エンジンスプレーにおけるノズル内キャビテーショ …...ht ht T T A dt h dM α (2) Owing to heat transfer μm Outline of 1994 version 0 –D Flash Boiling Spray

1

Doshisha University – Energy Conversion Research Center & Spray and Combustion Science Laboratory –

STAR Japanese Conference 2017（2017.7.6）

同志社大学「エネルギー変換研究センター」理工学部機械系工学科「噴霧・燃焼工学研究室」

千田二郎・松村恵理子

1. 当研究室でのモデリング研究の概要

2. CD-adapco 様との連携

3. 減圧沸騰噴霧とそのモデリング

4. キャビテーション誘起噴霧分裂モデル

5．キャビテーション気泡崩壊圧力の予測

エンジンスプレーにおけるノズル内キャビテーション現象の解析

Analytical Model on Nozzle inside Cavitation for Engine Spray based on Bubble Dynamics


1．ディーゼル噴霧解析の取り組み

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C5 C13

LIF Calculation

多成分蒸発噴霧解析Senda(Iclass-2003)

＊SMAC-壁面衝突液滴解析（1981），振動圧力場のキャビ気泡解析（1983）１キャビテーション気泡群を考慮したディーゼル燃料噴射系解析（1990；千田）２噴霧－壁面干渉モデル（1993～；千田）３減圧沸騰噴霧モデル（０次元）（1993；千田）４多成分燃料の気液平衡推算モデル（０次元）

（1993～；柴田・千田）５．修正TAB分裂モデル（1996 ；段・千田）６離散渦法を併用した噴霧解析（1996 ；段・千田）７多成分燃料蒸発モデル（多次元）（2000 ～；川野・千田）８壁面衝突モデルー多成分燃料対応

（2001；千田）と統合モデル（2002；松田・千田）９化学反応動力学（CHEMKIN）適用すす生成モデル

（2002～；北村・千田）10 Chem-KIVA(2003～；伊藤・千田）11 減圧沸騰噴霧モデル（多次元）（2004～）（川野・千田）12 Large Eddy Simulation（LES）

（2005～；堀・千田→現在＝分裂モデル；北口・藤井・千田）13 ノズル内キャビテーションモデル

(2006～；和田・千田→2010～松本・千田→2015～松村・千田）14 現象論的１次元多成分噴霧モデル（MBC適用）（2011～；松本・千田）

2


2. 株式会社CD-adapco様との連携

１．STAR Japanese Conferenceでの講演＊2013.5－「壁面に衝突する燃料噴霧のモデリング」－千田＊2013.12－「減圧沸騰噴霧の特性とモデリング」－松村＊2015.6－「多成分燃料噴霧の蒸発過程のモデル解析」－千田＊2016.6－「エンジンスプレーの分裂モデルの最適化」－千田

２．Star-CDへの同志社大学モデル実装の取組み＊2013.5～壁面衝突モデルを実装＊現在、減圧沸騰噴霧モデルの適用を実施中＊今後、下記内容を検討したい

・多成分燃料の蒸発モデル・各種噴霧の微粒化モデル ( MTAB,Wave-MTAB, LISA-MTAB )

・ノズル内キャビテーションモデル→噴霧形成– KIVA解析（本講演）（→Star – CDへ展開可能）→崩壊圧力予測– Star – CCM （本講演）


Contents






3


Proposal of Fuel Design Approach- What is Flash Boiling Spray ?


Pentane Flashing Spray Feature – Optical Measurement

Mie scattering photography from droplets

Spatial vapor concentration distributionby two-wave length IR absorption imaging

n-Pentane Spray(Pv=56.5KPa) injected into 21KPa ambient pressure

4


Atomization & Evaporation in Pressure atomizer Time & Spatial delay depending on Pinj , a , Ta

① Breakup delay of spray

tb

Pinj

この画像は表示できません。

②Evaporation of droplets→Heat Transfer process

この画像は表示できません。T

Tsat

t

q T A ta D

2Nu Re PrNu c a

028.65( )l

b

a inj a

dt

P P

③Evaporation length of spray

Pinj

Lev

2f f fm d U

tan( /2)a a f fm d x U q

SMD

Pinj

2P

R

s D ①

③Nozzleinternal flow

Turbulence flow②

Controlled by Aerodynamic Process : disturbance⇒ ligament⇒ droplets

Cavity

saturation


Atomization & Evaporation in Flash Boiling SprayNon Time & Spatial delay depending on Two Phase profile( DPbv(Dq))

bubble ligament

dropletsintact core

※ Evaporation due to Enthalpy balance of fuels without aerodynamic force

Bubble Nucleation rate

Evaporation rate = Bubble growth Rate

expA

N Ck q

D D 24

3A R sD

Rayleigh-Plesset Eq. 23 1( )

2w r

RR R P P

n

bvR P D

Vapor mass

fraction

t

1.0

Order of μs~ms DPbv

200 s

100 s

R

ts

Liquid jet or film Breakupby Bubbles growth

DPbv

Dq

P

T

Multi-Component

DPbv

DqT

P

Single Component

Breakup time

5

Doshisha University – Energy Conversion Research Center & Spray and Combustion Science Laboratory –9/26

Analytical model of flash boiling spray in this study

Vapor formation process

1

l b

d

Nucleation process

Bubble growth process

Droplet formation process

(1) By cavitation bubbles growth

3 31

4

3cb v n ndM N R R ρ

(3) By superheated degree

l st

fg

sh

sh

T T A dt

hdM

α

Droplet number = 2×Bubble number

bubble

bubble liquid

V

V Ve e

max

22 1

3W rR P P

rRR

3

0

0

20

n

W V r

RP P P

R R

s

12

2 4 4R R

R R R

s

and

Initial bubble diameter 2R0

2R0=20mm

120=1.11×10 exp -5.28N TD

-4.34exp -510

t

a f

fg

ht

ht

T T A dt

hdM

α

(2) Owing to heat transfer

μm

Outline of 1994 version 0 – D Flash Boiling Spray Model


Simulated Spatial Vapor Distribution for Mixing Fuel of C5 & C13 at 20030

14

28

42

56

70Dsi

tance

fro

m n

ozzl

e ex

it[m

m]

nC13H28(B.P.509K) / iC5H12(B.P.301K)(tinj=0.8 ms)

(a) (b) (c)

(a) Droplet radius[m]

(b)Vapor mass of iC5 [kg/m3]

(c) Vapor mass of C13 [kg/m3]

100 80 60 40 20 1

4.5 3.6 2.7 1.8 0.9 0.0

1.3 1.0 0.78 0.52 0.26 0.0

KH-RT modelRef) Reitz et al, SAE Paper 971591

Modified TAB modelRef) Senda et al, ICLASS-1997

Initial fuel properties

NIST HC mixture database( f(T) ⇒ f(T, P) )

Fuel injection

Injection of multicomponentfuel parcel

Breakup

Evaporation

Vapor-liquid equilibrium(non-ideal mixture)

Modified spalding model(Le=1 ⇒ Le=1)Two-zone model

Renewal of fuel properties

NIST mixture database( f(T) ⇒ f(T, P) )

6


Contents







C.Arcoumanis & M.Gavaises, et.al. , SAE 2002-01-0214

H.Hiroyasu & M. Arai,et..al. ; ICLASS91

String Cavitation

H.Watanabe et.al. ,Journal of Engine Research16(1):5-12(2015).

Cavitating Flow inside the Nozzle

7


Background and Purpose

Liquid length

Ref) Dan, T et al., SAE Paper 970352

Atomization

Turbulence flowCavity

Flow inside Nozzle

Aerodynamic + Turbulence flowHuh, K. Y. and Gosman, A. D., 1991.

Aerodynamic + Cavitation

Arcoumanis, C. and Gavaises, M., 1998.

Nishimura, A. and Assanis, D. N., 2000.


Background and Purpose

Shrinkage

Energy

Turbulence

Bubble growth

Evaporation of Fuel

Collapse

Energy

or

Aerodynamic + Cavitation

Arcoumanis, C. and Gavaises, M., 1998.

Nishimura, A. and Assanis, D. N., 2000.

8


(a) Change in bubble diameter(R0=3m, pinj=72MPa)

(b) pressure distribution

XC5=0.8(pv=0.165 MPa)

XC5=0.6(pv=0.118 MPa)

XC5=0.4(pv=0.075 MPa)

XC5=0.0(pv=0.0001 MPa)

XC5=0.0XC5=0.4XC5=0.6XC5=0.8

0 0.075 0.15 0.225 0.3

Distance from nozzle inlet [mm]

0

3

6

Pre

ssu

re [

MP

a] 0.75

2.25

1.5

R/R

0[-

]

Change in Bubble Radii inside Nozzle


5.0/ 32 CC

Ref)Lee, E., Huh, K. Y. and Koo, J-Y. Proc. ICLASS-97’ Seoul, 1997.

Ref) Huh, K. Y. and Gosman, A. D., Proc. The Inter. Conf. on Multiphase Flow, ’91-Tsukuba, 1991.

ttTt kCL e /2/3

1

1

/8 2

2

inlet

dnn

mt K

Cdl

uk

1

1

2 2

3

inlet

dn

mt K

Cl

uKee

C = 0.09 Ke = 0.27

TtAt LCL 2(Atomization length scale)

TtWt LCL 3

(Wavelength of surface perturbation)

Primary Breakup Model (Huh and Gosman) - Atomization Length Scale

Cd値はノズル内部のボイド率の情報を包含する．キャビテーション気泡の崩壊収縮以外の効果が乱れに与える影響をここで表現．

9


TtAt LCL 2(Atomization length scale)

TtWt LCL 3

(Wavelength of surface perturbation)

lblTc dCAACL 44 /2

X

X

Y

Y

X-X Y-Y

dn気泡が満たす面積: Ab

液体が満たす面積: Al

Primary Breakup Model (Present Model) - Length Scale -

TcWc LCL 3

TcAc LCL 2

Collapse and shrinkage of bubbles

新たに分裂する液滴を付加する


injcollapsecollapse QEk / injshrnikshrink QEk /

shrinkcollapsec kku 32' 'cTcTc uL

ur’

Primary Breakup Model– Atomization Time Scale

Additional Consideration in Present Model

Time scale (caivtation)

5.0

3

2

2

'

Wcgl

l

Wc

r

gl

gl

WLL

u

s

Wave growth time scale (cavitation)

WcTcA CC 41

Atomization time scale (cavitation)

AArd LCdtdr

(Qinj : Injected mass)

10


Bubble growth and shrinkage

rwl

PPRRR

1

2

3 2

R

R

RR

R

RPPP l

n

rvw

ss 4223

0

00

Energy induced by cavitation bubbles

Bubble nucleation

Nuclei number distribution

TkACN DD /exp

2

2

21 2

)log(logexp

)2(

log)(

R

R

eCRN n

Due to shock pressure

NPRRE brkcollapse max33

max3/4

brkbrkgR RRRPP /2/ 3maxmaxmax s

where

Due to bubble shrinkage

R

j

i

R

R

ishrink

i

i

drrVr

RRNE

1

22

24)(21

Criterion for primary breakup regimes

a: void fraction, acrit: critical void fraction

critaa

critaa

Flash boiling (1)

K-H instability (2)

(2)(1)

Secondary breakup

TAB model

Surface wave growthaccording to K-H instabilitytheory proposed by Huh and Gosman(3)

Determination of atomizationscale induced by nozzle flowLAt/tAt and cavitation bubblesLAc/tAc

Flash boilingmodel

Primary breakup

Cavitation Induced 1-D SprayBreakup Model in 2006


Predicted results of Spray Feature

XC5=0.8XC5=0.4XC5=0

Axia

l di

stan

ce f

rom

noz

zle

exit

[mm

]

0

50

75

25

parcels

nC5H12 vapor

nC13H28 vapor

No

imag

e

droplet radius [m]

700 35 52.517.5nC5H12 vapor conc. [kg/m3]

1.560 0.78nC13H28 vapor conc. [kg/m3]

0.60 0.3

exp.(shadowgraph)

Fuel : nC13H28 + nC5H12 pinj=70 MPa, Ta= 666 K, a=9.66 kg/m3Primary breakup: cavitation-induced model, Secondary breakup: TAB

11


Contents







Initiation Bubble growth Shrinkage Collapse

Turbulence

< Cavitation Phenomena>

pinj

pv

pmin

Distance from the inlet of nozzle hole

Pre

ssu

re pamb

Energy

Pinj : Injection Pressure

PV : Liquid Vapor Pressure

Cavitation Phenomena Inside the Nozzle

Expansion of dissolved air nuclei (Gas cavitation)

Liquid flashing as cavitation bubble (Vapor cavitation)

Basic Process of Cavitation Phenomena and Roughly Etimated Pressure Profile inside the Nozzle

12


Shrinkage Collapse

Turbulence

Initiation

N = 1.0×1012 [-/㎥] : Constant value

Growth

Bubble nucleation process in the Nozzle

The base condition on Star-CCM+ ＜Seed Density (default value)＞

N : The number of cavitation bubble nuclei

Our proposal Nucleation Rate Equation as a function of Liquid Superheating Degree derived from our previous work in 1994

Dq : Superheating degree [K]

expA

N Ck q

D

D

24

3A R sD

Constant [-] ：C k ： Boltzmann’s constant [J/K]

s ： Surface tension [N/m2] R ： Bubble radius [m]

R0 = 10 μm


Shrinkage Collapse

Turbulence

Initiation

Growth

Growth of cavitation bubbles : Rayleigh-Plesset equation

R : Bubble radius [m]

Pv : Saturated vapor pressure [Pa]

P: Pressure of fluid [Pa]

l : Liquid density [kg/m3]s l : Surface tension [N/m2]

Pw : Pressure at bubble wall [Pa]Approximation in Star-CCM+

22

3v

l

P PDR

DT

3

00

0

2 2 4n

l l lw v r

R RP P P

R R R R

s s

22

2

234

2v l l

l l l

P Pd R dR dRR

dt dt R R dt

s

23 1

2w

l

RR R P P

n : Polytropic index [-]

R0 : Initial bubble radius [m]μl : Coefficient of viscosity [Pa・s]

Pr0: Initial pressure of bubble surrounding fluid [Pa]

Bubble Growth process in the Nozzle

13


Eshrink [J] : Energy for the surrounding fluid induced when the bubbles contract rapidly → this energy is predicted

inside Star-CCM

Shrinkage Collapse

Turbulence

Growth

Ref) A.Shima et al., Tohoku univ. Institute for Fluid Sciences report46: 129-144(1981)

pmax [Pa] : The maximum shock wave pressure when bubbles collapse

Ecollapse [J] : Energy when bubbles collapse in whole cavitation region

Rbrk : Bubble radius at collapsing [m]

Pgmax : Pressure inside the bubble when a bubble reaches its maximum diameter [Pa]

v : velocity of the surrounding fluid [m/s]

Bubble Shrinkage and Collapse process

1

2 214

2

i

i

jr R

shrink lr R

i

E N v r dr

3

max max maxg brkP P R R

3max

43collapse brkE NP R

Initiation

Rbrk=1.0×10-6 [m] = constant


Shrinkage Collapse

Turbulence

Inception

Growth

kcollapse [J] : Turbulent energy by dividing these with Injected mass per time step

Q : Injected mass per time step

u’c [m/s] : Turbulence velocity component for nozzle outlet

2

3c collapseu k cu u

Additional Turbulent Velocity in the Liquid Flow derived from Cavitation

⇒u’ : Tubulent Energy in flow field

predicted by Star-CCM+

14


ws1 [mm] (45)

ls1 [mm] (20)

lh [mm] (17.5)

ls2 [mm] (50)

ws2 [mm] (50)

wh [mm] (3.75)

Outlet boundary(Pout=constant)

Entrance boundary(Pin=constant)

H2O

Air

CFD code STAR-CCM+(Ver.8.04.010)

Numerical method of multi-phase flow

Volume of Fluid (VOF) model

Pressure-velocity coupling method

SIMPLE method

Turbulence model Realizable k-ε model

Blended wall functionWall function

Vapor ( water vapor )Second Phase(1st.gas phase)

Main Phase(liquid phase)

Water

Second Phase(2nd.gas phase)

Air ( dissolved air )

Calculation Scheme and Domain


Inlet pressure 250Pin [kPa]

Outlet pressure 101.3Pout [kPa]

20ls [mm]Sac length

Hole length 17.5lh [mm]

Calculation time 30.0[msec]

Cavitation number [-] 0.51 ~ 0.65K

Vapor pressure of the liquid [kPa]Pv 5.6, 9.6, 15.7, 25.0

[deg.]Superheating degree Dq 10, 20, 30, 40

Mesh size 0.1 (Square)[mm]

[m]Initial bubble diameter d0 1.0×10-6

45wsSac width [mm]

Hole width wh [mm] 3.75

Reynolds number [-]Re× 105 0.34 ~ 0.62

Temperature of the liquid [K]Tl 310, 320, 330, 340

Calculation Conditions

15


Pmin

Pv2

Pv1

Δθ1

Δθ2

P

T

Pinj

Pmin

Pv2

Pv1

x

Pamb

Distance from the inlet of nozzle hole

※Pinj=Const.

0 10 20 30 40 500

2.0

4.0

6.0

8.0

Superheating degree Δθ [degree]

Bubble

num

ber

densi

ty

N×

10

11[1

/m3]

11 5.289.0 10 exp( )N q

D

Relation between Pv → Δθ and the Number of Initiated Bubble Nuclei

t = 30 ms after start of injection


Time History of Cavitation Region for each Superheating Degree

10 msec 20 msec 30 msecPhysical time

Δθ=10

Δθ=20

Δθ=30

Δθ=40

Volume Fraction [-]

0.0

1.0

0.5

(Air)

(Water)2.0

1.5

(Water)

(Vapor)

1.0

H2O

Air

※Pinj = 250 kPa

16


Relation between Superheating Degree and Ecollapse through Rmax and Pmax

0 10.02.0

Bubble number densityN×1011 [msec]

Maxi

mu

m s

ho

ck w

ave

pre

ssu

re P

max

[Pa

]

4.0 6.0 8.0

1.0E+12

1.0E+13

1.0E+11

1.0E+10

1.0E+90 10.02.0

Bubble number densityN×1011 [msec]M

axi

mu

m b

ub

ble

dia

me

ter

Rm

ax×

10

-5[m

]

4.0 6.0 8.00

2.0

4.0

6.0

8.0

10.0

3

max max maxg brkP P R R

3

max4

3collapse brkE NP R

※Rbrk=1.0×10-6 [m]※Pgmax=Pv

※Ecollapse [J] : Energy when bubblescollapse in whole cavitation region.

0 10Superheating degree

Δθ [degree]

Eco

llapse

[J]

20 30 400

1.0E+8

1.0E+7

1.0E+6

1.0E+5

1.0E+4


1. The number of cavitation bubble nuclei increase withthe increase in superheating degree. In addition,cavitation region grows into the downstreamdirection of the nozzle.

2. The increase of bubble number density affected Rmax,Pmax and Ecollapse. Thus, superheating degree shouldbe considered in order to evaluate atomization ofspray and erosion by cavitation.

Summary

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Documents

エンジンスプレーにおける ノズル内キャビテーショ …...ht ht T T A dt h dM α (2) Owing to heat transfer μm Outline of 1994 version 0 –D Flash Boiling Spray

エンジンスプレーにおけるノズル内キャビテーショ …...ht ht T T A dt h dM α (2) Owing to heat transfer μm Outline of 1994 version 0 –D Flash Boiling Spray