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...
TRANSCRIPT
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
Doshisha University – Energy Conversion Research Center & Spray and Combustion Science Laboratory –
1.ディーゼル噴霧解析の取り組み
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[mm
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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)
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Doshisha University – Energy Conversion Research Center & Spray and Combustion Science Laboratory –
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)
Doshisha University – Energy Conversion Research Center & Spray and Combustion Science Laboratory –
Contents
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
3
Doshisha University – Energy Conversion Research Center & Spray and Combustion Science Laboratory –
Proposal of Fuel Design Approach- What is Flash Boiling Spray ?
Doshisha University – Energy Conversion Research Center & Spray and Combustion Science Laboratory –
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
Doshisha University – Energy Conversion Research Center & Spray and Combustion Science Laboratory –
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
Doshisha University – Energy Conversion Research Center & Spray and Combustion Science Laboratory –
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
Doshisha University – Energy Conversion Research Center & Spray and Combustion Science Laboratory –
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
Doshisha University – Energy Conversion Research Center & Spray and Combustion Science Laboratory –
Contents
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
Doshisha University – Energy Conversion Research Center & Spray and Combustion Science Laboratory –
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
Doshisha University – Energy Conversion Research Center & Spray and Combustion Science Laboratory –
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.
Doshisha University – Energy Conversion Research Center & Spray and Combustion Science Laboratory –
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
Doshisha University – Energy Conversion Research Center & Spray and Combustion Science Laboratory –
(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
Doshisha University – Energy Conversion Research Center & Spray and Combustion Science Laboratory –
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
Doshisha University – Energy Conversion Research Center & Spray and Combustion Science Laboratory –
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
Doshisha University – Energy Conversion Research Center & Spray and Combustion Science Laboratory –
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
Doshisha University – Energy Conversion Research Center & Spray and Combustion Science Laboratory –
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
Doshisha University – Energy Conversion Research Center & Spray and Combustion Science Laboratory –
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
Doshisha University – Energy Conversion Research Center & Spray and Combustion Science Laboratory –
Contents
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
Doshisha University – Energy Conversion Research Center & Spray and Combustion Science Laboratory –
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
Doshisha University – Energy Conversion Research Center & Spray and Combustion Science Laboratory –
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
Doshisha University – Energy Conversion Research Center & Spray and Combustion Science Laboratory –
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
Doshisha University – Energy Conversion Research Center & Spray and Combustion Science Laboratory –
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
Doshisha University – Energy Conversion Research Center & Spray and Combustion Science Laboratory –
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
Doshisha University – Energy Conversion Research Center & Spray and Combustion Science Laboratory –
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
Doshisha University – Energy Conversion Research Center & Spray and Combustion Science Laboratory –
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
Doshisha University – Energy Conversion Research Center & Spray and Combustion Science Laboratory –
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
Doshisha University – Energy Conversion Research Center & Spray and Combustion Science Laboratory –
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
Doshisha University – Energy Conversion Research Center & Spray and Combustion Science Laboratory –
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
Doshisha University – Energy Conversion Research Center & Spray and Combustion Science Laboratory –
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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