Search

The purpose of this experimental study is to analyze the transient processes of the separation and reattachment of a turbulent boundary layer at the trailing edge of a splitter plate. The separation is driven by a steady pneumatic injection, considered here as an actuator controlling the mixing layer. Particle image velocimetry and hot-film measurements are performed at various stages of the processes. The results highlight the behavior of each transient. Analysis of the time scale of the processes is realized by means of bi-orthogonal decomposition. This gives essential information (e.g., time scale, qualitative features) for future applications using duty cycle mode to excite instabilities of the mixing layer.

The thrust of this paper is to validate, test and compare several Coherent Structure eduction methods utilizing the same data base. The flow chosen was that of an experimental study of a plane, incompressible, fully developed turbulent two-stream mixing layer. The mixing layer was chosen as the data base because it has been studied extensively from a coherent structures point of view. In addition, its characteristics (similarity, convection velocities, etc.) are well documented. There are also no wall effects so that comparisons between techniques are simplified. The data was collected from hot wire rakes with good spatial resolution thus allowing the contributors to apply and test different structure eduction techniques. The techniques chosen for discussion and used here have found wide utilization over the past decade, and all hold forth the promise of extensive application in the future. These include: Conditional Sampling (Vorticity-based and other methods); Wavelets; Pattern Recognition Analysis; Proper Orthogonal Decomposition; Stochastic Estimation; Topological Concept-based methods; Full Field Methods (e.g., pseudo flow visualization). All are illustrated by application to the mixing layer data base, and comparisons made between the results. This common study has shown that direct comparisons between results of several methods are now possible. Good quantitive and qualitative agreement between the different methods have been observed as well as some differences noted. As an example, the size of the averaged structures computed from the various methods compare to within 6 percent.

A reduced-order modelling (ROM) strategy is crucial to achieve model-based control in a wide class of flow configurations. In turbulence, ROMs are mostly derived by Galerkin projection of first-principles equations onto the proper orthogonal decomposition (POD) modes. These POD ROMs are known to be relatively fragile when used for control design. To understand more deeply this behaviour, a hierarchy of POD ROMs is studied and compared for a two-dimensional uncontrolled mixing layer. First, dynamical models based on POD are derived from the Navier–Stokes and the vorticity equations. It is shown that these models can exhibit for some truncation level finite-time blow-ups. A symmetrized quadratic model is then proposed to enforce the preservation of energy in the model. This formulation improves considerably the behaviour of the model, but the energy level is still overestimated. Subsequently, a nonlinear eddy-viscosity model with guaranteed stability is proposed. This model still leads to an imperfect description of the energy. Different 4D-Var identification strategies are then considered to improve the nonlinear eddy-viscosity model. It is shown that penalizing the time variation in the eddy-viscosity parameter leads to the best compromise in terms of description of the energy and of physical relevance of the eddy viscosity. Lastly, a statistical inference procedure is used to take into account the bias inherent of the sampling employed in the identification procedure. Joined probability density functions are then determined empirically for all the coefficients of the model, and a stochastic dynamical model is finally derived to study the influence on the long-term solution of different equiprobable sets of coefficients.

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.

An experimental study of the turbulent kinetic energy balance is performed in a LEBU manipulated turbulent boundary layer. The estimation of almost all the terms of the k-equation is obtained by hot wire anemometry. Near the manipulating device, strong alterations are observed, when compared with the natural conditions. The wake of the manipulator imposes two distinct zones. The lower part is characterized by negligible production compensated by diffusion, while, in the outer part, a large excess of production is balanced by diffusion and dissipation. The excess of dissipation rapidly vanishes downstream. The relaxation process is slower for production and diffusion.

This paper presents longitudinal space and space-time conventional velocity correlations measured in the wake of a two-dimensional flat-plate at zero incidence, with fully-turbulent boundary layers at its sharp trailing edge. Iso-correlation contour plots are given in the plane of symmetry and normal to this plane in the assumed asymptotic (in the mean velocity sense) part. Comparisons with initially laminar 2-D wake results show that the classical Double-Roller-Eddy model developed for initially laminar wakes is not adapted to initially turbulent wakes; on the other hand, comparison with supersonic wake of the same nature seems to confirm this conclusion. The lack of detailed experimental data in this field is outlined, together with the need of a refined theoretical approach to the coherent structures existing in such flows.