Computational fluid dynamics , uses

Computational fluid dynamics enables us to investigate the time-dependent behavior of what happens inside a reactor with spatial resolution from the micro to the reactor scale. That is to say, CFD in itself allows a multi-scale description of chemical reactors. To this end, for single-phase flow, the space resolution of the CFD model should go down to the scales of the smallest dissipative eddies (Kolmogorov scales) (Pope, 2000), which is inversely proportional to Re-3/4 and of the orders of magnitude of microns to millimeters for typical reactors. On such scales, the Navier-Stokes (NS) equations can be expected to apply directly to predict the hydrodynamics of well-defined system, resolving all the meso-scale structures. That is the merit of the so-called DNS. 

It is important to know how mixing can influence the selectivity of chemical reactions, and computational fluid dynamics (CFD) simulations are quite helpful in providing a deeper insight into this issue. The calculations are based on a laminar flow model where mixing takes place only by molecular diffusion (Figure 6.9). Let us focus on the competitive... 

David A. Kessler, Laboratory for Computational Physics and Fluid Dynamics, US Naval Research Laboratory, Washington, DC, USA... 

The radial distribution function plays an important role in the study of liquid systems. In the first place, g(r) is a physical quantity that can be determined experimentally by a number of techniques, for instance X-ray and neutron scattering (for atomic and molecular fluids), light scattering and imaging techniques (in the case of colloidal liquids and other complex fluids). Second, g(r) can also be determined from theoretical approximations and from computer simulations if the pair interparticle potential is known. Third, from the knowledge of g(r) and of the interparticle interactions, the thermodynamic properties of the system can be obtained. These three aspects are discussed in more detail in the following sections. In addition, let us mention that the static structure is also important in determining physical quantities such as the dynamic an other transport properties. Some theoretical approaches for those quantities use as an input precisely this structural information of the system [15-17,30,31]. 

The time-scale characteristic of size and/or composition changes in individual nuclei is obviously much longer than that of the detailed microscopic dynamics. In particular, the time-delay associated with spontaneous development of a "critical nucleus" has been a source of great computational difficulty in simulations of both liquid->-solid (3 and vapor->-liquid (34-42) phase transitions in simple classical fluids. Before turning to an analogous situation at the "nonequilibrium phase transitions" which are of immediate interest, therefore, let us first illustrate the key problems and innovations in simulation which are already evident in MD studies of low-order clustering and homogeneous nucleation in the vapor phase (34-42). 

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