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Journal Articles

Journal: Journal of Heat Transfer

Article Type: Research-Article

*. December 2017, 139(12): 122003.*

*J. Heat Transfer*Paper No: HT-17-1062

Published Online: June 27, 2017

Abstract

Conventional first-principle approaches for studying nonequilibrium processes depend on the mechanics of individual particles or quantum states and as a result require many details of the mechanical features of the system to arrive at a macroscopic property. In contrast, thermodynamics, which has been successful in the stable equilibrium realm, provides an approach for determining macroscopic properties without the mechanical details. Nonetheless, this phenomenological approach is not generally applicable to a nonequilibrium process except in the near-equilibrium realm and under the local equilibrium and continuum assumptions, both of which limit its ability to describe nonequilibrium phenomena. Furthermore, predicting the thermodynamic features of a nonequilibrium process (of entropy generation) across all scales is difficult. To address these drawbacks, steepest-entropy-ascent quantum thermodynamics (SEAQT) can be used. It provides a first-principle thermodynamic-ensemble based approach applicable to the entire nonequilibrium realm even that far-from-equilibrium and does so with a single kinematics and dynamics, which crosses all temporal and spatial scales. Based on prior developments by the authors, SEAQT is used here to study the heat and mass diffusion of indistinguishable particles. The study focuses on the thermodynamic features of far-from-equilibrium state evolution, which is separated from the specific mechanics of individual particle interactions. Results for nonequilibrium size (volume) and concentration effects on the evolutionary state trajectory are presented for the case of high temperature and low particle concentration, which, however, do not impact the generality of the theory and will in future studies be relaxed.

Proceedings Papers

*Proc. ASME*. IMECE2015, Volume 6B: Energy, V06BT07A015, November 13–19, 2015

Paper No: IMECE2015-53581

Abstract

Conventional first principle approaches for studying non-equilibrium or far-from-equilibrium processes all depend on the mechanics of individual particles or quantum states and as a result, require too many details of the mechanical features of the system to easily or even practically arrive at the value of a macroscopic property. In contrast, thermodynamics, which has been extremely successful in the stable equilibrium realm, provides an approach for determining a macroscopic property without going into the mechanical details. Nonetheless, such a phenomenological approach is not generally applicable to a non-equilibrium process except in the near-equilibrium realm and under the limiting local equilibrium and continuum assumptions, both of which prevent its application across all scales. To address these drawbacks, steepest-entropy-ascent quantum thermodynamics (SEAQT) can be used. It provides an ensemble-based, thermodynamics, first principles approach applicable to the entire non-equilibrium realm even that far-from-equilibrium and does so with a single kinematics and dynamics able to cross all temporal and spatial scales. Based on prior developments by the authors, this paper applies SEAQT to the study of mass and heat diffusion. Specifically, the study focuses on the thermodynamic features of far-from-equilibrium state evolution. Two kinds of size effects on the evolution trajectory, i.e., concentration and volume effects, are discussed.

Proceedings Papers

*Proc. ASME*. IMECE2015, Volume 6B: Energy, V06BT07A016, November 13–19, 2015

Paper No: IMECE2015-53726

Abstract

Oxygen reduction in a solid oxide fuel cell (SOFC) cathode involves a non-equilibrium process of coupled mass and heat diffusion and electrochemical and chemical reactions. These phenomena occur at multiple temporal and spatial scales, from the mesoscopic to the atomistic level, making the modeling, especially in the transient regime, very difficult. Nonetheless, multi-scale models are needed to improve an understanding of oxygen reduction and guide fuel cell cathode design. Existing methods are typically phenomenological or empirical in nature so their application is limited to the continuum realm and quantum effects are not captured. Steepest-entropy-ascent quantum thermodynamics (SEAQT) can be used to model non-equilibrium processes (even those far-from equilibrium) from the atomistic to the macroscopic level. The non-equilibrium relaxation is characterized by the entropy generation, and the study of coupled heat and mass diffusion as well as electrochemical and chemical activity are unified into a single framework. This framework is used here to study the transient and steady state behavior of oxygen reduction in an SOFC cathode system. The result reveals the effects on performance of the different timescales of the varied phenomena involved and their coupling. In addition, the influence of cathode microstructure changes on performance is captured.

Journal Articles

Article Type: Research-Article

*. July 2015, 137(4): 041601.*

*J. Energy Resour. Technol*Paper No: JERT-15-1104

Published Online: July 1, 2015

Abstract

This paper describes the upper level of a two-tiered sustainability assessment framework (SAF) for determining the optimal synthesis/design and operation of a power network and its associated energy production and storage technologies. The upper-level framework is described, and results for its application to a test bed scenario given by the Northwest European electricity power network presented. A brief description of the lower level of the SAF is given as well. In order to analyze the impact of microgrids (MGs) in the main network, two different scenarios are considered in the analysis, i.e., a network without MGs and a network with MGs. The optimization is carried out in a multi-objective, quasi-stationary manner with producer partial-load behavior taken into account via nonlinear functions for efficiency, cost, and emissions that depend on the electricity generated by each nonrenewable or renewable producer technology. Results indicate for the particular problem posed and for the optimal configurations found that including MGs improves the network relative to reductions in capital and operating costs and to increases in network resiliency. On the other hand, total daily SO2 emissions and network exergetic efficiency are not improved for the case when MGs are included.

Proceedings Papers

*Proc. ASME*. GT1993, Volume 3A: General, V03AT15A007, May 24–27, 1993

Paper No: 93-GT-156

Abstract

It has been shown in a number of studies that the Kalina cycle can have considerably higher efficiencies than the Rankine cycle. An especially advantageous application is as a bottoming cycle to a gas turbine. In this paper a gas turbine topping cycle has been assumed. Three different configurations of the Kalina bottoming cycle have been examined and compared. One is an original cycle (El-Sayed and Tribus, 1985) with a flash separator. In another configuration, a second feedwater heater is added and in a third a distillation column instead of a flash separator is used. The stages of the column are heated by exchanging heat with two different streams in the Kalina distillation condensation subsystem. For each configuration, the different compositions in the cycle have been varied. The First Law efficiency and the exergetic efficiency have been calculated as well as the rate of exergy loss in each unit. The results show that the cases with the best performance of each of the three configurations differ very little in efficiency. The original cycle has the highest efficiency for the conditions studied.

Proceedings Papers

*Proc. ASME*. IMECE2013, Volume 8B: Heat Transfer and Thermal Engineering, V08BT09A043, November 15–21, 2013

Paper No: IMECE2013-63596

Abstract

The equation of motion of steepest-entropy-ascent quantum thermodynamics (SEA-QT) was first postulated in the early 1980s with the intent of modeling the non-linear dynamic behavior encountered in nature, which the unitary (linear) dynamics of the Schrödinger-von Neumann equation cannot. The SEA-QT equation is used here to model the decoherence phenomenon between two distinguishable and indivisible elementary constituents of type spin–½ (e.g., quantum bits or qubits). The resulting set of non-linear, first-order differential equations is solved with a fourth-order-Runge-Kutta routine provided by Matlab ® . The time evolution of the state of the composite system as well as that of the reduced and locally-perceived states of the two constituents are traced from an initial non-equilibrium state of the composite along its relaxation towards stable equilibrium at constant system energy. An entangled and generally coherent, initial non-equilibrium state of the composite quantum system is prepared using a heuristic approach, which consists of randomly and homogeneously generating an initial point on the Bloch sphere for each of the constituents and then using a weighted average of their projections to arrive at an initial state for the composite. Results show how the initial entanglement and coherence between the two spin–½ constituents are reduced during relaxation towards a state of stable equilibrium. When the two particles are non-interacting, the initial coherence is lost once stable equilibrium is reached. When they are interacting, the coherence in the final stable equilibrium state is only that due to the interaction.

Proceedings Papers

Sergio Cano-Andrade, Michael R. von Spakovsky, Alejandro Fuentes, Chiara Lo Prete, Benjamin F. Hobbs, Lamine Mili

*Proc. ASME*. IMECE2012, Volume 6: Energy, Parts A and B, 1393-1408, November 9–15, 2012

Paper No: IMECE2012-87950

Abstract

In this paper, multiobjective optimization is proposed for evaluating the sustainable synthesis/design and operation of sets of small renewable and non-renewable energy production technologies coupled to power production/transmission/distribution networks via microgrids. The optimization is conducted over a quasi-stationary twenty four hour, winter period. Partial load behavior of the generators is included by introducing non-linear functions for efficiency, costs and emissions as a function of the electricity generated by each technology. A new index for resiliency is included in the multiobjective optimization model in order to account for the capacity of the power network system to self-recover to a new normal state after experiencing an unanticipated catastrophic event. Since sustainability/resiliency indices are typically not expressed in the same units, fuzzy logic and an explicit set of weighting factor methods are employed to calculate a composite sustainability-resiliency index. Results indicate for the particular problem posed that the inclusion of microgrids into the network leads to a better overall network efficiency, a reduction in life cycle costs, and an improved network resiliency. On the other hand, total life SO 2 emissions and network reliability are not improved for this particular case when microgrids are included.

Proceedings Papers

*Proc. ASME*. IMECE2011, Volume 4: Energy Systems Analysis, Thermodynamics and Sustainability; Combustion Science and Engineering; Nanoengineering for Energy, Parts A and B, 619-630, November 11–17, 2011

Paper No: IMECE2011-64444

Abstract

Experimental evidence is presented and compared with theoretical predictions from Quantum Thermodynamics, (QT) to examine whether or not the claims of QT are consistent with the existence and generation of entropy at atomistic scales. QT makes the assertion that entropy is an intrinsic property of matter in the same way that inertial mass, energy, and momentum are and must, thus, exist even for single particles. Entropy as defined by QT is a measure of the distribution of a system’s internal energy at any given instant of time amongst the available internal degrees of freedom, i.e., the energy eigenlevels of the system. In this paper, it is shown that QT predicts the internal relaxation of a 5-level rubidium system that is consistent with the experimental data and not explained by current theory, i.e. by Quantum Mechanics. In addition, it is demonstrated that the decay of so-called “cat states” for single ions that are contained in Paul traps and that interact with a heat reservoir is also consistent with the idea of the existence of entropy and entropy generation at atomistic scales. This is accomplished by comparing experimental data with the predictions made using an extension of the equation of motion of QT that allows for heat interactions.

Proceedings Papers

*Proc. ASME*. IMECE2008, Volume 8: Energy Systems: Analysis, Thermodynamics and Sustainability; Sustainable Products and Processes, 667-678, October 31–November 6, 2008

Paper No: IMECE2008-68065

Abstract

A stochastic modeling and uncertainty analysis methodology for energy system synthesis/design is proposed in this paper and applied to the development of the fuel processing subsystem (FPS) of a proton exchange membrane fuel cell (PEMFC) system. The FPS consists of a steam methane reformer, both high and low temperature water-gas shift reactors, a CO preferential oxidation reactor, a steam generator, a combustor, and several heat exchangers. For each component of the system, detailed thermodynamic, geometric, chemical kinetic, and cost models are developed and integrated into an overall model for the subsystem. Conventionally, in energy system synthesis/design, such models are treated deterministically, using a specific set of non-probabilistic input variable values that produce a specific set of non-probabilistic output variable values. Even though these input values, which include the specific load profile (i.e. electrical, thermal, and/or aerodynamic) for which the system or subsystem is synthesized/designed, can have significant uncertainties that inevitably propagate through the system to the outputs, such deterministic approaches are unable to quantify these uncertainties and their effect on the final synthesis/design and operation/control. This deficiency can, of course, be overcome by treating the inputs and outputs probabilistically. The difficulty with doing this, particularly when large-scale dynamic optimization with a large number of degrees of freedom is being used to determine the optimal synthesis/design and operation/control of the system, is that the traditional probabilistic approaches (e.g., Monte Carlo Method) are so computationally intensive that combined with large-scale optimization it renders the problem computationally intractable. This difficulty can be overcome by the use of approximate approaches such as the response sensitivity analysis (RSA) method based on Taylor series expansion. In this study, RSA is employed and developed by the authors for use with dynamic energy system optimization. Load profile and cost models are treated as probabilistic input values and uncertainties in output results investigated. The results for the uncertainty analysis applied to the optimization of the FPS synthesis/design and operation/control are compared with those found using a Monte Carlo approach with good results. In this paper, the FPS synthesis/design and operation optimization is treated as a multi-objective optimization problem to minimize the capital cost and operating cost simultaneously, and uncertainty effects on the optimization are assessed by taking uncertainties into account in the objectives and constraints. Optimization results show that there is little effect on the objective (the operating cost and capital cost), while the constraints (e.g., that on the CO concentration) can be significantly affected during the synthesis/design and operation/control optimization.

Proceedings Papers

*Proc. ASME*. IMECE2008, Volume 8: Energy Systems: Analysis, Thermodynamics and Sustainability; Sustainable Products and Processes, 679-689, October 31–November 6, 2008

Paper No: IMECE2008-68070

Abstract

Proton exchange membrane fuel cells (PEMFCs) are one of the leading candidates in alternative energy conversion devices for transportation, stationary, and portable power generation applications. Such systems with their own fuel conversion unit typically consist of several subsystems: a fuel processing subsystem, a fuel cell stack subsystem, a work recovery-air supply subsystem, and a power electronics subsystem. Since these subsystems have different physical characteristics, their integration into a single system/subsystem level unit make the problems of optimal dynamic system synthesis/design and operation/control highly complex. Thus, dynamic system/subsystem/component modeling and highly effective optimization strategies are required. Furthermore, uncertainties in the results of system synthesis/design and operation/control optimization can be affected by any number of sources of uncertainty such as the load profiles and cost models. These uncertainties can be taken into account by treating the problem probabilistically. The difficulty with doing this, particularly when large-scale dynamic optimization with a large number of degrees of freedom is being used to determine the optimal synthesis/design and operation/control of the system, is that the traditional probabilistic approaches (e.g., Monte Carlo Method) are so computationally intensive that combined with large-scale optimization it renders the problem computationally intractable. This difficulty can be overcome by the use of approximate approaches such as the response sensitivity analysis (RSA) method based on Taylor series expansion. Thus, in this paper, a stochastic modeling and uncertainty analysis methodology for energy system synthesis/design and operation/control which uses the RSA method is proposed and employed for calculating the uncertainties on the system outputs. Their effects on the synthesis/design and operation/control optimization of a 5kWe PEMFC system are assessed by taking the uncertainties into account in the objectives and constraints. It is shown that these uncertainties significantly affect the reliability of being able to meet certain constraints (e.g., that on the CO concentration) during the synthesis/design and operation/control optimization process. These and other results are presented.

Proceedings Papers

*Proc. ASME*. IMECE2008, Volume 8: Energy Systems: Analysis, Thermodynamics and Sustainability; Sustainable Products and Processes, 691-700, October 31–November 6, 2008

Paper No: IMECE2008-68073

Abstract

As primary tools for the development of energy systems, optimization techniques have been studied for decades. However, for large-scale synthesis/design and operation/control optimization problems, it may turn out that it is impractical to solve the entire problem as a single optimization problem. In this paper, a multi-level optimization strategy, dynamic iterative local-global optimization (DILGO), is utilized for the synthesis/design and operation/control optimization of a 5 kWe PEMFC (Proton Exchange Membrane Fuel Cell) system. The strategy decomposes the system into three subsystems: a stack subsystem (SS), a fuel processing subsystem (FPS), and a work and air recovery subsystem (WRAS) and, thus, into three optimization sub-problems. To validate the decomposition strategy, the results are compared with a single-level dynamic optimization, in which the whole system is optimized together. In addition, for the purpose of comparison between different optimization algorithms, gradient-based optimization results are compared with those for a hybrid heuristic/gradient-based optimization algorithm.

Proceedings Papers

*Proc. ASME*. IMECE2008, Volume 8: Energy Systems: Analysis, Thermodynamics and Sustainability; Sustainable Products and Processes, 471-480, October 31–November 6, 2008

Paper No: IMECE2008-67424

Abstract

A typical approach for modeling systems at a nanoscale in states of non-equilibrium undergoing an irreversible process is to use an ad hoc mixture of molecular dynamics (linear and nonlinear), i.e. classical mechanics, coupled to assumptions of stable equilibrium which allow one via analogy to incorporate equilibrium thermodynamic state information such as temperature and pressure into the modeling process. However, such an approach cannot describe the actual thermodynamic evolution in state which occurs in these systems since the equation of motion used (Newton’s second law) can only describe the evolution in state from one mechanical state to another. To capture the actual thermodynamic evolution, a more general equation of motion is needed. Such an equation has been proposed, i.e. the Beretta equation of motion, as part of a general theory, which unifies (not simply bridges as is the case in statistical thermodynamics) quantum mechanics and thermodynamics. It is called the unified quantum theory of mechanics and thermodynamics or quantum thermodynamics. This equation, which strictly satisfies all of the implications of the laws of thermodynamics, including the second law, as well as of quantum mechanics, describes the thermodynamic evolution in state of a system in non-equilibrium regardless of whether or not the system is in a state far from or close to stable equilibrium. This theory and its dynamical postulate are used here to model the storage of hydrogen in an isolated box modeled in 1D and 2D with a carbon atom at one end of the box in 1D and a carbon nanotube in the middle of the box in 2D. The system is prepared in a state with the hydrogen molecules initially far from stable equilibrium, after which the system is allowed to relax (evolve) to a state of stable equilibrium. The so-called energy eigenvalue problem is used to determine the energy eigenlevels and eigenstates of the system, while the nonlinear Beretta equation of motion is used to determine the evolution of the thermodynamic state of the system as well as the spatial distributions of the hydrogen molecules in time. The results of our initial simulations show in detail the trajectory of the state of the system as the hydrogen molecules, which are initially arranged to be far from the carbon atom or the carbon nanotube, are seen to spread out in the container and eventually become more concentrated near the carbon atom or atoms.

Proceedings Papers

*Proc. ASME*. IMECE2008, Volume 8: Energy Systems: Analysis, Thermodynamics and Sustainability; Sustainable Products and Processes, 701-710, October 31–November 6, 2008

Paper No: IMECE2008-68076

Abstract

An often used approach to the synthesis/design optimization of energy systems is to only use steady state operation and high efficiency (or low total life cycle cost) at full load as the basis for the synthesis/design. Transient and partial load operations are considered secondarily by system and control engineers once the synthesis/design is fixed (i.e. system testing with standard load profiles). This paper considers the system dynamics from the very beginning of the synthesis/design process by developing the system using a set of transient thermodynamic, kinetic, geometric as well as cost models developed and implemented for the components of a 5 kW PEMFC (Proton Exchange Membrane Fuel Cell) system. The system is composed of three subsystems: a stack subsystem (SS), a fuel processing subsystem (FPS), and a work and air recovery subsystem (WRAS). In addition, state space is used in a looped set of optimizations to illustrate the effect of the control system on the synthesis/design optimization and to develop a set of optimal multi-input, multi-output (MIMO) controllers consistent with the optimal synthesis/design of the PEMFC system. It is shown that these MIMO controllers correspond to the ones found in a non-looped optimization in which the gains for the controllers are part of the decision variable set for the overall synthesis/design and operation/control optimization. These last set of results are then compared with the optimizations results found with the traditional approach of using a single load point in order to show the advantage of the dynamic optimization.

Proceedings Papers

*Proc. ASME*. IMECE2007, Volume 6: Energy Systems: Analysis, Thermodynamics and Sustainability, 485-492, November 11–15, 2007

Paper No: IMECE2007-42932

Abstract

In 1976 and then again in 1984, a series of six groundbreaking papers were published (Hatsopoulos and Gyftopoulos, 1976; Beretta et al. 1984; Beretta, Gyftopoulos, and Park, 1985), presenting a new formulation of thermodynamics, which simply and elegantly extends in a unified fashion the concepts of thermodynamics to quantum mechanics and the concepts of quantum mechanics to thermodynamics. It does so without the bridge traditionally used, i.e. statistical mechanics, eliminating a number of the ambiguities, tautologies, and inconsistencies (including a built-in violation of the 2 nd Law) inherent in the presentations of both classical and statistical thermodynamics. This new formulation, called the Unified Quantum Theory of Mechanics and Thermodynamics , generalizes thermodynamics so that it applies to all systems large or small (including one particle systems) either in a state of thermodynamic (i.e. stable) equilibrium or not in a state of thermodynamic equilibrium. Intrigued by both the scientific and pedagogical possibilities of this new theory, the author began his own study and application of this new formulation in 1998. The present paper focuses on the foundational and pedagogical aspects of this new non-statistically based paradigm of physics and thermodynamics, which uses as its primitives inertial mass, force, and time and introduces the laws of thermodynamics in the most unambiguous and general formulations found in the literature. Not only does this new formulation or paradigm provide a clearer understanding of thermodynamics to the student and the practitioner, but it has the potential for revolutionizing how we understand and synthesize/design systems at a microscopic level since this paradigm, unlike the predominant statistically based paradigm of the last century and a half, allows one to extend down to the microscopic such concepts as generalized available energy (i.e. a special case of this property is the exergy) and entropy, properties which are already effectively applied to systems at the macroscopic level.

Proceedings Papers

*Proc. ASME*. IMECE2007, Volume 6: Energy Systems: Analysis, Thermodynamics and Sustainability, 643-654, November 11–15, 2007

Paper No: IMECE2007-42937

Abstract

Computational modeling of fuel cell electrode-catalyst layers is an important tool in understanding the different electrochemical reactions and transport phenomena occurring within fuel cell electrodes. Proper modeling of this layer is required for an accurate prediction of cell behavior which in turn can be used for the development of more efficient fuel cells. In macroscopic CFD approaches such layers are typically modeled as infinitely thin interfaces populated by sources and sinks or as very thin homogeneous porous layers. However, these layers are neither infinitely thin nor homogeneous and, thus, modeling in this fashion leads to a loss of information about the microstructure and its varying effects on the reacting mixture flows which pass through and into the structure. Thus, the utility of relying only on such macroscopic representations limits the general applicability of these macroscopic models as tools for design and for predicting fuel cell performance over a wide range of conditions. Furthermore, such macroscopic models cannot aid in the design of the electrode-catalyst layer itself. In order to address this latter point, a microscopic/mesoscopic modeling approach can be used, e.g., the Lattice Boltzmann Method (LBM), which models the reacting mixture flow through the porous microstructure of the electrode-catalyst layer. However, to do so requires reconstructing the porous geometry of this layer which can be done by using 2D microscopic images of cross-sections of the layer to generate 3D geometries from, for example, stochastic models which are relatively cost efficient and lead to similar structures with approximately the same characteristics of porosity, catalyst loading, three-phase boundaries, etc. as the original structure. Two such 3D reconstruction methods, i.e. one based on the granulometry law (one-point statistics) and the other on two-point statistics, are applied to a 2D SEM (scanning electron microscope) image of an SOFC electrode-catalyst layer and to the 2D SEM and TEM (transmission electron microscope) images for such a layer in a PEMFC. Results for these reconstructions are presented as are results for reacting mixture flow simulations through the two different reconstructed 3D SOFC structures using a 3D LBM approach. The development and application of a 3D LBM model for two-phase reacting mixture flows in PEMFC electrode-catalyst layer structures is in progress and will be reported in a future paper.

Proceedings Papers

*Proc. ASME*. IMECE2007, Volume 6: Energy Systems: Analysis, Thermodynamics and Sustainability, 265-277, November 11–15, 2007

Paper No: IMECE2007-42938

Abstract

The results of the application of an exergy-based method to highly dynamic, integrated hypersonic vehicle concepts are presented. Conventional aircraft systems and sub-systems traditionally are designed relying heavily on rules of thumb, individual experience, and rather simple, non-integrated tradeoff analyses, which are highly dependent on the evolutionary nature of vehicle development. In contrast, hypersonic vehicles may contain new sub-systems and revolutionary concepts for which there is no existing database to support an evolutionary synthesis/design approach. Thus, a simple tradeoff analysis becomes virtually impossible, particularly in light of the highly integrated, non-linear relationship between hypersonic vehicle sub-systems and the complexity of the missions involved. Therefore, the departure from existing databases and experience levels requires an integrated approach and a common metric for the synthesis/design of hypersonic vehicles to achieve an optimal synthesis/design. To that end, an exergy-based mission integrated methodology is introduced and compared to traditional measures (including a non-integrated approach) by applying these to the synthesis/design and operational optimization of a hypersonic vehicle configuration comprised of an airframe and a propulsion sub-system (consisting of inlet, combustor, and nozzle components). Results of these optimizations are presented and include a quantification of all vehicle losses in terms of exergy lost or destroyed, providing a common metric for the vehicle designer to identify where the largest improvements in vehicle performance can be made. Furthermore, via a number of parametric studies, the impacts of the design and operational decision variables on exergy destruction are discussed.

Proceedings Papers

*Proc. ASME*. IMECE2007, Volume 6: Energy Systems: Analysis, Thermodynamics and Sustainability, 493-502, November 11–15, 2007

Paper No: IMECE2007-42933

Abstract

Basing his work on a new formulation of thermodynamics called the Unified Quantum Theory of Mechanics and Thermodynamics first published in a series of four ground breaking papers in 1976 (Hatsopoulos and Gyftopoulos, 1976a, b, c, d), Beretta develops a dynamical postulate (Beretta et al. 1984; Beretta, Gyftopoulos, and Park, 1985) consistent both with the non-dynamical quantum mechanical postulates of the Unified Theory as well as with its thermodynamic ones (the 2 nd Law in particular). The theory itself simply and elegantly extends in a unified fashion the concepts of thermodynamics to quantum mechanics and the concepts of quantum mechanics to thermodynamics. It does so without the bridge traditionally used, i.e. statistical mechanics, eliminating a number of the ambiguities, tautologies, and inconsistencies (including a built-in violation of the 2 nd Law) inherent in the presentations of both Classical and Statistical Thermodynamics. This new formulation generalizes thermodynamics so that it applies to all systems large or small (including one particle systems) either in a state of thermodynamic (i.e. stable) equilibrium or not in a state of thermodynamic equilibrium. The Beretta equation of motion describes the time evolution of the state of a system via a density operator which is uniquely based on an unambiguous preparation of an ensemble of identical systems, i.e. the so-called homogenous or irreducible ensemble, and does so both for unitary and non-unitary reversible as well as irreversible processes. In this paper, we present a simple application of this general equation of motion to the time evolution of the entropy of a closed system comprised of a Boltzmann type gas consisting of one or of many particles undergoing an irreversible process. A number of different energy eigenlevels and initial states and their effects on entropy generation and the final state of maximum entropy, i.e. stable equilibrium, are examined. A simple time-dependent work interaction is introduced into the formulation to show how this in turn affects the evolution of the state of the system.

Journal Articles

Article Type: Research Papers

*. February 2009, 6(1): 011015.*

*J. Electrochem. En. Conv. Stor*Published Online: November 10, 2008

Abstract

Detailed thermodynamic, kinetic, geometric, and cost models are developed, implemented, and validated for the synthesis/design and operational analysis of hybrid solid oxide fuel cell (SOFC)-gas turbine-steam turbine systems ranging in size from 1.5 MWe to 10 MWe . The fuel cell model used in this research work is based on a tubular Siemens-Westinghouse-type SOFC, which is integrated with a gas turbine and a heat recovery steam generator (HRSG) integrated in turn with a steam turbine cycle. The current work considers the possible benefits of using the exhaust gases in a HRSG in order to produce steam, which drives a steam turbine for additional power output. Four different steam turbine cycles are considered in this research work: a single-pressure, a dual-pressure, a triple-pressure, and a triple-pressure with reheat. The models have been developed to function both at design (full load) and off-design (partial load) conditions. In addition, different solid oxide fuel cell sizes are examined to assure a proper selection of SOFC size based on efficiency or cost. The thermoeconomic analysis includes cost functions developed specifically for the different system and component sizes (capacities) analyzed. A parametric study is used to determine the most viable system/component syntheses/designs based on maximizing the total system efficiency or minimizing the total system life cycle cost.

Journal Articles

Article Type: Research Papers

*. February 2009, 6(1): 011005.*

*J. Electrochem. En. Conv. Stor*Published Online: November 4, 2008

Abstract

Solid oxide fuel cells (SOFC) are a promising technology for distributed electricity generation and cogeneration. Numerous papers have been published in the past several years proposing mathematical/computational fluid dynamics (CFD) models for predicting the transient and steady-state performance of such cells. In this paper, a detailed steady-state CFD model of a planar anode supported SOFC is proposed, which accounts for mass, thermal, and charge transport as well as electrochemistry and the chemistry of internal fuel reforming. Its main characteristics include the use of a continuous model for the electrochemistry, allowing one to examine different three-phase boundary geometries. This is an improvement over the typical model reported in literature, which utilizes an equivalent resistive circuit approach or a homogeneous distribution of three-phase boundaries. The model proposed here is used to simulate the degradation of anode, cathode, and electrolyte due to instabilities (e.g., anode oxidation due to fuel depletion) or to the delamination of the electrodes from the electrolyte. Such degradations result in a drop in cell performance but are difficult to predict without the use of models that can be helpful for diagnosis. The model is applied to experimental data available in literature both for the nondegraded and degraded cases.

Proceedings Papers

*Proc. ASME*. FUELCELL2005, 3rd International Conference on Fuel Cell Science, Engineering and Technology, 93-102, May 23–25, 2005

Paper No: FUELCELL2005-74046

Abstract

Throughout the last decade, a considerable amount of work has been carried out in order to obtain ever more refined models of proton exchange membrane (PEM) fuel cells. While many of the phenomena occurring in a fuel cell have been described with ever more complex models, the flow of gaseous mixtures in the porous electrodes has continued to be modeled with Darcy’s law in order to take into account interactions with the solid structure and with Fick’s law in order to take into account interactions among species. Both of these laws derive from the macroscopic continuum approach, which essentially consists of applying some sort of homogenization technique which properly averages the underlying microscopic phenomena for producing measurable quantities. Unfortunately, these quantities in the porous electrodes of fuel cells are sometimes measurable only in principle. For this reason, this type of approach introduces uncertain macroscopic parameters which can significantly affect the numerical results. This paper is part of an ongoing effort to address the problem following an alternative approach. The key idea is to numerically simulate the underlying microscopic phenomena in an effort to bring the mathematical description nearer to actual reality. In order to reach this goal, some recently developed mesoscopic tools appear to be very promising since the microscopic approach is in this particularly case partially included in the numerical method itself. In particular, the lattice Boltzmann models treat the problem by reproducing the collisions among particles of the same type, among particles belonging to different species, and finally among the species and the solid obstructions. Recently, a procedure based on a lattice Boltzmann model for calculating the hydraulic constant as a function of material structure and applied pressure gradient was defined and applied. This model has since been extended in order to include gaseous mixtures with different methods being considered in order to simulate the coupling strength among the species. The present paper reports the results of this extended model for PEM fuel cell applications and in particular for the analysis of the fluid flow of gaseous mixtures through porous electrodes. Because of the increasing computational needs due to both three–dimensional descriptions and multi-physics models, the need for large parallel computing is indicated and some features of this improvement are reported.