The Subsonic Potentialbased Fluid Element in ADINA
Acoustic fluid elements are frequently used to model water in pressure vessels, tanks, etc.
These elements model the mass of the water, and also wave propagation in the water.
The acoustic fluid elements are computationally very effective, since the acoustic
fluid elements are linear.
One effect that is not contained in the acoustic fluid elements is the Bernoulli effect
(½ρv^{2} term in the Bernoulli equation). Therefore the acoustic
fluid elements should not be used in regions where this effect is important.
The subsonic potentialbased fluid elements of ADINA can be used when the Bernoulli
effect needs to be accounted for. These elements are similar to the acoustic fluid elements,
except that this effect is included. Since the Bernoulli effect is nonlinear, the
subsonic potentialbased fluid elements are nonlinear.
Discharge of water from a tank
As a simple illustrative example of a problem in which the Bernoulli effect is important,
we consider the discharge of water from a tank, as shown in Figure 1 below:
Figure 1 Discharge of water from a tank. (a) Schematic (b) Mesh
This type of problem can easily be solved using the subsonic potentialbased elements. A
free surface potentialinterface is placed at the top of the tank, and an inletoutlet
potentialinterface is placed at the valve. The outlet pressure is specified at the valve.
In the first run, the outlet pressure is set to the hydrostatic pressure and the
gravity load is applied, all in one static load step. The pressure in the fluid
is the expected hydrostatic pressure. In the second (restart) run, the outlet pressure
is suddenly lowered to zero and a dynamic analysis is performed. Figure 2 shows
the results.
Figure 2 Discharge of water from a tank: Results
HDR blowdown experiment
As a practical example of a problem in which the Bernoulli effect is important, we
consider the HDR blowdown experiment V31.1. An important problem in the analysis
of light water nuclear reactors is to compute the response of the core barrel and
pressure vessel resulting from the loss of coolant in a pressurized water reactor.
The HDR (Heissdampfreaktor) safety project in Germany was developed to provide
experimental verification for computer programs used in this type of analysis.
Figure 3 below shows a diagram of the FSI model used to simulate the HDR blowdown experiment.
Figure 3 HDR blowdown experiment: FSI model
Subsonic potentialbased elements are used to model the fluid, and shell and solid
elements are used to model the structure. In the first run, the fluid internal pressure
is applied to the model in one static load step. In the second (restart) run, the
pressure at the pipe outlet is lowered to simulate a pipe break, and a dynamic analysis
is performed.
The animation at the top of this page shows the analysis results. The lefthandside
shows the pressure in the fluid and the righthand side shows the magnified deformations
of the structure. A very good comparison with experimental data is observed, see
the reference.
Clearly the subsonic potentialbased fluid element in ADINA is very effective in
this type of analysis.
Keywords:
Fluid structure interaction,
nuclear power plant,
blowdown experiment,
pipe break analysis,
HDR vessel,
subsonic potentialbased fluid element,
Bernoulli effect,
acoustic fluid
Reference

T. Sussman, J. Sundqvist, "Fluidstructure interaction analysis with a subsonic
potentialbased fluid formulation", Computers and Structures, 81 (2003), 949962.
