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Phenomenological Thermodynamics of Irreversible Processes

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A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Thermodynamics".

Deadline for manuscript submissions: closed (31 January 2018) | Viewed by 67052

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Prof. Dr. Yongqi Wang

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Guest Editor

Department of Mechanical Engineering, Technische Universität Darmstadt, 64287 Darmstadt, Germany
Interests: continuum mechanics and thermodynamics; theoretical fluid mechanics and computational fluid dynamics; granular flows and avalanches; multiphase flows; interface flows; rheology/flows of non-Newtonian fluids; hydrodynamics of lakes and limnology

Prof. Dr. Kolumban Hutter

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Guest Editor

c/o Laboratory of Hydraulics, Hydrology and Glaciology, Hoenggerbergring 26, HIA 58D, ETH, CH-8092 Zurich, Switzerland
Interests: continuum mechanics and thermodynamics; environmental fluid mechanics; physical oceanography and limnology; dynamics of glaciers and ice sheets; mechanics of granular materials; avalanching flows of snow; debris and mud; turbulence

Special Issue Information

Dear Colleagues,

Modern continuum thermodynamics amount to a collection of thermodynamic theories shearing common premises and a common methodology. There are theories of elastic, viscous and/or plastic materials, of materials with memory, of mixture and multiphase materials with microstructure or (multi)polar structures, some exhibiting discontinuous behavior or ordered structures (such as laminar versus turbulent patches). Generally, in the context of each theory, one considers all processes (compatible with classical conservation laws) that bodies composed of the prescribed material might admit. Moreover, there exist for the theoretical formulation universal physical principles, such as invariance and objectivity requirements, that have been abstracted from experience. Therefore, one can reduce the generality of the constitutive relations of dependent material variables by relying upon these principles. One of the most important principles is the second law of thermodynamics, one form of which is expressed by the entropy principle(s)—there are more than one—which are employed to describe the dissipative nature of the thermodynamic processes.

As just stated, there are various approaches to irreversible thermodynamics. Phenomenological thermodynamics is concerned with the analysis of actual phenomena with avoidance of full interpretation of molecular details by microscopic processes. Beyond the use of the established physical laws, this affords the postulation of closure statements (each at the generality of the model formulation for which the model is exploited). All these laws express some notion of irreversibility and the implications drawn from them necessarily differ from each other.

Entropy principles have been widely employed to restrict constitutive equations for various materials. The aim of this Special Issue is to provide a platform for compiling important recent and current researches on the applications of entropy principles in postulating material relations in various practical problems. Manuscripts that address these applications are particularly encouraged. Manuscripts that deal with other aspects in irreversible thermodynamic processes are also welcome.

Prof. Dr. Yongqi Wang
Prof. Dr. Kolumban Hutter
Guest Editors

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Keywords

Entropy principle
Thermodynamics
Irreversible processes
Irreversible thermodynamics
Second law of thermodynamics
Material relations Constitutive equations

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Published Papers (13 papers)

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Editorial

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15 pages, 356 KiB

Open AccessEditorial

Phenomenological Thermodynamics of Irreversible Processes

by Yongqi Wang and Kolumban Hutter

Entropy 2018, 20(6), 479; https://doi.org/10.3390/e20060479 - 20 Jun 2018

Cited by 4 | Viewed by 4104

Abstract

n/a Full article

(This article belongs to the Special Issue Phenomenological Thermodynamics of Irreversible Processes)

Research

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24 pages, 529 KiB

Open AccessArticle

Thermodynamically Constrained Averaging Theory: Principles, Model Hierarchies, and Deviation Kinetic Energy Extensions

by Cass T. Miller, William G. Gray and Christopher E. Kees

Entropy 2018, 20(4), 253; https://doi.org/10.3390/e20040253 - 5 Apr 2018

Cited by 5 | Viewed by 3929

Abstract

The thermodynamically constrained averaging theory (TCAT) is a comprehensive theory used to formulate hierarchies of multiphase, multiscale models that are closed based upon the second law of thermodynamics. The rate of entropy production is posed in terms of the product of fluxes and forces of dissipative processes. The attractive features of TCAT include consistency across disparate length scales; thermodynamic consistency across scales; the inclusion of interfaces and common curves as well as phases; the development of kinematic equations to provide closure relations for geometric extent measures; and a structured approach to model building. The elements of the TCAT approach are shown; the ways in which each of these attractive features emerge from the TCAT approach are illustrated; and a review of the hierarchies of models that have been formulated is provided. Because the TCAT approach is mathematically involved, we illustrate how this approach can be applied by leveraging existing components of the theory that can be applied to a wide range of applications. This can result in a substantial reduction in formulation effort compared to a complete derivation while yielding identical results. Lastly, we note the previous neglect of the deviation kinetic energy, which is not important in slow porous media flows, formulate the required equations to extend the theory, and comment on applications for which the new components would be especially useful. This work should serve to make TCAT more accessible for applications, thereby enabling higher fidelity models for applications such as turbulent multiphase flows. Full article

(This article belongs to the Special Issue Phenomenological Thermodynamics of Irreversible Processes)

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9 pages, 604 KiB

Open AccessArticle

Irreversibility and Action of the Heat Conduction Process

by Yu-Chao Hua, Tiao Zhao and Zeng-Yuan Guo

Entropy 2018, 20(3), 206; https://doi.org/10.3390/e20030206 - 20 Mar 2018

Cited by 26 | Viewed by 4808

Abstract

Irreversibility (that is, the “one-sidedness” of time) of a physical process can be characterized by using Lyapunov functions in the modern theory of stability. In this theoretical framework, entropy and its production rate have been generally regarded as Lyapunov functions in order to measure the irreversibility of various physical processes. In fact, the Lyapunov function is not always unique. In the represent work, a rigorous proof is given that the entransy and its dissipation rate can also serve as Lyapunov functions associated with the irreversibility of the heat conduction process without the conversion between heat and work. In addition, the variation of the entransy dissipation rate can lead to Fourier’s heat conduction law, while the entropy production rate cannot. This shows that the entransy dissipation rate, rather than the entropy production rate, is the unique action for the heat conduction process, and can be used to establish the finite element method for the approximate solution of heat conduction problems and the optimization of heat transfer processes. Full article

(This article belongs to the Special Issue Phenomenological Thermodynamics of Irreversible Processes)

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19 pages, 288 KiB

Open AccessArticle

Non-Conventional Thermodynamics and Models of Gradient Elasticity

by Hans-Dieter Alber, Carsten Broese, Charalampos Tsakmakis and Dimitri E. Beskos

Entropy 2018, 20(3), 179; https://doi.org/10.3390/e20030179 - 8 Mar 2018

Cited by 3 | Viewed by 5033

Abstract

We consider material bodies exhibiting a response function for free energy, which depends on both the strain and its gradient. Toupin–Mindlin’s gradient elasticity is characterized by Cauchy stress tensors, which are given by space-like Euler–Lagrange derivative of the free energy with respect to the strain. The present paper aims at developing a first version of gradient elasticity of non-Toupin–Mindlin’s type, i.e., a theory employing Cauchy stress tensors, which are not necessarily expressed as Euler–Lagrange derivatives. This is accomplished in the framework of non-conventional thermodynamics. A one-dimensional boundary value problem is solved in detail in order to illustrate the differences of the present theory with Toupin–Mindlin’s gradient elasticity theory. Full article

(This article belongs to the Special Issue Phenomenological Thermodynamics of Irreversible Processes)

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26 pages, 2338 KiB

Open AccessEditor’s ChoiceArticle

A Variational Formulation of Nonequilibrium Thermodynamics for Discrete Open Systems with Mass and Heat Transfer

by François Gay-Balmaz and Hiroaki Yoshimura

Entropy 2018, 20(3), 163; https://doi.org/10.3390/e20030163 - 4 Mar 2018

Cited by 26 | Viewed by 6114

Abstract

We propose a variational formulation for the nonequilibrium thermodynamics of discrete open systems, i.e., discrete systems which can exchange mass and heat with the exterior. Our approach is based on a general variational formulation for systems with time-dependent nonlinear nonholonomic constraints and time-dependent Lagrangian. For discrete open systems, the time-dependent nonlinear constraint is associated with the rate of internal entropy production of the system. We show that this constraint on the solution curve systematically yields a constraint on the variations to be used in the action functional. The proposed variational formulation is intrinsic and provides the same structure for a wide class of discrete open systems. We illustrate our theory by presenting examples of open systems experiencing mechanical interactions, as well as internal diffusion, internal heat transfer, and their cross-effects. Our approach yields a systematic way to derive the complete evolution equations for the open systems, including the expression of the internal entropy production of the system, independently on its complexity. It might be especially useful for the study of the nonequilibrium thermodynamics of biophysical systems. Full article

(This article belongs to the Special Issue Phenomenological Thermodynamics of Irreversible Processes)

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18 pages, 31650 KiB

Open AccessArticle

A Chemo-Mechanical Model of Diffusion in Reactive Systems

by Kerstin Weinberg, Marek Werner and Denis Anders

Entropy 2018, 20(2), 140; https://doi.org/10.3390/e20020140 - 22 Feb 2018

Cited by 8 | Viewed by 6250

Abstract

The functional properties of multi-component materials are often determined by a rearrangement of their different phases and by chemical reactions of their components. In this contribution, a material model is presented which enables computational simulations and structural optimization of solid multi-component systems. Typical Systems of this kind are anodes in batteries, reactive polymer blends and propellants. The physical processes which are assumed to contribute to the microstructural evolution are: (i) particle exchange and mechanical deformation; (ii) spinodal decomposition and phase coarsening; (iii) chemical reactions between the components; and (iv) energetic forces associated with the elastic field of the solid. To illustrate the capability of the deduced coupled field model, three-dimensional Non-Uniform Rational Basis Spline (NURBS) based finite element simulations of such multi-component structures are presented. Full article

(This article belongs to the Special Issue Phenomenological Thermodynamics of Irreversible Processes)

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41 pages, 2461 KiB

Open AccessArticle

Tsallis Extended Thermodynamics Applied to 2-d Turbulence: Lévy Statistics and q-Fractional Generalized Kraichnanian Energy and Enstrophy Spectra

by Peter W. Egolf and Kolumban Hutter

Entropy 2018, 20(2), 109; https://doi.org/10.3390/e20020109 - 7 Feb 2018

Cited by 7 | Viewed by 4403

Abstract

The extended thermodynamics of Tsallis is reviewed in detail and applied to turbulence. It is based on a generalization of the exponential and logarithmic functions with a parameter q. By applying this nonequilibrium thermodynamics, the Boltzmann-Gibbs thermodynamic approach of Kraichnan to 2-d turbulence is generalized. This physical modeling implies fractional calculus methods, obeying anomalous diffusion, described by Lévy statistics with q < 5/3 (sub diffusion), q = 5/3 (normal or Brownian diffusion) and q > 5/3 (super diffusion). The generalized energy spectrum of Kraichnan, occurring at small wave numbers k, now reveals the more general and precise result k^−q. This corresponds well for q = 5/3 with the Kolmogorov-Oboukov energy spectrum and for q > 5/3 to turbulence with intermittency. The enstrophy spectrum, occurring at large wave numbers k, leads to a k⁻^3q power law, suggesting that large wave-number eddies are in thermodynamic equilibrium, which is characterized by q = 1, finally resulting in Kraichnan’s correct k⁻³ enstrophy spectrum. The theory reveals in a natural manner a generalized temperature of turbulence, which in the non-equilibrium energy transfer domain decreases with wave number and shows an energy equipartition law with a constant generalized temperature in the equilibrium enstrophy transfer domain. The article contains numerous new results; some are stated in form of eight new (proven) propositions. Full article

(This article belongs to the Special Issue Phenomenological Thermodynamics of Irreversible Processes)

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24 pages, 654 KiB

Open AccessArticle

Macroscopic Internal Variables and Mesoscopic Theory: A Comparison Considering Liquid Crystals

by Christina Papenfuss and Wolfgang Muschik

Entropy 2018, 20(1), 81; https://doi.org/10.3390/e20010081 - 22 Jan 2018

Cited by 5 | Viewed by 4529

Abstract

Internal and mesoscopic variables differ fundamentally from each other: both are state space variables, but mesoscopic variables are additionally equipped with a distribution function introducing a statistical item into consideration which is missing in connection with internal variables. Thus, the alignment tensor of the liquid crystal theory can be introduced as an internal variable or as one generated by a mesoscopic background using the microscopic director as a mesoscopic variable. Because the mesoscopic variable is part of the state space, the corresponding balance equations change into mesoscopic balances, and additionally an evolution equation of the mesoscopic distribution function appears. The flexibility of the mesoscopic concept is not only demonstrated for liquid crystals, but is also discussed for dipolar media and flexible fibers. Full article

(This article belongs to the Special Issue Phenomenological Thermodynamics of Irreversible Processes)

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13 pages, 2725 KiB

Open AccessArticle

Energetic and Exergetic Analysis of a Transcritical N₂O Refrigeration Cycle with an Expander

by Ze Zhang, Yu Hou and Francis A. Kulacki

Entropy 2018, 20(1), 31; https://doi.org/10.3390/e20010031 - 18 Jan 2018

Cited by 7 | Viewed by 5224

Abstract

Comparative energy and exergy investigations are reported for a transcritical N₂O refrigeration cycle with a throttling valve or with an expander when the gas cooler exit temperature varies from 30 to 55 °C and the evaporating temperature varies from −40 to 10 °C. The system performance is also compared with that of similar cycles using CO₂. Results show that the N₂O expander cycle exhibits a larger maximum cooling coefficient of performance (COP) and lower optimum discharge pressure than that of the CO₂ expander cycle and N₂O throttling valve cycle. It is found that in the N₂O throttling valve cycle, the irreversibility of the throttling valve is maximum and the exergy losses of the gas cooler and compressor are ordered second and third, respectively. In the N₂O expander cycle, the largest exergy loss occurs in the gas cooler, followed by the compressor and the expander. Compared with the CO₂ expander cycle and N₂O throttling valve cycle, the N₂O expander cycle has the smallest component-specific exergy loss and the highest exergy efficiency at the same operating conditions and at the optimum discharge pressure. It is also proven that the maximum COP and the maximum exergy efficiency cannot be obtained at the same time for the investigated cycles. Full article

(This article belongs to the Special Issue Phenomenological Thermodynamics of Irreversible Processes)

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13 pages, 279 KiB

Open AccessArticle

Entropic Constitutive Relation and Modeling for Fourier and Hyperbolic Heat Conductions

by Shu-Nan Li and Bing-Yang Cao

Entropy 2017, 19(12), 644; https://doi.org/10.3390/e19120644 - 1 Dec 2017

Cited by 4 | Viewed by 3625

Abstract

Most existing phenomenological heat conduction models are expressed by temperature and heat flux distributions, whose definitions might be debatable in heat conductions with strong non-equilibrium. The constitutive relations of Fourier and hyperbolic heat conductions are here rewritten by the entropy and entropy flux distributions in the frameworks of classical irreversible thermodynamics (CIT) and extended irreversible thermodynamics (EIT). The entropic constitutive relations are then generalized by Boltzmann–Gibbs–Shannon (BGS) statistical mechanics, which can avoid the debatable definitions of thermodynamic quantities relying on local equilibrium. It shows a possibility of modeling heat conduction through entropic constitutive relations. The applicability of the generalizations by BGS statistical mechanics is also discussed based on the relaxation time approximation, and it is found that the generalizations require a sufficiently small entropy production rate. Full article

(This article belongs to the Special Issue Phenomenological Thermodynamics of Irreversible Processes)

28 pages, 3373 KiB

Open AccessArticle

The Mean Field Theories of Magnetism and Turbulence

by Peter W. Egolf and Kolumban Hutter

Entropy 2017, 19(11), 589; https://doi.org/10.3390/e19110589 - 3 Nov 2017

Cited by 8 | Viewed by 5098

Abstract

In the last few decades a series of experiments have revealed that turbulence is a cooperative and critical phenomenon showing a continuous phase change with the critical Reynolds number at its onset. However, the applications of phase transition models, such as the Mean Field Theory (MFT), the Heisenberg model, the XY model, etc. to turbulence, have not been realized so far. Now, in this article, a successful analogy to magnetism is reported, and it is shown that a Mean Field Theory of Turbulence (MFTT) can be built that reveals new results. In analogy to compressibility in fluids and susceptibility in magnetic materials, the vorticibility (the authors of this article propose this new name in analogy to response functions, derived and given names in other fields) of a turbulent flowing fluid is revealed, which is identical to the relative turbulence intensity. By analogy to magnetism, in a natural manner, the Curie Law of Turbulence was discovered. It is clear that the MFTT is a theory describing equilibrium flow systems, whereas for a long time it is known that turbulence is a highly non-equilibrium phenomenon. Nonetheless, as a starting point for the development of thermodynamic models of turbulence, the presented MFTT is very useful to gain physical insight, just as Kraichnan’s turbulent energy spectra of 2-D and 3-D turbulence are, which were developed with equilibrium Boltzmann-Gibbs thermodynamics and only recently have been generalized and adapted to non-equilibrium and intermittent turbulent flow fields. Full article

(This article belongs to the Special Issue Phenomenological Thermodynamics of Irreversible Processes)

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21 pages, 1262 KiB

Open AccessArticle

Thermodynamic Modelling of Supersonic Gas Ejector with Droplets

by Sergio Croquer, Sébastien Poncet and Zine Aidoun

Entropy 2017, 19(11), 579; https://doi.org/10.3390/e19110579 - 30 Oct 2017

Cited by 19 | Viewed by 6036

Abstract

This study presents a thermodynamic model for determining the entrainment ratio and double choke limiting pressure of supersonic ejectors within the context of heat driven refrigeration cycles, with and without droplet injection, at the constant area section of the device. Input data include the inlet operating conditions and key geometry parameters (primary throat, mixing section and diffuser outlet diameter), whereas output information includes the ejector entrainment ratio, maximum double choke compression ratio, ejector efficiency, exergy efficiency and exergy destruction index. In single-phase operation, the ejector entrainment ratio and double choke limiting pressure are determined with a mean accuracy of

18 %

and

2.5 %

, respectively. In two-phase operation, the choked mass flow rate across convergent-divergent nozzles is estimated with a deviation of

10 %

. An analysis on the effect of droplet injection confirms the hypothesis that droplet injection reduces by

8 %

the pressure and Mach number jumps associated with shock waves occuring at the end of the constant area section. Nonetheless, other factors such as the mixing of the droplets with the main flow are introduced, resulting in an overall reduction by

11 %

of the ejector efficiency and by

15 %

of the exergy efficiency. Full article

(This article belongs to the Special Issue Phenomenological Thermodynamics of Irreversible Processes)

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12 pages, 246 KiB

Open AccessArticle

Generalized Maxwell Relations in Thermodynamics with Metric Derivatives

by José Weberszpil and Wen Chen

Entropy 2017, 19(8), 407; https://doi.org/10.3390/e19080407 - 7 Aug 2017

Cited by 23 | Viewed by 6043

Abstract

In this contribution, we develop the Maxwell generalized thermodynamical relations via the metric derivative model upon the mapping to a continuous fractal space. This study also introduces the total q-derivative expressions depending on two variables, to describe nonextensive statistical mechanics and also [...] Read more.

α

-total differentiation with conformable derivatives. Some results in the literature are re-obtained, such as the physical temperature defined by Sumiyoshi Abe. Full article

(This article belongs to the Special Issue Phenomenological Thermodynamics of Irreversible Processes)

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