Modelling of the diffusion of fluid particles in turbulent flows approaching a circular cylinder by random Fourier modes and random flight |
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Authors: | Y. Sakai J. C. R. Hunt J. C. H. Fung G. Pedrizetti R. J. Perkins |
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Affiliation: | (1) Department of Mechanical Engineering, Nagoya University, 464-01 Nagoya, Japan;(2) Meteorological Office, London Road, RG12 2SZ Bracknell, Berkshire, U.K.;(3) Department of Mathematics, The Hong Kong University of Science & Technology, Clear Water Bay, Kowloon, Hong Kong;(4) Department of Civil Engineering, Universita' di Firenze, Firenze, Italy;(5) DAMTP, University of Cambridge, Silver Street, CB3 9EW Cambridge, U.K. |
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Abstract: | To investigate the diffusion of fluid particles around a cylinder in a turbulent flow, we have developed two new types of model for simulating the trajectory of particles:(1) a model combining random Fourier modes and random flight (RF); (2) a pure kinematic simulation (KS) by random Fourier modes. In model 1 the large-scale turbulence is simulated by a sum of random Fourier modes varying in space and time, and the small-scale random motion of particles is simply modelled by an Itô type of stochastic differential equation with a memory time comparable to the Lagrangian time scaleTsLof the small-scale motion. In model 2, both large- and small-scale turbulence is simulated using random Fourier modes. The change of turbulence around the cylinder is modelled by rapid distortion theory (RDT), although the small-scale motion of particles in the RF model is simply assumed to keep the homogeneous random behaviour. These models give very similar and realistic trajectories showing rapid changes of direction due to the small-scale motion. |
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Keywords: | turbulence diffusion random Fourier modes random flight rapid distortion theory |
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