Hydrodynamics and Control in Thermal-Fluid Networks

Theoretical, numerical and experimental studies of hydraulic, thermal and control aspects in fluid networks are presented. First, a one-dimensional differential-algebraic nonlinear model, based on first principles, representing the time-dependent behavior in networks is developed. A thermal-hydraulic analysis of a small network with three common control strategies for heating and cooling of buildings is carried out. PID controllers are used to respond to changes in the thermal load. The temperature difference between the chiller supply and return water is used as a criterion for comparison. Next, an experimental hydronic network featuring these control methodologies is used to complement the theoretical study by including all the complexities of the problem, such as valves hysteresis, dynamic time constants, imperfect actuators and imperfect sensors. Stability and reachability issues arise during the control process as a consequence of changing the thermal load. The importance of location and selection of the hardware used for control becomes evident. Control hardware placement is addressed next. The discrete space of possible locations for a specific layout is explored in order to find the best configuration. The hardware elements are a control valve and two booster pumps. Pumping action is divided among the two pumps to be able to look at different combinations. The change in operating conditions and the output reachabilities of the control system are used as criteria to compare the relative merits of different configurations. Finally, the mathematical model is extended to the study of large, possibly infinite, self-similar networks configured in the form of a regular branching tree. Each branch of the tree bifurcates with a constant diameter and length ratio. Since the local Reynolds number changes at every generation, the flow may transition from laminar to turbulent or relaminarize from turbulent to laminar. The global stability of the steady flow is demonstrated for friction laws for which viscous forces are nondecreasing functions of the flow rate, otherwise the flow may oscillate. In addition the control properties of the network hydrodynamics are investigated using valves and pumps as control elements to manipulate branch flow rates and nodal pressures.