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Design Basis Accident Analysis – Methods and Codes RELAP5 Constantine P. Tzanos Argonne National Laboratory March 23, 2001

Argonne National Laboratory

Scope ⇒

LWRs

⇒

Except for certain reactivity-initiated events, it is applicable to all Chapter 15 events ! ! ! ! !

⇒

LOCAs Loss of feedwater Steam line breaks Steam generator tube rupture ATWS

Transient and steady-state (accelerated transient until time derivative approaches zero)

Reactor Analysis & Engineering Division

Modeling Concept ⇒ ⇒ ⇒ ⇒ ⇒ ⇒

Transient one-dimensional flow of a two-phase flow fluid Full two-fluid model (HEM option) Eulerian mesh One-dimensional control volumes and interconnecting flow junctions Steam and water Noncondensables in vapor phase ! ! !

⇒

Nitrogen from accumulators Air in safety relief valve discharge piping Air in containment

Nonvolatile solute in liquid phase !

Dissolved boron salts

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Modeling Concept

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Hydrodynamic Model Mass Conservation ⇒

Sum of liquid and vapor equations ∂ 1 ∂ ( αgρg + α f ρf ) + A ∂x ( αgρgv g A + α f ρf v f A ) = 0 ∂t

⇒

(1)

Difference of the phasic mass equations ∂ 1 ∂ α ρ − α ρ + α gρg v g A − α f ρf v f A ) = 2Γ g ( ( g g f f) A ∂x ∂t

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(2)

Hydrodynamic Model (cont’d) Mass Conservation (cont’d) ⇒

Noncondensable mass fraction equation ∂ 1 ∂ α X ρ + α gρg Xn v g A ) = 0 ( ( g g n) A ∂x ∂t

⇒

Nonvolatile solute mass equation ∂ρb 1 ∂ ( α f ρf Cb v f A ) + =0 ∂t A ∂x

⇒

(3)

In vapor phase: Mixture pressures = sum of partial pressures

Reactor Analysis & Engineering Division

(4)

Hydrodynamic Model (cont’d) Conservation of Momentum ⇒

Sum of phasic equations ∂v g

∂v 2g 1 ∂v f 1 ∂v 2f ∂P α gρ g + α f ρf + α gρg + α f ρf =− + ρmB x ∂t ∂t 2 ∂x 2 ∂x ∂x − α gρgFWGv g − α f ρgFWFv f − Γ g ( v g − v f )

Reactor Analysis & Engineering Division

(5)

Hydrodynamic Model (cont’d) Mass Conservation (cont’d) ⇒

Difference of phasic equations 2  1 1  ∂P ∂v f 1 ∂v g 1 ∂v 2f − + − = − −  ∂t ∂t 2 ∂x 2 ∂x  ρg ρf  ∂x − FWGv g + FWFv f

∂v g

+

Γ g ρm v i − ( α f ρf v g + α gρg v f )  α gρ g α f ρ f

− ρmFI ( v g − v f )

ρm2  ∂ ( v g − v f ) −C ( ρgρf ) ∂t Reactor Analysis & Engineering Division

(6)

Hydrodynamic Model (cont’d) Conservation of Energy ⇒

Vapor 1∂ ∂ ∂  α ρ U + α ρ U v A + P α v A ( g g g ) A  ∂x ( g g g g ) ∂x ( g g ) ∂t   ∂α g = −P + Qig + Γighg* − Qgf + Γ w h′g + Q wg + DISSg ∂t

⇒

(7)

Liquid ∂ 1∂ ∂  α ρ U + α ρ U v A + P α v A ( f f f) ( ) ( ) f f f f f f  ∂t A  ∂x ∂x ∂α = −P f + Qif − Γigh*f + Qgf − Γ w h′f + Q wf + DISSf ∂t

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(8)

Hydrodynamic Model (cont’d) Conservation of Energy (cont’d) ⇒

Vapor Generation Rate Ps Hig ( Ts − Tg ) + Hif ( Ts − Tf ) P Γ g = Γig + Γ w = + Γw * * hg − h f

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(9)

Hydrodynamic Model (cont’d) ⇒

Qwg and Qwf = wall heat transfer rates to the vapor and liquid phases, respectively.

⇒

Qig and Qif = interfacial heat transfer rates from the interface to the vapor and liquid, respectively.

⇒

DISSg and DISSf = dissipation of energy due to irreversible degradation of kinetic energy to internal energy (only effects due to wall friction and pump efficiencies)

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Hydrodynamic Model (cont’d) Equations of State ⇒

ρf = f(P, Uf)

⇒

ρg = f(P, Ug, Xn)

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Numerical Scheme ⇒

Finite differencing with staggered spatial noding ! !

⇒

Semi-implicit scheme !

⇒

Scalar properties (pressure, energies, noncondensable quality, and void fraction) defined at cell center Vector quantities (velocities) defined on cell boundaries

Implicit evaluation for velocity in mass and energy transport terms, pressure gradient, and interface mass and momentum exchange terms

Nearly-implicit scheme when flow changes vary slowly with time

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Constitutive Models ⇒

Define the interaction of the phases with each other and the system boundaries ! ! ! !

Interphase heat and mass transfer Interphase drag Wall heat transfer Wall friction

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Constitutive Models

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Constitutive Models (cont’d)

Basic flow patterns in boiling two-phase flow Reactor Analysis & Engineering Division

Constitutive Models (cont’d) ⇒

Flow regime maps ! ! ! ! !

Horizontal flow in pipes Vertical flow in bundles and pipes High mixing flow in pumps Emergency core coolant mixer volume flow Flow regime transitions are functions of: ↵

Void fraction (αg) ↵ Average mixture velocity (vm) ↵ Boiling regime ! !

Flow regime models Flow regime and heat transfer regime dependent correlations for: ↵

Interface drag and shear ↵ Coefficient of virtual mass ↵ Wall friction and heat transfer ↵ Interface heat and mass transfer

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Constitutive Models (cont’d)

Reactor Analysis & Engineering Division

Constitutive Models (cont’d) ⇒

Interfacial Heat/Mass Transfer ! !

Mass transfer at saturated boundary driven by Tsat – Tbulk Vapor generation rate, Γg, per unit volume:  Ps    Hig ( Ts − Tg ) + Hif ( Ts − Tf ) P Γ g = Γig + Γ w = −   + Γw * * hg − h f

!

Wall heat transfer model q′′ = hg ( Tw − Trefg ) + hf ( Tw − Treff )

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Constitutive Models (cont’d) ⇒

Interfacial Drag Model !

Interfacial friction per unit volume: Fig = α gρgFIG ( v g − v f ) and Fif = α f ρf FIF ( v g − v f )

!

FIG and FIF are flow regime dependent

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Constitutive Models (cont’d) ⇒

Wall Friction Model !

Partitioning of wall friction between two-phases based on fraction of wall perimeter that is in contact with liquid

!

Contact fraction is flow regime dependent

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Constitutive Models (cont’d) ⇒

Heat Conduction Model !

Heat structures are coupled to fluid volumes to represent fuel pins, steam generator tubes, pipe walls, other solid structures

!

Finite difference solution of heat equation in one-dimensional rectangular, cylindrical or spherical geometry

!

Material properties are temperature dependent

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Process and Component Models ⇒

Specialized models to simulate phenomena too complex to model mechanistically !

Specialized flow phenomena ↵ ↵ ↵ ↵ ↵ ↵

Choking (Henry-Fauske model) Countercurrent flow flooding Form losses Two-phase mixture level Thermal stratification Phase separation at tees

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Process and Component Models ⇒

Component models ! ! ! ! ! ! ! ! !

⇒

Branch Separator Jet mixer Pump Turbine Valves Accumulator ECC mixer Annulus

Extensive array of control components to simulate system control functions

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Reactor Power Model ⇒

Point kinetics model

⇒

Fission plus decay heat power (ANS 1979 standard)

⇒

Actinide decay model to simulate very long transients

⇒

Kinetics time step ≤ hydrodynamic time step, with kinetics calculation at every hydrodynamic time level

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Nomenclature Îą Ď A v P U Q T X C h* H

= = = = = = = = = = = =

volume fraction density area velocity pressure specific internal energy heat transfer rate temperature mass fraction of volatile component solute concentration specific enthalpy (associated with interface mass transfer) product of heat transfer coefficient and interfacial area concentration

Reactor Analysis & Engineering Division

Nomenclature (cont’d) Γ B FWG FWF FI DISS

= = = = = =

Subscripts g f b m x w i s n

vapor generation rate body force wall drag coefficient for vapor wall drag coefficient for liquid interface drag coefficient energy dissipation (form kinetic to internal)

= = = = = = = = =

vapor liquid solute mixture x direction wall interface saturated nth component

Reactor Analysis & Engineering Division