A model of plasma expansion with chemical kinetics has been developed and compared with the free flow model results for a titanium oxide and a metallic titanium target. Optical emission spectroscopy has been applied to compare calculated results with experimental measurements. In the Ti atom time of flight (TOF) measurements, the shifts of peaks has been observed and explained by the results of numerical model as the effect of ion recombination. Our attention has been also focused on the influence of initial conditions on the plume expansion simulation. In particular, changing the initial speed, temperature, pressure and plume extension, the speed of expansion and the width of the TOF peak change. We have generalized the theoretical method here presented to calculate initial conditions for the plume expansion, which show the best agreement with experimental results.