RELAP5 Analysis of Two-Phase Decompression and Pressure Wave Propagation

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RELAP5 Analysis of Two-Phase Decompression and
Pressure Wave Propagation

• Nathan N. Lafferty, Martin L. deBertodano,
• Victor H. Ransom
• Purdue University
• November 18, 2008

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• Demonstrate capability of RELAP5 to model single
  and two-phase wave propagation (fast transients)
• Use of fine temporal and spatial discretizations
• Single-phase simulation benchmarked analytically
• Two-phase simulation compared to experiment
• Takeda and Toda experiment
• RELAP5 uncertainties for fast transients
• Steady-state interfacial area and heat transfer
• Choked flow model at low pressure
• Steady-state and fully developed flow interphase
  drag correlation

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Depressurization in Nuclear Systems

• Depressurization and propagation of rarefaction
  wave through piping to core
• Possible structural damage resulting in failure
  to maintain core geometry and cooling
• Provide conditions for structural damage modeling
  (not part of this research)

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RELAP5 Two-Fluid Model

• Conservation of mass

• Momentum balance

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Air Shock Tube Wave Propagation
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• Qualitative similarity
• Shock wave remains steep
• Rarefaction wave spreads as it propagates
• Quantitative similarity
• Pressure of Gas 2
• Analytic 1.402 MPa
• RELAP5 1.406 MPa (0.29 error)
• Shock wave velocity
• Analytic 400.96 m/s
• RELAP5 400.00 m/s (0.24 error)
• Velocity of Gas 2
• Analytic 84.49 m/s
• RELAP5 84.12 m/s (1.7 error)

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Takeda and Toda Experiment
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RELAP5 Model of Takeda and Toda Experiment

• Water filled vertical pipe under temperature
  gradient
• 283.7K at base
• 437.9 K at top
• 5.35 cm inner diameter
• 3.2 m length
• 99 nodes, each 3.32 cm in length
• Saturation pressure at top is 6.96 bar
• Subcooled liquid initially pressurized to 8.55
  bar at top
• Location of experiment pressure transducers (PT)
• PT 3 at 0.444 m from break
• PT 4 at 1.20 m from break
• PT 5 at 2.20 m from break
• 1.5 cm diameter junction for break orifice at top
  of pipe

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RELAP5 Model of Takeda and Toda Experiment

• Abrupt area change model employed
• Ransom Trapp critical flow model used
• 0.55 ms break delay time to match delay seen in
  experiment
• Effect of wall heat transfer examined, but
  effects proved negligible
• Due to short duration of transient fluid
  temperature change is less than 1 K

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• Fluid discharge through break causes pressure to
  drop below saturation pressure until nucleation
  occurs
• Nucleation of bubbles slows/stops pressure drop
  and causes flow to choke at reduced soundspeed
• Liquid is now in a state of
• Tension
• Superheat
• Vapor formation is thermally limited as spinodial
  limit is approached

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Wave Propagation and Reflection

• Initial pressure drop to nucleation pressure
  initiates propagation of a rarefaction wave
• Pressure of liquid decreased below saturation
• Initiates vaporization
• Waves reflected off solid boundaries in like
  sense with similar amplitude
• Waves reflected off constant pressure boundaries
  in opposite sense with similar amplitude

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Spatial Convergence

• 297 node model with nodal length of 1.077 m
  compared with 99 node model
• Shown at PT 5
• 99 node model is spatially converged

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Default Simulation PT 4

• Test for time step convergence (fast interphase
  processes)
• Comparison with experimental data

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Default Simulation 3D Plot
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Default Simulation 2D Contours

• Sound speed

Pressure
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Schematic of Pressure Drop and Rarefaction

• Initial pressure undershoot and void formation
• Sets pressure for rarefaction wave
• Rarefaction wave reflects off pipe end and
  returns to top of pipe
• More voiding and nonequilibrium effects occur

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Reflection at Region of Sound Speed Change

• Sound speed changes at two-phase region (Davis,
  Princetion Univ Press, 2000)
• 1500 m/s for single-phase
• 50 m/s for two-phase
• Equation to calculate amplitudes
• AR - amplitude of reflected wave
• AI - amplitude of incident wave
• AT - amplitude of transmitted wave
• cT - transmitted fluid sound speed
• cI - incident fluid sound speed
• Wave will reflect in opposite sense with a
  magnitude similar to the incident wave

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• Default simulation
• Rarefaction wave interacting with temperature
  gradient
• Subsequent voiding occurs
• Separate two-phase flow region appears
• Wave becomes trapped
• Two-phase region expands outward
• Nonequilibrium effects

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Effect of Discharge Coefficient at PT 3
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Interfacial Heat Transfer

• Superheated liquid bubbly flow regime (at break)
• Energy transfer from liquid to bubble interface
• Interfacial area
• concentration, ,
• important

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1/10 Bubble Diameter 0.5 Discharge Coefficient
PT 3
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1/10 Bubble Diameter 0.5 Discharge Coefficient
PT 4
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1/10 Bubble Diameter 0.5 Discharge Coefficient
PT 5
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Conclusions

• RELAP5 proved capable of simulating fast
  transients with depressurizations and acoustic
  pressure wave propagation
• RELAP5 simulation of air shock tube successfully
  validated with an analytic solution
• RELAP5 simulation of two-phase decompression and
  wave propagation benchmarked with experimental
  data
• Shortcomings in RELAP5 application identified
• Interfacial area concentration
• Choked flow model
• After adjustments the simulation produced better
  results
• Cause of dispersion and dissipation of wave
  identified as it being trapped inside a two-phase
  region

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End
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Justification for Bubble Diameter

• Bubble growth controlled thermally for duration
  of the experiment
• Bubble radius can be calculated using
  Plesset-Zwick theory with Rayleigh-Plesset
  equation

• Bubble radius magnitude less than 2.3 mm bubble
  radius from RELAP5
• Justifies 0.1 multiplication factor for Laplace
  Length

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Effect of Bubble Diameter PT 3
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Effect of Discharge Coefficient at PT 3

• Critical or Choked flow model is important in
  calculating initial pressure undershoot
• The RELAP5 Default simulation overpredicts the
  pressure undershoot
• Correlation by Alamgir and Lienhard used by
  RELAP5 for pressure undershoot
• Valid for pressure drop rates between 0.004 and
  1.803 Matm/s
• Pressure drop rate calculated to be 0.002 Matm/s
  based on experimental data by Takeda and Toda
• Subcooled discharge coefficient adjusted to
  correct for overprediction of pressure undershoot
• Equivalent to reducing break area
• Values less than 1.0 recommended for orifices
• Could be remnants of Mylar paper obstructing
  break flow

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Air Shock Tube

• RELAP5 model of air shock tube
• Validate use of RELAP5/MOD3.3 to predict
  single-phase wave propagation
• Benefit of air shock tube is analytic solution
  exists
• Gas 3 initialized at higher pressure than Gas 1
• Adiabatic and initially isothermal

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Critical Flow Model

• Comparison of
• Ransom-Trapp
• Henry-Fauske
• Ransom-Trapp matches experimental results better
  and was used