Thermal Modelling of Water-Based Floor Heating Systems - supply temperature optimisation and self-regulating effects

Abstract: Low temperature water-based concrete embedded floor heating systems are studied. The utilisation of low quality heat sources is facilitated by low temperature heating. Theoretical models which describe the transient thermal floor heating operation constitute the basis for the analysis. The combination of building, floor heating element, heat gains and control system is described by a set of theoretical models. In particular, a numerical floor heating element model is develop and verified by comparison with results from heat transfer software and published experimental results. A model based predictive control method is applied in order to find an optimised supply fluid temperature. The aim is to keep the upcoming operative temperature within a comfort interval and at the same time constrain the supply heat flux within practical limits. A discrete transient response factor method is utilised by a numerical optimisation algorithm that iteratively finds an optimised solution. The response factor method describes the relation between a piecewise constant supply heat flux and the succeeding shift in indoor temperature. The stability of the system has been studied; the initial delay time caused by the time needed for a heat front to conduct from the depth of the embedded circuit towards the interior sets a limit for the applied period time in the discrete response method. The predictive optimisation method has been applied in a realistic case where the operative temperature is successfully kept within the comfort interval. The self-regulation ability due to a thermal perturbance in the case of feed-forward controlled supply temperature is studied separately. Such system counteracts any non-periodic thermal perturbance by shifting the supplied heat flux in the opposite direction. The outcome is a more even indoor temperature and enhanced utilisation of heat gains. Transient response functions which quantify the involved thermal processes are derived by the developed model. It has been shown that the transient shift in supplied heat flux is given by two coupled processes. The first process is related to the propagation of heat towards the position of the embedded circuit due to the perturbance. The second process is related to the heat exchange along the embedded circuit due to the excitation of the supply temperature. The demand of an unchanged supply temperature connects the two processes (i.e. from the feed-forward supply temperature control). The self-regulation utilisation factor is defined as the ratio between the accumulated shift in supply heat flux and the energy content of a finite thermal perturbance. Buildings with small heat losses in combination with a high equivalent thermal conductance from the supply of the pipe circuit towards the interior yields a high self-regulation utilisation factor. Hence, self-regulation is an integrated phenomenon which depends on both the design of the floor heating element and the building.