fluid-structure interaction calculations of a large-break loss-of-coolant accident

VTT TECHNICAL RESEARCH CENTRE OF FINLAND

1

Fluid-Structure Interaction Calculations of aLarge-Break Loss-of-Coolant Accident

Antti Timperi

Kul-34.4551Postgraduate Seminar in Fluid Mechanics 3.5.2010


2

Introduction

Aim of the work has been to find practical tools for analyzing Fluid-Structure Interaction (FSI) problems found in nuclear and also other industries.

Large-Break Loss-Of-Coolant Accident (LBLOCA) is an important Design Basis Accident (DBA) situation. Rapid depressurization of the primary circuit causes loads on the reactor internals.

The motivation for studying more advanced simulation methods for analysis of DBA situations is to get more accurate, so-called ”best estimate”, analysis results.

LBLOCA in the VVER-440 type Pressurized Water Reactor (PWR) was used as a test case in earlier calculations.

Validation of LBLOCA calculations against the German HDR experiments is presented in the following.


3

HDR (Heißdampfreaktor) test facility vs. PWR

p = 110bar

Tcore = 308ºC

Tdowncomer = 240ºC

p = 125bar

Thot leg = 295ºC

Tcold leg = 265ºC


4

HDR test facility vs. PWR (cont.)

Quantity HDR PWR

Pressure, MPa 11 12.5

P0 − Psat, MPa 5.5 7

Tcore − Tdownc, °C 0…50 30

Break diameter, m 0.2 0.5

Break opening time, ms 1…2 ?

Core barrel length, m 7.6 8.1

Core barrel thickness, mm 23 50

Core barrel diameter, m 2.66 3.2

Maximum stress, MPa 100 230

Maximum displacement, mm 2 4…5


5

Overview of the calculations

AprosBoundary condition

Star-CDPropagation of

pressure transient

MpCCIWall position

MpCCIPressure loads

AbaqusStresses and deformation

of structures

MpCCI (Mesh-based parallel Code Coupling Interface) is middleware that has been developed at the Fraunhofer Institute

Motion of the core barrel is taken into account in the CFD calculation of pressure.


6

Pressure at the break location,measured data and APROS calculations:


7

Star-CD CFD model

PISO (“Pressure Implicit with Splitting of Operators”) pressure correction algorithm.

Water is treated as compressible:

Crank-Nicholson method for temporal discretization and MARS/central/central-upwind differencing for spatial discretization.

Standard k-ε model and standard wall functions for modeling turbulence.

)( 000 pp

~ 78 000 hex cells


8

ABAQUS structural model

Fully linear model with ~ 15 0008-node hexahedral elements.

Continuum shell and solid elements are used for matching geometry between CFD and FEM.

Implicit Newmark direct time integration.

Small amount of stiffness proportional damping was included to the RPV wall:2 % of critical damping at frequency 1000 Hz.


9

CFD-FEM calculation

Explicit, sequential solution strategy, i.e. loose numerical coupling. Stable (usually) in LBLOCA calculations, but has been found unstable in certain other applications.

Interpolation is used for transferring the coupling quantities between the CFD and FEM meshes.

Coupling quantities local fluid pressure (CFD → FEM) and nodal coordinates (FEM → CFD). Data is exchanged in each time step (∆t = 10 μs).

Star-CD analysis has a moving mesh, internal CFD mesh is smoothed by mesh morpher of MpCCI.


10

CFD-FEM calculation (cont.)

1. Star-CD sends pressure load corresponding to initial conditions to ABAQUS.

2. ABAQUS simulation advances one time step.

3. ABAQUS sends new nodal coordinates to Star-CD.

4. Star-CD simulation advances one time step.

5. Star-CD sends new pressure load to ABAQUS.

The sequence 2-5 is repeated for the duration of the simulation.


11

Acoustic-structural calculation

Models sound wave propagation and added mass effects, but effects of bulk flow, e.g. dynamic pressure, are neglected. Assumes small displacements.

Fluid is described as an acoustic medium (three-dimensional wave equation for pressure):

Linear constitutive behavior for the fluid (K is bulk modulus):

Reduces to Laplace equation for incompressible fluid (low-frequency structural motion):

0222

2

pct

p

p K u

02 p


12

Acoustic-structural calculation (cont.)

”Volumetric drag” γ can be added to model bulk viscosity or resistive porous material:

Fluid pressure and structural displacement are coupled on the fluid-structure interface:

A single system of equations is solved, i.e. the fluid and structure domains are solved simultaneously:

000

00.

.

..

.. ext

f

T

ff

R

P

D

K

SK

P

DC

C

P

DMS

M

p n u n

022 pcpp


13

Pressure in the reactor, CFD-FEM calculation:

p [Pa]

t = 5 ms 10 ms 15 ms 20 ms 25 ms


14

Stresses and deformations (x200), CFD-FEM calculation:

s [Pa]

t = 0 ms 5 ms 20 ms 40 ms 115 ms


15

Pressures, experiment vs. CFD-FEM:

z = 8.850 m, = 90°

4

5

6

7

8

9

10

11

12

0.00 0.05 0.10 0.15 0.20

Time [s]

Pre

ssu

re [

MP

a]

4

5

6

7

8

9

10

11

12

0.00 0.05 0.10 0.15 0.20

Time [s]

Pre

ssu

re [

MP

a]

4

5

6

7

8

9

10

11

12

0.00 0.05 0.10 0.15 0.20

Time [s]

Pre

ssu

re [

MP

a]

z = 7.780 m, = 270°

z = 5.505 m (core)

-2.0E-04

-1.0E-04

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

0.00 0.02 0.04 0.06 0.08 0.10

Experiment

CFD-FEM

-1.0

-0.5

0.0

0.5

1.0

0.00 0.05 0.10 0.15 0.20

Time [s]

Pre

ssu

re d

iffe

ren

ce [

MP

a]

z = 5.550 m, = 90°


16

Displacements of the core barrel, experiment vs. CFD-FEM:

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

0.00 0.05 0.10 0.15 0.20

Time [s]

Dis

pla

cem

ent

[mm

]

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

0.00 0.05 0.10 0.15 0.20

Time [s]

Dis

pla

cem

ent

[mm

]

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

0.00 0.05 0.10 0.15 0.20

Time [s]

Dis

pla

cem

ent

[mm

]

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

0.00 0.05 0.10 0.15 0.20

Time [s]

Dis

pla

cem

ent

[mm

]

z = 7.150 m, = 90° z = 7.150 m, = 270°

z = 5.550 m, = 90° z = 2.300 m, = 90°

-2.0E-04

-1.0E-04

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

0.00 0.02 0.04 0.06 0.08 0.10

Experiment

CFD-FEM


17

Pressures, experiment vs. acoustic model:

0

2

4

6

8

10

12

0.00 0.02 0.04 0.06 0.08 0.10

Time [s]

Pre

ssu

re [

MP

a]

0

2

4

6

8

10

12

0.00 0.02 0.04 0.06 0.08 0.10

Time [s]

Pre

ss

ure

[M

Pa

]

0

2

4

6

8

10

12

0.00 0.02 0.04 0.06 0.08 0.10

Time [s]

Pre

ssu

re [

MP

a]

z = 8.850 m, = 90° z = 5.550 m, = 90°

z = 5.505 m (core)

-2.0E-04

-1.0E-04

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

0.00 0.02 0.04 0.06 0.08 0.10

Experiment

Acoustic FEM

-1.0

-0.5

0.0

0.5

1.0

0.00 0.02 0.04 0.06 0.08 0.10

Time [s]

Pre

ssu

re d

iffe

ren

ce [

MP

a]

z = 5.550 m, = 90°


18

Displacements of the core barrel, experiment vs. acoustic model:

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.00 0.02 0.04 0.06 0.08 0.10

Time [s]

Dis

pla

cem

ent

[mm

]

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

0.00 0.02 0.04 0.06 0.08 0.10

Time [s]

Dis

pla

cem

ent

[mm

]

-1.0

0.0

1.0

2.0

3.0

4.0

0.00 0.02 0.04 0.06 0.08 0.10

Time [s]

Dis

pla

cem

ent

[mm

]

-3.0

-2.0

-1.0

0.0

1.0

2.0

0.00 0.02 0.04 0.06 0.08 0.10

Time [s]

Dis

pla

cem

ent

[mm

]

z = 7.150 m, = 90° z = 7.150 m, = 270°

z = 2.300 m, = 90° z = 2.300 m, = 270°

-2.0E-04

-1.0E-04

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

0.00 0.02 0.04 0.06 0.08 0.10

Experiment

Acoustic FEM


19

Conclusions on CFD-FEM calculations

The calculated fluid and structural quantities were in fairly good agreement with the experiment. Especially the overall structural behavior of the core barrel was predicted well.

The most significant phenomena of the LBLOCA were well captured by the calculation during the first 100 ms, when the largest loads occurred.

Strong boiling increased pressure significantly after 120 ms, which caused deviation of measured and calculated pressures (single-phase CFD model was used).


20

Conclusions on acoustic-structural calculations

The results were in good agreement with the experiment and with the CFD-FEM calculation during the early phase of the simulation when the flow velocity was negligible.

Loads and structural effects were highly over-predicted in the later phase when the effect of bulk flow of water became significant.

The method is considerably more efficient and more robust compared to the CFD-FEM method.

May be considered as an alternative tool for comparison calculations in future work.


21

General conclusions

Fairly coarse numerical meshes were sufficient for capturing the most important fluid transient and FSI phenomena.

The single-phase assumption used in the FSI calculations was adequate during the phase when the largest structural effects occurred, i.e. until ~ 100 ms.

The experiment had probably an unrealistically short break opening time, i.e. ~ 1 ms. Opening times of 15 ms and longer have been proposed in the literature.

fluid-structure interaction calculations of a large-break loss-of-coolant accident

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