Is Stokes number an appropriate indicator for turbulence modulation by particles of Taylor-length-scale size?

It has been established both numerically and experimentally [see, e.g., A. Ferrante and S. E. Elghobashi, “On the physical mechanisms of two-way coupling in particle-laden isotropic turbulence,” Phys. Fluids 15, 315 (2003); T. S. Yang and S. S. Shy, “Two-way interaction between solid particles and homogeneous air turbulence: Particle settling rate and turbulence modification measurements,” J. Fluid Mech. 526, 171 (2005)] that the Stokes number, τp/τk, can be used as an indicator to determine the extent to which small particles (dp<η) modify the turbulence structure for fixed values of their volume fraction and mass fraction, where dp, τp, η, and τk are the particle diameter, the response time, the Kolmogorov length, and time scales, respectively. The objective of the present study is to investigate whether the Stokes number can also be used as an indicator for the modulation of turbulence by particles of the Taylor-length-scale size, i.e., dp∼λ⪢η. We employ direct numerical simulation with an immersed boundary method to fully resolve the flow around 4800 freely moving particles of Taylor-length-scale size (dp∼λ) in decaying isotropic turbulence with initial Taylor-microscale Reynolds number, Reλ=110, using a computational mesh of 5123 grid points. Our results show that particles whose diameter dp∼λ⪢η and have identical τp (but different dp and/or ρp) can have different effects on isotropic turbulence. Thus, τp/τk should not be used as an indicator of turbulence modulation by these “large” particles.