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  • 1
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    Examination of large-scale structures in a turbulent plane mixing layer. Part 1. Proper orthogonal decomposition (1999)
    Cambridge University Press
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    Publication Date: 1999-07-25
    Description: 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.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 2
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    Examination of large-scale structures in a turbulent plane mixing layer. Part 2. Dynamical systems model (2001)
    Cambridge University Press
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    Publication Date: 2001-08-15
    Description: The temporal dynamics of large-scale structures in a plane turbulent mixing layer are studied through the development of a low-order dynamical system of ordinary differential equations (ODEs). This model is derived by projecting Navier-Strokes equations onto an empirical basis set from the proper orthogonal decomposition (POD) using a Galerkin method. To obtain this low-dimensional set of equations, a truncation is performed that only includes the first POD mode for selected streamwise/ spanwise (k1/k3) modes. The initial truncations are for k3 = 0; however, once these truncations are evaluated, non-zero spanwise wavenumbers are added. These truncated systems of equations are then examined in the pseudo-Fourier space in which they are solved and by reconstructing the velocity field. Two different methods for closing the mean streamwise velocity are evaluated that show the importance of introducing, into the low-order dynamical system, a term allowing feedback between the turbulent and mean flows. The results of the numerical simulations show a strongly periodic flow indicative of the spanwise vorticity. The simulated flow had the correct energy distributions in the cross-stream direction. These models also indicated that the events associated with the centre of the mixing layer lead the temporal dynamics. For truncations involving both spanwise and streamwise wavenumbers, the reconstructed velocity field exhibits the main spanwise and streamwise vortical structures known to exist in this flow. The streamwise aligned vorticity is shown to connect spanwise vortex tubes.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 3
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    Structure of a high-Reynolds-number turbulent wake in supersonic flow (1984)
    Cambridge University Press
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    Publication Date: 1984-06-01
    Description: An experimental study of a high-Reynolds-number turbulent wake in supersonic flow is performed using space and space–time correlation measurements by means of hot-wire anemometry. The correlations for the streamwise component of the mass-flux fluctuations are given for six stations starting from the trailing edge down to the asymptotic part. The validity of the Taylor's hypothesis is tested, the convection velocities are determined and the downstream evolution of the optimum space–time correlation is given; the frequency spectra are discussed and the integral lengths are analysed. Finally, the three-dimensional isocorrelation surfaces are given at the six test stations and discussed in relation to classical incompressible-flow results. The downstream evolution of the correlations shows that the two sides of the wake are statistically independent near the trailing edge, and a statistical link is gradually established during the wake development. A three-zonal description of wakes generated by fully developed turbulent boundary layers applies as well for mean quantities (velocity, width) as for turbulence correlations. In the near-wake region the overall structure of the isocorrelation curves is close to that observed in turbulent boundary layers in incompressible flows; some low-frequency phenomena are observed in this region. In the latest part of the wake, an asymptotic state is reached for all the correlation characteristics; the final state reached is not explained by the double-roller-eddy model established for lower-Reynolds-number wakes; it appears that wakes generated by fully turbulent boundary layers behave quite differently from initially laminar wakes, and new turbulent structure models for high-Reynolds-number wakes are to be devised. © 1984, Cambridge University Press. All rights reserved.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 4
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    On the coherent structures and stability properties of a leading-edge separated aerofoil with turbulent recirculation (2011)
    Cambridge University Press
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    Publication Date: 2011-08-19
    Description: The present study is motivated by a need to produce stability modes to assist in the understanding and control of unsteady separated flows. The flow configuration is a NACA 0015 aerofoil with laminar leading-edge separation and turbulent recirculation. In previous water tunnel experiments, this flow configuration was measured in an unperturbed (uncontrolled) separated state, and a harmonically perturbed (controlled) reattached state. This study presents numerical data of the unperturbed case, and recovers stability modes to describe the evolution of perturbations in this environment. The unperturbed flow is numerically generated using large eddy simulation. Its temporal properties are quantified via a Fourier analysis of the velocity time history at selected points in space. The leading-edge shear layer instability is characterized by instantaneous vortex structures, and the bluff body shedding is illustrated by proper orthogonal decomposition modes. Statistical measures of the velocity field agree well with the water tunnel measurements. Finally a stability analysis is undertaken using a triple decomposition to distinguish between the time averaged field, the unsteady scales of motion, and a coherent wave (perturbation). This analysis identifies that perturbations in the region immediately downstream of the separated shear layer have the highest spatial growth rates. The associated frequency is of the order of the sub-harmonic of the shear layer instability. © Cambridge University Press 2011.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 5
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    Development of a nonlinear eddy-viscosity closure for the triple-decomposition stability analysis of a turbulent channel (2010)
    Cambridge University Press
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    Publication Date: 2010-10-08
    Description: 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. © 2010 Cambridge University Press.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Published by Cambridge University Press
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