A semi-Lagrangian transport method for kinetic problems with application to dense-to-dilute polydisperse reacting spray flows

Abstract

For sprays, as described by a kinetic disperse phase model strongly coupled to the Navier-Stokes equations, the resolution strategy is constrained by accuracy objectives, robustness needs, and the computing architecture. In order to leverage the good properties of the Eulerian formalism, we introduce a deterministic particle-based numerical method to solve transport in physical space, which is simple to adapt to the many types of closures and moment systems. The method is inspired by the semi-Lagrangian schemes, developed for Gas Dynamics. We show how semi-Lagrangian formulations are relevant for a disperse phase far from equilibrium and where the particle-particle coupling barely influences the transport; i.e., when particle pressure is negligible. The particle behavior is indeed close to free streaming. The new method uses the assumption of parcel transport and avoids to compute fluxes and their limiters, which makes it robust. It is a deterministic resolution method so that it does not require efforts on statistical convergence, noise control, or post-processing. All couplings are done among data under the form of Eulerian fields, which allows one to use efficient algorithms and to anticipate the computational load. This makes the method both accurate and efficient in the context of parallel computing. After a complete verification of the new transport method on various academic test cases, we demonstrate the overall strategy's ability to solve a strongly-coupled liquid jet with fine spatial resolution and we apply it to the case of high-fidelity Large Eddy Simulation of a dense spray flow. A fuel spray is simulated after atomization at Diesel engine combustion chamber conditions. The large, parallel, strongly coupled computation proves the efficiency of the method for dense, polydisperse, reacting spray flows.

On Multi-Fluid models for spray-resolved LES of reacting jets

“…So the characteristic times for the two-way coupled system get shorter with higher liquid loading. This implies that the discrepancies introduced by spherical closures do not have a significant impact in the regions where loading is high, as suggested in Doisneau et al [18] and verified for the liquid core. In these regions, the overall dynamics is dominated by the liquid so the coupling actually maintains the velocities and temperatures close to equilibrium.…”

“…Euler-Euler modeling of sprays is known for requiring dedicated numerical methods and only recent progress has enabled its use [16]. A novel semi-Lagrangian transport scheme has been devised by Doisneau et al [18] together with a splitting method that efficiently enforces strong coupling between the two phases. This scheme achieves realizable transport of the moments, whatever the size and velocity reconstructions are, so that no clipping is needed.…”

“…In the following and without loss of generality, we consider one section so that indices k are replaced by a single section l. Multiple size intervals and the corresponding sets of moments can be used to describe polydispersity with higher accuracy [22,27,62]. This strategy is under development for the Spray A case [18]. We resort to two moments in size in the one section chosen.…”

“…But the challenges to enable spray-resolved simulations are i) a model that describes both phases accurately and is compatible with ii) a transport scheme that preserves the steep fronts and the vacuum zones, and iii) an overall integration strategy that achieves strong coupling efficiently in the context of massively-parallel computing. These requirements match the features of Euler-Euler spray modeling [16][17][18]. Such simulations can be costly, but can potentially be used as numerical experiments to devise next-generation subgrid models or datasets for Model Order Reduction [19,20].…”

A Model for Fuel Spray Formation with Atomizing Air

“…Kvasnak et al [8] included the effect of droplet deformation and breakup to their models. Recent advances for using Eulerian-Lagrangian approach for spray modelling was reported by Kolakaluri et al [9], Keller et al [10], and Doisneau et al [11], among others. Hoyas et al [12] performed two-dimensional Eulerian-Lagrangian spray simulations in the near-nozzle region.…”