Criterial Equation Research Articles

Analysis of the Mathematical Models for Identifying the Thickness of the Fouling Layer in Natural Gas Coolers

This article presents an analysis of three different approaches to the identification of the thickness of the fouling layer inside the pipes of natural gas (NG) coolers. At present, there is no existing simple analytical procedure for the identification of the fouling layer thickness. The authors of this article describe in detail the balance method, which required the use of a large number of physical parameters, changes in their sizes depending on the output temperature of the gas, the temperature of the cooling air, the air quantity, as well as the physical properties of both media. The computational model was robust, and its disadvantage was the iterative computation. The second analysed method was a dimensional analysis. It was applied using the Buckingham’s theorem to express the individual similarity criteria. In this method, 10 simplexes and two complexes were created. The fouling layer thickness, expressed using a derived criterial equation, exhibited real results. The third analysed method was based on analysing selected physical parameters with the use of a multiple regression analysis in MinitabX 18 software. The analysis showed that the fouling layer thickness depended on fewer parameters than the number of parameters assumed in the dimensional analysis or the balance method. The standard deviation that was identified in the multiple linear regression for a double crossflow cooler was 0.0667 and the value of reliability (the coefficient of determination of the multiple linear regression) R2 was 0.9985.

A Similarity Model of Specific Heat Loss Determined by Dimensional Analysis

This article describes an innovative method for the determination of heat flow (specific heat loss; linear heat flow density) from a one-metre length of a twin pipe directly-buried heat network. Such heat losses are currently described by applying analytical procedures based on the heat transfer theory. It is rather complicated to accurately express the heat loss using such procedures, due to the necessity to determine the individual values of thermal resistance. A simpler method to express heat loss is the balance method, as it requires measuring a temperature gradient Δt between the starting point of the heat network and the end point of the heat collection. A suitable measuring device must provide high-accuracy measurements of the temperature. In the case of very well-insulated distribution pipelines and short pipes, the temperature measurements must be accurate to the hundredths of a degree Celsius. It is impossible to install such devices as fixed equipment on every heat distribution network, due to such networks measuring many kilometres and the cost of the appropriate measuring technology. For the aforesaid reasons, the authors created a mathematical model for specific heat losses based on dimensional analysis. This method facilitates the identification of dimensionless criteria based on the relevant dimensional quantities. Functional correlations between the identified criteria may be identified on the basis of the results of physical or numerical experiments. In this study, a database of the results obtained from physical experiments conducted on two heat networks was used. The output of the similarity model was a function describing the heat flow from a one-meter pipe length that was applicable to various alternatives in relation to the geometrical, physical and boundary conditions. The standard deviation of a difference in the heat losses identified by applying the balance method and using the proposed criterial equation for a twin pipe directly-buried pre-insulated heat network was 0.515 W·m−1.

Теплообмен в охлаждаемых камерах сгорания теплогенераторов малой мощности

Introduction. The study of heat exchange in cooled combustion chambers and the influence of various factors on its intensity is a complex and relevant task. The analysis of theoretical and experimental data on heat exchange in combustion chambers of various plants has proven that current methods fail to take into account features of heat exchange in furnaces, having small geometric dimensions and, therefore, they cannot be used for their thermal calculation. Materials and methods. The author presents the experiments and the results of their generalization performed using the criterial equation. Generalization results are of great importance for analyzing heat transfer processes and the thermal analysis of cooled combustion chambers of small capacity heat generators. The contribution of radiative and convective components to complex heat exchange processes in combustion chambers of low-capacity boilers is evaluated using this generalized dependence. The author has identified qualitative and quantitative dependence of integral radiative and convective heat exchange on the main factors of operation of small combustion chambers. Results. The author has obtained generalizing criterial dependence that makes it possible to evaluate the contribution of radiative and convective components to complex heat exchange in combustion chambers of low-capacity boilers. Conclusions. The generalized criterial dependence, obtained by the author, can be used to identify the qualitative and quantitative dependence of integral radiative and convective heat transfer on the main geometric, physical and performance factors of operation of small capacity furnace chambers. The assessment of reliability of the experimental data, obtained by the author, has shown that the value of the limiting mean square error of determining the value of integral heat transfer Kh.t will be 3.24 %. For all experiments, the deviation of the calculated data from the experimental results with a 95 % probability does not go beyond the confidence interval of ±9.52 %.

Role of CCUS in carbon neutral power system

Achieving carbon neutrality by 2060 is an ambitious goal to promote the green transition of economy and society in China. Highly relying on coal and contributing nearly half of CO2 emission, power industry is the key area for reaching carbon-neutral goal. On basis of carbon balance, a criterial equation of carbon neutral for power system is provided. By means of the equation, the different effects of three technical approaches to achieve carbon neutrality, including energy efficiency improvement, shifting energy structure and CO2 capture, utilization and storage (CCUS) technology, had been evaluated. The results indicate that building a carbon-neutral power system requires comprehensive coordination between energy efficiency, renewable energy and CCUS technology. In particular, the unique role of CCUS in achieving carbon neutral target was investigated. For any power systems with fossil energy input, CCUS and negative emission technologies is indispensable to reach carbon neutrality. However, rather high energy consumption and costs is the critical gas deterring the large scale deployment of CCUS. Considering the specific conditions of China’s power industry, before the time window between 2030 and 2040 being closed, CCUS would either be ready for large scale deployment by reducing energy consumption and costs, or be phased out along with the most coal power plants. Conclusively, carbon neutral scenario will give CCUS the last chance to decarbonize the fossil fuel, which has great significance for China.

Повышение энергоэффективности тентового укрытия для окрашивания и сушки крупногабаритных металлоконструкций

This paper investigates temperature modes of painting large metal structures in a tent-type drying chamber for the purpose of quality assurance and improving energy efficiency of the coating process. The research of several options of air removal out of a tent cover was performed. A SolidWorks model for a drying chamber with a large painted metal structure was developed in order to figure out temperature fields, air speed, and air trajectory. The model considers the joint effect of free and forced convection as well as aerodynamics of inner tent space on heating efficiency. The energy-saving design of the tent cover, which allows preheating air before the calorifier, has been proposed. As a result, a criterial equation has been obtained and energy efficiency optimization software has been developed.

Some aspects of plate number estimation of plate heat exchangers (PHEs). A case study

Abstract For the proper estimation of the plate number (N) of a plate heat exchanger (PHE) – in addition to the flow rates and thermophysical properties of fluids –, an appropriate correlation is needed for convective heat transfer coefficient (α) calculation. When one does not have a criterial equation for the corresponding plate shape, we propose a selecting method for α. With the suggested relationships from literature, we calculate the plate number of a geometrically known, similar heat duty PHE and choose those relationships that give the same plate number with the known heat exchanger. In our case study, the plate number determined by any of the screened equations for whole milk preheating has almost the same value (n = 10 ± 1) regardless of the method used to solve the PHE model (plate efficiency and Nconverg or Kconverg convergence methods). For liquids’ thermophysical property estimation, we recommend averaging the values given by equations from literature, followed by equation fitting.

Criterial equation of carbon neutrality for power systems

By the end of 2020, most countries in the world have successively proposed carbon-neutral targets. Among them, the major economies in the world, such as the United States (USA), the European Union, Japan, and Canada, have proposed to achieve carbon-neutral targets by 2050. As the world’s largest carbon emitter, China has a total carbon emissions of more than 11.3 billion tons, accounting for about 30% of global carbon emissions. Therefore, the carbon emission reduction required for China is much higher than that of other economies, and its carbon-neutral tasks are obviously more complex and diversified. On 22 September 2020, the Chinese government announced in the 75th Session of the UN (United Nations) General Assembly (New York, USA) that China aims to achieve carbon neutrality before 2060. The announcement of the carbon-neutral target clearly indicated that China needs to carry out a self-revolution to achieve zero CO2 emissions before 2060. The concept of carbon neutrality is essentially a balance between carbon sources and carbon sinks. The carbon source is the process of releasing CO2 into the atmosphere, and the carbon sink is the process of absorbing CO2 from the atmosphere. Investigating the atmospheric system within a certain period, when the amount of CO2 emitted by all carbon sources into the system is equal to the amount of CO2 absorbed by all carbon sinks from the system, carbon neutrality can be achieved. There are various carbon sources and sinks in nature with complicated relationships. Among them, the most important carbon source related to human activities is energy production. In 2020, China’s power sector emitted about 4 billion tons of CO2 per year, which is close to 40% of the total emissions. Thus, the power sector is one of the key areas in emission reduction to achieve the carbon-neutral goal. Building a carbon-neutral power system is the only way to achieve decarbonization in the energy sector. Based on the carbon balance principle, this paper proposed the critical equation of carbon neutrality for power systems. And the further strategies in establishing a carbon-neutral power system were explored according to the carbon neutrality equation: (1) Improve energy efficiency thus reducing the consumption of carbonaceous energy; (2) adjust the energy structure and reduce the proportion of carbonaceous energy; (3) rebuild the balance of sources and sinks by adopting CO2 capture, utilization and storage (CCUS) technology to achieve low-carbon utilization of carbonaceous energy. Results indicate that, although improving energy efficiency of carbonaceous energy is effective in CO2 mitigation, it is limited by the declining energy saving potential of thermal power plants to be the main technical way in carbon emission reduction. Besides, increasing the proportion of renewable energy can quickly reduce the carbon emission intensity of the power system, which is currently the main technical way to reduce the CO2 emission of the power system. However, although energy conservation and the development of renewable energy can reduce the carbon emission intensity of the power system, the CCUS technology and the negative emission technology will be indispensable to achieve the goal of carbon neutrality. And the large-scale promotion of the CCUS technology must overcome technical obstacles of the rather high energy consumption of CO2 capture. Thus, building a carbon-neutral power system in the future requires a combination of energy efficiency, renewable energy and CCUS technology.

Determination of heat transfer criterial equation when cooling aluminum ingots

A big problem when casting aluminum ingots is the uneven structure formation, which leads to an increased rejection of products. Nonequilibrium structure elimination is carried out by heat treatment. To obtain the required aluminum ingots’ physicochemical properties, it is necessary to know the conditions of heat transfer between the ingots and the cooling air, i.e. a mathematical model of conjugate heat transfer is needed. The mathematical model obtained by the authors makes it possible to analytically investigate the ingots temperature and cooling air during heat treatment. This mathematical model assumes the heat transfer coefficient calculation. The existing criterion equations for determining the heat transfer coefficient have a drawback - the heat transfer coefficient according to these equations is calculated in circular channels, while heat transfer between aluminum ingots and air occurs in rectangular channels. The article describes the criterion equation identification for heat transfer, used in the analytical study, by the data of the experimental study.

Design and implementation of an energy-saving melting reactor

A physico-chemical model of zinc recovery, in the melt ideal mixing regime, has been developed. From the cold model experiments, the melt complete mixing time criterial equation is derived. Based on it, the parameters of pilot plant were calculated and consequently the experiments for validation were conducted. The value of specific volumetric productivity, which is the key factor for calculation of the industrial sample of the reactor has been determined. By the method of affine modeling, test results of the pilot plant on its industrial design were recalculated. The calculation results demonstrate that by the increase of reactor slag productivity from 0.693 t/h up to 30 t/h, the share of the effectively used heat will increase, the heat share of the cooling water will be decreased and the fuel consumption will be reduced approximately by 2.5, 2.7 and 3 times respectively. Furthermore, by processing of solid slag, the fuel consumption would be reduced by 1.5 times compared to the one in the fuming furnace processing melted slag. It would also be 3–4 times lower than waelz-kiln treating the granulated slag. Due to low level of the molten bath in the reactor where the height is about 0.2 m, the power consumption of the air blower would be approximately 2 times less than that in fuming furnace of height about 0.7 m.

A REGENERATIVE COOLING SYSTEM FOR THE CHAMBER OF A LIQUID-PROPELLANT ROCKET ENGINE WITH INTERCHANNEL COOLANT FLOW THROUGH A METAL MESH

The paper discusses a new method for regenerative cooling of the chamber of liquid-propellant rocket engines using the concept of interchannel coolant flow through a porous metal mesh made by vacuum diffusion welding of woven metal netting. It provides a theoretical rationale for switching from unidimensional (longitudinally channeled) flow to two-dimensional (interchannel) inter-mesh flow coolant through a porous mesh. It provides experimental data for hydraulic resistance and heat exchange in porous metal meshes. Based on the experimental data, a generalized criterial equation was obtained for surface heat release in the paths with interchannel two-dimensional intermesh coolant flow through metal mesh. The paper examines the efficiency of heat exchange in the paths with interchannel coolant flow. Key words: regenerative cooling, interchannel flow; vacuum diffusion technology, metal mesh; hydraulic resistance; heat exchange, heat exchange efficiency.

A regenerative cooling system for the chamber of a liquid-propellant rocket engine with interchannel coolant flow through a metal mesh

The paper discusses a new method for regenerative cooling of the chamber of liquid-propellant rocket engines using the concept of interchannel coolant flow through a porous metal mesh made by vacuum diffusion welding of woven metal netting. It provides a theoretical rationale for switching from unidimensional (longitudinally channeled) flow to two-dimensional (interchannel) inter-mesh flow coolant through a porous mesh. It provides experimental data for hydraulic resistance and heat exchange in porous metal meshes. Based on the experimental data, a generalized criterial equation was obtained for surface heat release in the paths with interchannel two-dimensional intermesh coolant flow through metal mesh. The paper examines the efficiency of heat exchange in the paths with interchannel coolant flow. Key words: regenerative cooling, interchannel flow; vacuum diffusion technology, metal mesh; hydraulic resistance; heat exchange, heat exchange efficiency.

БАГАТОКРИТЕРІАЛЬНА МОДЕЛЬ ЯКІСНОЇ ОЦІНКИ ТА ВИБОРУ СУЧАСНИХ ІМПУЛЬСНИХ РЕФЛЕКТОМЕТРІВ

A multicriteria model of qualitative assessment and selection of modern time-domain reflectometers is proposed in the article. The purpose of this study is to accelerate the procedure of determining the best model of the reflectometer from the appropriate company by creating a criterial equation based on modeling and visualization of multi-parameter quality criteria. A relational model of a set of modern time-domain reflectometers with structured data of technical and economic indicators has been developed. Conditional dimensional criteria for determining values based on dimension theory have been compiled. A multicriteria model of qualitative assessment of modern time-domain reflectometers in dimensionless coordinates has been constructed. A comparative analysis to determine the best model of the reflectometer of a certain company by parameters has been performed. To solve this problem, a set of modern time-domain reflectometers with structured data of technical and economic parameters in the form of a relational model is defined. It is proposed to use dimensional theory, physical modeling and to create conditional quality criteria based on the heuristic method. Comparative analysis shows that Megger company is the best in terms of dimensional criteria. The histogram compares technical and economic indicators of time-domain reflectometers of this company. As can be seen from the comparison of technical and economic indicators of Megger time-domain reflectometers, Megger Teleflex VX model, which has the best range and accuracy is the best one. The developed model allows to accelerate the design process and select the way to improve and ensure high quality for devices of this type.

Heat transfer of a spherical element with air-water aerosol in a cylindrical channel

The heat transfer from a single sphere suspended in a cylindrical channel with finely dispersed air-water (aerosol) flow is experimentally studied. Under stationary heating conditions, the values of the heat-transfer coefficients are obtained as dependent on the Reynolds number and the water mist rate. A physical model of heat transfer from the sphere surface with water mist-air flow is proposed, which allows evaluating the processes proceeding at the various stages of droplet evaporation in the flow near a heated surface and formation of a water film on the surface itself. The relative mass of the droplet moisture deposited on the sphere surface is estimated depending on the water mist rate and Reynolds number of the flow. A criterial equation is obtained that generalizes the experimental data in the form of the dependence of Nusselt number on the regime parameters of Reynolds, Weber, and the water-to-steam phase transition parameter is obtained.

Substantiation of regime parameters of vibrating conveyor infrared dryers

The analysis of constructive-technological schemes of vibrating conveyor machines for heat-exchange processing of bulk technological masses in the current mode is carried out, which allowed to substantiate the effectiveness of using a new modification of infrared dryers of vibration-wave execution with a flexible transporting body. For this scheme, a vibrating system is developed which mathematical modelling allowed to determine and substantiate the main parameters of the operating mode of the drive mechanism of the projected device. The experiments, using the developed research model, confirm and refine the results of theoretical analysis, energy efficiency and comparatively low metal consumption of the design structure. The difficulty of working with such a large number of factors led to the application of the second similarity theorem and the introduction of a mathematical model of the criteria of Stanton, Froude, Burdo, whose magnitudes are reflected through the main factors of influence and were found experimentally. After using the "dimension theory" and graph-analytic analysis of power functions, a criterial equation of the investigated process was obtained. This allows recommending the regime parameters and the design series of projected thermo-radiation dryers with vibration-wave transport of products when varying the main factors of influence.

The influence of the period switching frequency on the heat exchange of a regenerative air heater

A laboratory stand with a regenerative air heater, an automated system for control and measurement of air flow parameters and a nozzle designed to study the heat transfer of a package of parallel plates under non-stationary conditions for different periods are described. The technique of measuring the transient temperature of cold and hot coolant flows taking into account the inertia of thermocouples and the method of measuring the heat transfer coefficient of plates are presented. The time variations of the Nusselt number and the heat power transmitted by the nozzle for individual periods are shown. Values of the average Nusselt number for the period obtained in experiments with the packages of plates of different materials and thicknesses are generalized by a criterial equation convenient for engineering calculations of regenerative air heaters with sheet packing of various types.

Intensification of thermal and rheological processes in a scraped-surface apparatus

The operation parameters of a special heat exchange scraped-surface apparatus ware studied and mathematically described in the article. The feature of the apparatus was the use of perforated cleaning devices in order to increase the turbulence of a product. The developed device can be used in the dairy, meat, and fat and oil industry to cool cream, animal fats, margarine emulsions, cooking fats, and other viscous food products. The increase in the productivity of the apparatus was achieved as a result of the more intensive mixing of the cleaned wall layers with the bulk of the cooled product due to the presence of cylindrical holes in the slats with a diameter of at least 
 0.05–0.1 of the diameter of the working cylinder. As a result of processing experimental data on heat exchange taking into account energy dissipation, a calculated criterial heat exchange equation for the nonisothermal motion of products and their different flows – laminar and transient – was obtained explicitly. In addition, the article considers the effect of starting modes on the operation of apparatus with mixing devices. These data can make it possible to take into account the possible deviations of parameters caused by nonsteady operating modes. On the basis of the data obtained, we have proposed assumptions about the degree of impact of viscosity and inertia in the considered range of parameters on a starting mode. The results of the study are relevant since they allow us to intensify the thermal processes in this type of common apparatus by 10–12%.

Experimental Research of Valve Tightness at Different Closure Forces

Power valves are installed on almost all the pipelines of nuclear power plants performing the functions of regulation and shutting off the flow, so its failure often leads to emergencies. A particularly large number of failures is observed in motor-operated valves. Incorrect setting of the limiting clutch leads either to incomplete closure of the valve or to rod failure. Therefore, the valves are equipment of a nuclear power plant, which often falls into repair shops. Failures leading to an increase of valve leakage are especially dangerous for nuclear power plants. In this case, leakage of high-pressure valves leads to erosion of the sealing surfaces, which only increases the leakage. Thus, it is very important to determine the optimum rotational value when the valve is closed. The lack of conditions for closure force in the standards for valve leakage complicates the issue.
 A bench that allows working in the air with a pressure up to 3.5 MPa was developed on valve rod to study dependence of valve leakage on the rotational moment. Four independent parameters were measured: air pressure in front of the valve under study, closure force of the valve, volume of air loss through the valve and leakage time. A standard stop valve with a nominal diameter of 15 mm and a nominal pressure of 64 atm was used for the study.
 The determined dependence of the leakage on torque value allows recommending a gentler mode of valve closure without significantly reducing its tightness. As a result of experimental data processing, a criterial equation is obtained linking a leakage rate, pressure drop on the valve and a rotational moment value. The received criterial equation will allow defining the compromise between valve closure force and permissible leak level according to regulatory requirements. The analysis of the “leakage/rotational moment” diagram showed the possibility to reveal the damaged valves. This possibility may be used during the incoming inspection of the valves supplied to NPP, which should significantly improve the reliability of their operation.

Heat transfer in packet of parallel plates in the short-term processes

The description of the experimental stand (laboratory regenerative air preheater), the method for measuring the unsteady flow temperature and the results of experimental heat transfer studies of a package of plates (nozzles) of alloy steel AISI-430 with a 2 mm thickness for short-time periods with different durations are presented. The experimentally obtained mean Nusselt numbers are generalized by the criterial equation.

Perforated plate convective heat transfer analysis

The need for high performance heat exchangers has led to the development of many types of surfaces that enhance the rate of heat transfer. One of the heat exchanger types are the matrix heat exchangers. Matrix heat exchangers consist of a series of perforated plates, separated by a series of spacers. The present study experimentally investigates the overall heat transfer characteristics of flow through a perforated plate with 2 mm in diameter, the hole length to diameter ratio of 1 and 25.6% porosity. Numerical simulations were performed to determine the overall heat transfer in the function of geometric parameters. Reynolds numbers based on the perforated plate pitch were set in the range from 50 to 500. The results of the average Nusselt number prediction were compared with the related experimental correlations. The experimental data agreed on qualitatively with the results obtained using a CFD. Using these data, a Nusselt criterial equation was obtained.

Investigation of the Hydrodynamic Flow Pattern in Tubular Membrane Devices

The present work examines the hydrodynamic flow pattern in an industrial tubular baromembrane device on the example of commercially available membrane elements at pressures of 1.0–4.0 MPa. Experimental response curves and dependence curves of the longitudinal mixing coefficient were obtained as a function of the solution flow rate and the pressure in the membrane module. Based on this information, the criterial equation for calculating the longitudinal mixing coefficient was obtained. Numerical values of empirical coefficients are given, which can theoretically be used to calculate the longitudinal mixing coefficients as well as to predict the values for similar constructions of baromembrane systems operating at high transmembrane pressures.