A numerical formulation for fully resolved simulations of freely moving rigid particles in turbulent flows is presented. This work builds upon the fictitious-domain based approach for fast computation of fluid-rigid particle motion by Sharma & Patankar ([1] Ref. J. Compt. Phys., (205), 2005). The approach avoids explicit calculation of distributed Lagrange multipliers to impose rigid body motion and reduces the computational overhead due to the particle-phase. Implementation of the numerical algorithm in co-located, finite-volume-based, energy conserving fractional-step schemes on structured, Cartesian grids is presented. The numerical approach is first validated for flow over a fixed sphere at various Reynolds numbers and flow generated by a freely falling sphere under gravity. Grid and time-step convergence studies are performed to evaluate the accuracy of the approach. Finally, simulation of 125 cubical particles in a decaying isotropic turbulent flow is performed to study the feasibility of simulations of turbulent flows in the presence of freely moving, arbitrary-shaped rigid particles.