The P-DNS Method to Solve Particle-Laden Turbulent Fluid Flows

IDELSOHN, SERGIO; GIMENEZ, JUAN M.; EUGENIO OÑATE

ONLINE

Congreso; 15th World Congress on Computational Mechanics (WCCM-XV); 2022

Particle-laden flows refer to a kind of two-phase fluid flow in which one of the phases iscontinuously connected and the other phase is made up of small immiscible particles. Two-phaseflow modeling has a wide variety of scientific and engineering applications: dispersion ofcontamination in the atmosphere, fluidization in combustion processes, deposition of aerosols inaerosol drugs, spread of virus in the air, rain formation in clouds, sand and dust storms,protoplanetary disks, volcanic eruptions, geological sedimentation processes, pharmaceuticalsprays, liquid-fueled combustion and solid rocket motors, are examples of engineering processesthat involve particle-laden flows among many others.The equations governing interactions of particles with fluids in a particle-laden mixture have beenknown for many decades. However, their coupled dynamics often result in complex behaviorsuch as preferential concentration and turbulence modulation. These are still ongoing topics ofresearch. The starting point for a mathematical description of almost any type of fluid flow is theclassical set of Navier–Stokes equations (N-S). To describe particle-laden flows, these equationsmust be modified for the effect of the particles.Typically, the fluid is treated in a Eulerian frame, while the particles are treated in a Lagrangianway. However, problem with the Lagrangian treatment of the particles is that once the numberbecomes large, it may require a prohibitive amount of computational power to track a sufficientlylarge sample of particles required for statistical convergence. In addition, if the particles aresufficiently light, they behave essentially like a second fluid. This is the main objective of thispresentation.On the other hand, due to the interactions between turbulence structure and dispersed particles,turbulence characteristics of momentum and heat transport can be modified by the presence ofparticles. This last phenomenon is known as turbulence modulation and can lead to a significantincrease or decrease in the parameters that regulate turbulence.The authors presented in Ref. [1] a multi-scale method called Pseudo-Direct NumericalSimulation (P-DNS) [2] to study the phenomenon of turbulence modulation in a particle-ladenflows. However, in that article, the particles in both, the fine scale and the coarse scale, weretreated in a discrete way moving in a Lagrangian reference frame within the fluid. In thispresentation, the same P-DNS method will be used to simulate the presence of particles as acontinuum function that moves within the fluid. The result is similar to a fluid mixing problem,with the exception that now the coefficients that regulate the convection of one fluid with respectto the other, are obtained from a direct numerical simulation obtained on a finer scale solvedoffline. In this way, the need to represent each of the particles that move in the fluid is avoided.REFERENCES[1] J. Gimenez; S. Idelsohn; E. Oñate; R. Löhner. A multiscale approach for the numericalsimulation of turbulent flows with droplets ; Arch. Comp. Meth. Engrg.; (2021).[2] S. Idelsohn, J. Gimenez, N. Nigro, E. Oñate., The Pseudo-Direct Numerical SimulationMethod for Multi-Scale Problems Mechanics; Comp. Meth. Appl. Mech. Engrg. 380 (2021).