Numericl modeling of multi-component fuel combustion using rectivity djustment of chemicl rection mechnism Arsh Jmli nd Youngchul R Michign Technologicl University ABSTRACT High fidelity engine simultion requires relistic fuel models. Although typicl utomotive fuels consist of more thn few hundreds of hydrocrbon species, reserches show tht the physicl nd chemicl properties of the rel fuels could be represented by pproprite surrogte fuel models. It is desirble to represent the fuel using the sme set of physicl nd chemicl surrogte components. How-ever, when the rection mechnisms for certin physicl surrogte component is not vilble, the chemistry of the unmtched physicl component is described using tht of similr chemicl surrogte component t the expense of ccurcy. In order to reduce the prediction error while mintining the computtionl efficiency, method of on-the-fly rectivity djustment (ReAd) of chemicl rection mechnism is presented nd tested in the present study. The rectivity of rection mechnisms is djusted bsed on the locl composition of multi-component fuels nd fuel rdicls in the cylinder. The method is pplied to simulte engine combustion with multi-component fuel sprys nd its performnce is com-pred to tht of simultions with rection mechnism tht considers the full set of physicl/chemicl surrogte components. The results show tht the ReAd method improves the ccurcy of combustion prediction using single chemistry surrogte, while mintining superb computtionl efficiency. INTRODUCTION In four-stroke internl combustion engines, the pollution coming from the combustion products of fuels re still the min source of the pollution. In order to improve pre-diction ccurcy, more relistic fuel models re required in engine combustion simultions. However, petroleum-derived fuels consist of hundreds of hydrocrbon species, which Pge 1 of 6 mkes it too costly or imprcticl to consider ll hydrocrbon components found in numericl simultion. Therefore, in mny reserches, surrogte fuel method hs been employed by selecting limited number of representtive hydrocrbons tht cn mimic the behvior of trget fuel. Although single-component representtion for utomotive fuels physicl properties nd oxidtion chemistry hs been used for long time [1], its cler limittion in cpturing locl composition effects on combustion behvior nd emissions, especilly in dvnced combustion engines such s gsoline compression ignition (GCI) nd rectivity controlled compression ignition (RCCI) drove the use of multicomponent surrogte fuel modeling. Relible multi-component surrogte models need to be ble to represent both physicl properties nd chemicl kinetics of the trget fuel. However, improving fidelity of the model with detiled description of fuel components is limited by the prohibitive chemistry computtion time tht is required when using rection mechnisms within mny components. Hence, it is desirble to chieve computtionl efficiency by reducing the number of chemicl surrogtes t the minimum expense of ccurcy. Two-component chemicl surrogte pproch using the primry reference fuel (PRF) is used due to its simplicity in representing rectivity rnging from gsoline to diesel [2] [3], s well s the vilbility of its detiled rection kinetics mechnism. R et l. [4] studied the vporiztion of multicomponent surrogte fuel spry in engine operting condition. They found tht the vpor-fuel composition fter injection cn only be cptured by multi-component surrogte fuel model nd in return it cn directly ffect vporiztion rte nd ignition loction.
Annd et l. [5] represent the fuels physicl nd chemicl properties with two different set of surrogte components. They suggested mixture of physicl surrogtes (PS) tht cn describe the physicl behvior of fuel. They vlidted the surrogte fuel behvior by compring the hydrogento-crbon(h/c) rtio, cetne index, distilltion profile, specific grvity nd lower heting vlue of their model with experimentl dt. However, they suggested different chemicl-surrogte components bsed on the group chemistry of ech surrogte spices to describe the combustion of the fuel. This method is clled the group chemistry Representtive (GCR). R et l. [6] lter presented the physicl surrogte group chemistry (PSGCR) model. In the PSGCR model, the sme physicl nd chemicl surrogte components re used. Indeed, in the model ech physicl surrogte component hs its own combustion rection mechnism. The consistency between the physicl nd chemicl surrogte components mkes the PSGCR model useful combustion model in multi-component fuel simultion context. When the group chemistry representtion (GCR) is used in combustion modeling with limited number of chemicl surrogte components, n lterntive method is desired to compenste ccurcy reduction due to simplifiction of chemicl composition representtion. A method of on-the-fly rectivity djustment (ReAd) of chemicl rection mechnism is presented in this study. In this method, conditions re ssumed tht combustion of physicl surrogte components (typiclly mny) is represented by tht of few chemicl surrogtes (typiclly up to 3 components). The different rectivity of locl mixtures with different compositions is considered in the rection clcultion by djusting the rection rte coefficients of selected rections of the chemicl surrogte components. Detiled description of the method is given in the following section. The model ws implemented into n in-house multidimensionl CFD code, KIVA-CHEMKIN-MTU, nd vlidted with spry simultions. Comprison ws mde between the results of the single-surrogtebsed ReAd model nd the 14-component PSGCR model. NUMERICAL APPROACH Following R nd Reitz [6], the rectivity of locl mixture is expressed s the reltive rectivity index (RRI), which is well correlted to the verge mixture cetne number (CN). The verge mixture CN is clculted from individul components mole frction nd CN, CN = x i CN i. When the verge mixture CN is greter or smller thn tht of the chemicl surrogte, the rection rte coefficients of selected rections in the rection mechnism of the chemicl surrogte component re djusted such tht the ignition dely times of the chemicl surrogte mechnism mtch those corresponding the mixture CN for reference condition. In the model, only pre-exponentil fctor of the control rections is djusted. The extent of djustment, which is clled to be djustment fctor, of the pre-exponentil fctor is formulted s function of CN bsed on ignition dely times of stoichiometric fuel/ir mixtures clculted under constnt volume condition for n initil temperture of 850 K nd n initil pressure of 40 br. n-alknes re employed s RRI reference fuels to formulte the djustment fctor. In ddition, when the verge mixture CN is clculted, some rdicls s well s the fuel component my be included in order to consider the contribution of lrge rdicls nd intermedite species to the rectivity of the fuel. In the present model, those species re limited to species tht hve the sme C-number s the fuel component. For exmple, when n-heptne is employed s chemicl surrogte, n-heptyl rdicl, C 7H 15, is distributed to the mount of individul physicl surrogte components in the locl mixture ccording to their contribution to the verge CN. Following n RRI eqution for n-lknes [6], RRI = (1/ ) + b, with =20, b=12, the pre-exponentil fctors of the control rections re vried to mtch the ignition dely times of n-lknes with different CN, nd then correltion is formulted by fitting the mount of pre-exponentil fctor chnge, clled djustment fctor, nd the n-lkne CN dt. The selection of control rections is mde bsed on the ignition dely curve sensitivity nlysis, picking the most sensitive rections t low to intermedite tempertures (T < 1000 K). In the present model, three key rections, clled control rections, re selected s below. Rectivity Adjustment (ReAd) method C 7H 15O 2= C 7H 14OOH (C-1) Pge 2 of 6
C 7H 14OOH+O 2=O 2C 7H 14OOH nc 7H 16+HO 2=C 7H 15+H 2O 2 Pge 3 of 6 (C-2) (C-3) Control rection-1 (C-1), which is n isomeriztion rection, ffects ignition dely times t both low nd intermedite tempertures, while rection C-2, which is the second oxygen molecule ddition rection, minly ffects ignition dely times t intermedite tempertures. Control rection C-3 minly ffects ignition dely times t intermedite to high tempertures. Combintion of djustment of C-1 nd C-2 control rections llows to cpture rectivity chnge by mimicking the vrition of ignition dely curves of n- lknes, especilly with higher rectivity thn n- heptne. For exmple, when locl mixture with n verge CN of 68 is clculted with n-heptne mechnism (CN=56.5), the pre-exponentil fctors of rections C-1 nd C-2 re incresed to shortens ignition dely time tht corresponds to the vlue obtined from the RRI eqution (the interpolted vlue between those of n-octne (CN=64.4) nd n- nonne (CN=72.0)). When the locl mixture CN is lower thn tht of n- heptne the ignition dely times t high tempertures re likely to be much longer thn those of n-heptne. This behvior cn be cptured by combined djustment of C-1 nd C-3 rections. The fitted equtions for djustment fctor, denoted s S fctor, of ech control rection re shown below. When mixture CN is greter thn n-heptne, S fctor for control rections C-1 nd C-2 is given s S fctor,c 1 = (7.949 10 5 )CN 3 (1.455 10 2 )CN 2 + 0.8822CN 16.71 (1) S fctor,c 2 = (2.392 10 6 )CN 3 (3.381 10 4 )CN 2 + 0.03367CN 0.05936 (2) And, when the mixture verged rectivity is lower thn n-heptne, S fctor for control rections C-1 nd C-3 is given s S fctor,c 1 = 0.07571CN + 5.247 (3) S fctor,c 3 = (3.2269 10 3 )CN 2 0.4337CN + 15.07 (4) Fuel redistribution method It is notble tht one of the two drwbcks of the GCR pproch, i.e., misrepresenttion of the verge rectivity of the locl mixture composition cn be remedied by the rectivity djustment of the ReAd model. However, the inherent error induced by the grouping/redistributing processes still remins. The problem cn be resolved by rectivitybsed redistribution technique. The consumption rte of individul specie, ω i, is pproximted s ω i = m i t Following the rgument of R nd Reitz [6], the consumption rte is ssumed to be inversely proportionl to the chrcteristic rection time. Using the ignition dely time t reference condition, t ig, s the chrcteristic rection time nd employing RRI eqution to obtin t ig, Eq (5) becomes m i t ~ 1 τ ig,i or m i = k k = = k RRI i b k CN i b t τ ig,i /(RRI i b),where nd b re RRI eqution constnts for hydrocrbon chemicl clsses [6] nd k is proportionlity constnt. (5) (6) Totl fuel consumption m for given time step t is given s m = m i = k t CN i b or m i = (6) CN i b m (7) CN i b Therefore, the consumption of individul fuel components re determined from totl fuel consumption tht re clculted using the rection kinetics of the chemicl surrogte. Redistribution of grouped fuel fter the rection clcultion is done bsed on this individul consumption informtion, nd thus, the redistribution error of the GCR pproch cn be minimized. RESULTS AND DISCUSSION In order to vlidte the model, simultions were performed for 1) homogeneous mixture ignition processes t constnt volume, 2) HCCI engine
combustion, nd 3) spry combustion in constnt volume chmber. Simultions with the ReAd model turned on nd off were performed, nd compred with the reference results obtined using the PSGCR model. A single-component chemicl surrogte pproch ws employed using skeletl n-heptne rection mechnism extrcted from the PSGCR mechnism. When the ReAd model is tuned off, rection clcultion is done by the GCR model, tht is, ll the PS components re grouped nd ssigned to n- heptne for rection clcultion, nd then, updted fuel mount is redistributed to the PS components bsed on the mss frctions before the rection clcultion. () Homogeneous mixture ignition processes t constnt volume Figure 1 shows test results of rectivity djustment by the ReAd model. In Fig. 1(), it is seen tht the ignition dely times of higher rectivity fuels, i.e., n- decne nd n-dodecne, re well predicted by the ReAd model using the djustment fctor equtions (1) nd (2). For lower rectivity n-pentne nd n- hexne, The ReAd model lso performs well to cpture their ignition dely times, s shown in Fig. 1(b). Another vlidtion simultion ws performed for two-component fuel of 50% decline (C 10H 18) nd 50% n-hexdecne (C 16H 34) which hs n verge cetne number of 74.0. Autoignition of stoichiometric homogeneous fuel/ir mixture t constnt volume ws clculted for initil temperture of 850K nd initil pressure of 40br. Figure 2 shows profiles of temperture nd mss of the two components. As is expected, ignition clculted with the GCR method using the n-heptne rection kinetics (CN=56.5) ws more retrded thn the PSGCR cse. Note tht the composition of fuel does not chnge before nd fter the rection clcultion since the fuel components re redistributed bsed on the initil mss frction. This results in the sme consumption profiles of declin nd n-hexdecne, s shown in the figure. It is clerly seen tht the 2 nd dely time (time between the cool flme nd min ignition timings) is predicted to be significntly shortened by the PSGCR model. It is notble tht n-hexdecne (CN=100) is predicted to be consumed fster thn declin (CN=48). In prticulr, it is clerly seen tht consumption of high rectivity fuel component (b) Figure 1: Comprison of predictions of homogeneous mixture ignition dely times t constnt volume. () n-decne nd n-dodecne oxidtion, (b) n-pentne nd n-hexne oxidtion. drives the ignition process such tht significnt mount of the lower rectivity fuel is consumed t the time of min ignition. Compred to the n- heptne profile, it is lso seen tht the mount of consumption during the cool flme period is much more in the PSGCR cse. Applying the ReAd model dvnces the min ignition time, but not enough to cpture tht of the PSGCR model. The difference of consumption rtes of the two components is well represented by the ReAd model, lthough it is predicted to be more thn the PSGCR model. It is interesting tht the cool flme timings by the ReAd model is more dvnced thn the PSGCR model. This indictes tht there is room for improvement of djustment fctor clcultion by considering the effect of 2 nd dely of the chemicl surrogte component. Pge 4 of 6
diesel model is longer thn tht of n-heptne. The ReAd model well cptures the min ignition timing of the PSGCR model, but the cool flme timing is slightly retrded. This is resonble since the current rectivity djustment formul ws mde bsed on the min ignition dely times only. Spry Combustion in Constnt Volume Chmber Figure 2: Comprison of profiles of temperture nd mss of the two fuel components during constnt volume ignition. Initil pressure nd temperture re 40 br nd 850 K, respectively. HCCI Engine Combustion The ReAd model ws lso tested with homogeneous chrge compression ignition (HCCI) engine combustion. The compression rtio of the engine ws 10.5 nd the initil pressure nd temperture t intke vlve closure were 1.47 br nd 385 K, respectively. A 14-component diesel surrogte model with verge CN of 63.15 [7] ws used in the simultion. Profiles of pressure nd het relese rte of the three model cses re compred in Fig. 3. When multi-component sprys re injected into combustion chmber, not only thermodynmic sttes of the locl mixtures re distributed, but lso locl fuel compositions vry both sptilly nd temporlly. The ReAd model ws pplied to simulte diesel spry combustion in constnt volume chmber. The sme spry injection conditions s employed in the Spry-A of the engine combustion network (ECN) were used for vlidtion except tht the fuel ws replced with the 14- compoment diesel surrogte. Computtion ws performed with 2-D computtionl grid to sve computtion time considering the fct tht singlehole injector ws employed in the spry experiment. Figure 4: Comprison of locl mximum temperture profiles of spry combustion in constnt volume chmber. Figure 3: Comprison of profiles of pressure nd het relese rte of HCCI engine combustion. As is expected from the CN vlues of the diesel model nd n-heptne, the ignition time of diesel predicted by the PSGCR model is erlier thn tht by the n-heptne kinetics without the ReAd model. It is seen tht the 2 nd dely time by the surrogte Figure 4 shows comprison of profiles of locl mximum gs temperture in the combustion chmber predicted by the three models. The points t which the temperture rises rpidly indicte the ignition dely times. It is seen in the figure tht ignition dely time predicted by the PSGCR model is slightly erlier thn tht by the n-heptne kinetics with the ReAd model off. The ReAd model predicts dvncing ignition time compred to the no ReAd model cse, but it seems tht too much rectivity djustment ws mde to cpture the ignition dely time of the PSGCR cse. Possible resons for the discrepncy re two-fold; i) the current djustment Pge 5 of 6
fctor correltions were formulted with ignition dely times of stoichiometric chrge mixtures, nd ii) no chemicl clss effects were considered in the current djustment fctor correltions. Since the oxygen contents of the mbient gses in the simulted Spry-A simultion is 15%, the ignition is significntly delyed compred to the fresh ir cse (21% oxygen), nd thus the mixtures become len before the ignition time. In fct, the detiled locl equivlence rtio distribution shows tht the equivlence rtio t the ignition loction is bout 0.88. This indictes tht, long with the mixture CN, locl equivlence rtio hd better be considered s n dditionl prmeter in the formultion of the djustment fctor in order to improve performnce of the ReAd model. Fuel components in different chemicl clsses show different ignition dely curve chrcteristics. For exmple, n-lknes tend to show strong negtive temperture coefficient (NTC) behvior. On the contrry, iso-lknes tend to show wek NTC behvior. This chemicl clss effects were not modeled in the present ReAd model nd need to be considered for further improvement of the model. SUMMARY/CONCLUSIONS A method of on-the-fly rectivity djustment (ReAd) of chemicl rection mechnism is presented in this study. In this method, conditions re ssumed tht combustion of physicl surrogte components (typiclly mny) is represented by tht of few chemicl surrogtes (typiclly up to 3 components). The different rectivity of locl mixtures with different compositions is considered in the rection clcultion by djusting the rection rte coefficients of selected rections of the chemicl surrogte components. The performnce of the model is evluted under the different operting conditions. The results revel tht the ReAd model cn improve the shortcomings of the GCR model to some extend while mintining superb computtionl efficiency. Comprison of the chrcteristic time (ctc), representtive interctive flmelet (RIF), nd direct integrtion with detiled chemistry combustion models ginst opticl dignostic dt for multi-mode combustion in hevy-duty di diesel engine. Technicl report, SAE technicl pper, 2006. [2] H.J. Currn, P. Gffuri, W.J. Pitz, nd C.K. West-brook. A comprehensive modeling study of iso-octne oxidtion. Combustion nd flme, 129(3):253 280, 2002. [3] C.K. Westbrook, W.J. Pitz, M. Mehl, nd H.J. Currn. De-tiled chemicl kinetic rection mechnisms for pri-mry reference fuels for diesel cetne number nd sprk-ignition octne number. Proceedings of the Combustion Institute, 33(1):185 192, 2011. [4] R. Lemire, A. Fccinetto, E. Therssen, M. Ziskind, C. Focs, nd P. Desgroux. Experimentl comprison of soot formtion in turbulent flmes of diesel nd sur-rogte diesel fuels. Proceedings of the Combustion Institute, 32(1):737-744, 2009. [5] Y. R nd R.D. Reitz. A vporiztion model for discrete multi-component fuel sprys. Interntionl Journl of Multiphse Flow, 35(2):101 117, 2009. [6] K. Annd, Y. R, R.D. Reitz, nd B. Bunting. Surrogte model development for fuels for dvnced combustion engines. Energy & Fuels, 25(4):1474 1484, 2011. [7] Y. R nd R.D. Reitz. A combustion model for multi-component fuels using physicl surrogte group chemistry representtion (psgcr). Combustion nd Flme, 162(10):3456 3481, 2015. REFERENCES [1] S. Singh, R.D. Reitz, nd M.PB Musculus. Pge 6 of 6