**6. Conclusion**

To conclude, hydrodynamics behaviors of a droplet in space environment are key processes to understand the formation of primitive materials in meteorites. We modeled its three-dimensional hydrodynamics in a hypervelocity gas flow. Our numerical code based on the CIP method properly simulated the deformation, internal flow, and fragmentation of the droplet. We found that these hydrodynamics results accounted for many physical properties of chondrules.

### **7. References**


26 Will-be-set-by-IN-TECH

How about the distribution of sizes smaller than the maximum one? Kadono and his colleagues carried out aerodynamic liquid dispersion experiments using shock tube (Kadono & Arakawa, 2005; Kadono et al., 2008). They showed that the size distributions of dispersed droplets are represented by an exponential form and similar form to that of chondrules. In their experimental setup, the gas pressure is too high to approximate the gas flow around the droplet as free molecular flow. We carried out the hydrodynamics simulations of droplet dispersion and showed that the size distribution of dispersed droplets is similar to the Kadono's experiments (Yasuda et al., 2009). These results suggest that the shock-wave heating model accounts for not only the maximum size of chondrules but also their size

In addition, we recognized a new interesting phenomenon relating to the chondrule formation: the droplets dispersed from the parent droplet collide each other. A set of droplets after collision will fuse together into one droplet if the viscosities are low. In contrary, if the set of droplets solidifies before complete fusion, it will have a strange morphology that is composed of two or more chondrules adhered together. This is known as compound chondrules and has been observed in chondritic meteorites in actuality. The abundance of compound chondrules relative to single chondrules is about a few percents at most (Akaki & Nakamura, 2005; Gooding & Keil, 1981; Wasson et al., 1995). The abundance sounds rare, however, this is much higher comparing with the collision probability of chondrules in the early solar gas disk, where number density of chondrules is quite low (Gooding & Keil, 1981; Sekiya & Nakamura, 1996). In the case of collisions among dispersed droplets, a high collision probability is expected because the local number density is high enough behind the parent droplet (Miura, Yasuda & Nakamoto, 2008; Yasuda et al., 2009). The fragmentation of a droplet in the shock-wave heating model might account for the origin of compound

To conclude, hydrodynamics behaviors of a droplet in space environment are key processes to understand the formation of primitive materials in meteorites. We modeled its three-dimensional hydrodynamics in a hypervelocity gas flow. Our numerical code based on the CIP method properly simulated the deformation, internal flow, and fragmentation of the droplet. We found that these hydrodynamics results accounted for many physical properties

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**6. Conclusion**

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**0**

**17**

*Colombia*

**Flow Evolution Mechanisms**

*Grupo de Mecánica Computacional, Universidad de Los Andes*

The flow in cavities studies the dynamics of motion of a viscous fluid confined within a cavity in which the lower wall has a horizontal motion at constant speed. There exist two important reasons which motivate the study of cavity flows. First is the use of this particular geometry as a benchmark to verify the formulation and implementation of numerical methods and second the study of the dynamics of the flow inside the cavity which become very particular as the

Most of the studies, concerning flow dynamics inside the cavity, focus their efforts on the steady state, but very few study the mechanisms of evolution or transients until the steady state is achieved (Gustafson, 1991). Own to the latter aproach it was considered interesting to understand the mechanisms associated with the flow evolution until the steady state is reached and the steady state per se, since for different Re numbers (1,000 and 10,000) steady

In order to study the flow dynamics and the evolution mechanisms to steady state the Lattice Boltzmann Method (LBM) was chosen to solve the dynamic system. The LBM was created in the late 90's as a derivation of the Lattice Gas Automata (LGA). The idea that governs the method is to build simple mesoscale kinetic models that replicate macroscopic physics and after recovering the macro-level (continuum) it obeys the equations that governs it i.e. the Navier Stokes (NS) equations. The motivation for using LBM lies in a computational reason: Is easier to simulate fluid dynamics through a microscopic approach, more general than the continuum approach (Texeira, 1998) and the computational cost is lower than other NS equations solvers. Also is worth to mention that the prime characteristic of the present study and the method itself was that the primitive variables were the vorticity-stream function not as the usual pressure-velocity variables. It was intended, by chosing this approach, to understand in a better way the fluid dynamics because what characterizes the cavity flow is the lower wall movement which creates itself an impulse of vorticiy which is transported within the cavity by diffusion and advection. This transport and the vorticity itself create the

In the next sections steady states, periodic flows and feeding mechanisms for different Re

Reynolds (Re) number is increased, i.e. decreasing the fluid viscosity.

states are "similar" but the transients to reach them are completely different.

different vortex within the cavity and are responsible for its interaction.

numbers are going to be studied within square and deep cavities.

**1. Introduction**

**of Lid-Driven Cavities**

José Rafael Toro and Sergio Pedraza R.

