A new approach for computing the steady state fluid–structure interaction response of periodic problems

Abstract

A special type of fluid-structure interaction (FSI) problems are problems with periodic boundary conditions like in turbomachinery. The steady state FSI response of these problems is usually calculated with similar techniques as used for transient FSI analyses. This means that, when the fluid and structure problem are not simultaneously solved with a monolithic approach, the problem is partitioned into a fluid and structural part and that each time step coupling iterations are performed to account for strong interactions between the two sub-domains. This paper shows that a time-partitioned FSI computation can be very inefficient to compute the steady state FSI response of periodic problems. A new approach is introduced in which coupling iterations are performed on periodic level instead of per time step. The convergence behaviour can be significantly improved by implementing existing partitioned solution methods as used for time step coupling (TSC) algorithms in the time periodic coupling (TPC) framework. The new algorithm has been evaluated by comparing the convergence behaviour to TSC algorithms. It is shown that the number of fluid structure evaluations can be considerably reduced when a TPC algorithm is applied instead of a TSC. One of the most appealing advantages of the TPC approach is that the structural problem can be solved in the frequency domain resulting in a very efficient algorithm for computing steady state FSI responses.

BEM–FEM coupling for the analysis of flexible propellers in non-uniform flows and validation with full-scale measurements

“…In case of a periodic FSI problem, the periodicity can be used to get rid of the time step difference by using results from the same time step of a previous period. This coupling is called the time periodic coupling and has been described and investigated in previous work [16]. A time periodic coupling is the most obvious for the present work for several reasons.…”

“…Especially in case of a high ratio between fluid added mass and structural mass and an incompressible fluid, the solution process may not converge without a dedicated partitioned solution method [6]. Two of these partitioned solution methods have been investigated in a time step and time periodic framework in [16]. It has been shown that the Quasi-Newton inverse least squares (QN-ILS) method outperforms the Aitken under-relaxation method in any case.…”

“…An appealing advantage of the time periodic coupling is that it allows to solve for the structural equations in the frequency domain. That means that only the steady state response is obtained and any transients, which slow down the convergence to the steady state FSI solution, are not computed [16]. However, as shown, convergence problems as appearing in time step couplings due to strong fluid added mass effects, arise in time periodic couplings as well.…”

Boundary Element Modelling Aspects for the Hydro-Elastic Analysis of Flexible Marine Propellers

“…The FGDE-BEM model is the same as the FGDI-BEM model except that PROCAL solves only the disturbance velocity potential without the contribution of blade vibration velocities, φ, from the kinematic boundary condition of Equation (30). The blade vibration velocity and acceleration effects are included in the FSI analyses by means of the closed form expressions for fluid added mass and hydrodynamic damping.…”

“…The blade vibration velocity and acceleration effects are included in the FSI analyses by means of the closed form expressions for fluid added mass and hydrodynamic damping. The main advantage of this approach is that the fluid added mass and hydrodynamic damping can be explicitly included in the structural computation, which stabilizes the FSI solution and reduces CPU time [30].…”