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
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