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Time-Reversible Thermodynamic Irreversibility : One-Dimensional Heat-Conducting Oscillators and Two-Dimensional Newtonian Shockwaves

Hoover William Graham, Hoover Carol Griswold

Computational Methods in Science and Technology

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2022

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Vol. 28, No. 4

133--141

EN

We analyze the time-reversible mechanics of two irreversible simulation types. The first is a dissipative onedimensional heat-conducting oscillator exposed to a temperature gradient in a three-dimensional phase space with coordinate q, momentum p, and thermostat control variable ζ. The second type simulates a conservative two-dimensional N-body fluid with 4N phase variables {q, p} undergoing shock compression. Despite the time-reversibility of each of the three oscillator equations and all of the 4N manybody motion equations both types of simulation are irreversible, obeying the Second Law of Thermodynamics. But for different reasons. The irreversible oscillator seeks out an attractive dissipative limit cycle. The likewise irreversible, but thoroughly conservative, Newtonian shockwave eventually generates a reversible near-equilibrium pair of rarefaction fans. Both problem types illustrate interesting features of Lyapunov instability. This instability results in the exponential growth of small perturbations, ∝ e λt where λ is a “Lyapunov exponent”.

2

Time-symmetry breaking in Hamiltonian mechanics. Part 3, A memoir for Douglas James Henderson [1934–2020]

Hoover Wm. G., Hoover C. G.

Computational Methods in Science and Technology

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2020

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Vol. 26, No. 4

111--120

EN

Following Berni Alder [1] and Francis Ree [2], Douglas Henderson was the third of Bill’s California coworkers from the 1960s to die in 2020 [1, 2]. Motivated by Doug’s death we undertook better to understand Lyapunov instability and the breaking of time symmetry in continuum and atomistic simulations. Here we have chosen to extend our explorations of an interesting pair of nonequilibrium systems, the steady shockwave and the unsteady rarefaction wave. We eliminate the need for boundary potentials by simulating the collisions of pairs of mirror-images projectiles. The resulting shock and rarefaction structures are respectively the results of the compression and the expansion of simple fluids. Shockwaves resulting from compression have a steady structure while the rarefaction fans resulting from free expansions continually broaden. We model these processes using classical molecular dynamics and Eulerian fluid mechanics in two dimensions. Although molecular dynamics is time-reversible the reversed simulation of a steady shockwave compression soon results in an unsteady rarefaction fan, violating the microscopic time symmetry of the motion equations but in agreement with the predictions of macroscopic Navier-Stokes fluid mechanics. The explanations for these results are an interesting combination of two (irreversible) instabilities, Lyapunov and Navier-Stokes.

3

Effects of combustion products composition models on the exergetic analysis of spark-ignition engine fuelled with ethanol

Rufino Caio H., de Lima Alessandro J. T. B., Mattos Ana P., Allah Fazal U. M., Ferreir Janito V., Gallo Waldyr L. R.

Archives of Thermodynamics

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2019

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Vol. 40, no 3

27--42

EN

The engine simulations have become an integral part of engine design and development. They are based on approximations and assumptions. The precision of the results depends on the accuracy of these hypotheses. The simplified models of frozen composition, chemical equilibrium and chemical kinetics provide the compositions of combustion products for engine cycle simulations. This paper evaluates the effects of different operating conditions and hypotheses on the exergetic analysis of a spark-ignition engine. The Brazilian automotive market has the highest number of flex-fuel vehicles. Therefore, a flex-fuel engine is considered for simulations in order to demonstrate the effects of these different hypotheses. The stroke length and bore diameter have the same value of 80 mm. The in-cylinder irreversibility is calculated for each case at the closed part of the engine cycle. A comparative analysis of these hypotheses provides a comprehensive evaluation of their effects on exergetic analysis. Higher values of accumulated irreversibility are observed for the oversimplified hypothesis.

4

Hybrid cascade refrigeration systems for refrigeration and heating

Megdouli K., Ezzaalouni Y., Nahdi E., Mhimid A., Kairouani L.

Archives of Thermodynamics

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2018

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Vol. 39, no 2

73--95

EN

In this study a cooling ejector cycle coupled to a compression heat pump is analyzed for simultaneous cooling and heating applications. In this work, the influence of the thermodynamic parameters and fluid nature on the performances of the hybrid system is studied. The results obtained show that this system presents interesting performances. The comparison of the system performances with hydrofluorocarbons (HFC) and natural fluids is made. The theoretical results show that the a low temperature refrigerant R32 gives the best performance.

5

Entropy generation and thermodynamic analysis of solar air heaters with artificial roughness on absorber plate

Prasad R. K., Sahu M. K.

Archives of Thermodynamics

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2017

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Vol. 38, no. 3

23--48

EN

This paper presents mathematical modelling and numerical analysis to evaluate entropy generation analysis (EGA) by considering pressure drop and second law efficiency based on thermodynamics for forced convection heat transfer in rectangular duct of a solar air heater with wire as artificial roughness in the form of arc shape geometry on the absorber plate. The investigation includes evaluations of entropy generation, entropy generation number, Bejan number and irreversibilities of roughened as well as smooth absorber plate solar air heaters to compare the relative performances. Furthermore, effects of various roughness parameters and operating parameters on entropy generation have also been investigated. Entropy generation and irreversibilities (exergy destroyed) has its minimum value at relative roughness height of 0.0422 and relative angle of attack of 0.33, which leads to the maximum exergetic efficiency. Entropy generation and exergy based analyses can be adopted for the evaluation of the overall performance of solar air heaters.

6

Influence of nozzle hole diameter on the first and second law balance in a DI Diesel engine

Abbasi A., Emamverdi O.

Journal of Power Technologies

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2014

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Vol. 94, nr 1

20--33

EN

In the present work, influence of nozzle holes diameter is studied on the first and second law balance in DI Diesel engine. To this aim, the first law analysis is done by using the results of a three dimensional CFD model. The results show a good agreement with the experimental data. Also for the second law analysis, a developed in house computational code is applied. Behaviors of the results have a good accordance with the literature. The results show that increase in nozzle holes diameter increases both indicated work and heat loss to walls. Also about the second law terms, results declare that increase in nozzle holes diameter leads to increase in indicated work availability, heat loss availability, and entropy generation per cycle and decrease in combustion irreversibility and exhaust gas availability.

7

Comparison of a dual-fuel internal combustion engine performance for CNG and gasoline fuels

Ameri M., Kiaahmadi F., Khanaki M. M.

Journal of Power Technologies

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2012

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Vol. 92, nr 4

214--226

EN

In this paper, comparison of a dual-fuel internal combustion engine performance for CNG and gasoline fuels is evaluated at the steady-state condition by application of energy and exergy analysis using the experimental test results. The energy and exergy balances are calculated at different engine speeds. The results show that the energy and exergy of the heat rejection for gasoline and CNG fuels increases with increasing engine speed and the exergy efficiencies are slightly higher than the corresponding energy efficiencies. Moreover, the results show that the exergy efficiency for gas-fuel is higher than the gasoline-fuel exergy efficiency at all engine speeds. The results show that due to volumetric efficiency drop, power and torque of the gas-fuel engine is lower than gasoline-fuel one. Furthermore, the specific fuel consumption of the gas-fuel engine is lower than gasoline-fuel one. The results of this study have revealed that the most important source of the system inefficiency is the destruction of exergy by irreversible processes, mostly by the combustion. Moreover, it should be noted that liquid fuels like gasoline have many important advantages like much greater volumetric energy density, ease of transport and storage, which have made them as the preferred fuels for IC engines.

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Równoważność postulatu Plancka o nieodwracalności procesów przebiegających z tarciem i sformułowań drugiej zasady termodynamiki Clausiusa i Kelvina

Ziemba A.

Rudy i Metale Nieżelazne

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2008

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R. 53, nr 10

604-610

PL

Dwa klasyczne sformułowania drugiej zasady termodynamiki, Clausiusa i Kelvina [4], zostały przyjęte jako postulaty, będąc efektem kontynuacji pracy Carnota i uogólnienia wyników obserwacji procesów natury [1, 2]. Postulaty Plancka są takimi sformułowaniami drugiej zasady termodynamiki, których ważność można jednoznacznie zweryfikować na podstawie eksperymentów [3]. Postulaty przyjmuje się bez ścisłego dowodu, możliwe jest jednak dowodzenie ważności jednego sformułowania, po przyjęciu założenia o ważności dowolnego innego. Powszechnie znane są dowody równoważności sformułowań Kelvina i Clausiusa [4, 5], pierwszego i drugiego postulatu Plancka i sformułowania Kelvina [4], a także postulatów Plancka i sformułowania Kelvina [3]. W artykule zaproponowano dowody równoważności pierwszego postulatu Plancka, o nieodwracalności procesów przebiegających z tarciem, i sformułowań drugiej zasady termodynamiki Clausiusa i Kelvina. W dowodzie równoważności pierwszego postulatu Plancka i sformułowania Kelvina uwzględniono nie tylko ciepło tarcia mechanicznego, jak w dowodach przedstawionych w pracach [3, 4], lecz również ciepło tarcia wewnętrznego czynnika termodynamicznego. Pierwszy postulat Plancka może mieć zastosowanie do opisu i doskonalenia tych procesów technologicznych, w których tarcie odgrywa istotną rolę. Im więcej ciepła tarcia jest związane z procesem technologicznym, tym bardziej jest on odległy od wyidealizowanego pojęcia procesu odwracalnego. Szczególnie jest to widoczne w procesach przeróbki plastycznej i obróbki mechanicznej.

EN

Multiplicity of the second law of thermodynamics statements [6] points out on a universal occurrence of its phenomenological aspects in the processes appearing in the nature [7]. Two classical statements of the second law, Clausius' and Kelvin's statements [4], were accepted as the postulates, while being an effect of the Carnot's work continuation and generalization of results of the observation of the processes in the nature [1, 2]. The Planck's postulates are such second law statements, whose validity may be unequivocally verified by the experiments. Three Planck's postulates are directly connected with an essence of the second law, pointing out on a fact of the existence of the irreversible processes in the nature [3]. The postulates are taken as valid without strict proof; however it is possible to prove any one of the statements, if any of the others is accepted as a postulate. It means that all of the statements of the second law are equivalent, however it seems that more proofs of it cause the better understanding of the second law sense. Commonly well-known there are proofs of equivalence of the Kelvin's and the Clausius' statements [4, 5], the first and second Planck's postulates and the Kelvin's statement [4], also the Planck's postulates and the Kelvin's statement [3]. In this paper the equivalence of the first Planck's postulate, about irreversibility of the processes being proceeded with friction, and the Clausius' and the Kelvin's statements of the second law of thermodynamics are proposed. In the proof of equivalence of the first Planck's postulate and the Kelvin's statement not only heat coming from mechanical friction was taken into account, like in proofs presented in works [3, 4], but also heat coming from internal friction of a thermodynamical agent. The first Planck's postulate could be used to describe and optimize such technological processes, in which friction plays a significant role. The more heat coming from friction is accompanying the technological process, the more far it is from idealized concept of reversible process. Particularly it is noticed in the plastic working and machining processes.

9

Thermodynamic aspects of oxygen-deficient combustion

Rafidi N., Blasiak W.

Archives of Thermodynamics

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2005

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Vol. 26, no. 2

29-44

EN

The oxygen deficient combustion (ODC) is characterized by reactants of low oxygen concentration and high temperature. This work is devoted to analysis of such combustion process from the thermodynamic point of view. It demonstrated the possibilities for reducing thermodynamic irreversibility of combustion by considering the oxygen-deficient combustion process that utilities both gas- and heat-recirculation. Furthermore, an OC system utilizes oxygen as oxidizer has higher 1st and 2nd low efficiencies compared to an ODC system using air as oxidizer. This study is a technical guidance for further efficiency-improvement in combustion process especially because the temperature increase due to the reaction in an ODC system is mild.

10

Vibrational effect on heat transfer and entropy generation in a circular porous cavity

Mahmud S., Fraser R. A.

International Journal of Applied Mechanics and Engineering

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2004

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Vol. 9, no 3

523-533

EN

We investigate the nature of heat transfer and entropy generation for natural convection in a two-dimensional circular section enclosure vibrating sinusoidally perpendicular to the applied temperature gradient in a zero-gravity field. The enclosure is assumed to fill with porous media. The Darcy momentum equation is used to model the porous media. The full governing differential equations are simplified with the Boussinesq approximation and solved by a finite volume method. Whereas the Prandtl number Pr is fixed to 1.0. Results are presented in terms of the average Nusselt number (Nuav), entropy generation number (Nsav), Bejan number (Beav), and kinetic energy (KEav).