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  • 1
    Publication Date: 1989-12-01
    Description: A comparison of several commonly used turbulence models (including the K-e model and three second-order closures) is made for the test problem of homogeneous turbulent shear flow in a rotating frame. The time evolution of the turbulent kinetic energy and dissipation rate is calculated for these models and comparisons are made with previously published experiments and numerical simulations. Particular emphasis is placed on examining the ability of each model to predict equilibrium states accurately for a range of the parameter Q/S (the ratio of the rotation rate to the shear rate). It is found that none of the commonly used second-order closure models yield substantially improved predictions for the time evolution of the turbulent kinetic energy and dissipation rate over the somewhat defective results obtained from the simpler K-e model for the unstable flow regime. There is also a problem with the equilibrium states predicted by the various models. For example, the K-e model erroneously yields equilibrium states that are independent of Q/S while the Launder, Reece & Rodi model and the Shih-Lumley model predict a flow relaminarization when Q/S 0.39-a result that is contrary to numerical simulations and linear spectral analyses, which indicate flow instability for at least the range 0 Q/S 0.5. The physical implications of the results obtained from the various turbulence models considered herein are discussed in detail along with proposals to remedy the deficiencies based on a dynamical systems approach. © 1989, 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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  • 2
    Publication Date: 2019-06-28
    Description: Classically it was held that solutions to deterministic partial differential equations (i.e., ones with smooth coefficients and boundary data) could become random only through one mechanism, namely by the activation of more and more of the infinite number of degrees of freedom that are available to such a system. It is only recently that researchers have come to suspect that many infinite dimensional nonlinear systems may in fact possess finite dimensional chaotic attractors. Lyapunov exponents provide a tool for probing the nature of these attractors. This paper examines how these exponents might be measured for infinite dimensional systems.
    Keywords: THEORETICAL MATHEMATICS
    Type: NASA-CR-178291 , ICASE-87-28 , NAS 1.26:178291
    Format: application/pdf
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  • 3
    Publication Date: 2019-07-13
    Description: A variety of turbulence models, including five second-order closure models and four two equation models, are tested for the problem of homogeneous turbulent shear flow in a rotating frame. The model predictions for the time evolution of the turbulent kinetic energy and dissipation rate, as well as those for the equilibrium states, are compared with the results of physical and numerical experiments. Most of the two-equation models predict the same results for all rotation rates (omega/S) in which there is an exponential time growth of the turbulent kinetic energy and dissipation rate. The second-order closures are qualitatively superior since, consistent with physical and numerical experiments, they only predict this type of unstable flow for intermediate rotation rates in the range -0.1 less than or equal to omega/S less than or equal to 1.6. For rotation rates outside this range, there is an exchange of stabilities with a solution whose kinetic energy and dissipation rate decay with time. Although the second-order closures are superior to the two-equation models, there are still problems with the quantitative accuracy of thier predictions.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Symposium on Turbulent Shear Flows; Aug 21, 1989 - Aug 23, 1989; Stanford, CA; United States
    Format: text
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