solve the steady flamelet equation governing  an opposed jet diffusion flame and solutions are stored as a flamelet  library。  A  chemical  mechanism  for n-heptane

solution。 This time scale is currently implemented based on a one-step irreversible reaction for diesel combustion:

with  44  species  and  112  reactions  [6]  is  used      for

generating the library for diesel combustion while the mechanism for methane with 29 species and 49 reactions [7] is used for the library for simulating methane-air combustion。 The mean mass fractions stored in the library are determined from averaging the instantaneous  OPPDIF  solution  with  a  joint  PDF   for

and  as:

chem fuel o2 A

where A = 1。54e+10 and EA=77。3 kJ/mol。 These values are determined from a one-step reaction for tetradcane [8]。

Since this combustion model essentially uses a steady- state flamelet library displaced by a time scale, it is not applicable  to  predict  the  auto-ignition  delay  in  diesel

engines。 For engine simulations, the Shell model [9] is adopted to handle auto-ignition process。

Equation (3) is simplified by assuming statistical independence of and 。 This allows the mass fraction

to be averaged as:

LES TURBULENCE MODELS

For non-premixed turbulent combustion, the fuel must be mixed with oxidizer at the molecular level before they

can react。 Thus, the turbulent mixing plays a critical role and is mostly a controlling process。 To account for mixing,  the  parameters  which  serve  as  inputs  for the

where the probability distribution function (PDF)  P() is

assumed to be a beta distribution and  P() is assumed

Flamelet Time Scale combustion model, the mean mixture fraction, ˜ , mixture fraction variance, ~"2 ,  and

to be a lognormal distribution。 P()

and  P()

can be

scalar  dissipation  rate,  ˜   ,  need  to  be  obtained from

approximately      constructed      with      knowing     their

corresponding first and the second moments。 The second  moment  of  is  assumed  to  be  unity。   Thus,

determination of these PDF’s only requires the mean mixture fraction, ˜ , mixture fraction variance, ~"2 , and mean scalar dissipation rate ˜ 。 These quantities can be determined from the flow field with the help of LES turbulence   models   that   will   be   discussed   in     the

subsequent section。 As a summary, the flamelet library can be generated as mean species mass fractions indexed by three key parameters:

solving the flow field。 Due to the filtering on the original equations, some subgrid scale terms  appear  that can not be solved directly。 These unresolved terms are modeled using a dynamic LES modeling approach without assuming an eddy viscosity [10]。 With this approach, the subgrid quantities are dynamically determined from the resolved field such that the universal model coefficients that are used in the traditional zero-equation model [11] or one-equation model [12] are not necessary。

SUBGRID STRESS TENSOR MODEL

A one-equation non-viscosity LES model called the dynamic structure LES model [10] is used to  simulate the unclosed terms in the LES momentum equation: