## 66 Summary

The finite volume method ensures integral conservation of mass, momentum and energy and is, therefore, attractive for reactor engineering applications. The steps in applying the finite volume method to solve transport equations are listed below.

• Select appropriate solution domain (and boundary conditions).

• Divide the selected domain into an adequate (which may be verified by examining the grid dependence of predicted results) number of computational cells.

• Obtain a set of discretized equations by integrating transport equations over computational cells. This step requires use of various discretization and interpolation schemes.

• Select an appropriate algorithm to treat the various couplings and non-linearities.

• Select a corresponding method to solve the linearized algebraic equations.

• Implement these methods in a computer program and obtain results.

• Evaluate the results obtained.

Each of these steps has been discussed in detail in this chapter. Generally, second-order approximations for interpolation are adequate. Various second-order schemes and their modified versions to minimize non-physical 'wiggles' were discussed.   FIGURE 6.21 Influence of viscosity (Vector plots; contours of stream function: A = -0.001 and J = 0.001). Viscosity (a) 100 Pa.s; (b) 10 Pa.s; (c) 1 Pa.s.

The QUICK discretization scheme along with SMART or SHARP modifications, is recommended. Various algorithms for treating pressure-velocity coupling were discussed. The performance of these algorithms depends on flow conditions, degree of coupling between various equations, under-relaxation parameters and so on. Our experience of using the SIMPLER algorithm for a wide variety of reactors indicates that it is quite robust and efficient. A cubical reactor was considered to demonstrate FIGURE 6.22 Influence of viscosity (U profile at x = 0.5; Grid: 40 x 40). FIGURE 6.23 Influence of grid size for low viscosity fluid (/ = 0.001 Pa.s).

application of the finite volume method to flow simulations. Various aspects of practical flow simulations (including post-processing) were illustrated with the help of this example. Difficulties in obtaining grid-independent results for the case of turbulent flows were illustrated. The solution of model equations describing turbulent and other complex flows is discussed in the next chapter.

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