Numerical simulation cells

C) and Cgm denote the mean concentration in the occupied zone, concentration at a given point P, the mean concentration in the room, and the concentration at the outlet, respectively. To numerically simulate these parameters, the velocity field is first computed. Then a contaminant source is introduced at a cell (or cells) of a region to be studied, and the transport equation for contaminant C is solved. The transport equation for C is... 

Temperature field obtained by numerical simulations [23] behind the front of a fully developed (0.3 ms after the detonation initiation) detonation in hydrogen/air at 1 atm. Minimum computational cell size is 5 pm. (Courtesy of V. Gamezo.)... 

The presentation in this paper concentrates on the use of large-scale numerical simulation in unraveling these questions for models of two-dimensional directional solidification in an imposed temperature gradient. The simplest models for transport and interfacial physics in these processes are presented in Section 2 along with a summary of the analytical results for the onset of the cellular instability. The finite-element analyses used in the numerical calculations are described in Section 3. Steady-state and time-dependent results for shallow cell near the onset of the instability are presented in Section 4. The issue of the presence of a fundamental mechanism for wavelength selection for deep cells is discussed in Section 5 in the context of calculations with varying spatial wavelength. 

Large-scale numerical simulation for samples that are many times os large as the critical wavelength is perhaps the only way to develop a quantitative understanding of the dynamics of solidification systems. Even for shallow cells, such calculations will be costly, because of the fine discretizations needed to be sure the dynamics associated with the small capillary length scales are adequately approximated. Such calculations may be feasible with the next generation of supercomputers. 

Figure 2.9.9(a) shows a schematic representation of a thermal convection cell in Rayleigh-Benard configuration [8]. With a downward temperature gradient one expects convection rolls that are more or less distorted by the tortuosity of the fluid filled pore space. In the absence of any flow obstacles one expects symmetrical convection rolls, such as illustrated by the numerical simulation in Figure 2.9.9(b). 

Fig. 2.9.9 (a) Schematic cross section of a compartments at the top and bottom, respec-convection cell in Rayleigh-Benard configura- tively. (b) Velocity contour plot of typical tion. In the version examined in Refs. [8, 44], a convection rolls expected in the absence of any fluid filled porous model object of section flow obstacles (numerical simulation). 

Fig. 2.9.10 Maps of the temperature and of the experimental data. The right-hand column convection flow velocity in a convection cell in refers to numerical simulations and is marked Rayleigh-Benard configuration (compare with with an index 2. The plots in the first row, (al) Figure 2.9.9). The medium consisted of a and (a2), are temperature maps. All other random-site percolation object of porosity maps refer to flow velocities induced by p = 0.7 filled with ethylene glycol (temperature thermal convection velocity components vx maps) or silicon oil (velocity maps). The left- (bl) and (b2) and vy (cl) and (c2), and the hand column marked with an index 1 represents velocity magnitude (dl) and (d2).

Pressure drop and dispersion were the focus of work by Magnico (2003) who simulated flow at lower Re by direct numerical simulation (DNS) in beds of spheres with an in-house code. Tobis (2000) simulated a small cluster of four spheres with inserts between them to compare to his experimental measurements of pressure drop. Gunjal et al. (2005) also focused on flow and pressure drop through a small cell of spheres, in order to validate the CFD approach by comparison to the MRI measurements in the same geometry made by Suekane... 

As discussed in Chapter 2, a fully developed turbulent flow field contains flow structures with length scales much smaller than the grid cells used in most CFD codes (Daly and Harlow 1970).29 Thus, CFD models based on moment methods do not contain the information needed to predict x, t). Indeed, only the direct numerical simulation (DNS) of (1.27)-(1.29) uses a fine enough grid to resolve completely all flow structures, and thereby avoids the need to predict x, t). In the CFD literature, the small-scale structures that control the chemical source term are called sub-grid-scale (SGS) fields, as illustrated in Fig. 1.7. 

Wang, G., Mukherjee, P P, and Wang, C. Y. Optimization of polymer electrolyte fuel cell cathode catalyst layers via direct numerical simulation modeling. Electrochimica Acta 2007 52 6367-6377. 

Numerical simulations indicate that relay of cAMP pulses represents a different mode of dynamic behavior, closely related to oscillations. Just before autonomous oscillations break out, cells in a stable steady state can amplify suprathreshold variations in extracellular cAMP in a pulsatory manner. Thus, relay and oscillations of cAMP are produced by a unique mechanism in adjacent domains in parameter space. The two types of dynamic behavior are analogous to the excitable or pacemaker behavior of nerve cells. 

Hartmann, C. and Delgado, A. (2004). Numerical simulation of the mechanics of a yeast cell under high hydrostatic pressure. J. Biochem 37, 977-987. 

Ferguson J.R., Fiard J.M., Herbin, R., 1996. Three-dimensional numerical simulation for various geometries of solid oxide fuel cells. Journal of Power Sources 58, 109-122. 

Fig. 5.19 Potential distribution across the six cell cross-flow PEMFC stack at 4A discharge (after Liu et al., 2006). (Reprinted from Journal of Power Sources, Vol. 160, Liu, Z., Mao, Z., Wang, C., Zhuge, W., and Zhang, Y., Numerical simulation of min PEMLC stack , pp. 1111-1122, Copyright 2006, with permission from Elsevier.)...

Koh, J., Seo, H., Yoo, Y. and Eim, H. (2002) Consideration of numerical simulation parameters and heat transfer models for a molten carbonate fuel cell stack, Chemical Engineering Journal 87, 367-379. 

Masuda, H., Ito, K., Kakimoto, Y., Miyazaki, T., Ashikaga, K. and Sasaki, K., (2006) Numerical simulation of two-phase flow and transient response in polymer electrolyte fuel cell, in Proceedings of FUELCELL2006, The 4th International Conference on Fuel Cell Science Engineering and Technology, Irvine, CA, June 19-21. 

Pakalapati, S.R., Elizalde-Blancas, F. and Celik, I. (2007) Numerical simulation of solid oxide fuel cell stacks Comparison between a reduced order pseudo three-dimensional model and a multidimensional model, Proceedings of 5th ASME International Fuel Cell Science, Engineering and Technology Conference, New York, USA, June 18-20. 

Herbin, R. and Fiard, J.M., Three-dimensional numerical simulation of the temperature, potential and concentration for various geometries of SOFCs, in Proceedings of 1st European Solid Oxide Fuel Cell Forum, U. Bossel (Ed.), 1994, p. 317. 

During simulation of unconfined aquifers, care must be exercised to avoid dewatering numerical grid cells because of excessive pumping. If extraction well locations are assumed to be most prone to dewatering then either upper bounds on extraction rates or lower bounds on head at the well cell can be imposed on the pumping solution. Imposing explicit upper bounds on extraction may artificially eliminate the best solutions from consideration. With this in mind, the approach taken here is to impose lower... 

In Fig. 4 it can be observed that the numerical simulations result in viability profiles qualitatively similar to the experiment. However in contrast to the experiment, in the simulations a considerable fraction of the cells in the center remains viable. In addition the critical glucose level fitted is very high, 4.5 x 10 3 //mol mm-3 compared to the initial glucose concentration of 5 x 10 3 Hmol mm-3. 

Numerical simulations produce force-deformation data whose shape and magnitude is dependent on the initial parameters defined within the model, including the elastic modulus (E), the uninflated cell radius (rQ) and the initial stretch ratio (ls). Experimental data are fitted to these numerical simulations allowing intrinsic material properties to be derived. 

Direct simulation of polymer electrolyte fuel cell catalyst layers, presentation of a systematic development of the direct numerical simulation... 

Medronho RA, Schiitze J, Deckwer W-D (2005), Numerical simulation of hydrocyclones for cell separation, Latin Am. Appl. Res. 35 1-8. 

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