Entropy generation analysis as a design tool—A review

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Abstract

There is an acknowledged growing need for efficient and sustainable systems that use available energy resources in an “optimal” (including constraints) way. Such a goal cannot be effectively achieved without taking into account the limits posed by the second law of thermodynamics. A possible approach consists in the so-called entropy generation analysis, which possesses key features making it more attractive than traditional energy balance approaches. In fact, entropy generation analysis allows for a direct identification of the causes of inefficiency and opens up the possibility for designers to conceive globally more effective systems. Furthermore, thanks to its direct derivation from basic thermodynamic principles, entropy generation analysis can be in principle used for any type of energy conversion system. These attractive features have made entropy generation analysis a popular thermodynamic method for the design and the optimization of less unsustainable systems.

This paper presents a critical review of contributions to the theory and application of entropy generation analysis to different types of engineering systems. The focus of the work is only on contributions oriented toward the use of entropy generation analysis as a tool for the design and optimization of engineering systems. A detailed derivation of the existing entropy generation formulations is first presented, and the two more popular approaches are discussed: the entropy generation minimization (EGM) and the entropy generation analysis (EGA). The relevant literature is further classified in two categories, depending on whether the level of the analysis is global or local. This review will further clarify the use of entropy generation-based design methods, indicate the areas for future work, and provide the necessary information for further research in the development of efficient engineering systems.

Introduction

Since the very dawn of the human species, the need of constructing and operating efficient systems has proven to be a very powerful driver for technological development. This necessity was amplified by the introduction of energy conversion machines during the industrial revolution, leading engineers to study the best use of available energy resources and to the early development of thermodynamics [1]. More recently, the emphasis on efficiency and resources conservation has become crucial because of the currently perceived resource scarcity. As a consequence, second-law based methods that lead to guidelines for the analysis and improvement of engineering systems have become very attractive.The second law of thermodynamics asserts that the operation of real systems is unavoidably characterized by a loss of available work [2], [3]. This causes a decrease of the thermodynamic efficiency of a system with respect to an equivalent ideal (loss-free) process. Historically, the intuitive idea of loss of available work was first pointed out by Carnot. In his treatise [4], [5], he postulated that any machine with moving parts is characterized by a “loss of moment activity” due to friction and “violent effects” (which in modern terms would include both a mechanical cause of inefficiency, namely the effects of vibrations, and a thermodynamic cause, due to extreme non-equilibrium phenomena). The essence of the second law was discovered – albeit with some internal inconsistency – in 1824 by Lazare’s son, Carnot. Carnot [6] illustrated the concept of an ideal cycle that operates through a succession of reversible transformations (defined as a succession of equilibrium states). He argued that the efficiency of this cycle is – ceteris paribus – a function of the temperature of the heat reservoirs. Furthermore, Carnot correctly postulated that his ideal cycle represents a “limiting” cycle, in the sense that any real machine would achieve an efficiency lower than that of the ideal cycle. His ground-breaking work set the foundation for the concepts of thermodynamic reversibility and available work loss. Later, Clausius, Gibbs and Boltzmann [7], [8], [9], [10] gave a proper formulation of entropy and provided a mathematical foundation to the work of Carnot.It took over a century for the development of the modern concept of entropy to be completed, and here we shall dispense with the citation of the numerous and fruitful disputes among scientists, for which we direct interested readers to [11], and limit our task to briefly recall some of the currently accepted definitions. For a generic system the second law of thermodynamics states that the total entropy generation rate

is always non-negative, i.e.where S is the entropy of the system, Φi is the heat transfer rate that the system exchanges with the heat reservoir at temperature Ti and is a mass flow rate exiting (+) or entering (−) the system. According to the second law, the equality sign, i.e.

, holds only in the limit of reversible processes, while the inequality applies also to non-equilibrium processes.

The net work transfer rate

experienced by the system can be reformulated by combining Eq. (1) with the first law of thermodynamics [2]:

The thermodynamic limit of net work transfer rate occurs when a system operates reversibly, i.e.

:

Therefore, the destruction of available work is proportional to the entropy generation rate:

Which is the Gouy–Stodola theorem [12], [13]. Neither the work transfer nor the entropy generation rate are thermodynamic properties of the system: they depend on the operating conditions and especially from the boundary interactions. From Eq. (4) it follows that among all conversion systems characterized by the same upper limit

, the most efficient is the one that attains the minimum entropy generation rate.

The Gouy–Stodola theorem clearly indicates that an analyst can improve the performance of an existing system by conceiving a new design which is characterized by a lower entropy generation. In engineering, the method of identification and reduction of thermodynamic irreversibilities is commonly called entropy generation analysis (EGA). Its optimization counterpart, i.e. entropy generation minimization (EGM), aims at minimizing the losses of a system subject to a specified set of constraints.

Although the proportionality between entropy generation and destroyed useful work had been already emphasized by Gouy and Stodola [12], [13] and then used by others [14], [15], [16], [2], the interest in EGA and EGM was revived by the important contributions of Bejan [17], [18], [19], [20]. In his work, Bejan set the framework for EGA and EGM as a multidisciplinary discipline at the interface of several different fields (Fig. 1). The method is based on the application of principles of heat and mass transfer, thermodynamics and fluid dynamics for the construction of a realistic model of the system that is analysed. The model establishes a strong and explicit link between

, the topology and the physical features of the system: shapes, dimensions, operating conditions etc. This means that the model should be sufficiently detailed to capture both the phenomena that occur in the system and the effects of possible changes in the free variables that are considered, e.g. the operating conditions and/or the system geometry. The analyst exploits this link (that may be expressed by a correlation or a formula, or simply by the empirically acquired knowledge of a “trend”) in order to identify optimization opportunities, i.e. improved designs of the system, that allow a reduction (EGA) or the minimization (EGM) of . The distinct features of EGA and EGM are schematically represented in Fig. 2, Fig. 3. Entropy Generation Analysis is based on a heuristic approach [21]: the initial configuration of the system is subsequently improved by introducing possible design modifications. These changes are proposed by the analyst on the basis of critical examination of the results concerning obtained through the model of the system. Entropy generation minimization is a deterministic approach [21]: the main point is the definition of the entropy generation rate

as the objective function to be minimized, while critical parameters, such as dimensions or operating conditions are chosen as the design variables. Thus, an EGM analysis consists in the search of optimal design variables which minimize the entropy generation rate (Fig. 3).This paper reviews EGA and EGM as design tools in engineering, with particular emphasis on the improvement of thermodynamic performance of engineering systems. In the first part, studies based on black box modelling approach are reviewed. In the second part, the paper reviews the more recent approach to EGA and EGM in the framework of non-equilibrium thermodynamics. Furthermore, we point out possible misleading uses and pitfalls of entropy generation analysis.

Section snippets

Applications to systems involving heat transfer and fluid flow Earlier entropy generation studies were based on the use of black box models (sometimes referred to as “Control Volume Method” or “Lumped Parameters Method”), that imply the assumption of homogeneity inside of the control volume and makes it impossible to capture internal distributions of temperature, pressure, density, etc. Black box modelling typically involves the use of correlations for quantities such as average heat transfer rates and fluid friction, which are instead phenomenologically

Entropy generation formulation The entropy balance equation for an open system (Eq. (1)) provides a formulation for total entropy generation rate

that occurs within a generic system. Such a formulation is derived according to the postulate of equilibrium thermodynamics (ET) [49], [85]. In this framework, state variables are taken as independent of space coordinates: the system is assumed to be homogeneous, in the sense that physical quantities like density, temperature, pressure etc. are not allowed to change from

Conclusions and future work Entropy generation analysis and minimization constitute effective approaches for the improvement or optimization of the thermodynamic performance of engineering systems. The history of these approaches spans several decades and has led to the development of design methods, whose evolution was mainly driven by help of computational resources. While a very large number of publications is devoted to the analysis of entropy generation, this review is limited to the contributions that focus on the

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The concept you've described involves a black body with small holes containing different gases separated by glass, and the simulation indicates a temperature difference based on radiation characteristics. However, it's important to note that the second law of thermodynamics states that heat will flow from hotter to colder objects.

To address this apparent contradiction, it would be crucial to consider the overall energy balance, heat transfer mechanisms, and the specific conditions of the system. Conducting experiments to verify the simulation is a commendable approach, but the design and control of these experiments would need to be carefully thought out to isolate and understand the factors at play.

Additionally, consulting experts in thermodynamics and radiative heat transfer could provide valuable insights and help ensure the experimental setup is rigorous and accurately interprets the simulation results. Remember, simulations are models that may simplify real-world complexities, and careful experimentation is key to validating or refining these models.

I am not a COMSOL user, but it seems to me that radiation emissivity and absorption should not be assigned independent values at will, but must be interrelated through Einstein coefficients. Otherwise there will be no detailed equilibrium and equality of the temperatures.

This is a good suggestion, welcome to participate. But you have to start with the general principles of physics.