Effective semi-empirical model of nozzle thermo-chemical erosion in solid rocket motors

Solid rocket motors for launch vehicle, since their typical high operative pressure and long combustion time, are inherently subjected to nozzle throat erosion phenomena due to their intrinsic functioning. The nozzle ablation needs to be considered during the SRM design phase, in order to match the desired SRM performance, but also for the exploitation phase of the SRM, since it is important for the characterization of the SRM actual functioning (defined through non-ideal parameters and SRM actual efficiencies). The nozzle throat erosion entails performance loss, due to the reduction of the nozzle expansion ratio during time with respect to the initial one, which are the more relevant, the smaller is the SRM, for the same average operative pressure and combustion time. This paper presents an effective semi-empirical model of nozzle throat erosion of SRMs working in diffusionlimited regime (typical of modern aluminized propellant grains), which introduces the main dependency of the phenomenon: nozzle size and shape, propellant grain and nozzle thermal protections characteristics and motor operative conditions. The semi-empirical model is shown to be well correlated with full-CFD characterization of the nozzle throat erosion phenomena, for a wide range of SRMs and propellant grain, providing the assessment of the nozzle throat erosion in good agreement with the experimental data of the three solid stages of VEGA launch vehicle (P80, Zefiro 23 and Zefiro 9), for the static firing tests performed during VEGA development phase