Two-dimensional Free Shear Layers Research Articles

Numerical Analysis of Sweeping Jets for Active Flow Control Application

Abstract It has become apparent recently that the fluidic oscillators, also known as sweeping jets, can be used to create a combination of steady (streamwise vortices) and unsteady (spanwise vortices) forcing mechanisms which have the potential to fulfill many of the promises of active separation control. The fluidic oscillators contain no moving parts, but produce an unsteady component via a natural feedback loop inherent to their geometry. The oscillations are entirely self-induced and self-sustaining. Their simple and robust design and their effectiveness over a wide range of flow conditions make them more attractive than other flow control devices, such as synthetic jets and plasma actuators. Figure 1 shows the instantaneous jet generated in quiescent environment using the Improved Delayed Detached Eddy Simulation (IDDES) model, where the Large Eddy Simulation (LES) branch of the IDDES model is able to capture the turbulence structures properly. An instantaneous iso-surface of vorticity magnitude, colored by streamwise velocity for flow over a wall-mounted hump is depicted in Figure 2. As expected, a massive flow separation occurs behind the hump in the uncontrolled condition (Figure 2 (a)), with a nearly two-dimensional free shear layer at the edge of the separation line. Breakdown of the shear layer by an array of sweeping jets located slightly downstream of the separation line is seen in Figure 2 (b), which is followed by the elimination of the separation region behind hump. The three-dimensional structures generated by the sweeping jets are smaller and closer to the hump wall than those produced by the steady jets shown in Figure 2 (c). Presence of a large region of reversed flow near the hump wall in its aft section is also seen in the case of the steady jet. This study indicates a superior effectiveness of sweeping jets on separated flows.

Control of a three-dimensional turbulent shear layer by means of oblique vortices

The effect of local forcing on the separated, three-dimensional shear layer downstream of a backward-facing step is investigated by means of large-eddy simulation for a Reynolds number based on the step height of 10,700. The step edge is either oriented normal to the approaching turbulent boundary layer or swept at an angle of $$40^\circ $$ . Oblique vortices with different orientation and spacing are generated by wavelike suction and blowing of fluid through an edge parallel slot. The vortices exhibit a complex three-dimensional structure, but they can be characterized by a wavevector in a horizontal section plane. In order to determine the step-normal component of the wavevector, a method is developed based on phase averages. The dependence of the wavevector on the forcing parameters can be described in terms of a dispersion relation, the structure of which indicates that the disturbances are mainly convected through the fluid. The introduced vortices reduce the size of the recirculation region by up to 38%. In both the planar and the swept case, the most efficient of the studied forcings consists of vortices which propagate in a direction that deviates by more than $$50^\circ $$ from the step normal. These vortices exhibit a spacing in the order of 2.5 step heights. The upstream shift of the reattachment line can be explained by increased mixing and momentum transport inside the shear layer which is reflected in high levels of the Reynolds shear stress $$-\rho \overline{u'v'}$$ . The position of the maximum of the coherent shear stress is found to depend linearly on the wavelength, similar to two-dimensional free shear layers.

Numerical Investigation of Instabilities in Free Shear Layer Produced by NS-DBD Actuator

A numerical investigation of the effects of nanosecond barrier discharge on the stability of a two-dimensional free shear layer is performed. The computations are carried out using a compressible Navier-Stokes algorithm coupled with a thermodynamic model of the discharge. The results show that significant increases in the shear layer’s momentum thickness and Reynolds stresses occur due to actuation. Dependence on both frequency and amplitude of actuation are considered, and a comparison is made of the computed growth rates with those predicted by linear stability theory. Amplitude and frequency ranges for the efficient promotion of shear-layer instabilities are identified. Keywords—NS-DBD, plasma, actuator, flow control, instability, shear layer

Large eddy simulation of flow around wavy cylinders at a subcritical Reynolds number

The cross-flow around wavy cylinders of wavelength ratios λ/ D m from 1.136 to 3.333 are investigated at Re = 3000 using large eddy simulation (LES). The mean flow field and the near wake flow structures are presented and compared with those of a circular cylinder at the same Reynolds number. The mean pressure distributions are also calculated. The results show that the mean drag coefficients of the wavy cylinders are less than those of a corresponding circular cylinder due to a longer wake vortex formation length generated by the wavy cylinders. For a subcritical Reynolds number of 3000, a maximum drag coefficient reduction of up to 18% compared with a circular cylinder is obtained corresponding to an optimal wavelength ratio of λ/ D m around 1.9 and an amplitude ratio a/ D m of 0.152. The fluctuating lift coefficients of the wavy cylinders are also greatly reduced or even suppressed. These kinds of wavy surfaces lead to the formation of three-dimensional free shear layers which are more stable than purely two-dimensional free shear layers. Such free shear layers will only roll up into mature vortices at further downstream positions. This significantly modified the near wake structures and the pressure distribution around the cylinder. It was found that the wave amplitude to wavelength ratio a/ λ plays an essential role in determining the 3D vortex structure behind the wavy cylinders which has a significant effect on the reduction of the fluctuating lift and suppression of flow-induced vibration.

A study of streamwise vortex structure in a stratified shear layer

The existence of an organized streamwise vortical structure, which is superimposed on the well known coherent spanwise vorticity in nominally two-dimensional free shear layers, has been studied extensively. In the presence of stratification, however, buoyancy forces contribute to an additional mechanism for the generation of streamwise vorticity. As the spanwise vorticity layer rolls up and pulls high-density fluid above low-density fluid, a local instability results. The purpose of the current investigation is to force the three-dimensional instability in the stratified shear layer. In this manner, we experimentally observe the effect of buoyancy on the streamwise vortex tube evolution, the evolution of the buoyancy-induced instability, and the interaction between these two vortical structures. A simple numerical model is proposed which captures the relevant physics of the flow evolution. It is found that, depending on the location, streamwise vortices resulting from vortex stretching may be weakened or enhanced by the stratification. Buoyancy-induced vortex structures are shown to form where the unstable part of the interface is tilted by the streamwise vortex tubes. These vortices strengthen initially, then weaken downstream, the timescale for this process depending upon the degree of stratification. For initial Richardson numbers larger than about 0.03, the baroclinically weakened vortex tubes eventually disappear as the flow evolves downstream and the baroclinically generated vortices dominate the three-dimensional flow structure.

Baroclinic generation of streamwise vorticity in a stratified shear layer

The existence of an organized streamwise vortical structure, which is superimposed on the well known coherent spanwise vorticity in nominally two-dimensional free shear layers, has been studied extensively. In the presence of stratification, however, buoyancy forces contribute to an additional mechanism for the generation of streamwise vorticity. The purpose of the current investigation is to force the three-dimensional instability in the stratified shear layer. In this manner, we experimentally observe the effect of buoyancy on the streamwise vortex tube evolution, the evolution of the buoyancy-induced instability, and the interaction between these two vortical structures. It is found that streamwise vortices resulting from vortex stretching are weakened in regions of locally stable stratification. Buoyancy-induced vortex structures are shown to form where the unstable part of the interface is tilted by the streamwise vortex tubes. These vortices strengthen initially, then weaken downstream, the time scale for this process depending upon the degree of stratification. For initial Richardson numbers larger than about 0.03, the baroclinically weakened vortex tubes eventually disappear as the flow evolves downstream and the baroclinically generated vortices dominate the three-dimensional flow structure.

A numerical study of wave propagation in a confined mixing layer by eigenfunction expansions

It is well known that the growth rate of instability waves of a two-dimensional free shear layer is reduced greatly at supersonic convective Mach numbers. In previous works, it has been shown that new wave modes exist when the shear layers are bounded by a channel due to the coupling effect between the acoustic wave modes and the motion of the mixing layer. The present work studies the simultaneous propagation of multiple stability waves using numerical simulation. It is shown here that the coexistence of two wave modes in the flow field can lead to an oscillatory growth of disturbance energy with each individual wave mode propagating linearly. This is particularly important when the growth rates of the unstable waves are small. It is also shown here that the propagation of two neutrally stable wave modes can lead to a stationary periodic structure of rms fluctuations. In the numerical simulations presented here the forced wave modes are propagating at same frequency, but with different phase velocities. In order to track the growth of each wave mode as it propagates downstream, a numerical method that can effectively detect and separate the contribution of the individual wave is given. It is demonstrated that by a least square fitting of the disturbance field with eigenfunctions the amplitude of each wave mode can be found. Satisfactory results as compared to linear theory are obtained.

Do large structures control their own growth in a mixing layer? An assessment

This study makes a specific comparison between two different two-dimensional free shear layers: the T-layer which develops in time from an initial tangential velocity discontinuity separating the two half-spaces; and the S-layer which develops downstream of the origin where two uniform streams of unequal velocity are brought into tangential contact. The method of comparison is to assume that the vorticity of the S-layer is given parabolically by a Galilean mapping of that of the T-layer; to satisfy the appropriate boundary conditions in the S-layer and to compute the velocity induced at any point in the S-layer by its vorticity field; and to compare this velocity to that which can be derived from the velocity of the T-layer at corresponding points by a Galilean transformation of the velocity itself. The purpose of this calculation is to assess approximately how far the flow in the S-layer is from parabolic and, in particular, to what extent the perturbations induced upstream by large concentrations of vorticity found downstream are instrumental in hastening or retarding the subharmonic instability that leads to the formation of these large structures. The calculations suggest that this elliptic influence, or the feedback, in a mixing layer is relatively small, at least for small velocity ratios.

Effect of initial conditions on two-dimensional free shear layers

The influence of periodic perturbations on the development of two-dimensional free shear layers generated by a splitter plate was investigated in cases where the ratios of the two velocities u1 and u2 either side of the splitter plate were such that 0 < u1/u2 < 1. Investigations were carried out in both a suction and a blower wind tunnel. Results show that even very weak periodic perturbations caused by the wind tunnel may cause significant nonlinear spreading in the downstream development of the shear layer, a behaviour which is also observed when the shear layer is deliberately excited. Other things being equal, the effect of the disturbance is greater when flow separation at the splitter plate is turbulent than when it is laminar.No self-induced feedback frequencies were measured in the test section. All tonal components that were detected in the flow could be traced to external sources.The influence of trailing-edge thickness on the shear-layer development is found to become significant when it exceeds 50% of the sum of boundary-layer displacement thickness at the point of separation. As the trailing edge becomes thicker, the range over which the shear layer is self-similar is shifted farther downstream. This behaviour may be crucial for predicting the evolution of shear layers in high-speed flows having thin boundary layers at separation.The momentum thickness criterion for estimating the development length of the flow as suggested by Bradshaw is shown to be insufficient for two-stream layers, where additional parameters, e.g. the trailing-edge geometry, have to be taken into account. Discrepancies between previously published observations of shear layers, as well as the considerable scatter in reported measurements, may therefore, to a large extent, be attributable to contamination of the experimental facility.

PARTICLE DISPERSION BY COHERENT STRUCTURES IN FREE SHEAR FLOWS

ABSTRACT The dispersion of particles in turbulent flows is poorly understood. Previous approaches to this problem have been found to be inadequate for nonisotropic turbulent flows. An approach involving a new physical concept is presented. This approach assumes that coherent vortex structures control the particle dispersion process in free shear flows. A simple computational model employing Stuart's vortices is used to simulate particle motion in a two-dimensional free shear layer. The results of this simulation are in reasonable agreement with previous experiments. For the first time, experimental observations indicating particle dispersion rates greater than fluid dispersion rates in free shear flows can be plausibly explained.

An experimental investigation of the instability of an incompressible, separated shear layer

The investigation of a separated shear layer was undertaken to clarify the non-linear mechanisms associated with instability and transition to turbulence. Such an investigation is of practical importance since profiles which resemble the separated shear layer are a common occurrence.A two-dimensional free shear layer was formed by separation of a laminar boundary layer from a rearward-facing step. The free-stream speed was approximately 16 ft./sec. Hot-wire measurements were made in the region directly downstream of the plate trailing edge. The measurements included mean velocity profiles, frequency spectra of the longitudinal fluctuation, and root-mean-square amplitude and phase distributions of various spectral components of the longitudinal fluctuation. Several measurements were designed to detect the presence of periodic spanwise structure.The most important findings were: Significant non-linear distortion of the initial unstable wave occurred without periodic spanwise structure.Non-linear distortion was first manifest by the growth of a subharmonic oscillation, which was strongly intermittent. Numerous harmonics of the sub-harmonic oscillation were also present.Strong evidence suggests that secondary instabilities were present, which created still higher frequencies.