2
University of FukuiPhase change
Water is heated at 0.1MPa (Atomspheric pressure)
Increase of sensible heatρVCpΔT
Increase of steam ρVxLlv
(Energy is stored as a form of latent heat)Temp
x: Steam quality
Heating Heating Heating Heating Heating Heating
Liquid Liquid LiquidLiquid
Vapor VaporVapor
3
University of Fukui
Ice・Water・Steam 3D chart
Ice
Ice & Vapor
Ice
Water and vapor
Ice Super-heatedsteam
Criticalpoint
Vapor
Ice
Liquid
Triplepoint
6
University of Fukui
Boiling and condensation
Heated surface
satTwT
satwsat TTTSuperheat
−=Δ:
lT
lsatsub TTTSubcooling
−=Δ:
satT
Liquid filmCooling surface
Steam
satTvT
wT
satvsat TTTSuperheat
−=Δ:
wsatsub TTTSubcooling
−=Δ:
7
University of Fukui
Surface tension
Contact angle
Liquid(l)
Solid(s)
svσVapor(v)
lvσ
slσ
θσσσ coslvslsv +=
θ
Young’s equation
In case of large θ: bad wetness
8
University of Fukui
Vapor in superheated liquid
r
Superheated liquid
Vapor
rppp lv
σ2=−=Δ
( )vlsat
lvvl
sat TL
dTdp
ρρρρ−
=
Eq. of Clapeyron-Clasius
( )
rLT
rLTT
lvv
sat
lvvl
vlsatsat
ρσ
σρρ
ρρ
2
2
≈
−=Δ
9
University of Fukui
Boiling curve
(a) Start of boiling
(b) Nucleate boiling
(c) Nucleate boiling (d) Critical point
(e) Transition boiling
(f) Film boiling
10
University of Fukui
Flow regime in vertical or horizontal flow
気泡流Bubbly flow
スラグ流Slug flow
チャーン流(フロス流)Churn flow
環状噴霧流Annular -mist flow
噴霧流Mist flow
gg
Vertical flow
気泡流Bubbly flow
スラグ流Slug flow
波状流Wavy flow
環状流Annular flow
プラグ流Plug flow
層状流Stratified flow
g
Horizontal flow
11
University of FukuiFlow regime
0.01
0.1
1
0.1 1 10
BSSFFAAir/Water7 MPa
j l0 (m
/s)
jg0 (m/s)
Slug
Annular
Bubbly
Flow regime map for vertical flow
Froth
0.001
0.01
0.1
1
10
0.1 1 10 100
Present data
j (m/s)
j (m/s)
SlugPlug
Stratified Smooth StratifiedWavy
Annular
Bubbly
l
g
Flow regime for horizontal flow
12
University of Fukui
Quality x
gl
g
WWW
x+
=Wg: Vapor mass flow rate [kg/s]Wl: Liquid mass flow rate [kg/s]
Thermal equilibrium steam qualityisat: Enthalpy in aturated condition[J/kg]Llg: Latent heat of evaporation[kg/s]lgL
iix sat−=
lglg Lii
LTCpX satsubl
sub−
=Δ
=Δ ΔΤsub: Subcooling (K)Cpl: Specific heat [J/(kg・K)]
13
University of Fukui
Relationship between quality and void fraction
( ) lglggg
ggg
lllggg
ggg
lg
g
lg
g
uuu
uuu
GGG
WWW
x
αραραρ
αραραρ
−+=
+=
+=
+=
1
Gg: mass velocity of gas [kg/m2s]Gl: mass velocity of liquid [kg/m2s]
AA kk α=
AQ
j kk =
kkk uj α=kkkkkk juG ραρ ==
AGW kk =
onVoidfractik :α
k=l, g
ρ: density [kg/m3]
14
University of Fukui
Void-Quality correlation
( ) Sx
x
l
gg −
+=
11
1
ρρ
α
( )
50
11
1
1
.
g
l
xxe
xxe
eeS
⎪⎪⎭
⎪⎪⎬
⎫
⎪⎪⎩
⎪⎪⎨
⎧
⎟⎠⎞
⎜⎝⎛ −
+
⎟⎠⎞
⎜⎝⎛ −
+
−+=ρρ
Correlation of Smithe=0.4
Slip ratio
Void fraction
15
University of FukuiCharacteristic of void
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
計測値相関式
ボイド
率, α
(-)
熱平衡蒸気クォリティ, x (-)
圧力 7MPa
二相域単相域
gl
g
GGG
x+
=
gl
g
QQQ+
=α
Pressure
MeasuredCorrelation
Single-phase Two-phase
Thermal equilibrium quality
Voi
d fra
ctio
n
17
University of Fukui
Profile of void fraction and steam quality in the core
z=0
Exit
Inlet α=1
Void fraction
Heat flux
Steam quality
Steam quality in case of uniform heat flux
18
University of FukuiMoody’s chart
Reynolds number, Re
Hydraulicallysmooth
TurbulentTransition
λ=64/Re
Equ
ival
ent
rela
tive
roug
hnes
s, ε
/D
Laminar
Fric
tion
fact
or, λ
Reynolds number, Re
Hydraulicallysmooth
TurbulentTransition
λ=64/Re
Equ
ival
ent
rela
tive
roug
hnes
s, ε
/D
Laminar
Fric
tion
fact
or, λ
19
University of Fukui
Two-phase flow multiplier
222
211
2121
uP
uDilP
ρζ
ρλ
=Δ
=Δ
Pressure loss In single-phase flow
SPFTPF PP Δ=Δ 2φPressure loss In two-phase flow
Pressure loss by pipe wall friction
Pressure loss by local loss coefficient
20
University of FukuiFlow regime around a fuel pin
Single phase H.T.
Nucleate boilingSubcooled boiling
Saturated boiling
Forced convectiveevaporatin
Dryout
Pressure
Void fractionH.T.C.
Bubbly flow
Slug flowChurn flowAnnular flow
Annular mist flow
Mist flow
21
University of Fukui
Heat transfer coefficient for nucleate boiling
707035041007
.a
.
llvv
a.l
l
a plLqlPr.
khl
⎟⎠⎞
⎜⎝⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛×= −
σνρ
⎟⎠⎞
⎜⎝⎛−=
2.6exp79.0 25.0 pqTsΔ
Jens-LottesΔTs: K, q: W/m2, p: MPa
Kutateladze
Rohsenow67067070 .
l
v.
llvv
a
sf
.l
l
a
Lql
CPr
khl
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛=
−
ρρ
νρ
la: Capillary Const.