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DEVELOPMENT OF COMPUTATIONALMULTIFLUID DYNAMICS MODELS FORNUCLEAR REACTOR APPLICATIONS
Henryk AnglartRoyal Institute of Technology, Department of Physics
Division of Nuclear Reactor TechnologyStockholm, Sweden
SIAMUF-Seminarium, Forskningsöversikt – Flerfasströmning, Orenäs Slott, Glumslöv, 25-26 oktober 2006
2
Outline of the Presentation
• Introduction
• Prospective applications of CMFD innuclear field– focus on fuel assemblies
• Model description
• Example predictions
• Conclusions
SIAMUF-Seminarium, Forskningsöversikt – Flerfasströmning, Orenäs Slott, Glumslöv, 25-26 oktober 2006
3
Introduction
• CMFD is used for thermal-hydraulic analyses ofvarious parts of nuclear power plants:– Reactor cores and fuel assemblies
– Primary systems
– Containment systems
• Analysis of fuel assemblies has large potentialdue to:– Economical reasons (increased power)
– Safety reason (better estimation of thermal margins)
SIAMUF-Seminarium, Forskningsöversikt – Flerfasströmning, Orenäs Slott, Glumslöv, 25-26 oktober 2006
4
Typical LWR Fuel Assemblies
SIAMUF-Seminarium, Forskningsöversikt – Flerfasströmning, Orenäs Slott, Glumslöv, 25-26 oktober 2006
Top tie plate
Fuel rod
BoxWater cross
Spacer grid
Bottom tie plate
PWR fuelassembly
BWR fuelassembly
5
Typical Spacer Grid
SIAMUF-Seminarium, Forskningsöversikt – Flerfasströmning, Orenäs Slott, Glumslöv, 25-26 oktober 2006
Spacer grid is made of platewith 0.2-0.3 mm thickness.Grid height is ~30 mm, andside length ~65 mm
There are usually 7-8 spacergrids along assembly fulllength (~3.7 m)
6
Thermal Hydraulic Performanceof Fuel Assemblies
• Predictions of thermal-hydraulicperformance of fuel assemblies withspacers– Pressure drop
– Void fraction distributions
– Thermal margins, that is conditions whencritical heat flux occurs
SIAMUF-Seminarium, Forskningsöversikt – Flerfasströmning, Orenäs Slott, Glumslöv, 25-26 oktober 2006
7
Design of Fuel Assemblies
• For design purposes, it is interesting toknow the influence of geometry featureson the thermal performance:– Rod lattice pattern (pitch/diameter ratio, etc)
– Shape of sub-channels
– Spacer grid details (shape, mixing vanes, tabs,etc)
SIAMUF-Seminarium, Forskningsöversikt – Flerfasströmning, Orenäs Slott, Glumslöv, 25-26 oktober 2006
8
Four-Fluid Model – GoverningEquations
• Mass
• Momentum
• Energy
SIAMUF-Seminarium, Forskningsöversikt – Flerfasströmning, Orenäs Slott, Glumslöv, 25-26 oktober 2006
( ) ( ) ( )∑≠=
Γ−Γ=⋅∇+∂
∂ pN
kjjjkkjkkk
kkt ,1
Uραρα
( ) ( ) ( )( )[ ]
( ) ∑∑≠=≠=
+Γ−Γ
++∇−∇+∇⋅∇=⋅∇+∂
∂
pp N
kjjkj
N
kjjkjkjkj
kkkkT
kkekkkkkk
kkk pUUt
,1,1
MUU
gUUU
ρααµαραρα
( ) ( ) ( ) ∑∑≠=≠=
+Γ−Γ+=∇−⋅∇+∂
∂ pp N
kjjkj
N
kjjkjkjkjkk
ekkkkkk
kkk EHHQTHt
H
,1,1
λαραρα
U
9
Turbulence Model
SIAMUF-Seminarium, Forskningsöversikt – Flerfasströmning, Orenäs Slott, Glumslöv, 25-26 oktober 2006
∑≠=
++=pN
kjj
tkj
tkk
ek
,1
µµµµ lbbblbtlb dC UU −= αρµ µ
k
kk
tk
KC
ερµ µ
2=
Effective viscosity
laminar eddy
Interface-induced
( ) ( ) ( ) ( )kj
N
kjj
Kkj
N
kjjkjkjkj
Kkkk
ekkkkkk
kkk KKcKKSKKt
K pp
−+Γ−Γ+=∇−⋅∇+∂
∂∑∑
≠=≠= ,1,1
αµαραρα
U
( ) ( ) ( ) ( )kj
N
kjjkj
N
kjjkjkjkjkkk
ekkkkkk
kkkpp
cSt
εεεεαεµαεραερα εε −+Γ−Γ+=∇−⋅∇+
∂
∂∑∑
≠=≠= ,1,1
U
K-_ model
10
Interfacial Transfer Terms
• Mass– Homogeneous condensation
– Heterogeneous evaporation
• Momentum– Drag force
– Lift force
– Wall lubrication force
– Turbulent dispersion force
– Virtual mass
SIAMUF-Seminarium, Forskningsöversikt – Flerfasströmning, Orenäs Slott, Glumslöv, 25-26 oktober 2006
11
Subcooled Boiling Model
SIAMUF-Seminarium, Forskningsöversikt – Flerfasströmning, Orenäs Slott, Glumslöv, 25-26 oktober 2006
Γlb' ' =
hlb Tsat − Tl( )hfg
Γbl
bwg
w
fg
df N subcooled
q
hsaturated
''
''
''=
πρ
3
6
convection evaporation quenching
convection evaporation quenching
12
Computational Grid Used forSVEA Fuel Assembly
SIAMUF-Seminarium, Forskningsöversikt – Flerfasströmning, Orenäs Slott, Glumslöv, 25-26 oktober 2006
13
Phase Distribution in Two-PhaseBubbly Flows
Measured void fraction distribution in a 5x5 bundle: G = 1460.6 kg/m2/sp = 31.9 bar, q’’ = 543 kW/m2, inlet subcooling 6 K
SIAMUF-Seminarium, Forskningsöversikt – Flerfasströmning, Orenäs Slott, Glumslöv, 25-26 oktober 2006
14
Phase Distribution in Two-PhaseBubbly Flows
0
5
10
15
20
25
30
35
40
25 26 27 28 29 30
Subchannel Number
Voi
d fr
acti
on
MeasuredCalculated
Predicted void fraction distribution in a 5x5 bundle: G = 1460.6 kg/m2/sp = 31.9 bar, q’’ = 543 kW/m2, inlet subcooling 6 K
SIAMUF-Seminarium, Forskningsöversikt – Flerfasströmning, Orenäs Slott, Glumslöv, 25-26 oktober 2006
15
Two-Phase Annular Flow Model
• Additional mass, momentum and energyconservation equations are solved for liquid filmin annular flow
• Interfacial mass transfer includes– Evaporation– Entrainment– Deposition
• Wall shear model based on local film thickness• The modal enables prediction of dryout of the
liquid film
Workshop on Modelling and Measurements of Two-Phase Flows and Heat Transfer in NuclearFuel Assemblies, October 10-11 2006, KTH, Stockholm, Sweden
16
thinnest film measured dryout
G = 450 kg/m2/s,
p = 70.8 bar,
q = 1259 kW/m2,
inlet subcooling 15.8 K
Predicted thinnest liquid film is inneighborhood of rods which wentunder dryout
Annular Two-Phase Flows
6.344.7845.2
5.83.6633.6
6.213.9634.9
5.53.4132.3
6.163.9834.2
5.663.5533.1
6.653.8331.6
5.362.927.6
5.432.9427.8
6.043.9635.6
5.43.3432.0
5.973.3229.4
6.343.6030.6
6.623.8031.5
6.244.0635.9
5.303.2531.5
5.302.8427.2
5.773.1828.8
6.003.3630.3
5.904.0036.8
6.143.9434.0
5.433.4833.4
6.103.9435.3
5.934.0337.0
Inlet film mass flux, 10 -2 kg/ms
Outlet film mass flux, 10 -2 kg/ms
Outlet film thickness, 10 -6 m
Inlet film mass flux, 10-2 kg/ms
Outlet film mass flux, 10-2 kg/ms
Liquid film thickness, 10-6 m
SIAMUF-Seminarium, Forskningsöversikt – Flerfasströmning, Orenäs Slott, Glumslöv, 25-26 oktober 2006
17
thinnest film measured dryout
G = 1571 kg/m2/s,
p = 70.9 bar,
q = 2612 kW/m2,
inlet subcooling 10.5 K
Predicted thinnest liquid film is onthe rod which went under dryout
Annular Two-Phase Flows
42.1 30.6 30.6 29.3 29.9
29.8 26.5 26.0 26.0 32.1
29.2 25.7 25.7 26.4 31.2
28.8 25.6 24.9 25.9 32.9
29.4 31.1 30.9 32.8
SIAMUF-Seminarium, Forskningsöversikt – Flerfasströmning, Orenäs Slott, Glumslöv, 25-26 oktober 2006
18
Conclusions
• Current model can be applied for prediction ofphase distribution and heat transfer in dispersedtwo phase flows (bubbly and annular flows)
• Challenges for future development include:– Prediction of turbulence structure in fuel assembly
– Phase distributions in two-phase non-disperse flows
– Prediction of CHF (DNB and dryout) based onmechanistic principles
Workshop on Modelling and Measurements of Two-Phase Flows and Heat Transfer in NuclearFuel Assemblies, October 10-11 2006, KTH, Stockholm, Sweden
19
Conclusions (cont’ed)
• Future focus will be on development ofsub-models suitable for rod bundlegeometry
• Validation should be performed againstdetailed measurements in rod bundles– Validation against data obtained in pipes is
not enough
Workshop on Modelling and Measurements of Two-Phase Flows and Heat Transfer in NuclearFuel Assemblies, October 10-11 2006, KTH, Stockholm, Sweden