Dynamic modeling and validation of a micro-combined heat and power system with integrated thermal energy storage

Modular Approach for Modelling Warming up Process in Water Installations with Flow-Regulating Elements

“…In commonly used methods of modelling water installation warming-up processes, it is expected that modelled energy system is described by a certain number of equations concerning the laws of conservation: mass, energy and momentum with simultaneously defined boundary conditions. The set of differential equations obtained from the analysis is usually non-linear and should be reduced to linear form so that it is possible to use standard numerical methods to solve them [22].…”

“…In detail, two methods are employed for solving the problem described above: one is an algebraic approach and the other one is differential [22]. Models derived using the Energies 2021, 14, 4599 2 of 17 algebraic approach assume that either the system operates at steady-state or the transient response does not significantly impact the outcome of the analysis [23,24].…”

“…Modelled heat exchange systems can be divided into control elements related to other heat transport mechanisms, e.g., in a proton exchange membrane fuel cell, the first control element is an anode and a cathode, while the second control element is the liquid in the cooling channels [22]. Heat accumulation can then be considered independently in these two control elements.…”

“…For the simulation of the warming-up or cooling process of such systems, the average temperature of the fluid in the exchanger channels is taken into account, its rate of change is defined by the rate of stored energy [30]. The average fluid temperature is calculated on the basis of the inlet and outlet temperature of the analyzed device [22,31]. The heat flux received in the membrane heat exchanger, also under dynamic conditions, is calculated using lumped parameters based on the average wall temperature, average fluid temperature and the total heat exchange surface [9,22].…”

“…The average fluid temperature is calculated on the basis of the inlet and outlet temperature of the analyzed device [22,31]. The heat flux received in the membrane heat exchanger, also under dynamic conditions, is calculated using lumped parameters based on the average wall temperature, average fluid temperature and the total heat exchange surface [9,22]. This approach facilitates the calculations but makes it impossible to take into account the nonlinear distribution of wall and fluid temperature inside the heat exchanger.…”