Numerical Prediction of 3-D Vortex-Induced Vibration of Catenary Riser In Planar and Non-Planar Flows

Vortex-induced vibration (VIV) is one of the most critical issues in deepwater developments due to its resultant fatigue damage to subsea structures such as risers, pipelines and jumpers. Although VIV effects on slender bodies have been comprehensively studied over decades, very few studies have dealt with VIV modelling and prediction of catenary risers in current flows with varying directions leading to complex fluid-structure interactions. This study advances a numerical model to simulate and predict 3-D VIV responses of a catenary riser in three flow orientations, relative to the riser curvature plane, including concave/convex (planar) and perpendicular (non-planar) flows. The model is described by equations of cross-flow and in-line responses of the catenary riser coupled with the hydrodynamic forces modelled by the distributed nonlinear wake oscillators. A finite difference method is applied to solve the coupled fluid-structure dynamic system. To consider the approaching flow in different directions, the vortex-induced lift and drag forces are formulated by accounting for the effect of flow angle of attack and the riser-flow relative velocities. Results show VIV features of a long catenary riser exhibiting a standing and travelling wave response pattern. VIV response amplitudes and oscillation frequencies are predicted and compared with experimental results in the literature for both straight and catenary risers. Overall results highlight the model capability in capturing the effect of approaching flow direction on 3-D VIV of the curved inclined flexible riser.

Planar vortices in a bounded domain with a hole

<p style='text-indent:20px;'>In this paper, we consider the inviscid, incompressible planar flows in a bounded domain with a hole and construct stationary classical solutions with single vortex core, which is closed to the hole. This is carried out by constructing solutions to the following semilinear elliptic problem</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1111"> \begin{document}$ \begin{equation} \begin{cases} -\Delta \psi = \lambda(\psi-\frac{\kappa}{4\pi}\ln\lambda)_+^p,\quad &amp;\text{in}\; \Omega,\\ \psi = \rho_\lambda,\quad &amp;\text{on}\; \partial O_0,\\ \psi = 0,\quad &amp;\text{on}\; \partial\Omega_0, \end{cases} \;\;\;\;\;\;\;\;(1)\end{equation} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id="M1">\begin{document}$ p&gt;1 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M2">\begin{document}$ \kappa $\end{document}</tex-math></inline-formula> is a positive constant, <inline-formula><tex-math id="M3">\begin{document}$ \rho_\lambda $\end{document}</tex-math></inline-formula> is a constant, depending on <inline-formula><tex-math id="M4">\begin{document}$ \lambda $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M5">\begin{document}$ \Omega = \Omega_0\setminus \bar{O}_0 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M6">\begin{document}$ \Omega_0 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M7">\begin{document}$ O_0 $\end{document}</tex-math></inline-formula> are two planar bounded simply-connected domains. We show that under the assumption <inline-formula><tex-math id="M8">\begin{document}$ (\ln\lambda)^\sigma\leq\rho_\lambda\leq (\ln\lambda)^{1-\sigma} $\end{document}</tex-math></inline-formula> for some <inline-formula><tex-math id="M9">\begin{document}$ \sigma&gt;0 $\end{document}</tex-math></inline-formula> small, (1) has a solution <inline-formula><tex-math id="M10">\begin{document}$ \psi_\lambda $\end{document}</tex-math></inline-formula>, whose vorticity set <inline-formula><tex-math id="M11">\begin{document}$ \{y\in \Omega:\, \psi(y)-\kappa+\rho_\lambda\eta(y)&gt;0\} $\end{document}</tex-math></inline-formula> shrinks to the boundary of the hole as <inline-formula><tex-math id="M12">\begin{document}$ \lambda\to +\infty $\end{document}</tex-math></inline-formula>.</p>

Quantifying non-linearity in planar supersonic potential flows

ABSTRACTAn analysis is presented which allows the engineer to quantitatively estimate the validity bounds of aerodynamic methods based in linear potential flows a-priori. The development is limited to quasi-steady planar flows with attached shocks and small body curvature. Perturbation velocities are parameterised in terms of Mach number and flow turning angle by means of a series-expansion for flow velocity based in the method of characteristics. The parameterisation is used to assess the magnitude of non-linear term-groupings relative to linear groups in the full potential equation. This quantification is used to identify dominant nonlinear terms and to estimate the validity of linearising the potential flow equation at a given Mach number and flow turning angle. Example applications include the a-priori estimation of the validity bounds for linear aerodynamic models for supersonic aeroelastic analysis of lifting surfaces and panels.

On some invariant geometric properties in Hele-Shaw flows with small surface tension

In this paper, by applying methods from complex analysis, we analyse the time evolution of the free boundary of a viscous fluid for planar flows in Hele-Shaw cells under injection in the non-zero surface tension case. We study the invariance in time of α-convexity (for α ∈ [0, 1] this is a geometric property which provides a continuous passage from starlikeness to convexity) for bounded domains. In this case we show that the α-convexity property of the moving boundary in a Hele-Shaw flow problem with small surface tension is preserved in time for α ≤ 0. For unbounded domains (with bounded complement) we prove the invariance in time of convexity.