Upon combining the steady state flamelet solution with a
characteristic timescale, the time rate of change of species i can be written as:
where indicates filtering at the grid level and
is thewhere Y˜*
is the value of the mass fraction obtained from
LES Favre averaging。 ˜ij is the viscous term and often
approximated as [14]:
the flamelet library while Yi is the resolved mass fraction
used by CFD code, and
chem
is a characteristic
timescale obtained by expanding the reaction rate about the flamelet solution。
The characteristic time scale chem
represents the rate at
The subgrid stress tensorij
is defined as:
which each species proceeds towards its steady flamelet
This term represents the subgrid scale mixing effects。 Since it can not be determined from the resolved field, it
needs to be modeled。 The term is modeled using a j 2
tensor coefficient。 Using the dynamic procedure
proposed in [10], this found to be:
In Equation (16), the mixture fraction flux is defined as:
where Lij and L kk are the Leonard stress tensor and its trace respectively。 The Leonard stress tensor is:
The mixture fraction variance flux term in Equation (17)
is similarly given by:
The Leonard stress tensor can be determined from the
resolved field and a second filtered field, which is the resolved field filtered again by a test filter and this
process is denoted by
。 k is the subgrid kinetic energy:
The subgrid scale scalar dissipation rate is defined as:
The subgrid kinetic energy is solved from a transport equation, the modeled form of which is given by [10]:
The subgrid scale scalar dissipation rate sgs is modeled by a zero-equation model:
The model for the subgrid kinetic energy dissipation is also given in [10]:
It is straightforward to relate
to the mean scalar
dissipation rate used by the combustion model according to (2) and (20):
where is a coefficient determined by the filter [10]。 LES SCALAR TRANSPORT
The mean mixture fraction, ˜ , mixture fraction variance,
~"2 , and mean scalar dissipation rate, ˜ , represent mixing and need to be obtained from solving LES transport equations。 It should be mentioned that the
The diffusion term in Equation (16) can be approximated through a simple gradient assumption。
The approach to the dynamical structure model for subgrid stress is extended to modeling the subgrid mixture fraction flux term appearing in the Equation (16) and (17) [15]:
subgrid mixture fraction, defined by 柴油机大涡中小火焰模型模拟英文文献和中文翻译(3):http://www.youerw.com/fanyi/lunwen_100459.html