Joel Delville

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.

Pressure velocity coupling in a subsonic round jet

Abstract An experimental investigation involving simultaneous measurements of the radial distribution of velocity within the shear layer of a jet and the longitudinal distribution of pressure surrounding a jet is performed. The use of two statistical approaches (proper orthogonal decomposition, POD and linear stochastic estimation, LSE) permits the analysis, in terms of vortical structures, of the pressure fluctuations surrounding the jet. These structures are found to be responsible for the far-field noise emission. This method thus seems promising for providing a “structural model” of the turbulent flow field.

Generation of Three-Dimensional Turbulent Inlet Conditions for Large-Eddy Simulation

A method for generating realistic (i.e., reproducing in space and time the large-scale coherence of the flows) inflow conditions based on two-point statistics and stochastic estimation is presented. The method is based on proper orthogonal decomposition and linear stochastic estimation. This method allows a realistic representation with a minimum of information to be stored. Most of the illustrations of this method are given for a plane turbulent mixing layer that contains most of the basic features of organized turbulent flows. Examples of the application of the method are given first for the generation of inflow conditions for direct numerical simulation (DNS) and for large-eddy simulation from experimental results. Second, DNS results are used to generate realistic inflow conditions for two- and three-dimensional DNS, retaining only a minimum size of relevant information.

Coherent structures in subsonic jets : a quasi-irrotational source mechanism ?

The true global source of the farfield sound radiated from a subsonic jet is the entire dynamic found within the confines of the hydrodynamic field, a dynamic which comprises an unsteady compressive excitation of the medium resulting from turbulent mixing and unsteady temperature fluctuations, these being driven by a wide range of turbulence scales. Improved understanding, and subsequent modelling of the space-time character of the global source term has been acheived in the past through study of the different physical mechanisms implicated in its dynamic. The phenomena which have to date been accepted as important in terms of the radiated sound are (i) turbulent mixing and shear, (ii) fluctuating entropy, (iii) convective amplification and (iv) refraction and scattering of sound by the mean and turbulent components of the velocity field. Once identified as important, specific modelling strategies can and have been developed in order to deal with these phenomena. The existence of coherent structures in turbulent jets was identified as important in the 1970s and their role in the production of sound has received considerable attention in more recent years. However, direct identification of the causal link between this component of the turbulence and its sound field is a delicate matter due to the virtual impossibility of directly measuring the source dynamic of the flow, this being due to an overwhelming dominance of hydrodynamic energy in the source region, and a total absence of any hydrodynamic signature in the linear, acoustic region. As a result, modelling strategies where this component of the source term is concerned have remained, at best, highly empirical. An interesting region of the flow where our understanding of the relationship between the hydrodynamic cause and its acoustic effect is concerned is the near pressure field, found just outside the rotational region of the flow. In this region the signature of the sound production mechanism and its resultant sound field are both present, coincident in space and in time. This means that pressure measurements can here be used to study the space-time structure of the two with a view to discerning the causal relationship which links them. In this work, measurements performed in the near pressure field of an isothermal subsonic jet reveal a strong interaction mechanism between the reactive and propagating components of the pressure field associated with the coherent structures of the flow, the essential features of which are captured by a simple model. On account of the success of the model it is possible to draw a number of interesting conclusions concerning the sound production mechanism associated with these structures, the most important of these being that despite the rotational velocity field in which they exist, where their sound production is concerned they can be considered as a quasi-irrotational, or wavy-wall type source mechanism. The same observation in supersonic jets has led to considerable simplifications where noise prediction is concerned – instability wave models being thus appropriate. The results from this work illustrate how similar models may be appropriate for modelling the noise production by this component of the source mechanism, believed to be predominant where peak radiation is concerned.

Two-point correlations in high Reynolds number flat plate turbulent boundary layers

Two-point correlations of turbulent boundary layer are presented for Reθ of 9800 and 19,100. The results are based on wind tunnel measurements performed in the 30 cm thick boundary layer of the 21.6 m long LML (Laboratoire de Mécanique de Lille) boundary layer research facility. Simultaneous hot-wire probe measurements of the entire boundary layer at 143 different points on an array are used for computation of the two-point correlations. The two-point correlations in the streamwise–spanwise plane at 11 different wall-normal positions covering one boundary layer thickness in the spanwise direction show that the maximal extension of the correlations in the streamwise direction is bounded within ±3.5δ for both of the Reynolds number tested. The shapes of the positive correlations in the streamwise–spanwise plane at different wall-normal positions are similar throughout the boundary layer from nearly the freestream to the wall. The correlations in the streamwise–wall-normal plane for 11 different wall-normal reference positions also show that the correlations in some cases cover the entire boundary layer. The streamwise extent of the correlations in the streamwise–wall-normal plane is about 7–8 boundary layer thicknesses. Two-point correlation maps for the streamwise–wall-normal plane reveal the existence of non-zero correlations between even the intermittent region and near-wall region.

Polynomial identification of POD based low-order dynamical system

Low-order modelling based on POD approach has proved to be an efficient tool to analyze turbulent flows as well as to build control systems. In this paper, a novel method to identify low-order dynamical system (LODS) is proposed. This approach relies on the fact that all the POD-Galerkin LODS based on Navier–Stokes equations can be written in polynomial form. One proposes here to estimate the polynomial coefficients arising in such a formalism by the following. The projection coefficients of the flow field onto its POD basis and their time derivatives being known, a statistical approach involving correlations between these quantities, are used to provide an estimate of the coefficients of the dynamical system. The identification method is described and tested in the case of the analytical Lorenz system. Finally, the LODS identification is performed in the case of experimental data of a supersonic jet-mixing layer interaction. Dynamical systems based on flow visualizations are derived and lead to relevant short-time and long-term predictions.

A time-resolved estimate of the turbulence and sound source mechanisms in a subsonic jet flow

A dynamical estimate of the axial component of a Mach 0.60 axisymmetric jets turbulent velocity field is presented here using spectral linear stochastic estimation. The pressure field surrounding the exit of the jet is employed as the unconditional parameter in the estimation technique. A sub-grid interpolation method is used to improve the spatial resolution of the estimate. The model estimate is time-resolved and reconstructed using a purely experimental database. A decomposition of the model estimate using POD and Fourier-azimuthal techniques identifies the turbulent velocity modes that are responsible for driving the near-field pressure when compared with direct measurements of the jets modal features. In effect, the signatures left in the near pressure field by the turbulence are a result of the low-order structure, the higher azimuthal modes being inefficient in driving the hydrodynamic pressure. A direct calculation of the source field using a Lighthill approach is performed, from which the low-d...

Characterization of the organization in shear layers via the Proper Orthogonal Decomposition

Experiments are performed in an incompressible plane turbulent mixing layer, using various hot wire rake configurations. From these experiments, the Proper Orthogonal Decomposition is applied for kernels where the space-time correlation tensor is evaluated over different spatial meshes and velocity components configurations. The resulting decompositions are then discussed in terms of “characterization of the organization of the flow” for various scalar or vectorial approaches of the POD. An incrtial range law is evidenced. The instantaneous contribution of the first modes of the POD to the organization of the flow is analyzed. A dynamical behavior for the organization of the flow is observed from the correlation between the first two modes contribution.

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 310 000, 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...