2004-01-0561

Modelling a Dual-fuelled Multi-cylinder HCCI Engine Using a PDF based Engine Cycle Simulator

Amit Bhave, Markus Kraft Department of Chemical Engineering, University of Cambridge

Luca Montorsi Department of Mechanical and Civil Engineering, University of Modena and Reggio Emilia

Fabian Mauss Division of Combustion Physics, Lund University

Copyright © 2003 SAE International

ABSTRACT

Operating the HCCI engine with dual fuels with a large difference in auto-ignition characteristics (octane number) is one way to control the HCCI operation. The effect of octane number on combustion, emissions and engine performance in a 6 cylinder SCANIA truck engine, fuelled with n-heptane and isooctane, and running in HCCI mode, are investigated numerically and compared with measurements taken from Olsson et al. [SAE 2000-01-2867]. To correctly simulate the HCCI engine operation, we implement a probability density function (PDF) based stochastic reactor model (including detailed chemical kinetics and accounting for inhomogeneities in composition and temperature) coupled with GT-POWER, a 1-D fluid dynamics based engine cycle simulator. Such a coupling proves to be ideal for the understanding of the combustion phenomenon as well as the gas dynamics processes intrinsic to the engine cycle. The convective heat transfer in the engine cylinder is modeled as a stochastic jump process and accounts for the fluctuations and fluid-wall interaction effects. Curl's coalescence-dispersion model is used to describe turbulent mixing. A good agreement is observed between the predicted values and measurements for in-cylinder pressure, auto-ignition timing and CO, HC as well as NOx emissions for the base case. The advanced PDF-based engine cycle simulator clearly outperforms the widely used homogeneous model based full cycle engine simulator. The trends in combustion characteristics such as ignition crank angle degree and combustion duration with respect to varying octane numbers are predicted well as compared to measurements. The integrated model provides reliable predictions for in-cylinder temperature, CO, HC as well as NOx emissions over a wide range of octane numbers studied.

INTRODUCTION

Amidst the changing vehicle design, fuel production and infrastructure, internal combustion engine (ICE) would continue to maintain its cardinal role as the cheapest system through 2030 [1]. Homogeneous charge compression ignition (HCCI) also termed as controlled auto-ignition (CAI) is a combustion technology for IC engines and a potential future-engine-strategy for automobile companies. HCCI engine provides high thermal efficiencies and low NOx and particulate matter (PM) emissions. Similar to Spark Ignition (SI) engines, the charge is premixed thus reducing the PM emissions, and as in compression ignition direct injection (CIDI) engines, the charge is compression-ignited, reducing the throttling losses and leading to high efficiency. However, unlike SI or CIDI engines, the combustion occurs simultaneously at multiple sites throughout the volume with shorter combustion duration and is controlled primarily by chemical kinetics. HCCI engines can be scaled to virtually any size-class of transportation engines as well as used for stationary applications such as power generation and pipeline pumping [2,3,4]. Despite the advantages offered by HCCI engines, controlling HCCI combustion is a major hurdle for its commercialization. Techniques such as using dual fuels with a large difference in auto-ignition characteristics (octane number) [5], heating intake charge, external EGR and trapping residual burnt fraction are various options to overcome this challenge.

Combustion research communities and industry are contributing extensively into experimental and modelling efforts to facilitate the commercialization of these engines. In particular, the modeling studies have evolved from a simplistic single zone model to detailed full cycle models. HCCI models can be classified as closed volume and engine cycle models. The closed volume models consider a variable volume cylinder and employ

single zone [6,7], multi-zone [8,9,10], multi-dimensional CFD [11] or probability density function (PDF)-based [12,13,14] models to simulate the compression, combustion and expansion strokes in one engine cycle. Whereas, the engine cycle models have been implemented using single zone [15-18], multi-zone [19,20] or CFD [21] models in conjunction with an engine cycle simulator. These models perform multiple cycle simulations in which the convergence is achieved through a series of iterations to a steady state ignition. Furthermore, a full cycle simulation can also model gas exchange as well as the internal residue trapped in the engine cylinder.

The classical single zone model can predict the auto-ignition correctly by including detail chemical kinetics, as the combustion is primarily reaction-controlled. However the in-cylinder peak pressure is over-predicted and the emissions are not accurate as the model fails to account for the colder thermal boundary layer and crevices. Multi-zone models can model the effect of thermal boundary layer (also termed quench layer) and with detail chemical kinetics, predict the heat release and peak pressure better than single zone models, but at the expense of more computational cost. Multi-zone models generally fail to provide reliable predictions for CO and HC emissions. In addition the multi-zone models cannot account for the fluctuations in the zones and the chemical source terms are calculated by using the mean gas temperature and composition in the zones. In case of 3-D CFD engine models with detailed kinetic mechanisms, the computational time can easily run into days.

The much more sophisticated closed volume PDF-based stochastic reactor model (SRM) includes detailed kinetics and has been demonstrated to reliably predict combustion and emissions [12,13]. However, this approach involved splitting the engine cylinder into a rigid bulk zone (80% by mass) and a boundary layer zone (20%). Thus the model failed to account for the varying in-cylinder mass in the boundary layer [9]. In addition, with a deterministic convective heat loss model, the local inhomogeneity attributed to the thermal boundary layer was lost during mixing. To overcome these limitations, an improved PDF-based closed volume SRM has been introduced in ref. [14]. Its robustness was demonstrated in evaluating the effect of external EGR on HCCI combustion and emissions in comparison with measurements. In this paper, we present an integrated, improved PDF-based SRM in conjunction with a 1-D finite difference-based engine cycle simulator. The coupled model includes detailed kinetics and is applied to investigate the use of dual fuels as a control option for HCCI combustion. For this, we study the effect of octane number on HCCI combustion and CO, HC as well as NOx emissions. We also introduce an approach based on stochastic jump process and Woschni heat transfer coefficient, for modelling the convective heat loss in the engine cylinder. This accounts for the fluid-wall interactions and effect of fluctuations as described later. The paper is

organized as follows: The engine data and the numerical model implemented are described in detail in the next section. This is followed by the discussion related to comparison of model predictions with experimental results and finally, an octane number (ON) variation analysis is presented.

MODEL DESCRIPTION

In this section, the engine geometry and the operating parameters are specified, and the numerical models implemented are described in detail.

ENGINE DETAILS

The engine used for the analysis is a 12 liter, in–line 6 cylinder direct injection turbocharged SCANIA diesel engine converted to HCCI combustion operation as mentioned in ref. [5]. In Table I the main engine parameters are described. The engine has 4 valves per cylinder and the two intake ports are characterized by different geometries. The first one entering straight into the cylinder in order to have low fluid-dynamic losses and the second designed with a helicoidal shape to enhance the swirl coefficient. The original injection system has been replaced by a low pressure sequential system for port injection of gasoline. For each intake port one injector has been installed; thus different fuel mixtures could be tested and individually adjusted for each cylinder. Isooctane and n-Heptane are the two fuels used, and combined they closely represent primary reference fuel (PRF). Engine inlet temperature was fixed by means of an electrical heater placed between the compressor and the inlet manifold.

Table I: Basic engine parameters.

Total displacement [cm3] 11,705

Compression ratio 18:1

Bore [mm] 126.6

Stroke [mm] 154

Connecting rod [mm] 255

Intake Valve Opening 54° BTDC

Intake Valve Closing 78° ABDC

Exhaust Valve Opening 96° BBDC

Exhaust Valve Closing 52° ATDC

For the cases mentioned in this paper no boost pressure has been used. Both the pistons as well as the cylinder heads were in their original configuration, and no other engine parameters or devices have been modified.

Fitra

PDF

The esimulWestpressplenuIt alsdepemeanformutreatmmixtucompin ref

FigurPowestep, of thcombthe codegreemiss(i.e. lnumb

Coup

A sch1-D c

gure 1: GT-Power engine cycle map (left to right: intake pipe, intake manifold, fuel injectors, cylinders, crackin, exhaust manifold, turbine, exhaust pipe)

BASED ENGINE CYCLE MODEL

ngine cycle is built using GT-POWER, an engine ation code licensed by Gamma Technologies Inc., mont, IL. The code analyzes the dynamics of ure waves, mass flows and energy losses in ducts, m and intake and exhaust manifolds of the engine. o provides a fully integrated treatment of time–ndent fluid dynamics and thermodynamics by s of a one–dimensional (1-D) finite difference lation, incorporating a general thermodynamic ent of working fluids (air, air-hydrocarbon

res, and products of combustion). A rehensive description of the full-cycle code is given s. [16,22,23].

e 1 shows the engine cycle representation in GT-r. The 1-D code and the SRM interact at every time making it possible to address the mutual influence e engine fluid-dynamics phenomena and the ustion processes. Thus, it is possible to determine mbustion parameters, such as ignition crank angle e (CAD), duration, exhaust gas temperature and ions, as a function of the global engine parameters

oad, boost pressure, inlet temperature, fuel, octane er, EGR, turbocharger).

ling SRM and 1-D code

ematic of the coupling between the SRM and the ode is shown in Figure 2. At inlet valve closure

(IVC), the 1-D code passes the pressure P ,

temperature T , and mass of internal EGR 0

0 ( )EGRIm − as the initial condition to the SRM. From IVC till exhaust valve opening (EVO), SRM simulates the processes in the engine cylinder. During this interval, at each global time step, two variables namely, the convective heat transfer coefficient h and the cumulative burnt fraction

are used as progress variables and passed back to the 1-D code by the SRM. During a time step the SRM

g

bx

1-D CFD code

SRM

hg

xb

P0, T0, mI-EGR (at IVC)

Emissions (t)

P(t), T(t), IMEP, BSFC

Figure 2: Coupling between SRM and 1-D CFD codes

calculates )(ϑbx according to: tutb

tutb HH

HHx−−

=)(ϑ

tH

tuwhere, and are the enthalpies of formation of

the unburned and burned gases and is the enthalpy of formation of the current mixture. The CO, HC and NOx emissions as well as evolution of other chemical species are obtained from SRM at EVO. Whereas, the in-cylinder pressure and temperature evolution, and the engine performance characteristics such as IMEP, BSFC are given by the 1-D code. Keeping in mind the detailed nature of the full cycle model, only for cylinder-1 (Master Cylinder in Figure 1) combustion is evaluated by means of the SRM code for the purpose of computational efficiency. The same approach can be extended for modelling all the cylinders, however, for the remaining five cylinders, experimental cumulative burned mass fraction profiles calculated from the measured in-cylinder pressure and the overall injected fuel mass, are provided from an external file.

H tbH

A detailed chemistry evaluation consumes most of the computational time of a complete engine cycle. In order to limit the coupled cycles with detailed kinetic calculation, the flow inside the engine is first initialized using the 1-D code alone until the pressure, temperature and mass flow rates are stabilized. Then the coupled cycles are started. At the first coupled cycle, no information about the composition of exhaust gas is available; therefore an external file is read specifying the gas composition. For the subsequent coupled cycles, the exhaust composition as evaluated by the SRM code is used to specify the internal EGR composition.

SRM

The PDF-based SRM considers scalars such as temperature, mass fraction, density etc., as random variables with certain probability distribution. It is derived from the PDF transport equations for scalars using a statistical homogeneity assumption. SRMs have been rigorously explained in refs. [24-26].

The SRM considers quantities, such as total mass , volume , mean density

m( )tV ( )tρ and pressure ( )tP ,

as global and are assumed not to vary spatially in the combustion chamber. Calculation of global quantities has been discussed in detail before [12,13]. The local quantities such as chemical species mass fractions

and temperature T are treated as random variables and vary within the cylinder.

( ) SitYi ,, ,1…= ( )t

( ) ( ) ( )tTYYtt SS ,,,...,,,..., 111 =ΦΦ=Φ +

where, S is the number of chemical species. For variable density flows, the SRMs are generally represented in terms of mass density function (MDF), than PDF. The corresponding joint scalar MDF is represented by

( )tF S ,,..., 11 +ψψφ . The following partial differential equation (PDE) represents the SRM:

( ) ( )( ) ( )( )

( ) ( )

Mixing

212121

11

21

ψψψψψψψτ

β

ψψψψψ

ψψ

φ ddFFKC

tFUtFGTFt S

Si

i

∫∫=

Ψ∂∂

+Ψ∂∂

+∂∂

++

),,(

,)(,)(,

(1)

where the initial conditions are ( ) ( )ψψφ 00 FF =, , with:

+−= )(

21),,( 2121 ψψψδψψψK (2)

)( wv

g TTmc

AhU −−= (3)

The term on the R.H.S of Eq. (2) gives the effect of mixing on the MDF and is explained in detail later. The source term describes the change of the MDF due to chemical reactions and change in volume given by:

iG

∑=

=r

kkkj

ji

MG

1, ων

ρ (4) Si ,...,1=

Given the state F0N at time t0

Curl Mixing

Chemical Reaction, dV

Time marching: t0+∆t

Convection heat loss

Curl Mixing

Figure 3: Flowchart of the time splitting algorithm

( )dtdV

cP

Mu

cG

v

S

j

r

kkkj

jj

vS

111 1

,1 +

= ∑ ∑

= =+ ων

ρ (5)

To introduce the fluctuations, the third term on L.H.S. of Eq. (2) is replaced by the finite difference scheme:-

[ ]0)(,

),,,,()(),()(1

1

1111

<

−−−

+

+++

S

SSSS

U

thFhUtFUh

ψ

ψψψψψψ …

and

[0)(,

),,,,()(),()(1

1

1111

>

++−

+

+++

S

SSSS

U

thFhUtFUh

ψ

ψψψψψψ … ]

(6)

where, h is the fluctuation. For the present work h is a model parameter. The detailed algorithm for incorporating the convective heat transfer step, based on Eq. (1), Eq. (3) and Eq. (6) is explained in the next sub-section.

An equi-weighted Monte Carlo particle method with a second order time splitting algorithm [12,13,14] is employed to solve Eq. (1) numerically. Monte Carlo methods have been successfully applied to solve the PDF based transport equations [25,27]. The method involves the approximation of the initial density function by an ensemble of stochastic particles. The particles are then moved according to the evolution of the density function. Thus, depending on the mass of internal EGR, at IVC and the composition of the fresh air-fuel mixture, the SRM calculates the initial mass fractions of the chemical species. All the stochastic particles in the ensemble are allocated the same composition and the temperature at IVC. The time splitting algorithm is depicted in Figure 3. Variable corresponds to time at

IVC. is the deterministic global time step which is used for operator splitting. With time marching, convective heat loss, mixing and chemical reaction events are performed on the particle ensemble. The stopping time for this loop is at EVO.

0tt∆

The ODEs for species reaction rates and temperature are solved deterministically using backward differentiation formula (BDF) method of order 5. Another salient feature of SRM is that it can include detailed chemical kinetics, vital to model kinetics-controlled HCCI combustion. In this paper, a detailed kinetic mechanism containing 157 species and 1552 reactions has been used to simulate the ignition process. The H2-O2-CO-CO2 chemistry was taken from Yetter et al. [28]. The formaldehyde chemistry, known to be sensitive in the ignition of higher hydrocarbon fuels, has been described in a previous publication [29]. The methyl and methane chemistry is under publication. These parts of the chemistry are important, since they are responsible for a

large portion of the heat release. The C2-C5 chemistry mostly originates from Warnatz [30] and Baulch et al. [31,32]. The C6-C8 chemistry was developed according to a method developed by Curran et al. [33].

The sub-models for convective heat loss and mixing are discussed next.

Heat loss by convection

Woschni’s convective heat transfer coefficient has been implemented [34]. The convective heat loss is dependent on temperature of a stochastic particle )(iT , temperature of the cylinder wall and the convective

heat transfer coefficient h . The deterministic approach adopted in the previous works [12,13,22] to model convective heat loss, in which all the particles in an ensemble were moved according to Woschni’s heat transfer coefficient and wall area, fails to account for fluctuations. In this paper, the convective heat loss is modelled as a stochastic jump-process [25]. While the total heat transfer is the same as in case of deterministic approach (conserving the first moments), variances have been introduced in terms of stochastic fluctuations.

wT

g

The detailed algorithm is included in the Appendix. The parameter introduces fluctuations and the model parameter controls the magnitude of fluctuations.

Throughout the paper, C is set at 20 and the wall

temperature is fixed at 450 K. This temperature change of particles is equivalent to a physical situation in engine cylinder where the fluid particles in the bulk can travel to the wall and crevices during piston movement and get heated or cooled due to the interaction with the wall.

)(ihhC

wTh

Curl mixing model

A coalescence-dispersion (also termed as particle-pair interaction model) proposed by Curl, is implemented to mimic the physics of turbulent mixing [35]. The mixing algorithm is given in the Appendix. The, mixing takes place in randomly selected particle pairs. The Curl model is relatively simple to use and performs better for multiple reacting scalars as compared to the deterministic interaction by exchange with mean (IEM) model implemented previously [11,13].

RESULTS AND DISCUSSION

The SRM based engine cycle model as explained in previous sections is implemented to model the SCANIA engine with parameters given in Table I.

MODEL VALIDTION

The model was validated by comparing the predictions with the experimental results for a given set of

conditions. Table II gives the operating conditions of the base case.

For validation, the in-cylinder pressure profiles and the HC, CO and NOx emissions predicted by the model are compared with that obtained from experiments. For the

measurements considered in this paper, no external EGR has been used. However, the full-cycle model enables the evaluation of residual burned fraction (also termed as internal EGR). For the parameters and conditions given in Table I and Table II, the internal EGR estimated by the model, was found to be approximately 5-6% only. Thus during a coupled cycle, at IVC, GT-Power passes the amount of internal EGR to the SRM and based on this amount, the SRM code calculates the mass fractions of the species of the fresh mixture.

Initially, the convergence with respect to the number of coupled GT-Power–SRM cycles and the number of stochastic particles, is investigated in order to fix the number of cycles and number of particles for the validation and further ON variation studies. For this, the first 14 engine cycles were run using the GT-Power model only and then 3 coupled cycles (15

N

th, 16th and 17th) using GT- Power and SRM were employed. Figures 4-7 show the auto-ignition timing as well as CO,

Fc

0

2

4

6

8

10

12

-30 -20 -10 0 10 20 30 40

15th cycle16th cycle17th cycle

HC

[g/c

ycle

] x 1

02

CAD

Figure 6: HC emissions as a function of CAD for the coupled cycles.

Table II: Engine operating conditions for validation test.

Rpm 1500

Fuel Isooctane

λ 3.07

Octane number 100

Engine inlet temperature [K] 424

8

12

16

20

15th cycleOx

[mg/

cycl

e] x

103

-3

-2

-1

0

1

2

3

15 16 17 18 19

Ignition CAD

Igni

tion

CA

D

Coupled cycle number

Figure 4: Ignition CAD with respect to the number of coupled cycles.

0

4

8

12

16

20

24

28

32

-10 0 10 20 30 40

15th cycle16th cycle17 th cycle

CO

(g/c

ycle

) x 1

03

CAD

Figure 5: CO emissions as a function of CAD for the coupled cycles.

0

4

-30 -20 -10 0 10 20 30 40

16th cycle17th cycle

N

CAD

igure 7: NOx emissions as a function of CAD for the oupled cycles.

HC and NOx emissions obtained from the three coupled cycles. From Figures 4-7, two coupled cycles were considered to be sufficient to obtain a balance between steady state and computational efficiency. Hence 14 uncoupled cycles followed by two coupled ones have been implemented throughout this paper. For the convergence study with respect to the number of stochastic particles, N, Figure 8 shows the respective pressure profiles for N = 50, 100 and 200. The error in the pressure and emissions predictions while increasing the number from N = 100 to 200 was negligible, however the CPU time was almost double. Thus, for the present paper, 100 particles have been used with 16 cycles (14 uncoupled and 2 coupled), resulting in a computational time of about 7 h on a 1GHz Pentium III.

Figure 9 presents the comparison between the in-cylinder pressure predicted by the SRM-based and Homogeneous model-based, full-cycle simulations with the experimental results. The over-prediction in the peak pressure by the homogeneous model is obvious as it fails to account the inhomogeneities in temperature and composition in the cylinder. The CO emissions prediction by SRM-based and homogeneous model-based full cycle simulations is shown in Figure 10. Based on the pressure and emissions prediction, the SRM based full cycle model clearly outperforms the homogeneous model.

0

0.01

0.02

0.03

0.04

0.05

-10 -5 0 5 10 15 20 25 30

HomogeneousSRM

CO

(g/c

ycle

)

CAD

Figure 10: CO emissions predicted by Homogeneous and SRM based models.

0

20

40

60

80

-30 -20 -10 0 10 20 30

N = 50N = 100N = 200Expt.

P (b

ar)

CADFigure 8: Pressure profile with respect to N

10

20

30

40

50

60

70

80

90

-30 -20 -10 0 10 20 30

Expt.SRMHomoegeneous model

P (b

ar)

CAD

Figure 9: Pressure profile (Homogeneous reactor, SRM and measurements)

0

10

20

30

40

50

60

70

80

Expt.

SRM

CO (g/kWh) HC (g/kWh) NOX (mg/kWh)

Figure 11: CO, HC and NOx emissions

CO, HC and NOx emissions predicted by the SRM based model for the base case are plotted in Figure 11. An excellent agreement between model predictions and experimental results is obtained for HC, CO as well as NOx emissions. The NOx emissions are dependent on the local temperatures as well as the residence times of fluid particles.

Figure 12: In-cylinder temperature profile

0

2

4

6

8

10

12

14

16

400

600

800

1000

1200

1400

1600

1800

-40 -20 0 20 40 60 80

OH

T [K]

OH

[mas

s fr

actio

n] x

105

T [K]

CAD

0

5

10

15

20

25

-20 -15 -10 -5 0 5

OH HO

2

H2O

2

Mas

s fr

actio

n x

105

CAD Figure 13: Auto-ignition characteristics

TEMPERATURE DISTRIBUTION

To investigate the effect of convective heat loss on the PDF of the temperature, the validated model is used with the operating parameters same as given previously in Table II. Figure 12 depicts two views of the in-cylinder temperature distribution with respect to number of particles and crank angle degrees (CAD). To show the effect of convective heat transfer on the temperature of particles, the mixing event is turned off and at the end of each global time step, the particles are sorted such that the lowest temperature is assigned to the first particle and the highest to the hundredth. It can be observed that the particles in the range, approximately 40-100 burn instantaneously, thus having a very slight difference in peak temperatures, whereas the particles in the range 10-40 have a delayed ignition as compared to the earlier range and result in peak temperatures around 500 K less than the particles in 40-100 range. A rapid decline in temperature of particles in the range 1-10 is observed. Even at EVO, inhomogeneities exist; the temperature difference between coolest and hottest stochastic particles is approximately 300 K.

)(N

AUTO-IGNITION CHARACTERISTICS

Using the validated model case, HCCI ignition characteristics are illustrated in this sub-section. From ignition point of view, HCCI lies in the intermediate temperature ignition regime [36]. HCCI, liquid-fuelled diesel engine, knock in SI and rapid compression machine share a common ignition feature – the

Figure 14: OH and temperature peak with respect to CAD

0

5

10

15

20

25

30

400

600

800

1000

1200

1400

1600

1800

-30 -20 -10 0 10 20 30

HCHO

T [K]

HC

HO

[mas

s fr

actio

n] x

104

T [K]

CADFigure 15: HCHO and in-cylinder temperature comparison

accumulation of H2O2 until a sufficiently high temperature is reached (also referred as critical temperature) such that H2O2 decomposes into OH radicals. The OH radicals are then consumed by the fuel resulting in a rapid increase in temperature. Thus, the decomposition of H2O2 and consumption of fuel indicate ignition.

The evolution of the compositions of OH, HO2 and H2O2 radicals is shown in Figure 13. The chain branching steps in the intermediate as well as high temperature regimes has been well documented elsewhere [36]. The OH and formaldehyde (HCHO) have been observed to be closely related to the early cool flame and the main heat release stages. The peak OH level position

F

-15

-10

-5

0

5

10

60 65 70 75 80 85 90

Expt. (lower limit)SRMExpt. (upper limit)

Igni

tion

CA

D

Octane number

Figure 16: Ignition CAD vs octane number.

0

5

10

15

20

60 65 70 75 80 85 90

Expt. (lower limit)PDF modelExpt. (upper limit)

Com

bust

ion

dura

tion

(CA

D)

Octane number

Figure 17: Combustion duration vs. octane number

coincides with the peak temperature as shown in Figure 14. As depicted in Figure 15, the HCHO concentration increases rapidly as the temperature reaches 1000 K and reduces rapidly with further increase in temperature. The peak of HCHO level corresponds with start of main combustion in agreement with the ref. [18].

0

10

20

30

40

50

60

70

80

60 65 70 75 80 85 90

Expt.PDF model

CO

(g/k

Wh)

Octane number

igure 18: CO emissions vs. octane number

EFFECT OF OCTANE NUMBER VARIATION

Octane number (ON) is a practical measure of a fuel’s resistance to knocking and by definition it denotes the volume percentage of isooctane in an isooctane and n-Heptane mixture. Isooctane and n-Heptane are widely different in their auto-ignition characteristics and this fact is used to control the HCCI combustion and emissions.

In this section the model predictions are compared with the measurements for varying octane numbers. The number of particles, N, cycles and the parameter are kept the same as in the previous section. The operating conditions for this study are given in Table III.

hC

With the engine speed fixed at 1500 rpm and air-fuel ratio at 3.72, the octane number is varied from 61 to 86. Ignition CAD is the crank angle degree at which 10% of air-fuel mixture burns. Figure 16 depicts the behaviour of ignition-CAD with respect to octane number. As the octane number increases, the resistance to autoignition increases thus delaying the ignition CAD. Over the range of octane numbers, the predicted ignition CAD lies within the bands of the experimental results, thus showing a good agreement. The combustion duration, i.e the angle

between 10% and 90% burned fraction is shown in Figure 17.

With increase in octane number, the expected rise in CO and HC emissions due to incomplete oxidation is predicted correctly by the model. The experimental and model predictions for CO and HC emissions are plotted in Figures 18-19. The trends as well as magnitudes are predicted well as compared to the experimental results. The NOx emissions show a reverse trend with increase in octane number as shown in Figure 20. The NOx emissions predictions with varying octane number show a good agreement with the measurements. Figure 21 shows the effect of octane number variation on the in-cylinder temperature. As discussed before, increase in spontaneity to ignition, (decrease in octane number)

1

2

3

4

5

6

7

60 65 70 75 80 85 90

ExptSRM

NO

X (mg/

kWh)

Octane number

Figure 20: NOx emissions vs. octane number

0

5

10

15

20

25

60 65 70 75 80 85 90

ExptSRM

HC

(g/k

Wh)

Octane number

Figure 19: HC emissions vs. octane number

800

1000

1200

1400

1600

1800

-30 -20 -10 0 10 20 30

ON61ON66ON69ON78ON75ON82ON86

T (K

)

CADFigure 21: In-cylinder temperature sensitivity to

octane number.

Table III: Engine operating conditions for octane number ON variation study.

Rpm 1500

Fuel Isooctane and n-Heptane

Engine inlet temperature [K] 310

Engine inlet pressure [bar] 0.99

λ 3.72

Octane number Varied

results in advanced auto-ignition and thereby a higher peak temperature.

CONCLUSION

An integrated PDF-based stochastic reactor model was coupled with a commercial engine cycle simulator thus combining the advantages of the improved PDF-based closed volume model as well as full cycle simulations. The model can account for inhomogeneities in temperature and composition and model various features such as internal and external EGR and turbocharging. The coupling-interface was developed on the basis of two progress variables; cumulative burnt fraction and the convective heat transfer coefficient. A convective heat loss sub-model based on a stochastic jump process has been introduced. This sub-model accounts for the fluid-wall interactions and the fluctuations inherent in a practical engine.

The model was applied to simulate combustion and emissions and investigate the role of octane number as a control parameter for HCCI operation. For this, the model was applied to simulate a multi-cylinder, dual-fuelled, SCANIA engine operating in HCCI mode and the predictions have been compared with measurements and a previous numerical study. The robustness and accuracy of the predictive model is evident from the excellent agreement observed between model predictions and measurements for in-cylinder pressure and CO, HC as well as NOx emissions. The model clearly outperforms the widely used homogeneous model-based full cycle engine simulators. With the convective heat loss sub-model the integrated model was demonstrated to account for inhomogeneities in temperature.

After the rigorous validation, the model was also applied to study the effect of change in octane number on combustion and emissions. With an increase in octane number, the resistance to auto-ignition increases thus reducing the peak temperature. Increasing CO and HC emissions (incomplete oxidation) and the decrease in NOx emissions with increasing octane number was correctly predicted and showed a good agreement with the measurements. The trends observed in the measured combustion characteristics such as ignition crank angle degree and combustion duration over a wide range of octane numbers is reliably predicted by the integrated model.

To exploit the predictive nature of the integrated model, it will be applied to different HCCI configurations in order to develop operating window for HCCI and evaluate the effect of other control options (e.g. residual burnt fraction trapping). From the computational expense point of view, various alternative schemes (homogeneous coupled cycles followed by PDF-based coupled cycles, and adaptive particle ensemble size with respect to cycles) will be investigated to reduce the computational time.

ACKNOWLEDGMENTS

The authors are grateful to Prof. Bengt Johansson and his research group at the Department of Heat and Power Engineering, Lund University, Sweden for providing the measurements.

The authors would like to thank Cambridge Commonwealth Trust, British Chevening, ORS committee and EPSRC (GR/R53784) for the financial support.

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DEFINITIONS, ACRONYMS, ABBREVIATIONS

A Combustion chamber wall surface ABDC After Bottom Dead Center

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ATDC After Top Dead Center BBDC Before Bottom Dead Center BDF Backward Differentiation Formula BSFC Break Specific Fuel Consumption BTDC Before Top Dead Center

23. Gamma Technologies, GT-power User’s Manual and tutorial, Version 5.2, IL, USA, (2001).

CAD Crank Angle Degrees CAI Controlled Auto-Ignition

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CIDI Compression Ignition Direct Injection

hC Stochastic fluctuation parameter

δ Dirac delta distribution φ

c Mixing model parameter ϑ Crank angle degrees

vc Gas specific heat at constant volume λ Actual air–fuel ratio / stoichiometric air-

fuel ratio EGR Exhaust Gas Recirculation EVO Exhaust Valve Opening υ Stoichiometric coefficient F Mass density function ρ Density

gh Convective heat transfer coefficient ω Chemical source term τ Characteristic mixing time parameter h Fluctuation τ̂ Exponentially distributed waiting time )(ih Fluctuation for each particle π Parameter for waiting time

tH Enthalpy of formation of current mixture t∆ Global time step tbH Enthalpy of formation of burned gases ψ sample space variable

tuH Enthalpy of formation of unburned gases

φ random variable

HCCI Homogeneous Charge Compression Ignition APPENDIX

ICE Internal Combustion Engine IEM Interaction by Exchange with Mean

The algorithms for the coalescence dispersion based mixing model and the convective heat loss sub-model are presented in this Appendix.

IMEP Indicated Mean Effective Pressure IVC Inlet Valve Closure m Mass MDF Mass density function Heat loss algorithm

EGRIm − Mass of internal EGR In each global time step ( ), the heat transfer model is implemented as:

ttt ∆+→N Number of stochastic particles ON Octane Number

1. Generate the initial MDF according to the initial condition )(0 TF

ODE Ordinary Differential Equation P In-cylinder pressure P0 In-cylinder pressure at IVC PDE Partial Differential Equation 2. Calculate fluctuation h(i) for the particles PDF Probability Density Function PM Particulate matter

h

wi

i

CTTh −

=)(

)( PRF Primary Reference Fuel r Number of chemical reactions Rpm Revolutions per minute S Number of species

3. Wait an exponentially distributed time step τ̂

with the parameter: v

hg

cmNACh

p⋅

=)(π

SI Spark Ignition SRM Stochastic reactor model t time t0 time at IVC T In-cylinder temperature T0 In-cylinder temperature at IVC 4. Choose particle index according to uniform

distribution )(iT Current temperature of the ith particle

wT Wall temperature 5. Perform temperature jump T )()()( iii

new hT −=u Internal energy V In cylinder volume Vc Clearance volume 6. If t tt ∆+< , go to step 2. v Stoichiometric coefficient

bx Cumulative burned fraction Curl mixing algorithm

iY Mass fraction of species i In each global time step ( t ), the coalescence-dispersion mixing model is implemented as follows:

tt ∆+→ GREEK LETTERS 1. Generate the initial MDF according to the initial

condition )(0

TFβ Curl model constant

2. Choose two distinct particle indices according to uniform distribution

3. Wait an exponentially distributed time step τ̂ with the parameter:

τβ

π φ

⋅

−=

2)1(

)(NC

p

4. Perform mixing step:

[ ])()(21)()( )()()()( tttt qpqp φφτφτφ +=+=+

5. If t < , go to step 2. tt ∆+