28 Mai, 2020

Numerical Methods for solving Fluid-Structure Interaction – Case study: Tanks Sloshing

28 Mai, 2020

The advance of the computers power and numerical techniques are pushing the simulation boundaries further and further towards complex multi-physics phenomena in pursuing the best/optimal designs. Today’s tools allow engineers to tackle various complex problems in a matter of weeks or even days by performing numerical experiments from the comfort of their offices. One of this complex multi-physics challenges is represented by the coupled Fluid-Structure Interaction – FSI that encapsulates both structural and fluid fields. Although even the “structural” solving can pose difficulties due to different nonlinearities, such as plasticity or geometrical nonlinearities, the main effort is usually on the fluid side because its equations are inherently nonlinear.

There are two main approaches that can be used to solve the coupled fields: (1) monolithic when both fluid and solid equations are solved in a single matrix at each time step or (2) partitioned when two specialized solvers are used to evaluate independently the fluid and the structure responses which further are coupled at the interface. In the first method the fluid-solid interface interaction is solved inherently, particularity that makes the approach very efficient and robust. For the second method, interface variables like pressure and displacements are transferred between the two solvers. The main advantages of the latter approach are the possibility to use the best solvers/methods for each field (FVM for fluid and FEM for structure) and the advance in time can be done with different time steps for each solver (the solving and the coupling time increments can be different). The main drawback of the partitioned method is the additional complexity and uncertainty/error of the coupling, but it does not shadow the advantages.

Most of the simulations software available commercially today are using the partitioned method for FSI problems mainly because the method allows for much higher flexibility.

One of the practical applications that involves FSI is the sloshing phenomenon in tanks and reservoirs that presents a great interest for several industrial branches such as naval, aerospace, civil, automobile industry and nuclear engineering. In the animations below a fictitious case of violent sloshing in two configurations has been studied: with structure interaction and without – rigid walls. As one can see in the charts below the flexibility of the tank changes the fluid behaviour and the loads on the walls. The fluid part has been simulated using an inhomogeneous two phase FVM while the structure uses a FEM.

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