LES Combustion Modeling for Diesel
Engine Simulations
Bing Hu
Professor Christopher J. Rutland
Sponsors: DOE, Caterpillar
Background

Motivation
 Better predictive power: LES is potentially capable of capturing
highly transient effects and more flow structures
 New analysis capability: LES is more sensitive to initial and
boundary conditions than RANS such that it is better suitable for
studying cyclic variations and sensitivity to design parameters.

Primary components
 Turbulence model: a one-equation non-viscosity model called
dynamic structure model for subgrid scale stresses
 Scalar mixing models: a dynamic structure model for subgrid scale
scalar flux and a zero-equation model for scalar dissipation
 Combustion model: a flamelet time scale model
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Large Eddy Simulations
Actual u
u
 Spatial filtering
ui  ui  ui
LES averaged u
 Filtering of non-linear terms in
Navier-Stokes equations results in
subgrid scale terms needed to be
modeling
 ij  ui u j  ui u j
RANS averaged u
x

Smagorinsky
model
Dynamical structure model
use eddy viscosity
one equation model
k: sub-grid turbulent kinetic energy
Cij :dynamically determined tensor coefficient
 ij
 ij  cij k
  t Sij
3
Flamelet Time Scale Combustion Model

Overview
 Flamelet mixture fraction approach: each species is a function of mixture
fraction and stretch rate , this functional dependence is solved using a 1-D
flamelet code prior to the CFD computation

Yi  Yi ( ,

)
Use probability density function (PDF) to obtain mean values
q 1
Yi 
*
  Y ( ,  ) P( ,  )d d 
i
0

0
Modification for slow chemistry using a time scale
Yi  Yi *
Y i

t


Additional features
 PDF of mixture fraction is constructed from its first and second moment which
are solved from LES transport equations
 LES sub-grid model for scalar dissipation helps to construct PDF of stretch rate
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Jet Flame Tests (Sandia Jet Flames)
•
•
•
•
•
•
Sandia piloted flames are simulated to validate models
A coarse grid is used: 15cm x 15cm x 60cm, about 230,000 cells
Instantaneous temperature fields are presented below
Black curves represent stoichiometric mixture fraction
Reynolds number at fuel jet for flame D = 22,400
Reynolds number at fuel jet for flame E = 33,600
flame D
A Relatively stable flame
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flame E
Significant local extinctions
result in lower temperature
Engine Test Case (Caterpillar Diesel Engine)
bore X stroke (mm)
Displacement volume (L)
Compression ratio
Engine speed (rpm)
% Load
START OF INJECTION
-9 ATDC
Duration of injection (degree)
137.6 X 165.1
2.44
15.1
1600
75
21
12
Pressure [MPa]
Cylinder
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Experiment
10
Simulation
9
8
7
6
5
4
Mixture fraction variance
-10
-5
0
5
10
15
20
25
30
35
40
o
C A [ ATDC ]
470
Heat Release [J/Degree]
Mixture fraction
Experiment
Simulation
370
270
170
70
-30
-10
6
-5
0
5
10
15
20
CA [o ATDC]
25
30
35
40
Summary and Future Work

A flamelet time scale combustion model was
integrated with LES dynamical structure turbulence
and scalar mixing models

Model results agreed well with experiments of jet
flames and a diesel engine

More accurate spray models are to be integrated
with LES turbulence and scalar mixing models

More precise initial and inflow conditions are to be
generated for LES simulations
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