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Analysis & interpretation of solution

Assessing influence of numerical parameters on simulated results (grid spacing, time step...) Qualitative evaluation: whether key flow features are captured Quantitative evaluation/validation: understanding limitations of simulations (physical as well as numerical)

4 Abstract useful information from simulated results + Use this information for design and optimization

Achieving objectives of flow modeling

FIGURE 8.1 Mapping computational models onto CFD tools.

benefit of undertaking a flow-modeling exercise will determine the extent of resources made available to the project. Clear understanding of the role of fluid dynamic modeling in the overall project is essential. Detailed knowledge of fluid dynamics, analysis of space and time scales of the specific problem at hand and analysis of the available resources (computing resources, time, expertise and so on), are required to develop an appropriate modeling approach. The modeling approach devises ways of dividing the complex problems into tractable sub-problems and ways of achieving the project objectives within the allocated resources. A thorough knowledge of computer implementation of flow models is essential to evolve a suitable modeling approach. Steps in the implementation of a computational flow model on a computer are discussed below.

The basic elements of mapping a computational flow model on a computer are shown in Fig. 8.1. Some comments on developing a modeling approach were made in Chapter 1. Ways of devising a suitable modeling approach are discussed further in Chapter 9 with the help of practical examples. In this chapter, we essentially restrict the discussion to the basic elements which are necessary to generate simulated results from the flow model.

• Geometry modeling of the reactor under study. It is first necessary to select an appropriate solution domain to decouple the system under investigation from the surrounding environment. While finalizing the extent of the solution domain, care must be taken to understand and eliminate the influence of domain boundaries on the predicted flow results. Once the domain is finalized, it is important to decide what geometrical features are essential to model to capture the influence of equipment hardware on flow processes of interest. For example, if the near wall region is an important concern (say to estimate wall heat transfer coefficient), it is necessary to consider the geometry and shape of the wall accurately. If the interest is only in understanding global flow patterns, the complex shape of the wall may be approximated, without jeopardizing the utility of the simulations.

• Grid generation. To implement the finite volume method, it is necessary to divide the solution domain into a number of computational cells, this process being called 'grid generation'. As briefly mentioned in Chapter 1, either structured or unstructured grids may be employed. Prior knowledge of various relevant scales and likely regions of steep gradients helps in generating a suitable grid for the problem at hand. While generating the grids, care should be taken to avoid extremes of aspect ratios and skewness. It is also necessary to formulate grid sequencing and refinement strategies to understand the influence of grid spacing/distribution on simulated results. More often than not, it will be difficult to obtain a truly grid-independent solution for complex flows in industrial reactors. Systematic grid sequencing studies may help to derive maximum benefit from the simulated results, despite the non-availability of a truly grid-independent solution.

• Specification of necessary information/data related to flow process under consideration. Once a suitable grid is generated, the user has to specify the necessary information concerning the physicochemical properties of fluids such as molecular viscosity, density, conductivity etc. for the solution of model equations. If the process under consideration involves chemical reactions, all the other necessary data about reaction kinetics (and stoichiometry, heat of reaction etc.) need to be supplied. In addition to system-specific data, specification of boundary conditions on the edges/external surfaces of the solution domain is a further crucial aspect of the solution process. It is also necessary to provide all the information related to the numerical method selected to solve the model equations (under-relaxation parameters, time step, internal iterations and so on). It may sometimes be necessary to provide an initial guess to start the iterative solution procedure.

• Solution of model equations for the generated grid. Once the grid is generated and the required data are available, the main task of implementing a numerical method to solve the model equations can be initiated. The numerical solution involves formulation of algebraic equations by discretizing model equations on the generated grid, and solution of these algebraic equations until convergence using a suitable algorithm. Relevant details of numerical methods are discussed in Chapters 6 and 7. It is necessary to strike a balance between efficient implementation of numerical methods (which may be better if programs are developed for specific cases) and its general applicability.

• Analysis of simulated flow results. The solution process generates huge amounts of data about the simulated flow process (flow, species and temperature fields within the solution domain). With large numerical simulations, one may become lost in the sea of numbers in the absence of appropriate tools to analyze the simulation results. Appropriate analysis strategies and tools to implement these strategies must be developed to draw useful conclusions about the flow process under consideration. Some ways of identifying key flow features, such as vortices, are also useful for qualitative evaluation of simulation results. Methods and tools for error analysis and for validation are also essential to derive maximum information from the simulation results and to plan further studies.

The necessary computational tools required to carry out these steps are generally classified into three categories: pre-processors, solvers and post-processors. The temptation to give a brief review of some of the major available commercial CFD codes is resisted here since all these codes are fast evolving and the information available today may not be relevant even in the near future. The relevant CFD products of some of the leading vendors are listed in Table 8.1. The web sites mentioned in this table may be visited to get up-to-date information about these codes. Links to other available CFD codes may be found at www.cfd-online.com. Instead of comparing different CFD codes at their present stage, which may not be relevant for long, here we discuss some of the key issues which will be useful when evaluating CFD codes.

Although in many commercially available CFD codes, some capabilities of pre-and post-processors are bundled up with the solver, it will be useful to discuss the CFD tools by classifying them in the stated three categories. It is important to mention here that it is more useful to compare CFD codes based on underlying technological issues rather than based on their 'features'. The main technological issues in pre-processors, solvers and post-processors are listed in Table 8.2, and are discussed in the following sub-sections.

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