Eulerian Lagrangian Multiphase Model

[Odon Irving]

Iam simulating the two-phase solid particles - gas in an Eulerian-Lagrangian frame using DDPM and a vertical pipe. I activated the multiphase model and thus defined my solid phase and my gas phase. Within the solid phase, activate the 'Granular' option in addition to selecting its properties.

The first problem is a missing setting somewhere in the model. If you've been turning things on and off you may have caused a glitch in the set up. In that case you may have to start again if you can't find it.

The incomplete message means you're not tracking particles long enough: they're running out of integration steps before leaving the domain. However, the continuity equation is very definitely not happy so I suspect incomplete particles are the least of your problems.

Hello Rob, I am using DDPM because part of my research is track the particles in a Lagrangian framework including the particle volume fraction in it, and because the volume fraction of discrete phase is more than 10%.

You'll need to be more specific. Multiphase is a mix of understanding the application and required outcome AND how then to best model it. I've modelled cyclones with DPM, Ansys Rocky (DEM) and Eulerian: all three are correct approaches but each was to capture a different requirement.

If you use 22R2 the DDPM model has had some work done to help with higher volume fractions. I also suggest increasing the max number of steps on the DPM panel. If you're losing that many parcels as incomplete you have a lot of unaccounted mass to worry about: I assume you are tracking the particles as transient?

Hello Rob, unfortunately, I don't have the Ansys Rocky software, and the version we handle is 22R1.

Yes, I am tracking the particles as transient. Any comment about this option?

Now I am working with the option to increase the maximum number of steps; I have already started the calculation, and so far, it is tracking the particles.

We present a Computational Fluid Dynamics (CFD) framework for the numerical simulation of the Laser Metal Deposition (LMD) process in 3D printing. Such a framework, comprehensive of both numerical formulations and solvers, aims at providing a sufficiently exhaustive scenario of the process, where the carrier gas, modeled as an Eulerian incompressible fluid, transports metal powders, tracked as Lagrangian discrete particles, within the 3D printing chamber. On the basis of heat sources coming from the laser beam and the heated substrate, the particle model is developed to interact with the carrier gas also by heat transfer and to evolve in a melted phase according to a growth law of the particle liquid mass fraction. Enhanced numerical solvers, characterized by a modified Newton-Raphson scheme and a parallel algorithm for tracking particles, are employed to obtain both efficiency and accuracy of the numerical strategy. In the perspective of investigating optimal design of the whole LMD process, we propose a sensitivity analysis specifically addressed to assess the influence of inflow rates, laser beams intensity, and nozzle channel geometry. Such a numerical campaign is performed with an in-house C++ code developed with the deal.II open source Finite Element library, and publicly available online.

However, the complexity of the LMD process requires both model and numerical tools capable to cover a wide spectrum of physical phenomena that involve powder-particle transportation, interaction between particles and carrier gas, energy exchange with laser beam source, and then powder material phase-change (solid-liquid phase transition).

Many authors have published papers tackling such a process through Computational Fluid Dynamics (CFD) approaches, working with particle-tracking methods for predicting particle flow in a Lagrangian description, combined with Eulerian methods for describing the carrier gas flow. Zhang and Coddet developed three-dimensional CFD models in Ansys Fluent, solved using a Discrete Phase Modeling (DPM), i.e., a particle-tracking method that computes the particle dynamics, while Navier-Stokes equations have been considered to model the inert gas [2]. The same CFD numerical model is employed by Zeng et al. with the purpose of better understanding the powder deposition process and analyzing the influence of the geometrical and processing parameters, such as the standoff distance, the volumetric gas flow rate, and the powder mass flow rate, on the quality of the LMD printing technology [3].

Along the same perspective, similar approaches aiming at optimizing nozzle design and validating experimental measurements on the particle flow can be found in some early contributions [4, 5]. In particular, Tabernero et al. have used the particle tracking method implemented in the Ansys Fluent code to simulate the powder flux on a real continuous coaxial nozzle to predict the powder distribution shape, together with particle velocities and trajectories [4]. Arrizubieta et al. [5] have investigated optimal values of the carrier and shielding gases flow rates. Other works have employed numerical strategies based on DPM approaches to explore how nozzle geometry, powder properties, and feeding parameters can improve LMD process efficiency [6,7,8].

More recent contributions on gas/powder stream characteristics can be found in [9], where to perform the numerical modeling of a jet flow, Ferreira et al. have employed a 2D axisymmetric models of both the gas and powder streams, with a Reynolds Averaged Navier-Stokes (RANS) turbulent model implemented with the COMSOL Multiphysics software. The adopted Euler-Lagrange model revealed a good agreement between numerical and experimental results, pointing out the great impact of particle rebound conditions that should be linked to the particle concentration for a correct description of the powder stream structure, especially for nozzles with small exit diameters. Finally, the capability of fully Eulerian approaches and coupled Eulerian-Lagrangian approaches, both addressed to predict geometrical properties of the powder cone formed out from the nozzle, were investigated in [10]. By developing a customized OpenFOAM code and supported by experimental evidences, the authors proved how the Eulerian-Lagrangian approach, albeit more expensive than a fully Eulerian one, is able to accurately predict the experimented behavior, where the total flux divaricates in separate streams after the focal point.

The above-mentioned works neglect the thermal problem, i.e., the interaction between the particle flow and the laser beam source, aspects that play a crucial role in the entire LMD process. An interesting contribution in this direction is presented for instance in the work by Ibarra-Medina and Pinkerton [11], where a thermal coupling between powder flow and laser beam is proposed. In particular, in addition to various interactions that occur during the printing process, powder stream formation, powder heating and mass deposition into the melt pool are also considered and analyzed by using the commercial software CFD-ACE+. Numerical results have proved that mass concentration within the powder stream, overall powder stream heating, and mass deposition rate, are strongly dependent on the distance between the nozzle tip and the substrate. Wen et al. in [12] have also focused on laser-particle interaction process, which is treated through a model of particle temperature evolution: by considering particle morphology and size distribution based on real powder samples, they were able to predict the powder stream structure and the multi-particle phase change as liquid fraction evolution throughout the entire process.

A more recent contribution is provided in [13], where Guan and Zhao have developed a numerical model for powder stream dynamics and heating process to accurately describe the coaxial powder flow and its interaction with the laser beam. A RANS approach is proposed for turbulent continuum gas flows, while DPM describes the dynamic powder behavior. A two-way coupling approach is adopted to account for the momentum transfer between gas and powder, together with a thermal model for powder streams interacting with a Gaussian laser beam. The obtained results of powder stream are compared with the experimental results from published literature, showing a good agreement. Finally, in order to model complex free surface, fluid flow, thermal and laser interaction evolution, a novel multiphase thermo-fluid formulation based on a diffusive Level Set method coupled with the Navier-Stokes, energy conservation and radiative transport equations are implemented [14]. The reported results show that the penetration of the powder within the focal spot of the laser is favored by the large velocity of the particles, whereas the evaporation across the surface of the particles, due to laser absorption, drives powder motion either inside or outside the melt pool. Moreover, other features affecting the melt pool dimensions, such as the laser absorption, can be altered by a large amount of powder material that shields the melt pool from the energy source produced by the laser beam.

The current literature shows that several numerical strategies have been implemented to aid the design of LMD set-ups, leading to possible optimal conditions of minimizing thermal gradients and speeding up the whole deposition process [15], but a comprehensive numerical tool, modeling the various multiphysics phenomena involved in fluid-particles interaction, still lacks.

Within an Eulerian formulation we model the carrier gas as an advection-diffusion fluid problem combining Navier-Stokes with heat exchange equations; this is accompanied by a Lagrangian formulation for tracking powder particles that are modeled to exchange mass, momentum, and heat energy with the fluid and, at the same time, to evolve their liquid mass fraction according to laser beam source irradiation [16].

For this purpose, we developed a C++ code using the open source Finite Element library deal.II [17]. To accurately and efficiently represent the advection-diffusion problem [18], the Eulerian coupled problem is tackled through a fully nonlinear formulation of the Navier-Stokes equations, solved with a modified Newton-Raphson scheme. A stabilization method is introduced for heat equations in reason of high Pclet numbers (cf. [19,20,21,22]). In order to improve the performance of the Lagrangian problem, a parallel code is implemented for particles tracking.

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