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Conference on Turbulence and Interactions TI2006 May June Porquerolles France

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Conference on Turbulence and Interactions TI2006, May 29 - June 2, 2006, Porquerolles, France Turbulence modification by periodically modulated scale-dependent forcing A. K. Kuczaj†,?, B. J. Geurts†,‡, D. Lohse?, W. van de Water‡ †Multiscale Modeling and Simulation, J.M. Burgers Center, Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands ‡Fluid Dynamics Laboratory, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands, ?Physics of Fluids, J.M. Burgers Center, Department of Applied Physics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands, ?E-mail: ABSTRACT The response of turbulent flow to time-modulated forcing is studied by direct numerical simulation of the Navier-Stokes equations. The forcing is modulated via periodic energy input variations at a frequency ?. Such forcing of the large-scales is shown to yield a response maximum at frequencies in the range of the inverse of the large-eddy turnover time. Time-modulated broad-band forcing is also studied in which a wide spectrum of length-scales is forced simultaneously. If smaller length-scales are explicitly agitated by the forcing, the response maximum is found to occur at higher frequencies and to become less pronounced.

  • response maxima

  • flow has

  • scale forcing

  • dependent modulation

  • has become

  • turnover time

  • modulated turbulence


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Conference on Turbulence and Interactions TI2006, May 29  June 2, 2006, Porquerolles, France
Turbulence modification by periodically modulated scaledependent forcing
,∗ †,?A. K. Kuczaj, B. J. Geurts, D. Lohse, W. van de Water Multiscale Modeling and Simulation, J.M. Burgers Center, Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands Fluid Dynamics Laboratory, Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands, ? Physics of Fluids, J.M. Burgers Center, Department of Applied Physics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands, Email: a.k.kuczaj@utwente.nl
ABSTRACT The response of turbulent flow to timemodulated forcing is studied by direct numerical simulation of the NavierStokes equations. The forcing is modulated via periodic energy input variations at a frequencyω. Such forcing of the largescales is shown to yield a response maximum at frequencies in the range of the inverse of the largeeddy turnover time. Timemodulated broadband forcing is also studied in which a wide spectrum of lengthscales is forced simultaneously. If smaller lengthscales are explicitly agitated by the forcing, the response maximum is found to occur at higher frequencies and to become less pronounced. In case the forced spectrum is sufficiently wide, a response maximum was not observed. At sufficiently high frequencies the amplitude of the kinetic energy response decreases as1, consistent with theoretical predictions.
INTRODUCTION
Forcing of turbulent flow has been applied since many years in computational models, primarily aimed at studying basic problems of turbulence dynamics. Although forcing was successfully used in fundamental studies of classical turbu lence, so far explicit forcing has rarely been taken into account in modeling of turbulent flows that are of more direct interest in industrial applications.
Recently, turbulence driven by a timeperiodic energy input rate was theoretically analyzed [1,2] and the resonance maxima were predicted,
based on meanfield theory and simulations in volving the GledzerOhkitaniYamada (GOY) model and the reduced wave vector approxima tion (REWA). The resonance phenomenon was also confirmed by direct numerical simulations of the full Navier–Stokes equations [3].
On the experimental side, recent work concerning the timeperiodic energy injection rate to a fluid inthevonKa´rm´answirlgeometry[4],or,concerning flows that are periodically driven by two counterrotating stirrers [5], provides evidence that modulation in time of the external forcing can lead to different degrees of turbulence re sponsiveness. The magnitude of the response de pends on the modulation frequency and can de