(320b) Analyzing the Closed-Loop Response of a Mixing Process Using Computational Fluid Dynamics and Z-Transform

Computational fluid dynamics (CFD) is widely used for analyzing the performance of mixing unit operations in the chemical process industry and can yield insights that are difficult or impossible to obtain by experimental studies. Motivated by the need to reduce the cost of repeated CFD simulations, we have previously demonstrated how to combine CFD with the z-transform technique to provide a convenient method for analyzing the open-loop responses of both a lumped-parameter mixing process (Yin and Yu, 2014 AIChE Annual Meeting Paper 354913) and a distributed-parameter mixing process (Yin, 2015 AIChE Annual Meeting Paper 404589).

For our current study, we consider a more complex problem of the closed-loop response of a mixing process, such as the temperature or concentration in a stirred-tank reactor with negative feedback control subjected to a load change. In the pure-CFD approach, one would implement the feedback loop and control action on the boundary conditions through the compilation and linking of user-defined subroutines. In the course of generating responses to study the mixing process and to optimize the control strategy, this procedure would have to be repeated for multiple CFD simulation runs.

Instead of taking the pure-CFD approach, a more efficient method is to combine CFD with the z-transform technique. After using CFD to obtain an open-loop response of the mixing process, we can derive the z-transform transfer function of the mixing process and then construct the z-space model of the closed-loop system. To generate additional responses of the closed-loop system would then require only fast polynomial arithmetic operations instead of full CFD simulation runs. This approach of combining CFD and z-transform not only reduces the computation cost, it also simplifies the investigation of the effects of various parameters on the response and stability of the closed-loop system.