Nathan N. Lafferty, Martin L. deBertodano, Victor H. RansomPurdue University

November 18, 2008

• 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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• Conservation of mass

• Momentum balance

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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

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

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

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

Default Simulation 3D Plot

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Sound speed Pressure

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• 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

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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• Superheated liquid bubbly flow regime (at break)• Energy transfer from liquid to bubble interface

• Interfacial area concentration, , important

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• 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 region24

End

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• 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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• 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

• 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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• Comparison of – Ransom-Trapp– Henry-Fauske

• Ransom-Trapp matches experimental results better and was used