Effects of irreversible different parameters on performance of air standard dual-cycle

Transcription

1 Jurnal f Amerian Siene 0;7(3 Effets f irreersible different arameters n erfrmane f air standard dual-yle Reza Masudi Nejad, Puyan Alaei,* Shl f Engineering, Shahrerd Uniersity, Shahrerd, Iran Mehanis labratry, Azadi Aenue, Tehran, Iran *Crresnding authr: Puyan.alaei@gmail.m Abstrat: An irreersible air standard dual yle mdel is rsed in this aer. The erfrmane f an airstandard dual yle with heat transfer lss and ariable seifi heats f wring fluid is analyzed by using finitetime thermdynamis. The bjetie f this study is t analyze the effets f heat lss haraterized by a erentage f the fuel s energy, fritin and ariable seifi heats f wring fluid n the erfrmane f an air standard dual yle with a restritin f maximum yle temerature. The relatins between the wer utut and the mressin rati, and between the thermal effiieny and the mressin rati f the yle are deried. Mreer, the effets f heat transfer and glbal lsses lumed in a fritin lie term n the erfrmane f the yle are shwn by detailed numerial examles. [Jurnal f Amerian Siene 0;7(3: (ISSN: Keywrds: Air Standard, Finite-time thermdynamis, Dual yle, Pwer Outut, fritin.. Intrdutin A series f ahieements hae been made sine finite-time thermdynamis was used t analyze and timize real heat engines. Seeral authr shae alied finite-time thermdynamis (Andresen and Bejan and Chen et al. t the analysis and timizatin f the internal-mbustin engine. Mzurewih and Berry and Hffman et al. used mathematial tehniques frm timal-ntrl thery t determine the timal mtin f the istn in Ott and Diesel engines. Aizenbud and Band and Chen et al. determined the timal mtin f a istn, fitted t a ylinder ntaining a gas, umed with a gien heating rate and uled t a heat bath fr a finite time. The heat additin ress fr an air standard yle has been widely desribed as subtratin f an arbitrary heat lss arameter times the aerage temerature f the heat additin erid frm the fuel s hemial energy. Orl and Berry btained the wer and effiieny limits fr internal-mbustin engines. Angul-Brwn et al. and Chen et al. timized the wers f the Ott and Diesel engines with fritin lss during finite times. Klein studied the effet f heat transfer thrugh a ylinder wall n the wr utut f the Ott and Diesel yles. Chen et al. deried the relatins between net wer utut and the effiieny fr bth the Diesel and Ott yles, with nsideratins f heat transfer thrugh the ylinder wall. Blan and Wu and Lin et al. nsidered the effet f heat transfer thrugh a ylinder wall n the wr utut f the dual yle. On the basis f these inestigatins, the relatins gerning the net wer utut and the effiieny fr the dual yle with nsideratins f heat transfer lss and fritin-lie terms lss during a finite time are deried in this aer. heat transfer between the wring fluid and the enirnment thrugh the ylinder wall is nsidered and haraterized by a erentage f the fuel s energy; fritin lss f the istn in all the resses f the yle n the erfrmane is taen int aunt. Furthermre, we nsider the ariable seifi heats f the wring fluid that is signifiant in ratial yle analysis. The results btained in the study may ffer gd guidane fr design and eratin f the dual yle engine.. Thermdynami analysis An ideal air-standard dual yle is shwn in Fig.. The mressin ress ignitin is isentri ; the mbustin is mdelled by a reersible nstant lume ress 3and a nstantressure ress 3 4 ; the exansin ress 4 5is isentri; and the heat rejetin is a reersible nstant-lume ress 5. As is usual in FTT-heat engine mdels, we suse instantaneus adiabats. Fr the ishri branhes ( 3 and 5 and the isbari branh (3 4 in Fig., we rse that heating frm states t 4 and ling frm states 5 t reed arding t nstant temeratures; i.e. dt ( fr 3, 3 4 dt K dt ( fr 5, dt K ( htt:// 608 editr@ameriansiene.rg

2 Jurnal f Amerian Siene 0;7(3 and V /V T /T, (8 we hae TT /(, (9 4 TT /, (0 3 4 TT, ( 3 4 Figure. T s diagram fr a dual yle ( /( [ T4/( T. where T is the abslute temerature and t is the time. and are nstants. Integrating Eq. ( gies t K ( T T, t K ( T T, ( 3 4 where t and t are the heating and ling times, resetiely. Then, the yle erid is Substituting Eqs. (6 ( int Eq. (5 yields W P τ C T[ ( + T T T ( 4 4 / K( T4 T + K [ T T T } ( 4 }} (3 τ t + t K ( T T + K ( T T. (3 3 4 The wr utut is W C ( T T + C ( T T C ( T T, 5 (4 where C is the heat aaity at nstant lume, and C is the heat aaity at nstant ressure, i.e., the rdut f mass flw rate and the seifi heat. Thus, the wer utut is W P τ C T T + C T T C T T K ( T T + K ( T T ( 3 ( 4 3 ( (5 Defining the mressin rati,, the ressure rati, and the ut-ff rati, as fllws: where is the rati ( C / C f seifi heats. In seial ases, the dual yle bemes the Diesel yle r the Ott yle, i.e. when,. The ttal heat added t the wring-fluid during resses 3 and 3 4 is Q Q + Q A 3 34 C ( T T + C ( T T C [ T + ( T 4 (4 Fr an ideal dual yle, there are n irreersible lsses. Q α β( T + T A 4 α β( T + T, 4 (5 where α and β are tw nstants related t the mbustin and heat transfer. Cmbining Eqs. (4 and (5 yields V/V (T /T, (6 /(- P/P T /T, (7 3 3 T 4 α [ β + C T C + ( }/( β. Substituting Eq. (6 int Eqs. (3 and (4 yields (6 htt:// 609 editr@ameriansiene.rg

3 Jurnal f Amerian Siene 0;7(3 P C T [ ( + [ /( C + β α [ β + C ( T }} ( + C ( T }/( C + β}}} / K α [ β ( } /( C β T } + K T C T α [ β + C T + ( ( } α [ β + C T /( C + β T } T }}, (7 P C T [ ( where + [ /( C + β α [ β + C ( T }} C T α [ β + C ( ( T }/( C + β} }} + / K α [ β C ( T }/( C + β T } + K T ( ( T} α [ β + C /( C + β T } T }} b(, ( Q C α + β[( T } A /( C + β. (8 dx f µ µ µ, (9 dt where µ is a effiient f fritin whih taes int aunt the glbal lsses and x is the istn dislaement. Then, the lst wer is dw dx dx Pµ µ µ dt dt dt µ. (0 If we tae the istn mean elity as, x x x(, t t ( where xis the istn sitin at minimum lume and t is the time sent in the wer stre. Thus, the resulting wer utut is µ x b. (3 ( t The thermal effiieny f the yle is P η C T Q& A [ ( + [ /( C + β α [ β + C ( T }} C T α [ β + C ( ( T }/( C + β} }} / C ( α β T /( C + β} b( K α [ β + C ( ( ( } T }/( C + β T } + K T α [ β + C /( C + β T } T }}} / C ( α β T /( C + β}. T (4 Eqs. ( and (4 are the majr results f this aer. They determine the relatins between the wer utut P, effiieny η, mressin rati, and the ressure rati. The relatin between wer utut and effiieny may be btained using numerial alulatins. Tw limiting ases are manifested frm Eqs. ( and (4. The first ase, when, desribes the relatinshi f the wer and effiieny f the Diesel yle htt:// 60 editr@ameriansiene.rg

4 Jurnal f Amerian Siene 0;7(3 P C T + C + β α D ( [ /( [ + ( C β T } C T [ α ( + ( C β T /( C + β} }} / K [ α + ( C β T /( C + β T } + K T [ α + ( ( C β T /( C + β T } T }} b(, (5 η P C T( Q& OA + [/( C + β[ α + ( C β T ( } b( + + ( K K [ α ( C β T /( C + β T }} / C [ α + ( C β T /( C + β T }}, (8 η D P Q& D DA C T ( + [ /( C + β[ α + ( C β T T [ α ( + ( C β T /( C + β} }} / C ( α β T /( C + β} ( [ ( T /( C + β T } + K T [ α + ( C β ( T /( C b K α + C β + β T } T }}} / C ( α β T /( C + β} (6 when b 0, the result is the same as that f Chen et al. The send ase, when, desribes the relatinshi f the wer and effiieny f the Ott yle P C T ( + [/( C + β[ α + ( C β T ( }}/( K + K [ α + ( C β T /( C + β T }}} b(, (7 ( T4 /( T [ α + ( C β T /[( C + β T, (9 Where ( is the ressure rati fr the Ott yle. 3. Numerial examles T illustrate the reeding analysis, we hae τ 33.33ms, C J / K and C.003 j / K. Taing equal heating and ling times ( t t τ / 6.6 ms, the nstant temerature rates K and K are estimated as 6 6 K s / K and K s / K. We nsider µ 7σ with σ.9 g / s and σ is the fritin effiient f the exhaust and mressin stres. Taing the same alues f x and t as in Mzurewih s aer and fllwing the same redure t determine the lsses fr the full yle, we btain b 3.5 W. The maximum yle-temerature rati is τ 74/ The tyial arameter ranges f the fur arameters are (, α J / g, β J /[( g K and T K. The effets f n the wer utut s. effiieny ure fr α 3500 J / g, β J /[( g K and T 350 K are shwn in Fig.. The harateristi ure rresnds t the Diesel-yle erfrmane. The harateristi ure rresnds t the Ott-yle erfrmane. There is a maximum-wer utut int. When 6.5 and., the wer utut m arahes its maximum alue at Pmax 9.04 W and the rresnding effiieny is η The effet f β n the htt:// 6 editr@ameriansiene.rg

5 Jurnal f Amerian Siene 0;7(3 wer utut s. effiieny ure fr α 3500 J / g, T 350 K, b 3.5 W and. is shwn in Fig. 3. The effet f α n the wer utut s. effiieny ure fr β J /[( g K, b 3.5 W, T 350 K and. is shwn in Fig. 4. The effet f T n the wer utut s. effiieny ure fr α 3500 J / g, β J /[( g K, b 3.5 W and. is shwn in Fig. 5. The effets f b n the wer utut s. effiieny ure fr α 3500 J / g, β J /[( g K, T 350 K and. are shwn in Figs. 6. Figure 4. Effet f α n the P η harateristi. Figure. Effet f n the P η harateristi. Figure 5. Effet f T n the P η harateristi. Figure 3. Effet f β n the P η harateristi. Figure 6. Effet f b n the P η harateristi. 4. Cnlusins In this aer, the effets f ylinder wall heat-transfer and glbal lsses lumed in a fritinlie term n the erfrmane f a dual yle during a finite time are inestigated. The relatins between net wer utut, effiieny, mressin-rati, and the ressure rati are deried. The maximum wer htt:// 6 editr@ameriansiene.rg

6 Jurnal f Amerian Siene 0;7(3 utut and the rresnding effiieny and the maximum effiieny and the rresnding wer utut are als alulated. The results an als be alied t the erfrmane analysis f the Diesel and Ott yles. The detailed effet analyses are shwn by numerial examles. The results an ride signifiant guidane fr the erfrmane ealuatin and imrement f real dual engines. Referenes [ Andresen B, Salamn P, Berry RS. Thermdynamis in finite time. Phys Tday 984;(9:6 70. [ Bejan A. Entry-generatin minimizatin: the new thermdynamis f finite-size deies and finitetime resses. J Al Phys 996;79(3:9 8. [3 Chen L, Wu C, Sun F. Finite-time thermdynami timizatin r entry-generatin minimizatin f energy systems. J Nn- Equilib Thermdyn 999;4(4: [4 Mzurewih M, Berry RS. Otimal aths fr thermdynami systems: the ideal Ott yle. J Al Phys 98;53(:34 4. [5 Hffman KH, Watwih SJ, Berry RS. Otimal aths fr thermdynami systems: the ideal Diesel yle. J Al Phys 985;58(6:5 34. [6 Aizenbud BM, Band YB, Kafri O. Otimizatin f a mdel internal-mbustin engine. J Al Phys98;53(3:77 8. [7 Chen L, Sun F, Wu C. Otimal exansin f a heated wring-fluid with henmenlgial heattransfer. Energy Cners Mgmt 998;39(3/4: [8 Orl VN, Berry RS. Pwer and effiieny limits fr internal-mbustin engines ia methds f finite-time thermdynamis. J Al Phys 993;74(0:437. [9 Angul-Brwn F, Fernandez-Betanzs J, Diaz- Pi CA. Cmressin-rati f an timized Ottyle mdel. Eur J Phys 994;5(:38 4. [0 Chen L, Lin J, Lu J, Sun F, Wu C. Fritin effet n the harateristi erfrmanes f Diesel engines. Int J Energy Res 00;6(: [ Klein SA. An exlanatin fr bsered mressin-ratis in internal-mbustin engines. Trans ASME J Engng Gas-Turbine Pw 99;3(4:5 3. [ Chen L, Zen F, Sun F, Wu C. Heat-transfer effets n the net wr-utut and wer as funtin f effiieny fr an air standard Diesel yle. Energy, The Internatinal Jurnal 996;(:0 5. [3 Chen L, Wu C, Sun F, Wu C. Heat-transfer effets n the net wr-utut and effiieny harateristis fr an air standard Ott yle. Energy Cners Mgmt 998;39(7: [4 Blan DA, Wu C. The effets f mbustin n a wer-timized endreersible dual yle. Int J Pw Energy Sys 994;4(: [5 Lin J, Chen L, Wu C, Sun F. Finite-time thermdynami erfrmane f a dual yle. Int J Energy Res 999;3(9: //0 htt:// 63 editr@ameriansiene.rg