Keywords: Thermodynamics, Efficiency, Atkinson cycle, Dual combustion cycle, Heat transfer

Transcription

1 M.M. Rashidi * Associate Professor A. Hajiour M.Sc A. Fahimirad M.Sc omarison of Performances for Air- Standard Atkinson and Dual ombustion ycles with Heat ransfer onsiderations here are heat losses during the cycle of real engine that are neglected in ideal air-standard analysis. In this aer, the effect of heat transfer on the net outut work is shown and thermal efficiency of the air-standard Atkinson and the Dual combustion cycles are analyzed. omarison of erformances of the airstandard Atkinson and the Dual combustion cycles with heat transfer considerations are also discussed. We assumed that the comression and ower rocesses are adiabatic and reersible and any conectie, conductie and radiatie heat transfer to cylinder wall during the heat rejection rocess may be ignored. he heat loss through the cylinder wall is assumed to occur only during combustion and is further assumed to be roortional to aerage temerature of both the working fluid and cylinder wall. he results show that the net work outut ersus efficiency and the maximum net work outut and corresonding efficiency bounds are influenced by the magnitude of heat transfer. he results are of imortance to roide guidance for the erformance ealuation of ractical engines. Keywords: hermodynamics, Efficiency,, Dual combustion cycle, Heat transfer Introduction he engine is a tye of internal combustion engines, which was designed and built by James Atkinson in (882). he cycle is also called the Sargent cycle by seeral hysic-oriented thermodynamic books. By the use of cleer mechanical linkages, Atkinson s engine carried the exansion branch farther than any other existing engines. he Dual combustion cycle is another tye of internal combustion engine. In recent years, many attentions hae been aid to analyzing the erformance of internal combustion cycles. omarison of erformances for the air-standard Atkinson and the Otto cycles with heat * Associate Professor, Deartment of Mechanical Engineering, Engineering Faculty of Bu-Ali Sina Uniersity, Hamedan, Iran, mm_rashidi@yahoo.com orresonding Author, M.Sc, Young Researchers lub, Ayatollah Amoli Branch, Islamic Azad Uniersity, Amol, Iran, alirezahajiour@gmail.com M.Sc, Research and Deeloment enter (R&D), Iran Heay Diesel Mfg. o. (Desa), Amol, Iran, a.fahimirad@desa.ir

2 6 Iranian Journal of Mechanical Engineering Vol. 3, No. 2, Se. 202 transfer considerations and heat transfer effects on the erformance of an air-standard Dual combustion cycle did by Hou [] and [2]. Performance analyzing and arametric otimum criteria of an irreersible Atkinson heat-engine did by Zhao and hen [3]. Otimization of the Dual combustion cycle considering the effect of combustion on ower did by hen [4]. Performance of an endoreersibe with ariable secific heat ratio of working fluid did by Ebrahimi [5]. he results obtained in this work can hel us to understand how the net-work outut and efficiency are influenced by heat transfer during combustion, or the constant olume heat addition rocess. 2 ycle model he -s diagrams of the Atkinson and the Dual combustion cycles are shown in Figures (.a) and (.b). In the, the heat added in the isochoric rocess (2 3) and the heat rejected in the isobaric rocess (4 ). In the Dual combustion cycle the heat added in the isochoric and isobaric rocess (2 3) and (3 4), the heat rejected in the isochoric rocess (5 ). Figure.a -s diagram for the Figure.b -s diagram for the Dual combustion cycle 2. hermodynamics analysis of the air-standard Following the assumtion described aboe, rocess ( 2) is an isentroic comression from bottom dead center (BD) to to dead center (D). he heat addition takes lace in rocess (2 3), which is isochoric. he isentroic exansion rocess (3 4), is the ower or exansion stroke. he cycle is comleted by an isobaric heat rejection rocess(4 ). he heat added to the working fluid er unit mass is due to combustion. Assuming constant secific heats, the net work outut er unit mass of the working fluid is gien by the first-law of thermodynamics: w ( ) ( ), () Where and are the constant ressure and constant olume secific heat, resectiely; and, 2, 3 and 4 are the absolute temeratures at states, 2, 3 and 4. For the isentroic rocess ( 2) and (3 4), we hae

3 omarison of Performances for Air-standard Atkinson 7 k 2 r c, (2) V V V V V V ( ) ( ) ( ) ( ) ( ) r ( ), (3) V V V V V V 4 3 k 3 k k 2 k k k k c Where r is the comression ratio c (V / V 2) and k is the secific heat ratio ( / ). Additionally, since rocess (4 ) is isobaric, we hae V V (4) 4 4 Substitution of equations (2) and (4) into equation (3) yields (5) 3 4 ( ) k 2 he heat added er unit mass of the working fluid during the constant olume rocess (2 3) er cycle is reresented by the first-law of thermodynamics: qin ( ) 3 2 (6) Also the heat added to the working fluid during the constant olume combustion rocess can be gien in the following linear exression [2]: qin ( 3 2) (7) Where α, β are two constants related to combustion rocess and heat transfer, resectiely [] ombining equations (6) and (7) yields ( ) 2 3 Substitution of equation (2) into equation (8) gies 3 k [ ( ) rc ] (8) (9) Substituting of equations (2) and (9) into equation (5) gies 4 as a function of k k [ rc ( )] 4 ( ) (0) By combining the results obtained from equations (2), (9) and (0) into equation (), the net work outut er unit mass of the working fluid can be exressed in terms of as

4 8 Iranian Journal of Mechanical Engineering Vol. 3, No. 2, Se. 202 k k k ( ) rc k rc ( ) w rc ( ) () Similarly, substitution equations (2), (9) and (0) into equation (7) yields ( ) r k qin r k c c (2) Equation () diided by equation (2) gies the indicated thermal efficiency, k k k ( ) rc k rc ( ) rc ( ) w k qin k ( ) rc rc (3) hen, differentiating with resect to r c and seeking a maximum work outut, w max, by setting dw 0 dr (4) c We finally get a r a r a (5) 2k k c 2 c 3 0, a a 2 3 a,, ( ) k a a 2 (6) (7) (8) Note that w max can be obtained by substituting r c r cm into equation (). Furthermore, the corresonding thermal efficiency at maximum work outut η m, can be obtained by substituting r cm into equation (3). [] 2. 2 hermodynamics analysis of the air-standard Dual combustion cycle Following the assumtion described at the cycle model, Figure (.b) shows the temeratureentroy (-s) diagrams for the thermodynamic rocesses of an air-standard Dual combustion

5 omarison of Performances for Air-standard Atkinson 9 cycle. Process ( 2) is an isentroic comression from BD to D. he heat addition takes lace in two stes: rocess (2 3) is isochoric and rocess (3 4) isobaric. he isentroic exansion rocess (4 5) is the ower or exansion stroke. he cycle comleted by an isochoric heat rejection rocess (5 ). Assuming constant secific heats, the net work outut er unit mass of the working fluid is gien by the first-law of thermodynamics: w ( ) ( ) ( ), (9) Where and are the constant ressure and constant olume secific heat, resectiely; and, 2, 3, 4 and 5 are the absolute temeratures at states, 2, 3, 4 and 5. For the isentroic rocesses ( 2) and (4 5), we hae k 2 r c, (20) k r r 5 4, c (2) Where r c and r are the comression ratio (V / V 2) and the cut-off ratio (V 4/ V 3), and k is the secific heat ratio ( / ). he oerall heat inut er unit mass of working fluid er cycle can be reresented by the first-law of thermodynamics: q ( ) ( ) (22) in he heat added to the working fluid during the total combustion rocess can be gien in the following linear exression [2] q ( ) ( ) (23) in ombining equations (22) and (23) yields and 3 ( ) r, k ( ) 2 c (24) 4 k ( ) ( ) ( ) 3 rc /( ) (25) Substituting of equation (24) into equation (2) gies 5 as a function of

6 0 Iranian Journal of Mechanical Engineering Vol. 3, No. 2, Se. 202 k ( ) ( ) r c /( ) r 5 r c k (26) By combining the results obtained from equations (20), (24), (25) and (26) into equation (), the net work outut er unit mass of the working fluid can be exressed in terms of as k k ( 2 2 rc ) ( ) rc w k k k ( r r ) r c k r ( ) 2 c (27) Similarly, substituting equations (20), (24) and (25) into equation (23) yields k k k rc rc qin rc k rc / (28) Equation (27) diided by equation (28) gies the indicated thermal efficiency: w (29) q in hen, differentiating w with resect to r c and seeking a maximum work outut, setting w 0 r c w max, by (30) We finally get Where r cm 2k 2 b b b b b k b,, (3) (32) 2 k b2, 2 (33)

7 omarison of Performances for Air-standard Atkinson b r k 3, (34) b 5 k k b4, (35) Hence, w max occurs at r cm (the corresonding comression ratio at the maximum work outut condition). In other words, w max can be obtained by substituting r=r c cm into equation (27). Furthermore, the corresonding thermal efficiency at maximum work outut η m, can be obtained by substituting r cm into equation (29). [2] (36) 3 Results and discussion he net-work outut ersus efficiency characteristic and efficiency bound η m at maximum work deend on α, β and. he ranges for α, β, r and are kj/kg, kj/kg-k,.8 and K, resectiely. Additionally, =.003 kj/kg-k, = 0.76 kj/kg-k and k=.4. he effect of β on the w-η characteristic cures for the Atkinson and Dual combustion cycles at α = 3000 kj/kg, and = 350 K is indicated in Figure (2) increasing β corresonds to enlarging the heat loss and, thus, decreasing the amount of heat added to the engine. Accordingly, the maximum work and efficiency decrease with increasing β. he effect of α on the w-η characteristic cures for the Atkinson and Dual combustion cycles at β = 0.5 kj/kg-k and = 350 K is deicted in Figure (3) increasing α increase the amount of heat added to the engine due to combustion. Figure (4) shows the effect of intake temerature,, on the w-η characteristic cures for α =3500 kj/kg and β = 0.5 kj/kg-k. he results show that the maximum work and efficiency decrease as increases, and for a gien, the maximum net-work of is higher than for the Dual combustion cycle. he comression ratios (r cm ) that result in maximum work as a function of α and β are lotted in Figure (5) for a fixed β, r cm increases as α increase. Note that the comression ratios that maximize the work of the Dual combustion cycle are always higher than those for the at the same oerating conditions. he effects of α and β on the maximum work outut, w max, and the corresonding efficiency at w max η m, are demonstrated in Figure (6) and (7). Figure (6), Figure (7) Shows that an increase in β results in a decrease of w max (η m ).

8 2 Iranian Journal of Mechanical Engineering Vol. 3, No. 2, Se. 202 he effects of β and on the maximum work outut and the corresonding efficiency at the maximum work outut are shown in Figures (8) and (9), resectiely. It is seen that the heat loss arameter has a strong effect on the erformance of the cycle. Both w max and η m decrease as β and increases. he effects of α and on w max and η m are shown in Figures (0) and (). It is found that both w max and η m increase as the constant α increase =3000 (kj/kg), =350 (K), r = 2. =0.4 (kj/kg-k) =0.3 (kj/kg-k) w (kj/kg) =0.5 (kj/kg-k) Figure 2 Effect of β on the w ersus η characteristics =0.5 (kj/kg-k), =350 (K), r = 2. =3500 (kj/kg) =3250 (kj/kg) =3000 (kj/kg) w (kj/kg) Figure 3 Effect of α on the w ersus η characteristics.

9 omarison of Performances for Air-standard Atkinson =3500 (kj/kg), =0.5 (kj/kg-k), r = 2. =300 (K) =350 (K) =400 (K) w (kj/kg) Figure 4 Effect of on the w ersus η characteristics r cm, omression ratio at w max =350 (K) r = 2. =3500 (kj/kg) =3250 (kj/kg) =3000 (kj/kg) (kj/kg-k) Figure 5 omarison ratios at maximum net work for arious alues of α and β at = 350 K.

10 4 Iranian Journal of Mechanical Engineering Vol. 3, No. 2, Se =350 (K), r = 2. =3000 (kj/kg) =3250 (kj/kg) =3500 (kj/kg) w max (kj/kg) (kj/kg-k) Figure 6 Effects of α and β on w max =3500 (kj/kg) =3250 (kj/kg) =3000 (kj/kg) =350 (K), r = m (kj/kg-k) Figure 7 Effects of α and β on η m.

11 omarison of Performances for Air-standard Atkinson =3500 (kj/kg) 000 w max (kj/kg) =0.5 (kj/kg-k) =.0 (kj/kg-k) =.5 (kj/kg-k) (K) Figure 8 Effects of β and on w max =3500 (kj/kg) 0.7 =0.3 (kj/kg-k) m 0.6 =0.7 (kj/kg-k) 0.5 = (kj/kg-k) (K) Figure 9 Effects of β and on η m.

12 6 Iranian Journal of Mechanical Engineering Vol. 3, No. 2, Se =.0 (kj/kg-k), =350 (K), r = w max (kj/kg) =3500 (kj/kg) =3250 (kj/kg) =3000 (kj/kg) (K) Figure 0 Effects of α and on w max =.0 (kj/kg-k), =350 (K), r = 2. =3500 (kj/kg) =3250 (kj/kg) =3000 (kj/kg) 0.6 m (K) Figure Effects of α and on η m.

13 omarison of Performances for Air-standard Atkinson 7 4 onclusions he effects of heat transfer through the cylinder wall on the erformance of the Atkinson and the Dual combustion cycle are inestigated in this study. he relation between net-work outut and thermal efficiency is deried. Furthermore, the maximum work outut and the corresonding thermal efficiency at the maximum work outut are also are deried. In the analyses, the influence of four significant arameters, namely the heat transfer and combustion constant, comression ratio and intake air temerature on the net-work outut ersus efficiency characteristic, and the maximum work and the corresonding efficiency at maximum work are examined. omarisons of the erformances of the air-standard Atkinson and the Dual combustion cycles with heat transfer considerations are also discussed. he general conclusions drawn from the results of this work are as follows:. he maximum work outut and the corresonding efficiency at maximum work outut decreases as the heat transfer constant β increases. 2. he maximum work outut and the corresonding efficiency at maximum work outut increases as the combustion constant α increases. 3. he maximum work outut and the corresonding efficiency at maximum work outut decreases as the intake temerature ( ) increases. 4. For a gien alue of heat release during combustion (α) an increase in heat loss (β) leads to a decrease of the comression ratio (r cm ) that maximizes the work of the. References [] Hou, S.S., omarison of Performance of Air Standard Atkinson and Otto ycles with Heat ransfer onsiderations, Energy onersion and Management, Vol. 48, , (2007). [2] Hou, S.S., Heat ransfer Effects on the Performance of an Air Standard Dual ycle, Energy onersion and Management, Vol. 45, , (2004). [3] hen, J., and Zhao, Y., Performance Analysis Parametric Otimum riteria of an Irreersible Atkinson Heat-engine, Alied Energy, Vol. 83, , (2006). [4] hen, X.Y., Otimization of the Dual ycle onsidering the Effect of ombustion on Power, Energy onersion and Management, Vol. 38, , (997). [5] Ebrahimi, R., Effect of Mean Piston Seed, Equialence Ratio and ylinder Wall emerature on Performance of an Atkinson Engine, Mathematical and omuter Modeling, Vol. 53, , (20).

14 8 Iranian Journal of Mechanical Engineering Vol. 3, No. 2, Se. 202 Nomenclatures a : constant defined in equation (5) a 2 : constant defined in equation (5) a 3 : constant defined in equation (5) b : constant defined in equation (3) b 2 : constant defined in equation (3) b 3 : constant defined in equation (3) b 4 : constant defined in equation (3) b 5 : constant defined in equation (3) : constant ressure secific heat (kj/kg K) : constant olume secific heat (kj/kg K) k: k = / q in : heat added er unit mass to working fluid (kj/kg) r: cut-off ratio r c : comression ratio r cm : comression ratio at maximum work s: secific entroy (kj/kg K) r : ressure ratio i : temerature at state i (K) V i : olume at state i (m 3 ) w: net work outut er unit mass (kj/kg) w max : maximum work outut er unit mass of working fluid er cycle (kj/kg) Greek symbols α: constant related to combustion (kj/kg) β: constant related to heat transfer (kj/kg K) η: efficiency η m : corresonding thermal efficiency at maximum work outut

15 omarison of Performances for Air-standard Atkinson 9 چكيده در هنگام فرآيندهاي موتورهاي واقعي مقداري گرماي تلف شده وجود دارد كه در تحليل ايدهآل اين موتورها در نظر گرفته نميشود. در اين مقاله اثر انتقال حرارت روي كار خالص خروجي و بازده حرارتي چرخه استاندارد هوايي آتكينسون و چرخه احتراق دوگانه بررسي شده است. همچنين عملكرد چرخههاي آتكينسون و دوگانه نيز با هم مقايسه شده است. فرض شده است كه مراحل تراكم و قدرت بيدررو و برگشتپذير و بدون هيچ نوع انتقال حرارتي (اعم از جابجايي همرفت و تشعشعي) به ديواره سيلندر باشد. فقط اتلاف حرارتي صورت گرفته از طريق ديواره سيلندر در مرحله احتراق در نظر گرفته شده است. نتايج بدست آمده نشان ميدهد كه كار خالص خروجي در برابر بازده و كار خروجي بيشينه در برابر بازده وابسته به آن تا حد زيادي تحت تا ثير مقدار انتقال حرارت ميباشد. نتايج اين بررسي ميتواند به عنوان يك راهنماي مناسب براي بررسي عملكرد موتورهاي واقعي مورد استفاده قرار گيرد.