In regarding to the efficiency of KIVA for LES, from authors’  experience,  it  usually  takes  roughly  40~50%

st

f (

; Lean , Rich )

(37)

more time to run a LES simulation than RANS using  the

same mesh。 The extra computational time mainly comes from the test filtering process used by the dynamic   LES

where the subscript st means evaluating at the stoichiometric condition。 Taking the average of both sides of Equation (37) using the PDF of :

Lean Richmodels。RESULTS AND DISCUSSIONS

LES simulations of a turbulent reacting methane-air    jet

flame, known as the Sandia D flame [22], and a   heavy-

st f (alternatively,;Lean ,Rich )

duty diesel engine, Caterpillar 3400 series [23], have been performed。

JET FLAME SIMULATION

The experimental setup consists of a main fuel jet of diameter  7。2  mm  surrounded  by  a  burnt  gas  jet    of

st Lean Rich

f (

;Lean ,Rich )

diameter 18 mm。 The main jet composition is 25% methane and 75% air。 The Reynolds number based on the inlet of fuel stream is 22,400。 The flame is  stabilized

Employing the Chebyshev inequality to seek  the possible limiting value of mixture fraction within 96% confidence level:

above the burner tip by the co-flow jet。

A three-dimensional Cartesian mesh is used for the LES simulation。 A plane of this mesh is shown in Figure 1。

The grid cells are non-uniform in the radial and axial directions to refine the regions near the axis and burner exit while saving computation in other regions。  The mesh has dimensions approximately 15 cm x 15 cm x 60

Hence, the boundaries in the mixture fraction space  can

be estimated as:

cm and consists of 227,475 cells。 The top boundary condition is continuative outflow while the bottom boundary is a specified inflow。 The side boundaries are set as free-slip walls。 Specifically, the inflow velocity profile is approximated using a 1/7th power law。 In order to simulate the turbulent behavior of flow entering the domain, the subgrid kinetic energy is perturbed at the

inlet by imposing on the mean profile an unsteady sine wave having amplitude of 20% of the mean。

Figure 1。 Cutting plane view of computational mesh for Sandia flame D

Figure 2 shows an instantaneous  temperature  field of the simulated jet。 Also shown in this figure is the surface of the stoichiometric mixture fraction, which indicates the reaction zone。 The temperature distribution in Figure 2 qualitatively agrees with the fundamental experimental observation on the jet flame。 It can be seen that high temperature region are coincident with the  reaction zone。

between LES results and ensemble-averaged experimental results, the LES data must be time- averaged since LES yields time-dependent results。 The LES results are thus averaged over a sufficient  long time, say 0。02 second, after the startup transients have vanished (0。09 second)。 Figure 3 and Figure 4 show the axial distribution of temperature and radial temperature distribution at several downstream  locations respectively。 The agreements are generally good especially for the relatively coarse mesh used here。

Figure 3。 Centerline temperature versus axial distance from jet exit

Figure 2。 Instantaneous temperature [K] distribution, the black curve represent stoichiometric contour