Reduced-order modelling by POD-multiphase approach for fluid-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.

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Implicit Coupling of Partitioned Fluid-Structure Interaction Solvers Using a Reduced Order Model

35th AIAA Fluid Dynamics Conference and Exhibit ◽

10.2514/6.2005-5135 ◽

2005 ◽

Cited By ~ 3

Author(s):

Jan Vierendeels

Keyword(s):

Fluid Structure Interaction ◽

Reduced Order Model ◽

Order Model ◽

Fluid Structure ◽

Reduced Order ◽

Structure Interaction

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

Volume 8: 31st Conference on Mechanical Vibration and Noise ◽

10.1115/detc2019-98291 ◽

2019 ◽

Cited By ~ 1

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.

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

ASME 2010 7th International Symposium on Fluid-Structure Interactions, Flow-Sound Interactions, and Flow-Induced Vibration and Noise: Volume 3, Parts A and B ◽

10.1115/fedsm-icnmm2010-30133 ◽

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.

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

ASME 2011 Pressure Vessels and Piping Conference: Volume 4 ◽

10.1115/pvp2011-57787 ◽

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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