Eulerian—Lagrangian approach

Aerosol production and transport over the oceans are of interest in studies concerning cloud physics, air pollution, atmospheric optics, and air-sea interactions. However, the contribution of sea spray droplets to the transfer of moisture and latent heat from the sea to the atmosphere is not well known. In an effort to investigate these phenomena, Edson et al.[12l used an interactive Eulerian-Lagrangian approach to simulate the generation, turbulent transport and evaporation of droplets. The k-e turbulence closure model was incorporated in the Eulerian-Lagrangian model to accurately simulate... 

Multiphase flows involving dispersed phases (particles, droplets or bubbles) using mixed Eulerian-Lagrangian approaches both with one-way and two-way coupling... 

Eulerian approach can be reduced significantly (Sokolichin et al, 1997). Especially for dispersed flows with a high volume fraction of the dispersed phase, the increased computational requirements of mixed Eulerian-Lagrangian approaches should be mentioned as a disadvantage. 

Fig. 11. Typical computational results obtained by Lapin and Liibbert (1994) with a mixed Eulerian-Lagrangian approach. Liquid phase velocity pattern (left) and the bubble positions (right) in a wafer column (diameter, 1.0 m height, 1.5 m) where the bubbles are generated uniformly over its entire bottom. (Reprinted from Chemical Engineering Science, Volume 49, Lapin, A. and Liibbert, A., Numerical simulations of the dynamics of two-phase gas-liquid flows in bubble columns, p. 3661, copyright 1994 with permission from Elsevier Science.)...

FIGURE 4.1 Modeling approaches for multiphase flows, (a) Volume of fluid approach, (b) Eulerian-Lagrangian approach, (c) Eulerian-Eulerian approach. 

With a Eulerian-Lagrangian approach, processes occurring at the particle surface can be modeled when simulating particle trajectories (for example, the process of dissolution or evaporation can be simulated). However, as the volume fraction of dispersed phase increases, the Eulerian-Lagrangian approach becomes increasingly computation intensive. A Eulerian-Eulerian approach more efficiently simulate such dispersed multiphase flows. 

In the second part, flow in the vapor space of the separator, where the gas phase is a continuous phase, was modeled. An Eulerian-Lagrangian approach was used to simulate trajectories of the liquid droplets since the volume fraction of the dispersed liquid phase is quite small. The grid used for the vapor space is shown in Fig. 9.20. The simulated gas volume fraction distribution near the gas-liquid interface and corresponding gas flow in the vapor space are shown in Fig. 9.22. The gas volume fraction distribution and the gas velocity obtained from the model of the bottom portion of the loop reactor were used to specify boundary conditions for the vapor space model. In addition to the gas escaping from the gas-liquid interface, it is necessary to estimate the amount of liquid thrown into the vapor space by the vapor bubbles erupting at the... 

The main advantage of the Eulerian-Lagrangian approach (i.e., compared to the alternative Euler-Euler model described in the next subsection) is its flexibility with respect to the incorporation of the microscopic transport phenomena. Particle dynamics can in principle be described in detail, a particle size distribution can easily be incorporated, direct particle-particle interactions can be accounted for as well as the hydrodynamic interaction between neighboring particles. 

Unlike the aforementioned models, Fyhr and Rasmuson [41,42] and Cartaxo and Rocha [43] used an Eulerian-Lagrangian approach, in which the gas phase is assumed as the continuous phase and the solids particles are occupying discrete points in the computational domain. As a consequence, mass, momentum, and energy balance equations were solved for each particle within the computational domain. 

Three-dimensional steady-state calculations of drying process in vertical pneumatic dryer were performed by [21], The theoretical model is based on two-phase Eulerian-Lagrangian approach and incorporates advanced drying kinetics for wet particles. The model was utilized for simulation of the drying process of wet PVC and silica particles in a large-scale vertical pneumatic dryer. 

The main advantage of the Eulerian-Lagrangian formulation comes from the fact that each individual bubble is modeled, allowing consideration of additional effects related to bubble-bubble and bubble-liquid interactions. Mass transfer with and without chemical reaction, bubble coalescence, and redispersion, in principle, can be added directly to an Eulerian-Lagrangian hydrodynamic model. The main disadvantage of the Eulerian-Lagrangian approach is that only a limited number of particles (bubbles) can be tracked, such as when the superficial gas velocity is low (Chen et al., 2005), due to computer limitations. 

Besides the Eulerian—Eulerian approaches (say, TFM and SFM) discussed above, various Eulerian—Lagrangian approaches have been proposed and developed rapidly in recent years, say, CFD-DEM (Tsuji et al, 1993 Xu... 

The experiments reported by Horio et al (1988) were used to validate the EMMS/DP drag model for Eulerian—Lagrangian approaches. The riser was simplified with 2D, rectangular domain. In the simulations, air enters the riser from the bottom with a uniform superficial velocity, the top of the domain is set to be a pressure oudet for the gas phase, and the entrained particles are directly returned to the riser from the bottom to maintain the... 

TFM and the MP-PIC modeling that is partly continuum based. That is, subgrid modeHng is needed for both Eulerian-Eulerian and Eulerian-Lagrangian approaches. 

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