积耗散最小换热器的优化设计—外文翻译.doc

中文3430字 外 文 翻 译积耗散最小换热器的优化设计Entransy dissipation minimization for optimization of heatexchanger design性 质: 毕业设计 毕业论文教 学 院： 机电工程学院系 别：能源动力系学生学号： 学生姓名： 专业班级：热动1102指导教师： 职 称： 起止日期：2015.3.92015.4.9 积耗散最小换热器的优化设计李雪芳，郭江枫，徐明天&林城;程林学院热科学与技术，山东大学，济南250061，中国2010年7月16日收到；2011年3月15日接受摘要：本文以水平衡的逆流换热器为例，耗散理论应用于换热器的优化设计。在一定的条件下，分析确定最佳的管道纵横比。当传热面积或管道的容积是固定的，得到最优的质量速度和最小耗散率的解析表达式。结果表明，若降低换热器的不可逆耗散，则热交换面积必须尽可能加大，而质量流速应尽可能的减少。关键词：火积，换热器，优化设计由于化石燃料的逐渐枯竭，燃料价格肯定会上涨。因此，能源短缺是预见到制约经济和社会发展的不利因素。提高能源利用效率是解决能源危机的最有效的方法。换热器广泛应用于化学工业，炼油厂，电力工程，食品工业，和许多其他领域。因此，通过优化设计提高换热器的性能，减少不必要的能源消耗是很有价值的。换热器优化设计的目的可以分为两类：一是尽量减少换热器成本1-5；另一是减少基于热力学第二定律不可逆而制造的换热器6-10。第一种方法可以降低成本，但可能是以牺牲为代价换热器性能11。第二种方法表示的是最小熵的理论，就是所谓的“熵产悖论”8,11。通过电传导模拟，郭等人。定义一个新的物理概念，火积，它描述了传热性能 13 。基于这样的理念，换热器的等效热阻的定义确定换热器的传热不可逆性 14 。陈等人。应用耗散理论的传导问题 15 。郭等人。定义一个耗散数评价换热器性能，不仅避免了“熵产悖论”，但也可以表征换热器整体性能 12 徐等人， 16 开发了换热器有限的压降下的流摩擦耗散表达式。目前，基于耗散的热传导有限温度差和流动摩擦压降下的问题 14，16 ，郭等人提出的无量纲化方法 12 。定义了一个全面的耗散数。总火积耗散数为目标函数。假设我们试图证明，由于导管的纵横比或质量流速的变化，对两种积耗散温差下的热传导和流动阻力的影响下引起的有限的压降，分别都有一个对应的最佳管道的纵横比或质量流速。我们还开发了有公式可循的优化管的长径比和热交换器，用于优化设计质量速度。1耗散数积定义为一半产品的热容量和温度 (1)其中T是温度，qvh是定容热容量，CP是在恒定压力下的比热。现在，使用水平衡的逆流换热器为例，讨论在换热器中的耗散。假定冷热流体的压缩。进气温度和热、冷流体表示为T1和T2的压力，P1，P2，分别。同样，出口温度和压力是T1，T2和P1，P2。为平衡热交换器，热容量率比满足条件（其中m是质量流量）。对于一维换热器在目前的工作中，通常假设如稳定流动，与环境无热交换，并忽略动能和势能的变化以及纵向传导了。在换热器中，主要存在两种不可逆性：一是有限的温度差异下的热传导和第二流动摩擦压降下有限。因热传导有限温差下的耗散率写为 14 (2)相应的耗散数定义为 12 (3)其中Q是传热速率，是换热器效能e被定义为实际的热传递率达到最大可能的传热速率的比值。由于有限的压降下流动摩擦耗散表示为 16 (4)在P1和P2指在冷、热水压力下降，分别为1和2；有其相应的密度。在无量纲形式导致 (5)这是由于水流的摩擦耗散数。假设换热器表现为一个接近理想的换热器，然后（1-）要比团结 17 小。对于水-水换热器在通常的操作条件下，热水和冷水入口之间的温差，T=T1-T2，小于100 K，因此。因此，方程（5）可简化为 (6)因此，整体的耗散数变为 （7）对于一个典型的水平衡的换热器，传热单元数NTU可以推出，接近无穷大的效力趋于统一，那么c=1有效 17 （8）在传热单元数定义为U在这里是总传热系数，A是传热面积。假设固体壁的热传导阻力可以忽略，与对流换热相比，那么它是适当的对流换热系数H.因此取代U。 （9a）或者 （9b）在H1和H2的热、冷流体，对流换热系数是。在近乎理想的换热器的限制，Ntu远大于1，即 17 （10）从式（7）整体耗散数表示为 （11）公式右边的两个术语（11）对应于传热表面两侧的火积耗散。每侧，耗散数可以表示如下 （12）很明显，耗散热传导在有限温差下，第二耗散流动摩擦压降下是有限的。为简单起见，我们使用E不是EI表示耗散数换热器表面每一侧。注意，在方程的推导过程中（2）和（4），没有假设层流14,16；因此，上述结果的层流和湍流流动是适用的。2参数优化从理论上讲，换热器的有效性增加时，在热交换器降低不可逆耗散。由于耗散可以用来描述这些不可逆耗散 18,19 ，因此我们寻求管道长径比与质量流速优化最小耗散数E例如方程（12）。2.1最佳长宽比虽然在传热表面的一侧耗散数的总和可以表示为热传导的贡献有限的温度差和流动摩擦压降下有限的情况下，这两个因素对换热器的不可逆性的影响是强耦合的热交换器管居住在那边几何参数。因此，基于耗散最小化，可以得到换热器的最佳管径比等几何参数优化。回忆中的斯坦顿数St的定义St（Re）D，pr）和摩擦系数f（Re）D）： （13） （14）其中质量速度是G=m/a，L是流动路径的长度和D是管道的水力直径。引入无量纲的质量流速，让替代式。（13）和（14）代入式（12），我们得到 （15）显然，导管的纵横比4LD有两个方面对等式的右边的作用相反例如（15）。因此，存在一个最佳的管道纵横比减少积数。当雷诺兹数和质量速度是固定的，最大限度地减少耗散数导致以下表达式优化： （16）相应的最小耗散数 （17）从（16）和（17）可以发现，最佳管道的纵横比的降低和质量流速G增加，最小耗散数和无量纲质量速度成正比。注意，最小耗散数也依赖于雷诺兹数通过F和ST，的雷诺兹数的最小耗散数影响很弱，使许多传热表面的磨擦系数斯坦顿数的比例没有显着的变化随着雷诺兹数的变化17 。因此，最小耗散数主要由选定的无量纲质量流速确定。显然，其质量速度较小，工作流体较长的存留在传热表面和热交换器存在较低的不可逆耗散。2.2固定换热面积下的参数优化在换热器设计，换热面积是一个重要的考虑因素时，它占了一个换热器的总成本。因此在这一部分，我们讨论的一个固定的传热面积和换热器的优化设计。从水力直径的定义，一个侧的传热面积是AC是管道截面。这种表达可以放在无量纲形式 （18）其中一个是无量纲传热面积。替代式（18）代入式（15）的收益率 （19）显然，无量纲流速有相反的效果两个方面对等，等式为（19）；因此，存在一个最佳的无量纲流速使熵耗散数达到最小值时，A和雷诺兹数（Re）D。求解该优化问题的产生 （20） （21）由上可得（20）和（21）给出最优无量纲质量速度和最小耗散数，分别在固定A和雷诺兹数（Re）D.从这两方程，较大的传热面积明显对应较小的质量速度和低的耗散率。因此，需要减少不可逆耗散在热交换器的传热面积，但是必须应在条件允许的情况下采用。假设E和（Re）D是该换热器的最小传热面积 (22)和 （23）由（22）和（23）可得，我们可以看到一个低的耗散率对应于传热面积大或导管的纵横比。得到（21）和（22）是相同的，提供的产品为在给定的雷诺兹数达到最小值的表达式。2.3参数优化固定导管的体积在一些空间有限的情况下，如在海洋和航空航天应用，通过换热器占用的空间，在换热器设计的一个重要约束。因此，在这一部分，我们讨论了换热器的优化设计固定管体积下的约束管道体积V=LA可以写为 （24）其中V是无量纲的体积，是运动粘度。替代式（24）代入式（15）整理所得的方程，我们得到 （25）类似于公式（19），无量纲流速有两个方面相反的效果对等式（25）。因此，存在一个最佳的无量纲流速允许耗散数达到最小值时，V和雷诺兹数（Re）D。求解该优化问题的产生 （26） （27）由上（26）和（27）公式的最优无量纲质量速度和最小耗散数，分别在固定V和雷诺兹数（Re）D.由上（26）和（27）可以看到，管体最大可能导致最低的耗散率和最小质量流速。显然，限制管的体积限制是最可能限制最小耗散率的。当E和（Re）D是固定的，最小管体积 （28）由上（27）和（28）是等价的，产量为产品固定雷诺兹数下的最小可能值的表达式。3结语由水逆流换热器为例，目前的工作表明，热交换器的最佳管道纵横比所决定的雷诺兹数和流速下，当耗散数作为性能评价标准，分析得到了最优的管道纵横比的公式。固定的传热面积的限制下（或管体积）和雷诺兹数，它表明，存在一个最佳的无量纲流速的解析表达式；并给出了结果，如果采用降低换热器的不可逆耗散，最大可能的传热面积和最低的质量速度。这一结论如果是由壳体和耗散数为目标函数20，则可得到管式换热器优化设计得到的数值结果相吻合。从本研究中得到的结果，可以看出，传统换热器的设计优化，以总费用为目标函数通常牺牲换热器换热性能。此问题已通过数值结果表明 11 。在本文中 11 的分析可以看到，换热器性能的一个小的改进可以导致在节能和环保方面大的收益。因此，在换热器设计中，在总成本和换热性能的提高应同等对待。推动这个方向的新研究是非常很有用。参考文献1 Selbas R, Kizilkan O, Reppich M. 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In: Proceedings of the 14th International Heat Transfer Conference, Washington, 2010Entransy dissipation minimization for optimization of heatexchanger designLI XueFang, GUO JiangFeng, XU MingTian& CHENG LinInstitute of Thermal Science and Technology, Shandong University, Jinan 250061, ChinaReceived July 16, 2010; accepted March 15, 2011In this paper, by taking the water-water balanced counterflow heat exchanger as an example, the entransy dissipation theory isapplied to optimizing the design of heat exchangers. Under certain conditions, the optimal duct aspect ratio is determined analytically.When the heat transfer area or the duct volume is fixed, analytical expressions of the optimal mass velocity and the minimalentransy dissipation rate are obtained. These results show that to reduce the irreversible dissipation in heat exchangers, the heatexchange area should be enlarged as much as possible, while the mass velocity should be reduced as low as possible.entransy, heat exchanger, optimization designAs fossil fuels are gradually depleted, fuel prices will surelyrise. As a result, energy shortages are foreseen as a detrimentalfactor that could restrict economic and social development.Improving energy use efficiency is one of the mosteffective ways to address an energy crisis. Heat exchangersare widely applied in the chemical industries, petroleumrefineries, power engineering, food industries, and manyother areas. Therefore, it will be of great value to reduceneedless energy dissipation and improve the performance ofheat exchangers by optimizing their design.The objectives in heat exchanger design optimization canbe classified into two groups: one is minimizing costs ofheat exchangers 15; the other is minimizing irreversibilitybased on the second law of thermodynamics that occursin heat exchangers 610. The first approach can reducecosts, but possibly at the expense of sacrificing heat exchangerperformance 11. As representative of the secondapproach, entropy generation minimization suffers fromso-called “entropy generation paradox” 8,12.By analogy with electrical conduction, Guo et al. defineda new physical concept, entransy, which describes heattransfer capability 13. Based on this concept, the equivalentthermal resistance of a heat exchanger was defined toquantify heat transfer irreversibility in heat exchangers14.Chen et al. applied entransy dissipation theory to thevolume-to-pointconduction problem15. Guo et al. defined anentransy dissipation number to evaluate heatexchangerperformance that not only avoids the “entropy generationparadox” resulting from the entropy generation number, butcan also characterize the overall performance of heat exchangers12.Xu et al.16 developed an expression of theentransy dissipation induced by flow friction under finitepressure drop in a heat exchanger.The present work, based on expressions of entransy dissipationfrom heat conduction under finite temperature differencesand flow friction under finite pressure drops 14,16, and on the dimensionless method proposed by Guo etal. 12, defines an overall entransy dissipation numbers.The minimum overall entransy dissipation number is thentaken as an objective function. Under certain assumptionswe attempt to prove that since the variation in the duct aspectratio or mass velocity has opposing effects on the twotypes of entransy dissipations caused by heat conductionunder finite pressure drop, respectively, there is a correspondingoptimum in duct aspect ratio or mass velocity. We also develop analytically expressions for the optimal ductaspect ratio and mass velocity of a heat exchanger that are useful for design optimization.1 Entransy dissipation numberThe entransy is defined as one-half the product of heat capacity and temperature 13: (1)where T is the temperature, Qvh is the heat capacity at constant volume, and cp is the specific heat at constant pressure.Now, using the water-water balanced counter-flow heatexchanger as an example, we attempt to discuss the entransydissipation in heat exchangers.Assume that both the hot and cold fluids are incompressible.The inlet temperature and pressure of the hot andcold fluids are denoted as T1, P1 and T2, P2, respectively.Similarly the outlet temperature and pressure are T1,out, P1,outand T2,out, P2,out. For the balanced heat exchanger, the heatcapacity rate ratio satisfies condition(where m is the mass flow rate). For the one-dimensionalheat exchanger considered in the present work, the usualassumptions such as steady flow, no heat exchange withenvironment, and ignoring changes in kinetic and potentialenergies as well as the longitudinal conduction are made.In the heat exchanger, there mainly exist two kinds of irreversibility:the first is heat conduction under finite temperaturedifferences and the second is flow friction under finite pressure drops. The entransy dissipation rate caused by heat conduction under a finite temperature difference iswritten as 14 (2)The corresponding entransy dissipation number is defined as 12 (3)where Q is the heat transfer rate, is the heat exchangereffectiveness which is defined as the ratio of the actual heattransfer rate to the maximum possible heat transfer rate. The entransy dissipation due to flow friction under a finite pressuredrop is expressed as 16 (4)where P1 and P2 refer to the pressure drops in the hot and cold water, respectively; 1 and 2 are their corresponding densities. Putting in dimensionless form leads to (5)which is called the entransy dissipation number due to flow friction. Assuming that the heat exchanger behaves as a nearly ideal heat exchanger, then (1-) is considerably smaller than unity 17. For a water-water heat exchanger under usual operating conditions, the inlet temperature difference between hot and cold water，T=T1-T2，小于100 K, is less than 100 K,hence There fore, eq. (5) can be simplified to (6)Accordingly, the overall entransy dissipation number becomes (7)For a typical water-water balanced heat exchanger, the number of heat transfer units Ntu can be introduced, which approaches infinity as the effectiveness tends to unity. Since c=1, the effectiveness is 17 (8)where the number of heat transfer units is defined asHere U is the overall heat transfer coefficient, and A is the heat transfer area. Assuming that the heat conduction resistance of the solid wall can be neglected, compared with the convective heat transfer, then it is appropriate to replace U with the convective heat transfer coefficient h. Therefore (9a)or (9b)where h1 and h2 are the convective heat transfer co