J. P. Bonnet

Stochastic estimation and proper orthogonal decomposition: Complementary techniques for identifying structure

The Proper Orthogonal Decomposition (POD) as introduced by Lumley and the Linear Stochastic Estimation (LSE) as introduced by Adrian are used to identify structure in the axisymmetric jet shear layer and the 2-D mixing layer. In this paper we will briefly discuss the application of each method, then focus on a novel technique which employs the strengths of each. This complementary technique consists of projecting the estimated velocity field obtained from application of LSE onto the POD eigenfunctions to obtain estimated random coefficients. These estimated random coefficients are then used in conjunction with the POD eigenfunctions to reconstruct the estimated random velocity field. A qualitative comparison between the first POD mode representation of the estimated random velocity field and that obtained utilizing the original measured field indicates that the two are remarkably similar, in both flows. In order to quantitatively assess the technique, the root mean square (RMS) velocities are computed from the estimated and original velocity fields and comparisons made. In both flows the RMS velocities captured using the first POD mode of the estimated field are very close to those obtained from the first POD mode of the unestimated original field. These results show that the complementary technique, which combines LSE and POD, allows one to obtain time dependent information from the POD while greatly reducing the amount of instantaneous data required. Hence, it may not be necessary to measure the instantaneous velocity field at all points in spacesimultaneously to obtain the phase of the structures, but only at a few select spatial positions. Moreover, this type of an approach can possibly be used to verify or check low dimensional dynamical systems models for the POD coefficients (for the first POD mode) which are currently being developed for both of these flows.

Examination of large-scale structures in a turbulent plane mixing layer. Part 1. Proper orthogonal decomposition

Large-scale structures in a plane turbulent mixing layer are studied through the use of the proper orthogonal decomposition (POD). Extensive experimental measurements are obtained in a turbulent plane mixing layer by means of two cross-wire rakes aligned normal to the direction of the mean shear and perpendicular to the mean flow direction. The measurements are acquired well into the asymptotic region. From the measured velocities the two-point spectral tensor is calculated as a function of separation in the cross-stream direction and spanwise and streamwise wavenumbers. The continuity equation is then used for the calculation of the non-measured components of the tensor. The POD is applied using the cross-spectral tensor as its kernel. This decomposition yields an optimal basis set in the mean square sense. The energy contained in the POD modes converges rapidly with the first mode being dominant (49% of the turbulent kinetic energy). Examination of these modes shows that the first mode contains evidence of both known flow organizations in the mixing layer, i.e. quasi-two-dimensional spanwise structures and streamwise aligned vortices. Using the shot-noise theory the dominant mode of the POD is transformed back into physical space. This structure is also indicative of the known flow organizations.

Subsonic jet noise reduction by fluidic control : The interaction region and the global effect

A microjet arrangement comprising both penetration (or immersion) and convergence (jets oriented such that two jets of a pair interact with one another) is used to control a subsonic turbulent jet with a view to noise reduction. The acoustic effect of the so-called fluidevron system is comparable to chevrons and nonconverging microjets as far as the noise reduction is concerned. Detailed experimental measurements are performed for a main jet with Mach and Reynolds numbers of 0.3 and 310u2009000, respectively. A direct numerical simulation study is performed for a model, plane mixing-layer problem using the immersed-boundary method, in order to help understand the topological features of the fluidevron–mixing-layer interaction. In terms of modifications produced in the flow, two relatively distinct regions are identified: the near-nozzle region, 0 1, where the jet recovers many of the uncontrolled-jet flow ch...

Decomposition of mixing layer turbulence into coherent structures and background fluctuations

The eduction of coherent structures from cross-wire rake data in a fully turbulent incompressible mixing layer confirms the feasibility of a decomposition of a turbulent flow field, first suggested by Farge, as non-periodic non-equilibrium coherent structures interacting with a ‘thermalized’ broad-band turbulence. A simple wavelet coefficient decimation algorithm and orthogonalization yields non-periodic dominant flow structures and a background field that has a Gaussian distribution of velocities at the centerline. The coherent structures are classified in terms of their topology. The non-coherent background field has flat energy spectra and normal distribution of velocity components. Most background field statistics depend only weakly on the type of structure on which they are superposed. It may be possible to adapt existing subgrid scale models to this decomposition.

Development of a nonlinear eddy-viscosity closure for the triple-decomposition stability analysis of a turbulent channel

The analysis of the instabilities in an unsteady turbulent flow is undertaken using a triple decomposition to distinguish between the time-averaged field, a coherent wave and the remaining turbulent scales of motion. The stability properties of the coherent scale are of interest. Previous studies have relied on prescribed constants to close the equations governing the evolution of the coherent wave. Here we propose an approach where the model constants are determined only from the statistical measures of the unperturbed velocity field. Specifically, a nonlinear eddy-viscosity model is used to close the equations, and is a generalisation of earlier linear eddy-viscosity closures. Unlike previous models the proposed approach does not assume the same dissipation rate for the time- and phase-averaged fields. The proposed approach is applied to a previously published turbulent channel flow, which was harmonically perturbed by two vibrating ribbons located near the channel walls. The response of the flow was recorded at several downstream stations by phase averaging the probe measurements at the same frequency as the forcing. The experimentally measured growth rates and velocity profiles, are compared to the eigenvalues and eigenvectors resulting from the stability analysis undertaken herein. The modes recovered from the solution of the eigenvalue problem, using the nonlinear eddy-viscosity model, are shown to capture the experimentally measured spatial decay rates and mode shapes of the coherent scale.

On the benefits of hysteresis effects for closed-loop separation control using plasma actuation

Flow separation control by a non-thermal plasma actuator is considered for a NACA 0015 airfoil at a chord Reynolds number of 1.9u2009×u2009105. Static hysteresis in the lift coefficient is demonstrated for increasing and then decreasing sinusoidal voltage amplitude supplying a typical single dielectric barrier discharge actuator at the leading edge of the model. In addition to these open-loop experiments, unsteady surface pressure signals are examined for transient processes involving forced reattachment and natural separation. The results show that strong pressure oscillations in the relatively slow separation process, compared to reattachment, precede the ultimate massive flow separation. To enhance the contrast between the parts of the signal related to the attached flow and those related to the incipient separation, RMS estimate of filtered values of Cp is used to define a flow separation predictor that is implemented in feedback control. Two simple controllers are proposed, one based on a predefined threshol...

Analysis of a jet–mixing layer interaction

Abstract The improvement of mixing in free-shear flows via external jets has been proven efficient in subsonic and supersonic flows as well. However, the hyper-mixing process is not well known. The present study deals with an experimental and a numerical approach of the interaction of an external control jet with a turbulent mixing layer. The main conclusion is that an intermittent penetration of the control jet occurs both in supersonic and subsonic configurations. Moreover, all results tend to show that the control jet flapping frequency and the spacing between the structures involved downstream of the interaction are respectively very close to the frequency and wavelength of the Kelvin–Helmholtz structures at the impact location. Two hypotheses are provided in order to explain the mechanism of the interaction. The first one is based upon the interaction with the passage of Kelvin–Helmholtz structures in the mixing layer, the other deals with an intrinsic instability of such a flow configuration.

Coherent Structures: Past, Present and Future

It is now commonplace to recognize that coherent structures (OS’s), beautifully illustrated in the art of many cultures, but long held to be marginal (transitional, low-Reynolds-number) in the science and engineering of fluid turbulence, were brought back to the core of the field by the work of Townsend [31] and the explosion of literature following the paper of Brown & Roshko [10] and e.g Hussain [20].

TWO-DIMENSIONAL GRAM-CHARLIER RECONSTRUCTION OF VELOCITY CORRELATIONS

The two‐point statistics obtained in a two‐dimensional mixing layer and a three‐dimensional wall jet are reconstructed from the summation of Hermite Polynomials. The use of Hermite Polynomials allows the rigorous and progressive decomposition of the statistical field into separate components, Gaussian and non‐Gaussian. The influence of individual terms can then be investigated. Two different schemes are used: a one‐dimensional temporal reconstruction of data from both experiments, which is capable of providing excellent agreement with the measurements, and a two‐dimensional scheme with the mixing layer data, which captures spatial and temporal characteristics of the velocity cross‐correlation. It is demonstrated that the technique can also recover information that may be lost or missing between two measuring points thereby providing a complementary method to linear stochastic estimation.

Analysis of a plane turbulent mixing layer manipulated by a localized forced separation

The purpose of this experimental study is to analyze the effects of a forced separation, near the trailing edge of a splitter plate, on the development of a turbulent plane mixing layer. The separation was driven by a steady pneumatic injection, and is considered here as an actuator for controlling the spreading efficiency of the mixing layer. Particle image velocimetry and hot-wire measurements were performed for the natural and the manipulated regimes. The results highlight the capabilities of this control strategy to enhance mixing. Analysis of the turbulent field and coherent structure organization offers insight into the mechanisms responsible for this mixing enhancement.