積耗散最小換熱器的優(yōu)化設(shè)計外文翻譯

中文 3430 字 外 文 翻 譯 積耗散最小換熱器的優(yōu)化設(shè)計 Entransy dissipation minimization for optimization of heat exchanger design 性 質(zhì) : 畢業(yè)設(shè)計 畢業(yè)論文 教 學(xué) 院： 機電工程學(xué)院 系 別： 能源動力系 學(xué)生學(xué)號： 學(xué)生姓名： 專業(yè)班級： 熱動 1102 指導(dǎo)教師： 職 稱： 起止日期： 2015.3.9 2015.4.9 - 1 - 積耗散最小換 熱器的優(yōu)化設(shè)計 李雪芳，郭江楓，徐明天 &林城 ;程林學(xué)院熱科學(xué)與技術(shù)，山東大學(xué)，濟南 250061，中國 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換熱器為例，耗散理論應(yīng)用于換熱器的優(yōu)化設(shè)計。在一定的條件下，分析確定最佳的管道縱橫比。當(dāng)傳熱面積或管道的容積是固定的，得到最優(yōu)的質(zhì)量速度和最小耗散率的解析表達式。結(jié)果表明，若降低換熱器的不可逆耗散，則熱交換面積必須盡可能加大，而質(zhì)量流速應(yīng)盡可能的減少。 關(guān)鍵詞： 火積，換熱器，優(yōu)化設(shè)計 由于化石燃料的逐漸枯竭，燃料價格肯定會上漲。因此， 能源短缺是預(yù)見到制約經(jīng)濟和社會發(fā)展的不利因素。提高能源利用效率是解決能源危機的最有效的方法。換熱器廣泛應(yīng)用于化學(xué)工業(yè)，煉油廠，電力工程，食品工業(yè)，和許多其他領(lǐng)域。因此，通過優(yōu)化設(shè)計提高換熱器的性能，減少不必要的能源消耗是很有價值的。 換熱器優(yōu)化設(shè)計的目的可以分為兩類：一是盡量減少換熱器成本 1-5；另一是減少基于熱力學(xué)第二定律不可逆而制造的換熱器 6-10。第一種方法可以降低成本，但可能是以犧牲為代價換熱器性能 11。第二種方法表示的是最小熵的理論，就是所謂的“熵產(chǎn)悖論” 8,11。 通過電傳導(dǎo)模擬 ，郭等人。定義一個新的物理概念，火積，它描述了傳熱性能 13 。基于這樣的理念，換熱器的等效熱阻的定義確定換熱器的傳熱不可逆性 14 。陳等人。應(yīng)用耗散理論的傳導(dǎo)問題 15 。郭等人。定義一個耗散數(shù)評價換熱器性能，不僅避免了“熵產(chǎn)悖論”，但也可以表征換熱器整體性能 12 徐等人， 16 開發(fā)了換熱器有限的壓降下的流摩擦耗散表達式。 目前，基于耗散的熱傳導(dǎo)有限溫度差和流動摩擦壓降下的問題 14， 16 ，郭等人提出的無量綱化方法 12 。定義了一個全面的耗散數(shù)?？偦鸱e耗散數(shù)為目標(biāo)函數(shù) 。假設(shè)我們試圖證明，由于導(dǎo)管的縱橫比或質(zhì)量流速的變化，對兩種積耗散溫差下的熱傳導(dǎo)和流動阻力的影響下引起的有限的壓降，分別都有一個對應(yīng)的最佳管道的縱橫比或質(zhì)量流速。我們還開發(fā)了有公式可循的優(yōu)化管的長徑比和熱交換器，用于優(yōu)化設(shè)計質(zhì)量速度。 1 耗散數(shù) - 2 - 積定義為一半產(chǎn)品的熱容量和溫度 22121Eh TMCTQ pvh (1) 其中 T是溫度， qvh是定容熱容量， CP是在恒定壓力下的比熱?，F(xiàn)在 ，使用水平衡的逆流換熱器為例，討論在換熱器中的耗散。 假定冷熱流體的壓縮。進氣溫度和熱、冷流體表示為 T1和 T2的壓力， P1， P2，分別。同樣，出口溫度和壓力是 T1， T2和 P1， P2。為平衡熱交換器，熱容量率比滿足條件 1)()( 12 mcmcC （其中 m是質(zhì)量流量）。對于一維換熱器在目前的工作中，通常假設(shè)如穩(wěn)定流動，與環(huán)境無熱交換，并忽略動能和勢能的變化以及縱向傳導(dǎo)了。 在換熱器中，主要存在兩種不可逆性：一是有限的溫度差異下的熱傳導(dǎo)和第二流動摩擦壓降下有 限。因熱傳導(dǎo)有限溫差下的耗散率寫為 14 )(21)(21)(21)(212,222,11222211outout TmcTmcTmcTmcEr(2) 相應(yīng)的耗散數(shù)定義為 12 221121 )()()( TTmcErTTQ ErEr (3) 其中 Q熱速率的比值。由于有限的壓降下流動摩擦耗散表示為 16 2,22,22221,11,1111 lnlnlnln TT TTpmTT TTpmEoutoutoutoutp (4) 在 P1和 P2指在冷、熱水壓力下降，分別為 1和 2；有其相應(yīng)的密度。在無量綱形式導(dǎo)致 )1(1ln1)()()1(1ln1)()(11221112221212211TTTTTTTpcpTTTTTTTpcpEp(5) 這是由于水流的摩擦耗散數(shù)。假設(shè)換熱器表現(xiàn)為一個接近理想的換熱器，然后（ 1-）要比團結(jié) 17 小。對于水 -水換熱器在通常的操作條件下，熱水和冷水入口之間的溫差， T=T1-T2，小于 100 K，因此 )2,1(3 6 6.01 7 31 0 01 iTT 。因此，方程（ 5）可簡化為 - 3 - 212122212111ln1)()(ln1)()(TTTTpcpTTTTpcpEp (6) 因此，整體的耗散數(shù)變?yōu)?212122212111ln1)()(ln1)()()1(TTTTpcpTTTTpcpEpErE （ 7） 對于一個典型的水平衡的換熱器，傳熱單元數(shù) NTU可以推出，接近無窮大的效 力趨于統(tǒng)一，那么 c=1有效 17 NtuNtu 1（ 8） 在傳熱單元數(shù)定義為 pmcUANtu U在這里是總傳熱系數(shù)， A是傳熱面積。假設(shè)固體壁的熱傳導(dǎo)阻力可以忽略，與對流換熱相比，那么它是適當(dāng)?shù)膶α鲹Q熱系數(shù) H.因此取代 U。 21 )(1)( 11 hAhaUA （ 9a） 或者21111 NtuNtuNtu （ 9b） 在 H1和 H2的熱、冷流體，對流換熱系數(shù)是 )2,1()()(1 imchAN tu ii。在近乎理想的換熱器的限制， Ntu遠大于 1，即 17 Ntu11 （ 10） 從式（ 7）整體耗散數(shù)表示為 ln1)()(1ln1)()(12121222212111TTTTcpN tuTTTTcpN tuE（ 11） - 4 - 公式右邊的兩個術(shù)語（ 11）對應(yīng)于傳熱表面兩側(cè)的火積耗散。每側(cè)，耗散數(shù)可以表示如下 )2,1(ln)()(12121 ippTTTTcpiN tuEi iii（ 12） 很明顯，耗散熱傳導(dǎo)在有限溫差下，第二耗散流動摩擦壓降下是有限的。為簡單起見，我們使用 E不是 EI表示耗散數(shù)換熱器表面每一側(cè)。注意，在方程的推導(dǎo)過程中（ 2）和（ 4），沒有假設(shè)層流 14,16；因此，上述結(jié)果的層流和湍流流動是適用的。 2 參數(shù)優(yōu)化 從理論上講，換熱器的有效性增加時，在熱交換器降低不可逆耗散。由于耗散可以用來描述這些不可逆耗散 18,19 ，因此我們尋求管道長徑比與質(zhì)量流速優(yōu)化最小耗散數(shù) E例如方程（ 12）。 2.1 最佳長寬比 雖然 在傳熱表面的一側(cè)耗散數(shù)的總和可以表示為熱傳導(dǎo)的貢獻有限的溫度差和流動摩擦壓降下有限的情況下，這兩個因素對換熱器的不可逆性的影響是強耦合的熱交換器管居住在那邊幾何參數(shù)。因此，基于耗散最小化，可以得到換熱器的最佳管徑比等幾何參數(shù)優(yōu)化。 回憶中的斯坦頓數(shù) St的定義 St（ Re） D， pr）和摩擦系數(shù) f（ Re） D）： StDLNtu 4 （ 13） pGDLfpp24 2 （ 14） 其中質(zhì)量速度是 G=m/a， L是流動路徑的長度和 D是管道的水力直徑。引入無量綱的質(zhì)量流速， pGG 2 ，讓 21212ln)( TTTTcp替代式。（ 13）和（ 14）代入式（ 12），我們得到 22 441 GDLfStDLE （ 15） - 5 - 顯然，導(dǎo)管的縱橫比 4L D有兩個方面對等式的右邊的作用相反例如（ 15）。因此，存在一個最佳的管道縱橫比減少積數(shù)。當(dāng)雷諾茲數(shù)和質(zhì)量速度是固定的，最大限度地減少耗散數(shù)導(dǎo)致以下表達式優(yōu)化： 21)(1)4( fStGDLopt （ 16） 相應(yīng)的最小耗散數(shù) 21m in )(2 StfGE （ 17） 從（ 16）和（ 17）可以發(fā)現(xiàn)，最佳管道的縱橫比的降低和質(zhì)量流速 G增加，最小耗散數(shù)和無量綱質(zhì)量速度成正比。注意，最小耗散數(shù)也依賴于雷諾茲數(shù)通過 F和 ST，的雷諾茲數(shù)的最小耗散數(shù)影響很弱，使許多傳熱表面的磨擦系數(shù)斯坦頓數(shù)的比例沒有顯著的變化隨著雷諾茲數(shù)的變化 17 。因此，最小耗散數(shù)主要由選定的無量綱質(zhì)量流速確定。顯然，其質(zhì)量速度較小，工作流體較長的 存留在傳熱表面和熱交換器存在較低的不可逆耗散。 2.2 固定換熱面積下的參數(shù)優(yōu)化 在換熱器設(shè)計，換熱面積是一個重要的考慮因素時，它占了一個換熱器的總成本。因此在這一部分，我們討論的一個固定的傳熱面積和換熱器的優(yōu)化設(shè)計。 從水力直徑的定義，一個側(cè)的傳熱面積是 cADLA 4AC是管道截面。這種表達可以放在無量綱形式 14 GDLA （ 18） 其中一個是無量綱傳熱面積 mApA 21)2( 。替代式（ 18）代入式（ 15）的收益率 3211 fA GGA StE （ 19） 顯然，無量綱流速有相反的效果兩個方面對等，等式為（ 19）；因此，存在一個最佳的無量綱流速使熵耗散數(shù)達到最小值時， A和雷諾茲數(shù)（ Re） D。求解該優(yōu)化問題的產(chǎn)生 4122, )31(fStAG woptw （ 20） - 6 - 41322m in )27(4 StAfEw （ 21） 由上可得（ 20）和（ 21）給出最優(yōu)無量綱質(zhì)量速度和最小耗散數(shù)，分別在固定 A和雷諾茲數(shù)（ Re） D.從這兩方程，較大的傳熱面積明顯對應(yīng)較小的質(zhì)量速度 和低的耗散率。因此，需要減少不可逆耗散在熱交換器的傳熱面積，但是必須應(yīng)在條件允許的情況下采用。 假設(shè) E和（ Re） D是該換熱器的最小傳熱面積 2322123m in, 316StEfAww (22) 和StEDL wopt 134)4( （ 23） 由（ 22）和（ 23）可 得，我們可以看到一個低的耗散率對應(yīng)于傳熱面積大或?qū)Ч艿目v橫比。得到（ 21）和（ 22）是相同的，提供的產(chǎn)品為 EA21 在給定的雷諾茲數(shù)達到最小值的表達式。 2.3 參數(shù)優(yōu)化固定導(dǎo)管的體積 在一些空間有限的情況下，如在海洋和航空航天應(yīng)用，通過換熱器占用的空間，在換熱器設(shè)計的一個重要約束。因此，在這一部分，我們討論了換熱器的優(yōu)化設(shè)計固定管體積下的約束 管道體積 V=LA 可以寫為 2(R e)4 wDw GDLV （ 24） 其中 V是無量綱的體積， )/(8 vmVPVm 是運動粘度。替代式（ 24）代入式（ 15）整理所得的方程，我們得到 422 ( R e )( R e ) wDwwmDw GVfGStVE （ 25） 類似于公式（ 19），無量綱流速有兩個方面相反的效果對等式（ 25）。因此，存在一個最 佳的無量綱流速允許耗散數(shù)達到最小值時， V和雷諾茲數(shù)（ Re） D。求解該優(yōu)化問題的產(chǎn)生 6122 2, )fStV2 (R e)( DoptwG （ 26） 3122m in )4( R e )(3 StV fEwDw （ 27） - 7 - 由上（ 26）和（ 27）公式的最優(yōu)無量綱質(zhì)量速度和最小耗散數(shù)，分別在固定 V和雷諾茲數(shù)（ Re） D.由上（ 26）和（ 27）可以看到，管體最大可能導(dǎo)致最低的耗散率和最小質(zhì)量流速。顯然，限制管的體積限制是最可能限制最小耗散率的。 當(dāng) E和（ Re） D是固定的，最小管體積 232m in,(R e)427 StE fVw Dw （ 28） 由上（ 27）和（ 28）是等價的，產(chǎn)量為產(chǎn)品 31VEw 固定雷諾茲數(shù)下的最小可能值的表達式。 3 結(jié)語 由水逆流換熱器為例，目前的工作表明，熱交換器的最佳管道縱橫比所決定的雷諾茲數(shù)和流速下，當(dāng)耗散數(shù)作為性能評價標(biāo)準(zhǔn)，分析得到了最優(yōu)的管道縱橫比的公式。固定的傳熱面積的限制下（或管體積）和雷諾茲數(shù)，它表明，存在一個最佳的無量綱流速的解析表達式；并給出了結(jié)果，如果采用降低換熱器的不可逆耗散，最大可能的傳熱面積和最低的質(zhì)量速度。這一結(jié)論如果是由殼體和耗散數(shù)為目標(biāo)函數(shù) 20，則可得到管式換熱器優(yōu)化設(shè)計得到的數(shù)值結(jié)果相吻合。 從本研究中得到的結(jié)果，可以看出，傳統(tǒng)換熱器的設(shè)計優(yōu)化，以總費用為目標(biāo)函數(shù)通常犧牲換熱器換熱性 能。此問題已通過數(shù)值結(jié)果表明 11 。在本文中 11 的分析可以看到，換熱器性能的一個小的改進可以導(dǎo)致在節(jié)能和環(huán)保方面大的收益。因此，在換熱器設(shè)計中，在總成本和換熱性能的提高應(yīng)同等對待。推動這個方向的新研究是非常很有用。 參考文獻 1 Selbas R, Kizilkan O, Reppich M. 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In: Proceedings of the 14th International Heat Transfer Conference, Washington, 2010 - 9 - Entransy dissipation minimization for optimization of heatexchanger design LI XueFang, GUO JiangFeng, XU MingTian& CHENG LinInstitute of Thermal Science and Technology, Shandong University, Jinan 250061, ChinaReceived July 16, 2010; accepted March 15, 2011 In 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 design As 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 - 10 - 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 number The entransy is defined as one-half the product of heat capacity and temperature 13: 22121Eh TMCTQ pvh (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 1)()( 12 mcmcC (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 )(21)(21)(21)(212,222,11222211outout TmcTmcTmcTmcEr(2) The corresponding entransy dissipation number is defined as 12 221121 )()()( TTmcErTTQ ErEr (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 2,22,22221,11,1111 lnlnlnln TT TTpmTT TTpmEoutoutoutoutp (4) - 11 - 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 )1(1ln1)()()1(1ln1)()(11221112221212211TTTTTTTpcpTTTTTTTpcpEp(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 )2,1(3 6 6.01 7 31 0 01 iTT There fore, eq. (5) can be simplified to 212122212111ln1)()(ln1)()(TTTTpcpTTTTpcpEp (6) Accordingly, the overall entransy dissipation number becomes 212122212111ln1)()(ln1)()()1(TTTTpcpTTTTpcpEpErE (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 NtuNtu 1(8) where the number of heat transfer units is defined as pmcUANtu Here 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 21 )(1)( 11 hAhaUA (9a) - 12 - or21111 NtuNtuNtu (9b) where h1 and h2 are the convective heat transfer coefficients of the hot and cold fluids, respectively, and )2,1()()(1 imchAN tu iiNtu hA mc i i ii . In the nearly ideal heat exchangerlimit, Ntu 1, that is 17 Ntu11 (10) from eq. (7) the overall entransy dissipation number is expressed as ln1)()(1ln1)()(12121222212111TTTTcpN tuTTTTcpN tuE(11) The two terms on the right of eq. (11) correspond to the entransy dissipations of two sides of heat transfer surfaces. For each side, the entransy dissipation number can be expressed as follows: )2,1(ln)()(12121 ippTTTTcpiN tuEi iii(12) It is evident that the first term accounts for the entransy dissipationfrom the heat conduction under finite temperaturedifference and the second for the entransy dissipation from flow friction under finite pressure drop. For simplicity, we now use E instead of Ei to denote the entransy dissipation number for each side of the heat exchanger surface. Note that in the derivations of eqs. (2) and (4), there is no assumption that the flow is laminar 14,16; therefore, the above results are applicable for both laminar and turbulent flows. 2 Parameter optimization Theoretically, the exchanger effectiveness increases when the irreversible dissipation in the heat exchanger decreases. Since the entransy dissipation can be used to describe these irreversible dissipations 18,19, therefore we seek optimums in duct aspect ratio and mass velocity by minimizing the entransy dissipation number E based on eq. (12). 2.1 The optimum aspect ratio Although the entransy dissipation number on one side of a heat transfer surface can be expressed as the sum of the contributions of the heat conduction under the finite temperature difference and flow friction