conceptually  a  different  quantity  from  mixture fraction

variance。 But it is widely accepted that this quantity can be used to approximate mixture fraction variance [14]。 In this paper, these two names are used     interchangeably

for  convenience。  The  transport  equation  for  the mean

The  Leonard  terms  for  mixture  fraction  flux

mixture fraction and the mixture fraction variance are:

mixture fraction variance



2  are given respectively by:

To   overcome   these   deficiencies,   a   new   model for

conditional scalar dissipation rate model is proposed based   on   assuming   the   functional   dependence  on

mixture  fraction  following  Peters  [17]。  However,     the

restriction to the fixed boundaries in mixture fraction space  is  relaxed。  Starting  with  a  planar  2D  opposed

The final terms in Equations (16) and (17) are source terms contributed from the spray vaporization。 It is believed that the spray source term has significant impact on the profile of the subgrid mixture fraction  [16]。

diffusion flame configuration with partially premixed boundary conditions for mixture fraction and assuming constant local density:

However, due to lack of more precise LES models for

  

the subgrid scale term enclosed by the bracket in Equation (17), it is roughly modeled using the leading term of the series expansion for this term:

A MODEL FOR THE CONDITIONAL SCALAR DISSIPATION RATE

The scalar dissipation rate partially accounts  for turbulent mixing effects。 Additionally, it is a critical parameter to judge the possibility of local extinctions [1], which is an extremely unsteady phenomenon and possibly relevant to diesel combustion。 As discussed in [1], the conditioned scalar dissipation rate should be used    when    solving    the    flamelet    equation      (1)。

In this configuration, the boundary conditions as represented by limits could vary with time。 However, it is assumed that the internal flow field, particularly in the vicinity of the flame, responds to the limits instantaneously。 Thus, it can be solved as a quasi- steady problem。

The velocities can be related to a constant strain rate:

Accordingly, the scalar dissipation rate  conditioned at the  stoichiometric  mixture  condition  could  be  used to

u ax, v ay

(29)

better predict local extinctions。

Traditionally, the conditional scalar dissipation rate is modeled by assuming a functional dependence on mixture  fraction。  This  functional  dependence  can    be

By substituting velocities and looking at the balance equation along the x-axis (normal to the flame front), the balance equation reduces to a 1-D problem:

solved from an opposed diffusion flame or a mixing layer

configuration  [17]。  However,  the  function  obtained   in

such configurations assumes fixed  boundaries of mixture fraction that correspond to pure oxidizer and pure fuel respectively。 It is obvious that during the diesel combustion the boundaries in mixture fraction  space vary with time and the mixture fraction interval  becomes