Temperature controllability in cross-flow heat exchangers and long ducts

The performance of thermal control systems has, in recent years, improved in numerous ways due to developments in control theory and information technology. However, our understanding of controllability and related questions remain rudimentary. The main characteristics of thermal systems that we are interested in are their distributed nature and delay due to fluid advection from one point to another. Two basic systems, heat exchangers and long ducts, are investigated, and the following issues are addressed. (a) The first is controllability for which conductive-convective systems and cross-flow heat exchangers are examined in detail. In the heat exchanger, controllability results for different choices of the manipulated variable are presented. (b) The second is the control methodology for the outlet temperature in cross-flow heat exchangers. A transient model is developed and tested. The response of this system to control strategies is studied and the performance of a Proportional-Integral (PI) controller to disturbances in the system is presented. (c) The third is the effect of delay in heating or cooling in long ducts in which the flow velocity is the manipulated variable. The governing first-order partial differential equation is transformed to a nonlinear dynamical system represented by an integro-differential equation in the residence time of the fluid in the duct. Both Eulerian and Lagrangian versions of the equation are numerically solved. A PI-based controller is used to control the duct outlet temperature. Investigation of the linear stability of the system leads to a transcendental equation for which Pontryagin's Theorem can be applied. The stability map for the controller parameters is obtained and the effect of the residence time on the system stability is determined. Simple as well as sub- and super-critical Hopf bifurcations are found.