Transport computer simulation

Computer simulation of the reactor kinetic hydrodynamic and transport characteristics reduces dependence on phenomenological representations and idealized models and provides visual representations of reactor performance. Modem quantitative representations of laminar and turbulent flows are combined with finite difference algorithms and other advanced mathematical methods to solve coupled nonlinear differential equations. The speed and reduced cost of computation, and the increased cost of laboratory experimentation, make the former increasingly usehil. 

Computational fluid dynamics (CFD) is the numerical analysis of systems involving transport processes and solution by computer simulation. An early application of CFD (FLUENT) to predict flow within cooling crystallizers was made by Brown and Boysan (1987). Elementary equations that describe the conservation of mass, momentum and energy for fluid flow or heat transfer are solved for a number of sub regions of the flow field (Versteeg and Malalase-kera, 1995). Various commercial concerns provide ready-to-use CFD codes to perform this task and usually offer a choice of solution methods, model equations (for example turbulence models of turbulent flow) and visualization tools, as reviewed by Zauner (1999) below. 

There are basically two different computer simulation techniques known as molecular dynamics (MD) and Monte Carlo (MC) simulation. In MD molecular trajectories are computed by solving an equation of motion for equilibrium or nonequilibrium situations. Since the MD time scale is a physical one, this method permits investigations of time-dependent phenomena like, for example, transport processes [25,61-63]. In MC, on the other hand, trajectories are generated by a (biased) random walk in configuration space and, therefore, do not per se permit investigations of processes on a physical time scale (with the dynamics of spin lattices as an exception [64]). However, MC has the advantage that it can easily be applied to virtually all statistical-physical ensembles, which is of particular interest in the context of this chapter. On account of limitations of space and because excellent texts exist for the MD method [25,61-63,65], the present discussion will be restricted to the MC technique with particular emphasis on mixed stress-strain ensembles. 

F. Otalora, J. M. Garcia-Ruiz. Crystal growth studies in microgravity with the APCF. I. Computer simulation of transport dynamics. J Cryst Growth 752 141, 1997. 

Theory and Computer Simulation of Structure, Transport, and Flow of Fluid in Micropores... 

In this paper, we report recent progress made In our laboratory In using molecular theory and computer simulation to understand the structure, flow and transport of fluids confined by planar solid walls separated by a few molecular diameters. 

The attractive feature of LADM Is that once the fluid structure Is known (e.g., by solution of the YBG equations given In the previous section or by a computer simulation) then theoretical or empirical formulas for the transport coefficients of homogeneous fluids can be used to predict flow and transport In Inhomogeneous fluid. For diffusion and Couette flow In planar pores LADM turns out to be a surprisingly good approximation, as will be shown In a later section. 

Computer simulations of transport properties using Green-Kubo relations... 

Dearden, J. C. Townsend, M. S., Digital computer simulation of the drug transport process, in Proc. 2nd Symp. Chemical Structure-Biological Activity Relationships Quantitative Approaches (Suhl), Akademie-Verlag, Berlin, 1978, pp. 387-393. 

HSPF. The Hydrologic Simulation Program (FORTRAN) ( 1, 42) is based on the Stanford Watershed Model. Version 7 of HSPF incorporates the process models of SERATRA in its aquatic section, with several (user-selectable) options for sediment transport computations. HSPF includes the generation of transformation products, each of which is in turn subject to volatilization, phototransformation, biolysis, etc. 

The favourable properties which mark out vesicles as protocell models were confirmed by computer simulation (Pohorill and Wilson, 1995). These researchers studied the molecular dynamics of simple membrane/water boundary layers the bilayer surface fluctuated in time and space. The model membrane consisted of glycerine-1-monooleate defects were present which allowed ion transport to occur, whereby negative ions passed through the bilayer more easily than positive ions. The membrane-water boundary layer should be particularly suited to reactions which are accelerated by heterogeneous catalysis. Thus, the authors believe that these vesicles fulfil almost all the conditions required for the first protocells on earth ... 

Derrick studied the interaction of L-tryptophan and ibuprofen with human serum albumin (HSA),74 which is an abundant transport blood protein capable of binding efficiently several species.75 They acquired 1H NMR spectra of L-Tryptophan-HSA system for different ligand protein molar ratios, that is 3 1, 5 1, 7 1 and 10 1. The aromatic resonances of L-Tryptophan are difficult to be observed due to the overlap with HSA signals, even at 10 1 molar ratio, so that the spectral subtraction was performed. D values of L-Tryptophan were calculated by integration of the subtracted spectra and were in good agreement with those predicted by computer simulations. In the case of ibuprofen, only for 140 1 molar ratio, the resonances of ibuprofen are clearly visible also in this case, the... 

Voth, G. A., Computer simulation of proton solvation and transport in aqueous and bio-molecular systems, Acc. Chem. Res. 2006, 39, 143-150. 

Finally, a relatively new area in the computer simulation of confined polymers is the simulation of nonequilibrium phenomena [72,79-87]. An example is the behavior of fluids undergoing shear flow, which is studied by moving the confining surfaces parallel to each other. There have been some controversies regarding the use of thermostats and other technical issues in the simulations. If only the walls are maintained at a constant temperature and the fluid is allowed to heat up under shear [79-82], the results from these simulations can be analyzed using continuum mechanics, and excellent results can be obtained for the transport properties from molecular simulations of confined liquids. This avenue of research is interesting and could prove to be important in the future. 

ODE solver. Relative to non-stiff ODE solvers, stiff ODE solvers typically use implicit methods, which require the numerical inversion of an Ns x Ns Jacobian matrix, and thus are considerably more expensive. In a transported PDF simulation lasting T time units, the composition variables must be updated /Vsm, = T/At 106 times for each notional particle. Since the number of notional particles will be of the order of A p 106, the total number of times that (6.245) must be solved during a transported PDF simulation can be as high as A p x A sim 1012. Thus, the computational cost associated with treating the chemical source term becomes the critical issue when dealing with detailed chemistry. 

In a transported PDF simulation, the chemical source term, (6.249), is integrated over and over again with each new set of initial conditions. For fixed inlet flow conditions, it is often the case that, for most of the time, the initial conditions that occur in a particular simulation occupy only a small sub-volume of composition space. This is especially true with fast chemical kinetics, where many of the reactions attain a quasi-steady state within the small time step At. Since solving the stiff ODE system is computationally expensive, this observation suggests that it would be more efficient first to solve the chemical source term for a set of representative initial conditions in composition space,156 and then to store the results in a pre-computed chemical lookup table. This operation can be described mathematically by a non-linear reaction map ... 

An example of a smart tabulation method is the intrinsic, low-dimensional manifold (ILDM) approach (Maas and Pope 1992). This method attempts to reduce the number of dimensions that must be tabulated by projecting the composition vectors onto the nonlinear manifold defined by the slowest chemical time scales.162 In combusting systems far from extinction, the number of slow chemical time scales is typically very small (i.e, one to three). Thus the resulting non-linear slow manifold ILDM will be low-dimensional (see Fig. 6.7), and can be accurately tabulated. However, because the ILDM is non-linear, it is usually difficult to find and to parameterize for a detailed kinetic scheme (especially if the number of slow dimensions is greater than three ). In addition, the shape, location in composition space, and dimension of the ILDM will depend on the inlet flow conditions (i.e., temperature, pressure, species concentrations, etc.). Since the time and computational effort required to construct an ILDM is relatively large, the ILDM approach has yet to find widespread use in transported PDF simulations outside combustion. 

However, in practice, the integral must be evaluated using a stiff ODE solver or chemical lookup tables (see Section 6.9). Because transported PDF simulations are typically used for reacting flows with complex chemistry, the chemical-reaction step will often dominate the overall computational cost. It is thus important to consider carefully the computational efficiency of the chemical-reaction step when implementing a transported PDF simulation. 

Computer simulation of chemical reaction or reaction-transport systems has long been used in chemical engineering process design, and has more recently moved into the chemical research... 

Transport of mass, energy, and momentum in porous media is a key aspect of a large number of fiber-reinforced plastic composite fabrication processes. In design and optimization of such processes, computer simulation plays an important role. Recent studies [1-14] have... 

Over the last four decades or so, transport phenomena research has benefited from the substantial efforts made to replace empiricism by fundamental knowledge based on computer simulations and theoretical modeling of transport phenomena. These efforts were spurred on by the publication in 1960 by Bird et al. (6) of the first edition of their quintessential monograph on the interrelationships among the three fundamental types of transport phenomena mass transport, energy transport, and momentum transport. All transport phenomena follow the same pattern in accordance with the generalized diffusion equation (GDE). The unidimensional flux, or overall transport rate per unit area in one direction, is expressed as a system property multiplied by a gradient (5)... 

Expressions for the transport coefficients suitable for use in computational simulations of chemically reacting flows are usually based on the Chapman-Enskog theory. The theory has been extended to address in detail transport properties in multicomponent systems [103,178]. 

Single crystals of /S-A1203 are essentially two dimensional conductors. The conducting plane has hexagonal symmetry (honeycomb lattice). This characteristic feature made -alumina a useful model substance for testing atomistic transport theory, for example with the aid of computer simulations. Low dimensionality and high symmetry reduce the computing time of the simulations considerably (e.g., for the calculation of correlation factors of solid solutions). 

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