A Note On Crossing-trajectory Effects In Gas-particle Turbulent Flows
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In the frame of Lagrangian stochastic dispersion models used to predict the behaviour of small inertial particles moving in a turbulent flow, crossing-trajectory effects are generally accounted for by modifying the integral time scales according to the famous analysis of Csanady (J. Atmos. Sci., 20, pp. 201-208, 1963). Here, an alternative theoretical analysis of the time correlation of the fluid velocity fluctuations along a particle trajectory is presented. Analytical expressions of the integral time scales of the fluid seen by the particles in isotropic turbulence are first derived in the asymptotic limit where the mean relative velocity is much larger than the particle velocity fluctuations, then a correction is proposed to extend their applicability over the whole range of mean relative velocity. These expressions do not depend on the presumed shape of the two-point fluid velocity correlations. The predicted time scales in the transverse direction differ from some available proposals in the literature, but are in agreement with other analyses based on an assumed functional form of the turbulence spectrum, at least in the limit of large mean relative velocity.Additionally, some comparisons with numerical predictions obtained in a synthetic Gaussian turbulence show that the present theoretical results are in good agreement with the computations in a large range of mean relative velocity and particle inertia. Keywords: gas-particle flow, particle dispersion, crossing-trajectory, turbulence. 1 Introduction As is well known, the behaviour of small inertial particles moving in a turbulent flow can be described by means of Lagrangian stochastic models that consist in building a proper stochastic process to predict the instantaneous velocity of the fluid seen by a discrete particle. The so-called crossing-trajectory effect is observed when the fluid and particle mean velocities differ due to some external force
gas-particle flow, particle dispersion, crossing-trajectory, turbulence.