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Sloshing of liquids can be observed whenever a fluid in a tank or pool will be excited with a frequency close to the natural frequency of the fluid. This may cause large structural loads in the walls of tanks, their supports and anchors as well as in the concrete structure of pools. The goal was to establish a calculation method to analyze the sloshing effects in a realistic way. Due to the sensitivity of the nuclear society, it was required to perform a validation (benchmark) of the RADIOSS SPH‐method. Therefore we chose a couple of experimental tests and compared our results with these data. The chosen method represents a realistic behavior of the fluid and is transferred to real simulations. Two real simulations will be presented. The first will be a fuel storage tank (horizontal cylinder) of an emergency diesel generator under earthquake conditions which is filled with diesel fuel. The second will be a flooded containment of a reactor building under earthquake conditions. In both simulations a real time history earthquake spectrum is used. The results of both simulations are loads on the walls or concrete structures as well as the fluid behavior itself.
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Westinghouse Non-Proprietary Class 3 © 2014 Westinghouse Electric Company LLC. All Rights Reserved.
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Mathias ReichertBachelor of Engineering, Westinghouse Electric Germany GmbH
Co-Author: Benedykt Pacharzina
HTC 2014 – Munich, June 25th, 2014
Numerical Simulation of Liquid Sloshing with Smoothed Particle Hydrodynamics (SPH) Method in Nuclear Power Plant Facilities
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Westinghouse Non-Proprietary Class 3 © 2014 Westinghouse Electric Company LLC. All Rights Reserved.
Contents
• Numerical Methodology• Verification of the Calculation Method• Fuel Storage Tank• Concrete Containment• Conclusion
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Westinghouse Non-Proprietary Class 3 © 2014 Westinghouse Electric Company LLC. All Rights Reserved.
Numerical Methodology• SPH is a meshless numerical method based on interpolation
theory• Not based on particle physics theory• Continuum dynamics are transformed into integral equations
(kernel approximation)• Initially developed in astrophysics• Calculate interaction between structure and fluid
Meshless Method
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Westinghouse Non-Proprietary Class 3 © 2014 Westinghouse Electric Company LLC. All Rights Reserved.
Verification of the Calculation MethodDue to the sensitivity in the nuclear society it was essential to verify the numerical accuracy of the SPH method by a couple of benchmarks.• Collapse of a water column (2D-dam break)
• Collapse of a water column onto a wet bottom (2D)
• Collapse of a water column, central sloshing, no obstacles (3D)
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Westinghouse Non-Proprietary Class 3 © 2014 Westinghouse Electric Company LLC. All Rights Reserved.
Verification of the Calculation MethodCollapse of a water column (2D-dam break)
Source: Violeau, D. (2012): Fluid Mechanics and the SPH Method: Theory and Applications, Oxford University Press
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Westinghouse Non-Proprietary Class 3 © 2014 Westinghouse Electric Company LLC. All Rights Reserved.
Verification of the Calculation Method
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Westinghouse Non-Proprietary Class 3 © 2014 Westinghouse Electric Company LLC. All Rights Reserved.
Verification of the Calculation Method• Position of the water front
• Height of the water column
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Westinghouse Non-Proprietary Class 3 © 2014 Westinghouse Electric Company LLC. All Rights Reserved.
Verification of the Calculation MethodCollapse of water column onto a wet bottom (2D)
Results for 40.000 particles Results for 70.000 particles
Source: http://www.oxfordscholarship.com/doc/10.1093/acprof:oso/9780199655526.001.0001/acprof_9780199655526_graphic_055.jpg
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Westinghouse Non-Proprietary Class 3 © 2014 Westinghouse Electric Company LLC. All Rights Reserved.
Verification of the Calculation MethodCollapse of a water column, central sloshing, no obstacles (3D)
Source: Vorobeyev, A., Kriventsev, V. und Maschek, W. (2011): Nuclear Engineering and Design, Simulation of central sloshing experiments with smoothed particle hydrodynamics (SPH) method, Jour. of Nuclear Engineering and Design Vol. 241
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Westinghouse Non-Proprietary Class 3 © 2014 Westinghouse Electric Company LLC. All Rights Reserved.
Verification of the Calculation Method
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Westinghouse Non-Proprietary Class 3 © 2014 Westinghouse Electric Company LLC. All Rights Reserved.
Verification of the Calculation Method
• Method is compared to real experiments and represents the experimental results
• Parameter set is validated and represents the behavior of liquid sloshing
• All performed validation cases show the same fluid shape and velocity characteristics as documented in real experiments
Liquid sloshing can be represented by the SPH Method
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Westinghouse Non-Proprietary Class 3 © 2014 Westinghouse Electric Company LLC. All Rights Reserved.
Fuel Tank Model – General Description• Simulation of a fuel storage tank under earthquake excitation• Integrity of the fuel storage tank will be demonstrated• Comparison of the sloshing eigenfrequencies with Eurocode 8
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Westinghouse Non-Proprietary Class 3 © 2014 Westinghouse Electric Company LLC. All Rights Reserved.
Fuel Tank Model – Boundary Condition• The container shell, base construction and reinforcement are
modelled as SHELL elements• Contacts are defined between SPH particles and SHELL
elements of the steel structure
156613 SPH particles (53,7 m³)
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Westinghouse Non-Proprietary Class 3 © 2014 Westinghouse Electric Company LLC. All Rights Reserved.
Fuel Tank Model – Seismic Load• The earthquake excitation of the FE model is realized by
imposed displacement in all transition directions• The time history of the displacement is integrated by the time
history of the acceleration spectrum (real earthquake)
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Fuel Tank Model – Results
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Westinghouse Non-Proprietary Class 3 © 2014 Westinghouse Electric Company LLC. All Rights Reserved.
Fuel Tank Model – Results
1 2 3 4VX-X VelocityVY-Y Velocity
Global Velocity
Time [s]0 11 22 33 44 55-400
-300
-200
0
Vel
ocity
[mm
/s] 100
200
300
400
-100
1. Settle down due to gravity
2. Earthquake excitation
3. Earthquake excitation is set to zero
4. Pure fade away phase
Longitudinal Sloshing Transversal Sloshing
RADIOSS 0.122 s-1 0.467 s-1
Eurocode 8 /1/ 0.121 s-1 0.467 s-1
Source: DIN EN 1998-4:2006: Auslegung von Bauwerken gegen Erdbeben - Teil 4: Silos, Tankbauwerke und Rohrleitungen, Berlin: Beuth 2007
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Concrete Containment – General Description• Water sloshing inside a concrete containment will be analyzed in
case of an aftershock earthquake• Pressure loads and sloshing behavior as the main focus
VerticalOpening
Concrete Wall
Steel Containment
Bottom Floor
Water Surface
Internal Structure
Upper Floor
Reactor Vessel
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Concrete Containment – General Description• Due to the complexity of the calculation model two sections are
calculated with considering the vertical openings
Upper Floor
B
B
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Westinghouse Non-Proprietary Class 3 © 2014 Westinghouse Electric Company LLC. All Rights Reserved.
Concrete Containment – Boundary Condition• Symmetry boundary conditions are defined on the SPH particles• Concrete structure is modelled as stiff• Applicable time-history accelerations are integrated two times
into a time-history displacements using HyperGraph and applied on the concrete structure
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Concrete Containment – Results
Section B-B
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Concrete Containment – ResultsSection B-B
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Concrete Containment – Results
Section C-C
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Concrete Containment – ResultsSection C-C
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Concrete Containment – Results
Increased water level (3.4 m)
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Westinghouse Non-Proprietary Class 3 © 2014 Westinghouse Electric Company LLC. All Rights Reserved.
Conclusion
• SPH method simulates fluid sloshing in an accurate way• Results are comparable to experimental data• Visualization of results• Interaction between fluid and structure (pressure, stresses, etc.)• Complex geometries can be analyzed, while the Eurocode 8 is
limited to simple structures
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Westinghouse Non-Proprietary Class 3 © 2014 Westinghouse Electric Company LLC. All Rights Reserved.
Thank You for your attention!Any Questions?
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