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Application of LES to CFD
simulation of Diesel combustion
3604A058-2 Fumio KUWABARA
Background
Diesel Combustion
Internal conditions
Turbulent flow etc.
CFD code
Prediction Method
Now
Future
?
Calculation Results
Process
Ignition, Combustion, products
RANS
LES
Key aspects of turbulence
• Unsteady, aperiodic motion
• Turbulence is characterized by eddies or
instabilities
• Largest eddies are the same scale as the
flow and are often anisotropic
• Smaller eddies form off the larger eddies
and become more isotropic at smaller scales
What is Eddy?
Small Eddies
Large Eddies


Large eddies: anisotropic

Large eddies extract energy from the flow

Large eddies are and carry most of the turbulent energy

Directly affecting the mean fields
Small eddies: isotropic

Smaller eddies extract energy from larger eddies

The smaller scales act mainly as a sink for the turbulent energy
What is Turbulence Model?
Turbulence Simulation
resolved flow
turbulent flow
Turbulence Model
not resolved flow
Operation:
Separate the flow field
Turbulence Simulation
• Direct Numerical Simulation (DNS)
– Resolves the whole spectrum of scales
– No modeling is required
• Large Eddy Simulation (LES)
– Large eddies are directly resolved
– Smaller eddies are modeled
• Reynolds -Averaged Numerical Simulation （RANS）
– Solves “averaged” Navier-Stokes equations
– The most widely used approach for industrial flows
Turbulence Simulation （comparison）
Reynolds -Averaged
Numerical Simulation
More
useful
Large Eddy Simulation
Direct Numerical Simulation
More
Computational
Effort
&
Precision
Navier - Stokes Equations
Navier - Stokes Equations
for an incompressible fluid:
ui
0
xi
2

u
u
ui
 ui
1 p
i j



t
x j
 xi
x j x j
Unsteady
Advection
Pressure
Viscosity
RANS : What is
RANS?
ui
ui
fluctuating parts
ui
mean
Time
Decompose velocity into mean and fluctuating parts:
ui  ui  ui
1 N
ui  lim ui
N  N
n1
Reynolds -Average
RANS doesn’t resolve any scales of turbulence at all !
RANS : RANS equation
Reynolds -Averaged Navier -Stokes Equations
ui
Additional term
0
xi
ui uiu j
2ui
P
1 

  

 ij
t
x j
xi
x j x j  x j
 ij  uiuj
Reynolds stresses
Closure Problem
Turbulence Model
RANS : Eddy viscosity model
RANS equations require closure for Reynolds stresses:
2
1  ui u j 
 ij  2t Sij  ij k , Sij  


3
2  x j xi 
Turbulent Viscosity:
t 
Turbulent
Kinetic Energy:
Mean velocity
C k 2

1
k  uiui
2
Dissipation Rate of
Turbulent Kinetic Energy:
ui  ui u j 
     
x j  x j xi 
RANS : k-εmodel
Turbulent viscosity is determined from
t 
C k 2

Transport equations for turbulent kinetic energy and dissipation rate
are solved so that turbulent viscosity can be computed for RANS equations.
k equation
ui
k
  t k 


ui

 

   uiu j
xi xi   k xi 
x j
 equation
ui

  t  

2
ui

 C2 

  C1 uiuj
xi xi    xi 
k
x j
k
empirical constants
C  0.09, C1  1.44, C2  1.92, k  1.0,  1.3,
RANS : Result
Before
After
LES : What is LES?
This technique resolves the largest scales of
turbulence and models the smaller scales.
important
Large eddies
directly resolved
turbulent flow
not so important
Small eddies
modeled
Spatial filter
LES : Spatial filter
•
•
Select a spatial filter function G
Define the resolved-scale (large-eddy):

f  x    G  x  x,   f  x dx
•

GridScale
Find the unresolved-scale (small-eddy ):
f f  f
All Scale
SubGridScale
LES : LES equation
The Filtered Equations
ui
0
xi
Additional term
ui  uiu j 
2ui
P
 s




 ij
t
x j
xi
x j x j x j

   uiu j  uiu j
s
ij

Subgrid Scale （SGS）Stress
SGS Closure Problem
Smagorinsky model
LES : Smagorinsky model
LES equations require closure for SGS stresses.
1
1  ui u j 
 ij  2 sgs Sij  ij kk , Sij  


3
2  x j xi 
SGS eddy Viscosity
 sgs  Cs22 2Sij Sij
empirical constants （theory value）
Cs  0.23
need for adjustment to turbulent flow !
LES : Result
Before
After
A Study of application of LES
About Nishiwaki’s Study
Table 1 Calculation conditions
Cylinder bore×stroke (mm) 82.6×114.3
46  46  30
Fig. 1 Computational grid system
Compression ration
8.0
Intake valve closure
146 deg.BTDC
Engine Speed (rpm)
600
Wall temp. (K) const.
460
equivalent ratio φ
0.55
SGS model Cs =0.2
Fuel : isooctane
Reactions:29, Chemical species20
Results
Temp.
RANS
LES
RHR
Fig. 2 Fields of Temp and RHR at TDC
calculated by RANS（Left） ,LES（Right）
Criticism
• RANSモデルでは捕らることができない自着火空
間分布を予測できる可能性がある．
• モデル定数の補正が必要となるスマゴリンスキー
モデルを導入しているため，モデルの変更を考え
る必要がある．
• LESでは，噴流の濃度・空間的変化について把握
することが重要．
Future prospect on LES
• エンジン内流れのサイクル平均ではない非定常流れとし
て直接解析できる．そのため，ノッキングなどのサイクル
変動に起因する現象メカニズムの解明につながる．
• 乱流中の噴霧，燃焼過程を普遍性のある物理モデルで
表すことができる．流れパターンなどに一貫したモデルを
使用することで，新しい機構･代替燃料の導入に際しても
適用可能．
• NOX ，すすなどの微量有害物質の生成予測に対しては，
瞬時・局所の温度（濃度）分布の予測が可能．
THE END

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