Nonlinear Dynamics of Thermal - Hydraulic Networks

by Weihua Cai Thermal-hydraulic networks are widely used in the heating and cooling of building complexes, industrial processes, power plants, and in many other applications. A single pipe with a flow-control valve is a basic unit in a thermal-hydraulic network, and therefore transient pipe flow due to control-valve actuation is studied first. Different analytical approximations are applied to this nonlinear problem, and of these the homotopy analysis method is shown to be the most promising. The study is then extended to a simple piping network, for which the mathematical model is a set of nonlinear differential-algebraic equations. By constructing a homotopy deformation of these equations, a dynamical system is obtained which is more tractable than the original. The hydrodynamic and thermal interaction between subsystems as the network goes from one steady state to another is studied experimentally. A step change is introduced by manually actuating a valve in one loop, which results in temperature and pressure changes in the other loops. The response time of the temperature is found to be an order of magnitude higher than that of the flow rate, which is again an order of magnitude higher than for the pressure difference. There is significant interaction between the loops, and that it is dependent on the initial operating condition. The hydrodynamic and thermal responses are found to be Weihua Cai very different. The experimental results are explained using a mathematical model of the processes. Self-sustained flow and temperature oscillations occur in thermal-hydraulic networks with thermostatic control. Experiments are conducted of the synchronization of coupled oscillators set up by the simultaneous action of multiple controllers on different secondary loops. Frequency locking, phase synchronization as well as phase slips are observed to occur due to thermal-hydraulic coupling between the controllers. A simplified mathematical model of synchronization in a system with many thermostatically-controlled oscillators is developed. Each subsystem is coupled with its neighbors by conductive heat transfer, and they are arranged in the form of a ring. The properties of the system are discussed, and numerical simulations are performed. The results show the presence of a rich array of synchronization dynamics.