Modelling vortex-induced fluid–structure interaction

2007 ◽  
Vol 366 (1868) ◽  
pp. 1231-1274 ◽  
Author(s):  
Haym Benaroya ◽  
Rene D Gabbai
Keyword(s):  
Variational Approach ◽  
Equations Of Motion ◽  
Fluid Structure Interaction ◽  
Oscillator Model ◽  
List Type ◽  
Governing Equations ◽  
Fluid Structure ◽  
Reduced Order ◽  
Structure Interaction ◽  
Oscillator Models

The principal goal of this research is developing physics-based, reduced-order, analytical models of nonlinear fluid–structure interactions associated with offshore structures. Our primary focus is to generalize the Hamilton's variational framework so that systems of flow-oscillator equations can be derived from first principles. This is an extension of earlier work that led to a single energy equation describing the fluid–structure interaction. It is demonstrated here that flow-oscillator models are a subclass of the general, physical-based framework. A flow-oscillator model is a reduced-order mechanical model, generally comprising two mechanical oscillators, one modelling the structural oscillation and the other a nonlinear oscillator representing the fluid behaviour coupled to the structural motion. Reduced-order analytical model development continues to be carried out using a Hamilton's principle-based variational approach. This provides flexibility in the long run for generalizing the modelling paradigm to complex, three-dimensional problems with multiple degrees of freedom, although such extension is very difficult. As both experimental and analytical capabilities advance, the critical research path to developing and implementing fluid–structure interaction models entails formulating generalized equations of motion, as a superset of the flow-oscillator models; and developing experimentally derived, semi-analytical functions to describe key terms in the governing equations of motion. The developed variational approach yields a system of governing equations. This will allow modelling of multiple d.f. systems. The extensions derived generalize the Hamilton's variational formulation for such problems. The Navier–Stokes equations are derived and coupled to the structural oscillator. This general model has been shown to be a superset of the flow-oscillator model. Based on different assumptions, one can derive a variety of flow-oscillator models.

Extending a Van der Pol Based Reduced-Order Model for Fluid-Structure Interaction Applied to Non-Synchronous Vibrations in Turbomachinery

2021 ◽  
Author(s):  
Richard Hollenbach ◽  
Robert Kielb ◽  
Kenneth Hall
Keyword(s):  
Fluid Structure Interaction ◽  
Reduced Order Model ◽  
Van Der Pol Oscillator ◽  
Previous Model ◽  
Stable Limit ◽  
Order Model ◽  
Van Der Pol ◽  
Fluid Structure ◽  
Reduced Order ◽  
Structure Interaction

Abstract This paper expands upon a multi-degree-of-freedom, Van der Pol oscillator used to model buffet and Nonsynchronous Vibrations (NSV) in turbines. Two degrees-of-freedom are used, a fluid tracking variable incorporating a Van der Pol oscillator and a classic spring, mass, damper mounted cylinder variable; thus, this model is one of fluid-structure interaction. This model has been previously shown to exhibit the two main aspects of NSV. The first is the lock-in or entrainment phenomenon of the fluid shedding frequency jumping onto the natural frequency of the oscillator, while the second is a stable limit cycle oscillation (LCO) once the transient solution disappears. Improvements are made to the previous model to better understand this aeroelastic phenomenon. First, an error minimizing technique through a system identification method is used to tune the coefficients in the Reduced Order Model (ROM) to improve the accuracy in comparison to experimental data. Secondly, a cubic stiffness term is added to the fluid equation; this term is often seen in the Duffing Oscillator equation, which allows this ROM to capture the experimental behavior more accurately, seen in previous literature. The finalized model captures the experimental cylinder data found in literature much better than the previous model. These improvements also open the door for future models, such as that of a pitching airfoil or a turbomachinery blade, to create a preliminary design tool for studying NSV in turbomachinery.

Mitigation of Sliding Motion of a Cask-Canister by Fluid-Structure Interaction in an Annular Region

2011 ◽  
Author(s):  
Tomohiro Ito ◽  
Yoshihiro Fujiwara ◽  
Atsuhiko Shintani ◽  
Chihiro Nakagawa ◽  
Kazuhisa Furuta
Keyword(s):  
Equations Of Motion ◽  
Fluid Structure Interaction ◽  
Shaking Table ◽  
Annular Region ◽  
Test Model ◽  
Free Standing ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Sliding Motion ◽  
Standing Structure

The cask-canister system is a coaxial circular cylindrical structure in which several spent fuels are installed. This system is a free-standing structure thus, it is very important to reduce sliding motion for very large seismic excitations. In this study, we propose a mitigation method for sliding motion. Water is installed in an annular region between a cask and a canister. The equations of motion are derived taking fluid-structure interaction into consideration for nonlinear sliding motion analyses. Based on these equations, mitigation effects of sliding motions are studied analytically. Furthermore, a fundamental test model of a cask-canister system is fabricated and shaking table tests are conducted. From the analytical and test results, sliding motion mitigation effects are investigated.

Reduced-Order Modeling and Experimental Studies of Two-Way Coupled Fluid-Structure Interaction in Flapping Wings

2019 ◽  
Author(s):  
Ryan K. Schwab ◽  
Heidi E. Reid ◽  
Mark A. Jankauski
Keyword(s):  
Fluid Structure Interaction ◽  
Experimental Studies ◽  
Flapping Wing ◽  
Flexible Wings ◽  
Single Degree Of Freedom ◽  
Fluid Structure ◽  
Reduced Order ◽  
Structure Interaction ◽  
Rotation Stage ◽  
Computational Resources

Abstract Flapping, flexible wings deform under both aerodynamic and inertial loads. However, the fluid-structure interaction (FSI) governing flapping wing dynamics is not well understood. Conventional FSI models require excessive computational resources and are not conducive to parameter studies that consider variable wing kinematics or geometry. Here, we present a simple two-way coupled FSI model for a wing subjected to single-degree-of-freedom (SDOF) rotation. The model is reduced-order and can be solved several orders of magnitude faster than direct computational methods. We construct a SDOF rotation stage and measure basal strain of a flapping wing in-air and in-vacuum to study our model experimentally. Overall, agreement between theory and experiment is excellent. In-vacuum, the wing has a large 3ω response when flapping at approximately 1/3 its natural frequency. This response is attenuated substantially when flapping in-air as a result of aerodynamic damping. These results highlight the importance of two-way coupling between the fluid and structure, since one-way coupled approaches cannot describe such phenomena. Moving forward, our model enables advanced studies of biological flight and facilitates bio-inspired design of flapping wing technologies.

Simulation of Fluid Flow Using Reduced-Order Modeling by POD Approach Applied to a Fixed Tube Bundle System

2010 ◽  
Author(s):  
Marie Pomarede ◽  
Erwan Liberge ◽  
Aziz Hamdouni ◽  
Elisabeth Longatte ◽  
Jean-Franc¸ois Sigrist
Keyword(s):  
Dynamic Analysis ◽  
Steam Generator ◽  
Tube Bundle ◽  
Fluid Structure Interaction ◽  
Reduced Model ◽  
Steam Generator Tube ◽  
Fluid Structure ◽  
Reduced Order ◽  
Structure Interaction ◽  
Tube Bundles

Tube bundles in steam boilers of nuclear power plants and nuclear on-board stokehold are known to be exposed to high levels of vibrations. This coupled fluid-structure problem is very complex to numerically set up, because of its three-dimensional characteristics and because of the large number of degrees of freedom involved. A complete numerical resolution of such a problem is currently not viable, all the more so as a precise understanding of this system behaviour needs a large amount of data, obtained by very expensive calculations. We propose here to apply the now classical reduced order method called Proper Orthogonal Decomposition to a case of 2D flow around a tube bundle. Such a case is simpler than a complete steam generator tube bundle; however, it allows observing the POD projection behaviour in order to project its application on a more realistic case. The choice of POD leads to reduced calculation times and could eventually allow parametrical investigations thanks to a low data quantity. But, it implies several challenges inherent to the fluid-structure characteristic of the problem. Previous works on the dynamic analysis of steam generator tube bundles already provided interesting results in the case of quiescent fluid [J.F. Sigrist, D. Broc; Dynamic Analysis of a Steam Generator Tube Bundle with Fluid-Structure Interaction; Pressure Vessel and Piping, July 27–31, 2008, Chicago]. Within the framework of the present study, the implementation of POD in academic cases (one-dimensional equations, 2D-single tube configuration) is presented. Then, firsts POD modes for a 2D tube bundle configuration is considered; the corresponding reduced model obtained thanks to a Galerkin projection on POD modes is finally presented. The fixed case is first studied; future work will concern the fluid-structure interaction problem. Present study recalls the efficiency of the reduced model to reproduce similar problems from a unique data set for various configurations as well as the efficiency of the reduction for simple cases. Results on the velocity flow-field obtained thanks to the reduced-order model computation are encouraging for future works of fluid-structure interaction and 3D cases.

Hydroelastic Modeling of a Compliant Offshore Tower: Formulation

2003 ◽  
Author(s):  
Jinzhu Xia ◽  
Quanming Miao ◽  
Nicholas Haritos ◽  
Beverley Ronalds
Keyword(s):  
Oil And Gas ◽  
Equations Of Motion ◽  
Fluid Structure Interaction ◽  
Coupled System ◽  
Dynamic Responses ◽  
Variation Principle ◽  
Diffraction Radiation ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Radiation Theory

Offshore oil and gas can be produced using a variety of platform types. One option, the compliant offshore tower, has proven to be an economic solution in moderately deep water (300–600m). In this paper, the wave-induced global dynamic responses of a compliant tower in wind, current and waves are studied in the context of fluid-structure interaction. A beam undergoing transverse and axial motion models the vertical member of the tower. The beam is supported by a linear-elastic torsional spring at the bottom end and a point mass and a buoyant chamber is located at the top free end. The fluid forces on the beam are modeled using the Morison equation while the hydrodynamic forces on the chamber are obtained based on the three-dimensional diffraction-radiation theory. By applying Hamilton’s variation principle, the equations of motion are derived for the coupled fluid-structure interaction system. The non-linear coupled system equations that emanate from this new approach can then be solved numerically in the time domain.

Tackling FSI Simulation for FIV Problems in Tube Bundle Systems With POD Approach

2011 ◽  
Author(s):  
Marie Pomarede ◽  
Aziz Hamdouni ◽  
Erwan Liberge ◽  
Elisabeth Longatte ◽  
Jean-Franc¸ois Sigrist
Keyword(s):  
Nuclear Power ◽  
Power Plants ◽  
Tube Bundle ◽  
Fluid Structure Interaction ◽  
Flowing Fluid ◽  
Fluid Structure ◽  
Reduced Order ◽  
Structure Interaction ◽  
Flow Past ◽  
Steam Boilers

Tube bundles in steam boilers of nuclear power plants and nuclear on-board stokehold are known to be exposed to high levels of vibrations under flowing fluid. This coupled fluid-structure problem is still a challenge for engineers, first because of the difficulty to fully understand it, second because of the complexity for setting it up numerically. Although numerical techniques could help the understanding of such a mechanism, a complete simulation of a fluid past a whole elastically mounted tube bundle is currently out of reach for engineering purposes. To get round this problem, the use of a reduced-order model has been proposed with the introduction of the widely used Proper Orthogonal Decomposition (POD) method for a flow past a fixed structure [M. Pomare`de, E. Liberge, A. Hamdouni, E.Longatte, & J.F. Sigrist - Simulation of a fluid flow using a reduced-order modelling by POD approach applied to academic cases; PVP2010, July 18–22, Seattle]. Interesting results have been obtained for the reconstruction of the flow. Here a first step is to propose to consider the case of a flow past a fixed tube bundle configuration in order to check the good reconstruction of the flow. Then, an original approach proposed by Liberge (E. Liberge; POD-Galerking Reduction Models for Fluid-Structure Interaction Problems, PhD Thesis, Universite´ de La Rochelle, 2008) is applied to take into account the fluid-structure interaction characteristic; the so-called “multiphase” approach. This technique allows applying the POD method to a configuration of a flow past an elastically mounted structure. First results on a single circular cylinder and on a tube bundle configuration are encouraging and let us hope that parametric studies or prediction calculations could be set up with such an approach in a future work.

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