Transport simulation representative results

The thermal conductivity of polymeric fluids is very low and hence the main heat transport mechanism in polymer processing flows is convection (i.e. corresponds to very high Peclet numbers the Peclet number is defined as pcUUk which represents the ratio of convective to conductive energy transport). As emphasized before, numerical simulation of convection-dominated transport phenomena by the standard Galerkin method in a fixed (i.e. Eulerian) framework gives unstable and oscillatory results and cannot be used. 

Simulation of a fire resulting from a transport accident in a cross wind. The flame is visualized in yellow/red, while soot clouds are represented in black. (From Tieszen, S., private communication.)... 

Studies of the effect of permeant s size on the translational diffusion in membranes suggest that a free-volume model is appropriate for the description of diffusion processes in the bilayers [93]. The dynamic motion of the chains of the membrane lipids and proteins may result in the formation of transient pockets of free volume or cavities into which a permeant molecule can enter. Diffusion occurs when a permeant jumps from a donor to an acceptor cavity. Results from recent molecular dynamics simulations suggest that the free volume transport mechanism is more likely to be operative in the core of the bilayer [84]. In the more ordered region of the bilayer, a kink shift diffusion mechanism is more likely to occur [84,94]. Kinks may be pictured as dynamic structural defects representing small, mobile free volumes in the hydrocarbon phase of the membrane, i.e., conformational kink g tg ) isomers of the hydrocarbon chains resulting from thermal motion [52] (Fig. 8). Small molecules can enter the small free volumes of the kinks and migrate across the membrane together with the kinks. 

Resulting maps of the current density in a random-site percolation cluster both of the experiments and simulations are represented by Figure 2.9.13(b2) and (bl), respectively. The transport patterns compare very well. It is also possible to study hydrodynamic flow patterns in the same model objects. Corresponding velocity maps are shown in Figure 2.9.13(d) and (c2). In spite of the similarity of the... 

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 ... 

We have addressed several aspects of STE of ozone and the impact on tropospheric ozone levels. Using ozone observations in the upper troposphere and lower stratosphere from MOZAIC, we have examined the rdation between ozone and PV in the lower stratosphere. A distinct seasonality in the ratio between ozone and PV is evident, with a maximum in spring and minimum in fall associated with the seasonality of downward transport in the meridional circulation and of the ozone concentrations in the lower stratosphere. The ozone-PV ratio is applied in our tropospheric chemistry-climate model to improve the boundary conditions for ozone above the tropopause, to improve the representativity of simulated ozone distributions near synoptic disturbances and realistically simulate cross-tropopause ozone transports. It is expected that the results will further improve when the model is applied in a finer horizontal and vertical resolution. 

Abstract. In this chapter we discuss approaches to solving quantum dynamics in the condensed phase based on the quantum-classical Liouville method. Several representations of the quantum-classical Liouville equation (QCLE) of motion have been investigated and subsequently simulated. We discuss the benefits and limitations of these approaches. By making further approximations to the QCLE, we show that standard approaches to this problem, i.e., mean-field and surface-hopping methods, can be derived. The computation of transport coefficients, such as chemical rate constants, represent an important class of problems where the QCL method is applicable. We present a general quantum-classical expression for a time-dependent transport coefficient which incorporates the full system s initial quantum equilibrium structure. As an example of the formalism, the computation of a reaction rate coefficient for a simple reactive model is presented. These results are compared to illuminate the similarities and differences between various approaches discussed in this chapter. 

The results imply that the diffusion coefficient represents the thermally activated transport of electrons through the particle network. Indeed, these and subsequent studies have been interpreted with models that involve trapping of conduction band electrons or electron hopping between trap sites [158, 159]. An unexpected feature of the diffusion constants reported by Cao et al. is that they are dependent on the incident irradiance. The photocurrent rise times display a power law dependence on light intensity with a slope of -0.7. The data could be simulated if the diffusion constant was assumed to be second order in the electron concentration, D oc n. The molecular origin of this behavior is not well understood and continues to be an active area of study [157, 159]. 

Retention of ionic species modifies ionic concentrations in the feed and permeate liquids in such a way that osmotic pressure or electroosmotic phenomena cannot be neglected in mass transfer mechanisms. The reflexion coefficient, tr, in Equations 6.4 and 6.5 represents, respectively, the part of osmotic pressure force in the solvent flux and the diffusive part in solute transport through the membrane. One can see that when a is close or equal to zero the convective flux in the pores is dominant and mostly participates to solute transport in the membrane. On the contrary when diffusion phenomena are involved in species transport through the membrane, which means that the transmembrane pressure is exerted across an almost dense stmcture. Low UF and NF ceramic membranes stand in the former case due to their relatively high porous volume and pore sizes in the nanometer range. Recendy, relevant results have been published concerning the use of a computer simulation program able to predict solute retention and flux for ceramic and polymer nanofiltration membranes [21]. 

FIGURE 4-28 An example of output from ACID, a regional-scale model that simulates transport of S02 and sulfate, oxidation of S02 to sulfate, and sulfate deposition. Each contour represents the average airborne sulfate concentration in micrograms per cubic meter that would result in the Adirondacks region of New York per 1014 g of sulfur emitted annually anywhere along the contour line. For example, if a 1014 g/year source of S02 were sited in Tennessee, the resultant average addition to the airborne sulfate concentration in the Adirondacks would be 20 /cg/m3. 

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