Application of LES to CFD simulation of Diesel combustion

3604A058-2 Fumio KUWABARA

Background

Ignition, Combustion, products

LES

RANS

Prediction MethodCFD code

Turbulent flow etc.Internal conditions

Diesel Combustion

Future ?

Calculation ResultsProcess

Now

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?

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

What is Turbulence Model?

turbulent flow

resolved flow

not resolved flow

Turbulence Model

Operation:

Turbulence Simulation

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）

Large Eddy Simulation

Direct Numerical Simulation

Reynolds -Averaged

Numerical Simulation

Moreuseful

MoreComputational

Effort&

Precision

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:

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 !

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

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

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.

RANS : Result

Before

After

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.

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

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

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 !

LES : Result

Before

After

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

Results

RHR

Temp.

Fig. 2 Fields of Temp and RHR at TDCcalculated by RANS （ Left ） ,LES （ Right ）

RANS LES

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