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Direct numerical simulation of turbulence modulation by particles in isotropic turbulence

Published online by Cambridge University Press:  25 November 1998

MARC BOIVIN
Affiliation:
Laboratoire National d'Hydraulique, Electricité de France, 6 Quai Watier, 78400 Chatou, France Present address: IBM, 224, bd John Kennedy, 91105 Corbeil-Essonnes, France.
OLIVIER SIMONIN
Affiliation:
Laboratoire National d'Hydraulique, Electricité de France, 6 Quai Watier, 78400 Chatou, France Institut de Mecanique des Fluides, Institut National Polytechnique/ENSEEIHT, 31400 Toulouse, France
KYLE D. SQUIRES
Affiliation:
Mechanical and Aerospace Engineering Department, Arizona State University, Box 876106, Tempe, AZ 85287-6106, USA

Abstract

The modulation of isotropic turbulence by particles has been investigated using direct numerical simulation (DNS). The particular focus of the present work is on the class of dilute flows in which particle volume fractions and inter-particle collisions are negligible. Gravitational settling is also neglected and particle motion is assumed to be governed by drag with particle relaxation times ranging from the Kolmogorov scale to the Eulerian time scale of the turbulence and particle mass loadings up to 1. The velocity field was made statistically stationary by forcing the low wavenumbers of the flow. The calculations were performed using 963 collocation points and the Taylor-scale Reynolds number for the stationary flow was 62. The effect of particles on the turbulence was included in the Navier–Stokes equations using the point-force approximation in which 963 particles were used in the calculations. DNS results show that particles increasingly dissipate fluid kinetic energy with increased loading, with the reduction in kinetic energy being relatively independent of the particle relaxation time. Viscous dissipation in the fluid decreases with increased loading and is larger for particles with smaller relaxation times. Fluid energy spectra show that there is a non-uniform distortion of the turbulence with a relative increase in small-scale energy. The non-uniform distortion significantly affects the transport of the dissipation rate, with the production and destruction of dissipation exhibiting completely different behaviours. The spectrum of the fluid–particle energy exchange rate shows that the fluid drags particles at low wavenumbers while the converse is true at high wavenumbers for small particles. A spectral analysis shows that the increase of the high-wavenumber portion of the fluid energy spectrum can be attributed to transfer of the fluid–particle covariance by the fluid turbulence. This in turn explains the relative increase of small-scale energy caused by small particles observed in the present simulations as well as those of Squires & Eaton (1990) and Elghobashi & Truesdell (1993).

Type
Research Article
Copyright
© 1998 Cambridge University Press

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