This paper aims to numerically examine the effectiveness of a water spraying system in mitigating shock wave propagation. The system holds significant importance in various industrial applications, particularly in mitigating potential hydrogen explosions within the enclosed containment structures of nuclear reactors. A new reduced-order model has been developed for investigating the dispersion topology of particles. To validate the effectiveness of this model, its results are compared with those obtained from direct numerical simulations, providing a comprehensive understanding of particle dispersion dynamics. A series of numerical simulations, primarily in one- and two-dimensional settings, are conducted to investigate the interaction between shock waves and a cloud of polydispersed particles, considering both air and hydrogen-air mixtures as carrier gases. The findings reveal that the polydispersion of cloud particles, especially those with smaller diameters, exerts a more pronounced attenuation effect on shock wave propagation compared to the cases of monodispersed particles and particle-free scenarios.