Turbofan engine icing threatens compressor operation and service life. Ice crystal ingestion during cruise and descent phases of flight results in smaller, partially melted crystals entering the engine core. Here, crystals can stick to stationary surfaces driven by the presence of a water film, and evaporative and melting heat exchange with the mixed-phase crystals. Modelling of the ice crystal cloud conditions is needed to understand threat areas within the core and operating envelope and to provide a reliable basis for ice accretion modelling at solid surfaces. This thesis, therefore, enhances the accuracy and fidelity of ice crystal icing modelling for turbomachinery applications.The particular emphasis of the model development was in three-dimensional particle transport and accretion, especially in the context of compressor ice crystal icing. Traditionally, icing models have relied on simplified two-dimensional cases or complex three-dimensional studies lacking validation or accuracy assessments. This work bridged this gap by advancing the individual models relevant to icing and examining three-dimensional transport and accretion data.Specifically, warmed substrate accretion was modelled. This is characteristic of compressor ice crystal icing with through casing or through vane heat transfer. Existing codes were extended to three dimensions with turbophoresis and two-way mass energy coupling were introduced along with novel methods to capture the accretion shape and size. These enhancements were shown to be necessary to accurately simulate real-world turbomachinery representative geometry and test conditions, characterised by wall-bounded, highly turbulent, and accelerating flows. The results showed that incorporating turbophoresis and two-way coupling significantly improves the accuracy of transport model predictions, particularly when the melting rates of smaller particulates are considered. Particle melting is known to be a major influencer of accretion initiation.The study also significantly improved numerical integration and modelling of ice crystal icing particles interacting with the gas-phase and surfaces. A dual time stepping method was employed for particle tracking to enable unsteadiness in the gas-phase along the particle residence time. A literature-based stochastic bounce model was introduced to represent roughened surfaces, resulting in appreciable changes in mass and melting distribution after a single impact event. A multi-zone modelling scheme was developed to efficiently model the farfield flows typical of complex experimental test rigs in altitude icing facilities, while allowing test geometries of interest to be independently modelled based on derived boundary conditions.Simulation results of mixed-phase warmed substrate accretion were compared against representative compressor stator vane icing experiments. The findings highlighted the importance of considering wall conditions, as excess accretion on stator vane roots suggested inadequacies in current sticking models or the omission of downstream water and ice sliding along walls. The influence of runback water energy recovery and substrate conduction was characterised.The work advances the understanding of individual physical processes involved in ice crystal icing, providing an improved route to tackle turbofan compressor icing threats, mitigate maintenance costs, engine damage, and design inefficiencies.While the final model is not yet capable of modelling full rotating stages, most icing accretion occurs on stationary components. Thus it is still able to provide predictive insight into engine sub-systems and provides a route to engine certification by analysis in the future.