numerical simulation of liquid sloshing with smoothed particle hydrodynamics (sph) method in nuclear...

Westinghouse Non-Proprietary Class 3 © 2014 Westinghouse Electric Company LLC. All Rights Reserved.

1

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

2


Contents

• Numerical Methodology• Verification of the Calculation Method• Fuel Storage Tank• Concrete Containment• Conclusion

3


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

4


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)

5


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

6


Verification of the Calculation Method

7


Verification of the Calculation Method• Position of the water front

• Height of the water column

8


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

9


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

10



11



• 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

12


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

13


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)

14


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)

15


Fuel Tank Model – Results

16


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

17


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

18


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

19


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

20


Concrete Containment – Results

Section B-B

21


Concrete Containment – ResultsSection B-B

22



Section C-C

23


Concrete Containment – ResultsSection C-C

24



Increased water level (3.4 m)

25


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

26


Thank You for your attention!Any Questions?