Eventos Anais de eventos
COBEM 2023
27th International Congress of Mechanical Engineering
A study about the effects of extensibility in cantilevered pipes conveying fluid under VIV using a modular modeling methodology
Submission Author:
Daniel de Oliveira Tomin , SP
Co-Authors:
Daniel de Oliveira Tomin, Renato Maia Matarazzo Orsino, CELSO Pupo Pesce
Presenter: Daniel de Oliveira Tomin
doi://10.26678/ABCM.COBEM2023.COB2023-1681
Abstract
The aim of this paper is to obtain two planar nonlinear reduced-order models of a relevant, but still under-discussed topic in Fluid-Structure Interactions (FSI) literature, the slender cantilevered pipe conveying fluid subjected to vortex-induced vibrations due to external flow. One of the models considers an inextensible pipe and the other assumes an extensibility condition that is consistent with the conservation of fluid mass inside the tube and Poisson's ratio. The mathematical formulation combines two distinct classic FSI problems: i) The pipe ejecting fluid, which is an open system with an unique dynamical behaviour characterized by the presence of instability associated with a Hopf bifurcation, when a certain critical internal velocity threshold is reached (a previously related work showed that if this extensibility is considered when the ratio of axial and flexural stiffness is low, the critical velocity becomes higher when compared to inextensible models, also affecting the amplitude of the limit cycles encountered); ii) cross-flow vortex-induced vibrations in flexible cylinders, using a phenomenological wake oscillator model with experimental calibrated parameters for lower or upper branch tuning. The models are derived by applying the Extended Hamilton's Principle for nonmaterial volumes along with a modular based strategy, the Modular Modeling Methodology. This approach enables the consideration of nonlinearities associated with the extensibility, conservation of mass and VIV phenomenon by introducing redundant variables and subsystems, simplifying the mathematical manipulation and derivation to obtain the equations of motion of the original system through a recursive algorithm. Some numerical simulations of VIV lock-in scenarios in the upper branch tuning are analyzed. Generally, when only VIV is considered, the maximum transversal displacement of the free end is about 1.4 times the pipe diameter. If an internal velocity below the critical value is investigated, the amplitude is mitigated; and if a value sightly above is utilized, there is an amplification. Therefore, the critical internal flow velocity affects the maximum amplitude of the motion. For a given set of dimensionless parameters, this value changes between the models and different amplitude responses are obtained, showing that a coherent assumption for the extensibility is important in some scenarios.
Keywords
fluid-structure interaction (FSI), Pipe Conveying Fluid, VIV, modular modeling methodology, Phenomenological model, nonlinear dynamics
