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Ice crystals ingested by a jet engine at high altitude can partially melt and then accrete within the compressor, potentially causing performance loss, damage and/or flameout. Several studies of this ice crystal icing (ICI) phenomenon conducted in the RATFac (Research Altitude Test Facility) altitude chamber at the National Research Council of Canada (NRCC) have shown that liquid water is required for accretion. CFD-based tools for ICI must therefore be capable of predicting particle melting due to heat transfer from the air warmed by compression and possibly also due to impact with warm surfaces. This paper describes CFD simulations of particle melting and evaporation in the RATFac icing tunnel for the former mechanism, conducted using a Lagrangian particle tracking model combined with a stochastic random walk approach to simulate turbulent dispersion. Inter-phase coupling of heat and mass transfer is achieved with the particle source-in-cell method.