Mathematical modelling of a domestic heating system with stratified storage tank

A hybrid distributed parameter model of a heating system for domestic hot water is presented in this paper. This heating system comprises a condensing boiler (burner), a counter current heat exchanger, and a so-called stratified storage tank which is the state of the art domestic hot water storage unit. The paper presents the model for the different operational modes of the plant which are described by a finite state automaton representing the discrete-event dynamics and driving the underlying continuous-time dynamics of the storage tank, the heat exchanger, and the burner. These interconnected components are modelled by a system of six coupled, quasi-linear partial differential equations (PDEs) comprising diffusion-, convection-, and source terms. In order to perform numerical simulations, the set of PDEs is spatially discretized using the method of lines. Thereby, the influence of various discretization schemes on the temporal evolution of the traveling temperature profiles in the single components is investigated. A high resolution slope limiter scheme for the stratified storage tank and a higher order up--/downwind scheme for the heat exchanger and the burner are found to be an appropriate choice for the spatial discretization of the model equations in order to adequately cover the plant dynamics. Simulation results fortify the effectiveness of the chosen discretization schemes and show the excellent performance of the suggested model representing the measurement data.