI) of hydrogen is considered preferable for a future generation of hydrogen IC engines. However, hydrogen's low density requires high injection pressures for fast hydrogen penetration and sufficient in-cylinder mixing. Such pressures lead to chocked flow conditions during the injection process which result in the formation of turbulent under-expanded hydrogen jets. In this context, fundamental understanding of the under-expansion process and turbulent mixing just after the nozzle exit is necessary for the successful design of an efficient hydrogen injection system and associated injection strategies. The current study used large eddy simulation (LES) to investigate the characteristics of hydrogen under-expanded jets with different nozzle pressure ratios (NPR), namely 8.5, 10, 30 and 70. A test case of methane injection with NPR = 8.5 was also simulated for direct comparison with the hydrogen jetting under the same NPR. The near-nozzle shock structure, the geometry of the Mach disk and reflected shock angle, as well as the turbulent shear layer were all captured in very good agreement with data available in the literature. Direct comparison between hydrogen and methane fuelling showed that the ratio of the specific heats had a noticeable effect on the near-nozzle shock structure and dimensions of the Mach disk. It was observed that with methane, mixing did not occur before the Mach disk, whereas with hydrogen high levels of momentum exchange and mixing appeared at the boundary of the intercepting shock. This was believed to be the effect of the high turbulence fluctuations at the nozzle exit of the hydrogen jet which triggered Gortler vortices. Generally, the primary mixing was observed to occur after the location of the Mach disk and particularly close to the jet boundaries where large-scale turbulence played a dominant role. It was also found that NPR had significant effect on the mixture's local fuel richness. Finally, it was noted that applying higher injection pressure did not essentially increase the penetration length of the hydrogen jets and that there could be an optimum NPR that would introduce more enhanced mixing whilst delivering sufficient fuel in less time. Such an optimum NPR could be in the region of 100 based on the geometry and observations of the current study.

Supersonic Flow over a Finite-Width Rectangular Cavity

Two-component and stereoscopic particle image velocimetry measurements have been acquired in the streamwise plane for supersonic flow over a rectangular cavity of variable width, peering over the sidewall lip to view the depths of the cavity. The data reveal the turbulent shear layer over the cavity and the recirculation region within it. The mean position of the recirculation region was found to be a function of the length-to-width ratio of the cavity, as was the turbulence intensity within both the shear layer and the recirculation region. Compressibility effects were observed in which turbulence levels dropped, and the shear layer thickness decreased as the Mach number was raised from 1.5 to 2.0 and 2.5. Supplemental measurements in the crossplane and the planform view suggest that zones of high turbulence were affixed to each sidewall centered on the cavity lip, with a strip of turbulence stretched out across the cavity shear layer for which the intensity was a function of the length-to-width ratio. These sidewall features are attributed to spillage, which is greatly reduced for the narrowest cavity. Such effects cannot be found in experiments lacking finite spanwise extent.

Impact of turbulence on the prediction of linear aeroacoustic interactions: Acoustic response of a turbulent shear layer

A powerful model to predict aeroacoustic interactions in the linear regime is the perturbed compressible linearized Navier–Stokes equations. Thus far, the frequently employed derivation suggests that the effect of turbulence and its associated Reynolds stresses is neglected and a quasi-laminar model is employed. In this paper, dynamic perturbation equations are derived incorporating the effect of turbulence and its interaction with perturbation quantities. This is done by employing a triple decomposition of the instantaneous variables. The procedure results in a closure problem for the Reynolds stresses for which a linear eddy-viscosity model is proposed. The resulting perturbation equations are applied to a grazing flow in a T-joint for which strong shear layer instabilities at certain frequencies are experimentally observed. Passive scattering properties of the grazing flow are validated against the experiments performed by Karlsson and Åbom and perturbation equations being quasi-laminar. We find that prediction models must include the effect of Reynolds stresses to capture the aeroacoustic interaction effects correctly. Neglecting its effect naturally results in the over prediction of vortex growth at the frequencies of shear layer instability and therewith in an over prediction of aeroacoustic interactions.

Laminar and turbulent nozzle-jet flows and their acoustic near-field

We investigate numerically the effects of nozzle-exit flow conditions on the jet-flow development and the near-field sound at a diameter-based Reynolds number of ReD = 18 100 and Mach number Ma = 0.9. Our computational setup features the inclusion of a cylindrical nozzle which allows to establish a physical nozzle-exit flow and therefore well-defined initial jet-flow conditions. Within the nozzle, the flow is modeled by a potential flow core and a laminar, transitional, or developing turbulent boundary layer. The goal is to document and to compare the effects of the different jet inflows on the jet flow development and the sound radiation. For laminar and transitional boundary layers, transition to turbulence in the jet shear layer is governed by the development of Kelvin-Helmholtz instabilities. With the turbulent nozzle boundary layer, the jet flow development is characterized by a rapid changeover to a turbulent free shear layer within about one nozzle diameter. Sound pressure levels are strongly enhanced for laminar and transitional exit conditions compared to the turbulent case. However, a frequency and frequency-wavenumber analysis of the near-field pressure indicates that the dominant sound radiation characteristics remain largely unaffected. By applying a recently developed scaling procedure, we obtain a close match of the scaled near-field sound spectra for all nozzle-exit turbulence levels and also a reasonable agreement with experimental far-field data.

A modified PANS model for computations of unsteady turbulence cavitating flows

A modification to the PANS (partially averaged Navier-Stokes) model is proposed to simulate unsteady cavitating flows. In the model, the parameter fk is modified to vary as a function of the ratios between the water density and the mixture density in the local flows. The objective of this study is to validate the modified model and further understand the interaction between turbulence and cavitation around a Clark-Y hydrofoil. The comparisons between the numerical and experiment results show that the modified model can be improved to predict the cavity evolution, vortex shedding frequency and the lift force fluctuating in time fairly well, as it can effectively modulate the eddy viscosity in the cavitating region and various levels of physical turbulent fluctuations are resolved. In addition, from the computational results, it is proved that cavitation phenomenon physically influences the turbulent level, especially by the vortex shedding behaviors. Also, the mean u-velocity profiles demonstrate that the attached cavity thickness can alter the local turbulent shear layer.

Application of an all-speed implicit non-dissipative DNS algorithm to hydrodynamic instabilities

Context: An all-speed, implicit, non-dissipative and discrete kinetic energy conserving DNS algorithm is applied to three hydrodynamic instabilities which show many aspects of flow modeling such as transition to turbulence and turbulent mixing at low Mach numbers.Objective: Our aim is to extend the application area of these kinds of methods and also to perform their further assessments and improvements.Method: For this purpose, an in-house, fully implicit, fully parallel DNS solver was developed based on the algorithm using PETSc. A relaxing procedure to pressure in time was also adopted and implemented into the base algorithm to improve its convergence properties. The solver was applied to the problems including wide range of spatial and temporal scales simultaneously such as hydrodynamic instabilities where laminar, transitional and turbulent regimes are found together with varying Mach number regimes.Results: Numerical results for transition to turbulence in Taylor–Green Vortex (TGV), velocity-induced mixing in Turbulent Shear Layer (TSL), and gravity-induced mixing in Rayleigh–Taylor Instability (RTI) were presented in detail and successfully compared to previous experimental and numerical studies.Conclusions: It is confirmed that the algorithm is able to produce complex physical mechanisms behind these flows correctly. This study also shows that all-speed algorithms can be considered as very promising and attractive options for challenging problems in fluid dynamics.

Understanding and Reduction of Cruise Jet Noise at Aircraft Level

Within the LINFaN research project, Airbus and Rolls-Royce have jointly investigated the acoustic impact of supersonic jet noise on the fuselage of an Airbus A340 equipped with Rolls-Royce Trent 500 engines in cruise conditions. The main results are presented in this paper. The influence of chevron fan nozzles designed to reduce cruise jet noise on the rear fuselage is investigated. The characterization of both the acoustic field and the aerodynamic flow is carried out. The acoustic data are obtained from a microphone array on the rear fuselage. After specific data de-noising, the acoustic spectra radiated on the fuselage by only the right inner engine are estimated. Beamforming acoustic maps are also computed to localize the jet noise sources. Besides, the supersonic jet flows are characterized by RANS CFD approach. For the baseline round nozzle, the acoustic results show the presence of two distinct broadband shock-associated noise contributions on the fuselage. The first pattern is observed in the far aft section of the fuselage for Strouhal numbers based on the jet mixing diameter and velocity between St = 4 and 6. The other pattern, around St = 1, radiates preferably forward. In addition, the high frequency source is located between 4 and 5 mixed jet diameters past the secondary nozzle exhaust plane, while the low frequency source is located farther downstream between 7 and 8 mixed jet diameters. Shock-associated noise is usually associated with the interaction between shock cells and turbulent shear-layers. We postulate that the high-frequency noise component results from the interaction between the shock-cells in the secondary flow and the inner shear-layer, while the low-frequency component is due to the interaction between shock cells and the outer shear-layer. This interpretation is consistent with two observations. The first observation is a strong modification of the measured high frequency noise when the engine is pushed to high power. At this regime shock cells are present in the primary flow and the inner shear layer interacts with two supersonic flows, hence modifying emitted noise. The second observation is the reduction of low-and high-frequency noise by the introduction of chevron fan nozzles. The flow field results confirm the strong impact of chevrons on the structure of the shock cells in the fan stream: they are consistent with the experimental observations of the characteristic shock noise frequencies. For the Trent 500 engine, appropriate immersive fan chevrons may bring noise reductions by as much as 6dB SPL integrated over a relevant Strouhal number range [0.7; 2]. However, the reduction level due to the chevrons varies with the engine operating conditions. A given chevron nozzle may be found more efficient at reducing noise levels at low engine operating regime than at high regime.

The relation between unstable shear layer thicknesses and turbulence lengthscales

The relation between unstable shear layer thicknesses and turbulence lengthscales

Simulation of Subsonic Turbulent Nozzle Jet Flow and Its Near-Field Sound

A direct numerical simulation framework is developed and validated for investigating a jet-flow configuration in which a short cylindrical nozzle and the acoustic near field are included in the simulation domain. The nozzle flow is modeled by a potential flow core and a developing turbulent wall boundary layer, which is numerically resolved. The setup allows to create well-controlled physical nozzle-exit flow conditions and to examine their impact on near-nozzle flow dynamics, jet-flow development, and the near-field sound. Turbulence at the nozzle inflow is generated by the synthetic-eddy method using flat-plate boundary-layer direct numerical simulation data and imposed softly in a sponge layer. The jet Mach number in the present investigation is , the diameter-based jet Reynolds number is , and the maximum axial rms fluctuations attain 13% at the nozzle exit. The accuracy of the numerical results is checked by varying grid resolution and computational domain size. The rapid flow development in the changeover region from wall turbulence to the turbulent free shear layer within about one nozzle diameter is documented in detail. Near-field sound pressure levels compare favorably with experimental reference data obtained at the much higher Reynolds number of 780,000. This agreement is essentially attributed to a compensation of the effects of Reynolds number and turbulence level on the noise for which an empirical scaling is derived from published data. A brief comparison is also made to the jet sound field arising from a laminar nozzle-exit boundary layer.

Free turbulent shear layer in a point vortex gas as a problem in nonequilibrium statistical mechanics

This paper attempts to unravel any relations that may exist between turbulent shear flows and statistical mechanics through a detailed numerical investigation in the simplest case where both can be well defined. The flow considered for the purpose is the two-dimensional (2D) temporal free shear layer with a velocity difference ΔU across it, statistically homogeneous in the streamwise direction (x) and evolving from a plane vortex sheet in the direction normal to it (y) in a periodic-in-x domain L×±∞. Extensive computer simulations of the flow are carried out through appropriate initial-value problems for a "vortex gas" comprising N point vortices of the same strength (γ=LΔU/N) and sign. Such a vortex gas is known to provide weak solutions of the Euler equation. More than ten different initial-condition classes are investigated using simulations involving up to 32000 vortices, with ensemble averages evaluated over up to 103 realizations and integration over 104L/ΔU. The temporal evolution of such a system is found to exhibit three distinct regimes. In Regime I the evolution is strongly influenced by the initial condition, sometimes lasting a significant fraction of L/ΔU. Regime III is a long-time domain-dependent evolution towards a statistically stationary state, via "violent" and "slow" relaxations [ P.-H. Chavanis Physica A 391 3657 (2012)], over flow time scales of order 102 and 104L/ΔU, respectively (for N=400). The final state involves a single structure that stochastically samples the domain, possibly constituting a "relative equilibrium." The vortex distribution within the structure follows a nonisotropic truncated form of the Lundgren-Pointin (L-P) equilibrium distribution (with negatively high temperatures; L-P parameter λ close to -1). The central finding is that, in the intermediate Regime II, the spreading rate of the layer is universal over the wide range of cases considered here. The value (in terms of momentum thickness) is 0.0166±0.0002 times ΔU. Regime II, extensively studied in the turbulent shear flow literature as a self-similar "equilibrium" state, is, however, a part of the rapid nonequilibrium evolution of the vortex-gas system, which we term "explosive" as it lasts less than one L/ΔU. Regime II also exhibits significant values of N-independent two-vortex correlations, indicating that current kinetic theories that neglect correlations or consider them as O(1/N) cannot describe this regime. The evolution of the layer thickness in present simulations in Regimes I and II agree with the experimental observations of spatially evolving (3D Navier-Stokes) shear layers. Further, the vorticity-stream-function relations in Regime III are close to those computed in 2D Navier-Stokes temporal shear layers [ J. Sommeria, C. Staquet and R. Robert J. Fluid Mech. 233 661 (1991)]. These findings suggest the dominance of what may be called the Kelvin-Biot-Savart mechanism in determining the growth of the free shear layer through large-scale momentum and vorticity dispersal.

Numerical study of supersonic turbulent free shear layer

Numerical study of two-dimensional supersonic turbulent free shear layer is performed. The system of Fa-vre-Averaged Naveir-Stokes equations for multispecies flow is solved using ENO scheme of third-order in accuracy. The k-ε two-equation turbulence models with compressibility correction are applied to calculate the eddy viscosity coefficient. In order to produce the roll-up and pairing of vortex rings, an unsteady boundary condition is applied at the inlet plane. At the outflow, the non-reflecting boundary condition is taken. The obtained results are compared with available experimental data.