In solid rocket motors, aluminum particles are included in the propellant to improve the global performances but the distributed combustion of these droplets is suspected to be a driving mechanism of hydrodynamic instabilities. So the accurate simulation of reactive polydisperse sprays strongly coupled to unsteady gaseous flows appears as a major issue for solid rocket motor optimization. In this paper, we only focus on the evaporation process which is a relevant framework and a first validation step before taking into account combustion aspects. We choose a two size moment Eulerian Multi-Fluid method (MF) which has already proved its efficiency to deal with evaporating polydisperse sprays. The aim of this contribution is threefold : to design a numerical coupling method regarding both physics and requirements of industrial computations, to propose an evaporation scheme dedicated to complex evaporation models for MF systems and to implement both developments in an industrial-oriented code. The proposed time splitting strategy is based on a thorough analysis of the multiple timescale nature of evaporating two-phase flows and the constraint to optimize the cost/accuracy ratio. A series of numerical validations on the evaporation scheme are provided before testing the feasability and the potential of our coupling strategy on a simplified solid rocket motor configuration with the CEDRE code developed at ONERA.