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Pseudo-2D Model

In this approach, originally developed by Fuller et al. [18, 53] based on the porous electrode theory [42], the active material is assumed to consist of spherical particles with a specific size, and solid phase diffusion in the radial direction is assumed to be the predominant mode of transport. The electrolyte phase concentration (Cg) and the potentials (4 s,4 e) are assumed to vary along the principal (i.e., thickness) direction only, and are henceforth referred to as the x direction. In other words, this model implicitly considers two length scales (1D + 1D), that is, the r direction inside the spherical particle and the x direction along the thickness. All other equations described earlier continue to remain valid except the solid phase diffusion. Equation 25.19 and the corresponding boundary/initial conditions. The solid phase diffusion equation now takes the following form  [Pg.857]

The boundary condition at the surface (r = R) of the particle ensures the coupling between the lithium concentration in the solid phase and the reaction rate at the electrode/electrolyte interface. It is important to note that in the pseudo-2D framework, only diffusion within a solid particle is considered, while particle-to-particle diffusion in the solid matrix is neglected [34]. [Pg.858]


Pseudo-2D models can be especially valuable when a hierarchical strategy is employed, wherein CFD simulations are employed to obtain the transverse transport correlations that are then used in pseudo-2D models [26]. Results using this strategy for non-adiabatic microbumers are presented in subsequent sections. We use Fluent 6.2 [27] to solve a 2D eDiptic model for the combined flow, transport and reaction problem. To ensure accuracy of the Nu and Sh values computed, a non-uniform grid is chosen such that the smallest cell is 1 pm wide in the transverse direction in the fluid phase near the reactor wall. Simulations are performed for various operating conditions and Nu and Sh are computed using Equations (10.2) and (10.3). [Pg.293]

Alternatively, the dimensionless groups can be set constant in the pseudo-2D model using a crude average of the asymptotes of the two zones in the case of Nu. The last row in Table 10.1 shows such constant (i.e. not a function of axial distance) Nu and Sh (round) values. [Pg.298]

Table 10.1 Parameters for computing the Nusselt number (Nu) and Sherwood number (Sh) in the pseudo-2D model. The two columns of Nu values indicate the asymptotic values in the preheating zone (pre) and post-reaction zone (post). The last row indicates constant values used (these are crude averages for Nu values between the two zones). Table 10.1 Parameters for computing the Nusselt number (Nu) and Sherwood number (Sh) in the pseudo-2D model. The two columns of Nu values indicate the asymptotic values in the preheating zone (pre) and post-reaction zone (post). The last row indicates constant values used (these are crude averages for Nu values between the two zones).
Figure 10.12 Comparison of the axial profiles of (a) propane mass fraction, (b) wall and bulk gas temperature and (c) Nusselt number obtained from CFD simulations (symbols), pseudo-2D model with Nu/Sh fits (solid lines) and pseudo-2D model with constant Nu/Sh (dashed lines) near extinction, i.e. with ks = 20W/m K ... Figure 10.12 Comparison of the axial profiles of (a) propane mass fraction, (b) wall and bulk gas temperature and (c) Nusselt number obtained from CFD simulations (symbols), pseudo-2D model with Nu/Sh fits (solid lines) and pseudo-2D model with constant Nu/Sh (dashed lines) near extinction, i.e. with ks = 20W/m K ...
Figure 10.13 Comparison between temperature profiles predicted by the 2D CFD model and pseudo-2D model for homogeneous combustion of a stoichiometric propane-air mixture using a constant Nu value (last row ofTable 10.1). Redrawn from [18]. Figure 10.13 Comparison between temperature profiles predicted by the 2D CFD model and pseudo-2D model for homogeneous combustion of a stoichiometric propane-air mixture using a constant Nu value (last row ofTable 10.1). Redrawn from [18].
It is almost impossible to cover the entire range of models in Figure 25.1, and in this chapter we will limit ourselves to the different modeling approaches at the continuum level (micro-macroscopic and system-level simulations). In summary, there are computational models that are developed primarily for the lower-length scales (atomistic and mesoscopic) which do not scale to the system-level. The existing models at the macroscopic or system-level are primarily based on electrical circuit models or simple lD/pseudo-2D models [17-24]. The ID models are limited in their ability to capture spatial variations in permeability or conductivity or to handle the multidimensional structure of recent electrode and solid electrolyte materials. There have been some recent extensions to 2D [29-31], and this is still an active area of development As mentioned in a recent Materials Research Society (MRS) bulletin [6], errors arising from over-simplified macroscopic models are corrected for when the parameters in the model are fitted to real experimental data, and these models have to be improved if they are to be integrated with atomistic... [Pg.845]

X coordinate, and the pseudo-2D model was used to represent radial direction within electrode particles. To handle the multiphysics nature of this problem, the equations were simultaneously solved by a commercial finite element method (FEM) package. Figure 26.16 shows differential stresses between two different phases along the electrode thickness direction [55]. [Pg.896]

The rationale of using hybrid simulation here is that a classic diffusion-adsorption type of model, Eq. (2), can efficiently handle large distances between steps by a finite difference coarse discretization in space. As often happens in hybrid simulations, an explicit, forward discretization in time was employed. On the other hand, KMC can properly handle thermal fluctuations at the steps, i.e., provide suitable boundary conditions to the continuum model. Initial simulations were done in (1 + 1) dimensions [a pseudo-2D KMC and a ID version of Eq. (2)] and subsequently extended to (2 + 1) dimensions [a pseudo-3D KMC and a 2D version of Eq. (2)] (Schulze, 2004 Schulze et al., 2003). Again, the term pseudo is used as above to imply the SOS approximation. Speedup up to a factor of 5 was reported in comparison with KMC (Schulze, 2004), which while important, is not as dramatic, at least for the conditions studied. As pointed out by Schulze, one would expect improved speedup, as the separation between steps increases while the KMC region remains relatively fixed in size. At the same time, implementation is definitely complex because it involves swapping a microscopic KMC cell with continuum model cells as the steps move on the surface of a growing film. [Pg.22]

In this chapter both ID and 2D models (pseudo-homogeneous and heterogeneous) will be described and applied to hydrogen production for a standard reaction system (methane reforming). [Pg.2]

Our third example is a 2D pseudo-homogeneous model described and studied by Ferreira (2002) concerning the propagation of waves of temperature in a fixed bed. The governing dimensionless equation is... [Pg.615]

Sutkar VS, Deen NG, Mohan M, et al Numerical investigations of a pseudo-2D spout fluidized bed with draft plates using a scaled discrete particle model, Chem Eng Sci 104 790-807, 2013. [Pg.136]


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