Free Shear Layer Research Articles

The effect of vortex merging and non-merging on the transfer of modal turbulent kinetic energy content

A defining feature of the turbulent free shear layer is that its growth is hindered by compressibility effects, thus limiting its potential to sufficiently mix the injected fuel and surrounding airstream at the supersonic Mach numbers intrinsic to the combustor of air-breathing hypersonic vehicles. The introduction of streamwise vorticity is often proposed in an attempt to counteract these undesired effects. This fact makes the strategy of introducing multiple streamwise vortices and imposing upon them certain modes of mutual interaction in order to potentially enhance mixing an intriguing concept. However, many underlying fundamental characteristics of the flowfields in the presence such interactions are not yet well understood; therefore, the fundamental physics of these flowfields should be independently investigated before the explicit mixing performance is characterized. In this work, experimental measurements are taken with the stereoscopic particle image velocimetry technique on two specifically targeted modes of vortex interaction—the merging and non-merging of two corotating vortices. The fluctuating velocity fields are analyzed utilizing the proper orthogonal decomposition (POD) in order to identify the content, organization, and distribution of the modal turbulent kinetic energy content of the fluctuating velocity eigenmodes. The effects of the two modes of vortex interaction are revealed by the POD analysis which shows distinct differences in the modal features of the two cases. When comparing the low-order eigenmodes of the two cases, the size of the structures contained within the first ten modes is seen to increase as the flow progresses downstream for the merging case, whereas the opposite is true for the non-merging case. Additionally, the relative modal energy contribution of the first ten eigenmodes increases as the vortices evolve downstream for the merging case, whereas in the non-merging case the relative modal energy contribution decreases. The POD results show that the vortex merging process reorients and redistributes the relative turbulent kinetic energy content toward the larger-scale structures within the low-order POD eigenmodes. This result suggests that by specifically designing the vortex generation system to impose preselected modes of vortex interaction upon the flow it is possible to exert some form of control over the downstream evolution and distribution of the global and modal turbulent kinetic energy content.

Jet noise computation based on enhanced DES formulations accelerating the RANS-to-LES transition in free shear layers

The paper presents jet noise computations performed using the original and some recently proposed modified formulations of detached-eddy simulation, based on alternative definitions of the subgrid length-scale and/or a modified version of the subgrid Spalart-Allmaras model, which involves the Wall-Adapting Local Eddy-viscosity model. The modifications are aimed at the elimination or, at least, a significant weakening of a known flaw of detached-eddy simulation, namely, the severe delay of the Kelvin–Helmholtz instability and transition from fully modeled to mostly resolved turbulence in the free and separated shear layers. This flaw makes the original detached-eddy simulation formulation, in fact, non-applicable to the prediction of the noise of high Reynolds number jet flows when typical grids are used, and has led to the use of Implicit Large-Eddy Simulation instead. Based on examples of application of these modifications to such flows, already available in the literature, they were found capable of resolving the issue and providing quite accurate predictions of the aerodynamic characteristics and turbulent statistics of the high-Re jets. The study performed in the present work allows us to draw a similar conclusion regarding the accuracy of the enhanced detached-eddy simulation formulations in terms of jet-noise prediction. The new formulation gives noise results very close to those of ILES except at the highest frequencies, while being more general and less sensitive to grid resolution. In addition, it removes a (1–3) dB underestimation of the noise spectral maximums for the peak radiation direction, which is typical of ILES on fine grids.

Numerical simulation of turbulent flow between shrouded contra-rotating disks

The turbulent flow between shrouded contra-rotating disks was numerically studied with a two-layer turbulence model and a modified Launder–Sharma low-Reynolds number k- ε model. The dissipation rate decrease caused by solid body rotation was considered in the second model. The comparisons of the effectiveness between these two turbulence models for capturing the critical radius of flow structure transition and reproducing the flow velocity measurements data were presented. For the flow between shrouded disks rotating at the same speed but in opposite senses, that is, the angular velocity ratio of the two disks equals to −1, the Stewartson-type flow structure is found in the cavity. For the flow with one disk rotating more slowly than the other, Stewartson-type flow coexists with Batchelor-type flow, that is, Batchelor-type flow occurs radially outward of the stagnation point where two opposing boundary layer flows meet, and Stewartson-type flow occurs radially inward. The stagnation points near the slower disk move radially outward as the angular velocity ratio decreases toward −1. Theory of rotating fluids with the presence of centrifugal and Coriolis forces stemming from the disk rotation is employed to manifest the flow structure transition mechanisms as the rotation ratio of the disks is varied. The source of the earlier transition to turbulent flow in counter-rotating disk cavity compared with rotor-stator disk cavity is also explained through the research of instability of the flowing free shear layer formed by the counter secondary circulations. With the aid of the numerical results obtained from the two turbulence models, it is found that a more turbulent flow in the core can destroy the Batchelor-type flow and creates a larger Stewartson-type flow region.

Hybrid RANS/LES of turbulent flow in a rotating rib-roughened channel

In this paper, we investigate the effect of the Coriolis force on the flow field in a rib-roughened channel subjected to either clockwise or counter-clockwise system rotation using hybrid RANS/LES based on wall modelling. A simplified dynamic forcing scheme incorporating backscatter is proposed for the hybrid simulation approach. The flow is characterized by a Reynolds number of Re = 1.5 × 104 and a rotation number Ro ranging from −0.6 to 0.6. The mean flow speed and turbulence level near the roughened wall are enhanced under counter-clockwise rotation and suppressed under clockwise rotation. The Coriolis force significantly influences the stability of the wall shear layer and the free shear layers generated by the ribs. Consequently, it is interesting to observe that the classification of the roughness type relies not only on the pitch ratio, but also on the rotation number in the context of rotating rib-roughened flows. In order to validate the present hybrid approach, the first- and second-order statistical moments of the velocity field obtained from the simulations are thoroughly compared with the available laboratory measurement data.

Low-Re flow past an isolated cylinder with rounded corners

Direct numerical simulation is performed for flow past an isolated cylinder at Re=1,000. The corners of the cylinder are rounded at different radii, with the non-dimensional radius of curvature varying from R+=R/D=0.000 (square cylinder with sharp corners) to 0.500 (circular cylinder), in which R is the corner radius and D is the cylinder diameter. Our objective is to investigate the effect of the rounded corners on the development of the separated and transitional flow past the cylinder in terms of time-averaged statistics, time-dependent behavior, turbulent statistics and three-dimensional flow patterns. Numerical results reveal that the rounding of the corners significantly reduces the time-averaged drag and the force fluctuations. The wake flow downstream of the square cylinder recovers the slowest and has the largest wake width. However, the statistical quantities do not monotonically vary with the corner radius, but exhibit drastic variations between the cases of square cylinder and partially rounded cylinders, and between the latter and the circular cylinder. The free shear layer separated from the R+=0.125 cylinder is the most stable in which the first roll up of the wake vortex occurs furthest from the cylinder and results in the largest recirculation bubble, whose size reduces as R+ further increases. The coherent and incoherent Reynolds stresses are most pronounced in the near-wake close to the reattachment point, while also being noticeable in the shear layer for the square and R+=0.125 cylinders. The wake vortices translate in the streamwise direction with a convection velocity that is almost constant at approximately 80% of the incoming flow velocity. These vortices exhibit nearly the same trajectory for the rounded cylinders and are furthest away from the wake centerline for the square one. The flow past the square cylinder is strongly three-dimensional as indicated by the significant primary and secondary enstrophy, while it is dominated by the primary enstrophy (ωz2) for the rounded cylinders.

On the development of a turbulent jet subjected to aerodynamic excitation in the helical mode

Aerodynamic excitation has been used to introduce energy into the free shear layer at the outer edges of an axisymmetric free jet by injecting a pulsating secondary jet through a thin annular nozzle that surrounds and is concentric with the primary nozzle. In the present study, it has been found that the rate of mixing can be increased if the pulsations are applied in a sequential fashion around the circumference of the jet, so as to create helical vortices in the region close to the nozzle exit plane. Flow visualisation confirms the helical nature of the vortices and shows how these vortices are convected downstream with the main flow, strongly influencing the development of the primary jet. Two-component laser Doppler anemometry (LDA) was used to make measurements of the flow distributions in the developing jet for a number of flow conditions. These results have been analysed to extract various measures of the turbulent mixing, including the time averaged velocity distributions, and the higher order moments and spectral distributions of the turbulent velocity fluctuations. The present data confirm that introducing the excitation in a helical mode leads to an increased rate of entrainment and more rapid mixing, when compared with the toroidal excitation used in previous studies. These changes significantly increase the rate of development of the jet in the axial direction.

Stratified Turbulence and Mixing Efficiency in a Salt Wedge Estuary

AbstractHigh-resolution observations of velocity, salinity, and turbulence quantities were collected in a salt wedge estuary to quantify the efficiency of stratified mixing in a high-energy environment. During the ebb tide, a midwater column layer of strong shear and stratification developed, exhibiting near-critical gradient Richardson numbers and turbulent kinetic energy (TKE) dissipation rates greater than 10−4 m2 s−3, based on inertial subrange spectra. Collocated estimates of scalar variance dissipation from microconductivity sensors were used to estimate buoyancy flux and the flux Richardson number Rif. The majority of the samples were outside the boundary layer, based on the ratio of Ozmidov and boundary length scales, and had a mean Rif = 0.23 ± 0.01 (dissipation flux coefficient Γ = 0.30 ± 0.02) and a median gradient Richardson number Rig = 0.25. The boundary-influenced subset of the data had decreased efficiency, with Rif = 0.17 ± 0.02 (Γ = 0.20 ± 0.03) and median Rig = 0.16. The relationship between Rif and Rig was consistent with a turbulent Prandtl number of 1. Acoustic backscatter imagery revealed coherent braids in the mixing layer during the early ebb and a transition to more homogeneous turbulence in the midebb. A temporal trend in efficiency was also visible, with higher efficiency in the early ebb and lower efficiency in the late ebb when the bottom boundary layer had greater influence on the flow. These findings show that mixing efficiency of turbulence in a continuously forced, energetic, free shear layer can be significantly greater than the broadly cited upper bound from Osborn of 0.15–0.17.

Scaling and statistics of large-defect adverse pressure gradient turbulent boundary layers

The purpose of this article is to test similarity laws and scaling ideas, as well as characterize turbulence behaviour of large-defect adverse-pressure gradient turbulent boundary layers using six experimental and numerical databases including a new direct numerical simulation of a strongly decelerated non-equilibrium turbulent boundary layer. In the latter flow, at a moderate Reynolds number, the mean velocity profiles depart from the classical law of the wall throughout the inner region including in the viscous sublayer and they do not follow the log law. However, the agreement is excellent with the extended law of the wall that accounts for the pressure gradient for the viscous sublayer. The Reynolds stress components are not self-similar in the viscous sublayer when the velocity defect is important, but they scale reasonably well with the pressure-viscous scales.Detailed comparisons of the six different flows are made in the outer region. In order to do such comparisons, an outer region velocity scale analogous to the commonly defined free shear layer velocity scales is introduced. It is found that the investigated one-point velocity statistics in the upper half of large-defect boundary layers resemble those of a mixing layer: mean velocity defect, Reynolds stresses, turbulent kinetic energy budgets, uv correlation factor and structure parameter −〈uv〉/2k. The dominant peaks of turbulence production and Reynolds stresses are located roughly in the middle of the boundary layer. The profiles of the uv correlation factor reveal that u and v become less correlated throughout the boundary layer as the mean velocity defect increases, especially near the wall. The structure parameter is low in the large-defect disequilibrium boundary layers, similar to large-defect equilibrium flows and mixing layers and decreases as the mean velocity defect increases. All large-velocity-defect boundary layers analysed are found to be less efficient in extracting turbulent energy from the mean flow than zero-pressure-gradient turbulent boundary layers, even throughout the outer region.

Experimental characterization of turbulent subsonic transitional–open cavity flow

Turbulent subsonic “transitional–open” cavity flow was investigated by wind-tunnel tests. The investigated cavity configuration had a length-to-depth ratio of 6.25 and a width-to-depth ratio of 2. The cavity was exposed to a free-stream Mach number of 0.40 and a Reynolds number (based on cavity depth) of $$1.6\times 10^6$$ , with a turbulent incoming boundary layer. Measurements of velocity and wall pressures were taken simultaneously, which enabled the analysis of velocity–pressure cross-correlations. Special attention is paid to the shear layer that develops over the cavity and an emphasis is placed on the analysis of its characteristics and its stability. Application of linear hydrodynamic stability theory, together with examining velocity–pressure cross correlations, revealed that the behavior of the cavity shear layer is analogous to a free shear layer, approximately up to mid-length of the cavity, where further downstream nonlinear interactions occur.

Numerical simulation and global linear stability analysis of low-Re flow past a heated circular cylinder

We perform two-dimensional unsteady Navier–Stokes simulation and global linear stability analysis of flow past a heated circular cylinder to investigate the effect of aided buoyancy on the stabilization of the flow. The Reynolds number of the incoming flow is fixed at 100, and the Richardson number characterizing the buoyancy is varied from 0.00 (buoyancy-free case) to 0.10 at which the flow is still unsteady. We investigate the effect of aided buoyancy in stabilizing the wake flow, identify the temporal and spatial characteristics of the growth of the perturbation, and quantify the contributions from various terms comprising the perturbed kinetic energy budget. Numerical results reveal that the increasing Ri decreases the fluctuation magnitude of the characteristic quantities monotonically, and the momentum deficit in the wake flow decays rapidly so that the flow velocity recovers to that of the free-stream; the strain on the wake flow is reduced in the region where the perturbation is the most greatly amplified. Global stability analysis shows that the temporal growth rate of the perturbation decreases monotonically with Ri, reflecting the stabilization of the flow due to aided buoyancy. The perturbation grows most significantly in the free shear layer separated from the cylinder. As Ri increases, the location of maximum perturbation growth moves closer to the cylinder and the perturbation decays more rapidly in the far wake. The introduction of the aided buoyancy alters the base flow, and destabilizes the near wake shear layer mainly through the strain-induced transfer term and the pressure term of the perturbed kinetic energy, whereas the flow is stabilized in the far wake as the strain is alleviated.

Design and analysis of a novel muffler for wide-band transmission loss, low back pressure and reduced flow-induced noise

With the advancements in quiet engine technology, reduction of the fan noise sources, and use of higher mean flow speeds, the aerodynamic noise generation due to unsteady and turbulent mean flow in the ducts of automotive exhaust muffler may become a significant source of exhaust noise, thereby limiting the net insertion loss of the muffler. Three-pass double-reversal muffler is often used in automotive exhaust systems. This muffler is characterized by a fairly wide-band transmission loss (TL) curve as well as relatively low back pressure. However in the flow-reversal end chambers, it produces a lot of aerodynamic noise due to impingement of jets on the end plates, generation of free shear layer and vortex shedding. This paper deals with the design and analysis of the muffler with a novel feature (tubular bridges in the end-chambers) specially configured to minimize the free shear layer in the end chambers of the three-pass double-reversal muffler as well as to provide adequate acoustic transmission loss and to further reduce the back pressure of the muffler. The TL curve predicted by means of the 1-D integrated transfer matrix (ITM) approach is validated against the 3-D FEM and compared with that of the base muffler (without tubular bridges). Back pressure of the configuration with tubular bridges, estimated by means of the lumped flow-resistance network, is shown to be considerably less than that of the base muffler. (C) 2016 Institute of Noise Control Engineering.

Flow structure and resistance over subaquaeous high‐ and low‐angle dunes

AbstractA prominent control on the flow over subaqueous dunes is the slope of the downstream leeside. While previous work has focused on steep (~30°), asymmetric dunes with permanent flow separation, little is known about dunes with lower lee slope angles for which flow separation is absent or intermittent. Here we present a laboratory investigation where we systematically varied the dune lee slope, holding other geometric parameters and flow hydraulics constant, to explore effects on the turbulent flow field and flow resistance. Three sets of fixed dunes (lee slopes of 10°, 20°, and 30°) were separately installed in a 15 m long and 1 m wide flume and subjected to 0.20 m deep flow. Measurements consisted of high‐frequency, vertical profiles collected with a Laser Doppler Velocimeter. We show that the temporal and spatial occurrence of flow separation decreases with dune lee slope. Velocity gradients in the dune leeside depict a free shear layer downstream of the 30° dunes and a weaker shear layer closer to the bed for the 20° and 10° dunes. The decrease in velocity gradients leads to lower magnitude of turbulence production for gentle lee slopes. Aperiodic, strong ejection events dominate the shear layer but decrease in strength and frequency for low‐angle dunes. Flow resistance of dunes decreases with lee slope; the transition being nonlinear. Over the 10°, 20°, and 30° dunes, shear stress is 8%, 33%, and 90% greater than a flat bed, respectively. Our results demonstrate that dune lee slope plays an important but often ignored role in flow resistance.

The effect of upstream edge geometry on the acoustic resonance excitation in shallow rectangular cavities

The flow-excited acoustic resonance phenomenon is created when the flow instability oscillations are coupled with one of the acoustic modes of a confined duct, which in turn generates acute noise problems and/or excessive vibrations. In this study, the effect of the upstream edge geometry on attenuating these undesirable effects is investigated experimentally for flows over shallow rectangular cavities with two different aspect ratios of L/D = 1 and 1.67, where L is the cavity length and D is the cavity depth, for Mach number up to 0.45. The acoustic resonance modes of the cavity are self-excited due to the development of free shear layers over the cavity mouth. Twenty four different upstream cavity edges are investigated in this study, including round edges, chamfered edges, vortex generators, and spoilers with different sizes and configurations. The results for each upstream cavity edge are compared with the base case where sharp edge is used. Most of the spoiler edges are found to be effective in suppressing the pressure amplitude of the excited acoustic resonance. Hot-wire measurements that were taken along the lateral direction downstream of the spoilers reveal the existence of secondary vortices generated by the spoilers, orthogonal to the cavity shear layer, which results in suppressing the resonance. The performance of each spoiler depends on its specific geometry (i.e. thickness, height, and angle) and the size and strength of the orthogonal vortices that can be generated. A summary of the results is presented in this paper.

Complex terrain effects on wake characteristics of a parked wind turbine

In order to extend lifetime and enhance energy production of wind turbines in complex terrain it is important to learn about their wake characteristics. Hence, wind-tunnel experiments are carried out to analyze the wind-turbine wake downwind of a mountain. The wind-tunnel simulation of the neutrally stratified atmospheric boundary layer (ABL) developing above a flat terrain is first generated using the well established Counihan approach. Once a well developed ABL simulation is achieved for a flat terrain, three various mountain models are separately exposed to that ABL simulation, as well as the flat terrain as a reference case. Wake characteristics of a single wind-turbine model in the wake of those four various terrain models are then studied. The ratios between the height of different mountains to the wind-turbine hub height are 0, 0.417, 0.833, 0.833 (0.417) for the flat terrain, small mountain, large mountain, mountain with a bay, respectively. For the mountain with a bay, there are two different ratios between the mountain height and the wind-turbine hub height; 0.833 at the lateral edges of the mountain, 0.417 in the lateral center of the mountain. All three mountain models are 600mm long in the main wind direction and 1000mm wide laterally to the main wind direction. Small mountain model is 100mm uniformly high, large mountain model is 200mm uniformly high. The mountain with a bay model is 200mm high with a normal slope to 100mm height in the lateral center of the mountain model, whereas this cavity is 200mm wide in the lateral direction. The calculated ABL simulation length scale factor is 1:300, and it is applied on mountain models and the wind-turbine model as well. The wind-turbine model is designed to correspond to commonly used prototype wind turbines. The experiments are carried out for the wind-turbine model in parking position to analyze trends expected in a strong wind situation, when there is no rotation of the rotor blades. Wake characteristics analyzed with respect to the mean wind velocity, turbulence intensity and velocity power spectra indicate several important findings. In particular, the observed flow retardation is more exhibited near the ground surface and the mountains. The mountain-induced flow disturbance enhances with increasing the size and complexity of the mountains. Turbulence intensity in the wake of the mountain and wind turbine is considerably larger than in the atmospheric boundary layer. Velocity power spectra are strongly influenced by the terrain complexity, whereas the effects of the mountain and surface roughness are mostly constrained up to the double mountain height. There is a strong energy content at frequencies corresponding to a free shear layer separating from the mountain ridge. Dominant turbulence structures are displaced vertically, as the wake is transported with the flow in the main wind direction.

鼻腔内遷移流れの可視化計測

The nasal cavities are characterized by extremely complex three-dimensional structure. Modeling of airflow in the nasal cavities is important for evaluating nasal function such as olfaction, filtration, heat transfer and humidification. The aim of this study is to reveal experimentally the transitional nature in image-based realistic model human nasal airways by flow visualization. The inspiratory airflow pattern was visualized using the dye injection method and particle image velocimetry (PIV). As a result, significant differences were observed between flow in the right and left cavities, indicating strong dependence on the local geometry. Flow instability was first evident via oscillation of dye filament position in the upper and lower portion of the left cavity, whereas the flow was stable in the middle portion of the left cavity and in almost the entire portion of the right cavity. The high turbulent kinetic energy (TKE) values were observed in the free shear layer at the edge of the jet.

鼻腔内遷移流れに及ぼす流入速度分布の影響

The nose plays an important role by filtering, warming, and humidifying inspired air. Thus, modeling of airflow in the nasal cavities is important for evaluating nasal functions. Recently, experimental studies showed that airflow in nasal cavity has unsteadiness such as laminar to turbulent transitional flow3,4. Because of advances in computing performance, direct numerical simulation (DNS) was performed to predict transitional airflow in the nasal cavity without turbulence models5. Several studies prescribed simplified flat inflow velocity profile, whereas Taylor et al. 6 showed that the use of truncated inflow in models of nasal inspiration affects the flow within the nasal cavity. The present study investigates the effect of inflow velocity profile on transitional flow during steady nasal inspiration with DNS. As a result, a breakdown of a free shear layer is confirmed behind the nasal valve in the natural velocity profile, whereas, in the flat velocity profile, shear layer is stable. The inflow boundary profile is found to affect the stability of a free shear layer behind the nasal valve. Therefore it is important to consider actual inflow velocity profile surrounding the external face to predict transitional flow in the nasal cavity.

Definition of Turbulent Boundary-Layer with Entropy Concept

The relationship between the entropy increment and the viscosity dissipation in turbulent boundary-layer is systematically investigated. Through theoretical analysis and direct numerical simulation (DNS), an entropy function f s is proposed to distinguish the turbulent boundary-layer from the external flow. This approach is proved to be reliable after comparing its performance in the following complex flows, namely, low-speed airfoil flows with different wall temperature, supersonic cavity-ramp flow dominated by the combination of free-shear layer, larger recirculation and shocks, and the hypersonic flow past an aeroplane configuration. Moreover, f s is deduced from the point of energy, independent of any particular turbulent quantities. That is, this entropy concept could be utilized by other engineering applications related with turbulent boundary-layer, such as turbulence modelling transition prediction and engineering thermal protection.

Nonlinear dynamics of large-scale coherent structures in turbulent free shear layers

Fully developed turbulent free shear layers exhibit a high degree of order, characterized by large-scale coherent structures in the form of spanwise vortex rollers. Extensive experimental investigations show that such organized motions bear remarkable resemblance to instability waves, and their main characteristics, including the length scales, propagation speeds and transverse structures, are reasonably well predicted by linear stability analysis of the mean flow. In this paper, we present a mathematical theory to describe the nonlinear dynamics of coherent structures. The formulation is based on the triple decomposition of the instantaneous flow into a mean field, coherent fluctuations and small-scale turbulence but with the mean-flow distortion induced by nonlinear interactions of coherent fluctuations being treated as part of the organized motion. The system is closed by employing a gradient type of model for the time- and phase-averaged Reynolds stresses of fine-scale turbulence. In the high-Reynolds-number limit, the nonlinear non-equilibrium critical-layer theory for laminar-flow instabilities is adapted to turbulent shear layers by accounting for (1) the enhanced non-parallelism associated with fast spreading of the mean flow, and (2) the influence of small-scale turbulence on coherent structures. The combination of these factors with nonlinearity leads to an interesting evolution system, consisting of coupled amplitude and vorticity equations, in which non-parallelism contributes the so-called translating critical-layer effect. Numerical solutions of the evolution system capture vortex roll-up, which is the hallmark of a turbulent mixing layer, and the predicted amplitude development mimics the qualitative feature of oscillatory saturation that has been observed in a number of experiments. A fair degree of quantitative agreement is obtained with one set of experimental data.

Measurements in the annular shear layer of high subsonic and under-expanded round jets

An experimental study has been undertaken to document compressibility effects in the annular shear layers of axisymmetric jets. Comparison is made of the measured flow development with the well-documented influence of compressibility in planar mixing layers. High Reynolds number (~106) and high Mach number jets issuing from a convergent nozzle at nozzle pressure ratios (NPRs) from 1.28 to 3.0 were measured using laser Doppler anemometry instrumentation. Detailed radial profile data are reported, particularly within the potential core region, for mean velocity, turbulence rms, and turbulence shear stress. For supercritical NPRs the presence of the pressure waves in the inviscid shock cell region as the jet expanded back to ambient pressure was found to exert a noticeable effect on shear layer location, causing this to shift radially outwards at high supercritical NPR conditions. After a boundary layer to free shear layer transition zone, the turbulence development displayed a short region of similarity before adjustment to near-field merged jet behaviour. Peak turbulence rms reduction due to compressibility was similar to that observed in planar layers with radial rms suppression much stronger than axial. Comparison of the compressibility-modified annular shear layer growth rate with planar shear layer data on the basis of the convective Mach number (M C) showed notable differences; in the annular shear layer, compressibility effects began at lower M C and displayed a stronger reduction in growth. For high Mach number aerospace propulsion applications involving round jets, the current measurements represent a new data set for the calibration/validation of compressibility-affected turbulence models.

Numerical Study of the Particle Dispersion on a Supersonic Shear Layer

The numerical study of the two-dimensional supersonic hydrogen-air mixing in the free shear layer is performed. The system of the Favre-Averaged Navier-Stokes equations for multispecies flow is solved using the ENO scheme of the third order accuracy. The k-ε two-equation turbulence models with compressibility correction are applied to calculate the eddy viscosity coefficient. The dispersion of the particles is studied by following their trajectories in the shear layer by Euler method. In order to produce the roll-up and pairing vortex rings, an unsteady boundary condition is applied at the inlet plane. At the outflow, the non-reflecting boundary condition is taken. The influence of different Mach numbers on the formation of vorticity structures and shear layer growth rate are studied. The obtained results are compared with the available experimental data and the numerical results of other authors. The numerical simulation of the particle dispersion in the shear layer with large scale vortical structure is conducted.