Computational fluid dynamics simplification

As stated above the equations of fluid mechanics (l)-(3) are solvable with a closed analytic solution for only a small number of flows. Therefore two common approaches are used for real flows Simplification of the equations usually based on a combination of approximation, dimensional considerations and empirical input and/or Computational Fluid Dynamics (CFD). We will focus our comments on three common methods of CFD, that is solving the equations numerically on computers. 

Two basic approaches are often used for fluidized bed reactor modeling. One approach is based on computational fluid dynamics developed on the basis of the mass, momentum, and energy balance or the first principle coupled with reaction kinetics (see Chapter 9). Another approach is based on phenomenological models that capture the main features of the flow with simplifications by assumption. The flow patterns of plug flow, CSTR (continuous-stirred tank reactor). 

Equation (3) provides details of gas flow movements. The full treatment requires a rigorous computational fluid dynamics (CFD) tool. Startup and transient processes as well as variations in certain operating parameters may have a sizeable effect on flow and concentration profiles, but the effect on overall electrochemical performance of the cell is not necessarily of the same order. Sometimes it is desirable to make a simplification such as assuming laminar flow to reduce the computation cost and allow quick estimates of certain flow properties. For example, the pressure drop of a laminar flow through a channel can be estimated as... 

An alternative approach to seeking simplifications to the Navier-Stokes equations is to accept the full set of equations, but approximate each term in the equation with a simpler form that permits solutions to be developed. Although the resulting equations are only approximately correct, the advent of modern digital computers has allowed them to be written with great fineness, so that highly accurate solutions are achieved. These techniques are called computational fluid dynamics (CFD). 

A suitable mesh for modeling fluid dynamics, heat transfer, mass transfer and current conservation using a 3D geometry would require very large computational resources. Some simplifications are usually necessary. 

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