This paper is on an Eulerian-Eulerian (EE) approach that utilizes Godunov’s scheme to deal with a running shock that interacts with a cloud of particles. The EE approach treats both carrier phase (fluid phase) and dispersed phase (particle phase) in the Eulerian frame. In this work, the fluid equations are the Euler equations for the compressible gas while the particle equations are based on a recently developed model to solve for the number density, velocity, temperature, particle sub-grid scale stresses, and particle sub-grid scale heat fluxes. The carrier and dispersed phases exchange momentum and heat, which are modeled through incorporating source terms in their equations. Carrier and dispersed phase equation form a hyperbolic set of differential equations, which are numerically solved with Godunov’s scheme. The numerical solutions are obtained in this work for a two-dimensional normal running shock interacting with a rectangular cloud of particles. The results generated by the EE approach were compared against the results that were generated by a well-stablished Eulerian-Lagragian (EL) approach that treats the carrier phase in an Eulerian frame, while does the dispersed phase in a Lagrangian framework where individuals particles are traced and solved. For the considered configuration, the EE approach reproduced themore »
Sparse identification of multiphase turbulence closures for coupled fluid–particle flows
In this work, model closures of the multiphase Reynolds-averaged Navier–Stokes (RANS) equations are developed for homogeneous, fully developed gas–particle flows. To date, the majority of RANS closures are based on extensions of single-phase turbulence models, which fail to capture complex two-phase flow dynamics across dilute and dense regimes, especially when two-way coupling between the phases is important. In the present study, particles settle under gravity in an unbounded viscous fluid. At sufficient mass loadings, interphase momentum exchange between the phases results in the spontaneous generation of particle clusters that sustain velocity fluctuations in the fluid. Data generated from Eulerian–Lagrangian simulations are used in a sparse regression method for model closure that ensures form invariance. Particular attention is paid to modelling the unclosed terms unique to the multiphase RANS equations (drag production, drag exchange, pressure strain and viscous dissipation). A minimal set of tensors is presented that serve as the basis for modelling. It is found that sparse regression identifies compact, algebraic models that are accurate across flow conditions and robust to sparse training data.
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- Journal of Fluid Mechanics
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- National Science Foundation
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