Analysis of entropy generation in a hydrogen-enriched turbulent non-premixed flame

The analysis of local entropy generation and exergy loss was performed in a turbulent non-premixed H₂-enriched CH₄–air bluff-body flame. Detailed chemical kinetic, transport properties, and turbulence-chemistry interaction were taken into account in using laminar flamelet model for the simulation of combustion process via an in-house, finite volume code. The analysis was based on local entropy generation calculation. Results showed that thermal conduction made the most contribution to entropy generation followed by chemical reaction and mass diffusion, while the contribution of viscous dissipation was negligible. Entropy generation resulting from thermal conduction occurs in a large volume of the domain, while entropy generation resulting from chemical reaction and mass diffusion occurs only near the bluff surface. The effect of H₂ addition to fuel and air preheating on the entropy generation rate was investigated. It was observed that entropy generation and exergy loss were decreased by H₂ addition, mainly due to a decrease in the chemical reaction component of entropy generation, while entropy generation resulting from thermal conduction slightly increased and entropy generation resulting from mass diffusion remained almost constant. Entropy generation resulting from heat conduction by preheating combustion air decreased, while entropy generation resulting from chemical reaction and mass diffusion remained almost constant. The decrease of thermal conduction contribution in entropy generation is so significant that, by preheating air up to 750 K in the case of pure CH₄, chemical reaction becomes the main source of irreversibility. These investigations show that H₂ addition and preheating the combustion air both lead to the improvement of the second law efficiency, although the second law efficiency is more sensitive to flame structure and air temperature.     

Optimum wall thickness ratio based on the minimization of entropy generation in a viscous flow between parallel plates

The influence of the geometrical and physical parameters on entropy generation for a viscous flow between infinite parallel walls of finite thickness is studied by solving the momentum and energy conservation equations. The conjugate heat transfer problem in the fluid and solid walls is solved analytically using thermal boundary conditions of the third kind at the outer surfaces of the walls and continuity of temperature and heat flux across the fluid–wall interfaces. Analytic solutions for the velocity and temperature fields in the fluid and walls are used to calculate the local and global entropy generation rate. Conditions under which this quantity is minimized are determined for certain suitable combination of geometrical and physical parameters of the system. Special attention has been given to the effect of the wall thickness on the entropy generation rate. It is found that the global entropy generation reaches a minimum for specific values of the wall thickness ratio, when the other parameters are fixed.     

Analysis of entropy generation distribution in micro-combustors with baffles

This study presents the analysis of entropy generation distribution in H₂/air premixed flame in micro-combustors with baffles. The numerical simulation of combustion is performed with the help of Ansys Fluent code. The entropy generation rates are derived from entropy transport equation and calculated based on the numerical results. The entropy generation caused by various irreversible processes such as chemical reaction, thermal conduction and mass diffusion are studied in micro-combustors with baffles. The effects of the height of the baffles, H₂/air mass flow rate and equivalence ratio are investigated. It is found that a higher baffle will lead to more entropy generation and relatively larger destruction of available energy. The exergy efficiency decreases significantly when the H₂/air mass flow rate is increased. The lean and rich H₂/air mixture shows an obvious lower entropy generation rate and higher exergy efficiency than the stoichiometric mixture.     

Effects of hydrogen addition on entropy generation in ultra-lean counter-flow methane-air premixed combustion

In this paper, entropy generation in hydrogen enriched ultra-lean counter-flow methane–air premixed combustion confined by planar opposing jets is investigated for the first time. The effects of the effective equivalence ratio and volume percentage of hydrogen in fuel blends on entropy generation are studied by numerical evaluating the entropy generation equation. The lattice Boltzmann model proposed in our previous work, instead of traditional numerical methods, is used to solve the governing equations for combustion process. Through the present study, four interesting features of this kind of combustion, which are quite different from that reported in previous literature on entropy generation analysis for hydrogen enriched methane–air combustion, are revealed. For a given effective equivalence ratio, the total entropy generation number can be approximated as a linear increasing function of the volume percentage of hydrogen in fuel blends for all cases investigated in the present study.     

Local entropy generation for saturated two-phase flow

This paper addresses the estimation of local entropy generation rate for diabatic saturated two-phase flow of a pure fluid. Two different approaches have been adopted for this thermodynamic characterization: the separated flow model using the classical vapor flow quality, and the mixture model, using the thermodynamic vapor quality. Based on these two models, two distinct expressions for the local entropy generation have been proposed. The analysis explicitly shows the contribution of heat transfer and pressure drop respectively to the local entropy generation. The contribution due to phase-change process is also determined using the mixture model. The developed formulation is applied to analyze the thermodynamic performance of enhanced heat transfer tubes under different conditions. It is shown that enhanced tubes may be a relevant solution for reducing entropy generation at low mass velocities whereas smooth tubes remain the best solution at higher ones.     

Analysis of entropy generation in non-premixed hydrogen versus heated air counter-flow combustion

In this paper, entropy generation in non-premixed hydrogen versus heated air counter-flow combustion confined by planar opposing jets is investigated for the first time. The effects of the volume percentage of hydrogen in fuel mixture and the inlet Reynolds number (corresponding to the global stretch rate) on entropy generation are studied by numerical evaluating the entropy generation equation. The lattice Boltzmann model proposed in our previous work, instead of traditional numerical methods, is used to solve the governing equations for combustion process. Through the present study, three interesting features of this kind of combustion, which are quite different from that reported in previous literature on entropy generation analysis for diffusion hydrogen-air flames, are revealed. Moreover, it is observed that the whole investigated domain can be divided into two parts according to the predominant irreversibilities. The total entropy generation number can be approximated as a linear increasing function of the volume percentage of hydrogen in fuel mixture and the inlet Reynolds number for all the cases under the present study. It is very interesting that most characteristics in this kind of diffusion combustion also can be found in its premixed counterpart investigated in our previous work. Especially, the critical Reynolds numbers determining the order of the predominant irreversibilities in this type of diffusion flame are same as its premixed counterpart, although the flow and scalar fields between them are quite different.     

Local entropy generation analysis on passive high-concentration DMFCs (direct methanol fuel cell) with different cell structures

In this paper, the local entropy generation analysis has been conducted based on a two-dimensional, two-phase, non-isothermal DMFC (direct methanol fuel cell) model, the entropy generation contributed by the chemical reactions, heat transfer, mass diffusion, and viscous dissipation is investigated. Then, the performance of fuel cells with different methanol barrier layers and electrolyte membranes have been studied based on the local entropy generation analysis. Results indicate that the entropy generation during cell operation is mainly caused by the irreversible electrochemical reactions, and that the entropy generated by mass diffusion and viscous dissipation can be considered negligible. The entropy generated by heat transfer is about two magnitudes less than the entropy generated by the electrochemical reactions in the passive DMFCs operating near room temperature. The overall entropy generation rate in a DMFC can be decreased by increasing the thickness of the methanol barrier layer and decreasing the thickness of the electrolyte membrane.     

Entropy generation analysis in a monolithic-type solid oxide fuel cell (SOFC)

The aim of the paper is to investigate possible improvements in the geometry design of a monolithic solid oxide fuel cells (SOFCs) through analysis of the entropy generation terms. The different contributions to the local rate of entropy generation are calculated using a computational fluid dynamic (CFD) model of the fuel cell, accounting for energy transfer, fluid dynamics, current transfer, chemical reactions and electrochemistry. The fuel cell geometry is then modified to reduce the main sources of irreversibility and increase its efficiency.     

Gas-phase transport and entropy generation during transient combustion of single biomass particle in varying oxygen and nitrogen atmospheres

Transient combustion of a single biomass particle in preheated oxygen and nitrogen atmospheres with varying concentration of oxygen is investigated numerically. The simulations are rigorously validated against the existing experimental data. The unsteady temperature and species concentration fields are calculated in the course of transient burning process and the subsequent diffusion of the combustion products into the surrounding gases. These numerical results are further post processed to reveal the temporal rates of unsteady entropy generation by chemical and transport mechanisms in the gaseous phase of the reactive system. The spatio-temporal evolutions of the temperature, major chemical species including CO, CO₂, O₂, H₂ and H₂O, and also the local entropy generations are presented. It is shown that the homogenous combustion of the products of devolatilisation process dominates the temperature and chemical species fields at low concentrations of oxygen. Yet, by oxygen enriching of the atmosphere the post-ignition heterogeneous reactions become increasingly more influential. Analysis of the total entropy generation shows that the chemical entropy is the most significant source of irreversibility and is generated chiefly by the ignition of volatiles. However, thermal entropy continues to be produced well after termination of the particle life time through diffusion of the hot gases. It also indicates that increasing the molar concentration of oxygen above 21% results in considerable increase in the chemical and thermal entropy generation. Nonetheless, further oxygen enrichment has only modest effects upon the thermodynamic irreversibilities of the system.     

Numerical analysis of entropy generation through non-grey gas radiation in a cylindrical annulus

This study is devoted to analyze the radiative heat transfer of non-grey gas confined in a cylindrical annulus with isothermal walls. The radiative heat transfer equation is resolved through the Ray Tracing method, which is associated to the statistical narrow bands correlated–k (SNBcK) model to compute the medium radiative properties. Special focus is given on the components of radiative entropy generation and its dependency on geometrical and thermodynamic parameters. The results show that entropy generation is greatly affected by gas and wall temperatures. Moreover, the dominance between wall radiative entropy generation and the volumetric one depends mainly on differences between gas and wall temperatures.     

Local entropy generation and exergy analysis of the condenser in a direct methanol fuel cell system

This paper aims to identify the irreversibilities in the condenser of a direct methanol fuel cell (DMFC) system and present possible enhancements in its design through local entropy generation analysis (L-EGA). For this purpose, the local entropy generation terms originating from heat and mass calculated from results of a pseudo two-phase computational fluid dynamic (CFD) model of the condenser. Through this analysis, the total irreversibilities due to heat and mass transfer are calculated locally (e.g., film boundary layer, vapour-gas boundary layer) under the variable operating conditions of a DMFC (undersaturated, saturated, and supersaturated conditions of the cathode exhaust gas). Moreover, the exergy destruction ratio of condenser is found to estimate the exergy performance of the condenser. The results show that in the case of supersaturated cathode exhaust gas (CEG) flow, the entropy generation rate due to mass transfer in the film region is found as 0.032 W/(m·K) which is 18 times higher than that for the undersaturated CEG flow. However, entropy generation rate due to mass transfer decreases significantly when the hot flow is just over the film region. In the film region, the entropy generation rates originating from heat transfer are found as 0.0055 W/(m·K) (for the undersaturated case), 0.0032 W/(m·K) (for the saturated case), and 0.0015 W/(m·K) (for the supersaturated case). Moreover, the maximum exergy destruction ratio is found as 0.72 when the CEG is undersaturated and the CEG velocity is 0.18 m/s, while the lowest exergy destruction ratio is calculated as 0.28 when the CEG is saturated.     

A modified micro reactor fueled with hydrogen for reducing entropy generation

In order to reduce the entropy generation of premixed hydrogen/air flame in the micro combustion chamber, the combustion chamber of the old micro reactor is modified by gradually varying the diameter of the combustion chamber. Extensive numerical investigations about the entropy generation of premixed hydrogen/air flame in old and modified micro reactors are conducted under various hydrogen mass flow rates, hydrogen/air equivalence ratios, solid materials and inlet/outlet diameter ratios. Results suggest that the modified micro reactor has lower total entropy generation than that of the old micro reactor. This is attributed to that the temperature gradient of the burned gas in the modified micro reactor is lower than that in the old micro reactor after chemical reactions. Finally, the largest descent percentages of total entropy generation are achieved under various conditions, which provide significant reference values for hydrogen energy usage under micro scale combustion.     

Analysis of entropy generation in hydrogen-enriched ultra-lean counter-flow methane–air non-premixed combustion

In this paper, entropy generation in hydrogen-enriched ultra-lean counter-flow methane–air non-premixed combustion confined by planar opposing jets is investigated for the first time. The effects of the effective equivalence ratio and the volume percentage of hydrogen in fuel blends on entropy generation are studied by numerically evaluating the entropy generation equation. The lattice Boltzmann model proposed in our previous work, instead of traditional numerical methods, is used to solve the governing equations for combustion process. Through the present study, five interesting features of this kind of combustion, which are quite different from that reported in previous literature on entropy generation analysis for hydrogen-enriched methane–air combustion, are revealed. The total entropy generation number can be approximated as a linear increasing function of the volume percentage of hydrogen in fuel mixture and the effective equivalence ratio for all the cases under the present study.     

Numerical analysis of entropy generation in mixed convection flow with viscous dissipation effects in vertical channel

A numerical investigation is performed into the entropy generated within a mixed convection flow with viscous dissipation effects in a parallel-plate vertical channel. In performing the analysis, it is assumed that the flow within the channel is steady, laminar and fully developed. The governing equations for the velocity and temperature fields in the channel are solved using the differential transformation method. The numerical results for the velocity and temperature fields are found to be in good agreement with the analytical solutions. The entropy generation number (N_s), irreversibility distribution ratio (Φ) and Bejan number (B_e) of the mixed convection flow are obtained by solving the entropy generation equation using the corresponding velocity and temperature data.     

Effects of wall thermal conductivity on entropy generation and exergy losses in a H2-air premixed flame microcombustor

Microcombustion is a promising method for fulfilling the energy requirements of small-scale systems currently powered by portable batteries. However, its applications rely upon mitigation of heat losses, which adversely affect flame stability and performance. Heat losses in turn depend upon wall properties, especially thermal conductivity. It is thus necessary to systematically investigate the relationship between wall thermal conductivity and microcombustor performance using the exergy analysis. In this work, entropy generation rates of different irreversible processes in an annular microcombustor were computed for stoichiometric hydrogen-air mixture using CFD simulations of reactive flow for wall thermal conductivities in the range 0.1-325 W/m K. Chemical reaction, heat conduction, and mass diffusion were the dominant contributors to entropy generation, in the decreasing order. Irreversibilities due to combustion decreased as thermal conductivities increased. Diffusion contributions were most sensitive to the changes in thermal conductivity but chemical reaction and heat conduction contributions changed marginally. Results showed that walls did not contribute significantly to entropy generation, but increased wall heat losses at higher thermal conductivities adversely affected the exergetic performance of microcombustor through availability losses and by influencing the flow gradients. Based on the results of this study, wall thermal conductivity in the range 0.1-1.75 W/m K was found suitable in order to obtain uniform wall temperature profiles and high exergetic efficiencies.     

Numerical analysis of entropy generation in mixed-convection MHD flow in vertical channel

A numerical analysis is performed of the entropy generation within a combined forced and free convective magnetohydrodynamic (MHD) flow in a parallel-plate vertical channel. The MHD flow is assumed to be steady state, laminar and fully developed. The analysis takes account of the effects of both Joule heating and viscous dissipation. The nonlinear governing equations for the velocity and temperature fields are solved using the differential transformation method (D.T.M.). It is shown that the numerical results are in good agreement with the analytical solutions. The numerical values of the velocity and temperature are used to derive the corresponding entropy generation number (N_s) and Bejan number (B_e) within the vertical channel under asymmetric heating conditions. The results show that the minimum entropy generation number and the maximum Bejan number occur near the centerline of the channel. Overall, the results confirm that the differential transformation method provides an accurate and computationally-efficient means of analyzing the nonlinear governing equations of the velocity and temperature fields for MHD flow.     

Effect of entropy change of lithium intercalation in cathodes and anodes on Li-ion battery thermal management

The entropy changes (ΔS) in various cathode and anode materials, as well as in complete Li-ion batteries, were measured using an electrochemical thermodynamic measurement system (ETMS). LiCoO₂ has a much larger entropy change than electrodes based on LiNi_xCo_yMn_zO₂ and LiFePO₄, while lithium titanate based anodes have lower entropy change compared to graphite anodes. The reversible heat generation rate was found to be a significant portion of the total heat generation rate. The appropriate combinations of cathode and anode were investigated to minimize reversible heat generation rate across the 0-100% state of charge (SOC) range. In addition to screening for battery electrode materials with low reversible heat, the techniques described in this paper can be a useful engineering tool for battery thermal management in stationary and transportation applications.     

Novel and optimal integration of SOFC-ICGT hybrid cycle: Energy analysis and entropy generation minimization

Integrating fuel cells with conventional gas turbine based power plant yields higher efficiency, especially solid oxide fuel cell (SOFC) with gas turbine (GT). SOFCs are energy efficient devices, performance of which are not limited to Carnot efficiency and considered as most promising candidate for thermal integration with Brayton cycle. In this paper, a novel and optimal thermal integration of SOFC with intercooled-recuperated gas turbine has been presented. A thermodynamic model of a proposed hybrid cycle has been detailed along with a novelty of adoption of blade cooled gas turbine model. On the basis of 1st and 2nd law of thermodynamics, parametric analysis has been carried out, in which impact of turbine inlet temperature and compression ratio has been observed on various output parameters such as hybrid efficiency, hybrid plant specific work, mass of blade coolant requirement and entropy generation rate. For optimizing the system performance, entropy minimization has been carried out, for which a constraint based algorithm has been developed. The result shows that entropy generation of a proposed hybrid cycle first increases and then decreases, as the turbine inlet temperature of the cycle increases. Furthermore, a unique performance map has also been plotted for proposed hybrid cycle, which can be utilized by power plant designer. An optimal efficiency of 74.13% can be achieved at TIT of 1800 K and r_p,c 20.