  We study by means of an Eulerian-Lagrangian model the statistical properties
of velocity and acceleration of a neutrally-buoyant finite-sized particle in a
turbulent flow statistically homogeneous and isotropic. The particle equation
of motion, beside added mass and steady Stokes drag, keeps into account the
unsteady Stokes drag force - known as Basset-Boussinesq history force - and the
non-Stokesian drag based on Schiller-Naumann parametrization, together with the
finite-size Faxen corrections. We focus on the case of flow at low
Taylor-Reynolds number, Re_lambda ~ 31, for which fully resolved numerical data
which can be taken as a reference are available (Homann & Bec 651 81-91 J.
Fluid Mech. (2010)). Remarkably, we show that while drag forces have always
minor effects on the acceleration statistics, their role is important on the
velocity behavior. We propose also that the scaling relations for the particle
velocity variance as a function of its size, which have been first detected in
fully resolved simulations, does not originate from inertial-scale properties
of the background turbulent flow but it is likely to arise from the
non-Stokesian component of the drag produced by the wake behind the particle.
Furthermore, by means of comparison with fully resolved simulations, we show
that the Faxen correction to the added mass has a dominant role in the particle
acceleration statistics even for particle with size in the inertial range.
