Front propagation model

The present research has treated important parts of the modeling of combustion and NOx formation in a biomass grate furnace. All parts resulted in useful approaches. For all these approaches successful first steps were taken. Currently, more research is underway to obtain improved results NH3 production is measured in the grid reactor with the tunable diode laser, detailed kinetics will be attached to the front propagation model, including the measured NH3 release functionalities, and for the turbulent combustion model heat losses are taken into account. In addition, the fuel layer model has to be coupled to the turbulent combustion model in the furnace. 

FIGURE 1.26. (a) Schematic representation of the oxidized site distribution in an electronically conducting polymer film according to the Aoki phase propagation model, (b) Conductive front propagation modeled as a random distribution of oxidized chains with each chain starting from a random location on the support electrode surface, (c) An assembly of conductive one-dimensional pillar fibrils of various lengths. 

The model is a straightforward extension of a pool-fire model developed by Steward (1964), and is, of course, a drastic simplification of reality. Figure 5.4 illustrates the model, consisting of a two-dimensional, turbulent-flame front propagating at a given, constant velocity S into a stagnant mixture of depth d. The flame base of width W is dependent on the combustion process in the buoyant plume above the flame base. This fire plume is fed by an unbumt mixture that flows in with velocity Mq. The model assumes that the combustion process is fully convection-controlled, and therefore, fully determined by entrainment of air into the buoyant fire plume. 

The DDT mechanism for this case Is similar but not identical to that of Case B. A convective flame front propagates ahead of the compressive waves which are necessary to form a precursor shock front. In modeling DDT the convective front (and its consequences) must be included because of its influence on dp/dt in the ignition region... 

Guslander and co-workers developed another simple skeleton model on the basis of the CGYN model, named Cobaltolator, which consists of only four steps (167). Numerical simulations with this model showed that it can reproduce the main features of the oscillation reaction, and it can also simulate the front propagation found by Boga et al. 

Direct comparison with earlier measurements by Ronney et al. [5] of turbulent front propagation in constant-density TC flow was not possible because the lowest normalized turbulence intensities they considered are twice as large as the highest values achieved in the present study. However, good agreement of their results for constant-density front propagation in high-intensity turbulence with the constant-density theoretical model of Yakhot [16], and a comparison... 

With this model, the microstructure of the combustion wave was studied, and compared with experimental results (Hwang et al, 1997 Mukasyan et al, 1996). For example, sequences of combustion front propagation at the microscopic level, obtained experimentally and by calculation, are shown in Fig. 24. In addition, it was demonstrated that fluctuations in combustion wave shape and propagation correlate with the heterogeneity of the reactant mixture (e.g., porosity and particle size). 

The constraint of a collision in a given sequence in our simple chain model means that there is a shock front propagating through the system, a front which reverses its direction every time an end atom collides with the hard walls. When a perfectly ordered crystal hits a hard wall, one can understand how a dispersion-free propagation of a shock wave is possible. The new feature is that such a shock front was seen in full MD simulations of impact heated clusters, using realistic forces, and has been recently studied in more detail. ... 

Iwamoto K., Brachwitz F., Nomoto K., Kishimoto N., Hix R., and Thielemann F.-K. (1999) Nucleosynthesis in Chandrasekhar mass models for Type la supemovae and constraints on progenitor systems and burning-front propagation. Astrophy. J. Suppl. 125, 439—462. 

Figure 7 Front propagation for two different model times ( 3 < t ). Time corresponds to time t in Figure 6. See Figure 6 for calculation details. At 13, fluid composition (a) is at steady state, but solid composition (b) is not (cf. Figure 6). At 14, both solute and geochemical fronts are propagating, and neither fluid nor rock compositions are in steady state.

Proposed mechanisms of solids production from unconsolidated sand reservoirs have been discussed (102,103). Dusseault and Santarelli (104) proposed a mechanism for massive solids production from poorly consolidated sandstones that was based on a general plastic yield of the reservoir brought about by a high pressure drawdown in the yielded region. The vertical stress that the reservoir experiences was also a contributing factor. Subsequently, Geilikman et al. (105-108) developed a model for continuous solids production from unconsolidated heavy oil reservoirs as a yield front propagation. This is different from predictive models previously discussed (45, 46), which dealt with transient and catastrophic production but which did not discuss continuous production explicitly. 

The fliamelet model for diffusion flames has been developed at the RWTH Aachen describing in a simplified manner the flame front of a multi-dimensional flow. The flame front is assumed to be locally one-dimensional. By introducing an appropriate coordinate, e.g., fuel-mass ratio, the determination of flame structure and of flame front propagation can be separated [79]. 

This chapter starts vdth an introduction to modeling of chromatographic separation processes, focusing on different models capable to describe the dynamics of front propagation phenomena in the columns and the plant peripherals. A short introduction into numerical solution methods as well as an overview regarding methods for the consistent determination of the free model parameters, especially those of the thermodynamic submodels, is given. Methods of different complexity and experimental effort are presented. Finally, it will be illustrated that appropriate models can simulate experimental data with rather high accuracy. This validation is demonstrated both for standard batch elution and for a more complex multicolumn operation mode. 

Section 6.2 presents various models capable to describe front propagation phenomena in chromatographic columns. It has to be kept in mind that these models account only for effects occurring within the packed bed. A HPLC plant, however, consists of several additional equipment and fittings besides the column. Therefore, the effect of this extra column equipment has to be accounted for to obtain reasonable agreement between experimental results and process simulation. Peripheral equipment (e.g., pipes, injection system, pumps, and detectors) causes dead times and mixing. Thus, it can contribute considerably to the band broadening measured by the detector. 

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