xv
NOMENCLATURE
AHRR = apparent heat release rate
ATAC = active thermo-atmosphere combustion ATDC = after top dead center
BDC = bottom dead center
BMEP = break mean effective pressure BSFC = brake specific fuel consumption BTDC = before top dead center
CA = crank angle
CAD = crank angle degree
CFD = computational fluid dynamics CI = compression ignition
CTC = characteristic timescale combustion DDM = discrete droplet model
DI = direct injection DNS = direct numerical simulation DOI = duration of injection EGR = exhaust gas recirculation EOI = end of injection
EVC = exhaust valve closure EVO = exhaust valve open GDI = gasoline direct injection HC = unburned hydrocarbons
HD = heavy duty
HCCI = homogeneous charge compression ignition HRR = heat release rate
Kgf = kilograms of fuel
KH-RT = Kelvin-Helmholtz Rayleigh-Taylor IC = internal combustion
ID = ignition delay
IMEP = indicated mean effective pressure IVC = intake valve closure
LES = Large Eddy Simulation LIF = Laser Induced Fluorescence LII = Laser Induced Incandescence
LISA = Linearized Instability Sheet Atomization LTC = low temperature combustion
MK = modulated kinetics
NOx = oxides of nitrogen
NSC = Nagle-Strickland-Constable
PCCI = partially premixed charge compression ignition PDF = probability density function
PFI = port-fuel-injection PM = particulate matter PRF = primary reference fuel
RANS = Reynolds Averaged Navier Stokes
xvi RNG = Re-normalized group
RPM = revolutions per minute
SCOTE = Sincle Cylinder Oil Test Engine SI = spark ignition
SMD = Sauter Mean Diameter SOI = start of injection
TAB = Taylor-Analog-Breakup TDC = top dead center
Arabic Symbols
A = pre-exponential constant in CTC model Af04 = pre-exponential constant in Shell model cp = heat capacity
Da = Damkohler number
Dl = laminar diffusivity DT = turbulent molecular diffusivity E = activation energy
G = non-reactive scalar in G-equation h = specific enthalpy
I = total number of reactions; specific internal energy J = total number of reactions,
k = chemical reaction rate constant; turbulence kinetic energy K = total number of species
Nu = Nusselt number
p = pressure
PrT = Prandtl number
Re = Reynolds number
Ru = universal gas constant S = rate of strain tensor
Sl = laminar flame speed
ScT = Schmidt number
t = time
T, T0 = fluid temperature, inner layer temperature u, u′, u′′ = flow velocity vector, conventional average
turbulence intensity, Favre average turbulence intensity
V = fluid volume
W = species molecular weight We = Weber number
[X] = species concentration Y = species mass fraction
Greek Symbols
αT = turbulent thermal diffusivity
β = temperature dependence coefficient ε = dissipation rate of turbulence kinetic energy δl = laminar flame thickness
xvii κ = mean flame front curvature
λ = heat conductivity of fluid µT = turbulent dynamic viscosity
ν = stoichiometric coefficient of chemical reactions νT = turbulent kinematic viscosity
ρ = fluid density
σ = viscous stress tensor
τC = characteristic timescale in CTC model
τlam = laminar timescale in Damkohler combustion strategy τchem = chemical timescale in Damkohler combustion strategy φ = equivalence ratio
χ = chemical species symbol
Subscripts
b = backward elementary reaction step; burnt mixture f = forward elementary reaction step
g = gaseous properties
i = reaction index, i = 1, · · · , I k = species index, k = 1, · · · ,K l = liquid properties
u = unburned mixture
Superscripts
c = terms due to chemical reactions T = vector or matrix transpose
