Calculation of indoor air temperature using dimensionless parameters for integrated climate control systems

Introduction. It is noted that the improvement of the technology for calculating the thermal regime of premises in the conditions of automation of climate systems is still relevant. The aim of the work is to find a universal dependence of the air temperature in the building premises on time in conditions of a jump in heat access or heat loss for the integral law of regulating the compensatory heat flow from microclimate systems. In the form of a scientific hypothesis, we consider the statement about the power nature of such a dependence with the presence of a maximum and an asymptotic tendency to zero. Materials and methods. The study involves the use of basic equations that relate the most significant components of heat flows in rooms serviced by microclimate systems equipped with integrated controllers under conditions of abrupt changes in thermal disturbances. The method of dimension analysis is used to identify dimensionless complexes that are essential for obtaining engineering dependencies, as well as software calculation of sums of infinite series with a given accuracy, numerical solution of nonlinear equations, and the method of power series economization. Results. An analytical expression is found for changes in room temperature under integrated control of climate equipment under conditions of a jump in heat availability, which has the form of an infinite series in degrees of a dimensionless parameter that characterizes the properties of the room and the automation system. A simplified expression for the deviation of air temperature is obtained and a formula for the required control time is derived, as well as its estimation is given on the example of one residential building in the climatic conditions of Moscow. Conclusions. It is shown that the dependence of the air temperature in a room serviced by microclimate systems with integrated controllers on time is represented in a universal dimensionless form, suitable for any objects regardless of their specific characteristics. The previously discovered relationships for the moment of maximum deviation and the value of the dynamic control error depending on the air exchange of the room, the transmission coefficient of the controller and the room’s own heat stability are confirmed and refined.