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Application of LES to CFD simulation of Diesel combustion
3604A058-2 Fumio KUWABARA
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Background
Ignition, Combustion, products
LES
RANS
Prediction MethodCFD code
Turbulent flow etc.Internal conditions
Diesel Combustion
Future ?
Calculation ResultsProcess
Now
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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
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What is Eddy?
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
Small Eddies
Large Eddies
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What is Turbulence Model?
turbulent flow
resolved flow
not resolved flow
Turbulence Model
Operation:
Turbulence Simulation
Separate the flow field
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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
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Turbulence Simulation ( comparison)
Large Eddy Simulation
Direct Numerical Simulation
Reynolds -Averaged
Numerical Simulation
Moreuseful
MoreComputational
Effort&
Precision
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Navier - Stokes Equations
21i ji i
j i j j
u uu up
t x x x x
0i
i
u
x
Unsteady Advection Pressure Viscosity
Navier - Stokes Equations for an incompressible fluid:
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RANS : What is RANS?
i i iu u u
1
1lim
N
i iN
n
u uN
Time
iuiu
iu
Decompose velocity into mean and fluctuating parts:
Reynolds -Average
mean
fluctuating parts
RANS doesn’t resolve any scales of turbulence at all !
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RANS : RANS equation
0i
i
u
x
2 1i ji i
ijj i j j j
u uu uP
t x x x x x
ij i ju u Reynolds stresses
Reynolds -Averaged Navier -Stokes Equations
Additional term
Closure Problem
Turbulence Model
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RANS : Eddy viscosity model
2 12 ,
3 2ji
ij t ij ij ijj i
uuS k S
x x
1
2 i ik u u
2
t
C k
RANS equations require closure for Reynolds stresses:
Turbulent Viscosity:
Turbulent Kinetic Energy:
ji i
j j i
uu u
x x x
Dissipation Rate of Turbulent Kinetic Energy:
Mean velocity
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RANS : k-εmodel
2
t
C k
t ii i j
i i k i j
uk ku u ux x x x
2
1 2t i
i i ji i i j
uu C u u Cx x x k x k
1 20.09, 1.44, 1.92, 1.0, 1.3,kC C C
k equation
equation
empirical constants
Turbulent viscosity is determined from
Transport equations for turbulent kinetic energy and dissipation rate are solved so that turbulent viscosity can be computed for RANS equations.
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RANS : Result
Before
After
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LES : What is LES?
turbulent flow
Large eddies
Small eddies
Spatial filter
directly resolved
modeled
important
not so important
This technique resolves the largest scales of turbulence and models the smaller scales.
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LES : Spatial filter
• Select a spatial filter function G• Define the resolved-scale (large-eddy):
• Find the unresolved-scale (small-eddy ):
f f f
,f x G x x f x dx
GridScale
SubGridScaleAll Scale
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LES : LES equation
0i
i
u
x
2i j si i
ijj i j j j
u uu uP
t x x x x x
sij i j i ju u u u Subgrid Scale ( SGS) Str
essSGS Closure Problem
Smagorinsky model
Additional termThe Filtered Equations
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LES : Smagorinsky model
1 12 ,
3 2ji
ij sgs ij ij kk ijj i
uuS S
x x
2 2 2sgs s ij ijC S S
0.23sC
LES equations require closure for SGS stresses.
empirical constants ( theory value )
SGS eddy Viscosity
need for adjustment to turbulent flow !
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LES : Result
Before
After
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A Study of application of LES
Fig. 1 Computational grid system
46 46 30
Cylinder bore×stroke (mm) 82.6×114.3
Compression ration 8.0
Intake valve closure 146 deg.BTDC
Engine Speed (rpm) 600
Wall temp. (K) const. 460
equivalent ratio φ 0.55
Table 1 Calculation conditions
Reactions:29, Chemical species20
SGS model Cs =0.2
About Nishiwaki’s Study
Fuel : isooctane
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Results
RHR
Temp.
Fig. 2 Fields of Temp and RHR at TDCcalculated by RANS ( Left ) ,LES ( Right )
RANS LES
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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.
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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.
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THE END