Abstract
The paper presents a new method for modelling the warming up process of a water system with elements regulating the flow in a stochastic manner. The paper presents the basic equations describing the work of typical elements which the water installation is composed of. In the proposed method, a new computational algorithm was used in the form of an iterative procedure enabling the use of boundary conditions that can be stochastically modified during the warming-up process. A typical situation, when such a modification is processed, is the regulation of the medium flow through two-way or three-way valves or applying additional heat source. Moreover, the presented method does not require the transformation of the differential equations, describing the operation of individual elements, into a linear form, which significantly facilitates analytical work and makes it more flexible. The example of analysis of the operation of water installation used for controlling temperature of the process gases in a chemical installation shows the functionality and flexibility of the method. The adopted calculation schematics enable changing the direction of the heat flow while the heat exchanger is in operation. Additionally, the sequence of calculation processed in modules describing operation of installation elements is elective (there is no situation that output parameters from one element are used as input parameters for other element in the same calculation step).
Highlights
The problems of dynamics of heating and cooling process in elements of heat and mass transfer matter practically in district heating, [1,2], cooling and air-conditioning systems [3,4,5,6], electronics, chemical systems [7,8] and in devices where unsteady heat transfer is a standard operating mode, e.g., Stirling engines [9,10]
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
Differential approach for modelling of water installation warming-up process can grasp the dynamic response of the system, but it requires numerical solution of the problem described by nonlinear differential equations
Summary
The problems of dynamics of heating and cooling process in elements of heat and mass transfer matter practically in district heating, [1,2], cooling and air-conditioning systems [3,4,5,6], electronics, chemical systems [7,8] and in devices where unsteady heat transfer is a standard operating mode, e.g., Stirling engines [9,10]. Differential approach for modelling of water installation warming-up process can grasp the dynamic response of the system, but it requires numerical solution of the problem described by nonlinear differential equations In this approach, the temperatures are considered as searched variables in the analyzed points of the system [26]. 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 This approach, in the case of proton exchange membrane fuel cell modelling, micro-combined heat and power system, made it possible to map the temperatures in the analyzed points having a maximum root mean square error of 2.38 ◦ C over an operating range of approximately. The paper presents an example of modelling the warming-up process of a water installation controlling the operation of chemical reactors typically used in industry
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