New Phenomenological Six-Zone Combustion Model for Direct

690

Energy & Fuels 2009, 23, 690–703

New Phenomenological Six-Zone Combustion Model for Direct-Injection Diesel Engines Alain Maiboom,* Xavier Tauzia, Samiur Rahman Shah, and Jean-François He´tet Internal Combustion Engine Team, Laboratory of Fluid Mechanics, UMR 6598 CNRS, Ecole Centrale de Nantes, BP 92101, 44321 Nantes Cedex 3, France ReceiVed September 1, 2008. ReVised Manuscript ReceiVed NoVember 13, 2008

A new phenomenological multizone combustion model has been developed for direct-injection (DI) diesel engines based on the well-known Dec’s “conceptual” model for DI diesel combustion as well as spray models from Siebers et al. (liquid- and vapor-phase fuel penetration, spray spreading angle, and lift-off length). The model distinguishes six zones and provides local information, such as mean equivalence ratio and temperature in the various zones. A validation of the model is performed while varying main engine parameters, such as engine speed and load, inlet air temperature, exhaust gas recirculation (EGR) rate, boost pressure, or the injection pressure. The model is able to calculate the rate of heat release (ROHR) with good accuracy, whereas the variation of calculated local parameters (core spray and flame temperature, lift-off length, and corresponding equivalence ratio) can be used to explain the main tendencies on engine-out NOx and particulate matter (PM) emissions observed on the engine test bench.

1. Introduction Passenger cars powered by diesel engines have shown great success in Europe over the past decade because of low fuel consumption with high specific power and torque. Nevertheless, to comply with ever more stringent emission standards, particularly regarding NOx and particulate matter (PM) emissions, such as EURO 6 in Europe, diesel engine manufacturers have to find new in-cylinder combustion strategies and/or complex after-treatment devices to reduce their emissions. The study and development of a new in-cylinder emissions control strategy can be performed by measuring global engineout emissions and cylinder pressure (giving the instantaneous heat release rate).1 Such global studies are numerous in the literature, dealing with the influence of engine parameters on engine-out emissions and fuel consumption, such as, for instance, injector nozzle geometry,2 exhaust gas recirculation (EGR) rate,3-5 boost pressure,3-5 inlet air temperature,4,5 injection pressure,2,5 or compression ratio.6 The downside of such studies is that they do not provide any local information in the combustion chamber. * To whom correspondence should be addressed. Telephone: +33-240-37-68-80. Fax: +33-2-40-37-25-56. E-mail: [email protected]. (1) Heywood, J. B. Internal Combustion Engines Fundamentals; McGrawHill: New York, 1988. (2) Karra, P.; Kong, S.-C. Diesel emission characteristics using high injection pressure with converging nozzles in a medium-duty engine. SAE Tech. Pap. 2008-01-1085, 2008. (3) Wakisaka, Y.; Hotta, Y.; Inayoshi, M.; Nakakita, K.; Sakata, I.; Takano, T. Emissions reduction potential of extremely high boost and high EGR rate for an HSDI diesel engine and the reduction mechanisms of exhaust emissions. SAE Tech. Pap. 2008-01-1189, 2008. (4) Maiboom, A.; Tauzia, X.; He´tet, J.-F. Experimental study of various effects of exhaust gas recirculation (EGR) on combustion and emissions of an automotive direct injection diesel engine. Energy 2008, 33, 22–34. (5) Maiboom, A.; Tauzia, X.; He´tet, J.-F. Influence of high rates of supplemental cooled EGR on NOx and PM emissions of an automotive HSDI diesel engine using an LP EGR loop. Int. J. Energy Res. 2008. (6) Curesente, V.; Pacaud, P.; Gatellier, B. Reduction of the compression ratio on a HSDI diesel engine: Combustion design evolution for compliance the future emissions standards. SAE Tech. Pap. 2008-01-0839, 2008.

On the contrary, local visualizations, such as high-temperature chemiluminescence imaging,7 particulate image velocimetry (PIV),8 or natural flame luminosity imaging,9 applied in a constant-volume combustion vessel or an optical single-cylinder engine, provide various qualitative or quantitative local information in the combustion chamber, permitting the study of combustion and emission formation processes. Elsewhere, the main disadvantage of local studies is their complexity and associated cost. Moreover, they cannot take into account some phenomena appearing on a multicylinder standard diesel engine, such as the intake air limitation, because of the turbocharging system, or the cylinder-cylinder dispersions (such as, for instance, the inlet temperature and gas composition dispersions because of EGR). Finally, experiments performed on optical engines are not fully representative for a standard engine. Actually, Aronsson et al.10 have shown that the rate of heat release (ROHR) and the emissions are a little different on an optical engine compared to an all-metal standard engine, because of the lower heat conductivity of the optical parts, whose consequences are a lower heat loss to the wall, a higher temperature of in-cylinder-trapped gas, a reduced ignition delay, and a shorter and faster premixed combustion that modifies the emissions formation processes. The use of combustion models is another way to obtain some information concerning the combustion process. On the one hand, phenomenological combustion models (one-zone or (7) Idicheria, C. A.; Pickett, L. M. Effect of EGR on diesel premixedburn equivalence ratio. Proc. Combust. Inst. 2007, 31, 2931–2938. (8) Hildingsson, L.; Hultqvist, A.; Miles, P. The effect of swirl and injection pressure phasing on flow structures and mixing in an HSDI diesel engine. THIESEL 2006 Conference on Thermo- and Fluid Dynamic Processes in Diesel Engines, 2006. (9) Fang, T.; Coverdill, R. E.; Lee, C. F.; White, R. A. Combustion and soot visualization of low temperature combustion within an HSDI diesel engine using multiple injection strategy. SAE Tech. Pap. 2006-01-0078, 2006. (10) Aronsson, U.; Chartier, C.; Horn, U.; Andersson, O.; Johansson, B.; Egnell, R. Heat release comparison between optical and all-metal HSDI diesel engines. SAE Tech. Pap. 2008-01-1062, 2008.

10.1021/ef800735d CCC: $40.75  2009 American Chemical Society Published on Web 01/09/2009

Six-Zone Combustion Model for DI Diesel Engines

multizone) are mostly simple and very practical because of their fast calculation speed. Several phenomenological combustion models are presented in the literature based on the fact that, in today’s direct-injection (DI) diesel engines, the ROHR is mainly controlled by the mixing process between air and fuel.11-19 For instance, the calculation of the instantaneous ROHR in Barba’s11 or Chmela’s models12,13 is expressed as a function of the instantaneous available fuel mass and the density of the turbulent kinetic energy (calculated with a simplified 0D approach). Using the probability density function theory adapted to the 0D combustion modeling and using complex chemistry look-up tables, Mauviot18 has proposed some improvements of Chmela’s model to take into account complex combustion modes [EGRincurred low-temperature combustion (LTC) and homogeneous charge compression ignition (HCCI) combustion]. The downside of these models is that they are principally dedicated to the calculation of the ROHR and are thus inadequate when trying to have some “local” information in the combustion chamber. On the other hand, computational fluid dynamics (CFD) models have seen great improvement in the last few decades and are presumably the best way to calculate local parameters in the combustion chamber.20 That is why they are often used when trying to interpret global studies obtained on a test bench.2 Elsewhere, their main disadvantage is their calculation time. Intermediate combustion models, quasi-dimensional multizone, are proposed in the literature21-24 and have been widely used to study and find new in-cylinder strategies for emission control, (11) Barba, C.; Burkhardt, C.; Boulouchos, K.; Bargende, M. A phenomenological combustion model for heat release prediction in highspeed DI diesel engines with common-rail injection. SAE Tech. Pap. 200001-2933, 2000. (12) Chmela, F. G.; Orthaber, G. C. Rate of heat release prediction for direct injection diesel engines based on purely mixing controlled combustion. SAE Tech. Pap. 1999-01-0186, 1999. (13) Chmela, F. G.; Pirker, G. H.; Wimmer, A. Zero-dimensional ROHR simulation for DI diesel enginessA generic approach. Energy ConVers. Manage. 2007, 48, 2942–2950. (14) Lakshminarayanan, P. A.; Aghav, Y. V.; Dani, A. D.; Mehta, P. S. Accurate prediction of the rate of heat release in a modern direct injection diesel engine. Proc. Inst. Mech. Eng., Part D 2002, 216, 663–675. (15) Arre`gle, J.; Lopez, J. J.; Garcia, J. M.; Fenollosa, C. Development of a zero-dimentional diesel combustion model. Part 1: Analysis of the quasisteady diffusion combustion phase. Appl. Therm. Eng. 2003, 23, 1301– 1317. (16) Arre`gle, J.; Lopez, J. J.; Garcia, J. M.; Fenollosa, C. Development of a zero-dimentional diesel combustion model. Part 2: Analysis of the transient initial and final diffusion combustion phases. Appl. Therm. Eng. 2003, 23, 1319–1331. (17) Tauzia, X.; Maiboom, A.; Chesse´, P.; Thouvenel, N. A new phenomenological heat release model for thermodynamical simulation of modern turbocharged heavy duty diesel engines. Appl. Therm. Eng. 2006, 26, 1851–1857. (18) Mauviot, G.; Albrecht, A.; Poinsot, T. J. A new 0D approach for diesel combustion modeling coupling probability density function with complex chemistry. SAE Tech. Pap. 2006-01-3332, 2006. (19) Lafossas, F.-A.; Marbaix, M.; Menegazzi, P. Development and application of a 0D DI diesel combustion model for emissions prediction. JSAE Tech. Pap. 20077304, 2007. (20) Vishwanathan, G.; Reitz, R. D. Numerical predictions of diesel flame lift-off length and soot distributions under low temperature combustion conditions. SAE Tech. Pap. 2008-01-1331, 2008. (21) Nishida, K.; Hiroyasu, H. Simplified three-dimensional modelling of mixture formation and combustion in a DI diesel engine. SAE Tech. Pap. 890269, 1989. (22) Hountalas, D. T.; Mavropoulos, G. C.; Zannis, T. C. Comparative evaluation of EGR, intake water injection and fuel/water emulsion as NOx reduction techniques for heavy duty diesel engines. SAE Tech. Pap. 200701-0120, 2007. (23) Rakopoulos, C. D.; Antonopoulos, K. A.; Rakopoulos, D. C.; Hountalas, D. T. Multi-zone modeling of combustion and emissions formation in DI diesel engine operating on ethanol-diesel fuel blends. Energy ConVers. Manage. 2008, 49, 625–643. (24) Jaine, T. Simulation ze´rodimensionnelle de la combustion dans un moteur diesela` injection directe. Ph.D. Thesis, Universite´ d’Orleáns, Orleáns, France, 2004.

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such as intake water injection22 or fuel-water emulsion,22 or the study of new fuels.23 In these models, the fuel jet is divided into several discrete volumes, called “zones”, formed along and across the direction of the fuel. In general, each zone has its own history as the spray penetrates into the air environment of the combustion chamber,21-24 while the calculation of the spray penetration is based on Hiroyasu’s approach.25 More recently, some researchers, such as Dec et al.,26,28-34 have observed the combustion phenomenon in DI diesel engines in detail and have proposed a “conceptual” model of DI diesel combustion that gives a qualitative evolution of the fuel jet and zones development and combustion, which is of particular interest for researchers who develop new combustion models. The aim of the present paper is to propose a new six-zone phenomenological combustion model based on the well-known “conceptual” model proposed by Dec et al.,26 being able to simulate the evolution of main fuel jet parameters (spray angle, liquid- and vapor-phase fuel penetrations, lift-off length, and corresponding air/fuel ratio) as well as mean temperatures in each zone, thus permitting the interpretation of main experimental trends when modifying load, speed, injection timing, inlet temperature, EGR rate, and boost pressure. 2. Model Description A detailed description of the phenomenological multizone combustion model is given below. Main submodels are (i) an injection rate model based on instantaneous injection rate measurements, (ii) the spray models from Siebers et al.28-31 for the description of the fuel jet (maximum liquid-phase fuel penetration, vapor-phase fuel penetration, spray spreading angle, lift-off length, and corresponding air-fuel equivalence ratio), (iii) a model for the ambient gas entrainment by the fuel jet based on the spray model, (iv) a premixed and diffusion combustion model partially based on Barba’s simplified 0D turbulent kinetic calculation,11 and (v) an energy balance in each zone giving corresponding mean temperatures. 2.1. Zone Description. The combustion chamber is divided into six zones, as shown in Figure 1. Zone 1: “Liquid” zone, from the nozzle hole to the maximum liquid penetration. Zone 2: Air-fuel mixture between the maximum liquid penetration L and the lift-off length H. If H > L, zone 2 contains the fuel that is completely evaporated downstream of the liquid (25) Hiroyasu, H.; Arai, M. Fuel spray penetration and spray angle of diesel engines. Trans. JSAE 1980, 21, 5–11. (26) Dec, J. E. A conceptual model of DI diesel combustion based on laser-sheet imaging. SAE Tech. Pap. 970873, 1997. (27) Bruneaux, G.; Auge´, M.; Lemenand, C. A study of combustion structure in high pressure single hole common rail direct injection using laser induced fluorescence of radicals. In the 6th International Symposium on Diagnostics and Modeling of Combustion in Internal Combustion Engines, 2004. (28) Naber, J. D.; Siebers, D. L. Effects of gas density and vaporization on penetration and dispersion of diesel sprays. SAE Tech. Pap. 960034, 1996. (29) Siebers, D. L. Scaling liquid-phase fuel penetration in diesel sprays based on mixing-limited vaporization. SAE Tech. Pap. 1999-01-0528, 1999. (30) Higgins, B. S.; Mueller, C. J.; Siebers, D. L. Measurements of fuel effects on liquid-phase penetration in DI sprays. SAE Tech. Pap. 1999-010519, 1999. (31) Siebers, D. L.; Higgins, B.; Pickett, L. M. Flame lift-off on directinjection diesel fuel jets: Oxygen concentration effects. SAE Tech. Pap. 2002-01-0890, 2002. (32) Pickett, L. M.; Siebers, D. L. Non-sooting, low-flame temperature mixing-controlled DI diesel combustion. SAE Tech. Pap. 2004-01-1399, 2004. (33) Pickett, L. M.; Siebers, D. L. Soot in diesel fuel jets: Effects of ambient temperature, ambient density, and injection pressure. Combust. Flame 2004, 138, 114–135. (34) Tree, D. R.; Svensson, K. I. Soot processes in compression ignition engines. Prog. Energy Combust. Sci. 2006, 33, 272–309.

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Maiboom et al.

Figure 3. Instantaneous injection rate for three operating points. Figure 1. Zone description.

penetration. If H < L, zone 2 contains the liquid fuel downstream of the lift-off length. Zone 3: Premixed combustion zone that consists of the combustion of the air-fuel vapor phase that has been prepared during ignition delay. Zone 4: Diffusion combustion zone from the lift-off length to the vapor-phase fuel penetration. Zone 5: Diffusion flame surrounding zones 3 and 4. Zone 6: Surrounding gas (air and EGR). Main assumptions are as follows: (i) Assumptions relative to Siebers et al. spray models28-31 are given in the Appendix. (ii) The various jets are supposedly free and identical. No interaction is supposed between various jets (from the multiholes injector) and between jets and combustion chamber walls. (iii) No interaction is supposed between the pilot and principal sprays. The evolution of the various zones is given in Figure 2. Sstart is the vapor-phase fuel penetration of the first injected fuel “package”, whereas Send is the penetration of the last injected fuel “package”. Sdiff is the penetration of the fuel that is located at the lift-off length at start of combustion (SOC) and separates zone 3 (premixed combustion) from zone 4 (diffusion combustion). The penetrations Sstart, Send, and Sdiff are calculated with the spray penetration model from Siebers et al. given in the Appendix. Contrary to the experiments conducted by Siebers et al. in a combustion vessel, the various thermodynamic conditions in the combustion chamber (pressure, temperature, and density) are continually varying. This may change the spray evolution. Because the combustion is located near top dead center (TDC), it is supposed

Figure 2. Evolution of various zones.

that the slight variation of thermodynamic conditions has little impact on spray evolution. Thus, the various thermodynamic conditions that appear in the spray models are calculated at the start of injection (SOI) and maintained constant for the calculation of spray evolutions. The liquid-phase fuel penetration is equal to Sstart before it reaches the maximum liquid penetration L. After the end of injection (EOI), all of the fuel is evaporated when Send reaches the maximum liquid penetration L. One difficulty is the modeling of the spray evolution between EOI and end of combustion (EOC). Very few studies were found in the literature describing the spray evolution after EOI (spray penetration, air/fuel mixing process, etc.). Thus, because of a lack of quantitative models for fuel jet description after EOI, the spray evolution after EOI is described such as before EOI. 2.2. Injection Rate. On DI diesel engines, the combustion and emission formation processes are strongly correlated to the fuel jet development and, thus, to the instantaneous injection rate. Instantaneous injection rates were measured for various operating points. A phenomenological injection rate model is developed, distinguishing various phases: the delay between the start of injector actuation and the start of fuel injection (approximately constant, independent of the rail pressure) and the opening and closing of the needle. The various tracts are supposedly linear, and the corresponding slopes are assumed to be proportional to the rail pressure. The tract where the injection rate is approximately constant is modeled with Bernoulli’s relation (given in the Appendix). The agreement between measured and calculated rates is fairly good. A comparison is presented in Figure 3 for three different injection rates. Furthermore, the spray models from Siebers et al. have been developed on the basis of experimental results obtained with a quasiconstant injection rate. Thus, Siebers et al. spray models have to



be adapted when modeling injection rates with high instantaneous variations. These are due to variations of both the hydraulic area of the injector nozzle hole and injection velocity. Two adaptations have been tested, one supposing a constant hydraulic area (with a varying injection velocity) and another supposing a constant injection velocity (and a varying hydraulic area)

dminj(t) ) FfSnoz(t)Uf with Uf ) Uf_bernoulli dt

(1)

The calculated spray penetrations obtained with these two hypotheses have been compared to spray penetrations measured in an optical single-cylinder engine. The first model gives a very slow penetration after SOI, and the global trend is very different from the measured one. On the contrary, the second model gives a quick penetration after SOI, as observed on the optical engine, and the global trend is very near the measured one. This second model is thus retained. The injection velocity Uf is calculated with Bernoulli’s relation (eq A10 in the Appendix). 2.3. In-Cylinder Gas Entrainment. The fuel masses in zones 1 and 2 are given by

dminj dminj dmf,1 (t) ) (t) (t - ∆tevap) dt dt dt

(2)

dminj dminj dmf,2 (t) ) (t - ∆tevap) (t - ∆tcomb) dt dt dt

(3)

where ∆tevap and ∆tcomb are the times needed for the spray to reach the maximum liquid-phase fuel penetration and the lift-off length, respectively. After SOC, the vapor fuel masses available in zones 3 and 4 are given by

dmf,b,pre dmf,3 (t) ) (t) dt dt

(4)

dminj dmf,4 dmf,b,diff (t) ) (t - ∆tcomb) (t) dt dt dt

(5)

The ambient gas (air and EGR) entrainment process (from zone 6 into the spray) is deduced from the Siebers et al. spray model. The constant spray angle along the jet results in a constant entrainment of ambient gases. Thus, the available ambient gases in each zone can be expressed as

(∫ m (t) ) n (∫ (t) ) n (∫ FS

x)L

ma,1(t) ) nN

x)0 x)H

ma,3

a,2

N

N

x)Sdiff

x)L

x)Sstart

fs dx fs + Φ(x)

) fs dx F S (x) fs + Φ(x) ) fs dx - fsm (x) fs + Φ(x) )

FaSspray(x) a spray

(6)

(t)

(7)

(t)

a spray

(t)

f,b,pre(t)

(8)

(∫

ma,4(t) ) nN

x)Sdiff

x)Send

FaSspray(x)

fs dx fs + Φ(x)

)

(t)

4

(

Sspray(x) ) π

∑ i)1

ma,i(t)

(10)

)

df + x tan(R/2) 2

(11)

2.4. Premixed Combustion. As in Barba’s model,11 the premixed combustion is divided into two stages. The first stage of the premixed combustion is supposed to be controlled by flame propagation in premixed zone 3. The turbulent flame speed St is calculated by11

u′ Sl

c2

Pcyl P0

c4

( )( )

Sl ) Sl,0

Ta T0

c3

(12) (13)

where c1, c2, c3, and c4 are empirical coefficients.1,11 The ignition is supposed to occur at the lift-off length, as described in the “conceptual” combustion model from Dec et al.26 The flame location is thus the result of the penetration of zone 3 in the combustion chamber and the flame propagation in zone 3. Thus, the flame location xf is given by

xf ) Sdiff +

∫

t

t)SOC

St(t)dt

(14)

Before the flame reaches the maximum vapor-phase fuel penetration, the burning rate is thus controlled by the flame speed and the equivalence air/fuel ratio at xf (first stage)

dmf,b,pre 1 (t) ) keffnNFaSspray(xf) S (t) if dt fs + Φ(xf) t Φ(xf) g 1 (fuel excess) (15) dmf,b,pre Φ(xf) (t) ) keffnNFaSspray(xf) S (t) if dt fs + Φ(xf) t Φ(xf) < 1 (air excess) (16) Just after SOC, the flame is propagating in fuel-rich cross-sections of the spray, with air being the limiting factor (eq 15). Then, the flame reaches cross-sections with lower equivalence fuel/air ratios, with fuel becoming eventually the limiting factor (eq 16). Moreover, keff is an empirical coefficient, lower than 1. This coefficient has been added because the calculated ROHR during premixed combustion overestimates the measured one. This can have various explanations: (i) At each cross-section x, the air-fuel mixture is not homogeneous, with the core spray being richer than the spray periphery (close to the stoichiometry). Thus, when the flame is propagating in zone 3, the fuel quantity able to burn is lower than in the well-mixed configuration. (ii) Moreover, one assumption made in the spray penetration model from Siebers et al. is that the flow is quasi-steady with a uniform growth rate (i.e., a constant spreading angle). When modeling injections with high instantaneous variations, the spreading angle just after SOI is overestimated. Thus, the model overestimates the gas entrainment just after SOI. When the flame reaches the vapor-phase fuel penetration (xf ) Sstart) (corresponding to the “premixed peak” on the ROHR diagram), the diffusion flame (zone 5) completely envelopes the downstream portion of the jet (zones 3 and 4), as described in Dec’s conceptual model.26 The unconsumed fuel in zone 3 is burning in a diffusion combustion mode (stage 2). The burning rate is supposed to be proportional to the fuel availability (by air excess) or air availability (by fuel excess)

dmf,b,pre ma,3(t) (t) ) kpre dt fs

- fsmf,b,diff(t) (9)

ma,6(t) ) ma,cyl -

( ( ))

St(t) ) Sl 1 + c1

if mf,3(t) g

ma,3(t) (fuel excess) fs (17)

dmf,b,pre ma,3(t) (t) ) kpremf,3(t) if mf,3(t) < (air excess) dt fs (18) The constant kpre is calculated to ensure the continuity of the burning rate when changing the premixed combustion stage. 2.5. Mixing-Controlled Combustion. The mixing-controlled combustion is described with a mixing-frequency approach based on a 0D calculation of the density of turbulent kinetic energy k, as in the models from Barba11 or Chmela.12,13 A formula very close to Barba’s is used


fmix(k) )

Maiboom et al.

Vmix √cGcm2 + ckk ) kdiff 3 lmix V

(19)

cyl

nN

Vmix is a characteristic mixing velocity. cGcm2 corresponds to a mixing velocity induced by the ambient gas aerodynamic (swirl and squish), whereas ckk corresponds to a mixing velocity induced by the turbulence. During injection, the mixing process between ambient gases and fuel is mainly controlled by the turbulence induced by the fuel jet, whereas after EOI, swirl and squish flows can play an important role.11 The instantaneous turbulence variation rate is the result of the turbulence production by the spray and the turbulence dissipation11

cdiss 3 dk dk ) cspray spray k2 dt dt d0

(20)

The production of turbulence by the spray is given by11

dk 1 dEcin,spray ) dt spray mcyl dt

(

dEcin,spray 1 1 ) dt 2 nNFfSnoz

(21)

)( ) 2

dminj dt

3

Figure 4. Mass transfers between the various zones after SOC.

results, it is supposed that the only influence of pilot combustion is the modification of the ignition delay of the main combustion and that most of the emissions (NOx and PM) are produced during main combustion. 2.7. Energy Balance. Mean temperatures in the various zones are obtained with an energy balance: the temperature Ta of ambient gases, the flame temperature T5, as well as the mean temperature T3/4 of zones 3 and 4. Mass transfers between the various zones are given by

dm3/4 dminj(t - ∆tcomb) dmf,b,diff dm5-3/4 ) + dt dt dt dt

(28)

dm5 dmair dmf,b,diff dm5-3/4 ) + dt dt dt dt

(29)

dmair dma )dt dt

(30)

(22)

The burning rate during the mixing-controlled combustion in zone 4 is related to the mixing frequency and the limiting factor

ma,4(t) dmf,b,diff (t) ) fmix(k) dt fs

ma,4(t) if mf,4(t) g (fuel excess) fs (23)

dmf,b,diff ma,4(t) (t) ) fmix(k)mf,4(t) if mf,4(t) < (air excess) dt fs (24) As a matter of fact, the mixing process between ambient gases and fuel is controlled by two different processes: the model of air entrainment by the jet gives the available air and fuel quantities in each zone (macroscopic scale), whereas the mixing frequency approach describes the microscopic mixing process in zone 4 (diffusion of ambient gases into the core spray). Finally, the ROHR is deduced from the burning rate

dmf,b,pre dQpre (t) ) LHV (25) dt dt dmf,b,diff dQdiff (t) ) LHV (26) dt dt dmf,b dQpre dmf,b,pre dmf,b,diff dQ (t) ) LHV ) LHV + (t) + ) dt dt dt dt dt dQdiff (t) (27) dt

(

)

2.6. Ignition Delay and Pilot Combustion. Because the combustion model is used to interpret experimental emission trends, the ignition delay is not computed in the version of the model presented here, but the experimental one (deduced from the cylinder pressure trace) is used here as an “entry”. When using the model as a predictive tool (as for instance when simulating the whole engine behavior), it is necessary to add an ignition delay submodel, as performed in a previous version of the model.35 Moreover, the pilot combustion can be modeled as principal combustion, with premixed and diffusion parts. A first version of the model has been developed, computing both pilot and main combustions,35 but it is necessary to use two sets of empirical coefficients.35 In the version of the model presented here, the pilot combustion is not computed. For the interpretation of experimental

The air excess in zone 5 (diffusion flame) is supposed to be constant at a value near 1. x5 is an empirical coefficient that represents the part of the spray mass that is localized in the flame. Thus, the mass transfer from the flame to the spray core is given by (Figure 4)

dm5-3/4 dmair dmf,b,diff dmf,b,diff ) - (1 - x5)λ5 fs + x5 (31) dt dt dt dt air (partially burnt)

burnt fuel

An energy balance gives the variation of the mean temperature in each zone

(

dm5-3/4 dT3/4 γ3/4 - 1 dminj(t - ∆tcomb) ) hf (H) + h5 dt rm3/4 dt dt T3/4 dV3/4 u3/4 dm3/4 dmf,b,diff h3 -(γ3/4 - 1) - (γ3/4 - 1) dt V3/4 dt r3/4m3/4 dt (γ3/4 - 1) dyi,3/4 (32) ui,3/4 r dt

)

(

∑

)

dmf,b,diff dm5-3/4 dT5 γ5 - 1 dQc dmair ) + h + h3/4 h5 dt rm5 dt dt a dt dt T5 dV5 u5 dm5 (γ5 - 1) dyi,5 - (γ5 - 1) (33) ui,5 (γ5 - 1) V5 dt r5m5 dt r dt

∑

dTa γa - 1 dmair Ta dVa ua dma )- (γa - 1) - (γa - 1) dt rma dt Va dt rama dt (γa - 1) dyi,a (34) ui,a r dt

∑

2.8. Empirical Coefficient Determination. The empirical coefficient cH for the lift-off length (eq A17 in the Appendix) is deduced from visualizations obtained on an optical single-cylinder engine. As shown in Figure 5 and described by Musculus,36 the lift-off length is longer on the windward side of the jet relative to the in(35) Maiboom, A.; Tauzia, X.; He´tet, J.-F.; Cormerais, M. A 5-zones phenomenological combustion model for DI diesel engine for a wide range of operating conditions. In the FISITA 2006 World Automotive Congress, 2006.


Energy & Fuels, Vol. 23, 2009 695 Table 2. Specifications of the Test Engine type compression ratio number of cylinders number of valves per cylinder combustion chamber type injection system number of injection holes injection nozzle diameter (mm) maximum injection pressure (bar) fuel

turbocharged (VGT), intercooled 18:1 4 4 re-entrant bowl-in-piston common-rail piezoelectric second generation 7 0.150 1600 diesel

Table 3. Operating Points Figure 5. Flame visualization on an optical single-cylinder engine. Table 1. Values of Empirical Coefficients cH cspray cdiss cG ck kdiff keff c1

1.02 × 1010 5 3 0.5 1 5 0.5 0.5

cylinder swirl flow (“upswirl”). Furthermore, cycle-cycle and jet-jet variations are observed.36 A mean value between the various jets and the various cycles is taken at the leeward side (“downswirl”). The empirical value 0.26 appearing in the spray spreading angle model (eq A13 in the Appendix) was changed to 0.45, so that calculated spray penetration best fits with the measured value (an increase of the calculated spray angle results in a decrease of the calculated spray penetration). The necessity to modify this value can be attributed to the geometry of the injector nozzle hole. The values of other empirical coefficients appearing in the spray model were not modified. Empirical coefficients relative to combustion (cspray, cdiss, cG, ck, kdiff, keff, and c1) are determined with a mathematical optimization method to best fit experimental ROHR for some reference operating points. The empirical coefficients relative to the premixed combustion (keff and c1) are determined with experimental ROHR obtained with purely premixed combustions (obtained at low load operating conditions without pilot injection). The empirical coefficients relative to the mixing-controlled part of combustion were calculated in a second step. Their values are given in Table 1. 2.9. Numerical Solving. The differential equations are solved with the Euler method. The time step chosen corresponds to a fixed crank angle of 0.072 °CA. This time step was found to be sufficiently small, such that the influence of the time step on the calculated parameters was negligible. Therefore, the computing time was not optimized. A more sophisticated numerical algorithm, such as a fourth-order Runge-Kutta algorithm, would be appropriate if the computing time becomes a major issue.

engine speed (rpm) approximate IMEP (bar) rail pressure (bar) pilot quantity (mg/stroke) main quantity (mg/stroke) SOI1 (°CA) SOI2 (°CA) boost pressure (bar)

A

B

1670 8.0 870 1.5 22.5 351.9 365.8 1.18

1450 6.4 690 1.5 17.5 354.9 365.8 1.07

The engine specifications are given in Table 2. The model is tested on two operating points at low-load conditions, such as those encountered in the European emissions test cycle for lightduty vehicles (composed of four urban driving cycle and one extra-urban driving cycle). The corresponding engine speed, indicated mean effective pressure (IMEP), injection parameters, as well as boost pressure are given in Table 3. For each operating point, injection quantities are held constant and, thus, the IMEP is slightly changed for the various modifications tested (inlet temperature and EGR rate). 3.1. Model Results. 3.1.1. Influence of the Inlet Temperature. The first parameter tested is the change of inlet temperature, for operating point A, with pilot injection. The inlet temperature of fresh air is controlled separately, allowing control over the temperature Tin after mixing with EGR gases. The EGR rate is fixed at 15%. The measured NOx and PM emissions are given in Figure 6 versus the inlet temperature. As depicted, NOx emissions are only slightly changed when increasing Tin from 29 to 65 °C, whereas PM emissions are increased. Without local information, these results may be difficult to interpret. Experimental and calculated ROHR are given at 29 and 65 °C inlet temperature Tin in Figure 7. As shown, the increase of the inlet temperature results in a slight decrease of the ROHR, because of a reduced in-cylinder gas density. Actually, with pilot injection, the ignition delay of the main injection is very short, so that main combustion is principally mixing-controlled (diffusion combustion). Thus, when maintaining injection parameters, the fuel jet entrains the

3. Results and Discussion The model is compared to global measurements (ROHR) obtained on an engine test bench and is used to interpret measured emission trends when some engine parameters are varied. The engine used is a 2.0 L water-cooled high-speed direct-injection (HSDI) diesel engine, equipped with a variable geometry turbine (VGT), an intercooler, and an HP EGR loop. The emission measurement techniques, the evaluation of the mean gross ROHR based on the measured in-cylinder pressure, as well as an error analysis are presented in a previous paper.4 (36) Musculus, M. P. B. Effects of the in-cylinder environment on diffusion flame lift-off in a DI diesel engine. SAE Tech. Pap. 2003-010074, 2003.

Figure 6. Measured influence of the inlet temperature on NOx and PM emissions, operating point A.


Maiboom et al.

Figure 8. Calculated zone temperatures while varying the inlet temperature, operating point A.

Figure 7. (a) Instantaneous injection rate and experimental and calculated ROHR for an inlet temperature of (b) 29 °C and (c) 65 °C, operating point A.

same volume of ambient gases (air and EGR). As a matter of fact, the fuel jet entrains less fresh air with reduced in-cylinder gas density, resulting in a lower oxygen-fuel mixing and lower ROHR. Calculated ROHR are in rather good qualitative and quantitative agreement with experimental ones. Moreover, the decrease of the ROHR peak when increasing Tin is captured by the combustion model, although this decrease is slightly underestimated. It can be noticed that calculated ROHR curves present sharp bends that correspond to abrupt transitions between the various stages appearing in the description of the premixed and mixing-controlled combustions.

Figure 9. Calculated lift-off length and equivalence ratio while varying the inlet temperature, operating point A.

Corresponding calculated mean zone temperatures are given in Figure 8. Calculated lift-off length and equivalence ratio at lift-off length when varying Tin are given in Figure 9. It has been shown that the location of flame lift-off on diesel fuel jet plays an important role in the soot formation process, by allowing fuel and air to mix upstream of the lift-off length (i.e., prior to any combustion).31-34 Just downstream of the liftoff length, the partially premixed air-fuel mixture undergoes a premixed combustion that generates a significant local heat release and fuel-rich product gas that becomes the “fuel” for the diffusion flame at the jet periphery. The soot formation was shown to be directly dependent upon the equivalence fuel-air ratio at the lift-off length.31-34 Moreover, the inside temperature of the spray where soot is produced is another fundamental


Figure 10. Measured influence of EGR rate on NOx and PM emissions, operating point A.

parameter that controls the soot production rate; soot formation increases with increased core spray temperature.34 Under 1500-1600 K, no soot is produced regardless of the equivalence ratio.32 Finally, it has been shown that the flame temperature is the main parameter that controls soot oxidation at the jet periphery. In our model, core spray temperature T3/4, equivalence ratio Φ(H), and flame temperature T5 are used to interpret soot emissions. As shown in Figure 9, the lift-off length is decreased when increasing Tin, resulting in an increased fuel/air equivalence ratio at the lift-off length. As depicted in Figure 8, the core spray temperature T3/4 as well as the flame temperature T5 are unchanged with an increased inlet temperature. Thus, the soot oxidation at the jet periphery is unchanged, whereas the soot production is increased, resulting in an increase of PM emissions as described earlier. Finally, the very slight variation of the flame temperature explains the slight variation of NOx emissions. As for simulated ROHR, it can be noticed that the temperatures of the simulated zones present sharp bends because of the abrupt transitions between the various stages appearing in the description of the premixed and mixing-controlled combustions. 3.1.2. Influence of the EGR Rate at a Constant Boost Pressure and Constant A/F. Another test made is the increase of the EGR rate, first at a constant boost pressure and then at a constant A/F, each time with and without pilot injection. At constant boost pressure, the increase of the EGR rate results in a decreased in-cylinder oxygen quantity. A constant A/F is obtained by the increasing boost pressure. This is obtained by closing the VGT vanes. The temperature Tin of inlet gases after mixing with EGR is maintained constant. When pilot injection is suppressed, main injection quantity is increased to maintain a constant total injection quantity. The influence of EGR on NOx and PM emissions for operating point A is given in Figure 10.


First of all, for a given EGR rate, NOx emissions are higher and PM emissions are lower without pilot injection. Without pilot injection, main combustion is mainly premixed and the mean equivalence fuel/air ratio of the mixture formed during ID must be too low for soot inception, explaining why PM emissions are very low without pilot injection for this engine running on operating point A. Furthermore, when increasing the EGR rate, NOx emissions are decreased, thus entering a low NOx and low PM combustion mode, which is near the MK combustion concept from Kimura et al.37 Experimental and calculated ROHR with pilot injection are given in Figure 11 at 0% EGR, 12.8% EGR at a constant boost pressure (compared to 0% EGR), and 10.1% EGR at a constant A/F. Corresponding calculated mean zone temperatures are given in Figure 12. Calculated lift-off length and equivalence ratio when varying the EGR rate with pilot injection at a constant boost pressure and a constant A/F are given in Figure 13. First of all, it can be noticed that calculated ROHR are in good agreement with experimental ones when varying the EGR rate. The decrease of the flame temperature T5 while increasing the EGR rate explains the reduction of NOx emissions, whether at constant boost pressure or constant A/F. Moreover, the increase of the EGR rate results in an increase of the lift-off length and a decrease of the O2 concentration in surrounding gases, thus resulting in a slight decrease of the equivalence ratio at the lift-off length. At the same time, the core spray temperature T3/4 is decreasing when increasing the EGR rate, whether at constant Pboost or A/F. As a matter of fact, the soot production rate in the core spray is lowered with an increased EGR rate. The soot oxidation rate is reduced too, because of a reduced flame temperature. The reduction of the soot oxidation rate seems to be greater that the reduction of soot production, explaining why PM emissions are increasing with the EGR rate. Furthermore, the decrease of the flame temperature at the start of combustion (before temperature peak) with an increased EGR rate seems to be slightly higher at constant Pboost compared to constant A/F, explaining why the decrease in NOx emissions is slightly higher at constant Pboost. Experimental and calculated ROHR without pilot injection are given in Figure 14 at 0% EGR, 16.4% EGR at a constant boost pressure, and 15.6% EGR at a constant A/F. Corresponding calculated mean zone temperatures are given in Figure 15. It must be underlined that, without pilot injection, the ROHR peak is twice as high as compared to the case with pilot injection. This trend is predicted by the combustion model with good agreement. The decrease of the ROHR peak while increasing the EGR rate at constant Pboost is captured by the combustion model. However, some differences between experimental and calculated ROHR can be noticed: without EGR or with 15.6% EGR at constant A/F (parts a and c of Figure 14, respectively), the calculated premixed peak is a little too high and attained too early compared to the experimental one, whereas it is underestimated with 16.4% EGR at a constant Pboost. The combustion speed during premixed combustion is strongly correlated to the propagation speed of the premixed flame in zone 3. The latter is dependent upon the equivalence ratio at the premixed flame location. Thus, it seems that the flame propagation speed is a little overestimated without EGR and 15.6% EGR at a constant A/F and underestimated with 16.4% EGR at a constant Pboost. The calculation of the premixed part of combustion (which is particularly important at low-load (37) Kimura, S.; Aoki, O.; Kitahara, Y.; Aiyoshizawa, E. Ultra-clean combustion technology combining a low-temperature and premixed combustion concept for meeting future emissions standards. SAE Tech. Pap. 2001-01-0200, 2001.


Maiboom et al.

Figure 12. Calculated zone temperatures while varying the EGR rate with pilot injection, operating point A.

Figure 11. Experimental and calculated ROHR while varying the EGR rate with pilot injection, operating point A.

conditions without pilot injection) could thus be improved. Some additional experimental local studies would be very helpful. As with pilot injection, the decrease in flame temperature explains the decrease in NOx emissions. While this decrease in flame temperature is higher at constant Pboost compared to constant A/F, the decrease in NOx emissions with the EGR rate is higher at constant Pboost. 3.1.3. Influence of the EGR Rate at a Constant Injection and Constant ROHR. Finally, the combustion model is used to interpret the engine-out NOx and PM emissions when increasing the EGR rate with or without injection readjustment for operating point B. The emissions are given in Figure 16. The corresponding experimental ROHR and cylinder pressures are

Figure 13. Calculated lift-off length and equivalence ratio while varying the EGR rate with pilot injection, operating point A.

given in Figures 17 and 18, respectively. Because the temperature of EGR gases is maintained at a level over 120 °C to avoid condensation, which may damage (corrosion) or foul inlet manifold and inlet valves, it is not possible to maintain a constant inlet temperature Tin when increasing the EGR rate over 18%. Thus, three levels of intake gas temperature are tested when increasing the EGR rate (given in Figure 16). When increasing the EGR rate without injection readjustment, the whole combustion process is shifted further into the expansion stroke, as described in previous research.4,5,38,39 In particular, the ignition delay is increased, thus increasing the premixed part of combustion, which can lead to a higher ROHR peak, such as, for instance, for operating point B (Figure 17a). To maintain a constant ROHR and cylinder pressure (Figures



Figure 14. Experimental and calculated ROHR while varying the EGR rate without pilot injection, operating point A.

Figure 15. Calculated zone temperatures while varying the EGR rate without pilot injection, operating point A.

17b and 18b, respectively), both the rail pressure and start of main injection were changed while increasing the EGR rate. Experimental and calculated ROHR are given in Figure 19 at 0 and 29% EGR with and without injection readjustment (parts c and b of Figure 19, respectively). Corresponding calculated mean zone temperatures are given in Figure 20. The calculated lift-off length and equivalence ratio are given in Table 4. As can be seen, the combustion model gives a qualitative good agreement with experimental ROHR while varying the

EGR rate on operating point B, although some differences appear, in particular when maintaining injection parameters, probably because of an underestimation of the ROHR of premixed combustion. However, the qualitative trends on mean zone temperatures can be used to interpret experimental emission trends. The large reduction of flame temperature results in a large decrease of NOx emissions, whether at constant injection or constant ROHR. Furthermore, when increasing the EGR rate at constant injection, the equivalence ratio at the lift-off length is almost constant, whereas the core spray temperature is decreasing. The soot production rate may thus decrease with an increased EGR rate. At the same time, with the flame temperature being reduced with an increased EGR rate, the soot oxidation rate at the jet

(38) Ladommatos, N.; Abdelhalim, S. M.; Zhao, H.; Hu, Z. Effects of EGR on heat release in diesel combustion. SAE Tech. Pap. 980184, 1998. (39) Egnell, R. The influence of EGR on heat release rate and NO formation in a DI diesel engine. SAE Tech. Pap. 2000-01-1807, 2000.


Maiboom et al.

Figure 16. Measured influence of the EGR rate on NOx and PM emissions, operating point B.

Figure 18. Experimental cylinder pressures while varying the EGR rate, operating point B.

periphery is decreased too. The latter seems to be more important than the decrease in the soot production rate because measured PM emissions at the exhaust are higher. Moreover, the equivalence ratio at the lift-off length is increasing with EGR at constant ROHR, while the decrease of the core spray temperature is less important than at constant injection. The soot production rate must therefore be higher at constant ROHR compared to constant injection, at a given EGR rate, thus explaining why the PM emissions increase when EGR is higher at constant ROHR. 3.2. Model Limits and Perspectives. The combustion model has shown some discrepancies in the calculated ROHR compared to experimental ones. Many explanations are possible, because some phenomena are not described or the description of some others may be oversimplified. Actually, the description and modeling of the following phenomena would be necessary when trying to improve the model: (i) It has been shown that the calculation of the premixed part of combustion (ROHR and corresponding temperatures) could be improved. (ii) Pickett et al. have experimentally demonstrated that ignition processes affect diesel lift-off stabilization, with fuels with shorter ignition delays producing generally shorter lift-off lengths.40 (iii) Some researchers41-43have shown that jet-wall interactions have a large impact on combustion and emission formation processes (in particular, soot), with the gas entrainment of a jet

Figure 17. Experimental ROHR while varying the EGR rate, operating point B.

(40) Pickett, L. M.; Siebers, D. L.; Idicheria, C. A. Relationship between ignition processes and the lift-off length of diesel fuel jets. SAE Tech. Pap. 2005-01-3843, 2005. (41) Pickett, L. M.; Lopez, J. J. Jet-wall interaction effects on diesel combustion and soot formation. SAE Tech. Pap. 2005-01-0921, 2005.


Figure 19. Experimental and calculated ROHR while varying the EGR rate, operating point B.

interacting with a wall being different from those for a single isolated free jet. The jet confinement causes combustion products to be redirected toward the incoming jet, causing, in particular, the lift-off length to shorten.41 (iv) The proximity of adjacent jets also affects the flow field of entrained gases;36 the assumption that each jet from the multihole injector is independent is one of the most critical (42) Bruneaux, G. Mixing process in high pressure diesel jets by normalized laser induced exciplex fluorescence. Part 1: Free jet. SAE Tech. Pap. 2005-01-2100, 2005. (43) Bruneaux, G. Mixing process in high pressure diesel jets by normalized laser induced exciplex fluorescence. Part 2: Wall impinging versus free jet. SAE Tech. Pap. 2005-01-2097, 2005.


Figure 20. Calculated zone temperatures while varying the EGR rate, operating point B. Table 4. Calculated Lift-off Length and Equivalence Ratio, Operating Point B 0 XEGR (%) Tin (°C) 25 constant injection H (cm) 1.19 Φ(H) 5.43 constant ROHR H (cm) 1.19 Φ(H) 5.43

9 25

16 25

23 42

29 46

1.32 5.07

1.43 4.85

1.50 5.20

1.52 5.93

1.23 5.43

1.24 5.61

1.25 6.31

1.19 7.70

ones. (v) Finally, recent studies have shown that the nozzle geometry has a large influence on spray penetration and combustion.44,45 Thus, taking into account the nozzle geom-


Maiboom et al.

etry in the computation of the spray and combustion evolutions seems to be a major possible improvement.

The new multizone phenomenological combustion model that was presented gives some new in-cylinder information compared to existing 0D phenomenological combustion models. Several comparisons between measured and calculated ROHR were performed. Although some differences were shown, the present model is able to find principal trends when varying engine load and speed, boost pressure, or EGR rate and can be used to interpret experimental emission trends (NOx and PM). Some perspectives are proposed to improve the description of some aspects of the fuel jet development and combustion: (i) the modeling of the interactions between the various injections, to run with multi-injections, (ii) the modeling of the interactions between adjacent jets and between jets and combustion chamber walls, (iii) the prediction of pollutant emissions, and (iv) the taking into account of chemistry when running under LTC conditions (EGR-incurred LTC and HCCI combustion). These perspectives will be investigated by the authors in their future works. Appendix Main equations of the Siebers et al. spray model are given below. Siebers et al.28-31 have studied typical DI diesel sprays with a single-hole common-rail-type injector in a constant volume quiescent combustion vessel under various operating conditions, such as injection pressure, fuel temperature, injector orifice diameter, gas density, gas temperature, or O2 concentration (simulating the recirculation of exhaust gases). On the basis of their experimental visualizations and jet theory applied to a simplified model of spray, they have proposed a liquid- and vapor-phase fuel penetration model. Main assumptions are a uniform velocity profile, a constant injection velocity with an instantaneous start, no velocity slip between the fuel and the entrained air, and a quasi-steady flow with a uniform growth rate. The dimensionless penetration time ˜t can be expressed as a function of the dimensionless penetration distance s˜28 (A1)

x0 )

(A2)

˜t ) t′ t+

(A3)

where t′ and s′ are the coordinates referenced to the project origin and s+ and t+ are time and length scales used for nondimensionalized time and length coordinates, given by 1 ( F˜ -F˜ m ) tan(R/2) 1 ( F˜ -F˜ m ) U tan(R/2)

s+ ) df F˜ 1/2 t+ ) df F˜ 1/2

2

(A4) (A5)

f

with (44) Payri, R.; Salvador, F. J.; Gimeno, J.; Zapata, L. D. Diesel nozzle geometry influence on spray liquid-phase fuel penetration in evaporative conditions. Fuel 2008, 87, 1165–1176. (45) Benajes, J.; Molina, S.; Gonzalez, C.; Donde, R. The role of nozzle convergence in diesel combustion. Fuel 2008, 87, 1849–1858.

(A8)

m df 2 tan(R/2)

(A9)

Uf ) Cv

2

Pf - Pa Ff

(A10)

An accurate inverse penetration correlation giving the penetration as a function of time is given by28 s˜ ≈

˜t , n ) 2.2 (1 + ˜tn/2)1/n

(A11)

The equivalence ratio at any axial location can be expressed as28 Φ(x) )

2fs

(A12)

√1 + 16x˜2 - 1

A spray spreading angle model was developed on the basis of experimental results from schlieren imaging29

[( )

tan(θ/2) ) 0.26

Fa Ff

0.19

]

- 0.0043

Ff Fa

(A13)

The relationship between R “model” and the measured spray angle θ is given by29 tan(R) ) 0.66 tan(θ) (A14) Furthermore, a scaling law for the maximum penetration distance of the liquid-phase fuel was developed. The model is based on the fact that, in sprays from current-technology direct injectors, fuel vaporization is controlled by the entrainment of high-temperature ambient gases (air and EGR) and the overall transport and mixing process of fuel and ambient gases throughout the spray cross-section. Fuel atomization would not be the limiting process.29 The maximum penetration distance of the liquid-phase fuel is given by29,30

(

L˜ ) 0.41 s′ s+

(A7)

Cd Ca

Cv )

with s˜ )

(A6)

df ) √Cad0

4. Conclusions

˜t ) s˜ + s˜ √1 + 16s˜2 + 1 ln(4s˜ + √1 + 16s˜2) 2 4 16

Ff Fa

F˜ )

with B)

)

2 2 +1 -1 B(Ta, Pa, Tf)

ha(Ta, Pa) - ha(Ts, Pa - Ps) hf(Ts) - hf(Tf, Pa)

(A15)

(A16)

Finally, it has been shown that the location of flame lift-off on diesel fuel jet plays an important role in combustion and emission processes, particularly on soot production, by allowing fuel and air to mix upstream of the lift-off length (i.e., prior to any combustion).31-34 Just downstream of the lift-off length, the partially premixed air-fuel mixture is undergoing a premixed combustion that generates a significant local heat release and a fuel-rich product gas that becomes the “fuel” for the diffusion flame at the jet periphery downstream of the lift-off length. The soot production can be directly correlated to the local fuel/air equivalence ratio at the lift-off length. No soot is produced when it is less than approximately 2.32 By measuring the lift-off length in a constant volume quiescent combustion vessel, Siebers et al. have proposed the following scaling law for the lift-off length, depending upon the injector nozzle hole



diameter, ambient temperature and density, injection velocity, and the stoichiometric fuel mass fraction (ratio of fuel mass/ total mixture mass)31 H ) cHTa-3.74Fa-0.85d00.34uf Zst-1

(A17)

Vmix ) mixing velocity (m s-1) V ) volume (m3) x ) spray coordinate (m) xf ) flame coordinate (m) XEGR ) EGR rate (%) Zst ) stoichiometric fuel mass fraction

Nomenclature A/F ) air/fuel ratio Ca ) area contraction coefficient Cd ) discharge coefficient Cv ) velocity contraction coefficient cdiss ) empirical coefficient cG ) empirical coefficient cH ) empirical coefficient ck ) empirical coefficient cspray ) empirical coefficient cm ) mean piston velocity (m s-1) d0 ) geometric nozzle orifice diameter (m) df ) effective nozzle orifice diameter (m) Ecin,spray ) spray kinetic energy (kg m2 s-2) fs ) ambient gas mass necessary for the combustion of 1 kg of fuel fmix ) mixing frequency (Hz) h ) specific enthalpy (J kg-1) k ) density of turbulent kinetic energy (m2 s-2) kdiff ) empirical coefficient kpre ) empirical coefficient (s-1) keff ) empirical coefficient lmix ) characteristic mixing length (m) L ) liquid length (m) m ) mass (kg) nN ) number of nozzle holes P ) pressure (Pa) s′ ) distance in reference to the spray origin (m) s+ ) distance scale used for the non-dimensionalized distance (m) s˜ ) dimensionless penetration distance Sdiff ) penetration of fuel located at the lift-off length at SOC (m) Send ) penetration of the last injected fuel “package” (m) Sspray ) spray section (m2) Snoz ) nozzle hole area (m2) Sl ) laminar flame velocity (m s-1) Sstart ) spay tip penetration (m) St ) turbulent flame velocity (m s-1) t′ ) time in reference to the spray origin (s) t+ ) time scale used for the non-dimensionalized time (s) ˜t ) dimensionless penetration time T ) temperature (K) Ts ) saturation temperature (K) Uf ) fuel velocity at the nozzle exit (m s-1)

Greek Symbols R ) “real” spray spreading angle (deg) θ ) “model” spray spreading angle (deg) F ) density (kg m-3) F˜ ) density ratio ∆tcomb ) time for fuel to reach the lift-off length ∆tevap ) time for fuel to reach the maximum liquid-phase fuel penetration Φ ) fuel/air equivalence ratio Subscripts a ) ambient gas b ) burnt cyl ) cylinder diff ) diffusion f ) fuel in ) inlet inj ) injected pre ) premixed AbbreViations CA ) crank angle (deg) CFD ) computational fluid dynamics DI ) direct injection EGR ) exhaust gas recirculation EOC ) end of combustion EOI ) end of injection HCCI ) homogeneous charge compression ignition HP ) high pressure HSDI ) high-speed direct injection ID ) ignition delay IMEP ) indicated mean effective pressure (bar) LHV ) lower heating value (J kg-1) LTC ) low-temperature combustion PIV ) particulate image velocimetry ROHR ) rate of heat release (W) SOC ) start of combustion SOI ) start of injection SOI1 ) start of pilot injection SOI2 ) start of main injection VGT ) variable geometry turbine EF800735D

New Phenomenological Six-Zone Combustion Model for Direct

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