The Subsonic Potential-based 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 (½ρv2 term in the Bernoulli equation). Therefore the acoustic fluid elements should not be used in regions where this effect is important.
The subsonic potential-based 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 potential-based fluid elements are nonlinear.
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:
This type of problem can easily be solved using the subsonic potential-based elements. A free surface potential-interface is placed at the top of the tank, and an inlet-outlet potential-interface 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.
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.
Subsonic potential-based 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 left-hand-side shows the pressure in the fluid and the right-hand side shows the magnified deformations of the structure. A very good comparison with experimental data is observed, see the reference.
Clearly the subsonic potential-based fluid element in ADINA is very effective in this type of analysis.