Calculation Of Heat Exchange Research Articles

Engineering Calculation and Experimental Study of a Cone-Shaped Coil Heat Exchanger

To improve the characteristics of heat and power equipment, it is necessary to develop new designs of heat exchangers, increase the efficiency of heat exchange surfaces, apply modern approaches to the design and calculation of heat exchangers, and create new technologies for their production. The paper proposes modern compact coil heat exchangers of the in pipe type with a variable bending radius of the helical spiral and the engineering method calculating the thermohydrodynamic characteristics of such devices. The calculation of a coilheat exchanger with a linearly varying bending radius of a helical spiral (cone-shaped coil heat exchanger) has been performed. They performed the experimental study of heat transfer in a cone-shaped coil heat exchanger of the pipe-in-pipe type. They obtained the empirical formulas for the Nusselt number and hydraulic resistance coefficient. It has been established and experimentally confirmed that cone-shaped coil heat exchangers are morecompact and efficient in comparison with the known cylindrical coils. It is proposed to modernize the hot water preparation unit in one of the residential buildings in the city of Kazan (Russia) by replacing the outdated shelland-tube heat exchanger with a compact cone-shaped coil heat exchanger, which made it possible to reduce the duration of hot water preparation significantly, to reduce the costs of the heating medium and, thus, to reduceconsumer costs.

Development of Simulation Tool for Ground Source Heat Pump Systems Influenced by Ground Surface

The authors developed a ground heat exchanger (GHE) calculation model influenced by the ground surface by applying the superposition theorem. Furthermore, a simulation tool for ground source heat pump (GSHP) systems affected by ground surface was developed by combining the GHE calculation model with the simulation tool for GSHP systems that the authors previously developed. In this paper, the outlines of GHE calculation model is explained. Next, in order to validate the calculation precision of the tool, a thermal response test (TRT) was carried out using a borehole GHE with a length of 30 m and the outlet temperature of the GHE calculated using the tool was compared to the measured one. The relative error between the temperatures of the heat carrier fluid in the GHE obtained by measurement and calculation was 3.3% and this result indicated that the tool can reproduce the measurement with acceptable precision. In addition, the authors assumed that the GSHP system was installed in residential houses and predicted the performances of GSHP systems using the GHEs with different lengths and numbers, but the same total length. The result showed that the average surface temperature of GHE with a length of 10 m becomes approximately 2 °C higher than the average surface temperature of a GHE with a length of 100 m in August.

Calculating the Efficiency of Complex Shaped Fins

In the calculation of heat exchangers with individual finned tubes or continuous fin heat exchangers, i.e., plate-fin and tube heat exchangers (PFTHEs), it is necessary to determine the efficiency of complex fins. Usually, these are circular or rectangular fins mounted on circular, elliptical, or oval tubes as well as flattened tubes. In case of PFTHEs, the continuous fin is divided into virtual fins, which are rectangular for an inline pipe layout or hexagonal for a staggered pipe arrangement. This paper presents a procedure based on the finite element method for determining the efficiency of fins of any shape placed on tubes of any shape. The article shows examples of calculating the efficiency of virtual fins in most commonly used PFTHEs. The research also assesses the accuracy of determining the efficiency of complex-shaped fins using approximated methods such as the equivalent circular fin method (Schmidt’s method) and the sector method. The efficiency of a fin as a function of heat transfer coefficient for four different, most common geometries in PFTHEs was depicted. An example of determining the efficiency of a hexagonal fin using various methods for air velocities measured at the exchanger inlet was presented.

A coupled CFD approach for performance prediction of fin-and-tube condenser

This article developed a novel numerical model for accurately predicting the thermal performance of fin-and-tube condenser, which coupled heat transfer between the air and refrigerant side. The heat exchange calculation between the air and refrigerant side was alternatively performed by coupling the tube wall temperatures. Meanwhile, the air side flow and heat transfer characteristics among the fin plates were achieved by porous media approach. Based on this model, the numerical studies were conducted for investigating the effects of air inlet temperature and frontal velocity on the thermal performance of such heat exchanger. Results showed that the predicted overall heat transfer rate was within the range of ±10% compared with the experimental data. It indicated that the porous media model was able to predict the thermal and flow characteristics of air side in a fin-and-tube condenser, and furthermore it could be used for the optimal design of such heat exchanger.

Heat Exchange under the Evaporation and Boiling of a Film Showering a Bundle of Horizontal Finned Tubes

An algorithm for calculating heat exchange in the course of evaporation and boiling of a film that showers a bundle of finned tubes is described and a comparison of calculated and experimental data is performed. The calculated parameters are in quite satisfactory agreement with the experimental data.

Analysis of Relaxation Time of Temperature in Thermal Response Test for Design of Borehole Size

A new practical method for thermal response test (TRT) is proposed herein to estimate the groundwater velocity and effective thermal conductivity of geological zones. The relaxation time of temperature (RTT) is applied to determine the depths of the zones. The RTT is the moment when the temperature in the borehole recovers to a certain level compared with that when the heating is stopped. The heat exchange rates of the zones are calculated from the vertical temperature profile measured by the optical-fiber distributed temperature sensors located in the supply and return sides of a U-tube. Finally, the temperature increments at the end time of the TRT are calculated according to the groundwater velocities and the effective thermal conductivity using the moving line source theory applied to the calculated heat exchange rates. These results are compared with the average temperature increment data measured from each zone, and the best-fitting value yields the groundwater velocities for each zone. Results show that the groundwater velocities for each zone are 2750, 58, and 0 m/y, whereas the effective thermal conductivities are 2.4, 2.4, and 2.1 W/(m∙K), respectively. The proposed methodology is evaluated by comparing it with the realistic long-term operation data of a ground source heat pump (GSHP) system in Kazuno City, Japan. The temperature error between the calculated results and measured data is 6.4% for two years. Therefore, the proposed methodology is effective for estimating the long-term performance analysis of GSHP systems.

ПОКАЗНИКИ РОБОТИ ПАРОГЕНЕРАТОРА Е - 1- 9 ПРИ ПЕРЕВЕДЕННІ НА СПАЛЮВАННЯ ТВЕРДИХ ВИДІВ ПАЛИВ

In the work it is noted that the use of renewable fuels for the production of heat and electricity under conditions of energy shortages is an urgent task today. The numerical studies of the performance of the steam generator E-1-9 in the combustion of wood, coal, peat, straw wastes were carried out. The analysis of literary information on the experimental studies of boilers using alternative fuels has been carried out. Based on the analysis of the literature, it is shown that for wide use of alternative fuels in low power boilers (up to 3 MW), thorough experimental studies of the combustion processes of such fuels and appropriate adjustments of the Normative method are required. To study the performance of the steam generator, a mathematical model of the boiler was created, which was implemented in the MSExcel. The mathematical model consists of four modules: module of calculations of volumes of combustion products, module of calculations of heat exchange in a furnace, module of calculations of heat exchange in a convective beam, module of calculations of heat exchange in a cast iron economizer. The influence of the coefficient of excess air on the adiabatic temperature and the flue gas temperature at the outlet of the furnace is investigated. It is shown that as the coefficient of excess air increases, the adibat temperature decreases, which is explained by the fact that more cold air enters the furnace. For peat and wood, the values of the adiabatic temperature are close. The adiabatic temperature for coal is almost 350 ° C higher than that of wood. The influence of the coefficient of excess air on the efficiency of the steam generator is analyzed. It is shown that the highest value of the efficiency is the steam generator when burning coal, which is explained by the higher heat of combustion and lower moisture content of the fuel. Comparison of pollutant emissions in the case of solid fuel combustion in a steam generator.

Method of Calculation and Comparative Characteristics of Heat Exchangers with Heat Transfer Enhancement by Various Random Elements

Consideration has been given to the method of enhancement of a heat-transfer process due to the use of small random metallic elements (packings) in channels of heat-exchange apparatuses. The packings ensure a laminar-to-turbulent transition and a considerable increase in heat-transfer coefficients (of 30 to 60 times). Structures of two modern packing elements and their technical data have been given, as well as expressions to calculate hydraulic-resistance and heat-transfer coefficients. On the basis of a modified method of the thermal number of transfer units, expressions have been obtained for calculation of the tube length and the heat-transfer surface when random packings are used as intensifiers of the process in the apparatuses. Basic parameters of the obtained expressions are the heat-transmission coefficient and modified Peclet (Bodenstein) numbers with the coefficients of reverse mixing of heat-transfer agents. Empirical coefficients at Peclet numbers have been identified using a diffusion model of the structure of a heat-transfer agent flow. The obtained expressions permit taking account of the influence of the reverse mixing of heat-transfer agents on the structural characteristics of a heat exchanger. Examples of calculations of heat exchangers without intensifiers and with random packings have been given. It has been shown that during the heat exchange with different media, the overall dimensions of the heat exchangers are reduced 20 to 25 times. The use of random packings in heat exchangers with media of high viscosity is pressing, since the packings initiate a turbulent regime of flow of heat-transfer agents.

Calculation of Heat Exchange on the Surface of a Flexible Heat Exchanger for Use in Mobile Hospitals

Currently, the world is characterized by quite a large number of military conflicts, manmade disasters and natural disasters. Every year, about 50 thousand people die from various natural disasters in the world. The report of the UNISDR notes that natural disasters that occurred in the world between 1998 and 2017 led to the death of 1.3 million people (more than half of them – due to earthquakes). The analysis shows that human losses could be significantly less with rapid first aid. This requires the presence of a field hospital located as close as possible to the lesion. Currently, field hospitals for various purposes are produced. The heating system of the field hospital modules plays an important role in the operation. A heating system is proposed, which includes a vortex heat generator and heating devices made of polyvinyl chloride. The system is characterized by low weight and quick access to the operating mode. However, in the literature there is no method for calculating the heat exchange coefficient in a closed space, which is formed by flexible heater surface and an enclosing wall. Based on the analysis of criterion dependences and experimental data, new criterion equations for calculating the heat exchange coefficient for an arbitrary location of heaters in space are obtained. The following dependence is built lgNu = f(lg(Gr×Pr)), which allows to determine value of heat exchange coefficient for given range of temperature. A method of intensification of the heat exchange process by creating an artificial roughness is proposed. Graph is done to determine growth rate of heat exchange СK, which is included in criterion equation. The use of artificial roughness allowed increasing the heat transfer coefficient by 28 % and the thermal power of the heating device by about 26 %.

Experimental investigation and mathematical model of a heat exchanger with porous metal inserts

When creating and manufacturing heat exchangers, one of the main tasks is to increase the efficiency of heat transfer. The use of porous metals in heat exchangers is one of the promising ways to increase the heat transfer intensity, which determines the relevance of the study. The paper provides an overview of the status of this issue on literary sources. The purpose of the work is to conduct an experimental study of a heat exchanger with porous materials, to compile a mathematical model that allows analytical calculations of such heat exchangers, to confirm the correctness of the compiled model experimentally. An experimental bench has been created to study a heat exchanger that uses porous aluminum. The hot fluid is warm water that flows through pipes passing through a porous metal. The cold coolant flowing through the pores is freon, which cools the water. A schematic diagram and description of the stand are presented. A test cycle has been conducted. A comparison of the heat transfer intensity for materials of different porosity is given. Using standard methods for calculating heat exchangers in this case is not possible due to the lack of standard methods for determining the area of the inner surface with pores. In the course of the work, the standard equation describing the cooling of a porous body was proposed to be supplemented by the function of distributed heat sources. As a result, we have obtained a mathematical model of the heat exchanger under consideration in a simplified form, which can be used in technical calculations. The calculation results by the obtained method are correlated with the data of experiments. Deviations of empirical and theoretical data are within acceptable limits. The results obtained make it possible to use porous metals in order to increase the heat transfer intensity in the manufacture of heat exchangers. This technique allows calculations with an unknown heat exchange surface area, taking into account the heat capacity and heat of phase transition, if any. According to the methodology, the article is experimental-theoretical. Experiments are being conducted on the created laboratory bench. In parallel, calculations are made according to the developed mathematical model. The results are compared. Conclusions are made of a theoretical and applied nature.

Calculation of the Geometrical Parameters of the Heat Exchanger Type “Pipe in Pipe” with a Spiral-Coiled Channel

The designs of the modern type of twisting devices include spring-twisted channels, which to use as innovative heat exchange elements of tubular apparatuses. The paper presents a method for determining the equivalent diameter of the tube and intertubular space in a heat exchanger apparatus of the type “tube-in-tube” with a spring-twisted channel which composed of tori closely adjacent to each other. Based on the integral calculus, formulas are obtained for calculating the equivalent diameters of the tube and annular space in a tube-in-tube apparatus with a spring-twisted channel. The results of experiments on heat transfer are generalized by criterial equations, in which the equivalent diameter is used as the characteristic size. It is shown that the equivalent diameters of the examined channels differ from each other by no more than 5%. The results of this work can be used in the design and calculations of promising heat exchangers with intensified heat transfer.

Method of heat exchangers calculation for combined-cycle gas turbine plants in operation modes that differ from the nominal ones

We carried out a comparison of methods for calculating heat exchangers of combined-cycle gas turbine plants (CCGTP) in variable-load operation modes. It is shown that for calculations of waste heat boilers with complex thermal circuits and a large number of heat exchangers it is advisable to use approximate methods for calculations.

Experimental verification of design calculations of the internal combustion engine cooling system

The article presents a comparative analysis of calculation results and measurement results of cooling module built on the basis of design calculations. The computations were made in software dedicated to the calculations of heat exchangers. The measurements were performed on a cooling system mounted in a special purpose vehicle together with a combustion engine, which was loaded by an engine dynamometer. Based on the comparison between input data for calculations and results of measurements, differences were found, therefore changes were proposed to be made in the model.

Special Features of the Computer Simulation of the Radiation Heat Exchange of a Spacecraft in a Specular-Diffuse Approximation

The special features of the computer simulations of the radiation heat exchange calculations of spacecraft (SC) with a specular-diffuse approximation of the nature of the surface reflection according to the algorithms, which directly calculate the radiation exchange factors by the Monte Carlo (MC) method, and according to the author’s algorithm, which calculate them by determining the specular exchange factors of the absorbed radiation, are considered. The effects of approximating the model’s geometric surface approximation method and calculation algorithm on the results of calculating the fluxes and temperature are shown.

APPROXIMATE ANALYTICAL SOLUTION OF THE PROBLEM OF CONJUGATE HEAT TRANSFER BETWEEN THE BOUNDARY LAYER AND THE ANISOTROPIC STRIP

Optimization of technological processes in metallurgy related to transfer and use of heat energy makes more complicated demands for calculation of heat exchange. Therefore, the work, the approximate analytical method for solving the conjugate problems of viscous gas-dynamic boundary layer and thermal conductivity in the anisotropic strip, has been developed. The paper uses modern numerical methods for solving differential equations in partial derivative and analytic methods on the basis of an integral transform of Fourier and Laplace. Boundary equations have been solved analytically with certain simplifications, and the problem of anisotropic heat conduction has been solved analytically. The heat flows are determined analytically by the longitudinal variable at the interface boundary. It has been established that temperature increase of the external surface contributes to that all factors directly impacting on the magnitude of heat flows act towards their reduction. The analytical solution for the problem of thermal conductivity in the anisotropic strip with a general type of anisotropy when the heat flows from the boundary layer are determined at the boundaries is obtained. The conducted research for the temperature of external boundary and heat flow from gas to it demonstrates that with increasing the degree of longitudinal anisotropy the surface temperature of the strip downstream increases from increasing longitudinal heat conduction An original conjugation method using the continuous heat flows, and temperatures at the interface boundary is found. The numerical results for the heat flows and temperatures at the interface boundary have been obtained and analyzed.

Experimental study of heat transfer outside C-shaped tube in water tank

Experimental system was set up to study the heat transfer performance outside the C-shaped tube in water tank. Thermal oil and desalted water were chosen as tube inside and outside fluid separately and a series of experiments were performed. Experimental data show that in the vertical direction tank water temperature stratification occurs during the heating process and in the horizontal direction tank water temperatures keep nearly uniform. The changing regularity between tube outside wall temperature and tank water temperature is analyzed. Bubble movement is also photographed and it plays an important role in boiling heat transfer. Nusselt number and heat flux of the horizontal and vertical tube units at three representative times are calculated and agree well with the results based on McAdams natural convection correlations, Rohsenow subcooled and saturation boiling correlations, which can provide a basis for the heat transfer calculation of heat exchangers of this kind.

Calculation of Radiation Heat Exchange in the Model of Specular-Diffuse Reflection and Direct and Diffuse Transmission

The general solution to the radiation exchange problem in the zone method is given in the system of surfaces in the presence of nonparticipating medium for the model of specular-diffuse reflection and direct and diffuse transmission. The reflection indicatrix for all surfaces of the considered system of bodies is assumed as a superposition of diffuse and specular components of reflection, and the transmitted radiation for transparent materials—as a superposition of direct and diffuse transmission. The cornerstone of the offered approach is in obtaining the exchange radiation factors by the semi-analytical method by solving a system of linear algebraic equations that include specular exchange factors or diffuse configuration factors of radiation. This allows one to combine exact computational methods of diffuse reflection and diffuse transmission through diffuse configuration factors with methods of direct ray tracing for accounting of specular reflection and direct transmission. Solutions for all possible particular models of reflection and transmission are provided. The solution for diffuse transmission by the semi-analytical method is obtained for the first time. Results of the numerical experiments confirming accuracy and efficiency of the offered approach are given.

Modeling heat transfer in gas-particle mixtures: Calculation of the macro-scale heat exchange in Eulerian–Lagrangian approaches using spatial averaging

Heat transfers in dilute gas-particle mixtures are often modeled using hybrid Euler–Lagrange descriptions, treating the carrier fluid via an Eulerian representation and following each particle in a Lagrangian framework. One of the focal issues in these models is the calculation of the macro-scale heat transfer between the continuous phase and particles. In the standard approach, the heat transfer for each particle is considered to vary linearly with the average temperature difference between the particle and the fluid. Here, we use the method of volume averaging with closure to filter the heat transfer equations at the micro-scale and derive a closed form of the heat transfer rate, which is significantly different from the standard case. The primary difference is that the heat transfer for a given particle does not only depend on the temperature of the particle but also depends on the temperatures of all other particles within the averaging volume. This yields a matrix of heat exchange coefficients that captures indirect particle–particle exchanges at macro-scale. Using simple model cases, we validate our approach, compare it to the standard heat transfer model and show that it degenerates toward the standard model only in specific cases.

Ill-posed Boundary-value Problem for a System of Partial Differential Equations with Two Degenerate Lines

This paper is devoted to the investigation of ill-posed boundary-value problem for system of parabolic type equations with changing time direction with two degenerate lines. The problem under consideration is ill-posed in the sense of J. Hadamard, namely, there is no continuous dependence of the solution on the initial data. Such equations have many different applications, for example, describe the processes of heat propagation in inhomogeneous media, the interaction of filtration flows, mass transfer near the surface of an aircraft, and the description of complex viscous fluid flows. As possible applications should also indicate the task of calculating heat exchangers, in which the counter flow principle is used. Theorems on the uniqueness and conditional stability of a solution on a set of well-posedness are proved. We construct a sequence of approximate (regularized) solutions that are stable on the set of well-posedness

Impact of temperature fluctuation on anaerobic fermentation process of upgrading bioreactor under solar radiant heating

Upgrading bioreactor under solar radiant heating can maintain the anaerobic fermentation process by utilizing absorption and scattering of solar energy in media to improve slurry temperature. Finding the suitable correction factor of temperature fluctuation for calculating kinetic rate of microbial fermentation process can improve simulation accuracy of microbial fermentation process. In present work, a coupled model for simulating the processes of photothermal transmission and anaerobic fermentation was built. Experimental and numerical researches about the anaerobic fermentation process of upgrading bioreactor were made to investigate the effect of temperature fluctuation on the kinetic rate of biochemical reactions. The results show that the temperature fluctuation has big effects on the biochemical reaction rate of each substance in the fermentation process. The n values for calculating heat exchange number BT are discrepant for both different reactants and temperature differences. For instance, when the temperature difference is bigger than 4 K, n = 2 is suitable to the one of cow dung in reactor A, and n = 3 is suitable to the one of pig dung and straw pitch in reactor B. The effect of n values on daily biogas production of straw is bigger than the one of cow dung, since hydrolytic bacteria are more sensitive to temperature fluctuation.