The discrete Green's function paradigm for two-way coupled Euler–Lagrange simulation

We outline a methodology for the simulation of two-way coupled particle-laden flows. The drag force that couples fluid and particle momentum depends on the undisturbed fluid velocity at the particle location, and this latter quantity requires modelling. We demonstrate that the undisturbed fluid velocity, in the low particle Reynolds number limit, can be related exactly to the discrete Green's function of the discrete Stokes equations. In addition to hydrodynamics, the method can be extended to other physics present in particle-laden flows such as heat transfer and electromagnetism. The discrete Green's functions for the Navier–Stokes equations are obtained at low particle Reynolds number in a two-plane channel geometry. We perform verification at different Reynolds numbers for a particle settling under gravity parallel to a plane wall, for different wall-normal separations. Compared with other point-particle schemes, the Stokesian discrete Green's function approach is the most robust at low particle Reynolds number, accurate at all wall-normal separations. To account for degradation in accuracy away from the wall at finite Reynolds number, we extend the present methodology to an Oseen-like discrete Green's function. The extended discrete Green's function method is found to be accurate within $6\,\%$ at all wall-normal separations for particle Reynolds numbers up to 24. The discrete Green's function approach is well suited to dilute systems with significant mass loading and this is highlighted by comparison against other Euler–Lagrange as well as particle-resolved simulations of gas–solid turbulent channel flow. Strong particle–turbulence coupling is observed in the form of turbulence modification and turbophoresis suppression, and these observations are placed in context of the different methods.

Progresses in Particle-Laden Flows Simulations in Multistage Turbomachinery With OpenFOAM

Numerical simulations of particle-laden flows have received growing attention in the last decade, due to the broad spectrum of industrial applications in which discrete phases prediction is of interest. Among these, ingestion of particles by turbomachinery is an area that is seeing vivid research and studies. The most common technique to tackle this kind of problem is the Eulerian-Lagrangian method, in which individual particles are tracked inside the domain. At the same time, in multi-stage turbomachinery simulations interfaces are needed to couple the flow solution in adjacent domains in relative motion. In this work, an open-source extension for Lagrangian simulations in multistage rotating machines is presented in the foam-extend environment. Firstly, a thorough discussion of the implementation is presented, with particular emphasis on particle passage through General Grid Interfaces (GGI) and mixing planes. Moreover, a mass-conservative particle redistribution technique is described, as such a property is requested at interfaces between Multiple Reference Frame (MRF). The peculiarities of the algorithm are then shown on a relevant test-case. Eventually, three turbomachinery applications are presented, with growing complexity, to show the capabilities of the numerical code in real-life applications. Simulation results in terms of erosion and impacts on aerodynamic surfaces are also presented as examples of possible parameters of interest in particle-laden flow computations.