MODELING OF FLUID-STRUCTURE INTERACTION

Abstract

▪ Abstract The interaction of a flexible structure with a flowing fluid in which it is submersed or by which it is surrounded gives rise to a rich variety of physical phenomena with applications in many fields of engineering, for example, the stability and response of aircraft wings, the flow of blood through arteries, the response of bridges and tall buildings to winds, the vibration of turbine and compressor blades, and the oscillation of heat exchangers. To understand these phenomena we need to model both the structure and the fluid. However, in keeping with the overall theme of this volume, the emphasis here is on the fluid models. Also, the applications are largely drawn from aerospace engineering although the methods and fundamental physical phenomena have much wider applications. In the present article, we emphasize recent developments and future challenges. To provide a context for these, the article begins with a description of the various physical models for a fluid undergoing time-dependent motion, then moves to a discussion of the distinction between linear and nonlinear models, time-linearized models and their solution in either the time or frequency domains, and various methods for treating nonlinear models, including time marching, harmonic balance, and systems identification. We conclude with an extended treatment of the modal character of time-dependent flows and the construction of reduced-order models based on an expansion in terms of fluid modes. The emphasis is on the enhanced physical understanding and dramatic reductions in computational cost made possible by reduced-order models, time linearization, and methodologies drawn from dynamical system theory.

Filtered POD‐based low‐dimensional modeling of the 3D turbulent flow behind a circular cylinder

“…Dowell and Hall [28] used reduced order modelling for fluid-structure interaction. They used temporal pre-filtering to impose periodicity and indirectly remove small and stochastic spatial structures.…”

Linear control of oscillator and amplifier flows1

“…The additional driving term accounts for the discrepancy between the true measurement y and the estimatorproduced measurementŷ (from equation (10b)), and the manner in which this discrepancy enters the equation for the estimated state is determined by the Kalman gain L. This gain follows from an optimization problem: we wish to minimize the variance of the estimation error e = q−q while observing the governing equations (10). A variational formulation of this optimization problem produces the following algebraic Riccati equation…”

“…Instabilities in a laminar boundary layer can cause transition to turbulence and consequently increase drag and heat transfer on aircrafts [1][2][3][4] ; reactive-flow instabilities 5 can give rise to nonstoichiometric combustion and thus increase the output of environmentally harmful side products; thermoacoustic instabilities in combustion chambers can lead to strong vibrations and material fatigue 6,7 ; magnetically induced instabilities in tokamak configurations can be detrimental to sustaining the plasma fusion process 8,9 ; the onset of vortex-induced vibrations can bring about substantial damage to flexible structures 10,11 . These examples are but a few that illustrate the need for and potential benefit of controlling instabilities in advanced fluid devices.…”

A matrix free, partitioned solution of fluid–structure interaction problems using finite volume and finite element methods

“…Other examples of such problems include structural loads on ships [7], flow induced vibrations in nuclear power plants [8] and wind response of buildings [9]. Though recent years have seen much research going into the development of FSI modelling technology [10,11,12,13,14], the efficient and robust modelling of large-scale, strongly-coupled systems which involve complex geometries is still a work in progress. In this paper, we develop and evaluate a fully-coupled, matrix-free methodology as a contribution towards this challenge.…”