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Atmospheric air is always contaminated by liquid or solid particles of different size, concentration and chemical composition. This leads to performance degradation during the operation of stationary or flying gas turbines. Erosion and the deposition of particles along the flow path are of particular importance. Multiple numerical studies investigated the influences of these phenomena. However, the basic challenge of modelling the particle wall interaction and its data spread with sufficient accuracy remains. In this work a model that estimates the statistical spread of rebound data due to target surface roughness through analytical considerations is presented. The model predicts the local impact angle of an individual particle by evaluating how deep a particle can theoretically penetrate the target surface with respect to its size. Based on roughness profiles which have been found to be characteristic for performance deterioration in compressor application a sensitivity study is conducted. A dimensionless roughness parameter Φ R was found that characterizes the effect of target surface roughness on rebound spread data. The spread model is connected with a quasi-physical model, to evaluate the effect of surface roughness for a particle's individual rebound behaviour. The synthesized data is discussed by taking into account measurement data reported in literature.

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Erosion damage and particle deposition are crucial wear phenomena in gas turbine engines. As a result, compressor efficiency decreases, stability margin reduces, and maintenance cost increases. Hence, predicting these phenomena in an accurate manner is of paramount importance for a cost-efficient, safe, and sustainable operation. Erosion and particle deposition in the annulus are affected by particle transportation in the fluid and particle-wall interaction. The latter involves the particle impact, the potential damage of the surface and/or the particle, and the particle rebound. Particle rebounds are statistical in nature due to the target surface roughness, the variability in particle sizes, and superimposed effects caused by particle shapes as well as particle rotation and particle break-up during contact. Multiple studies investigated the statistics of particle rebound, providing empirical-based models for median and spread. However, modeling the particle-wall interaction and its data spread on a transparent physical basis allows separating the effect of target roughness from superimposed effects. The presented article pursues this objective by assessing the statistical spread of particle rebound data through multiple techniques and utilizing their interdependencies. It combines experimental, numerical, and analytical considerations. For the first time, coherent boundary conditions for the experimental, numerical and analytical setup allow the distinction of the effect of roughness from the integral effect of the superimposed phenomena. A sandblast test rig equipped with laser measurement equipment was used to measure particle rebound from flat titanium and stainless steel plates at different angles. The numerical setup is developed under OpenFOAM 6 using a RANS solver for transient simulations with compressible media in combination with one-way coupled particle flows. The numerical model includes the rebound spread model proposed by Altmeppen et al. combined with the quasi-analytical rebound model proposed by Bons et al. The statistical spread of particle rebound is investigated for roughness levels that are similar to the ones of deteriorated high-pressure compressor blades as discussed by Gilge et al. The measured surface roughness of the experimentally investigated targets is used as input parameters to the numerical framework. The rebound statistics obtained in the numerical simulation are compared to the rebound data measured in the experiment. Based on this study, conclusions are drawn about which part of the rebound spread is attributable to surface roughness and which is caused by superimposed effects. It was found that the effect of surface roughness as characterized by Altmeppen et al. contributes in the order of 46 % to the rebound spread for small impact angles. However, the share in spread due to roughness gradually decreases with increasing global impact angles to a level of 13 % for angles close to 90°. The remaining percentage of rebound spread is attributed to superimposing phenomena. In addition to the rolling and sliding of aspherical particles, further phenomena such as plastic deformation and erosion of the roughness peaks during contact and the associated dissipation of energy gain in importance for steeper impact angles. Therefore, the effect of surface roughness should not be neglected in numerical simulations of particle-laden flows. Modeling the superimposed phenomena which are observed to be dominating at high impact angles opens up a further field of research.

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