Erosion Modelling in Turbomachinery CFD

Abstract

The prediction of fan and compressor blade erosion owing to particle ingestion poses a challenging problem to state-of-the-art turbomachinery CFD. Material wear by impacting particles leads to a change of shape of the leading and trailing edges of the blades, an over-all reduction of blade chord length and an increase of surface roughness. While the prediction of this process is currently relying on fully empirical methods based on company experience, a semi-empirical approach based on numerical simulation is aspired in the future. For a reliable numerical prediction, a multi-phase approach with separate representations of the continuous and the dispersed phase is necessary. While the former is modelled with the classical Finite-Volume Navier-Stokes method, the latter is captured using a Lagrangian particle-tracking ansatz. Making several assumptions, viz. a neglection of the volume fraction of the dispersed phase and the drag reduction due to large particle numbers, the reduction of the particles to moving mass points and the lumping of several physical particles to a representative computational particle, a force balance - the Basset-Boussinesq-Oseen (BBO) equation with a posteriori extensions - is evaluated over each computational particle. Forces evaluated, among others, include aerodynamic drag, pressure, gravitational, centripetal and Coriolis forces. The particle movement is subsequently computed by integration of the particle acceleration. Since the dispersed phase fraction is small enough for the flows under consideration, a one-way coupling, in which feedback of the dispersed on the continuous phase can be safely neglected, is employed. Turbulent dispersion is taken care of by invoking a Discrete Eddy Model (DEM). The material wear caused by particle impacts is generally a non-trivial function of a wide variety of parameters, including particle mass and shape, impact angle and velocity as well as the material properties of the wall and the particle. It is usually determined by more or less simplified empirical relations, here, the approach of Tabakoff and Grant is used. The Lagrangian particle tracker based on the BBO equation and the erosion model have been implemented in the TRACE code, the DLR solver for turbomachinery flows. Specific features include a mixing-plane treatment with pitch-ratio scaling enabling multi-stage computations, particle break-up modelling and variable restitution coefficients. The capabilities of the solver for erosion prediction is demonstrated on various testcases.