atw - International Journal for Nuclear Power | 10.2020

atw Vol. 65 (2020) | Issue 10 ı October
RESEARCH AND INNOVATION 514
Planned entry for
This work is funded
by the German
Federal Ministry of
Economic Affairs and
Energy under grant
number 1501579 on
the basis of a decision
by the German
Bundestag.
The simulations are
performed with the
code version Open-
FOAM-v7 developed
by the OpenFOAM
Foundation.
Water Hammer Simulation in Pipe Systems
with Open Source Code OpenFOAM
Paul Fuchs and Marco K. Koch
Water hammer phenomena can
generally be divided into two main
parts, the direct and the indirect
phenomena. For the direct water
hammer phenomena, a shock wave
is induced due to the sudden deceleration
of a fluid leading to a local
rise in pressure. The shock wave then
travels through the pipe system and
effects like wave reflection, interference,
superposition are to be
concerned. Furthermore, the valve
closure time as well as the deformation
of the pipe influences the quality
and quantity of the shock wave. On
the other hand, the indirect water
hammer is induced when a local
pressure drop below vapor pressure
leads to evaporation and creation of
steam bubbles. When the pressure
rises again above vapor pressure and
especially big steam bubbles implode
the surrounding water is rapidly
accelerated causing a secondary shock
wave once a sudden deceleration
occurs at impact. [LUE13]
To gain sufficient knowledge of the
important physical effects regarding a
water hammer phenomena detailed
CFD analysis are performed using
the open source code OpenFOAM.
Effects like propagation of shock
waves, cavitation and fluid structure
interaction will be included in the
code as there is no default capability
to model such phenomena. [GRE19]
In order to test the applicability of
the default code as well as the newly
implemented cavitation model two
water hammer experiments at the test
facility “Heißdampfreaktor” (HDR)
will be modelled under simplified
conditions. The implementation of
the cavitation model basis within
the Volume of Fluid (VOF) based,
fully compressible, multi fluid solver
compressibleMultiphaseInterFoam is
described also discussing model
strength, restrictions and weaknesses.
The simulation results for the two
experiments will be compared with
and without cavitation model in order
Introduction During a loss of coolant accident (LOCA) in certain types of boiling water
reactors the continuous undersupply of cooling water eventually leads to the degradation of the
reactor core. In order to prevent such an accident, the loss of cooling water is prevented through
fast closing valves in the cooling circuit. However, the valve closing process can induce a so called
water hammer phenomena in the pipe systems which can damage structures within the cooling
circuit. [GIO04]
to qualify and quantify the cavitation
influence during the water hammer
phenomena. At the end potential code
improvements and upcoming work is
shortly presented.
Model basis and cavitation
model implementation
The Volume of Fluid (VOF) based
solver compressibleMultiphaseInter-
Foam is fully compressible as density
can be computed with multiple accessible
equations of state (EOS) also
regarding thermal effects. The
interface tracking method between
multiple non mixable fluids allows for
a detailed representation of interface
motion including surface tension
effects. However, the mesh resolution
at the interface needs to be very
high in order to give accurate results
leading to high computational costs
for complex multiphase flows. In
general, this method is used for free
surface flows or in combination with
so called mixture models to model the
free surface of bigger bubbles within a
continuous fluid. In this study the
VOF method is used to model the free
surface between water and steam in
the upper RDB as well as macroscopic
cavitation effects in the check valve
region and in the pipe system as mass
transfer across the interface is well
described for this method. [WAR13]
[GRE19]
In order to model the water
hammer experiments without temperature
driven phase change in the
upper RPV (Figure 3) a continuous
non-condensable steam phase a g
(eq. 3) is considered. For the pressure
driven phase change a mass transfer
term
regarding the
condensation rate and vaporization
rate is added to the continuity
equation for water a l (eq. 1)
and condensable steam a v (eq. 2)
[YU17]:
(1)
(2)
(3)
Using the expansion of the convection
term
and expressing the time
plus the advective derivative
as the resulting set of equations
can be summed to formulate the
velocity divergence as [YU17]
(4)
With equation 4 and an artificial
compression Term C to keep interfaces
sharp the final set of transport
equations can be expressed as [YU17]
[GRE19]:
(5)
(6)
(7)
Similarly the pressure equation is
modified by subtracting the source
term from the incompressible
part leading to following formulation
Research and Innovation
Water Hammer Simulation in Pipe Systems with Open Source Code OpenFOAM ı Paul Fuchs and Marco K. Koch