84 Postprocessors

Numerical solutions of model equations generate large sets of numbers. Appropriate post-processing tools are essential to analyze and to interpret these simulation results. Many commercial CFD codes provide in-built post-processing facilities or allow results to be exported to other post-processing packages. The key issues in evaluating CFD post-processors are briefly summarized in Table 8.2.

The first component in the analysis of simulation results is usually checking the degree of convergence and estimating numerical errors. These facilities are usually incorporated in solvers rather than in separate post-processors. Most CFD codes report normalized residuals. It is important to evolve criteria to judge the adequacy of residual reduction suitable for the application under consideration: different variables often need different residual reduction criteria. The progress of residual reduction and the distribution of residuals often indicate whether the numerical solution is adequate. A facility to report sub-domain or global balances is also useful for examining the adequacy of the numerical solution. Once adequate convergence (more often than not, multiple criteria are needed to ensure adequate convergence) has been confirmed, the simulation results may be studied in several ways.

Two of the most common ways of examining simulation results are: (1) vector plots, in which the length of every arrow indicates the magnitude of the local velocity, and the direction of the arrow indicates the direction of the local velocity; and (2) contour plots, which represent the predicted field in the form of constant value contours. Superimposing a vector plot of two components of velocity on the contours of the remaining component of velocity is often done to provide information about the three velocity components in a plane. Most post-processors allow such vector or contour plots on any arbitrarily defined planes or surfaces within the solution domain. Other options to visualize simulation results, such as three-dimensional iso-surfaces, particle streak lines, and particle tracks can reveal important features of the predicted flow field. Automatic feature detection facilities are offered by some of the advanced visualization tools, which may be able to automatically detect 'trailing vortices' behind impeller blades and are, therefore, useful for verifying whether the simulation results have captured essential features of the flow or not. Additional facilities such as different options for coloring vectors or iso-surfaces, perspective views, overlaying different views and so on, are often useful to clearly understand interactions between different variables of interest and to enhance the quality of the results presented.

For quantitative validation of simulation results, it is often necessary to compare predicted profiles (of velocity or other variable of interest) with experimental data: X-Y plotting facilities are useful for this purpose. Most post-processors allow the user to import tabulated data for comparison with simulation results. Facilities to calculate the usual global quantities of interest to reactor engineers, such as overall pressure drop, dispersed phase volume fraction, heat or mass transfer rates and so on, are necessary to address reactor engineering concerns. Most codes allow use of user-defined routines to evaluate different quantities of interest, which may then be displayed using the standard tools discussed above.

It is often necessary to evolve problem-specific post-processing strategies in order to extract as much information as possible from the generated numbers. The need for good post-processing tools is even greater when detailed post-processing studies indicate that the agreement between simulation results and experimental data is not satisfactory. Under such circumstances the user needs to understand the simulation results to identify possible causes for the observed discrepancies. Rather than blindly blaming the underlying model, careful post-processing of simulation results may reveal a wealth of information which will be useful for further development of a mathematical model. When the simulated flow results look satisfactory, the reactor engineer has to extract useful information for further use. Generally, different models are used to address different practical reactor-engineering projects (refer to discussion in Chapter 1). More often than not, flow models are used to obtain the desired information for the other intermediate reactor models such as mixing cell models. Some such examples are discussed in the next chapter (Chapter 9). Post-processing tools should allow easy exchange of information among different levels of models. Such an exchange, until recently, used to be manual or via a case-specific in-house interface. However, there is an increasing trend to automate the information exchange so that flow information from the CFD model can be exported to intermediate reactor models, and reaction information may be imported to CFD code from such reactor models. Development of these interfaces is still in the early stages and more up-to-date information may be found on different web sites (for example, see www.pfd.ie).

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