MODELING OF MULTICOMPONET FUEL EFFECTS IN INTERNAL COMBUSTION ENGINES

Transcription

1 MODELING OF MULTICOMPONET FUEL EFFECTS IN INTERNAL COMBUSTION ENGINES Yangbng Zeng and Cha-Fon Lee Department of Mechanca and Industra Engneerng Unversty of Inos at Urbana-Champagn INTRODUCTION Engne fues typcay consst of many dfferent hydrocarbon components that vaporze at dfferent bong pont temperatures. In order to keep computatona costs ow, however, tradtona engne computatons were made wth the assumpton of a snge component fue wth a snge bong pont. Under ths assumpton, the faster vaporzaton of ghter components and the sower vaporzaton of heaver components are not captured. Consequenty, the mxng and combuston process can not be adequatey represented. Therefore, computatons wth mutcomponent fue capabe of representng ths effect are desred. An essenta probem for mutcomponent fue computatons s how to descrbe fue vaporzaton. Dfferent from snge-component substance, mutcomponent fues vaporze n a more transent manner. In genera, the composton aways vares, and ts spata dstrbuton s aso non-unform. There were ntensve studes n teratures and severa knds of modes have been deveoped to descrbe ths unsteady vaporzaton behavor for mutcomponent dropet and fm (two forms that fue exsts n engnes). However, most of these modes are ether computatonay ntensve or nsuffcenty accurate. Ths paper outned a numerca method for mutcomponent fue computatons wth reatvey ow computatona cost whe wth hgh accuracy. The startng pont s the KIVA-3V code [1], whch has been extensvey used n engne computatons due to ts capacty n modeng turbuence, spray dynamcs and chemca reacton and ts fexbty n handng the engne-ke geometry. However, ths code s mted to snge component fues. Extended efforts have been made to mode mutcomponent fue effects [2-6]. In ths study, the snge component representaton for fue was extended to a mutcomponent representaton, and part of property evauaton methods were repaced by more accurate methods. Two newy deveoped mutcomponent vaporzaton modes for dropet and fm were used to descrbe fue vaporzaton n engnes [4-6]. These two modes take nto account mportant mechansms nvoved, such as preferenta vaporzaton, fnte dffuson, nterna crcuaton, surface regresson, and non-dea behavor n hgh-pressure envronments [4-6]. However, ther computatona cost s ony sghty hgher than those of the vaporzaton modes n the orgna code and s much ower than those of other modes wth smar accuracy n teratures [4-6]. The deveoped method was used to nvestgate ar/fue mxture preparaton n a port fue njecton (PFI) spark gnton engne under the cod startng condton snce mutcomponent fue effects are most sgnfcant under ths condton. The computed engne s a four-vave pent-roof engne. The fue s composed of four components and t produces a dstaton curve smar to that of an actua gasone fue [7]. Computatona resuts were compared wth expermenta resuts of excpex fuorescence measurements for fue vapor n-cynder dstrbuton. The tme-resoved nformaton on qud and vapor mass was provded and dscussed. Effects of engne operatng parameters ncudng swr ntensty, engne speed and njecton tmng on the n-cynder fue dstrbuton were aso presented. NUMERICAL MODEL In the KIVA-3V code, parce representaton s used for qud fue. Each parce (dropet or fm) s tracked ndvduay, and the two-way coupng between the qud fue and the carryng gas s mpemented by a Pont- Source-Voume method [1]. Two major ssues needed address are how to determne the momentum, mass and heat transfer rates between two phases and how to descrbe the responses of the parce, and these ssues are covered by the two vaporzaton modes presented beow. Dropet Vaporzaton Mode Sem-emprca correatons for drag, the Nusset number, and the Sherwood number are used to evauate the momentum, heat and mass transfer rate between two phases. In ths study, the correatons deveoped by Jn and Borman [8] were used, and the vaporzaton rate (.e. the mass transfer rate) s gven by ω = D Sh ς B d (1) g

2 where ω s the vaporzaton rate, D g the gas phase mass dffusvty coeffcent, Sh the Sherwood number, ς the correcton factor for the effect of Stephan fow, B the transfer number, and d the dropet dameter. Subscrpt stands for component. Due to the dffuson resstance nsde the dropet and preferenta vaporzaton, the property dstrbutons wthn the dropet are non-unform n genera. In ths study, ths non-unformty represented by the dfference between the surface and average vaues s gven by an ordnary dfferenta equaton wth respect to tme t [5], d Φd.2E( PeV ) φr D - d = Φ (2) 2 2 dt E( Pe ) R 4.49 D V where Φ d s the dfference between the surface and average vaues for the temperature T or mass fracton Y, D the effectve therma or mass dffusvty coeffcent, φ the heat or speces mass dffusona fux at the dropet surface, R the dropet radus, and E the correcton factor for the effect of surface regresson. The effect of surface regresson s quantfed by a non-dmensona varabe Pe V defned as [5] PeV = R ω D (3) whch represents the rato of the therma or mass dffusona tme scae to the surface regresson tme scae. When Pe V s sma (.e., sow vaporzaton rate), the effect of surface regresson s neggbe and thus the steady profes of temperature and mass fractons wthn the dropet are quadratc. However, ths quadratc profe w shft to a dstrbuton showng a structure smar to that of the boundary ayer fow, wth decreasng boundary ayer thckness as Pe V ncreases [5]. E(Pe V ) s defned as the rato of the dfference of surface and average vaues to the dfference at Pe V = subject to the same boundary condtons. Through theoretca anayss, the authors found the expresson for E(Pe V ) [5], and t s gven by, R Φ 3 R r Φ R Φ R r 2 3 Φ 2 E( PeV ) = dr ( dr) r dr dr ( dr) r dr (4) 3 r r 3 r r r r Fm Vaporzaton Mode Based on the boundary ayer equatons and the Prandt mxng-ength theory, O Rourke and Amsden [9] deveoped a modfed wa functon to determne the transfer rate between the fm and the adjacent gas. Foowng the same strategy, the authors extended t to ncude mutcomponent fue effects, and the speces vaporzaton rate ω s gven by [6] ω = HY ς B, (5) where H Y s the overa dffusvty, ς the correcton factor for the effect of Stephan fow, and B the transfer number. Subscrpt refers to component. The mass fracton and temperature dstrbutons wthn the fm are non-unform as we because of fnte therma and mass dffuson speeds. The authors recenty deveoped a mode for ths non-unformty usng a thrdorder poynoma to smuate the temperature and mass fracton unsteady profes wthn the fm. Ths mode reduces the governng equatons for mass and energy transport to a set of ordnary dfferenta equatons [29]. Wth ths mode, the surface temperature s gven by [6] d T s q = α ( δ 3 T T 4T ) 2 s w + m (6) dt δ k where T s s the fm surface temperature, α s the qud phase therma dffusvty coeffcent, δ s the fm thckness, q the heat fux to the fm, k the qud phase conductvty coeffcent, T w the wa temperature, and T m the fm average temperature. The dfference between the surface and average mass fractons for component s gven by [6] d( Y s Y m) 4 Γ = [ η 3( 12 )] 2 Y s Y m (7) dt ρδ PeV =

3 where Y s s the surface mass fracton, Y m the average mass fracton, Γ the qud phase mass dffusvty coeffcent, ρ the qud densty, and η the speces mass dffusona fux at the fm surface. Phase Equbrum In a hgh-pressure envronment, the assumpton of dea gas and qud behavor s nvad. Consequenty, the Raout aw s not approprate to gve the thermodynamca equbrum reaton between gas phase and qud phase at the dropet or fm surface. To account for the effect of non-dea behavor at hgh pressure, the Peng- Robnson equaton of state was used to cacuate the compressbty factor and fugacty for gas phase and qud phase. By equatng speces fugactes at qud phase and gas phase, the equbrum reaton s determned. Property Evauaton Accurate property evauatons are cruca for computatons of mutcomponent fue vaporzaton. In ths study, a propertes are temperature- and composton-dependent wth the correcton of hgh-pressure effect f appcabe [1]. The qud phase property s determned n the reference of average composton and temperature, and the gas phase property s evauated usng a one-thrd rue. RESULTS AND DISCUSSIONS A the above modes have been mpemented nto the KIVA-3V code and verfed wth expermenta and computatona data on soated dropets and fms [4-6]. The deveoped method was then used to smuate ar/fue mxture preparaton process for a PFI spark-gnton engne durng the cod startng phase. Under the cod startng condton, the mutcomponent fue effects are the most remarkabe snce the fue vaporzaton s ncompete and deta vaporzaton hstory s mportant. The computed engne s a producton 2.5L, V-6 engne that has been nvestgated ntensvey n the Spray and Engne Research Laboratory at the Unversty of Inos at Urbana-Champagn [7]. The fue s composed of 15% sopentane, 2% hexane, 45% sooctane, and 2% decane by mass producng a dstaton curve smar to that of a Caforna Phase II gasone as shown n Fg. 1. Four cases are reported n ths paper wth dfferent swr ntensty, engne speed and njecton tmng as summarzed n Tabe 1. Hgh swr s accompshed by deactvatng the secondary ntake vave. Cosed vave njecton starts at 36 o BTDC (of the ntake stroke), whe open vave njecton starts at o ATDC when the ntake vave s fuy open. The njected spray s a sod cone spray wth a spray ange of 7.5 and an SMD of 9 µm. Computatona resuts were frst compared wth an excpex fuorescence measurement [7] for vapor ncynder dstrbuton to further verfy the deveoped method. It s worthy to menton that the expermenta mages are quatatve and have not been corrected for aser ntensty cross-secton profe and absorpton of the ncdent aser ght by the fuorescence dopants [7]. Fgure 2 shows both the computed vapor densty and measured vapor fuorescence mage of the ght component C 6 H 14 n the center pane of the cynder at the eary stage of the ntake stroke (5 o ATDC) for Case 1. The box n the computatona mage ndcates magng regon of the correspondng experment. It can be seen that the computed resut agrees reasonaby we wth the measured one. The vapor mages for the ate stage of the compresson stroke (31 o ATDC) were shown n Fg. 3. The dstrbuton becomes more dsperse and unform due to the mxng. The smar mages for Case 2 was shown n Fgs. 4 and 5. Good agreements between the computatona and the expermenta mages were aso obtaned. Compared wth Case 1, more fue s accumuated n the eft sde of the cynder at the eary stage of the ntake stroke, and the dstrbuton becomes more unform at the ate stage of the compresson stroke. Fgure 6 shows the varaton of the tota speces vapor mass (normazed by the njecton mass) versus crank ange for Case 1. The vaporzaton rate for a components decreases graduay wth ncreasng crank ange before the ntake vave opens. Ths decrease s prmary due to part of spray convertng nto fm partces. Rght before the ntake vave opens, the vaporzaton s amost frozen because the fm on the ntake port wa and the vave stem reaches equbrum wth the surroundng gas. Once the ntake vave opens, the ntake charge moton sgnfcanty ncreases the vaporzaton rate by transportng the accumuated vapor mass and part of fm mass nto the cynder. However ths promoton for vaporzaton dmnshes graduay after the ntake vave fuy opens. Snce ony tte of qud fue enters the cynder, the promoton for vaporzaton due to hgh-temperature created by compresson s not observed. It was aso shown that fue voatty pays an mportant roe n the vaporzng behavor. Neary 7 percent of C 5 H 12 vaporzed, and n contrast, tte of C 1 H 22 vaporzed. Therefore, ghter components account for hgher percentage n the fue vapor than n the njected fue. Fgure 7 shows the pot of

4 tempora hstory of n-cynder qud mass normazed by the njecton mass. The sudden ncrease occurrng at CA = 61 s due to the cosure of the ntake vave and the consequent change of regon defnton. It s seen that more mass of heaver components s nduced nto cynder. The overa percentage of each component for the ncynder qud fue s shown n Fg. 8. Compared to nta composton, the percentage of the heavest component C 1 H 22 s amost doubed, whe that of the ghtest component C 5 H 12 becomes ony one-thrd. Ths trend s n contrary wth that for the vapor phase. These facts ndcate that t s very naccurate to use a snge component fue to represent a mutcomponent fue for cod startng computatons snce the n-cynder fue composton of ether the qud phase or the gas phase s sgnfcanty dfferent from the njected fue. Fgures 9 and 1 shows the varaton of normazed vapor and qud mass nduced nto the cynder for four cases. The observed trends are n consstent wth the expermenta resuts [7]. The comparson between Cases 1 and 2 ndcates that the hgher swr brngs n more qud and vapor nto the cynder. Ths s prmary due to the neary doubed ntake charge veocty, whch ncreases the vaporzaton rate and the turbuence eve. The entraned vapor masses for Cases 1 and 3 are cose n spte of the arge dfference n ther engne speeds (12 rpm vs. 2 rpm). For ower speed case, the veocty and turbuence ntensty n the ntake port and cynder are ower, and thus the vaporzaton rate n turns s sower. However, vaporzaton takes onger at ower engne speed. The combned effects resut n engne speed havng weak nfuence on the nduced fue mass. It s aso noted that ess qud fue mass s brought nto the cynder n the ow speed case due to the ntake charge moton beng not strong enough to strp the fm off the ntake wa and the vave surface. The comparson of Cases 4 and 1 shows that open-vave njecton causes more fue vapor to be entraned nto the cynder, whch s hepfu for gnton and combuston. However, t aso brngs n much more qud fue most key resutng n hgh hydrocarbon emssons. CONCLUSIONS A method for modeng mutcomponent fue effect n engnes has been deveoped. It has the advantage of hgh accuracy and ow computaton cost. The deveoped method was used to smuate the ar/fue mxture preparaton for a PFI spark gnton engne under the cod startng condton. It was found that the voatty of a fue component pays an mportant roe n determnng ts n-cynder behavor. Effects of engne operatng parameters (swr ntensty, engne speed and njecton tmng) on the n-cynder fue dstrbuton were aso reproduced. ACKNOWLEDGMENTS Ths work was supported n part by the Natona Scence Foundaton under grant No. CTS , wth Farey Fsher as technca montor, and by Ford Motor Company. We aso thank Dar-Lon Chang and Yu-Yu Lee for ther assstance on preparng the manuscrpt. REFERENCES 1. Amsden, A., KIVA-3V: A Bock-Structured KIVA Program for Engnes wth Vertca or Canted Vaves, Los Aamos Natona Laboratory Report LA MS, Ayoub, N. S. and Retz, R. D., Mutdmensona Modeng of Fue Effects and Spt Injectons on Dese Engne Cod-Startng, Journa of Propuson and Power, Vo. 13, No. 1, Abraham, J. and Mag, V., A Mode for Mutcomponent Dropet Vaporzaton n Sprays, SAE Paper 98511, Zeng, Y. and Lee, C. F., A Mutcomponent Dropet Preferenta Vaporzaton Mode for Spray Computatons, The Frst Jont Meetng of the Unted States Sectons of the Combuston Insttute, Washngton, DC, March Zeng, Y. and Lee, C. F., A Mode for Mutcomponent Spray Vaporzaton n a Hgh Pressure and Hgh Temperature Envronment, Interna Combuston Engne Dvson of ASME 1999 Fa Engne Technoogy Conference, Ann Arbor, MI, Zeng, Y. and Lee, C. F., A Mutcomponent Fue Fm Vaporzaton Mode for Mutdmensona Computatons, Accepted for pubcaton n Journa of Propuson and Power, Key-Zon, P. L., Styron, J. P., Lee, C. F., Lucht, R. P., Peters, J. E. and Whte, R. A., Mutcomponent Lqud and Vapor Fue Measurements n the Cynder of a Port Injected, Spark Ignton Engne, Accepted for pubcaton n Combuston Symposum, 1998.

5 8. Jn, J. D. and Borman, G. L., A Mode for Mutcomponent Dropet Vaporzaton at Hgh Ambent Pressures, SAE Paper 85264, O Rourke, P. J. and Amsden, A. A., A Partce Numerca Mode for Wa Fm Dynamcs n Port-Injected Engnes, SAE Paper , Red, R. C., Prausntz, J. M., and T. K. Sherwood, The Propertes of Gases and Lquds, 3 rd ed., McGraw-H, New York, NY, Tabe 1. Engne operatng parameters Injecton Tmng Swr Engne Speed (rpm) Case 1 Cosed-Vave Low 12 Case 2 Cosed-Vave Hgh 12 Case 3 Cosed-Vave Low 2 Case 4 Open-Vave Low Temperature ( o F) % Evaporated (by Vo)1 Dstaton Curves Fue Bend CA Phase II C5 C6 C8 C Fg. 1 Comparson of dstaton curves between the used Fg. 6 The varaton of speces vapor mass versus mutcomponent fue and CA Phase II gasone crank ange for Case 1 a. computaton b. experment Fg. 2 Vapor phase dstrbuton of C 6 H 14 at 5 o ATDC of the ntake (Case 1) a. computaton b. experment Fg. 3 Vapor phase dstrbuton of C 6 H 14 at 31 o ATDC of the ntake (Case 1)

6 a. computaton b. experment Fg. 4 Vapor phase dstrbuton of C 6 H 14 at 5 o ATDC of the ntake (Case 2) a. computaton b. experment Fg. 5 Vapor phase dstrbuton of C 6 H 14 at 31 o ATDC of the ntake (Case 2) C5 C6 C7 C C5 C6 C8 C Fg. 7 The varaton of speces n-cynder qud mass versus crank ange for Case Fg. 8 The varaton of overa mass fracton for ncynder qud mass versus crank ange Case 1 Case 2 Case 3 Case Case 1 Case 2 Case 3 Case Fg. 9 Comparson of nduced fue vapor mass for four cases Fg. 1 Comparson of nduced fue qud mass for four cases