Scope and objective

Direct Dual Fuel Stratification (DDFS)

Crank angle (

^o

ATDC)

-400 -350 -300 -250 -200 -150 -100 -50 0 50 RCCI

SOI3

Gasoline PFI Diesel CRI

DDFS Gasoline CRI Diesel CRI

SOI1 SOI2

P

Gasoline CRI (single fuel)PPC

(dual fuel)RCCI

(dual fuel)DDFS

Figure 1-8: Illustration of SCCI, RCCI, and DDFS combustion concepts reproduced from [4].

PFI, CRI, and SOI denote port fuel injection, common-rail direct injection, and start of injection, respectively. The area of each box represents the relative quantity of each injection.

gasoline. Similar to the RCCI combustion, an early injection of gasoline is used in the DDFS combustion to have premixed background charge, then accompanied by direct injection of diesel to generate some degrees of inhomogeneities in both reactivity and equivalence ratio. These first two injections are designed to control the start of the main combustion occurring at about 10^◦CA before the TDC (bTDC). Inspired by the PPC, the DDFS combustion utilizes direct injection of remaining gasoline right bTDC to control the combustion rate. As such, DDFS combustion can achieve capability to independently control ignition timing and combustion duration by combining reactivity stratification with diffusion-limited gasoline injection [4, 31, 32]. However, the effect of the timing of the late gasoline injection on the combustion process of both fuel stratification is not well-understood.

1.6 Scope and objective

Recent advancement and progress in experimental studies have provide valuable insights into the overall characteristics of HCCI combustion process. However, engine experiments can provide only limited information such as the overall pressure and HRR, 2-D line-of-sight chemilumines- cence or planar images of select species. The more in-depth insight into the physical-chemical interactions occurring in a combustion chamber is still elusive. Thanks to high-fidelity direct numerical simulations (DNSs), fundamental understanding of the in-cylinder combustion pro- cess including combustion modes, flame speed, turbulence-chemistry interactions, controlling

1.6 Scope and objective species and reactions of the HCCI-type engines can be achieved. A better understanding of the ignition characteristics of HCCI engines will assist the research and development of prototypes of HCCI engines in extending the high-load limit and improving fuel efficiency.

With the help of DNSs, the objective of the present study is (1) to provide better understand- ings of the effect of thermal and compositional stratification levels under different low-to-high temperature regimes and fuel compositions on the overall ignition characteristics of HCCI com- bustion; (2) to investigate the relative effect of temperature/equivalence ratio/reactivity strati- fication coupled with the turbulence intensity under HCCI/SCCI/RCCI on combustion modes using several different fuels including primary reference fuels (PRF)–a blend of n-heptane and iso-octane, n-heptane, and biodiesel; (3) to identify the key species and critical reactions un- der SCCI/RCCI by using chemical explosive mode analysis (CEMA); and (4) to elucidate the effect of the late-direct-injection timing on the combustion process of direct dual fuel stratifica- tion (DDFS) by developing a pseudo-iso-octane model with the capabilities of reproducing the timing and duration of the late direct injection.

The thesis is organized as follows. First, Chapter 2 is devoted to discussing the formulation of chemically reacting flows and numerical methods used in the present study. Next, the ignition characteristics of lean primary reference fuel/air mixtures with temperature inhomogeneities are investigated in Chapter 3. Ignition of a lean biodiesel/air mixture with temperature and com- position inhomogeneities at high pressure and the intermediate temperature is then numerically studied in Chapter 4. In Chapter 5, the ignition characteristics of a leann-heptane/air mixture with temperature and composition inhomogeneities relevant to HCCI and SCCI combustion.

The ignition characteristics and chemical aspects of a lean PRF/air mixture under RCCI/SCCI conditions are elucidated in Chapters 6 & 7. Chapter 8 is to investigate the effect of injection timing on the ignition of lean PRF/air/EGR mixtures under direct dual fuel stratification condi- tions. Finally, in the last chapter 9, the conclusions are briefly summarized and the implications and contributions of this study are highlighted.

Formulation of compressible reacting

flows and numerical methods

2.1 Governing equations for reacting flows in conservative form In this chapter, the governing equations of the fully compressible multi-component reacting flows in conservative form are introduced [35], and then the numerical methods and boundary conditions used in the present study are discussed.

2.1 Governing equations for reacting flows in conservative form

A system of conservation equations for the fully compressible reacting flows with detailed chem- istry and transport is briefly reviewed here. The detailed description can be found in [36, 37].

The conservation equations for mass, momentum, energy and species are written as

∂ρ

∂t + ∂

∂x_α(ρu_α) = 0, (2.1.1)

∂ρ

∂t(ρu_α) + ∂

∂xβ

(ρu_αu_β) =− ∂p

∂xα

+ ∂τ_βα

∂xβ

+ρ

N

X

i=1

Y_if_i,α α= 1,2,3, (2.1.2)

∂

∂t(ρe₀) + ∂

∂xα

[(ρe₀+p)u_α] =−∂q_α

∂xα

+ ∂

∂xβ

(τ_βαu_α) +ρ

N

X

i=1

Y_if_i,α(u_α+V_i,α), (2.1.3)

∂

∂t(ρYi) + ∂

∂xα

(ρuαYi) =− ∂

∂xα

(ρYiVi,α) +Wiωi i= 1, ..., N, (2.1.4)

wheretis time,x_α the spatial coordinate of directionα in a rectangular Cartesian system,ρ is the mass-averaged density,uα is the flow velocity in directionα,pis the pressure,fi,αthe body force per unit mass on speciesiin directionα,Yiis the mass fraction of speciesi,N is the total number of species, andWiis the molecular weight of speciesi. ωiis the molar production rate of speciesi. e0 is the specific total energy (internal energy plus kinetic energy). Henceforth,α and β denote spatial indices whileiandj are used to denote species indices unless stated otherwise.

Note that since the summation of theN species equations yields the continuity equation, only (N−1) species equations are solved such that one species such as nitrogen N₂ is evaluated from the conservation relation,PN

i=1Y_i= 1.

The specific total specific energy is calculated as follows:

et= u_αu_α

2 +h−p

ρ = u_αu_α

2 +

N

X

i=1

hiYi−p

ρ (2.1.5)

whereh is the total enthalpy including sensible and chemical energy.

Constitutive relationships

The equation of state of an ideal gas mixture is

p=ρRuT /W, (2.1.6)

whereR_u and W is universal gas constant and the mixture molecular weight, respectively.

The mixture molecular weight,W, is defined as

W =

N

X

i=1

Y_i/W_i

!⁻¹

=

N

X

i=1

X_iW_i, (2.1.7)

whereYi andXi respectively are the mass and mole fractions of species and they are related by Yi/Wi =Xi/W.

For an ideal gas mixture, the enthalpy is evaluated through the thermodynamic relationships

h=

N

X

i=1

hiYi, hi =hi0+ Z T

T0

cp,idT, cp=

N

X

i=1

cp,i/Yi, cp−cv =Ru/W, (2.1.8)

whereh_i andh_i⁰ is the enthalpy and the formation enthalpy of speciesiat temperatureT₀, and c_p andc_v are the specific heat capacity at constant volume and pressure, respectively.

The stress tensor, τ_βα, the species diffusion velocities,Vi,α, and the heat flux vector,qα, are respectively evaluated as

τβα=µ ∂u_β

∂xα

+∂u_α

∂x_β −2 3δβα

∂u_k

∂x_k

, (2.1.9)

Vαi= 1 Xi

N

X

i=1

Yj

Xj

Dijdαj−D^T_i ρYi

∇_α(lnT) (2.1.10)

qα =−λ∂T

∂x_α +ρ

N

X

i=1

hiYiVi,α. (2.1.11)