1. Nathan N. Lafferty, Martin L. deBertodano,
RELAP5 Analysis of Two-Phase Decompression and Pressure Wave Propagation
Nathan N. Lafferty, Martin L. deBertodano,
Victor H. Ransom
Purdue University
November 18, 2008

2. Single-phase simulation benchmarked analytically
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 ……

3. 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)

4. RELAP5 Two-Fluid Model
Conservation of mass
Momentum balance

5. Air Shock Tube Wave Propagation5

6. Qualitative similarity
Shock wave remains steep
Rarefaction wave spreads as it propagates
Quantitative similarity
Pressure of Gas 2
Analytic MPa
RELAP MPa (0.29% error)
Shock wave velocity
Analytic m/s
RELAP m/s (0.24% error)
Velocity of Gas 2
Analytic m/s
RELAP m/s (1.7% error)

7. Takeda and Toda Experiment

8. 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 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

9. 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

10. Liquid is now in a state of
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

11. 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

12. Spatial Convergence
297 node model with nodal length of m compared with 99 node model
Shown at PT 5
99 node model is spatially converged

13. Default Simulation PT 4
Test for time step convergence (fast interphase processes)
Comparison with experimental data

14. Default Simulation 3D Plot

15. Default Simulation 2D Contours
Sound speed
Pressure

16. 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

17. 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

18. 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

19. Effect of Discharge Coefficient at PT 3

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

21. 1/10 Bubble Diameter & 0.5 Discharge Coefficient PT 3

22. 1/10 Bubble Diameter & 0.5 Discharge Coefficient PT 4

23. 1/10 Bubble Diameter & 0.5 Discharge Coefficient PT 5

24. 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

25. End

26. 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

27. Effect of Bubble Diameter PT 3

28. 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 and Matm/s
Pressure drop rate calculated to be 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

29. 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

30. Critical Flow Model Comparison of
Ransom-Trapp
Henry-Fauske
Ransom-Trapp matches experimental results better and was used