scholarly journals MATHEMATICAL MODELING OF TECHNOLOGICAL MODES OF HEAT-PUMPING SYSTEMS FOR TECHNOLOGICAL PROCESSES

2021 ◽  
pp. 85-91
Author(s):  
Boris Kotov ◽  
Vladimir Grishchenko ◽  
Yuriy Pantsir ◽  
Igor Garasimchuk
Keyword(s):  
Mathematical Model ◽  
Automatic Control ◽  
Heat Pump ◽  
Material Balance ◽  
Heat Pumps ◽  
Practical Implementation ◽  
Industrial Complex ◽  
Energy Potential ◽  
The Mathematical Model ◽  
Heat Carriers

One of the ways to increase the energy efficiency of the process of heat supply of technological facilities and production facilities of the agro-industrial complex is the use of heat pumps. Their use allows to increase the energy potential of heat carriers. To optimize the mode parameters and create systems for automatic control of the heat pump installation, it is necessary to establish a relationship between the parameters of the processes occurring in the elements of the installation by creating a mathematical model of non-stationary thermal modes. In the analysis of recent studies and publications, it is established that the calculations of processes in heat pumps are presented mainly for stationary modes of operation without taking into account the dynamics of the condenser. If the dynamic modes of individual elements are given, then they are described by mathematical models of considerable complexity, which greatly complicates their practical implementation. In the article, the heat pump installation, as an object of modeling, is considered as a physical system, which consists of four series-connected elements: evaporator, condenser, compressor, throttle valve forming a closed circuit. The principle of operation of a simple heat pump installation is explained by the scheme and schedule of the theoretical cycle of the steam compressor heat pump. To simplify the mathematical model, certain assumptions were made: the change in the parameters of liquid, vapor and air varies in a straight line, the thermophysical characteristics of the material of heat exchangers, air and vapor flows, heat transfer coefficients do not depend on temperature and are average for the cycle. On the basis of thermal and material balance the corresponding differential equations which make mathematical model of dynamics of change of parameters of the heat exchanger have been made. The mathematical model is supplemented by a simulation model in the MatLAB / Simulink computer environment, as well as graphical interpretations of dynamic characteristics. The developed mathematical model of dynamics of thermal processes in the heat pump installation can be used for calculation of parameters of heating and cooling of streams of heat carriers and creation of system of automatic control of them.

Thermal Modeling of a Reversing Valve in a Refrigeration System

2003 ◽  
Author(s):  
Shirish Raichintala ◽  
Manohar Kulkarni
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Heat Pump ◽  
Pressure Losses ◽  
Heat Leakage ◽  
Theoretical Predictions ◽  
Work Input ◽  
Compressor Work ◽  
Mass Leakage ◽  
The Mathematical Model

A mathematical model of a reversing valve was developed in order to evaluate the losses and for determining the effects of a reversing valve, on the performance of a heat pump. This mathematical model of the reversing valve was tested using the experimental data of Fang and Nutter (1999). The theoretical predictions made by this model agreed with that of the experimental data. Further, the mathematical model isolated the pressure losses due to friction; pipe-fittings, mass-leakage and heat transfer from the total losses. The evaluation of constituent losses assisted in detecting a faculty reversing valve, and also determining the effect of mass leakage and heat leakage on the compressor work input and COP of the heat pump.

Thermohydraulic Analysis of Ground as a Heat Source for Heat Pumps Using Vertical Pipes

1996 ◽  
Vol 118 (4) ◽  
pp. 300-305 ◽  
Author(s):  
M. T. Kangas
Keyword(s):  
Computer Simulation ◽  
Heat Source ◽  
Heat Pump ◽  
Thermal Energy ◽  
System Performance ◽  
Thermal Effects ◽  
Heat Pumps ◽  
The Other ◽  
Heat Extraction ◽  
Energy Potential

In this study, the use of the ground as the heat source for a heat pump was studied by computer simulation. The heat extraction system consisted of vertical pipes drilled into the ground where groundwater was present. Along with available thermal energy, potential environmental effects, such as freezing and thermal pollution, were examined. It was found that the presence of groundwater enhances system performance by decreasing the possibility of freezing but, on the other hand, increases the range of thermal effects in the ground. The temperature of the ground as well as extraction arrangements also have a significant effect on system performance.

The Mathematical Model for the Generation of the Cylindrical Gear With Curved Cycloidal Teeth

2007 ◽  
Author(s):  
Iulian Stanasel ◽  
Adrian Ghionea ◽  
Ionut Ghionea ◽  
Petru Ungur ◽  
Oana Stanasel
Keyword(s):  
Mathematical Model ◽  
Production Costs ◽  
Reference Plane ◽  
Practical Implementation ◽  
Work Piece ◽  
Special Device ◽  
Technological Parameters ◽  
Cylindrical Gear ◽  
Processing Machine ◽  
The Mathematical Model

The performed studies regarding the cylindrical gears with curved teeth or in V showed that a uniform distribution of the load on the flanks is hard to realise, generally being necessary later finishing processing or modifying the gear by camber or flanking, which suppose supplementary expenses. On the basis of these mentions and taking into account the advantages of curved bevel gear, the purpose of this paper is to present an original study regarding the mathematical model for generation of a curved cylindrical gear with high performances. The cycloidal gear was chosen after a technical and an economical study regarding on the possibility of practical implementation with the lowest production costs using a special device, adapted on a Phauter processing machine of cylindrical gear. This was the main reason for choosing a cycloidal profile from several types of curved teeth (cycloidal arc, circle arc, Archimede’s spiral, involute arc). So, the main aim of the paper is to determine the equations of the flanks of cylindrical wheel with curved teeth in oblong cycloidal arc, in order to establish if the technical generation is possible. The curved cylindrical teeth with cycloidal flanks is generated by rolling with straight mobile line and continuous division by using a milling cutter with 1, 2, 3, 6 groups of knifes equidistantly placed, fixed on an adaptable device on a Phauter processing machine. The two curves which define the flank are simultaneously generated by correlated motions, and the flanks of the wheel part result as a roll of successive positions of generating hook materialized by the cutting edge of the tool. The shape of the contact curve between the conjugated surfaces of generating element and the wheel part can be obtained if you are taking into account the kinematic condition. Using this condition you can determine the relationship between the kinematic, geometric and technological parameters. The line of the flanks is studied in the reference plane and in parallel planes with this, and the profile of the flanks is determined in perpendicular planes on the work piece axis. Based on the parametric equations it was made the simulation program in MATLAB that indicates that this gears can be obtained, and constitutes the first step in practical manufacturing of this kind of gears. By analyzing the obtained shape they result useful conclusions for the manufacturing of the involute-tooth gear with curved oblong cycloidal arc. On the other hand, using Solid Edge it was made the spatial modeling of the cylindrical gear with curved cycloidal teeth that allows next FEA studies regarding on the contact and bending stress.

The Numerical Simulation of the Solar-Air Dual-Source Heat Pump System

2011 ◽  
Vol 138-139 ◽  
pp. 305-309
Author(s):  
Chao Zhang ◽  
Xiao Dan Zhao ◽  
Guang Hui Zhou
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Heat Pump ◽  
Parameter Method ◽  
Heat Sources ◽  
The Novel ◽  
Pump System ◽  
Heat Pump System ◽  
Dual Source ◽  
The Mathematical Model

The heat pump technology which is as an effective energy-saving technology has attracted more and more attentions. A novel solar-air dual-source heat pump system which could synchronously use two heat sources has been provided. In this paper, the mathematical model of the new heat pump system has been built and the calculation accuracy of the mathematical model has been proved. Based on a novel solar-air dual-source heat pump system, the mathematical models of the thermophysical parameters of working fluids, compressor, capillary, condenser, evaporator, and heat pump system have been established. The distribution parameter method has been adopted in the mathematical models of condenser and evaporator. Three operation modes of the novel solar-air dual-source heat pump system have been simulated. The simulated results and the experimental results have been compared. The experiments of the novel solar-air dual-source heat pump system have been accomplished in the constant temperature and humidity laboratory. The compared results show that the error is less than 10%.

Selection of Method for Underwater Robot Control

2010 ◽  
Vol 164 ◽  
pp. 149-154 ◽  
Author(s):  
Piotr Szymak
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Numerical Analysis ◽  
Automatic Control ◽  
Robot Control ◽  
Underwater Vehicle ◽  
Underwater Robot ◽  
Underwater Robots ◽  
The Mathematical Model ◽  
Selection Of

Automatic control of motion of underwater robots, particularly along desired trajectory, requires application of proper controllers taking into account dynamics of the underwater robot and features of the marine environment. In the paper the mathematical model of an underwater vehicle [2] and the architecture of designed control system [4] have been presented. Moreover, selected results of numerical analysis in the form of comparison of different course controllers have been provided.

scholarly journals IMPLEMENTATION OF THE METHODS OF IDENTIFICATION OF STATIC CONTROL OBJECTS

2017 ◽  
pp. 72-78
Author(s):  
Sergey Pachkin ◽  
Sergey Pachkin ◽  
Roman Kotlyarov ◽  
Roman Kotlyarov
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Automatic Control ◽  
Automatic Control System ◽  
Mathematical Description ◽  
Control Object ◽  
Parametric Identification ◽  
Identification Problem ◽  
Temperature Control System ◽  
The Mathematical Model

One of the main tasks solved in the development of automatic control systems is the identification of the control object, which consists in obtaining its mathematical description. The nature and type of the mathematical model is determined by the goals and tasks for which it will be used. In the present case, the aim of obtaining the model is the synthesis of an automatic control system. Proceeding from the requirements of control problems, the identification problem consists in determining the structure and parameters of the mathematical model that ensure the best similarity of the model and object responses to the same input action. The article considers the experimental method of obtaining a mathematical description of the control object based on the results of measuring its input and output parameters and then processing the obtained results. The control object is the EP10 emulator made by the Oven Company, which is a miniature furnace. The emulator is used in experimental research in the process of commissioning using thermostat controls, and also applicable for educational purposes as part of training and research stands. As a result of structural identification with subsequent adjustment of the coefficients with the help of parametric identification, a model of the control object in the form of a second order aperiodic link is obtained. Parameters and type of the mathematical model allowed to make calculations and determine the parameters of adjustment of the TRM251 PID-controller. The software implementation of the automatic control system in the MatLAB environment made it possible to evaluate transient processes in a closed system. Thus, the calculation and analysis of the automatic control system in the first approximation were made. The final result can be obtained at the stage of commissioning the automatic temperature control system in the EP10 emulator using adaptation algorithms.

Modelling of external filter cake profile along the well during drilling

2014 ◽  
Vol 54 (1) ◽  
pp. 319 ◽  
Author(s):  
Azim Kalantariasl ◽  
Abbas Zeinijahromi ◽  
Pavel Bedrikovetsky
Keyword(s):  
Mathematical Model ◽  
Velocity Profile ◽  
Filter Cake ◽  
Thickness Distribution ◽  
Material Balance ◽  
Force Balance ◽  
Predictive Tool ◽  
Physiochemical Properties ◽  
Cake Thickness ◽  
The Mathematical Model

This paper presents a new mathematical model to predict the steady-state external filter cake thickness distribution and velocity profile along the wellbore during overbalanced drilling. Several models have been suggested for the prediction of external cake thickness using the force balance method. Yet, a comprehensive literature survey reveals that electrostatic forces and the permeate force correction factor have been neglected, while both can significantly change the conditions of particle detachment from the cake surface. Torque balance of hydrodynamic (lifting, tangential and permeate drag), gravity and electrostatic (DLVO) forces along with Darcy’s law and material balance is used to investigate the conditions of particle attachment/detachment on the cake surface. The results show strong effects of mud chemistry, particle size, cake permeability, tangential flow velocity, overbalance pressure, and Young’s modulus on the external filter cake thickness and velocity profile. The mathematical model can be applied as a predictive tool for the estimation of filter cake thickness. It allows for the calculation of external filter cake distribution using the physiochemical properties of mud and particles.

AI OPTIMIZATION OF THE EXOTHERMIC REACTION OF ETHYLENE OXIDE WITH WATER

2021 ◽  
pp. 2150033
Author(s):  
Khaled A. Al-Utaibi ◽  
Ayesha sohail ◽  
Andleeb Zafar ◽  
Rana Talha ◽  
Sadiq M. Sait
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Ethylene Oxide ◽  
Ethylene Glycol ◽  
Exothermic Reaction ◽  
Plug Flow ◽  
Material Balance ◽  
Chemical Species ◽  
Future Research ◽  
The Mathematical Model

A computational framework, for the numerical approximation of the exothermic reaction of ethylene oxide (EO) with water, to form ethylene glycol is presented in this paper. Ethylene Glycol also known as Mono-ethylene Glycol (MEG), is a diol with a boiling of 198[Formula: see text]C and conventionally produced through hydrolysis of ethylene oxide which is obtained through the oxidation of ethylene. It is used as an excellent automobile coolant as the 1:1 ratio mixture of MEG with Water boils at 129[Formula: see text]C and freezes at [Formula: see text]C. Other than its use as an antifreeze, it is also used as a reagent during the production of polyester fibers, pharmaceutics, cosmetics, hydraulic fluids, printing inks, explosives, polyesters and paint solvents. The mathematical model presented here, consists of an energy balance and a material balance system, described in an axisymmetric coordinate system. The optimized resulting values using the artificial intelligence approach are summarized in this paper. We derive an analytical solution. The analytical solution for the mathematical model equations is in general not possible for this model but it may be possible to derive an analytical solution to this mathematical model if we consider the equation for the conservation of material (chemical species) as a formulation for plug flow and isothermal conditions. Noteworthy findings are reported in this paper for future research.

Estimación del potencial energético del gas pobre obtenido de la gasificación del bagazo de caña de azúcar en gasificadores de lecho fijo de corriente descendente utilizando el modelo cinético de tasa finita

2020 ◽  
pp. 28-41
Keyword(s):  
Mathematical Model ◽  
Sugarcane Bagasse ◽  
Calorific Value ◽  
Quasi Equilibrium ◽  
Energy Potential ◽  
Language Version ◽  
The Poor ◽  
El Sistema ◽  
Python Programming ◽  
The Mathematical Model

Estimación del potencial energético del gas pobre obtenido de la gasificación del bagazo de caña de azúcar en gasificadores de lecho fijo de corriente descendente utilizando el modelo cinético de tasa finita Cesar Zavala, Victor Petrell Universidad Nacional de Ingeniería, Lima, Perú. Recibido el 29 de diciembre del 2019. Revisado el 24 de febrero del 2020. Aceptado el 2 de marzo del 2020 DOI: https://doi.org/10.33017/RevECIPeru2020.0004/ Resumen El propósito de este trabajo es estimar el potencial energético del gas pobre obtenido de la gasificación de bagazo de caña de azúcar utilizando gasificadores de lecho fijo de corriente descendente en Perú a través de un nuevo modelo matemático que considera el tamaño de los fragmentos de biomasa. Para este propósito, tuvimos que determinar el área dedicada al cultivo de la caña de azúcar, la cantidad de caña de azúcar producida por cada área cultivada, la cantidad de bagazo obtenida de la caña de azúcar y la proporción de humedad y residuos secos, utilizando datos estadísticos peruanos. El modelo matemático de Prokash Roy se consideró modificando las constantes del equilibrio químico y las tasas de reacciones químicas que se controlan cinéticamente a velocidad finita, porque en realidad el sistema se comporta como un cuasi equilibrio. Para este modelo modificado, la humedad del bagazo debe ser inferior al 20% pero no debe estar completamente seca. Los resultados fueron validados con los datos experimentales de Jayah. Además, se utilizó una nueva codificación en el lenguaje de programación Python versión 3.x, utilizando una plataforma interactiva llamada Jupyter Notebook, que también hace posible predecir la composición, el máximo valor calorífico inferior del gas pobre y la temperatura de la zona pirooxidación. La estimación del potencial energético del gas pobre a partir de la gasificación del bagazo de la caña de azúcar fue de 19396.6 TJ por año como valor máximo y 16843.7 TJ por año como valor mínimo. Descriptores: Gasificación, potencial energético, gasificador de tiro descendente, residuos agrícolas. Abstract The purpose of this work is to estimate the energy potential of poor gas obtained from sugarcane bagasse gasification using downward-flow gasifiers in Peru through a new mathematical model that considers the size of biomass fragments. For this purpose, we had to determine the area dedicated to the cultivation of sugarcane, the amount of sugarcane produced by each cultivated area, the amount of bagasse obtained from sugarcane and the proportion of moisture and dry residue, using Peruvian statistical data. The mathematical model of Prokash Roy was considered by modifying the constants of chemical equilibrium and the rates of chemical reactions that are kinetically controlled at finite speed, because actually the system is behaving as a quasi-equilibrium. For this modified model, the humidity of the bagasse should be less than 20% but should not be completely dry. The results were validated with the experimental data of Jayah. In addition, a new coding was used in the Python programming language version 3.x, using an interactive platform called Jupyter Notebook, which also make possible to predict the composition, the maximum lower calorific value of the poor gas and the temperature in the pyrooxidation zone. The estimation of the energy potential of the poor gas from the gasification of sugarcane bagasse was 19396.6 TJ per year as a maximum value and 16843.7 TJ per year as a minimum value. Keywords: Gasification, energy potential, downdraft gasifier, agricultural residues.

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