Strongly coupled dynamics

EPX implements kinematic constraints of many kinds to provide boundary conditions and couplings between entities, such as unilateral contact between different pieces of structures, fluid-structure interaction or coupling between different formulation (pipe SPH-Finite Elements, Discrete Elements-Finite Elements…).

Arbitrary numerical parameters are avoided in the way these constraints are enforced, mainly by means of a dual approach through Lagrange Multipliers.

Below are given two demonstrative examples of the capabilities of EPX for strongly coupled systems.

Simulation of nuclear waste container drop experiments

Transportation of nuclear waste container is especially sensitive to accidental drops. Fall can result in a mechanical damage of the container, which can cause environmental pollution by radionuclides.

The container damage depends on the impact velocity and the angle between falling container and the surface on which the container falls.

Experiments cannot cover all the possible variants of drops, because it would result an unacceptable price.

Therefore numerical simulation such kind of accidental drops is an essential step in the nuclear waste container safety analysis.

Vertical drop simulation

Oblique drop simulation

Lashing drop simulation

Simulation of the mechanical consequences of a LOCA in a Pressurized Water Reactor

The Loss Of Coolant Accident (LOCA) is the one of the main reference accidents for Pressurized Water Reactors (PWR), consisting in a breach in one of the main primary pipes. At the breach level, pipe sections on both sides are considered completely open. From the initial conditions inside the primary loop (i.e. liquid water at 300°C and 150 bars), a brutal depressurization occurs, with a diphasic jet at the breach. A rarefaction wave propagates through the entire primary loop and produces mechanical loadings on core structures inside the main vessel. The consequences of theses loadings must be quantified to ensure that they do not prevent the safety devices to work for a correct and safe stop of the reactor.

The computational model in EPX must integrate both the main vessel and the pipes of the entire primary circuit, to be able to simulate the breach effects and the wave propagations in the loop. To do so, EPX is equipped with original 1D-pipe elements, able to represent the flow along the main loops of the primary circuits at lower cost and taking into account special components such as pumps, as well as continuous and localized head losses. These pipe elements are coupled through links to classical 3D elements for both fluid and structure needed to represent phenomena inside the primary vessel (see Figure 2 for an example of LOCA simulation model).

Mixed LOCA model of PWR primary circuit: 1D pipe elements, 3D volumetric elements for fluid inside primary vessel, 3D shell elements for internal structures

Pressure drop in the reactor during the accident

Flow inversion inside the main vessel and stress in internal structures

FSI Simulation of a Non-Linear Transient Response of a Pipeline to a Pressure Pulse

The aims at validating the capability of the EUROPLEXUS fast dynamics code to predict a highly non-linear dynamic response of a water-filled thin-walled pipe to a strong pressure pulse. Three numerical models are compared. The first one is a purely fluid model, with the pipe supposed rigid and fixed. The second model is a FSI model, which uses flexible pipeline elements with intrinsic coupling between fluid and pipe. The third model is a general 3D FSI model with a special interface coupling between the fluid volume and the shell mesh of the structure. It is shown that both pipeline and 3D FSI models of EUROPLEXUS give realistic predictions of the global non-linear behavior of the pipe under a strong pressure pulse.

For the transducers P₄ to P₁₀ situated in the flexible pipe, the amplitude of the incident wave is reduced almost twice due to the radial pipe expansion.

For the transducer P₂ one can observe a sudden pressure drop at about 1.2 ms after the pressure peak occurring This sudden pressure drop to atmospheric pressure is due to a rarefaction wave generated by the expansion of the flexible Nickel pipe and propagating in the opposite direction, i.e. back to the rigid pipe. The rarefaction wave generates cavitation of water.

The use of the general 3D model with a shell modelling of the pipe allows a very accurate representation of two wrinkles observed in the experiment. When using a refined piping mesh in the 3D calculation the results are improved only locally near the concrete wall. 

Hypothetical core disruptive accident (HCDA) – MARA 2 experiment 

In fast breeder reactor (LMFBR) it is assumed that the core of the nuclear reactor has melted partially and the interaction with liquid sodium has created high pressure bubble in the core. The experimental test MARA 2 simulates the explosive phenomenon in a flexible vessel.