CARNOT CYCLE WITH EXTERNAL AND INTERNAL IRREVERSIBILITIES ANALYZED IN THERMODYNAMICS WITH FINITE SPEED WITH THE DIRECT METHOD

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1 Stoian PERESCU, Charles ARMAN, Adrian BEJAN, Monica COSEA, Catalina DOBRE CARNO CYCLE WI EERNAL AND INERNAL IRREVERSIBILIIES ANALYZED IN ERMODYNAMICS WI FINIE SPEED WI E DIREC MEOD Stoian PERESCU, Charles ARMAN, Adrian BEJAN, Monica COSEA, Catalina DOBRE UNIVERSIY POLIENICA OF BUCARES, DEPARMEN OF ENGINEERING ERMODYNAMICS DUKE UNIVERSIY, DEPARMEN OF MECANICAL ENGINEERING, DURAM, U.S.A. Rezumat. Se analizează un ciclu Carnot direct cu ireversibilităţi externe (datorate diferenţelor de temperaturi la surse), cât şi cu ireversibilităţi interne (datorate vitezei finite). Ciclul ireversibil Carnot este reprezentat într-o diagramă -S originală, unde se evidenţiază lucrul mecanic pierdut (exergia) din cauza diverselor ireversibilităţi, generate în timpul funcţionării maşinii cu viteză finită. Se dezvoltă o metodă de calcul analitic (numită Metoda Directă din ermodinamica cu Viteză Finită) cu ajutorul căreia se evidenţiază efectul pe care îl are viteza pistonului în cadrul ireversibilităţilor interne, asupra performanţelor maşinii (randament şi putere, exprimate analitic ca funcţie de viteză). Se prezintă un exemplu de rezultate pentru o serie de valori ale vitezei unui ciclu Carnot, caracterizat de o temperatură ridicată, la sursa caldă ( K). Se determină expresia analitică a temperaturii optime necesare obţinerii unui randament maxim al ciclului Carnot, în funcţie de viteza pistonului. Exemplul este dezvoltat şi în scopul determinării unei temperaturi optime, necesare obţinerii unei puteri maxime a ciclului Carnot, într-un anumit interval de valori ale vitezei pistonului. Cuvinte-cheie: ciclu Carnot ireversibil, ireversibilităţi interne şi externe, ermodicnamica cu Viteză Finită, optimizarea temperaturii, optimizarea vitezei, generarea entropiei, randamentul ireversibilităţii, Metoda Directă. Abstract. A Carnot engine operating on a closed cycle and having both external and internal irreversibilities is analyzed. he internal irreversibilities are caused by losses generate by finite piston speed and the external irreversibilities are caused by heat transfer through a temperature difference. he irreversible Carnot cycle is displayed on a original -S property coordinates in a manner that accurately illustrates the lost ork (Exergy losses) due to the irreversibilities (internal and external). A method for calculating the effect of the piston speed on the internal irreversibilities of Carnot cycle is developed and an example of the results is shon for a range of values of cycle high temperature ( K). Using the results of this example, the optimal Carnot engine efficiency is determined as a function of piston speed. he example is extended to include the determination of the optimal system temperature for Maximum Carnot engine poer over a range of piston speeds. Keyords: irreversible Carnot cycle, internal and external irreversibilities, Finite Speed hermodynamics, temperature optimization, speed optimization, entropy generation, Second La Efficiency, Direct Method.. INRODUCION Much has been ritten about the Carnot cycle, both ith and ithout external irreversibilities [- 5]. oever, only in the 9s attention focused on analysis of the Carnot cycle that also includes internal irreversibilities [6-8]. In 99 an extremely important paper [9] has been presented at Florence World Energy Research Symposium, Energy for the st Century: Conversion, Utilization and Environmental Quality, Firenze, Italy. hat paper had a very important role in the development of hermodynamics ith Finite Speed (FS) and the Direct Method, for analytical evaluation of the performances of irreversible cycles ith internal and external irrevesibilities. hat paper as based on a previous one [8], hich actually opened a series of papers [-] regarding the analysis of irreversible Carnot cycle ith finite speed, hich contributed essentially to the development of hermodynamics ith Finite Speed and the Direct Method [-] up to the maximum performance of it - hich is the validation for Stiling engines operating in 6 regimes []. he present analysis is based on papers [8] and [9]. ere e ant to sho the impact they had on the development of Engineering Irreversible hermodynamics hich today goes in the direction of unification of hermodynamics in Finite ime ith hermodynamic ith Finite Speed []. ERMOENICA / 7

2 CARNO CYCLE WI EERNAL AND INERNAL IRREVERSIBILIIES ANALYZED IN ERMODYNAMICS he Carnot cycle ith no internal or external irreversibilities is shon on temperature - entropy (-S) coordinates in Figure as the area bounded by the path here the temperature of the heat source is and the temperature of the heat sink is C. C C Fig.. Carnot Cycle ith External Irreversibilities (Endoreversible). Superimposed on this diagram is a Carnot cycle operating beteen the same heat source and sink temperatures but ith external irreversibilities. his externally irreversible Carnot cycle is bounded by the path he crosshatched area bounded by the path is proportional to the lost available ork in the process of the heat transfer through the finite temperature difference C. oever, the crosshatched area bounded by the path in this diagram does not directly represent the lost available ork in the heat transfer K Q Q S Q Q Q Q through the finite temperature difference. his is a shortcoming of presenting the processes as shon in Fig... AN EERGEICAL CORREC -S DIAGRAM he lost available ork in a process may also be termed, by definition, the lost exergy. Fig. shos an internally reversible but externally irreversible Carnot cycle that receives heat Q from a source at temperature. he heat is transferred through a finite temperature difference to the temperature of the orking fluid of the cycle,, g. his irreversible heat transfer causes an entropy increase of the cycle fluid S -S. he area bounded by c---b-c is proportional to the total heat transfer and, since no loss of energy is assumed, this area must equal the area bounded by c- - -a-c. Since the area c- - -b-c is contained in both these area, the net areas and b- - -a-b must be equal. Stated differently, S and the available ork lost in, g S the heat transfer process, Q Q is converted to heat Q. his is the lost ork generated by the external irreversibility of the heat transfer through a temperature difference. A -S diagram presented as in Fig. shos the losses in direct proportion, alloing for a more accurate assessment of their relative importance. W LOS APPARENLY W COMMON O BO CYCLES Q Q WPRODUCED IN REVERSIBLE CYCLE E NEW CYCLEIREEVERSIBLE ANERGY Q L Q,g Q L Q L irr Q Q L L LOS IN E NEW CYCLE Q Q Q Q Q L L Q c b a S S S S S S J/ K Fig.. Internally Reversible Carnot Cycle ith External Irreversibilities. 8 ERMOENICA /

3 Stoian PERESCU, Charles ARMAN, Adrian BEJAN, Monica COSEA, Catalina DOBRE he -S diagram of Fig. is scaled to provide a numerical example. In this example,. units of heat are supplied by the source at the temperature of K. he engine receives this heat at 9K and rejects heat to sink at K. he entropy decrease of the source can be seen to be units/k and the entropy increase during the heat addition process in he Carnot cycle is. units/9 K or. units/k. he external irreversibility is then. units/k. he external irreversibility is shon to produce S K. units/k 666 units of anergy A Carnot cycle engine may operate ith external irreversibilities in both the heat addition and the heat rejection processes and, in addition, may have internal irreversibility during the adiabatic expansion process. he -S diagram for a cycle operating ith these irreversibilities is shon in Fig.. he cycle shon in this diagram has the same amount of heat transferred from the source as given in Fig.. oever, the cycle is altered to include a lo temperature of K for the cycle fluid and the area resulting from the loss due to the heat transfer through a temperature difference of K to the K sink temperature, irr C is shon. his area, -- -e- is small compared ith the area representing the loss due to heat transfer to the system because of the relatively small temperature difference through hich the heat is transferred. Nevertheless, these temperature differences provide a realistic comparison in practical application such as, for example, a vapor cycle receiving heat from combustion gases and rejecting heat in a condenser that uses cooling ater from the environment. he effect of the internal irreversibility during the adiabatic expansion process is shon in Fig. ith the expansion end point at. he adiabatic irreversibility causes an increase in entropy and produces the anergy ad.irr. exp, shon as the area bounded by a-e-f-d-a in Fig.. An area equivalent to area could be plotted as the area bounded by ad.irr.exp in Fig.. his clearly illustrates the loss of ork due to the irreversible adiabatic expansion relative to the net remaining ork. he -S diagram is scaled to illustrate the loss due to irreversible heat transfer from the cold temperature of the cycle C to the sink temperature. he loss = C - S ac.5 5 units of anergy. irr K Q Q c Q Q W Q AnQ lost W irr.ext., C W irr.ext int irr. C irr b Wlost Q irr e K Vapor temperature,g Adiabatic irreversible expansion f eat source temperature Vapor temperature C,g C K Water temperature ad.irr.exp Fig.. Externally and internally irreversible Carnot cycle. a S J K ERMOENICA / 9

4 CARNO CYCLE WI EERNAL AND INERNAL IRREVERSIBILIIES ANALYZED IN ERMODYNAMICS Likeise the loss in the irreversible adiabatic expansion for an adiabatic efficiency of 9 percent is C - S ad.5 5 units of anergy. he irreversible adiabatic compression is not shon in Fig. in the interest of diagram simplicity and because it parallels the analysis for an irreversible adiabatic expansion. For example, an adiabatic compression efficiency of 9 percent ould also result in an entropy increase of.5 units and a 5 units increase in anergy.. OPIMISAION ANALYSIS FOR A CARNO ENGINE WI INERNAL AND EERNAL IRREVERSIBILIIES A closed cycle Carnot engine is modeled analytically and is shon -S coordinates in Fig.. he engine has external irreversibility due to heat transfer from the source at fixed temperature,, to the cycle high temperature,, during the isothermal heat addition process -. It has internal irreversibilities due to finite piston speed during only the adiabatic compression and expansion processes. he sink temperature and the cycle lo temperature are the same. his temperature,, is fixed but the cycle high temperature, is a variable parameter. he irreversible adiabatic compression and expansion processes are modeled using an expression for the first la of thermodynamics for processes at finite speed [9-6]: a du δqirr pi dv () c a ith: the contribution of finite speed ( a k ; c c R ); p i instantaneous average pressure. he equations for adiabatic irreversible processes of ideal gases ith constant specific heat are obtained upon setting δq equal to zero in eq. () and integrating [5, 6-]: a k a k c c V V From this equation could be expressed as: () a k k c V V irr () a V V c For a compression process ith finite speed c, e could express irr. cpr as folloing: or more simple: a c a a a c irr.cpr c c a a a irr.cpr c c cc () (5) In the case a cc the last term could be neglected in comparison to the others, so: a a irr.cpr c c (6) but: c R and c R. With a first approximation for from adiabatic reversible compression e get:, e get a first approxi- Introducing c in mation for it: irr.cpr k V V c V V k V R c V irr. cpr k (7) k a a V c c V (8) For a better approximation e can no compute from the equation of irreversible adiabatic compression: k V irr.cpr (9) V k V irr.cpr V c R R () Introducing no the value c from eq. () in eq. (6) e get a better approximation for irr. cpr : a irr.cpr c c V here is given by eq. (8). irr. cpr k a V irr.cpr () No e ill use this result for computation of entropy variation in the case of an adiabatic irreversible process of compression ith finite ERMOENICA /

5 Stoian PERESCU, Charles ARMAN, Adrian BEJAN, Monica COSEA, Catalina DOBRE speed. Because entropy is a function of state only, e can express it ith the ell knon formula: f Vf S Sf Si mcvln mrln i Vi () From eq. (): k V irr V () R With () in () and knoing that c v k for perfect gas: k R V V Sirr mcvlnirr m ln mrln k V V he last to terms ill be cancelled, and e get finally: S ln () irr mc v In this expression e can use either eq. () or eq. (8), depending of the degree of approximation e need. So, in a first approximation, ith irr from eq. (8), e get: k. ln a a V S irr cpr mcv (5) c c V In a similar manner e can sho that for an adiabatic and irreversible expansion is: and: irr irr. exp k a a V irr.exp c c V k a a V Sirr.exp mcvln c c V (7) (6) We no could combine the eq. (5) and eq. (7) in the folloing form: k a a V Sad.irr mcvln c c V (8) here the upper sign indicates compression and the loer sign indicates expansion. For the compression process -, eq. (8) becomes: k acpr acpr V Sad.irr.cpr mcvln c c V S S mc ln (9) ad.irr.cpr v And for the expansion process -, eq. (8) becomes: k aexp aexp V Sad.irr.exp mcvln c c V S S mc ln () ad.irr.exp v For the isothermal process -, eq. () becomes: S S S mrln p () p he actual thermal efficiency of a Carnot cycle engine ith irreversibilities is: C C act Q S Q S S S S S () Upon substitution of the expression for the entropy changes from eq. (9), () and () and noting the R cv / k, the efficiency of the irreversible Carnot cycle shon in Fig. becomes: ln act p k ln () p When the piston speed is much less than the speed of sound in the gas or hen acpr c and aexp c eq. () may be simplified to: act p k ln () p acpr ith: c and: aexp. c When the piston speed during compression and expansion is the same, eq. () simplifies to: a act (5) c p k ln p ERMOENICA /

6 CARNO CYCLE WI EERNAL AND INERNAL IRREVERSIBILIIES ANALYZED IN ERMODYNAMICS he actual rate of doing ork or poer output of the cycle, assuming that heat transfer is generated by a finite, is: act act act W Q KA (6) here: K is the overall heat transfer coefficient and A is the heat transfer area. he folloing terms are defined: Non dimensional poer: P W Carnot reversible efficiency: act ND (7) KA CC and an irreversibility coefficient: here: C IIad.irr a C p c kln p (8) (9) () Upon substitution eqs. (5), (6), (8)-(9) into eq. (7) one gets: ND CC IIad.irr P Equation () may also be ritten: here: P ND () C () (). RESULS OF OPIMISAION OF AN IRREVERSIBLE CARNO CYCLE ENGINE he non-dimensional poer ill be optimized using the results of the above analysis applied to a Carnot engine operating on the cycle shon in Fig.. he irreversibility coefficient, II for a given cycle fluid, depends only on the cycle high temperature,, and the piston speed,. Its value has been determined using air as the cycle fluid and the results are plotted in Fig. 5 over a range in from K to K and for from to 5 m/s. K Q Q ab a b Q Qab KA Q Fig.. Internal ireversibilities. ir. cpr ir.exp his figure shos that the irreversibility coefficient decreases ith increased piston speed, as expected, and that the irreversibility coeficient decreases more rapidly ith piston speed at loer cycle high temperatures. he internal irreversibilities are shon to be more important hen the irreversible cycle efficiency is loer. Fig. 5. he influence of the piston speed and the temperature on the irreversible coefficient. he non-dimensional poer as determined from eq. () is shon in Fig. 6 as a function of the cycle high temperature and piston speed. he reversible Carnot efficiency is shon for comparison purposes. he non-dimensional poer is seen to have a maximum value for any fixed piston speed or internal irreversibility and this maximum occurs at increasingly higher temperatures as the piston speed or internal irreversibility increases. S ERMOENICA /

7 Stoian PERESCU, Charles ARMAN, Adrian BEJAN, Monica COSEA, Catalina DOBRE herefore, as a first approximation, in eq. () is assumed constant in seeking an analytic expression for the optimum temperature to maximize the nondimensional poer. his approach is necessary because the maximization equation for P ND using eq. (7) is analytically intractable. Ibrahim [6] has shon that ith constant, the value of that maximizes the poer expressed by eq. () is: Fig. 6. he non-dimensional poer as a function of the cycle high temperature and piston speed. Also, these maximum values decrease ith increased piston speed. he optimum temperature,, is shon in Fig. 7 as a function of piston speed. opt opt () Although this is a simple expression, the value of is not knon. oever, an iterative method is available to approximate the value of opt. he value of opt is approximated by first considering the case here the speed is zero ( = ). When =, from eq. () and the cycle is internally reversible and externally irreversible. his reduces equation () to: opt (5) If equation (5) is substituted into eq. (), the result, after re-arrangement of terms, is: Fig. 7. he effect of piston speed on optimum temperature. he parameter is shon as a function of and in Fig. 8. he value of is seen to change little in the region of optimal temperatures (from 8 K to K). Fig. 8. he influence of and piston speed on parameter. C (6) Upon substitution of eq. (6) in the expression from eq. () one gets: of opt C ( ) opt (7) his ne optimum value of the temperature is the first approximation of the temperature to maximize the non-dimensional poer hen the piston speed is not zero and hen therefore both internal and external irreversibilities are accounted for. Values of opt ere obtained graphically as illustrated in Fig. 9. Comparison of the results of the to methods shos good agreement and lends confidence that a first iteration provides sufficiently accurate results for most purposes. oever, it is possible to improve the accuracy of the results by making a second iteration. An improved approximation can be made by using the value of opt, as obtained by means of eq. (7), instead of in eq. (). ERMOENICA /

8 CARNO CYCLE WI EERNAL AND INERNAL IRREVERSIBILIIES ANALYZED IN ERMODYNAMICS act C Eq. () after rearrangement: () Fig. 9. Graphical determination of optimal temperature. When this is done eq. () becomes: C ( ) opt (8) Eq. (8) can be rearranged to have the folloing form: C (9) When the effect of piston speed is included, eq. () becomes: opt( ) () Substitution of eq. (9) into eq. () results in a more accurate approximation of the value of opt,. Further refinement to increase accuracy beyond this second approximation is possible but is unlikely to be arranted in most applications. he maximized poer can no be calculated for the internally irreversible Carnot engine ith. It is evaluated using eq. (7) or eq. () opt( ) and substituted for in eq. (). he results in terms of the non-dimensional poer is: P opt opt ND,max () Similarly, the efficiency of the Carnot cycle may be calculated by substituting opt( ) from eq. () into eq. (5), resulting in: act C () he efficiency of an internally reversible, externally irreversible Carnot cycle is (Curzon-Ahlborn [] expression): CA () his occurs hen no internal irreversibility due to the piston speed ( = ) exists and, therefore. When internal irreversibility exists, piston speed, eq. () may be modified as follos: act (5) here and depends on the piston speed. Noting eq. () and eq. (5) C (6) 5. E IMPAC OF E CARNO CYCLE WI EERNAL AND INERNAL IRREVERSIBILIIES ANALISYS ON E DEVELOPMEN OF ERMODYNAMICS WI FINIE SPEED AND E DIREC MEOD, AND ENDENCY OF UNIFICAION BEWEEN F AND FS A recent book [] explains the origins of paper [9], its impact on the Development of hermodynamics ith Finite Speed and the present tendency of unification beteen hermodynamics ith Finite ime and hermodynamics ith Finite Speed. he ork on paper [9] as the beginning of cooperation ith Charles arman for years. e contributed in so many papers and books published together ith many co-orkers (from Romania: G. Stanescu, M. Costea,. Florea, C. Petre, O. Malancioiu, G. Popescu, N. Boriaru, V. Petrescu, and from France: M. Feidt) to the Development of hermodynamics ith Finite Speed and the Direct Method [-]. ERMOENICA /

9 Stoian PERESCU, Charles ARMAN, Adrian BEJAN, Monica COSEA, Catalina DOBRE Actually, the year marked 5 years from the beginning of hermodynamics ith Finite Speed (FS), in hich the Direct Method as invented [-] and then validated [, ]. Everybody entering in this field of research is asking: hat is it the Direct Method, ho to use it and hat do e get from it? A very synthetic anser is: e get analytical expressions for Efficiency and Poer (as function of speed), hich are of course very useful for Optimization and better Design of hermal Machines. Getting such ne tools for better design as and should be the main objective of any ne branch of Irreversible hermodynamics. As the present analysis has shon, the first step of the unification of F and FS process already started [9] ith the correction of the famous formula of Curzon-Ahlborn, here the nice radical appears in the Carnot Cycle Efficiency like in eq. (), ith the optimum temperature of the gas, eq. (). As it is very ell knon, these formulas take into account only external irrevesibilities. Based on the Fundamental Equation of FS First La for Processes ith Finite Speed analytical corrections in these formulas, taking into account internal irreversibilities generated by the Finite Speed of the piston,, in addition to the external ones ere made here, obtaining the folloing equations: for Carnot Efficiency ith external and internal ireversibilities generated by finite speed, eq. (5). for optimum temperature, here the internal irreversibility, generated by finite speed is taken into account, in adition to the external irreversibilities, eq. (7). A second step of the unification process [, ], did a comparison beteen FS and F approaches of a Carnot cycle emphasizing that FS can take into account both irrevesibilities, using its fundamental equations and the Direct Method. ence, the critics of Gyftopulous [5] and Moran [6, 7] ill not apply to any papers in FS here e did take into account both internal and external irreversibilities. More recently the unification beteen FS and F continued ith 5 very important papers for this process and also for recognition of the Direct Method from FS Poer [6-]. In these ne developments, the equation of the First La for Processes ith Finite Speed, (from FS), together ith the Direct Method play an essential role, and they are the success guaranty, because only starting ith fundamentals (understanding irreversibility mechanisms), and expressing them quantitatively in fundamental equations can finally conduct to validation. Also, the large applicability field of FS and the Direct Method, from the classical Stirling engines [,, 8, 9, 5, 5], solar Stirling motors [5, 5, 5, 56, 58], Stirling refrigeration and Stirling heat pumps [], to Otto cycle [8], Diesel Cycle [9], Carnot direct cycle [9,,,, 8], Carnot refrigeration cycle [9], Otto-Stirling hybrid cycle [55, 57, 58] and Brayton cycle as emphasized [6-]. For of the most performing Stirling engines (orking in 6 operating regimes) [], for 5 (the most performing) solar Stirling motors [5, 5, 56] and for a refrigeration Stirling machine [59, 6] the computation schemes developed based on the Direct Method ere validated. We hope that hermodynamics ith Finite Speed is an important step toard the development of a more poerful Engineering Irreversible hermodynamics, hich could be a synthesis (or unification ) beteen hermodynamics ith Finite Speed and hermodynamics in Finite ime. 6. CONCLUSIONS Analysis and optimization approach of an irreversible Carnot engine operating on a closed cycle have been presented. Equations have been developed for the internally and externally irreversible Carnot cycle. he internal irreversibility has been related to finite piston speed. he Curzon-Ahlborn expression for the externally irreversible Carnot cycle as modified in order to include also internal irreversibility. Equations for the optimum cycle temperature, maximum poer, and efficiency for the internally and externally irreversible cycle are presented. he corrections are shon to increase ith increased piston speed and to be significant at high but realizable piston speeds. he optimum temperature corresponding to maximum poer is shon to increase ith increased piston speed. he impact of these achievements on the Development of hermodynamics ith Finite Speed and on the present tendency of unification beteen hermodynamics ith Finite ime and hermodynamics ith Finite Speed is discussed. NOMENCLAURE A Area [m ] a Coefficient c Average molecular speed [m s - ] c v Specific heat at V = ct [J kg - s - ] K Overall heat transfer coefficient [W m - K - ] k Ratio of the specific heats m Mass [kg] p Pressure [Pa] Q eat [J] R Gas constant [J kg - K - ] S Entropy [J K - ] emperature [K] FS hermodynamics ith Finite Speed ERMOENICA / 5

10 CARNO CYCLE WI EERNAL AND INERNAL IRREVERSIBILIIES ANALYZED IN ERMODYNAMICS F hermodynamics ith Finite ime U Internal energy [J] V Volume [m ] W Work [J] W Poer output [W] Piston speed [m s - ] Subscripts act Actual ad Adiabatic cpr Compression C Cold CA Curzon-Ahlborn exp Expansion Related to the source,g, Related to the gas at the source REFERENCES irr Irreversible ND Non-dimensional opt Optimum Due to the piston speed Related to the gas at the source Ambient. Novikov, I.I., he Efficiency of Atomic Poer Stations (A Revie), J. Nuclear Energy II, Vol. 7, Pergamon Press Ltd., London, pp. 5-8, Curzon, F. L., B. Ahlborn, Efficency of a Carnot Engine at Maximum Poer Output, Am. J. Phys., Vol., pp.-, Andresen, B., Finite-ime hermodynamics, Physics Laboratory II, University of Copenhagen, 98.. Bejan, A., Advanced Engineering hermodynamics, Wiley, Ne York, Feidt, M., hermodynamique et Optimisation Energetique des Systèmes et Procédés, echnique et Documentation, nd edition, Lavoisier, Paris, Ibrahim, O.M., Klein, S.A., Mitchell, J.W., Economic Evaluation of the Maximum Poer Efficiency Concept, ASME Winter Annual Meeting, Atlanta, Georgia, USA, Dec. -6, 99., and in: J. of Engineering Gas urbine Poer, 5, Lampinnen, M., Vuorisalo, J., eat Accumulation Function and Optimization of eat Engines, J. Appl. Phys., 69 (), Petrescu, S., Stanescu, G., Costea, M., he Study for Optimization of the Carnot Cycle hich develops ith finite Speed, Proc. of International Conference on Energy Systems and Ecology, ENSEC 9, Craco, Poland, ed. by J. Szargut, Z. Kolenda, G. satsaronis and A. Ziebik, Vol., pp , Petrescu, S., arman, C., Bejan, A., he Carnot Cycle ith External and Internal Irreversibilities, Florence World Energy Research Symposium, Energy for he st Century: Conversion, Utilization and Environmental Quality, Firenze, Italy, July 6-8, 99.. Petrescu, S., Costea, M., Feidt, M., Optimization of a Carnot Cycle Engine using Finite Speed hermodynamics and the Direct Method, Proc. of the Inter. Conf. on Efficiency, Costs, Optimization, Simulation and Environmental Impact of Energy Systems, ECOS, edited by A. Öztürk and Y. A. Gögüs, Istanbul, urkey, Vol. I, pp. 5-6,.. Petrescu, S., Feidt, M., arman, C., Costea, M., Optimization of the Irreversible Carnot Cycle Engine for Maximum Efficiency and Maximum Poer through Use of Finite Speed hermodynamic Analysis, ECOS Conference, Ed. by G. satsaronis et al., Berlin, Germany, Vol. II, pp. 6-68,.. Petrescu, S., arman, C., Costea, M., Feidt, M., hermodynamics ith Finite Speed versus hermodynamics in Finite ime in the Optimization of Carnot Cycle. Proc. of the 6-th ASME-JSME hermal Engineering Joint Conference, aaii, USA, March 6-,.. Petrescu, S., arman, C., Costea, M., Feidt, M., Petre, C., Optimization and Entropy Generaton Calculation for hermodynamic Cycles ith Irreversibility due to Finite Speed, Proceedings of the 8 th International Conference on Efficiency, Cost, Optimization, Simulation and Enviromental Impact of Energy Systems, ECOS5, rondheim, Noray, Vol. II, p , 5.. Petre, C., (Advisers: S. Petrescu, M. Feidt, A. Dobrovicescu), Utilizarea ermodinamicii cu Viteza Finita in Studiul si Optimizarea ciclului Carnot si a Masinilor Stirling, PhD hesis, University Politehnica of Bucharest and University. Poincaré of Nancy, Petrescu, S., arman, C., Petre, C., Costea, M., Feidt, M. Irreversibility Generation Analysis of Reversed Cycle Carnot Machine by using the Finite Speed hermodynamics. Rev. ermotehnica, Ed. AGIR, Anul III, Nr., Romania, -8, Feng,.J., Chen, L.G., Sun, F.R., Optimal ratios of the piston speeds for a finite speed endoreversible Carnot heat engine cycle. Revista Mexicana de Fisica, 56(), pp. 5-,. 7. Feng,.J., Chen, L.G., Sun, F.R., Optimal ratio of the piston for a finite speed irreversible Carnot heat engine cycle, International Journal of Sustainable Energy, (6), pp. -5,. 8. Feng,.J., Chen, L.G., Sun, F.R., Effects of unequal finite speed on the optimal performance of endoreversible Carnot refrigeration and heat pump cycles, Int. Journal of Sustainable Energy, (5), pp. 89-,. 9. Chen, L.G., Feng,.J., Sun, F.R., Optimal piston speed ratios for irreversible Carnot refrigerator and heat pump using finite time thermodynamics, finite speed thermodynamics and the direct method, Journal of Energy Institute, 8(), pp. 5-,.. Bo Yang, Chen, L.G., Sun, F.R., Performance analysis and optimization for an endoreversible Carnot heat pump cycle ith finite speed of piston, Int. Journal of Energy Environment,.. Petrescu, S., arman, C., Costea, M., Florea,., Petre, C., Advanced Energy Conversion, Bucknell University, Leisburg, Pennsylvania, USA, 6.. Petrescu, S., ratat de Inginerie ermica. Principiile ermodinamicii. (reatise on Engineering hermodynamics. he Principles of hermodynamics), Ed. AGIR, Bucuresti, Romania, 7.. Petrescu, S., Costea, M., et al., Development of hermodynamics ith Finite Speed and Direct Method, Ed. AGIR, Bucuresti,.. Petrescu, S., Contributions to the study of interactions and processes of non-equilibrium in thermal machines, Ph.D hesis, Polytechnic Institute of Bucharest, Romania, Petrescu, S., Petrescu, V., he Principles of hermodynamics, Ed. ehnica, Bucharest, Romania, Petrescu, S., Lectures on Ne Sources of Energy, elsinki University of echnology, Otaniemi, Finland, Petrescu, S., Petrescu, V., Methods and Models in Engineering hermodynamics, Editura ehnica, Bucharest, Romania, Petrescu, S. Iordache, R., Stanescu, G., Dobrovicescu, A., he First La of hermodynamics for Closed Systems, Considering the Irreversibilities Generates by Friction Piston-Cylinder, the hrottling of the Working Medium and the Finite Speed of Mechanical Interaction, ECOS 9, Zaragoza, Spain, June 5-9, Stoicescu, L., Petrescu, S., hermodynamic State ransformations Developing ith finite constant Speed, Polytechnic Institute of Bucharest Bulletin, Vol. VI, Nr. 6, Romania, 96.. Stoicescu, L., Petrescu, S. hermodynamic State ransformations Developing ith Finite Variable Speed, 6 ERMOENICA /

11 Stoian PERESCU, Charles ARMAN, Adrian BEJAN, Monica COSEA, Catalina DOBRE Polytechnic Institute of Bucharest Bulletin, Vol. VII, Nr., Romania, Petrescu, S. Costea, M., arman, C., Florea,., Application of the Direct Method to Irreversible Stirling Cycles ith Finite Speed, International Journal of Energy Research, Vol. 6, pp ,.. Petrescu, S., Costea, M., irca-dragomirescu, G., Dobre, C., Validation of the Direct Method and its applications in the optimized Design of the hermal Machines for the increase of the Efficiency,8-9 Aug, ASR Conference, Craiova, Romania,.. Stoicescu, L. Petrescu, S., he First La of hermodynamics for echnical Processes ith Finite Constant Speed in Closed Systems, Polytechnical Institute of Bucharest Bulletin, Vol. VI, 5/96, Romania, 96.. Petrescu, C., arman, C., Petre, C., Costea, M., Feidt, M., Irreversibility Generation Analysis of Reversible Cycle Carnot Machine by using the Finite Speed hermodynamics, Revista ermotehnica, AGIR, Bucuresti, Romania, (), -8, Petrescu, S., arman, C., he Connection beteen the First and Second La of hermodynamics for Processes ith Finite Speed. A Direct Method for Approaching and Optimization of Irreversible Processes, Journal of the eat ransfer Society of Japan, Vol., No. 8, Petrescu, S., arman, C., Costea, M., Petre, C., Dobre C., Irreversible Finite Speed hermodynamics (FS) in Simple Closed Systems. I. Fundamental Concepts, Revista ermotehnica, Editura AGIR, Bucuresti, Romania,, pp. 8-8, Stoicescu, L., Petrescu, S., hermodynamic Cycles ith Finite Speed, Bulletin I.P.B., Bucharest, Romania, Vol. VII, No., pp. 8-95, Petrescu, S., Cristea, A. F., Boriaru, N., Costea, M., Petre, C., Optimization of the Irreversible Otto Cycle using Finite Speed hermodynamics and the Direct Method, Proc. of the th WSEAS Int. Conf. on Mathematical and Computational Methods in Science and Engineering (MACMESE8), Computers and Simulation in Modern Science, Bucureşti, Ed. N. Mastorakis, Vol II, p.5-56, 7-9 Noiembrie Romania, Petrescu, S., Boriaru, N., Costea, M., Petre, C., Stefan, A., Irimia, C., Optimization of the Irreversible Diesel Cycle using Finite Speed hermodynamics and the Direct Method, Bulletin of the ransilvania University of Braşov, Vol. (5) Series I, No., Ed. Univ. ransilvania, pp. 87-9, 9.. Petrescu, S., Zaiser, J., Petrescu, V., Lectures on Advanced Energy Conversion-Vol. II, course: MEC-, Bucknell University, Leisburg, PA-787, USA, pp. 8, Petrescu, S., Zaiser, J., Petrescu, V., Advanced Energy Conversion-Vol. I, course MEC-, Bucknell University, Leisburg, PA-787, USA, pp. 96, January Petrescu, S., Stanescu, G., he Direct Method for studding the irreversible processes undergoing ith finite speed in closed systems, ermotehnica, No., Editura ehnica, Bucharest, 99.. Petrescu, S., Stanescu, G., Petrescu, V., Costea, M., A Direct Method for the Optimization of Irreversible Cycles using a Ne Expression for the First La of hermodynamics for Processes ith Finite Speed, Proc. of the st Conference on Energy IEC9, Marrakesh, Morocco, pp , 99.. Petrescu, S., Petrescu, V., Stanescu, G., Costea, M., A Comparison beteen Optimization of hermal Machines and Fuel Cells based on Ne Expression of the First La of hermodynamics for Processes ith Finite Speed, Proc. of the st Conference on Energy IEC 9, Marrakesh, Morocco, pp , Gyftopulous, E.P., Fundamentals of analysis of processes, Energy Conversion & Management, Vol. 8, pp. 55-5, Moran, M.J., A Critique of Finite ime hermodynamics, Proc. of ECOS 98, Nancy, France, edited by A. Bejan, M. Feidt, M.J. Moran and G. satsaronis, Nancy, France, pp. 7-5, Moran, M.J., On Second La Analysis and the failed promises of Finite ime hermodynamics, Energy,, pp , Stanescu, G., (Adviser: S. Petrescu), he study of the mechanism of irreversibility generation in order to improve the performances of thermal machines and devices, Ph. D. hesis, U.P.B., Bucharest, Petrescu, S., arman, C., Petrescu, V., Stirling Cycle Optimization Including the Effects of Finite Speed Operation, Proc. of ECOS 96, Stockholm, Seden, ed. P. Alvfors et. al., pp. 67-7, Costea, M., Petrescu, S., arman, C., he Effect of Irreversibilities on Solar Stirling Engine Cycle Performance, Energy Conversion & Management, Vol., pp. 7-7, Petrescu, S., Costea, M., Malancioiu, O., Feidt, M., Isotheral Processes treated base on the First La of hermodynamics for Processes ith Finite Speed, Vol. Conf. BIRAC, Bucharest,. 5. Florea,., Petrescu, S., Florea, E., Schemes for Computation and Optimization of the Irreversible Processes in Stirling Machines, Leda & Muntenia, Constanta,. 5. Petrescu, S., arman, C., Costea, M., Popescu, G., Petre, C., Florea,., Analysis and Optimisation of Solar/Dish Stirling Engines, Proceedings of the st American Solar Energy Society Annual Conference, Solar, Sunrise on the Reliable Energy Economy, Reno, Nevada, vol.cd, ISBN: Editor: R. Campbell-oe, June 5-, USA,. 5. Petrescu, S., arman, C., Costea, M., Florea,., Petre, C., Feidt, M., A Scheme of Computation, Analysis, Design and Optimization of Solar Stirling Engines, he 6-th ECOS Conference, Copenhagen, Denmark, ed. N. oubak, et.al., Vol.I, pp. 55-6, June - July,. 55. Cullen, B., McGovern, J., Petrescu, S., Feidt, M., Preliminary Modelling Results for Otto-Stirling ybrid Cycle, ECOS 9, Foz de Iguasu, Parana, Brazil, pp. 9-, August - September, Petrescu, S., Petre, C., Costea, M., Malancioiu, O., Boriaru, N., Dobrovicescu, A., Feidt, M., arman, C., A Methodology of Computation, Design and Optimization of Solar Stirling Poer Plant using ydrogen/oxygen Fuel Cells, Energy, Volume 5, Issue, pp McGovern, J., Cullen, B., Feidt, M., Petrescu, S., Validation of a Simulation Model for a Combined Otto and Stirling Cycle Poer Plant, Proc. of ASME, th Int. Conf. on Energy Sustainability, ES, May 7-, Phoenix, Arizona, USA,. 58. Petrescu, S., irca Dragomirescu, G., Feidt, M., Dobrovicescu, A., Costea, M., Petre, C., Dobre, C., Combined eat and Poer Solar Stirling Engine, ECOS-, 5-7 June, Lausanne, Siss,. 59. Petrescu, S., Costea, M., Feidt, M., Les cycles des machines à froid et des pompes à chaleur à vitesse finie, Rev. Entropie, No., pp. 8-5,. 6. Petrescu, S., Grosu, L., Costea, M., Rochelle, P., Dobre, C., Petre, C., Analyse théorique et expérimentale d une machine à froid de Stirling, Bulletin of I.P. Iaşi, om LVI (L), Fascicola a, secţia Construcţii de maşini, pp. -5,. Acknoledgements he ork has been funded by the Sectorial Operational Programme uman Resources Development 7- of the Romanian Ministry of Labour, Family and Social Protection through the Financial Agreement POSDRU/88/.5/S/6. ERMOENICA / 7