Attenuation of turbulence in a periodic cube by finite-size spherical solid particles

To investigate the attenuation of turbulence in a periodic cube due to the addition of spherical solid particles, we conduct direct numerical simulations using an immersed boundary method with resolving flow around each particle. Numerical results with systematically changing particle diameters and Stokes numbers for a fixed volume fraction $\Lambda$ show that the additional energy dissipation rate in the wake of particles determines the degree of the attenuation of turbulent kinetic energy. On the basis of this observation, we propose the formulae describing the condition and degree of the attenuation of turbulence intensity. We conclude that particles with the size proportional to $\lambda/\sqrt{\gamma}$, where $\lambda$ and $\gamma$ are the Taylor length and the mass density ratio between particles and fluid, most significantly reduce the intensity of developed turbulence under the condition that $\gamma$ and $\Lambda$ are fixed.