The control of metal cleanliness has always been a concern for metallurgists since inclusions directly influence the mechanical properties of alloys. In most metallurgical routes, a refining treatment of the liquid alloy is performed, in particular with the aim of improving the metal cleanliness that is achieved via a better control of particle contents and particle size. Since the efficiencies of inclusion removal mechanisms increase with inclusion size, the turbulent aggregation process plays a major role in all refining treatments. Interaction between particles such as aggregation is usually modelled through kinetics kernels which may be difficult to estimate. This paper contributes to express turbulent aggregation kernel taking into account the hydrodynamic effects at the inclusion scale. The numerical approach combines three numerical techniques, a Lattice Boltzmann Method to resolve the flow, an immersed boundary method for the particle-fluid interactions and a Lagrangian tracking for the motion of individual particles. Deterministic simulations of spherical particle pair trajectories leading to collision or avoidance allow us to calculate statistical kernels in a shear flow. The results show a strong influence of the short distance hydrodynamic effects on the collision kernel, particularly when the diameter ratio of the two interacting particles is far from unity. An application of this new aggregation kernel is applied to simulate the time evolution of the particle size distribution in a typical steel gas-stirred ladle.