Although dry ice blasting seems to be a common way of industrial dirt cleaning, so far, a few scientists have addressed their research on this method. This way of dirt removal is based on polluted surface treatment with a high-speed dry-ice air mixture. The cleaning mechanism is carried on by three main phenomena: thermal effect (cooling), abrasion using flow kinetic energy and sublimation. The final force impacting the cleaning surface is a sum of three components: a force of compressed air, a force of solid CO2 particles caused by their velocity and a sublimation force caused by sudden phase change supported by rapid volume growth. One of the crucial issues related to the described cleaning mechanism are parameters of the blasting mixture. The main system component influencing those parameters is the nozzle. The study aimed to analyse selected operational parameters' impact on the dry-ice blasting nozzle operation. For that purpose, a mathematical model of the supersonic, two-phase flow with particle-wall collision mass consumption was built and implemented in the Ansys CFX numerical environment. The crucial part of the modelling was proper dry-ice particles treatment, as their behaviour in the supersonic nozzle has not been well described in the literature so far. The presented model was validated against experimental data, so it can be treated as a valuable tool for further developing dry-ice blasting systems. Simultaneous analysis of modelling and experiment results allows withdrawing precious conclusions. Bench tests confirmed that greater particles are more prone to remove the pollution. The model covers several groups of particles analysis in the field of their behaviour in the nozzle and in the outflow. Particles' transport efficiency was analysed, taking into account vide range of operating parameters. Smaller particles reach higher velocities and are more prone to velocity change due to particle-flow interactions. Massive particles reach maximum velocity in the throat region and then slightly slow down. Nozzle efficiency seems to be independent of particles' mass flow rate in the considered range. Phase change heat consumed due to particle sublimation in the nozzle grows with the particles' mass flow rate and decreases with inlet air pressure in most cases. The knowledge presented in the study may lead to dry-ice blasting process optimisation and contribute to blasting medium and energy savings due to the effective use of the blasting system.