We analyze the aggregation-fragmentation dynamics of inertial particles in a synthetic turbulent flow. This flow is able to reproduce some of the properties of homogeneous isotropic turbulence at the dissipative scale. We consider that aggregation events happen under particle collision, whether fragmentation occurs due to shear forces exerted on the particle by the flow field. We investigate how the time scales of the flow and of the aggregation/fragmentation events can influence the size distribution of aggregates at the steady state.