(578g) Discrete Tangent Based Sensitivity Analysis Method in Computational Fluid Dynamics (CFD) for Stirred Tank Reactors

One of the major challenges in the chemical industry is the optimal design of reactors for fluid mixing applications. Formation of poorly mixed zones can lead to significant losses in yield. Localization of energy can lead to losses in yield and reduced product quality, and can cause damage to the equipment. Optimal reactor design therefore requires the study of various factors, such as the geometry of the reactor, baffles and the impellers, impeller speed, flow rate of the feed, feed composition, feed location, etc., to understand their impact on the reactor performance. Traditional CFD analysis solvers typically require users to set up, solve, and view results for a single configuration. To view results when some variations are made in the original configuration, users need to set up another configuration and solve it. Comparisons can then be made based on the results obtained by solving a number of such configurations separately. This methodology can, however, become tedious when solving for numerous small variations. In addition, the traditional approach does not account for uncertainties and tolerances, both in inputs and in predictions. When the goal is to improve design and achieve a target performance, it becomes necessary for a solver to be able to account for such uncertainties and variations.

In this paper we present a numerical approach that enables computation of the sensitivity of solutions to variations in input parameters without the need for multiple single-point solutions. We use a discrete tangent methodology using operator overloading capabilities of C++ to propagate derivatives from inputs through the entire solution algorithm so that derivatives of all computed quantities with respect to any quantity of interest are determined. Thus information about the dependence on input parameters is available not only for reduced quantities such as performance metrics but for entire fields, and this can be very valuable in providing visual insight into the problem. Quantities for which sensitivity information is desired are defined in terms of a parameter and the solution as well as its derivatives are computed about the nominal value specified for this parameter. Differentiating parameters can include all the physcial parameters such as boundary conditions and material properties as well as numerical parameters such as empirical constants used in physical models and solver settings. Sensitivity analysis provides a richer information set than a single-point solution - the values and their gradients with respect to the selected parameters in the entire domain.

In this study, we will present our results for the Residence Time Distribution and flow profiles in stirred tank reactors, and their sensitivity to various parameters such as the inlet flow rate, the impeller speed, and the fluid properties. Our sensitivity results will be compared with results obtained from multiple single-point simulations using traditional solvers.