Shear Layer Dynamics Research Articles

SHEAR LAYER AND WAVE STRUCTURE OVER PARTIALLY SPANNING CAVITIES

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

Comparison of heat transfer distributions on a flat plate impinged by under-expanded jets from a convergent nozzle and a circular orifice

Experiments are carried out for a circular orifice and a nozzle for the same contraction ratio to explore the heat transfer characteristics. The pressure ratios covered in this study are 2.36, 3.04, 3.72, 4.4 and 5.08 for jet to plate distances (z/d) of 2, 4, 6 and 8. The presence of vena contracta and absence of the stagnation bubble in the orifice flow are confirmed from the surface pressure distributions. It is found that higher Nusselt number for the orifice than the nozzle are due to different shock structures and shear layer dynamics. Peak Nusselt number is found as high as 84 % than that for the nozzle. In the wall jet region, the heat transfer rates for the orifice and nozzle are almost of the same order, thus producing steeper temperature gradients under similar operating conditions. The average heat transfer rates are almost 25 % higher for the orifice than that of the nozzle. The recovery factors are in general higher in case of orifice than the nozzle. However, this has not resulted in decreasing the heat transfer rates due to shear layer dynamics.

Noise generation by a cylindrical cavity in subsonic flow

Following a previous experimental study of the noise generated by cylindrical cavities placed in subsonic flows, this work investigates mechanisms involved in the noise generation by a cylindrical cavity placed in a turbulent boundary layer, via numerical simulation. The cavity has a radius of r =5 cm and a depth of 10 cm. Flows are computed at Mach numbers of 0.2, 0.26 and 0.32, and the numerical boundary layer, of thickness 17 mm, is perturbed upstream of the cavity. Simulations are performed by solving the unsteady compressible Navier-Stokes equations using low-dispersion and low-dissipation finite-difference schemes. The LES approach is based on the explicit application of a selective filtering to the flow variables to take into account the dissipative effects of the subgrid scales. Numerical results are compared to the available experimental data presented in previous work, including mean flow aspects, flow statistics and acoustics. The numerical results are then examined in more detail in particular with regard to the origin of the well-defined tones observed in the acoustic far field. A simple feedback model coupling shear layer dynamics with depth mode acoustic resonance is shown to yield good frequency predictions.

Low-dimensional model of spatial shear layers

The aim of this work is to develop nonlinear low-dimensional models to describe vortex dynamics in spatially developing shear layers with periodicity in time. By allowing a free variable g(x) to dynamically describe downstream thickness spreading, we are able to obtain basis functions in a scaled reference frame and construct effective models with only a few modes in the new space. To apply this modified version of proper orthogonal decomposition (POD)/Galerkin projection, we first scale the flow along y dynamically to match a template function as it is developing downstream. In the scaled space, the first POD mode can capture more than 80% energy for each frequency. However, to construct a Galerkin model, the second POD mode plays a critical role and needs to be included. Finally, a reconstruction equation for the scaling variable g is derived to relate the scaled space to physical space, where downstream spreading of shear thickness occurs. Using only two POD modes at each frequency, our models capture the basic dynamics of shear layers, such as vortex roll-up (from a one-frequency model) and vortex-merging (from a two-frequency model). When arbitrary excitation at different harmonics is added to the model, we can clearly observe the promoting or delaying/eliminating vortex merging events as a result of mode competition, which is commonly demonstrated in experiments and numerical simulations of shear layers.

Parametric study on self-sustained oscillation characteristics of cavity flameholders in supersonic flows

Large eddy simulations were performed to study cavity self-sustained oscillation characteristics in supersonic flows. Calculations use the hybrid Reynolds-averaged Navier–Stokes (RANS)/large-eddy simulation (LES) method to predict unsteady-state flowfields. The calculations consider the effects of various flow or geometry parameters, including the inflow boundary layer thickness, Reynolds number, freestream Mach number, three dimensionality, and cavity configurations (length-to-depth ratio and cavity aft wall angle included). The results show that thick inflow boundary layer changes the oscillation mechanism in high-Mach-number flows while affects little at low Mach number. Reynolds number has little influence on the oscillation mechanism and the resonance frequencies. The simulated results suggest that the coupling between the shear-layer dynamics and the cavity acoustics is greatly reduced at high Mach numbers. The physical mechanisms in cavity oscillations shift from the vortex-acoustics resonance mechanism (Rossiter's model) to closed-box acoustics mechanism with the Mach number increase. Calculations on three-dimensional (3D) cavity configurations have further verified the validity of the 2D calculation results. Increasing cavity length-to-depth ratio makes the resonance frequency bands more complex. Decreasing the aft wall angle does not change the resonance frequency modes a lot except in the high-Mach-number flow.

Application of a BEM time stepping algorithm in understanding complex unsteady propulsion hydrodynamic phenomena

We solve the problem of unsteady potential flow around a system of arbitrarily moving rigid or flexible, lifting or non-lifting bodies, in an infinite fluid free of distributed vorticity. For the solution we use a time stepping algorithm and a potential based formulation of the corresponding free BVP. Nonlinear free shear layer dynamics are included in our modeling. This is a major innovation in treating complex unsteady propulsion problems since no simplifying assumptions (like that of a helicoidal wake) are used regarding the wake model. Bilinear quadrilateral elements are used to describe body and shear layer geometry at each time t. Three types of Kutta conditions can be alternatively applied for the determination of the shed vorticity from lifting bodies. The theoretical and numerical aspects of the method are presented followed by a number of applications, elucidating the qualitative and quantitative physical characteristics of a number of complex unsteady propulsion problems.

Dynamics of shallow lateral shear layers: Experimental study in a river with a sandy bed

Shallow lateral shear layers forming between flows with different velocities, though essential for mixing processes in natural streams, have been examined only in laboratory settings using smooth, fixed‐bed channels. This paper reports the results of an experimental study of a shear layer in a straight reach of a natural river where the layer, in contrast to the two‐dimensional structure observed in the laboratory, is highly three‐dimensional. The study included pronounced transverse pressure gradients, which influenced shear layer structure compared to flume experiments. It also introduces an analysis that complements conventional theory on mixing layers. The lateral velocity gradient between the flows downstream from a splitter plate placed in the river, the principal controlling factor, was adjusted for three experimental runs to determine the influence of different gradients on shear‐layer dynamics. In each run, detailed three‐dimensional measurements of mean and turbulent characteristics were obtained at five cross sections downstream from the splitter plate. Although experimental results agreed with conventional mixing‐layer theories with respect to turbulence, the dynamics of the shear layers were dominated by the mean lateral fluxes of momentum. After re‐examining the governing equations, we developed a parabolic equation describing the shear layer evolution and several scaling relations for essential terms of the energy budget: mean and turbulent lateral fluxes of momentum, turbulent kinetic energy, and dissipation rates. The study also provides insight into the spectral dynamics of turbulence in the shear layer and clarifies previous observations reported for confluences in natural streams.

Application of the k–ω turbulence model for a wind-induced vibration study of 2D bluff bodies

This paper is concerned with the question of an appropriate turbulence model for the computational modelling of bridge deck aero-elasticity. A detailed examination of the suitability of different turbulence models for simulating various aero-elastic phenomena leads to the conclusion that the two equation k–ω RANS turbulence model strikes the right balance between computational efficiency and accuracy in simulating the flow regime. In order to test this hypothesis a rectangular prism with B/D=4 is taken as an example structure and the flutter derivatives are identified from FSI simulations for both low and medium turbulent flow regimes. The simulations are carried out using a block iterative sequential coupling routine that allows for the exploitation of existing fluid and structural solvers. The results show that the k–ω can adequately model the motion induced shear layer dynamics that are necessary for simulating FSI. The results also demonstrate the potential benefits of computational FSI studies in that flutter derivatives (and other aerodynamic coefficients) can readily be obtained without some of the problems encountered in wind tunnel tests.

Low-dimensional models of a temporally evolving free shear layer

We develop low-dimensional models for the evolution of a free shear layer in a periodic domain. The goal is to obtain models simple enough to be analysed using standard tools from dynamical systems theory, yet including enough of the physics to model nonlinear saturation and energy transfer between modes (e.g. pairing). In the present paper, two-dimensional direct numerical simulations of a spatially periodic, temporally developing shear layer are performed. Low-dimensional models for the dynamics are obtained using a modified version of proper orthogonal decomposition (POD)/Galerkin projection, in which the basis functions can scale in space as the shear layer spreads. Equations are obtained for the rate of change of the shear-layer thickness. A model with two complex modes can describe certain single-wavenumber features of the system, such as vortex roll-up, nonlinear saturation, and viscous damping. A model with four complex modes can describe interactions between two wavenumbers (vortex pairing) as well. At least two POD modes are required for each wavenumber in space to sufficiently describe the dynamics, though, for each wavenumber, more than 90% energy is captured by the first POD mode in the scaled space. The comparison of POD modes to stability eigenfunction modes seems to give a plausible explanation. We have also observed a relation between the phase difference of the first and second POD modes of the same wavenumber and the sudden turning point for shear-layer dynamics in both direct numerical simulations and model computations.

Feedback shear layer control for bluff body drag reduction

Drag reduction strategies for the turbulent flow around a D-shaped body are examined experimentally and theoretically. A reduced-order vortex model describes the interaction between the shear layer and wake dynamics and guides a path to an efficient feedback control design. The derived feedback controller desynchronizes shear-layer and wake dynamics, thus postponing vortex formation. This actuation is tested in a wind tunnel. The Reynolds number based on the height of the body ranges from 23000 to 70000. We achieve a 40% increase in base pressure associated with a 15% drag reduction employing zero-net-mass-flux actuation. Our controller outperforms other approaches based on open-loop forcing and extremum-seeking feedback strategies in terms of drag reduction, adaptivity, and the required actuation energy.

Step Geometry and Countercurrent Effects in Dump Combustor, Part 1: Cold Flow

Nonreacting flow in a backward-facing step combustor is studied while employing a novel countercurrent shear (or counterflow) concept. Counterflow is used to manipulate the turbulent shear layer created by the step to increase turbulent burning velocities, and thereby, reduce ignition delay time. Unfortunately, this concept also leads to a smaller residence time because of a shorter recirculation vortex. These competing challenges of achieving higher burning velocities and longer residence time demand modification of the step geometry. Changes in the step geometry will alter the size and characteristics of the recirculation vortex and the shear layer dynamics within the combustor. These issues are addressed in this paper via a numerical study. For the simulations, Reynolds-averaged Navier–Stokes equations are solved in the framework of the realizable k–� turbulence model. A two-layer approach is used for the near-wall modeling. The paper includes a detailed account of the benefits of countercurrent shear technology, a parametric study based on step-geometry modifications, and an aerodynamic performance evaluation.

The structure of Kelvin–Helmholtz vortices with super-sonic flow

We have done two-dimensional simulations of the Kelvin–Helmholtz instability (KHI) with super-sonic flow using the CIP method. The linear analyses of a simple uniform density case show that the KHI cannot grow vigorously when the velocity jump is more than twice the sound speed (when the flow speed relative to the vortex is super-sonic). In this study, by situating a high density contrast across the shear layer, we set the flow in only one of the sides to be super-sonic and then show that the KHI does grow and rolls up a vortex. The formation of a shock is essential for the KHI vigorous growth and the structure of the vortex is strongly influenced by the shock geometry. The results should have substantial implications to velocity shear layer dynamics involving large density jump, such as planetary magnetospheric boundary layers.

Time-Series and Time-Averaged Characteristics of Subsonic to Supersonic Base Flows

Physics of cylindrical base flows ranging from subsonic to supersonic speeds at zero angle of attack are computationally investigated. Time-series and time-averaged investigations of base flows show distinctive characteristics at subsonic, transonic, and supersonic regimes. Normalized time-averaged base pressure decreases proportionally with respect to increasing freestream dynamic pressure in the subsonic regime of M ∞ 1.5. Normalized base pressure fluctuations sharply increase at transonic speeds, whereas they decrease with increasing freestream Mach number at subsonic and supersonic speeds. Appearance of unsteady local shock waves change the characteristics of base pressure distinctively at the transonic speeds. Spectra of the base pressure show one clear peak at subsonic speeds (related to the shear layer dynamics), two clear peaks at transonic speeds (related to the shear layer dynamics and its subharmonic), and three major peaks at supersonic speeds (related to the shear layer dynamics, its subharmonic, and an additional mechanism). Instability of the free shear layers has dominant influence on the overall base flowfield over a wide range of Mach numbers ranging from subsonic to supersonic speeds. However, at supersonic speeds, an additional mechanism of instability within the recirculating region is possibly at work and has dominant influence on the flowfield. The dominant mechanisms significantly cause the strong Mach number dependence of the high-pressure region which is strongly related to the base pressure. The spectrum analysis suggests that the substantial base pressure fluctuations are caused by the pulsing of the flow inside the recirculating region.

Toward Smart Control of Turbulent Jet Mixing and Combustion

Recent progress in active control of jet mixing and combustion is introduced. Miniature electromagnetic flap actuators are mounted on the periphery of an axisymmetric nozzle exit. It is demonstrated that even weak disturbances introduced into the initial shear layer by these actuators can significantly modify the large-scale vortical structures. This control technique is extended to the control of methane/air mixing and diffusion combustion by using a coaxial jet nozzle with the same flap actuators. As a result, the flame characteristics can be much improved in terms of stability and emission. Direct numerical simulation of a confined coaxial jet control has also been carried out. Although the distributed actuators are modeled somewhat ideally, DNS clearly demonstrates enormous effects of the present control scheme on the initial shear layer dynamics and concentration mixing.

Observations of the near-field structures of the glottal flow

The three-dimensional glottal jet was measured downstream from a self-oscillating physical model of the vocal folds using several techniques, including grid-based hotwire anemometry, high-speed flow visualization, and particle image velocimetry. Coherent flow structures were extracted from the spatio-temporal data using principal component analysis (PCA). The glottal jet resembled planar jets through static slitlike orifices. The direction of the jet core axis oscillated in the medial-lateral direction. Also, there was a positive correlation between the dynamics of shear layers around the laminar jet core and flow structures in the transitional region. This finding was similar to the dynamics of planar jets where jet flapping was observed previously. This can be understood in terms of an antisymmetric array of large-scale vortices being convected downstream. This antisymmetric mode of coherent vortex structures acts as an acoustic dipole that could effect the dynamics of the shear layers in the laminar core region. Thus, our observations help to understand the dynamics of the acoustic near-field of the glottal oscillator and suggest a possible feedback mechanism for source-tract coupling.

Velocity measurements in a developed open channel flow in the presence of an upstream perturbation

The effect of a near-free surface disturbance imposed on an open channel flow in the presence of low and high background turbulence is studied using a two-component laser Doppler anemometer. A bluff body located near the entrance of the flume was used to generate the free surface disturbance and the velocity characteristics were measured at a downstream location where the flow is fully developed. Experiments were conducted in two sets of flow fields. In the first set, the basic condition was an undisturbed open channel flow on a smooth bed, which is then compared with a flow with free surface disturbance. In this set, the turbulence levels are relatively lower and comparable with typical laboratory flume conditions. In the second set, the basic condition is a flow over a train of fixed two-dimensional bed forms, which is then compared with a flow with both bed forms and free surface disturbance. In the presence of the bed forms, there is continuous generation and sustenance of turbulence resulting in significantly higher background turbulence levels. The turbulence levels in the second set are comparable to natural open channel flows. Within the first set, though the mean profiles in inner coordinates are nearly identical, differences can be noticed in the mean defect profiles, while the Coles' parameter and the normalized turbulence levels are reduced in the presence of the free surface disturbance. Furthermore, quadrant decomposition indicates that in the presence of the free surface disturbance, three of the four quadrants are significantly altered. In the second set, the increased background turbulence due to the existing shear layer dynamics has an overwhelming influence on the flow characteristics while the free surface disturbance has a secondary role.

TOWARD SMART CONTROL OF TURBULENT JET MIXING AND COMBUSTION(Keynote Lecture)

Recent progress in active control of jet mixing and combustion is introduced. Miniature electromagnetic flap actuators are mounted on the periphery of an axisymmetric nozzle exit. It is demonstrated that even weak disturbances introduced into the initial shear layer by these actuators can significantly modify the large-scale vortical structures. This control technique is extended to the control of methane/air mixing and diffusion combustion by using a coaxial jet nozzle with the same flap actuators. As a result, the flame characteristics can be much improved in terms of stability and emission. Direct numerical simulation of a confined coaxial jet control has also been carried out. Although the distributed actuators are modeled somewhat ideally, DNS clearly demonstrates enormous effects of the present control scheme on the initial shear layer dynamics and concentration mixing.

Cavity Oscillation Mechanisms in High-Speed Flows

An experimental study was conducted to investigate the physics underlying the oscillation cycle of high-Mach- number, turbulent, open-cavity flows. The specific aim was to investigate how the interaction between the cavity acoustics and the shear-layer dynamics is affected by increasing Mach number. In the experiments the freestream Mach numbers tested were 2 and 5, the cavity length-to-depth ratio was 6, and the primary measurements made were of fluctuating surface pressures. The shear-layer-acoustics coupling was investigated by testing the cavity both with and without a plate covering over 80% of the cavity. The cover plate isolated the cavity from the free shear layer above it. In the Mach 2 cavity flow, the uncovered-cavity resonance frequencies agree well with those predicted by Rossiter's model. On the other hand, the resonance frequencies measured in the covered cavity do not agree with Rossiter's model but instead are consistent with a model that is based on closed-box acoustics. At Mach 5, both the uncovered and covered cavities have resonance frequencies that agree equally well with both Rossiter's model and closed-box acoustics. The success of a pure acoustics model suggests that the coupling between the shear-layer dynamics and the cavity acoustics is greatly reduced at high Mach numbers. Based on a consideration of the physical mechanisms implicit in Rossiter's model, it is argued that its successful prediction of the resonance frequencies in high-Mach-number cavity flows is largely coincidental and likely does not reflect the correct modeling of the flow physics.

A visualization study of fluid-structure interaction between a circular cylinder and a channel bed

Flow visualization was used to study the fluid-structure interaction between a circular cylinder and a shallow turbulent open channel flow. The Reynolds number ranged from R$_{eD}$=1500-4400 based on the cylinder diameter, and from R$_{eH}$=7,800-27,600 based on the channel hydraulic radius. The cylinder was mounted vertically on the channel bed and the flow depth-to-cylinder-diameter ratio was varied from d/D=7.0-11.7. Tests were carried out over smooth and rough beds, with the rough beds being either permeable or impermeable. The study showed that the horseshoe vortex forming at the cylinder-bed junction affects many of the flow structures, including the mode of vortex shedding, the shear layer dynamics, the vortex formation length, and the width of the near-wake region. The influence of the horseshoe vortex can be recognized throughout the depth of flow; however, its influence decreases with an increase in distance from the channel bed. It was also possible to discern that the bed roughness resulted in a change to the above interaction and the permeability of the bed resulted in additional changes.

Staggered circular cylinders immersed in a uniform planar shear flow

Two circular cylinders of equal diameter, arranged in staggered configurations with dimensionless centre-to-centre pitch ratios of P/ D=1.125 and 1.25, were immersed in a uniform planar shear flow with a dimensionless shear parameter of K=0.05 and a Reynolds number of Re=5.0×10 4. The mean aerodynamic forces and the vortex shedding frequencies were measured for the upstream and downstream cylinders at each pitch ratio. Under uniform flow conditions, where there is no shear, the cylinders behave as a single bluff body with a single vortex shedding process. The aerodynamic force coefficients on both cylinders, and the Strouhal number, undergo complex changes as the incidence angle is varied from α=0° to 90°. At several critical incidence angles there are discontinuous changes in, or extreme values of, the aerodynamic force coefficients. These are related to the shear layer dynamics between the upstream and downstream cylinders at lower incidence angles, and the changes to the gap flow between the cylinders and the effect of base bleed at higher incidence angles. The effects of the uniform planar shear flow were mostly seen in the aerodynamic forces, particularly for the mean drag coefficient, where there was a reduction in drag for the upstream cylinder at all incidence angles, a reduction in drag for the downstream cylinder at higher incidence angles, small changes in the lift coefficient on the upstream cylinder, and shifts in the critical incidence angles. In contrast, the behaviour of the Strouhal number was generally unchanged, although a small reduction in Strouhal number was observed. Planar shear flow more strongly influenced the staggered cylinders at higher incidence angles, where it had an influence on the direction and strength of the gap flow, seen in the movement of two critical incidence angles, which was accompanied by a weakening of the vortex shedding process.