Second law analysis of a waste heat recovery steam generator

In recent years a great deal of attention is focussed on the efficient utilization of energy resources with minimum heat loss. There is a growing interest on second law analysis to minimize the entropy generation in various thermal units and thereby to improve and optimize the design and performance. In the present work, a waste heat recovery steam generator is considered, which consists of an economizer, an evaporator and a super heater. The unit produces superheated steam by absorbing heat from the hot flue gases. A general equation for the entropy generation has been proposed, which incorporates all the irreversibilities associated with the process. By using suitable non-dimensional operating parameters, an equation for entropy generation number is derived. The effect of various non-dimensional operating parameters, on the entropy generation number are investigated. The role of gas specific heat, non-dimensional inlet gas temperature difference ratio (τ), heat exchanger unit sizes (NTUB, NTUS, NTUE) on entropy generation number are also reported. The results will help to understand the influence of different non-dimensional operating parameters on entropy generation number, which in turn will be useful to optimize the performance of the unit.     

Thermodynamic optimization of tree-shaped flow geometries

In this paper we optimize the performance of several classes of simple flow systems consisting of T- and Y-shaped assemblies of ducts, channels and streams. In each case, the objective is to identify the geometric configuration that maximizes performance subject to several global constraints. Maximum thermodynamic performance is achieved by minimization of the entropy generated in the assemblies. The boundary conditions are fixed heat flow per unit length and uniform and constant heat flux. The flow is assumed laminar and fully developed. Every geometrical detail of the optimized structure is deduced from the constructal law. Performance evaluation criterion is proposed for evaluation and comparison of the effectiveness of different tree-shaped design heat exchangers. This criterion takes into account and compare the entropy generated in the system with heat transfer performance achieved.     

Conflation of ε-Ntu and EGM design methods for heat exchangers with uniform wall temperature

This paper conflates two heat exchanger design approaches – the ε-N_tu (effectiveness–number of transfer units) and the EGM (entropy generation minimization) – focusing on heat exchangers with uniform wall temperature, i.e. condensers and evaporators. An algebraic formulation which expresses the dimensionless rate of entropy generation as a function of the heat exchanger geometry (number of transfer units), the thermal-hydraulic characteristics (friction factor and Colburn j-factor), and the operating conditions (heat transfer duty, core velocity, surface temperature, and fluid properties) is derived. It is shown that there does exist a particular number of transfer units which minimizes the dimensionless rate of entropy generation. An algebraic expression for the optimum heat exchanger effectiveness, based on the working conditions, heat exchanger geometry and fluid properties, is also presented. The theoretical analysis led to the conclusion that a high effectiveness heat exchanger design does not necessarily provide the best thermal-hydraulic performance.     

Optimization of peripheral finned-tube evaporators using entropy generation minimization

The peripheral finned-tube (PFT) is a new geometry for enhanced air-side heat transfer under moisture condensate blockage (evaporators). It consists of individual hexagonal (peripheral) fin arrangements with radial fins whose bases are attached to the tubes and tips are interconnected with the peripheral fins. In this paper, experimentally validated semi-empirical models for the air-side heat transfer and pressure drop are combined with the entropy generation minimization theory to determine the optimal characteristics of PFT heat exchangers. The analysis is based on three independent parameters, i.e., porosity, equivalent particle diameter and particle-based Reynolds number. The total heat transfer rate is a fixed constraint. The optimal heat exchanger configurations, i.e., those in which the entropy generation number reaches a minimum, are calculated for constant heat flux and constant tube wall temperature boundary conditions. Performance evaluation criteria of fixed geometry, fixed face area and variable geometry were implemented. In all cases, it was possible to determine a combination of independent parameters that provided a minimum entropy generation rate.     

H形对流传热脉管的熵产率最小构形优化

针对H形对流传热脉管,以脉管区域面积和通道总表面积为约束,在线热流密度恒定时,基于熵产生最小化进行了构形优化,给出了无量纲总熵产量和无量纲单位传热负荷的总熵产率与脉管组合级数、无量纲质量流量和无量纲泵功率的完整解析关系式及优化算例.结果表明:给定通道总表面积与文献中给定通道总体积约束的优化结果是不同的;无量纲单位传热负...     

Effect of Conjugate Heat Transfer on Entropy Generation in Slip-Driven Microflow of Power Law Fluids

We analyze the entropy generation characteristics in a non-Newtonian microflow under the influence of interfacial slip as modulated by the conjugate transport of heat. We consider power law model to represent the constitutive behavior of the non-Newtonian fluid. In this analysis, we analytically solve the transport equations employing the thermal boundary condition of the third kind at the exterior wall surface accounting for the effect of conjugate heat transfer. We demonstrate that the slip flow–driven alteration in convective transport of heat and its nonlinear interaction with viscous dissipation, as modulated by fluid rheology and conjugate transport of heat, gives rise to a minimum entropy generation rate of the system. We determine the optimum value of the geometrical parameter—that is, the channel wall thickness and the thermophysical parameters, such as the Biot number and Peclet number—leading to a minimum entropy generation rate in the system. The results of this analysis could be of helpful in designing microsystems/devices typically used for electronic cooling, micro-heat pipes, and micro-heat exchangers.     

Entropy generation in condensation in the presence of high concentrations of noncondensable gases

The physical mechanisms of entropy generation in a condenser with high fractions of noncondensable gases are examined using scaling and boundary layer techniques, with the aim of defining a criterion for minimum entropy generation rate that is useful in engineering analyses. This process is particularly relevant in humidification-dehumidification desalination systems, where minimizing entropy generation per unit water produced is critical to maximizing system performance. The process is modeled by a consideration of the vapor/gas boundary layer alone, as it is the dominant thermal resistance and, consequently, the largest source of entropy production in many practical condensers with high fractions of noncondensable gases. Most previous studies of condensation have been restricted to a constant wall temperature, but it is shown here that for high concentrations of noncondensable gases, a varying wall temperature greatly reduces total entropy generation rate. Further, it is found that the diffusion of the condensing vapor through the vapor/noncondensable mixture boundary layer is the larger and often dominant mechanism of entropy production in such a condenser. As a result, when seeking to design a unit of desired heat transfer and condensation rates for minimum entropy generation, minimizing the variance in the driving force associated with diffusion yields a closer approximation to the minimum overall entropy generation rate than does equipartition of temperature difference.     

A robust learning based evolutionary approach for thermal-economic optimization of compact heat exchangers

This paper presents a robust, efficient and parameter-setting-free evolutionary approach for the optimal design of compact heat exchangers. A learning automata based particle swarm optimization (LAPSO) is developed for optimization task. Seven design parameters, including discreet and continuous ones, are considered as optimization variables. To make the constraint handling straightforward, a self-adaptive penalty function method is employed. The efficiency and the accuracy of the proposed method are demonstrated through two illustrative examples that include three objectives, namely minimum total annual cost, minimum weight and minimum number of entropy generation units. Numerical results indicate that the presented approach generates the optimum configuration with higher accuracy and a higher success rate when compared with genetic algorithms (GAs) and particle swarm optimization (PSO).     

蜡油加氢装置换热网络分析与优化

洛阳石化蜡油加氢装置由反应、分馏、富氢气体脱硫、热回收和产汽系统以及装置公用工程部分等组成,设计年加工能力220×104t/a,以减压蜡油、焦化蜡油和脱沥青混合油为原料,采用抚顺石油化工研究院开发的FFHT蜡油加氢处理工艺技术,催化剂采用FF-18型,主要生产低硫含量的精制蜡油,同时副产少量石脑油和柴油,富氢气体经脱硫后送至制氢装置作原料.利用换热网络优化软件PINCH2.0,对蜡油加氢装置换热网络进行模拟,得出现行工艺条件下换热网络最小冷却公用工程和最小加热公用工程用量,提出以现行换热网络的操作工艺为基础,停运分馏塔进料加热炉,提高反应进料加热炉热负荷,在不增加装置换热网络换热器换热面积前提下,充分利用装置现有换热器换热面积余量,增大换热器的换热负荷.实施换热网络优化方案后,降低蜡油加氢装置耗能105.5kg标油/h,年运行时间以8400h计算,年实现节能886.2t标油,标油价格按照3600元/t计算,年实现经济效益319万元;装置进料量按照295t/h计算,则降低装置综合能耗0.358kg标油/t原料.     

An investigation of cross-corrugated heat exchanger primary surfaces for advanced intercooled-cycle aero engines (Part-I: Novel geometry of primary surface)

The present study aims to develop a novel cross-corrugated primary surface for an intercooler in an aero-engine. Cross-corrugated primary surface heat exchangers are proposed for such applications due to their relatively high “volume goodness” and thus the potential for light weight designs. In the present study, modified primary surface geometries were analyzed using three-dimensional numerical simulation. The fully developed airflow in a cross-corrugated matrix unit cell was modeled with a low-Reynolds number k–ε turbulence model using steady incompressible Reynolds-Averaged Navier–Stokes (RANS) equations. The numerical approach was validated against experimental data for conventional cross-corrugated surfaces. The calculated pressure drop and heat transfer capacity of the novel surfaces were assessed in terms of the Fanning friction factor and Nusselt number while the overall performance was estimated using the volume and area goodness factors. Finally, the investigation on the pressure loss mechanism was achieved through a simplified analysis of the entropy generation.     

Effect of maximum and minimum heat capacity rate on entropy generation in a heat exchanger

This paper presents a theoretical analysis of a heat exchanger with a negligible fluid flow pressure drop to determine whether it is better to operate the heat exchanger with the minimum or maximum heat capacity rate of the hot fluid from entropy generation point of view. Entropy generation numbers are derived for both cases, and the results show that they are identical, when the heat exchanger is running at a heat capacity ratio of 0.5 with heat exchanger effectiveness equaling 1. An entropy generation number ratio is defined for the first time, which has a maximum value at ε = 1/(1+R) for any inlet temperature ratio. When R equals 0.1, 0.5 and 0.9, the entropy generation number ratio receives a maximum value at an effectiveness equaling 0.91, 0.67 and 0.526, respectively. When R=0.9, the entropy generation number ratio is the same for all inlet temperature ratios at ε=0.8. The results show that the entropy generation number ratio is far from 1 depending on the inlet temperature ratio of the cold and hot fluid. The results are valid for parallel‐flow and counterflow heat exchangers. Copyright © 2010 John Wiley & Sons, Ltd.     

Entropy generation minimization in turbulent mixed convection flows

This paper reports the results of a numerical investigation of turbulent mixed convection from a symmetrically heated vertical channel, bathed by a steady upward flow of cold air. The computations have been performed using FLUENT 6.2 by employing the k–ε model for turbulence with enhanced wall treatment. The entropy generation rates due to (i) heat transfer across a finite temperature difference and (ii) irreversibility due to fluid friction have been calculated as post-processed quantities with the computed velocity and temperature profiles. Optimal inlet velocities at which the total entropy generation rate reaches a minimum value are found to exist, for every set of heat flux and aspect ratio. Further, this optimum velocity turns out to be independent of the aspect ratio and increases linearly with the heat flux. Simple and easy to use correlations for the optimum Reynolds number and the dimensionless average wall temperatures corresponding to the optima are developed. Plots of total entropy generation rate against the velocity clearly demonstrate that near the optimum conditions, buoyancy does not have a significant role to play in deciding the optimum. For the range of parameters considered in this study, it is seen that for optimum conditions, the ratio of the entropy generation due to fluid friction to total entropy generation rate, known in literature as the Bejan number, varies within a narrow band (0.14–0.22).     

污垢对管内层流换热性能影响的热力学分析和评价

采用热力学第二定律，分别在恒壁温和恒热流两种典型工况下分析了污垢对管内层流换热性能的影响；引入单位传热量的熵增率对污垢管道的热力学性能进行了评价；讨论了管内流体雷诺数(无污垢时)、量纲为1的入口换热温差、量纲为1的热流密度和污垢层厚度等参数对单位传热量熵增率的影响；并把结果和紊流时的对应工况进行了比较。结果可为工程上换热设备的优化设计提供依据。     

Entropy generation and pumping power in a turbulent fluid flow through a smooth pipe subjected to constant heat flux

In a heat exchange process, heat transfer and pumping power requirements are the two main considerations. Efforts made to increase heat transfer in a fluid flow usually cause increase in the pumping power requirement. In an effort to avoid inefficient utilization of energy through excessive entropy generation, a thermodynamic analysis of turbulent fluid flow through a smooth duct subjected to constant heat flux has been made in this study. The temperature dependence of the viscosity was taken into consideration in determining the heat transfer coefficient and friction factor. It was shown that the viscosity variation has a considerable effect on both the entropy generation and the pumping power. Pumping power to heat transfer ratio and the entropy generation per unit heat transfer can become very large especially for low heat flux conditions.     

Entropy Generation Minimization Versus Thermal Mixing Due to Natural Convection in Differentially and Discretely Heated Square Cavities

Uniform temperature distribution is a key parameter in many thermal processing applications. A considerable amount of additional energy is used to enhance the fluid mixing in order to maintain the temperature uniformity, but that affects the overall efficiency of the process. In this article, an alternate approach is proposed for maintaining uniform temperature via various distributed/discrete heating strategies while maintaining the minimal entropy generation. The system of laminar natural convection in differentially and discretely heated square cavities filled with various materials (molten metals, air, aqueous solutions, oils) is considered, and finite element simulations are performed for a range of Rayleigh numbers (Ra = 10³–10⁵). Entropy generation is evaluated using finite-element basis sets for the first time in this work, and the derivatives at particular nodes are estimated based on the functions within adjacent elements. Analysis of entropy generation in each case is carried out and a detailed investigation of entropy production due to local heat transfer and fluid friction irreversibilities is presented. It is found that a high thermal mixing may not be the optimal situation for achieving uniform temperature distribution based on entropy production. A greater degree of temperature uniformity with moderate thermal mixing may correspond to minimum entropy generation with distributed heating. Further, based on entropy generation minimization approach, it has been thermodynamically established that the distributed heating methodology with multiple heat sources may be the energy efficient strategy for attaining adequate uniform temperature distribution with minimum entropy generation.     

Entropy generation analysis of fully-developed turbulent heat transfer flow in inward helically corrugated tubes

The entropy generation analysis of fully-developed turbulent heat transfer flow in inward helically corrugated tubes was numerically performed by using a Reynolds stress model. The simulations were conducted for a smooth tube and five cases of corrugated tubes with Reynolds number (Re) ranging from 10,020 to 40,060 at a constant wall temperature condition. The effects of corrugation pitch and height on the flow patterns as well as local thermal and frictional entropy generation are detailed in the near wall region. The results indicate that the local heat transfer entropy generation is significantly evident at the sub-layer region and the detached vortex region, and the local thermal entropy is improved with increases in the secondary flow. Local friction entropy generation is mainly located at the windward of the corrugation and the severely turbulent fluctuation region and is mainly induced by the velocity gradient. The average friction entropy generation exhibits an exponential growth, while the average heat transfer and the total entropy generation display a linear growth trend with increased Re. The average Bejan number (Be) exhibits an exponential decline, and the minimum value can reach 0.69. From a comprehensive viewpoint, it is optimal for the Re to be lower than 30,050. When Re <20,030, higher and dense corrugations are beneficial. When 20,030?Hl/D?=?0.08 is not recommended.     

Entropy Generation of Natural Convection Heat Transfer in a Square Cavity Using Al2O3–Water Nanofluid

Entropy generation of an Al₂O₃–water nanofluid due to heat transfer and fluid friction irreversibility has been investigated in a square cavity subject to different side‐wall temperatures using a nanofluid for natural convection flow. This study has been carried out for the pertinent parameters in the following ranges: Rayleigh number between 10⁴ and 10⁷ and volume fraction between 0 and 0.05. Based on the obtained dimensionless velocity and temperature values, the distributions of local entropy generation, average entropy generation, and average Bejan number are determined. The results are compared for a pure fluid and a nanofluid. It is totally found that the heat transfer, and entropy generation of the nanofluid is more than the pure fluid and minimum entropy generation and Nusselt number occur in the pure fluid at any Rayleigh number. Results depict that the addition of nanoparticles to the pure fluid has more effect on the entropy generation as the Rayleigh number goes up.     

Optimization for a heat exchanger couple based on the minimum thermal resistance principle

Following the brief introduction to the concept of a physical quantity, entransy, the equivalent thermal resistance of a heat exchanger couple is defined based on the entransy dissipation. The minimum thermal resistance principle is applied to obtain the optimal heat capacity rate of the medium fluid and the optimal allocation of heat exchangers thermal conductance, which correspond to the maximum heat transfer rate in the heat exchanger couple. In addition, analytical expression for the optimal heat capacity rate of the medium fluid is derived, whose reciprocal equals the sum of the reciprocal of the individual heat capacity rate of the hot and cold fluids, just like the case of two electrical capacitors in series. Numerical results in the variation of the thermal resistance and the heat transfer rate with the medium fluid heat capacity rate or the thermal conductance allocation agree with the theoretical analyses. Finally, for comparison, the entropy generation rate is also calculated to obtain its relation with the thermal performance of the heat exchanger couple. The results show that there is no one-to-one correspondence of the minimum entropy generation rate and the maximum heat transfer rate. This indicates that the minimum entropy generation principle cannot be used for optimizing the heat exchanger couple.     

Entropy generation and its relation to heating and cooling requirements of a metal hydride hydrogen storage reactor

In this paper a metal hydride hydrogen storage reactor is analyzed from heat and mass transfer and entropy generation points of view. A transient two dimensional energy equation along with suitable reaction kinetics and entropy balance equation is solved numerically. Results are obtained keeping hydrogen flow rates constant during absorption and desorption. For a fixed mass of metal hydride in the reactor the amount of hydrogen transferred and the time in which the transfer takes place are kept fixed. Using the mathematical model the entropy generated during the process and the external cooling and heating fluid requirements are obtained. Results show how improvement in the design and/or operating conditions leads to reduced cooling and heating requirements and lower entropy generation. For the system considered in the study the internal heat transfer characteristics of the hydride bed are seen to influence the reactor performance significantly. With improved bed heat transfer the required heat transfer fluid temperature during desorption can be reduced and that during absorption can be increased significantly. This automatically leads to lower entropy generation and a more economic system operation. It is expected that the methodology proposed and the results presented in this study will be useful in the optimal design of metal hydride reactors for a variety of practical applications, including hydrogen storage.     

Entropy generation for natural convection by heated partitions in a cavity

Entropy generation for natural convection in a partitioned cavity, with adiabatic horizontal and isothermally cooled vertical walls, is studied numerically by both a FORTRAN code and the commercially available CFD-ACE software. Effects of the Rayleigh number, the position of the heated partition, and the dimensionless temperature difference on the local and average entropy generation rate are investigated. Proper scale analysis of the problem showed that, while fluid friction term has nearly no contribution to entropy production, the heat transfer irreversibility increases monotonically with the Nusselt number and the dimensionless temperature difference.