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喜歡就充值下載吧。資源目錄里展示的文件全都有，請(qǐng)放心下載，有疑問(wèn)咨詢QQ:414951605或者1304139763 = 喜歡就充值下載吧。資源目錄里展示的文件全都有，請(qǐng)放心下載，有疑問(wèn)咨詢QQ:414951605或者1304139763 = Proc. Natl. Acad. Sci. USAVol. 78, No. 4, pp. 1986-1988, April 1981Applied Physical SciencesFinite-time thermodynamics:Engine performance improved by optimized piston motion(Otto cycle/optimized heat engines/optimal control)MICHAEL MOZURKEWICH AND R. S. BERRY Department of Chemistry and the James Franck Institute, The University of Chicago, Chicago, Illinois 60637 Contributed by R. Stephen Berry, December 29, 1980ABSTRACT The methods of finite-time thermodynamics are used to find the optimal time path of an Otto cycle with friction and heat leakage. Optimality is defined by maximization of the work per cycle; the system is constrained to operate at a fixed frequency,so the maximum power-is obtained. The result is an improvement of about 10% in the effectiveness (second-law efficiency) of a conventional near-sinusoidal engine.Finite-time thermodynamics is an extension ofconventional thermodynamics relevant in principle across the entire span of the subject, from the most abstract level to the most applied. The approach is based on the construction of generalized thermodynamic potentials (1) for processes containing time or rate conditions among the constraints on the system (2) and on the determination of optimal paths that yield the extrema corresponding to those generalized potentials.Heretofore, work on finite-time thermodynamics has concentrated on ratheridealized models (2-7) and on existence theorems (2), all on the abstract side of the subject. This work is intended as a step connecting the abstract thermodynamic concepts that have emerged in finite-time thermodynamics with the practical, engineering side of the subject, the design principles of a real machine. In this report, we treat a model of the internal combustion engine closely related to the ideal Otto cycle but with rate constraints in the form ofthe two major losses found in real engines. We optimize the engine by controlling the time dependence of the volume-that is, the piston motion. As a result, without undertaking a detailed engineering study, we are able to understand how the losses are affected by the time path of the piston and to estimate the improvement in efficiency obtainable by optimizing the piston motion.THE MODELOur model is based on the standard four-stroke Otto cycle. This consists of an intake stroke, a compression stroke, a power stroke, and an exhaust stroke. Here we briefly describe the basic features of this model and the method used to find the optimal piston motion. A detailed presentation will be given elsewhere. We assume that the compression ratio, fuel-to-air ratio, fuel consumption, and period of the cycle all are fixed. These constraints serve two purposes. First, they reduce the optimization problem to finding the piston motion. Also,they guarantee that the performance criteria not considered in this analysis are comparable to those for a real engine. Relaxing any of these constraints can only improve the performance further.We take the losses to be heat leakage and friction. Both of these are rate dependent and thus affect the time response of the system. The heat leak is assumed to be proportional to the instantaneous surface of the cylinder and to the temperature difference between the working fluid and the walls (i.e., Newtonian heat loss). Because this temperature difference is large only on the power stroke, heat loss is included only on this stroke. The friction force is taken to be proportional to the piston velocity, corresponding to well-lubricated metal-on-metal sliding;thus, the frictional losses are directly related, to the square ofthe velocity. These losses are not the same for all strokes. The high pressures in the power stroke make its friction coefficient higher than in the other strokes. The intake stroke has a contribution due to viscous flow through the valve.The function we have optimized is the maximum work per cycle. Because both fuel consumption and cycle time are fixed, this also is equivalent to maximizing both efficiency and the average power.In finding the optimal piston motion, we first separated the power and nonpower strokes. An unspecified but fixed time t was allotted to the power stroke with the remainder of the cycle time given to the nonpower strokes. Both portions of the cycle were optimized with this time constraint and were then combined to find the total work per cycle. The duration t of the power stroke was then varied and the process was repeated until the net work was a maximum.The optimal piston motion for the nonpower strokes takes a simple form. Because of the quadratic velocity dependence of the friction losses, the optimum motion holds the velocity constant during most of each stroke. At the ends of the stroke, the piston accelerates and decelerates at the maximum allowed rate. Because the friction losses are higher on the intake stroke, the optimal solution allots more time to this stroke than to the other two. The piston velocity as a function of time is shown in Fig.1.The power stroke was more difficult to optimize because ofthe presence of the heat leak. The problem was solved by using the variational technique of optimal control theory (8). The formalism yields the equation of motion of the piston as a fourthorder set of nonlinear differential equations. These were solved numerically. The resulting motion is shown in Fig. 1 for the entire cycle.The asymmetric shape of the piston motion on the power stroke arises from the trade-off between friction and heat leak losses. At the beginning of the stroke the gases are hot, capable of yielding high efficiency, and the rate of heat loss is high. It is therefore advantageous to make the velocity high on this part of the stroke. As work is extracted, the gases cool and the rate of heat leakage diminishes relative to frictional losses. Consequently the optimal path moves to lower velocities as the power stroke proceeds.The solutions were obtained first with unlimited acceleration and then with limits on acceleration and deceleration. The latter situation yields a result familiar in other contexts under the name of turnpike solution (9). The system tries to operate as long as possible at its optimal forward and backward velocities, by accelerating and decelerating between these velocities at the maximum rates. In this way, the system spends as much time as possible moving along its best or turnpike path.RESULTSParameters for the computations were taken from ref. 10 or, in the case of the friction coefficient, adjusted to give frictional losses of the magnitude cited in ref. 10. Those parameters are given in Table 1. The results of the calculations of some typical cases are given in Table 2, where they are compared with the conventional Otto cycle engine having the same compression ratio but a standard near-sinusoidal motion. The effectiveness (the ratio of the work done to the reversible work, also called the second-law efficiency) is slightly higher for the optimized engine whose piston-acceleration is limited to 5 x 103 m/sec2 ，the maximum of the conventional engine of the first row. If the piston is allowed to have 4 times the acceleration of the conventional engine, the effectiveness increases 9%; if the acceleration is unconstrained, the improvement in effectiveness goes up to 11%.These values are typical, not the most favorable. If the total losses of the conventional engine are held approximately constant but shifted to correspond to about 80% larger heat loss and about 60% smaller friction loss, the gain in effectiveness goes up, reaching more than 17% above the effectiveness of the corresponding conventional engine.The principal source of the improvement in use of energy in this analysis is in the reduction of heat losses when the working fluid is near its maximum temperature. This is why the improvement is greater for engines with large heat leaks and low friction than for engines with relatively better insulation but higher friction.Finally, it is instructive to examine the path of the piston in time, for the optimized engine and for its conventional counterpart. The position of the piston as a function of time is shown for these two cases in Fig. 2.In closing, let us emphasize the unconventional approach to optimizing a thermodynamic system illustrated by this work. Instead of controlling heat rates, heat capacities, conductances, friction coefficients, reservoir temperatures, or other usual parameters of thermodynamic engines, we have controlled the time path of the engine volume.We thank Dr. Morton Rubin for helpful comments and suggestions. This work was supported in part by a grant from the Exxon Education Foundation.REFERENCE1. Hermann, R. (1973) Geonetry, Physics and Systems (Dekker,New York). Proc. Nati. Acad. Sci. USA 78 (1981)2. Salamon, P., Andresen, B. & Berry, R. S. (1977) Phys. Rev. A 14,2094-2102.3. Curzon, F. L. & Ahlborn, B. (1975) Am. J. Phys. 43, 22-24.4. Andresen, B., Berry, R. S., Nitzan, A. & Salamon, P. (1977)Phys. Rev. A 15, 2086-2093.5. Rubin, M. (1979) Phys. Rev. A 19, 1272-1276, 1277-1289.6. Salamon, P., Nitzan, A., Andresen, B. & Berry, R. S. (1980)Phys. Rev. A 21, 2115-2129.7. Gutkowicz-Krusin, D., Procaccia, I. & Ross, J. (1978) J. Chem. Phys. 69, 3898-3906.8. Hadley, C.F.G. & Kemp, M. C. (1971) Variational Methods in Economics (North-Holland, Amsterdam).9. Sen, A., ed. (1970) Growth Economics (Penguin, Baltimore,MD).10. Taylor, C. F. (1966) The Internal Combustion Engine in Theory and Practice (MIT Press, Cambridge, MA), Vol. 1, pp. 158-164; Vol. 2, pp. 19-20.Proc。 全國(guó)。 Acad。 Sci。 美國(guó)卷. 78，第 4 頁(yè)。 1986-1988， 1981年4月應(yīng)用的物理學(xué)有限時(shí)間熱力學(xué)：優(yōu)化活塞行動(dòng)改進(jìn)的發(fā)動(dòng)機(jī)性能(奧托循環(huán)或優(yōu)化熱引擎或最優(yōu)控制)MICHAEL MOZURKEWICH和 R. S. BERRY 化學(xué)系和詹姆斯法朗克研究所，芝加哥大學(xué)，芝加哥，伊利諾伊州 60637 由R.斯蒂芬莓果貢獻(xiàn)， 1980年12月29日摘要： 利用有限時(shí)間熱力學(xué)方法發(fā)現(xiàn)奧托循環(huán)的優(yōu)先時(shí)間路徑及摩擦和熱滲漏。 最優(yōu)性由工作的最大化定義每個(gè)周期; 系統(tǒng)被控制在一個(gè)固定的內(nèi)，因此便能獲得最大動(dòng)力。 結(jié)果是每一個(gè)常規(guī)近正弦的發(fā)動(dòng)機(jī)改善了大約10%的效率(第二定律效率)。有限時(shí)間熱力學(xué)是引伸常規(guī)熱力學(xué)相關(guān)原則上橫跨主題的整個(gè)間距，從最抽象的水平到廣泛的應(yīng)用。 方法是根據(jù)廣義熱力學(xué)潛力的創(chuàng)立(1)為包含時(shí)間或?qū)υ谙拗浦械臈l件估計(jì)在系統(tǒng)之內(nèi)(2)和在產(chǎn)生對(duì)應(yīng)于那些廣義潛力的極值的最佳路徑的計(jì)算。迄今為止，有限時(shí)間熱力學(xué)的工作集中于較為理想化的模型(2-7)和存在性定理(2)，且全部集中在抽象方面。這項(xiàng)工作是希望作為一個(gè)步驟連接在實(shí)用的有限時(shí)間熱力學(xué)方面涌現(xiàn)了的抽象熱力學(xué)概念，工程學(xué)方面的課題，一臺(tái)實(shí)用機(jī)器的設(shè)計(jì)的原則。在這個(gè)報(bào)告中，我們用接近理想的奧多周期來(lái)研究?jī)?nèi)燃機(jī)模型，但由于頻率限制使得在實(shí)際的發(fā)動(dòng)機(jī)中是以二主要損失的形式存在。 我們通過(guò)“控制”時(shí)間改善活塞運(yùn)動(dòng)來(lái)優(yōu)化發(fā)動(dòng)機(jī)的性能。 結(jié)果，沒(méi)有進(jìn)行一項(xiàng)詳細(xì)的工程學(xué)研究，我們能夠通過(guò)受活塞的時(shí)間路徑的影響和優(yōu)化活塞行動(dòng)獲得效率的改善的估計(jì)來(lái)了解是怎么損失的。模 型我們的模型是基于標(biāo)準(zhǔn)的四沖程奧托循環(huán)。這包括進(jìn)氣沖程、壓縮沖程、作功沖程和排氣沖程。 我們?cè)谶@里簡(jiǎn)要地描述這個(gè)模型和發(fā)現(xiàn)優(yōu)化活塞行動(dòng)的使用方法及基本特點(diǎn)。 在別處將給一個(gè)詳細(xì)的介紹。我們假設(shè)，壓縮比、空燃比、燃油消耗率和時(shí)間全部是固定的。這些制約因素有兩個(gè)目的。首先，他們利用減少優(yōu)化問(wèn)題來(lái)找到活塞運(yùn)動(dòng)。 并且，他們保證在這分析沒(méi)考慮的性能準(zhǔn)則與那些是為一個(gè)實(shí)用的發(fā)動(dòng)機(jī)做比較的。 放松這些限制中的任一個(gè)可能進(jìn)一步改善性能。我們采取的損失是熱滲漏和摩擦。 這兩個(gè)是依靠效率來(lái)影響系統(tǒng)的時(shí)間反應(yīng)。 熱泄漏假設(shè)是圓筒的瞬間表面和與在工作流體和墻壁之間的溫差比例(即，牛頓熱耗)。 由于這個(gè)溫度區(qū)別最大是在作功沖程，熱滲漏是只包含在這個(gè)沖程中。摩擦力與活塞速度成正比，對(duì)應(yīng)于潤(rùn)滑良好的金屬表面；因此，摩擦損失也直接與速度正方形有關(guān)。 這些損失在所有沖程中是不同樣的。高壓在作功沖程使它的摩擦系數(shù)高于在其他沖程。 進(jìn)氣沖程得益于。我們優(yōu)選的作用是確定每循環(huán)的最大功率。 由于燃料消費(fèi)和周期是固定的，這也與最大化效率和平均功率是等效的。在尋找優(yōu)選的活塞行程時(shí)，我們首先分離了有能量和無(wú)能量的沖程。 非特指，但確定的時(shí)間 t 是指作功沖程中無(wú)能量沖程剩下的時(shí)間。 循環(huán)的兩個(gè)部分優(yōu)選以一個(gè)限制時(shí)間和然后結(jié)合找到每循環(huán)的總工作量。 時(shí)間 t的作功沖程后來(lái)變化了，并且這個(gè)過(guò)程會(huì)被重覆，直到凈工作量達(dá)到最大值。采取一個(gè)簡(jiǎn)單形式來(lái)描述無(wú)能量沖程的最佳活塞運(yùn)動(dòng)。在每個(gè)沖程的大多數(shù)時(shí)間，由于摩擦損失與速度的二次方成比例，最宜的運(yùn)動(dòng)依賴于速度常數(shù)。 在沖程的末期，活塞以允許的最大效率加速并且減速。 由于摩擦損失在進(jìn)氣沖程較高，與其他兩個(gè)相比，這個(gè)最佳的解決辦法是把更多的時(shí)間分配到這個(gè)沖程?；钊俣扰c作用時(shí)間的關(guān)系顯示在圖1中。由于熱泄漏的出現(xiàn)，作功沖程更難優(yōu)選。問(wèn)題是通過(guò)使用最優(yōu)控制理論的變化技術(shù)解決的 (8)。利用實(shí)際情況的非線性的微分方程產(chǎn)生活塞的運(yùn)動(dòng)方程式。 這些都是實(shí)際數(shù)值。整個(gè)循環(huán)運(yùn)動(dòng)的結(jié)果顯示在圖1上。 圖1 活塞速度與作用時(shí)間的關(guān)系，從作功沖程開(kāi)始。最大允許的加速度是2 x 104 m/sec2?；钊袆?dòng)的不對(duì)稱的形狀在作功沖程中的摩擦和熱泄漏損失之間交替出現(xiàn)。在沖程初氣體是熱的，能產(chǎn)生高效率，并且散熱率高。在作功沖程中得益于活塞速度高。這個(gè)沖程被選出，氣體冷卻率和熱泄漏相對(duì)于摩擦損失減少。 結(jié)果，當(dāng)作功沖程進(jìn)行時(shí)，最佳路徑的移動(dòng)速度更低。解決的辦法在加速度和上首先獲得了極大的加速度然后迅速減速。后者情況以“收費(fèi)公路”解決方案在其他環(huán)境下產(chǎn)生一個(gè)交叉結(jié)果 (9)。在這些速度之間以最高效率進(jìn)行加速和減速，使系統(tǒng)盡量的在它的最佳的向前和向后速度操作下盡可能延長(zhǎng)。 這樣，系統(tǒng)花費(fèi)同樣多時(shí)間盡可能沿它的最佳路徑移動(dòng)。結(jié) 果計(jì)算的參量從參考10中獲取，在給定的摩擦系數(shù)下，通過(guò)參考10中的變量調(diào)整摩擦損失的大小。 那些參量在表1中給出。一些典型的情況下的計(jì)算結(jié)果見(jiàn)表2，但在一個(gè)標(biāo)準(zhǔn)近正弦運(yùn)動(dòng)下，他們與常規(guī)奧托循環(huán)的發(fā)動(dòng)機(jī)相比有同一壓縮比。為了優(yōu)化發(fā)動(dòng)機(jī)使第一列的常規(guī)發(fā)動(dòng)機(jī)最大值，活塞加速度被限制在5 x 10 m3/sec2內(nèi)，使得有效利用率 (有用功與可逆功的比率，也稱第二定律效率)稍微提高。 如果發(fā)動(dòng)機(jī)的活塞允許有4個(gè)時(shí)間的加速度，有效率將增加9%；如果加速度是不受強(qiáng)制的，有效率比以前將增加11%。表1 發(fā)動(dòng)機(jī)參數(shù)*發(fā)動(dòng)機(jī)參數(shù)：壓縮比=8在最小容積的活塞位置=1厘米位移= 7 cm汽缸直徑(b) = 7.98 cm汽缸容量(v) = 400 cm3周期(t) = 33.3毫秒/3600轉(zhuǎn)每分鐘熱力學(xué)參量： 壓縮沖程 作功沖程最初的溫度 333K 2795K摩爾氣體 0.0144 0.0157恒定熱容量 容量 2.5R 3.35R汽缸壁溫度(T) = 600 K可逆循環(huán)的動(dòng)能 (WR)= 435.7 J 可逆的能力(WR/I)= 13.1千瓦損失條件：摩擦系數(shù)(a) = 12.9 kg/sec熱泄漏系數(shù)(K)= 1305 千克/ (度/sec3)每循環(huán)的時(shí)間損耗和摩擦損失的能量= 50 J *參量數(shù)據(jù)根據(jù)參考書(shū)目10.表2 結(jié)果(所有能量單位用焦耳)在作功沖程上所用的時(shí)間；WP在作功沖程完成的工作量；WT，每循環(huán)的凈工作量；WF，摩擦損失的能量；WQ，工作中的熱泄漏損失的能量； Q，熱泄漏；TF，作功沖程結(jié)束時(shí)的溫度；，有效利用率。這些改善是顯而易見(jiàn)的，但不是最有利的。如果傳統(tǒng)發(fā)動(dòng)機(jī)的總損失是保持大約固定的常數(shù)，但是減少高于80%的熱耗和低于60%的摩擦損失，有效利用率獲得提高，到達(dá)傳統(tǒng)發(fā)動(dòng)機(jī)有效利用率的17%以上。當(dāng)潤(rùn)滑油流過(guò)發(fā)動(dòng)機(jī)的最高溫度附近時(shí)，在這個(gè)分析過(guò)程中的改善的主要來(lái)源是熱耗的減少。 這就是為什么在較大的摩擦力下改善發(fā)動(dòng)機(jī)的熱泄漏和降低摩擦損失比發(fā)動(dòng)機(jī)使用更好的絕緣材料要好，。最后，在相應(yīng)時(shí)間內(nèi)為優(yōu)化發(fā)動(dòng)機(jī)和為它的傳統(tǒng)對(duì)應(yīng)部分，它是指導(dǎo)研究活塞運(yùn)動(dòng)的最佳路徑的方法?；钊奈恢煤妥饔脮r(shí)間的關(guān)系顯示在圖2上在結(jié)束時(shí)，讓我們強(qiáng)調(diào)在這工作中說(shuō)明了一個(gè)熱力學(xué)的系統(tǒng)非傳統(tǒng)的優(yōu)化被方法。而不是控制熱效率、熱容量、傳熱、摩擦系數(shù)、冷卻水溫度，或者熱力發(fā)動(dòng)機(jī)的其他通常參量，我們控制了發(fā)動(dòng)機(jī)容量時(shí)間路徑。我們感謝Morton Rubin博士為我們做到有用的評(píng)論和建議。 我們的部分經(jīng)費(fèi)由Exxon 教育基金提供。 圖2 在作功、排氣、進(jìn)氣和壓縮沖程中優(yōu)化的()和傳統(tǒng)的()活塞運(yùn)動(dòng)比較； 最佳路徑的最大加速度被限制在2 x 104 m3/sec2參考文獻(xiàn)1. Hermann, R. (1973) Geonetry, Physics and Systems (Dekker,New York). Proc. Nati. Acad. Sci. USA 78 (1981)2. Salamon, P., Andresen, B. & Berry, R. S. (1977) Phys. Rev. A 14,2094-2102.3. Curzon, F. L. & Ahlborn, B. (1975) Am. J. Phys. 43, 22-24.4. Andresen, B., Berry, R. S., Nitzan, A. & Salamon, P. (1977)Phys. Rev. A 15, 2086-2093.5. Rubin, M. (1979) Phys. Rev. A 19, 1272-1276, 1277-1289.6. Salamon, P., Nitzan, A., Andresen, B. & Berry, R. S. (1980)Phys. Rev. A 21, 2115-2129.7. Gutkowicz-Krusin, D., Procaccia, I. & Ross, J. (1978) J. Chem. Phys. 69, 3898-3906.8. Hadley, C.F.G. & Kemp, M. C. (1971) Variational Methods in Economics (North-Holland, Amsterdam).9. Sen, A., ed. (1970) Growth Economics (Penguin, Baltimore,MD).10. Taylor, C. F. (1966) The Internal Combustion Engine in Theory and Practice (MIT Press, Cambridge, MA), Vol. 1, pp. 158-164; Vol. 2, pp. 19-20.