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RELAP5 Analysis of Two-Phase Decompression and Pressure Wave PropagationPowerPoint Presentation

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

- 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
- ……

Depressurization in Nuclear Systems two-phase wave propagation (fast transients)

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)

RELAP5 Two-Fluid Model two-phase wave propagation (fast transients)

- Conservation of mass

- Momentum balance

Air Shock Tube Wave Propagation two-phase wave propagation (fast transients)

5

- Qualitative similarity two-phase wave propagation (fast transients)
- 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)

- Pressure of Gas 2

Takeda and Toda Experiment two-phase wave propagation (fast transients)

RELAP5 Model of Takeda and Toda Experiment two-phase wave propagation (fast transients)

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 two-phase wave propagation (fast transients)

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

Wave Propagation and Reflection saturation pressure until nucleation occurs

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

Spatial Convergence saturation pressure until nucleation occurs

- 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

Default Simulation PT 4 saturation pressure until nucleation occurs

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

Default Simulation 3D Plot saturation pressure until nucleation occurs

Schematic of Pressure Drop and Rarefaction saturation pressure until nucleation occurs

- 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 saturation pressure until nucleation occurs

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

- Default simulation saturation pressure until nucleation occurs
- 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

Effect of Discharge Coefficient at PT 3 saturation pressure until nucleation occurs

Interfacial Heat Transfer saturation pressure until nucleation occurs

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

1/10 Bubble Diameter & 0.5 Discharge Coefficient PT 3 saturation pressure until nucleation occurs

1/10 Bubble Diameter & 0.5 Discharge Coefficient PT 4 saturation pressure until nucleation occurs

1/10 Bubble Diameter & 0.5 Discharge Coefficient PT 5 saturation pressure until nucleation occurs

Conclusions saturation pressure until nucleation occurs

- 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

End saturation pressure until nucleation occurs

Justification for Bubble Diameter saturation pressure until nucleation occurs

- 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

Effect of Bubble Diameter PT 3 saturation pressure until nucleation occurs

Effect of Discharge Coefficient at PT 3 saturation pressure until nucleation occurs

- 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

Air Shock Tube saturation pressure until nucleation occurs

- 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

Critical Flow Model saturation pressure until nucleation occurs

- Comparison of
- Ransom-Trapp
- Henry-Fauske

- Ransom-Trapp matches experimental results better and was used

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