Eulerian-Lagrangian approach fraction

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. 

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... 

As a matter of fact, in comparison with the Euler-Lagrangian approach, the complete Eulerian (or Euler-Euler) approach may better comply with denser two-phase flows, i.e., with higher volume fractions of the dispersed phase, when tracking individual particles is no longer doable in view of the computational times involved and the computer memory required, and when the physical interactions become too dominating to be ignored. Under these circumstances, the motion of individual particles may be overlooked and it is wiser to opt for a more superficial strategy that, however, still has to take the proper physics into account. 

The second broad area in Section 6.2 is concerned with particles. For the separation of particles from a fluid or fractionation of particles, one can adopt an Eulerian appmach to determine the particle concentration variation as observed by an observer located at a fixed coordinate (jqy,z). In such an approach, the fluid velocity is also what is determined by an observer at (jqy,z) as a function of time. However, an alternative approach, the Lagrangian approach, is frequently preferred and will be adopted often. The Lagrangian description of particle motion is obtained by an observer who rides on the particle. The geometrical coordinates (jqy,z) of the particle/observer change with time as the particle changes its location in the device in response to fluid motion and other forces, external and/or diffusive, acting on the particle. In such an approach, the coordinates (x,y,z) of a particle are dependent variables whose values as a function of time in the separation device are of interest. These equations, called trajectory equations, are also provided in Section 6.2. 

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