HOMOGENEOUS CHARGE COMPRESSION IGNITION ENGINE: A SIMULATION STUDY ON THE EFFECTS OF INHOMOGENEITIES

Transcription

1 Paper No ICE-275 ICE-Vol. 34-2, 2000 Sprng Techncal Conference ASME 2000 HOMOGENEOUS CHARGE COMPRESSION IGNITION ENGINE: A SIMULATION STUDY ON THE EFFECTS OF INHOMOGENEITIES Peter Magaard, Faban Mauss Dvson of Combuston Physcs Lund Insttute of Technology P.O. Box 8, 2200 Lund Sweden Phone : +46(0) E-mal : faban.mauss@forbrf.lth.se Markus Kraft Department of Chemcal Engneerng Unversty of Cambrdge Cambrdge CB2 3RA UK Phone : +44(0) E-mal : markus_kraft@cheng.cam.ac.uk ABSTRACT A new stochastc model for the HCCI engne s presented. The model s based on the PaSPFR-IEM model and accounts for nhomogenetes n the combuston chamber whle ncludng a detaled chemcal model for natural gas combuston consstng of 53 chemcal speces and 590 elementary chemcal reactons. Wth ths model the effect of temperature dfferences caused by the thermal boundary layer and crevces n the cylnder for a partcular engne speed and fuel to ar rato s studed. The boundary layer s dvded nto a lamnar flm layer and a turbulent buffer zone. There are also colder zones due to crevces. All zones are modeled by a characterstc temperature dstrbuton. The smulaton results are compared wth experments and a prevous numercal study employng a PFR model. In all cases the PaSPFR-IEM model leads to a better agreement between smulatons and experment for temperature and pressure. In addton a senstvty study on the effect of dfferent ntenstes of turbulent mxng n the combuston s performed. Ths study reveals that the gnton delay s a functon of turbulent mxng of the hot bulk and the colder boundary layer. INTRODUCTION The Homogeneous Charge Compresson Ignton (HCCI) engne s a promsng alternatve to the exstng Spark Ignton (SI) engnes and Compresson Ignton (CI) engnes. As n a desel engne, the fuel s exposed to suffcently hgh temperature for autognton to occur, but for HCCI a homogeneous fuel/ar mxture s used. The homogeneous mxture s created n the ntake system as n a SI engne, usng a low-pressure njecton system or by drect njecton wth very early njecton tmng. To lmt the rate of combuston, very dluted mxtures have to be used. Compared to the desel engnes the HCCI has a nearly homogeneous charge and vrtually no problems wth soot and NOx formaton. On the other hand HC and CO levels are hgher than n conventonal SI engnes. Overall, the HCCI engne shows hgh effcency and fewer emssons than conventonal nternal combuston engnes. The effcency of the HCCI engne has prevously been shown by a number of experments. Parts of the experments have been complemented by numercal studes modelng the engne as a plug flow reactor (PFR) [][2]. In these smulatons the gnton delay tmes for a set of dfferent parameters were nvestgated. The results ndcate that local nhomogenetes are responsble for dfferences between measurements and smulaton results. One way of accountng for these nhomogenetes s to use multple zones to model boundary layer effects. Such work has recently been performed usng a 0 zone-model for the HCCI engne [2]. Another way s to use a model that s based on the probablty densty functon of the physcal varables that are mportant n the combuston process. If one wshes to study chemcal reactons n detal, smplfyng assumptons have to be ntroduced because the numercal cost to solve a model that descrbes chemstry and all aspects of flow would be too hgh. 63 Copyrght 2000 by ASME

2 One way to reduce ths cost s to assume that chemcal speces and temperature are random varables wth a Probablty Densty Functon (PDF) that does not spatally vary n the combuston chamber.e. temperature and composton can fluctuate. Ths assumpton s not as strong as the assumpton made n case of the PFR model where the physcal quanttes are not random varables and they are homogeneous all over the combuston chamber. The purpose of ths paper s to ntroduce a new smulaton model featurng the partally strred plug flow reactor (PaSPFR) as descrbed n refs. [3][4]. Numercal smulatons of the gnton process n the HCCI engne wll be performed usng a detaled chemcal model for butane and lower alkanes n the framework of the PaSPFR. The reacton mechansm contans 53 chemcal speces and 590 elementary chemcal reactons. In the PaSPFR model the unclosed term for turbulent mcromxng has been modeled by the smple determnstc IEM mxng model. The PaSPFR model wll be used n an attempt to mprove on prevous numercal smulatons of the HCCI process takng fluctuatons n temperature that are nduced by the colder thermal boundary layer nto account. The results of the new PDF based model and the old PFR model are compared to the experment n ref []. Addtonally, we perform a senstvty study on the nfluence of turbulent mxng on gnton delay. The effect of dfferent mxng ntenstes on the mean of temperature and pressure as well as ther standard devaton (STD-DEV) wll be dscussed. NOMENCLATURE Abbrevatons HCCI : Homogeneous Charged Compresson Ignton PFR : Plug Flow Reactor PaSPFR : Partally strred Plug Flow Reactor PDF : Probablty Densty Functon MDF : Mass Densty Functon IEM : Interacton by Exchange wth the Mean mxng model STD-DEV : Standard Devaton ATDC : After Top Dead Center BTDC : Before Top Dead Center BBTC : Before Bottom Dead Center : Crank Angle Degree CR : Compresson rato RPM : Revolutons per mnute a A B C v C φ F φ Arabc symbols : Crank radus : Cylnder surface area : Bore : Specfc heat at constant volume : Proportonalty constant : Jont scalar mass densty functon h l l M M m p T t Q R R x V V c w (n) Y α εˆ ε φ φ Θ ν j ρ τ τ φ ψ ω j : Specfc enthalpy of speces : Connectng rod : Integral length scale : Molecular weght of speces : Mean molecular weght : Mass : Pressure : Temperature : Tme : Source term : Unversal gas constant : Autocorrelaton coeffcent : Volume : Compresson volume : Mass weght for PDF : Mass fracton of speces Greek Symbols : Heat transfer coeffcent : Emssvty : Dsspaton : Equvalence rato : Jont scalar random vector : : Stochometrc coeffcents : Densty : Turbulent velocty tme scale : Turbulent scalar tme scale : Jont scalar sample varable : Rate of reacton j Sub- and Superscrpts BL : Index for boundary layer Bulk : Index for bulk I : Index for scalars J : Index for reactons n : Index for scalar state S : Number of chemcal speces R : Number of reactons w : Wall PREVIOUS MODEL AND EXPERIMENTAL RESULTS The expermental results used n ths work are the same as those descrbed n [].The expermental setup s as follows : A sx-cylnder Volvo TD00 seres truck desel s used, modfed for one-cylnder use, and converted to HCCI operaton. The engne data are gven n Table, addtonal detals can be found n [] and [2]. The smplest possble combuston chamber geometry s used,. e. a flat pston crown gvng a pancake combuston chamber. Common commercally avalable natural gas s used as fuel [2]. The predomnate compound of the natural gas s methane, wth a non-neglgble content of other gases, manly hgher hydrocarbons such as ethane, propane and butane (see Table 2 64 Copyrght 2000 by ASME

3 for detals). Table : Volvo TD00 engne parameters. Dsplaced Volume 600 cm 3 Table 3: Intal values for the smulatons of engne case (60 BTDC). φ CR T [K] P [BAR] RPM Bore Crank radus Stroke Connecton Rod mm 70 mm 40 mm 260 mm The prevous numercal studes model the HCCI engne as a smple PFR and thus gnore nfluences of local nhomogenetes n the cylnder. An example of results from the prevous work can be seen n Fgure n ref. []. Exhaust Valve Open Exhaust Valve Close Inlet Valve Open 39 BBDC (at mm lft) 0 BTDC (at mm lft) 5 ATDC (at mm lft) mean sngle cycle calculated Inlet Valve Close 3 ABDC (at mm lft) T (K) Table 2 : Natural gas components. Component Mole-% Mass-% Methane Ethane Propane n-butane + hgher Ntrogen Carbon doxde The engne s run on natural gas at fuel-ar ratos of φ = Four dfferent engne speeds are used: 800, 000, 200 and 400 rpm. These engne speeds are chosen as beng representatve for normal use consderng that maxmum torque for a normal CI-operatng TD00-seres desel s acheved at 400 rpm and the engne dle speed s rpm. In ths work we wll focus on the operatng condtons stated n Table 3, measured at 60 BTDC. The fact that the fuel and oxdzer s assumed to be perfectly mxed gves a very steep ncrease n temperature upon gnton. In realty not all of the mxture wll reach gnton condtons at exactly the same tme, whch results n a less steep gnton curve as seen n the expermental results n Fgure Tme () Fgure : Numercal results from the PFR model compared wth experments. The TD00 engne s n ths case run at 000 rpm and φ = The jagged lne represents results from a sngle expermental engne cycle and the broken lne s ts smoothed verson. Because of the use of a detaled reacton mechansm n the PFR model the gnton tmng s however predcted correctly. The oscllatons n the sngle cycle curve are due to pressure oscllatons. The temperature s evaluated drectly from the pressure. The orgn of the pressure oscllatons s not fully understood. Most lkely the rate of combuston s so fast that the pressure gradent n the cylnder generates vbratons n the engne structure. These then result n volume changes n the cylnder and hence pressure oscllatons [prvate communcaton wth B. Johansson]. MODELING THE BOUNDARY LAYER As stated above the assumpton of homogenety s responsble for a too hgh temperature rse rate durng gnton. To overcome ths assumpton we model nstead the exstence of a colder boundary layer of gas near the cylnder wall. The thckness of ths boundary layer has recently been 65 Copyrght 2000 by ASME

4 nvestgated expermentally on the TD00 seres engne [7]. These experments suggest that the thckness of the boundary layer s approxmately 3 mllmeters. The same result can be obtaned from Heywood [8] for the general case. For the current HCCI engne setup a boundary layer of 3 mm corresponds to approxmately 0 % of the dsplaced cylnder volume. Snce the boundary layer s assumed to be sgnfcantly cooler than the bulk gasses the total gas mass n the boundary layer wll more lkely be 5-20 %. Addtonally we have to account for colder flud parcels n crevces. The boundary layer can be descrbed by applyng theores for the flow of a flud passng a sold surface. It s therefore assumed to consst of a thn flm layer mmedately adjacent to the cylnder wall plus a buffer zone between ths and the turbulent bulk flow [9]. The crevces are represented by the frst fve partcles and the flm layer corresponds to partcle numbers 6 to 5 as llustrated n Fgure 2. Wthn the flm layer we have a strong ncrease n temperature. Ths s reflected by the large varance of temperature of the flm layer partcles. In the lamnar zone heat s transferred prmarly through conducton. 650 characterstcs for the HCCI engne are comparable to these results. Ths assumpton can be justfed by the fact that the same pancake shaped combuston chamber s used n the two setups and that there s no nfluence on the flow from a propagatng flame front n the expermental nert case. The fluctuatng velocty component s defned by the turbulence ntensty u as t0 + t 2 u = lm u dt t t t0 and the ntegral length scale l I s defned as l I = 0 R dx where R x s the autocorrelaton coeffcent of the fluctuatng velocty. The turbulence mxng tme scale s n ths case defned as the relaton between the ntegral length scale and the fluctuatng velocty component x ½ T (K) Flm Buffer zone τ li τ φ = = C C u φ φ 500 where C φ s a model constant. The turbulent energy dsspaton rate ε s gven by Partcle number ( ) u 3 ε =. l I Fgure 2: Temperature dstrbuton n the boundary layer. The temperature ncreases from the wall temperature and asymptotcally approaches the bulk gas temperature. As one approaches the bulk of the cylnder the temperature ncreases asymptotcally towards the bulk gas temperature (llustrated by the Buffer zone n Fgure 2). In the fgure above the wall temperature s 450K and the hot bulk gas s 650K. The boundary layer s modeled usng 50 flud partcles representng the 3mm radus adjacent to the cylnder wall. TURBULENT PHENOMENA IN THE ENGINE Expermental results performed on the Volvo TD00 seres engne gve a quanttatve descrpton of the turbulent behavor of the gases n the cylnder []. These experments have been performed when the engne s run n lean SI mode and for the nert case. In the followng we wll assume that the turbulence Measurements of turbulence ntensty n the cylnder show fluctuatons n the range of m/s from 20 BTCD to 20 ATDC. The ntegral length scale s n the range of 0-8 mm. Ths gves turbulence mxng tme scale n the order of 0.0s and a dsspaton rate n the order of 0 m 2 /s 3. THE STOCHASTIC REACTORMODEL In order to account for the nhomogenetes n the combuston chamber we use a stochastc reactor model PaSPFR-IEM as descrbed n [3]. The assumpton of homogenety for speces mass fractons and temperature that has been made prevously n [] s replaced by the assumpton of statstcal homogenety. Ths means that the jont scalar PDF does not vary wthn the combuston chamber. In the followng we dstngush between global and local quanttes. Global quanttes are mass m, volume V(t), mean densty ρ(t) and pressure p(t). We assume that global quanttes do not vary spatally n the combuston chamber. Local quanttes are chemcal speces mass fractons Y (t), 66 Copyrght 2000 by ASME

5 =,...,S and temperature T(t). They can vary wthn the combuston chamber and are assumed to be random varables. Ther jont random vector s defned as Φ ( + t) = ( Φ,..., Φ S ) = ( Y,..., YS, T ) and the correspondng jont scalar mass densty functon (MDF) s gven by FΦ ( Ψ,..., ΨS + ; t) assumng spatal homogenety as proposed n the PaSPFR model. Its tme evoluton s gven by the followng MDF-transport equaton FΦ ( Ψ; t) + t Ψ Ψ CΦ ( ( Ψ 2 τ ( Q ( Ψ) F Φ ) F Φ Φ ( Ψ; t)) = ( Ψ; t)) where the ntal condtons are gven as F Φ ( Ψ;0) = F0 ( Ψ). The brackets. denote the mean accordng to F φ and C φ /τ s a measure for the ntensty of scalar mxng. The model constant C φ s set to 2.0 and the turbulent tme scale s estmated from the experment as mentoned above. The rght hand sde of ths equaton descrbes the mxng of the scalars due to turbulent dffuson. Ths model s called IEM model and s known to have some defcences but due to ts smplcty and low numercal cost t has been appled (detals n Ref. [3]). The term Q descrbes the change of the MDF due to chemcal reactons, change n volume, and heat losses. Q S + R M Q = ν, jω j =,..., S ρ j= RT M = ( h ), j j p c + M ν ω ρ c ( αa( T T c v S v = w R j= ) + Aσεˆ( T 4 T 4 W )) v dv dt The convectve heat transfer coeffcent s obtaned from the Woschn equaton [8], σ s the Stefan-Boltzmann constant and the emssvtyεˆ of methane [0] s used. Besdes the MDF equaton the tme evoluton of the global quanttes has to be computed. The change of volume V( Θ (t) ) n terms of s gven by V π B ( Θ( t) ) = V + l + a a cos( l a sn Θ( t)) 2 c as n [8]. Mean densty can be calculated as m ρ ( t ) =, V ( t) pressure s gven by the deal gas law p ( t) = ρ( t) R T M where T s the mean temperature accordng to the MDF and M s the expected mean molecular weght. These equatons as well as the transport equaton of the MDF have to be solved smultaneously. For ths work the stochastc reactor model s mplemented nto the exstng code for HCCI engne calculatons as descrbed n [5][6]. The soluton procedure s based on a stochastcally weghted partcle method and a hgher order operator splttng technque. Detals of the numercal procedure wll be publshed separately. INTIAL CONDITIONS The smulatons for the auto-gnton process were made usng ntal values obtaned from the experments at 60 BTDC descrbed n Table 3. The speces composton n the boundary layer and the bulk s assumed to be dentcal. The only scalar varable that vares s temperature. The ntal MDF s gven by BL ( BL+ ) ( BL+ ) F 0( Ψ) = w δ ( Ψ Ψ ) + w δ ( Ψ Ψ ) n= Bulk The weghts BoundaryLayer (n) w are chosen to be w mbl = BL m B ulk : : n =,..., BL n = BL + wth m=m BL + m bulk beng the mass of the fuel-ar mxture n the combuston chamber. m BL s the mass of fuel-ar mxture n the (n) boundary layer and m bulk s the bulk. The scalars Ψj for j=,...,s are the chemcal speces mass fractons and are all set to the same value to meet the condtons n Table 3. The temperature n the boundary layer Ψ S + : n =,..., BL s set accordng to the temperature profle dsplayed n Fgure 2. The temperature n the bulk Ψ S + : n = BL + s set to a value to match the ntal mean temperature n the combuston chamber. For the present case we model the boundary layer by choosng a turbulent mxng tme scale (τ) of 0.02s and 20 % of the total gas mass n the boundary layer. 67 Copyrght 2000 by ASME

6 RESULTS AND DISCUSSION In the followng secton we wll demonstrate the capabltes of the new model and compare numercal results from ths model to expermental results and results from the prevous model descrbed n []. In ths case the engne s operatng at 000 rpm wth a fuel to ar rato of Ths s the case descrbed n Table 3. P [Pa] Experment Prevous model 3 partcles 5 partcles 7 partcles pressure s affected. Choosng 5 flud partcles gves a smulated result nearly dentcal to the expermental results. The new model generally produces results sgnfcantly closer to the experments than the prevous model. Fgure 4 shows the temperature hstory for the same case. The expermental temperature hstory s not drectly measured but calculated from the pressure measurements usng a very smple -zone model. Therefore the smulated temperature s not drectly comparable to the expermental results n ths fgure. Fgure 5 llustrates the standard devaton (STD-DEV) of the calculated temperature for the smulaton. Agan the number of flud partcles representng the lamnar part of the flm layer s vared from 3 to 7. The STD-DEV s slowly decreasng durng the frst nert part of the compresson stroke due to the temperature mxng of flud parcels n the bulk and n the boundary layer. At around 3 BTDC the bulk gntes whch leads to a rapd ncrease of Fgure 3: Pressure hstory. New model compared to expermental results and prevous model. STD-DEV of temperature (K) partcles 5 partcles 7 partcles T [K] Experment Prevous model 3 partcles 5 partcles 7 partcles 000 Fgure 4: Temperature hstory. New model compared to expermental results and prevous model. Fgure 3 llustrates the pressure hstory for ths case. The number of flud partcles representng the lamnar part of the flm layer and the crevces s vared from 3 to 7. The shape of the gnton curve s ndependent of the number of cold partcles n ths part of the flm layer but gnton tmng and maxmum 0 Fgure 5: STD-DEV of temperature hstory. STD-DEV. Whle the gnton process s progressng the STD- DEV decreases untl most of the boundary layer has gnted. The dfference n STD-DEV between the tme before gnton and after gnton ndcates that not all parts of the boundary layer are fully burnt. Generally one can conclude from these frst results that the mplementaton of the SRM greatly mproves the numercal smulaton of the HCCI process. The IEM mxng model does descrbes mxng adequately f the ntal dstrbuton of partcles n crevces and boundary layer s suffcently good. In the followng sectons 5 flud partcles are chosen to represent the lamnar part of the flm layer. SENSITIVITY STUDY In ths secton a senstvty study on the new model wll be presented. It wll study the effects of varyng the turbulence tme scale (τ). 68 Copyrght 2000 by ASME

7 In Fgure 6 the turbulence mxng tme scale s vared from 0.s to 0.000s. The result of ths study shows that a very slow mxng (τ=0.s) wll promote a very early gnton of the hot spots n the cylnder snce they do not mx wth the cold spots. understood. From ths graph t s evdent that the bulk gntes earler n the slow mxng cases than the fast mxng cases because t s not cooled by mxng wth the boundary layer. As a consequence we fnd a decrease n the maxmum value of the STD-DEV wth ncreasng mxng ntensty. As mxng becomes more effcent a tme delay between gnton of the colder and hotter spots s notced Tau = E- s Tau = E-2 s Tau = E-3 s Tau = E-4 s To observe the effects of mxng n the fast mxng cases Fgure 8 s useful. For τ = 0.00s the mxng s close to perfect before gnton and the STD-DEV s an order of magntude smaller than for the two slow mxng cases. For τ = 0.000s the mxng s so fast that no STD-DEV readng s notceable. T (K) Fgure 6: Senstvty study on turbulence mxng tme scale (τ). As one ncreases the nfluence of mxng by decreasng τ the gnton s delayed. At a value of τ of 0.00s the mxng s now so effcent that a very large regon of the fuel and ar STD-DEV Tau = E- s Tau = E-2 s Tau = E-3 s Tau = E-4 s STD-DEV Tau = E- s Tau = E-2 s Tau = E-3 s Tau = E-4 s 0 Fgure 7: STD-DEV of temperature hstores for the senstvty study on turbulence tme scale. mxture wll gnte smultaneously. At an even smaller value of τ the stuaton s n essence smlar to the homogeneous case and a very steep slope on the gnton curve s observed. By observng the STD-DEV of temperature for ths study n Fgure 7 the mxng effects descrbed above can be better Fgure 8: STD-DEV of temperature. Close-up on the faster mxng cases. CONCLUSION In the present work a new model for the numercal smulaton of the combuston process n the HCCI engne has been presented. Ths model s based on the PaSPFR-IEM model. It s capable of smulatng nhomogenetes n the cylnder caused by the thermal boundary layer adjacent to the cylnder walls. The model results have been verfed aganst engne measurements and results from a PFR model. Generally the new model shows very promsng results by sgnfcantly mprovng the results from the PFR model. The smulated gnton curves for temperature and pressure are n very good agreement wth the experments. The modelng of the boundary layer n the cylnder results n a more smooth gnton curve as the cold and hot spots n the cylnder gnte at dfferent tmes. The STD- DEV of temperature gves evdence that not all of the boundary layer s burnt. Ths mght explan the excess of unburnt hydrocarbons from the HCCI engne. The IEM mxng model, as smplest mxng model, needs to be replaced by more realstc models to smulate the mxng process n the engne. Furthermore a seres of senstvty studes have been 69 Copyrght 2000 by ASME

8 carred out where the consequences of dfferent ntenstes of turbulent mxng have been nvestgated. The gnton delay tme s senstve to the mxng tmes. Very slow mxng wll result n early gnton of the hot spots followed by a delayed gnton of the colder ones. Very fast mxng wll produce a case smlar to the homogeneous case. Future work wll nclude the mplementaton of a more detaled mxng model e.g. the Curl mxng model. Ths wll ncrease the demand on CPU-tme but wll gve a more accurate descrpton of the mxng processes takng place n the cylnder. Further expermental results wll verfy the boundary layer model as used n ths work. Johansson B.: On cycle to cycle varatons n spark gnton engnes, Doctoral Thess, Lund Insttute of Technology, Aceves S. M., Flowers D. L., Westbrook C. K., Smth J. R., Ptz W.: A Mult-Zone Model for Predcton of HCCI Combustons and Emssons, SAE ACKNOWLEDGMENTS We would lke to thank Dr. Techn. Bengt Johansson, Dvson of Heat and Power, Lund Insttute of Technology, for some very useful dscussons on the turbulent characterstcs of the HCCI engne. Fnancal support from Caterpllar s kndly acknowledged. REFERENCES. Amneus P., Nlsson D., Mauss F., Chrstensen M., Johansson B.: HCCI Engne : Experments and Detaled Knetc Calculatons, COMODIA 98, p M Chrstensen., Johansson B., Amneus P., Mauss F.: Supercharged HCCI engne, SAE-paper , Kraft M. : Stochastc Modellng of Turbulent Reactng Flow n Chemcal Engneerng, VDI Verlag, Fortschrttsberchte des VDI, Rehe 6, #39, Procaccn C., Kraft M., Fey H., Bockhorn H., Longwell J.P., Sarofm A., Smth K. A.: PIC formaton durng the combuston of smple hydrocarbons n nhomogeneous ncneraton systems, Twenty-Seventh Symposum (Internatonal) on Combuston, The Combuston Insttute, p , Hajreza S., Mauss F., Sundén B.: Investgaton of End- Gas Temperature and Pressure Increases n Gasolne Engnes and Relevance for Knock Occurrence, SAE Bood J., Bengtsson P-E, Mauss F., Burgdorf K., Denbratt I. : Knock n Spark-Ignton Engnes: End-Gas Temperature Measurements Usng Rotatonal CARS and Detaled Knetc Calculatons of the Autognton process, SAE Hultqvst A., Chrstensen M., Johansson B., Franke A., Rchter M., Alden M.: A Study of the HCCI Combuston Process by Chemlumnescence Imagng, SAE Heywood J. B.: Internal combuston engne fundamentals, McGraw-Hll, Perry R. H.: Perry s chemcal engneers handbook 6 th edton, McGraw-Hll 0 Hottel H.C.: Radant Heat Transmsson, ed. W.H. Adams, 3 rd ed., McGraw-Hll, Copyrght 2000 by ASME