Polydisperse evaporating spray study is complex due to the influence of a large number of physical parameters. Several studies have performed CFD simulations to investigate the cooling performance of water spray systems, but a few have investigated their impact upon heat exchangers. For industrial applications, developing a new and simple approach to simulate polydisperse evaporating sprays upon complex 3D geometries is of great interest. Thus this paper is the first contribution to a CFI) numerical tool development to study water spray impact on heat exchangers and presents a CFD water spray model. The spray model is divided into two steps: the spray formation and its dispersion in air flow. The spray development step describes the moment from droplet injection to the position where droplet velocity equals air velocity. This position and the spray dimension are accessed through the droplet trajectory analysis, while the amount of liquid water evaporated is obtained by integrating the droplet size decrease equation. This first part provides boundary conditions for the second step used in a 3D CFD software: CodeSaturne. This CFD code solves the Navier-Stokes equations for the spray with the k-epsilon turbulence model. Three transport variables are introduced: the liquid potential temperature, theta(L), the total water specific humidity, q(w) which are conservative variables for the evaporation processes; and the total number, of droplets, N-c. The droplet evaporation is added to the N-c equation through a source term approach. A lognormal law is also used to represent and follow the evolution of the droplet spectra. The model results are compared with experimental results from droplets injected in counter-flow configurations in a wind tunnel. Temperature fields show good agreements with the experimental data. Finally, this paper provides a parametric analysis of water evaporation and air cooling upon a specified surface. The impacts of the relative humidity, spray angle, water mass flow rate and droplet size distribution are investigated. Our approach is an alternative to classical Lagrangian approaches used in spray applications. It provides accurate and consistent results with low computational time in comparison with the literature.