An improved sub-grid scale flow model for transient fuel spraysAn improved sub-grid scale flow model for transient fuel sprays

Federico Perini, Rolf D. ReitzFederico Perini, Rolf D. Reitz

Motivation Sub-grid scale near-nozzle flow modelingMotivation

• Combustion efficiency and noise control in engines require multiple injection strategies

• Transients become a relevant part of the injection, affecting spray jet

Sub-grid scale near-nozzle flow modeling

• A sub-grid scale, transient flow prediction

(usgs) is used for the spray calculation• Transients become a relevant part of the injection, affecting spray jet properties

• Computational efficiency of the model is crucial to extend its operationto realistic engine geometries & multiple nozzles

instead than under-resolved momentumcell values

( ) +∆+′=

uθθθ

sgstsgspn dt ,

Efficient collision modeling with extended outcomes

• Estimate Radius-of-Influence (ROI) based on a tetrahedralization of the

to realistic engine geometries & multiple nozzles

∆ dt

( )

( )

−=−+

∆+

+∆+′=

urEuu

uθθθ

nnBuvwB

sgsp

sgstsgspn

B

mSm

dt

dt

,

,

1

• Estimate Radius-of-Influence (ROI) based on a tetrahedralization of the drops inside the computational parcel

SρprpVc rkd =

∑∈

Ω∉

′−+

∆+′

Ω∈

Ω∉∆+

∆

=

jet

33

4jet

jet

3

p,13

4

p0,

p,13

4

nn

tpn

Bpp

ipp

p

Bpp

uvw

rd∆t

dtrN

dt

dtrN

S

θθθ

πρ

πρ

3 4V Nk

rROI

−= π

• Implicit coupled solution with SIMPLE solver

β

Lθ

Sθ

relθ 0r ( )∑∈

Ω∈

′−

∆+

+∆+′

Ω∉

′−+

=4

jet

3

p

3

jet

pdt13

4

p,13

ip

nn

sgstpn

Bpp

nn

p

Bpp

u

rdt

rN

rd∆t

rN

θuθθ

θ

r

πρ

πρ

3

9

4

26p

Vp N

krROI

−= π

• ROI-based collision estimation is O(n2), n number of particles filter

impossible collisions based on squared distance function between two

• Implicit coupled solution with SIMPLE solver

• Transient turbulent gas-jet model used tothe effective gas jet assumption:

Lρ

impossible collisions based on squared distance function between twodroplets within the timestep

( ) ( ) ( )( ) cbtatttttdtf relrel ++=−+−+== 22

0,20,10,20,1

22

21

2 ,2, xxθxxθxx

v Strouhalu

xf≈=

( ) ( ) exp1,

−−+= ∫

t

ttx uu

• Pre-processing filter of eligible parcel couples by running a kd-tree

( ) ( ) ROItdtttifpossiblecollisionabt ≤∆≤>→−= minminminmin &&02( ) ( )

( ) ( ) ( )2

0

,,,

exp1,0

=

−−+= ∫

axisentrsgs

t

tinjaxis

txxftrx

ttx

uu

uu

• Pre-processing filter of eligible parcel couples by running a kd-treebased radius-of-influence search

2SROI

1SROI

eligibleeligible

not

( )2

22

2121

,,

+

=

entr

sgs

Kx

rtrxu

• Stokes number and turbulent entrainment

Ltθ∆GA-based study of spray model constants

• Deterministic bouncing, stretching separation (‘grazing’), reflexiveseparation, coalescence prediction

LROI

Ltθ∆

• 5 objective functions: vapor penetration, liquidstandard deviation, mixture fraction distribution

• 6 optimized model variable: CRT, CΛRT, B1, St, Kentr

separation, coalescence prediction

6

7

Spray A, C12

H26

, 900K, O2=0.0, t

inj=1.5ms

Experiment

simulation 1

liq

uid

pen

etra

tio

n [

cm]

Initial ramp

2

3

4

5

pen

etra

tio

n [

cm]

0.4

0.6

0.8

liq

uid

pen

etra

tio

n [

cm]

1f

2f

0 0.5 1 1.5 2

x 10-3

0

1

time [s]

0 1

0

0.2

time [s]

UNIVERSITY OF WISCONSIN -

grid scale flow model for transient fuel spraysgrid scale flow model for transient fuel sprays

Funding Sponsor – Sandia National LaboratoriesFunding Sponsor – Sandia National Laboratories

nozzle flow modeling 0.16 nozzle flow modeling

vel.particle

vel.field

=

=

θ

u0.08

0.12

0.16

mix

ture

fra

ctio

n [

-]

experiment

simulation

z = 30 mm

r20 30 40 50mm

axial vel.particle=θ

x

r

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.04

distance [cm]

mix

ture

fra

ctio

n [

-]

z

axial

Validation• Sandia Spray A and mixture preparation in a light duty optical diesel engine

Buu =

θ

dragF

distance [cm]

sgsuu =

Buu =

θ36 µs16 µs 76 µs56 µs 116 µs 136 µs 0

0.2

0.4

SIMPLE solver iteration maintained

jetΩ

B 0.4

0.6

0.8

SIMPLE solver iteration maintained

represent the sub-grid scale flow field using1

[cm]

1.5

Squish planepinj = 500 bar

Squish planepinj = 860 bar

Squish planepinj = 1220 bar

p

IStokesτ

τ=≈

( )( )

0 ,∂

−

−inj

dt u

u ττ

ττ

0

0.5

1

1.5

ex

perim

en

t

ex

perim

en

t

ex

perim

en

t

( )( )

( )0 ,

∂

∂

−

−−

inj

inj

inj

dxxSt

t uu τ

τ

ττ

τ

1.5

0

0.5

1

sim

ula

tion

CA = -15.0 CA = -10.0 CA = -5.0phi [-]

Rim plane

sim

ula

tion

CA = -15.0 CA = -10.0 CA = -5.0

Rim plane

CA = -15.0

sim

ula

tion

CA = -10.0 CA = -5.0

Rim plane

0

0.5

1

1.5

1.5

ex

perim

en

t

ex

perim

en

t

ex

perim

en

t

function fentr are model constants

based study of spray model constants 0

0.5

1

sim

ula

tion

CA = -15.0 CA = -10.0 CA = -5.0phi [-]

Bowl plane

CA = -15.0

sim

ula

tion

CA = -10.0 CA = -5.0

Bowl plane

sim

ula

tion

CA = -15.0 CA = -10.0 CA = -5.0

Bowl plane

transient, steady state liquid penetration and distribution

entr, γmax

0

0.5

1

1.5

1.5

exp

eri

men

t

Bowl plane

exp

eri

men

t

Bowl planeBowl plane

exp

eri

men

t

1.2

1.4

liq

uid

pen

etra

tio

n [

cm]

Spray A, C12

H26

, 900K, O2=0.0, t

inj=1.5ms

( )lσ

phase

4f 0

0.5

1

1.5

sim

ula

tio

n

CA = -15.0 CA = -10.0 CA = -5.0phi [-]

sim

ula

tio

n

CA = -15.0 CA = -10.0 CA = -5.0

CA = -15.0

sim

ula

tio

n

CA = -10.0 CA = -5.0

0.4

0.6

0.8

1

liq

uid

pen

etra

tio

n [

cm]

l 3f

References[1] Perini F and Reitz RD, “An effieient atomization, collision and sub-grid scale momentum

coupling model for transient vaporizing engine sprays”, Int J Multiphase Flow, submitted,

2

x 10-4time [s]

0 0.5 1 1.5 2

x 10-3

0

0.2

time [s]

l coupling model for transient vaporizing engine sprays”, Int J Multiphase Flow, submitted, 2015

ENGINE RESEARCH CENTER As of April 17, 2015