Abstract. The accuracy of hydraulic calculations is determined by the accuracy of the mathematical models inherent in their foundation. The results of calculations, obtained by different models, and differing from each other by 5-10% is considered identical. The present study examines classical ways of finding the Chezy formula that are used for calculations of free-flow pipelines. These formulas differ from each other not only in parameters but also in the form of the functional dependence. The equation, underlying the hydraulic calculations, is nonlinear. Its solution is possible only in the number of well-established methods. It offers numerical computing to find pipelines diameters and their filling, as well as the algorithm to realize it. It conducts numerical experiment to compare pipelines diameters and filling and flow velocities. It presents frequency characteristics to distribute the parameters under analysis. For a specific example, the difference of cost of pipes, the diameters of which was found using the various formulas for coefficient Chezy, was calculated.
The article provides an analysis of existing solutions for choosing shell-and-tube heat exchangers for the needs of hot water supply. When constructing a mathematical model of heat transfer, an approximation of the criterial dependencies describing this process was used. The error estimation of approximating dependencies is presented. The mathematical model of heat balance was used in a numerical experiment. The significance of the influence on the heat transfer efficiency of the parameters of the heat exchanger was established by the results of a numerical experiment. The results of a numerical experiment made it possible to develop criteria for choosing heat exchangers. Keywords: hot water supply, heat exchanger, mathematical modeling, selection criteria
Formation of balance of thermal energy and the heat carrier for a thermal network is carried out for the purpose of increase of efficiency of work of the heat supplying organization. The standard approach proposes to write off the difference between the released and realized heat energy for heat losses. The article proposes a new approach to the formation of the balance of thermal energy and coolant. It includes statistical analysis of telemetry data relating to the released thermal energy. Heat consumption was estimated by contractual load for heating, ventilation and hot water supply. In the mathematical model of the thermal balance for each term weight coefficients were introduced. To obtain the numerical values of these coefficients, the method of least squares was used. The results of checking the adequacy of mathematical models that take into account or neglect thermal losses are presented. The obtained coefficients for the mathematical model of heat balance were used for the mathematical model of mass balance. The results can be used to predict the cost of production and transmission of heat energy and coolant, to assess the efficiency of the heat network and the formation of tariff applications for the future.
The purpose of the study is to test the hypothesis about the possibility of using telemetry data to identify heat supply objects. The article considers 4 models approximating telemetry data. Determination coefficients and standard deviations were used to select the best model. The residuals were analyzed for randomness, and the absence of shifts and trends. The consistency of the frequency distribution of the residuals with the normal distribution was checked. The significance of the coefficients included in the approximating functions is estimated. Regression analysis was used to obtain the coefficients of 4 models for each of the 7 objects. The Pearson test confirmed the consistency of the distribution of the residuals of one of the models with a normal distribution for all objects. The significance of the coefficients included in all models was confirmed using Student’s t-distribution. The proposed models take into account the flow rate of the coolant and the temperature of the outside air. The dependences obtained do not contradict the physics of the process, both in the field of observation and beyond its boundaries. With certain restrictions on the coefficients of the model, it is possible to obtain numerical values of the parameters of heat supply objects - the average temperature of the indoor air and the required heating load, which confirms the hypothesis that telemetry data can be used to identify the parameters of heat supply objects.
Solar thermal system are its constituent elements with their connection between each other, thermal processes within them and also input/output data. The conjunction of external and internal factors determines the efficiency of solar thermal system. No excess heat as well as its deficiency displays us high level efficiency of system. The initial data for modeling of solar thermal systems functioning are dissimilar. Parameters of system’s equipment are constant. Solar radiation amount and water consumption are variable data. The more close initial data to reality, the more definite simulated result is. The main problem is in unpredictability of water consumption by the reason of daily regime and requirement of each user. In this way user is the most instable element of the system. In this study the input data for mathematical modeling of solar thermal systems was analyzed. The climatic databases and standard specifications of hot water demand were also analyzed. The operability estimation method for solar thermal systems with variable input data was offered. The extent of suitability of any solar thermal system can be defined by certain characteristic. The value of this characteristic displays energy accumulation process.
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