Physics – Fluid Dynamics
Scientific paper
2010-12-23
Physics
Fluid Dynamics
13 pages, 11 figures
Scientific paper
A novel scheme is presented for the direct numerical simulation of two-way coupling between a particle and an incompressible fluid flow maintained in a high-Reynolds-number turbulent regime. The main idea consists in combining a Fourier pseudo-spectral method for the fluid with an immersed-boundary technique to impose the no-slip boundary condition on the surface of the particle. This scheme is shown to converge as the power 3/2 of the spatial resolution. This behavior is explained by the $L_2$ convergence of the Fourier representation of a velocity field displaying discontinuities of its derivative. Benchmarking of the code is performed by measuring the drag and lift coefficients and the torque-free rotation rate of a spherical particle in various configurations of the carrier flow. Such studies show a good agreement with experimental and numerical measurements from other groups, and validate the code. A study of the turbulent wake downstream the sphere is also reported. The mean velocity deficit is shown to behave as the inverse of the distance from the particle, as predicted from classical similarity analysis. This law is reinterpreted in terms of the principle of "permanence of large eddies" that relates infrared asymptotic self-similarity to the law of decay of energy in homogeneous turbulence.
Bec Jeremie
Grauer Rainer
Homann Holger
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