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Advanced Mathematical Modeling Technology for Heat Storage and Conversion Systems

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A special issue of Energies (ISSN 1996-1073). This special issue belongs to the section "J: Thermal Management".

Deadline for manuscript submissions: closed (15 December 2022) | Viewed by 33120

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Prof. Dr. Dawid Taler

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Guest Editor

Department of Heat Processes, Air Protection and Waste Disposal, Faculty of Environmental and Energy Engineering, Cracow University of Technology, 31-155 Cracow, Warszawska Street 24, Poland
Interests: mathematical modelling of heat exchangers, steam boilers, and heat storage units; inverse heat transfer problems; CFD modelling and experimental studies of thermal and flow processes in heat exchangers, boilers, and heat storage units; dynamics of heat exchangers, heat storage units, and steam boilers; strength and performance monitoring of large steam boilers; measurement of heat flux and heat transfer coefficient; measurement of the unsteady-state temperature of the flowing fluid; development of new correlations for the friction factor and nusselt number in the laminar, transition and turbulent flow inside tubes; online monitoring the fouling of the boiler heating surfaces; improving the steam boiler flexibility using pressurized hot water storage units
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Dr. Magdalena Jaremkiewicz

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Guest Editor

Department of Energy, Faculty of Environmental and Energy Engineering, Cracow University of Technology, Al. Jana Pawla II 37, 31-864 Cracow, Poland
Interests: thermodynamics; heat transfer; thermal and flow measurements; inverse heat; transfer problems; renewable energy sources; power plant technology; performance and strength monitoring of power plant machinery

Special Issue Information

Dear Colleagues,

We are inviting submissions to a Special Issue of the Energies Journal on the subject area of “Advanced Mathematical Modeling Technology for Heat Storage and Conversion Systems”. Thermal energy storage units are usually used when the heat flow rate or electrical power is too high during a certain period of 24 hours, and too low during another period of 24 hours. In solar systems, we have an excess of heat or electricity during the day and its insufficiency during the night. The opposite situation occurs in thermal power plants and CHP (combined heat and power) plants. Excess electricity is produced during the night and during the day (when summer is hot), and in the evening, there is usually a peak demand for electricity. Thermal energy units (pressurized hot water tanks) can be used to accumulate thermal energy in hot water in periods with a low demand for electrical energy when electricity prices are low. During peak electrical load, the hot water tanks are discharged to increase the maximum electrical load of the power plant. The accumulation of energy in the metal filling is used in rotary heat regenerators. They are commonly used in ventilation and air-conditioning systems in buildings for heat recovery from the hot air coming out of the building into the atmosphere. Rotary regenerators in power boilers are used to heat external air using flue gases.

The topics of interest in this Special Issue include different advanced mathematical methods and models used for simulation of heat storage, and conversion systems applied both in the conventional and renewable energy areas.

The advanced mathematical models of interest for publication include but are not limited to:

Solar systems, thermal power plants, and CHP plants with direct storage of heat in single-fluid tanks containing liquid of uniform temperature or in hot liquid storage tanks with a stratification (thermocline tanks);

Dual-media heat storage units with loosely packed solid materials such as rocks, ceramic spherical or cylindrical elements, and capsules with phase change materials (PCM);
Dual-media heat storage units in which fluid flows through tubes or channels situated in storage material, which can be solid such as magnetite, concrete, soil, sand, wax, chamotte brick, etc. or liquid such as water, oil, molten salts, etc.;
Electrically heated heat accumulators;
Accumulation of heat in the ground and buried underground tanks;
Thermochemical storage systems;
Design and modeling of operation of thermal storage systems.

Prof. Dawid Taler
Assoc. Prof. Magdalena Jaremkiewicz
Guest Editors

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Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Energies is an international peer-reviewed open access semimonthly journal published by MDPI.

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Keywords

mathematical modeling of heat storage units
dual-media heat storage units
hot liquid storage tanks with a stratification
phase change materials
electrically heated heat accumulators—conventional and dynamically discharged accumulators
heat accumulation in the ground

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Published Papers (11 papers)

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Research

28 pages, 17598 KiB

Open AccessArticle

3D Numerical Analysis of a Phase Change Material Solidification Process Applied to a Latent Thermal Energy Storage System

by Tulio R. N. Porto, João A. Lima, Tony H. F. Andrade, João M. P. Q. Delgado and António G. B. Lima

Energies 2023, 16(7), 3013; https://doi.org/10.3390/en16073013 - 25 Mar 2023

Cited by 3 | Viewed by 2284

Abstract

The techniques for releasing thermal energy accumulated in periods of high availability to meet the demand in periods of low energy supply contribute to the continuity of the cycles involved in thermodynamic processes. In this context, phase change materials are capable of absorbing and releasing large amounts of energy in relatively short periods of time and under specific operating conditions. However, phase change materials have low thermal conductivity and need to be coupled with high-thermal-conductivity materials so that the heat flux can be intensified and the energy absorption and release times can be controlled. This work aims to numerically study the solidification process of a phase change material inserted into a triplex tube heat exchanger with finned copper walls to intensify the thermal exchange between the phase change material and the cooling heat transfer fluid, water, that will receive the energy accumulated in the material. This work proposes the 3D numerical modeling of the triplex tube heat exchanger with finned walls and meets the need for numerical models that allow for the analysis of the full geometry of the latent heat thermal energy storage system and the thermal and fluid dynamic phenomena that are influenced by this geometry. Results of the temperature, liquid fractions and velocity fields during phase transformations are presented, analyzed and validated with experimental data, presenting average errors of below 5%. The total material discharge time was approximately 168 min, necessary for the complete solidification of the phase change material, with water injected into the triplex tube heat exchanger at a flow rate of 8.3 L/min and a temperature of 68 °C. The solidification process occurred more slowly in the same direction as the length of the triplex tube heat exchanger, and from 80% of the material in the solid state, the difference between the solidification time for z = 0 and z = 480 mm was 30 min. The fluid dynamic conditions developed in the latent heat thermal energy storage system promoted a maximum negative heat flux of −6423 w/m² to the annular internal surface and −742 w/m² to the annular external surface, representing a heat removal process nine times less intense on the external surface. The total energy released to the cooling heat transfer fluid was 239.56 kJ/kg. Full article

(This article belongs to the Special Issue Advanced Mathematical Modeling Technology for Heat Storage and Conversion Systems)

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15 pages, 3228 KiB

Open AccessArticle

Estimation of Total Solar Transmittance for Twin-Wall Polycarbonate Sheet with Rectangular Structure on the Basis of Experimental Research

by Zbigniew Zapałowicz and Oliwer Wojnicki

Energies 2022, 15(4), 1360; https://doi.org/10.3390/en15041360 - 14 Feb 2022

Cited by 5 | Viewed by 2769

Abstract

The consumption of heat energy as well as electric power in an exploitation process of a building construction depends among others on properties of materials applied to construct its partitions. Increasingly, glass is being replaced by plastics in transparent partitions, including multi-wall polycarbonate sheets. Light transmission and solar radiation transferred to the object’s inside through transparent partitions are decisive factors for its lighting and energy balance. The present paper presents an analysis, on an experimental basis, of the changes of total solar transmittance (TST) for a clear twin-wall polycarbonate sheet with a rectangular structure applied as a swimming pool enclosure. Research shows that values of the above parameter do not depend meaningfully on cloudiness but on time of day. Values of TST can change in the daytime depending on incidence angles and on shares of direct and diffusive solar radiation in global solar radiation. TST values are in the range 0.6–0.7, and they are lower than the value of 0.8, which is given by the producer in the product card. Full article

(This article belongs to the Special Issue Advanced Mathematical Modeling Technology for Heat Storage and Conversion Systems)

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20 pages, 2669 KiB

Open AccessArticle

Electrohydrodynamic Enhancement of Phase Change Material Melting in Circular-Elliptical Annuli

by Kun He, Lei Wang and Jiangxu Huang

Energies 2021, 14(23), 8090; https://doi.org/10.3390/en14238090 - 3 Dec 2021

Cited by 6 | Viewed by 2324

Abstract

Phase change material (PCM) has received significant attention due to its great potential for thermal energy storage. However, the major undesirable property of PCM is related to its low thermal conductivity. In this work, the electrohydrodynamic (EHD) enhancement of PCM melting in circular-elliptical annuli is investigated numerically by using the lattice Boltzmann method (LBM). The key motivation for our choice of the elliptical shape is due to the fact that the more curved elliptical surface corresponds to stronger charge injection strength, which may lead to stronger flow field, and the consequent increase of heat transfer rate. The influences of several non-dimensional parameters, including electric Rayleigh number T, thermal Rayleigh number (

R a

) and the aspect ratio (

A R

) of the inner ellipse are investigated in detail. Based on the numerical results, it is found that the radial electro-convective flow induced by the external electric field makes a significant contribution to the enhancement of melting heat transfer, and specially, the maximum time saving in some cases is more than

85 %

. Moreover, we observe that when the Coulomb force is dominant over the buoyancy force, no matter the inner elliptical tube is oriented horizontally or vertically, the total melting times in these two cases are nearly the same, and the melting performance obtained for the circular electrode is usually better than the other cases. However, when the flow regime is dominated by the buoyancy force, the use of a slender vertical-oriented elliptical electrode instead of the circular one is more efficient. Full article

(This article belongs to the Special Issue Advanced Mathematical Modeling Technology for Heat Storage and Conversion Systems)

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18 pages, 3807 KiB

Open AccessArticle

Thermal Analysis of Solid/Liquid Phase Change in a Cavity with One Wall at Periodic Temperature

by Shogo Tomita, Hasan Celik and Moghtada Mobedi

Energies 2021, 14(18), 5957; https://doi.org/10.3390/en14185957 - 19 Sep 2021

Cited by 12 | Viewed by 2854

Abstract

In this study, heat transfer in a square cavity filled with a Phase Change Material (PCM) under a sinusoidal wall temperature during solidification and melting is analyzed. All surfaces of the cavity are insulated except one surface, which is under the sinusoidal temperature change. The governing equations and boundary conditions are made dimensionless to reduce the number of governing parameters into two as dimensionless frequency and Stefan number. The governing equations were solved numerically by using Finite Volume Method for a wide range of Stefan number (0.1 < Ste < 1.0) and dimensionless frequency (0.23 <

ω^{*}

< 2.04). Based on the obtained results, a chart in terms of Stefan number and dimensionless frequency is obtained to divide the heat transfer process in the cavity into three regions as uncompleted, completed, and overheated phase-change processes. For the uncompleted process, some parts of the cavity are inactive, and no phase change occurs in those parts of the cavity during the melting and freezing process. For the overheated phase change, the temperature of the cavity highly increases (or decreases), causing the sensible heat storage to compete with latent thermal storage. In the completed process, almost all thermal storage is done by the utilization of latent heat. The suggested graph helps thermal designers to avoid wrong designs and predict the type of thermal storage (sensible or latent) in the cavity without doing any computations. Full article

(This article belongs to the Special Issue Advanced Mathematical Modeling Technology for Heat Storage and Conversion Systems)

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25 pages, 14791 KiB

Open AccessFeature PaperArticle

Heat Transfer in Flow Past Two Cylinders in Tandem and Enhancement with a Slit

by Li-Chieh Hsu and Che-Wei Liang

Energies 2021, 14(2), 308; https://doi.org/10.3390/en14020308 - 8 Jan 2021

Cited by 7 | Viewed by 3043

Abstract

This study aimed to determine the flow structures and heat transfer for flow past a tandem cylinder array and the effect of a slit on the enhancement of heat transfer. Different distances between cylinders and inclination angles of the slit were simulated to determine the effects on the flow pattern and heat transfer. Overall, the Nusselt number of the array is increased by 6–15% with applying a slit on a cylinder. However, in some special conditions, the slit induces two kinds of flow pattern transforms which are Suppression and Revival. The suppression mode inhibits the vortex shedding and reduces the heat transfer. In contrast, the revival mode triggers the vortex shedding and increases heat transfer. Full article

(This article belongs to the Special Issue Advanced Mathematical Modeling Technology for Heat Storage and Conversion Systems)

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15 pages, 4212 KiB

Open AccessArticle

Experimental Performance Evaluation of an Integrated Solar-Driven Adsorption System in Terms of Thermal Storage and Cooling Capacity

by M.T. Nitsas, E.G. Papoutsis and I.P. Koronaki

Energies 2020, 13(22), 5931; https://doi.org/10.3390/en13225931 - 13 Nov 2020

Cited by 4 | Viewed by 1940

Abstract

Heat-driven coolers provide a reliable and environmentally benign alternative to traditional electrically powered chillers. Their main advantage is that they can be driven using low enthalpy heat sources. A solar system is installed at the school of Mechanical Engineering of National Technical University of Athens in order to examine the potential of thermal storage and solar cooling under Athens climatic conditions. The cooling effect is produced using a dual bed, single stage, zeolite/water adsorption chiller with cooling capacity of 10 kW at its nominal conditions of operation. Both vacuum tube collectors and hybrid photovoltaic thermal collectors are installed in order to supply the system with heat. The system is evaluated in terms of solar collectors’ useful energy production, heat stored in the intermediate buffer and cooling system’s performance. It is observed that the cooling system operates satisfactorily under Athens climatic conditions achieving a maximum cooling capacity of 3.7 kW and an average COP around 0.5. Full article

(This article belongs to the Special Issue Advanced Mathematical Modeling Technology for Heat Storage and Conversion Systems)

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13 pages, 9377 KiB

Open AccessArticle

Effect of Heat Source Placement on Natural Convection from Cylindrical Surfaces

by Andrej Kapjor, Peter Durcansky and Martin Vantuch

Energies 2020, 13(17), 4334; https://doi.org/10.3390/en13174334 - 21 Aug 2020

Cited by 3 | Viewed by 3060

Abstract

Placement of heat source can play a significant role in final heat output, or heat source effectivity. Because of this, there is a need to analyze thermal fields of the heat exchange system by natural convection, where the description by criterion equations is desired, as the net heat output from tubes can be quantified. Based on known theoretical models, numerical methods were adapted to calculate the heat output with natural air flow around tubes, where mathematical models were used to describe the heat transfer more precisely. After validation of heat transfer coefficients, the effect of wall and heat source placement was studied, and the Coanda effect was also observed. The heat source placement also has an effect at the boundary layer, which can change and therefore affect the overall heat transfer process. The optimal wall-to-cylinder distance for an array of horizontal cylinders near a wall was also expressed as a function of the Rayleigh number and number of cylinders in the array. Full article

(This article belongs to the Special Issue Advanced Mathematical Modeling Technology for Heat Storage and Conversion Systems)

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18 pages, 3673 KiB

Open AccessArticle

Influence of the Thermometer Inertia on the Quality of Temperature Control in a Hot Liquid Tank Heated with Electric Energy

by Dawid Taler, Tomasz Sobota, Magdalena Jaremkiewicz and Jan Taler

Energies 2020, 13(15), 4039; https://doi.org/10.3390/en13154039 - 4 Aug 2020

Cited by 11 | Viewed by 4206

Abstract

This paper presents the medium temperature monitoring system based on digital proportional–integral–derivative (PID) control. For industrial thermometers with a complex structure used for measuring the temperature of the fluid under high pressure, the accuracy of the first-order model is inadequate. A second-order differential equation was applied to describe a dynamic response of a temperature sensor placed in a heavy thermowell (industrial thermometer). The quality of the water temperature control system in the tank was assessed when measuring the water temperature with a jacketed thermocouple and a thermometer in an industrial casing. A thermometer of a new design with a small time constant was also used to measure temperature. The quality of water temperature control in the hot water storage tank was evaluated using a classic industrial thermometer and a new design thermometer. In both cases, there was a K-type sheathed thermocouple inside the thermowell. Reductions in the time constant of the new thermometer are achieved by means of a steel casing with a small diameter hole inside which the thermocouple is precisely fitted. The time constants of the thermometers were determined experimentally with a jump in water temperature. A digital controller was designed to maintain the preset temperature in an electrically heated hot water tank. The function of the regulator was to adjust the power of the electrical heater to maintain a constant temperature of the liquid in the tank. Full article

(This article belongs to the Special Issue Advanced Mathematical Modeling Technology for Heat Storage and Conversion Systems)

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14 pages, 1839 KiB

Open AccessArticle

Recovery of Cenospheres and Fine Fraction from Coal Fly Ash by a Novel Dry Separation Method

by Jan Wrona, Witold Żukowski, Dariusz Bradło and Piotr Czupryński

Energies 2020, 13(14), 3576; https://doi.org/10.3390/en13143576 - 11 Jul 2020

Cited by 17 | Viewed by 2951

Abstract

Aluminosilicate microspheres are a valuable fraction of coal fly ash with diverse applications due to their low density. Currently, there is no efficient and ecologically rational method of cenosphere recovery from fly ash. A combination of dry methods for the recovery of both fine ash particles and aluminosilicate microspheres from coal fly ash is presented. It is comprised of fluidised bed separation followed by screening and pneumatic separation in a free-fall air chamber. Fluidised bed separation was assisted by a mechanical activator to prevent agglomeration. This step reduced the portion of material that required further treatment by 52–55 wt.%, with the recovery of microspheres exceeding 97%. Then, the concentrates were individually subjected to pneumatic separation. The final separation product for the fly ash containing 0.64 wt.% cenospheres was a cenosphere concentrate that constituted about 17 wt.% of the initial fly ash. The recovery of cenospheres was around 81%. Usage of a combination of dry methods allowed for maintaining almost 83 wt.% of the raw material in its dry form. Furthermore, the produced fly ash grain fractions could be used for different industrial purposes. Full article

(This article belongs to the Special Issue Advanced Mathematical Modeling Technology for Heat Storage and Conversion Systems)

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19 pages, 11875 KiB

Open AccessArticle

On Mixed Convection Squeezing Flow of Nanofluids

by Sheikh Irfan Ullah Khan, Ebraheem Alzahrani, Umar Khan, Noreena Zeb and Anwar Zeb

Energies 2020, 13(12), 3138; https://doi.org/10.3390/en13123138 - 17 Jun 2020

Cited by 10 | Viewed by 2495

Abstract

In this article, the impact of effective Prandtl number model on 3D incompressible flow in a rotating channel is proposed under the influence of mixed convection. The coupled nonlinear system of partial differential equations is decomposed into a highly nonlinear system of ordinary differential equations with aid of suitable similarity transforms. Then, the solution of a nonlinear system of ordinary differential equations is obtained numerically by using Runge–Kutta–Fehlberg (RKF) method. Furthermore, the surface drag force

C_{f}

and the rate of heat transfer

N_{u}

are portrayed numerically. The effects of different emerging physical parameters such as Hartmann number (M), Reynold’s number (Re), squeezing parameter (

β

), mixed convection parameter

λ

, and volume fraction (

φ

) are also incorporated graphically for

γ —

alumina. Due to the higher viscosity and thermal conductivity ethylene-based nanofluids, it is observed to be an effective common base fluid as compared to water. These observations portrayed the temperature of gamma-alumina ethylene-based nanofluids rising on gamma-alumina water based nanofluids. Full article

(This article belongs to the Special Issue Advanced Mathematical Modeling Technology for Heat Storage and Conversion Systems)

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18 pages, 3037 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

The Application of Molten Salt Energy Storage to Advance the Transition from Coal to Green Energy Power Systems

by Wojciech Kosman and Andrzej Rusin

Energies 2020, 13(9), 2222; https://doi.org/10.3390/en13092222 - 2 May 2020

Cited by 20 | Viewed by 3674

Abstract

The paper presents technical solutions for a power grid that undergoes the elimination of a significant number of coal-based power generating units. The purpose of the solutions is to adapt the existing machines with sufficient lifespans to the new operating conditions. In particular these include steam turbines. The steam turbines’ cycles may be extended with energy storage systems based on a molten salt. This allows to increase the flexibility of the power generating units while maintaining the largest possible efficiency of the power generation. The solutions presented here allow to connect the steam turbines cycles to renewable energy sources and reduce the overall number of the units that create the fundamental layer of the power grid. The analysis of the solutions involves numerical modeling. The paper describes the assumptions and the results of the modeling for chosen cases of the modernization. The researched considered a number of options that differed in the investment costs and the resulting performance. Full article

(This article belongs to the Special Issue Advanced Mathematical Modeling Technology for Heat Storage and Conversion Systems)

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