Reversible Thermodynamic Cycle Research Articles

Performance map and theoretical analysis of Carnot battery technology via novel reversible Rankine-based cycle

Carnot battery technology offers a good solution for storing the energy for later use. There are various types of Carnot batteries, and the Rankine-based cycle stands out due to its efficiency in power generation. Carnot battery can be configured as a stand-alone system, in which the heat pump and heat engine are installed separately. This approach, though, necessitates additional components, leading to high initial investment costs. As an alternative approach, a reversible system that reduces the number of components can be a promising alternative. This article reported the analysis of the Carnot battery implemented via a novel reversible Rankine-based thermodynamic cycle (so-called RRTC). This RRTC system is designed using one expander for both the organic Rankine cycle and heat pump modes (i.e., a throttle valve in the heat pump mode is replaced by an expander). The mathematical modeling simulation and its results are described, highlighting the performance map of the RRTC. Simulations were made for nine selected working fluids, focusing on their thermal properties. Among nine working fluids studied, R152a emerged as the most promising for RRTC applications due to its superior power-to-power performance of 1.57, surpassing other working fluids for which performances below 1.50 were obtained. The results show that a relative difference below 10% was likely observed between simulation results with and without Baumann's correlation. Moreover, Ba(OH)2·8 H2O and acetamide offer a less phase change material mass required in the storage system, achieving thermal energy storage mass sizing ratio of 0.35–1.55 and 0.39–1.71, respectively.

A Preliminary Design and Modeling Analysis of Two-Phase Volumetric Expanders for a Novel Reversible Organic Rankine-Based Cycle for Carnot Battery Technology

Carnot battery technology appears to be a promising solution to increase the development of power generation and offers a good solution for high-capacity, day-to-day energy storage. This technology may utilize the waste heat and store the electricity to recover it later. This article reports the preliminary analysis of a specially designed Carnot battery configuration employing a novel reversible Rankine-based thermodynamic cycle (RRTC). In this case, one volumetric expander is not only installed to generate power from a heat engine, but also to recover power during heat pump operating mode. The preliminary design and modeling results were obtained based on calculations taken from working fluid thermal properties of propane with some specific boundary conditions (i.e., secondary fluid hot temperature of 348.15 K, cooling temperature of 228.15 K, and waste heat temperature of 338.15 K). The results show that isentropic efficiency, pressure, and volumetric expansion ratio from both heat engine and heat pump operating modes are important parameters that must be taken into account when designing the two-phase expander for RRTC. The obtained results show that a designed two-phase volumetric expander in RRTC features a pressure ratio of 2.55 ± 1.15 and a volumetric ratio of 0.21 ± 0.105, and the Carnot battery may achieve the performance of 0.50–0.98.

Preliminary Numerical Investigation on the Optimization of a Single Bunch of Elastocaloric Elements to be Employed in an Experimental Device

Nowadays about 20% of the worldwide energy consumption is attributable to refrigeration almost based on vapor compression. In the scientific literature in the class of the eco-friendly cooling technologies alternative to vapour compression there is solid state cooling. In this field, the scientific community has devoted the attention specifically toward elastocaloric refrigeration. Elastocaloric refrigeration is based on the latent heat associated with the transformation process of the martensitic phase, found in Shape Memory Alloys (SMA) when they are subjected to uniaxial stress cycles of loading and unloading. SMAs are characterized by the mechanical property of being able to return to the initial form once the uniaxial stress has been removed. By exploiting this effect in a reverse regenerative thermodynamic cycle called Active elastocaloric regenerative refrigeration cycle (AeR), a satisfactory cooling effect is achievable. In this paper, the results of a numerical investigation conducted, through a 2-D model, on a single bunch of elastocaloric elements are shown. Specifically, the heat transfer and the energy performances are studied both by varying the geometrical parameters of the elements and by varying the auxiliary fluid (air) velocity.

Phase transition in hydrophobic weak polyelectrolyte gel utilized for water desalination

By this article, we continue studying weak polyelectrolyte hydrogels and their application as a desalination agent. We modeled the desalination process as a four-step reversible thermodynamic cycle transferring ions from a low salinity solution to a high salinity one. The cycle implies reversibility at any stage, therefore the method can achieve the maximum thermodynamic efficiency, comparable to the reverse osmosis. As a driving force for ions movement, we use the fact that compression of the gel leads to a decrease in the gel ionization degree, and therefore to a release of ions entrapped in the gel. We considered the gel composed of ionogenic units modified by hydrophobic pendants and showed that this modification significantly increases the number of transferred ions. This increase is caused by a first-order phase transition originated from an interplay between repulsive electrostatic and attractive steric interactions. The transition happens during hydrogel compression. At a certain pressure, the gel collapses abruptly, changing its volume almost to that of a dry state, and releases almost all ions collected inside. Employing the phase transition allows us to model the desalination cycle, which transfers a much larger number of ions and works at rather low pressures <10bar.

A note on the overall efficiency of back-to-back Carnot cycles

The overall efficiency of a reversible thermodynamic cycle comprising steps around the periphery of back-to-back Carnot cycles is equal to the efficiency-weighted average heat-energy inputs taken over all of the cycles. A proof of this assertion is straightforward and brief enough to be suitable for classroom presentation.

Nernst and Ettingshausen effects in the Laughlin geometry

The ideal reversible thermodynamic cycle visualization of the Nernst effect in Laughlin geometry, excluding the kinetic contribution is proposed. The Ettingshausen effect is also treated in the fashion using the reverse cycle. The corresponding values of the off-diagonal thermoelectric coefficients are expressed through the ratio of the entropy budget per magnetic flux. Our approach enlightens the profound thermodynamic origin of the relation between the Nernst effect and magnetization currents.

An Analysis of Pumped Thermal Energy Storage With De-coupled Thermal Stores

Results from the first demonstration of Pumped Thermal Energy Storage (PTES) were published in 2019, indicating an achieved turn-round efficiency of 60-65% for a system capable of storing 600kWh of electricity. PTES uses a theoretically reversible thermodynamic cycle involving compression and expansion stages with constant pressure heat addition and rejection to hot and cold thermal stores. Energy storage turn-round efficiency largely depends on the isentropic efficiencies of the compression and expansion equipment, the thermal effectiveness of the thermal stores, the presence of circuit pressure drops, heat leaks to and from the system and electrical machine efficiencies. We present a simulation model of a PTES system which is used to produce an inventory of the relative magnitudes of the various system losses. We consider the feasibility of a large-scale, 1GWh nominal storage capacity, PTES system with de-coupled thermal stores; and provide comparison with the so far more investigated, coupled system. Based on ambitious yet realistic component performances, we calculate an energy storage turn around efficiency of 65.3% and 59.5% for the coupled and de-coupled systems respectively. Even with dwell times in the charged state as long as 5 days, a turn-round efficiency of over 50% is still predicted in both systems; suggesting that PTES could offer a viable large-scale, long duration energy store.

Symmetry of reversible thermodynamics

<p indent=0mm>Symmetry is very important in physics. However, most of the current thermodynamic literature focuses on asymmetrical concepts. For example, the second law of thermodynamics states that even in a reversible thermodynamic cycle, the heat input to a system cannot be entirely transformed to work. Therefore, generally work is considered to be a higher grade of energy than heat. Another example is that thermodynamic cycles are evaluated based on the heat efficiency as the performance criterion, while reversed cycles use the coefficient of performance (COP) as their performance criterion. That is, the second law of thermodynamics and its related principles, theorems, laws, performance criteria, and parameters are all asymmetric. Meanwhile, according to the concept of symmetry, there could be another set of asymmetric principles, laws, performance criteria and parameters, which are corresponding to the second law of thermodynamics. These new concepts, new physical quantities and new understandings include the work entropy as the core physical quantity for a reversed cycle. The work entropy is actually the system volume, but with a new physical meaning corresponding to heat entropy. A second concept is that the volume work quantity has a grade, i.e. the pressure. A higher pressure of work can yield more heat through a reversed cycle driven by the same amount of volume work comparing to the volume work with a lower pressure. A third concept is that the heat quantity and the work quantity have the same grade for reversible conditions. The reasons are stated in two points. On one hand, not all the heat in a reversible thermodynamic cycle can be transformed to work because the ambient temperature cannot reach absolute zero, hence there must be a certain amount of heat flows to the heat source with a lower temperature. On the other hand, in reversible reversed cycles, not all work input can be transformed to heat, neither. That is because the ambient pressure cannot reach absolute vacuum (zero pressure). Through this comparison it can be seen that the volume work and heat have the same grade in reversible thermodynamics. A fourth concept is that thermodynamic cycles can also have a coefficient of performance (COP_w), and it can be used as a performance criterion. The applications of these theoretical results could provide a deeper understanding of some thermodynamic quantities. First, entropy (thermal entropy) and exergy (thermal exergy) could be used to describe the ability of a heat engine to produce work, while the volume (work entropy) and work exergy could be used to describe the ability of a heat pump to produce heat from work. Second, since the grade of volume work in a reversible reversed cycle is the pressure, the work at high pressure into a system will improve the coefficient of performance (COP_h) of reversible reversed cycles. Third, new thermodynamic cycles produce work from pressure sources with coefficient of performance (COP_w) greater than 1 could be possibly proposed, and the work generated by these cycles could be greater than the work generated from a Carnot cycle for the same temperature limits.

Work entropy and work exergy

Clausius proposed a reversible thermodynamic cycle made up of three isothermal processes and three adiabatic processes to establish the theorem of the equivalence of the transformation of heat to work and the transformation of heat at a higher temperature to a lower temperature. Then, he derived the Clausius equality and the concept of entropy (later called thermal entropy to prevent confusion). Similarly, this study uses a reversible reversed thermodynamic cycle made up of three isobaric processes and three isochoric processes to establish the theorem of the equivalence of the transformation of work to heat and the transformation of work at a higher pressure to a lower pressure, and then derives a corresponding equality for a reversed thermodynamic cycle and the concept of work entropy. The work entropy is shown to be equal to the system volume which is the core physical quantity of a reversed thermodynamic cycle. Although this is not a new quantity, the work entropy gives the volume a new physical interpretation corresponding to thermal entropy. Next, by analogy with the definition of exergy (later called thermal exergy to prevent confusion), the work exergy is defined as the maximum heat output that can be transformed from the work in a system at pressure p though a reversed p - V cycle under ambient pressure. Furthermore, the work exergy of the working medium is defined as the sum of the heat that the working medium outputs though a series of reversed p-V cycles and the heat that the working medium outputs directly as the temperature varies, as the working medium changes reversibly from any state to the state in balance with the environment. The physical meanings of the work entropy and the work exergy are illustrated with comparisons to the thermal entropy and the thermal exergy. When it changes reversibly from any state to the state in balance with the environment, the working medium with more thermal entropy will have more unavailable energy T 0( ST – S T0) and, thus, less thermal exergy, if the system outputs work through a reversible thermodynamic cycle. In contrast, the working medium with more work entropy will have less unavailable energy p 0( V 0– V ) and, thus, more work exergy, if the system outputs heat through a reversible reversed thermodynamic cycle. Thus, the work entropy can measure the unavailable energy of the working medium while the work exergy can measure the available energy of the working medium. The pressure-work entropy diagram can be used to intuitively analyze a reversed thermodynamic cycle. Finally, a least action principle is proposed for reversible thermodynamic processes. When the heat-to-work action, Δ S / Q reaches a minimum, the optimal heat-to-work process is obtained that is the combination of an isothermal process and an adiabatic process. When the work-to-heat action, Δ V / W reaches a maximum, the optimal work-to-heat process is obtained that is the combination of an isobaric process and an isochoric process.

Entransy analysis of reversible thermodynamic cycles based on the conservation of entransy equation and its application

Entropy analyses and entropy generation analyses have been widely used to analyze and optimize thermal processes. For instance, the entropy generation minimization principle has been used to optimize heat transfer processes, heat transfer systems and thermodynamic cycles. However, some studies have reported that the entropy generation minimization principle cannot derive the optimal results for pure heat transfer processes and heat transfer systems without heat-work conversion processes. The concept of entransy and the principle of the least entransy dissipation-based thermal resistance were proposed for these problems, and they have been widely applied to optimize pure heat transfer processes and systems. Besides, the concept of work entransy was developed for irreversible thermodynamic cycles involving heat-work conversion processes, and it is defined as the product of the work and the temperature. This concept was then used as the entransy analysis approach to optimize thermodynamic cycles. However, previous studies applying the work entransy concept mainly focused on (1) the relation between the work entransy loss and the endoreversible thermodynamic cycle efficiency, and (2) the optimization of practical thermodynamic cycles involving irreversible processes. There have been few such studies of reversible thermodynamic cycles or combined cycles. This article analyzes reversible thermodynamic cycles and combined thermodynamic cycles using the entransy analysis method with a derivation of the conservation of entransy equation. First, the entransy conservation equation for a reversible thermodynamic process is derived, which introduces the concept of heat entransy and heat-work entransy flow. They are both process dependent physical quantities. The corresponding entransy conservation equation is then derived for a reversible thermodynamic cycle. The equation shows that there are two different conservation equations for reversible thermodynamic cycles, i.e. the energy conservation equation (1st law of thermodynamics) and the entransy conservation equation. Meanwhile, according to thermomass theory, the entransy is nothing else but the relative energy. The entransy conservation equation can be used to analyze the performance of reversible thermodynamic cycles. On the other hand, since the entropy returns to the initial value in a reversible thermodynamic cycle, an entropy analysis cannot evaluate the performance of reversible thermodynamic cycles. Second, a combined heat engine-heat pump cycle is taken as an example application of entransy analysis. In the philosophy of entransy analyses, the performance indicator of the combined cycle is its net heat entransy flow. For the properly chosen parameters, the combined cycle can be regarded as an ideal voltage transformer. Therefore, this kind of combined cycle can be referred to as a temperature transformer, which is different from the absorption temperature transformer. A diagram is introduced to show the total effect of the combined cycle to help understand the combined cycle. Finally, two practical cases, i.e. combined cycles for heating and refrigeration, are chosen to show applications of this entransy analysis approach. The concept of entransy efficiency of combined cycles is introduced to evaluate the performance of the combined cycles.

The other half of the principle of heat-work conversion cycles: The theorem, principle and core physical quantity of reversed cycles

Engineering thermodynamics mainly focuses on the principles and methods for the heat-work conversion and to improve heat-work conversion efficiency. In current literatures, discussions are mainly focused on the heat-work cycles, which converts heat to work. Besides, the core physical quantity of heat-work cycles is entropy, which presents the heat-work conversion ability of the system. As for reversed cycles, the discussions are not quite detailed, and most of them applied the theory for heat-work cycles directly on reversed cycles. However, its well known that heat cannot be fully converted to work in a reversible thermodynamic cycle, which leads an efficiency less than 1. For reversed cycles, the heat output from the cycle can be much more than the net work the cycle costs, which derives a coefficient of performance (COP) more than 1. This phenomenon implies the principles of heat-work conversion in ordinary heat-work cycles and reversed cycles are somehow different, and some problems are naturally drawn as follows: (1) Is the COP of the reversed Carnot cycle the maximum possible COP for all reversed cycles within two temperature limits? (2) Heat can be judged from its quality, i.e. its temperature, and does the mechanical work have its quality? To answer these questions, this work analyzed and discussed the theorem, principle, and core physical quantity of reversed thermodynamic cycles. First, the principle for ordinary thermodynamic cycles are briefly reviewed, including the Carnot theorem and its proof, and the derivation of the concept of entropy from the Clausius original approach. Second, current conclusions of reversed cycles are reviewed and the air compression refrigeration cycle is taken as an example. The analysis comparing two cycles within given temperature limits presented that for given two temperature limits, the COP of the reversed Carnot cycle is the minimum possible COP, which is different from current conclusions. The quality of volumetric work is then discussed, and a new reversed cycle named reversed p-V cycle is proposed, which operates between two given pressure limits. The analysis indicates that this cycle is the best reversed cycle operating between two given pressure limits. Based on these discussion, the theorem and principle for reversed cycles corresponding to the second law and the Carnots theorem are derived and proved using the Clausius approach. The performance of the newly proposed reversed p-V cycle is investigated and compared with the reversed Carnot cycle operating within the same temperature limits, and results present that the COP of the reversed p-V cycle is much higher than the COP of the reversed Carnot cycle within the same temperature limits. Finally, from the equation of an arbitrary reversed cycle, it can be seen that the volume has a similar physical interpretation in the reversed cycles to the entropy in thermodynamic cycles, and it can be named as the work-entropy. In summary, the reversed cycles are analyzed, and its theorem, principles and core physical quantity are investigated.

Entropy, Carnot Cycle, and Information Theory.

The fundamental intuition that Carnot had in analyzing the operation of steam machines is that something remains constant during the reversible thermodynamic cycle. This invariant quantity was later named “entropy” by Clausius. Jaynes proposed a unitary view of thermodynamics and information theory based on statistical thermodynamics. The unitary vision allows us to analyze the Carnot cycle and to study what happens when the entropy between the beginning and end of the isothermal expansion of the cycle is considered. It is shown that, in connection with a non-zero Kullback–Leibler distance, minor free-energy is available from the cycle. Moreover, the analysis of the adiabatic part of the cycle shows that the internal conversion between energy and work is perturbed by the cost introduced by the code conversion. In summary, the information theoretical tools could help to better understand some details of the cycle and the origin of possible asymmetries.

Reply to the Comments on: Tian Zhao et al. The Principle of Least Action for Reversible Thermodynamic Processes and Cycles. Entropy 2018, 20, 542.

The purpose of this reply is to provide a discussion and closure for the comment paper by Dr. Bormashenko on the present authors’ article, which discussed the application of the principle of least action in reversible thermodynamic processes and cycles. Dr. Bormashenko’s questions and misunderstandings are responded to, and the differences between the present authors’ work and Lucia’s are also presented.

Comments on "The Principle of Least Action for Reversible Thermodynamic Processes and Cycles", Entropy 2018, 20, 542.

The goal of this comment note is to express my concerns about the recent paper by Tian Zhao et al. (Entropy 2018, 20, 542). It is foreseen that this comment will stimulate a fruitful discussion of the issues involved. The principle of the least thermodynamic action is applicable for the analysis of the Carnot cycle using the entropy (not heat) generation extrema theorem. The transversality conditions of the variational problem provide the rectangular shape of the ST diagram for the Carnot cycle.

The Principle of Least Action for Reversible Thermodynamic Processes and Cycles.

The principle of least action, which is usually applied to natural phenomena, can also be used in optimization problems with manual intervention. Following a brief introduction to the brachistochrone problem in classical mechanics, the principle of least action was applied to the optimization of reversible thermodynamic processes and cycles in this study. Analyses indicated that the entropy variation per unit of heat exchanged is the mode of action for reversible heat absorption or heat release processes. Minimizing this action led to the optimization of heat absorption or heat release processes, and the corresponding optimal path was the first or second half of a Carnot cycle. Finally, the action of an entire reversible thermodynamic cycle was determined as the sum of the actions of the heat absorption and release processes. Minimizing this action led to a Carnot cycle. This implies that the Carnot cycle can also be derived using the principle of least action derived from the entropy concept.

Reversible and irreversible heat engine and refrigerator cycles

Although no reversible thermodynamic cycles exist in nature, nearly all cycles covered in textbooks are reversible. This is a review, clarification, and extension of results and concepts for quasistatic, reversible and irreversible processes and cycles, intended primarily for teachers and students. Distinctions between the latter process types are explained, with emphasis on clockwise (CW) and counterclockwise (CCW) cycles. Specific examples of each are examined, including Carnot, Kelvin and Stirling cycles. For the Stirling cycle, potentially useful task-specific efficiency measures are proposed and illustrated. Whether a cycle behaves as a traditional refrigerator or heat engine can depend on whether it is reversible or irreversible. Reversible and irreversible-quasistatic CW cycles both satisfy Carnot's inequality for thermal efficiency, η≤ηCarnot. Irreversible CCW cycles with two reservoirs satisfy the coefficient of performance inequality K≤KCarnot. However, an arbitrary reversible cycle satisfies K≥KCarnot when compared with a reversible Carnot cycle operating between its maximum and minimum temperatures, a potentially counterintuitive result.

Reversible thermodynamic cycle analysis for capacitive deionization with modified Donnan model

It is a widely accepted principle that a thermodynamically reversible desalination process should consume the Gibbs free energy of separation. This principle has been shown in reverse osmosis and has important practical implications in reducing its energy consumption. Capacitive deionization (CDI) with carbon electrodes, a desalination process based on electrical double layer (EDL) formation, should also follow such a principle when it operates in a thermodynamically reversible way. Inspired by a previous thermodynamic analysis on a three-stage reversible CDI process using the Gouy-Chapman-Stern model, we conducted a thermodynamic analysis of a four-stage reversible CDI cycle using the modified Donnan model. This analysis better reflects the cyclic nature of practical CDI operations and account for the significant EDL overlap in nanosized micropores of realistic CDI electrodes. Our analysis of CDI cycles with different separations and final discharge voltages shows that the electrical work to complete a four-stage cycles is numerically exactly identical to the Gibbs free energy of separation, as long as the cycle is operated in a thermodynamically reversible manner.

Experimental study of the structure of vapor phase during boiling of R134a on heat exchange surfaces of heat pump

The heat supply by means of heat pumps is considered now as a rational method of local heating which can lead to economy of primary fuel. At use of low-potential heat, for example, the heat of a ground (5 … 18 °C) or ground waters (8 … 10°C) only small depressing of temperature of these sources (on 3 … 5°C) is possible that demands application of heat exchangers with intensified heatmass transfer surfaces. In thermal laboratory of TOT department the 200 W experimental installation has been developed for research of process of boiling of freon R134a. The principle of action of the installation consists in realisation of reverse thermodynamic cycle and consecutive natural measurement of characteristics of elements of surfaces of heat exchangers of real installations at boiling points of freon from-10°C to +10°C and condensing temperatures from 15°C to 50 °C. The evaporator casing has optical windows for control of process of boiling of freon on ribbed on technology of distorting cut tubes. Temperature measurement in characteristic points of a cycle is provided by copper-constantan thermocouples which by means of ADT are connected to the computer that allows treat results of measurements in a real time mode. The structure of a two-phase flow investigated by means of the optical procedure based on laser technique.

Evaluation thermodynamic perfection of the cogeneration cascade machines cycles

One of the promising trends in the refrigerating engineering is building machines for industrial processes with the simultaneous use of two thermal effects (heat and cold). The fundamental possibility to build machines, operating on a complex reverse thermodynamic cycle with the production of low-grade cold and high-grade heat is considered. Such machines are called heating cascade machines. The synthesis of cyclic machine solutions for various pairs of materials, based on thermodynamic analysis by the “method of cycles” is carried out. The analysis of the supercritical cycle of the upper cascade with R744 by the entropy-cycle method is performed. It is shown that the compound Carnot-Lorenz cycle (“triangular”) should be chosen as the cycle model. The problem of determining the degree of thermodynamic perfection of the cascade cycle, which takes into account the simultaneous production of two thermal effects – cold and heat is solved. An example of the calculation of the machine characteristics under variable input parameters: temperature in the condenser-evaporator and the pressure in the gas cooler is given. The comparison with the characteristics of the cascade machine, operating in the same mode, but with one thermal effect – the production of cold, which showed the benefits of heating cycles is performed. It is proved that, given the simultaneous high temperatures of the heat produced and low temperature of the cold produced in the cascade heating machine, energy performance is quite high. General recommendations – in terms of energy saving, heating cascade units and machines, operating with R744 as a working substance of the upper cascade and the cycle in the supercritical region with the simultaneous heat and cold production should be designed.

Minimization of the Surface Area of a Radiating Cooler of Spacecraft NPP with a Combined Energy Conversion System

The possibility of reducing the surface area of the radiating cooler of a spacecraft NPP with direct energy conversion by transformation of the shed heat by means of machine converters (heat engines and heat pumps) operating in a direct or reverse thermodynamic cycle. It is shown that heat engines and heat pumps used as low-temperature attachments to a direct-conversion setup can reduce the specific surface area of a radiating cooler with a definite combination of thermodynamic ideality indices of direct and machine converters. The regions of expedient use of heat engines and heat pumps are determined.