## Three-dimensional effects on flag flapping dynamics ; [and], Study and modeling of incompressible highly variable density turbulence in the bubbly wake of a transom stern

##### Author(s)

Banerjee, Sankha, Ph. D. Massachusetts Institute of Technology
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##### Alternative title

3-dimensional effects on flag flapping dynamics

3D effects on flag flapping dynamics

##### Other Contributors

Massachusetts Institute of Technology. Department of Mechanical Engineering.

##### Advisor

Dick K.P. Yue.

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Part I: A classic problem in the field of fluid-structure interaction is the flapping-flag instability. Fluid-mechanical studies of the phenomenon date back to the 19th century, increased in number in recent years with increasingly accurate representations for the coupled fluid-structure interaction. The problem continues to attract attention because the effect of fluid forces and aspect ratio on stability is non-obvious. In the first part of the flapping studies, we examine three-dimensional effects on the flapping dynamics of a flag, modeled as a thin membrane, in a uniform fluid inflow. We consider periodic span-wise variations of length (ignoring edge effects) characterized by discrete span-wise wavenumber. Using linear stability analysis we show the increase in stability with discrete span-wise wavenumber. We confirm the stability analysis and study the nonlinear responses of three-dimensional flapping, using direct numerical simulation of the Navier-Stokes equations on a moving body-fitted computational grid for thin membrane structure undergoing arbitrarily (large) displacement. We perform direct numerical simulations, initialized using normal modes we derive, up to Reynolds number 1000 based on L. For nonlinear evolutions, we identify and characterize the effect of span-wise variations on the fundamental modes and responses of flapping in terms of span-wise standing wave (SW) and travelling wave (TW) modes respectively in the absence and presence of cross flow; and their corresponding flag displacements and wake vortex structures. We report for TW, the flag flapping and vortex shedding frequencies and angles are matched, and are related to the corresponding shedding frequency of SW. When both SW and TW modes are present due to stabilization of drag by the cross-flow, the fluid-flag response trends to be dominated over time by TW with continuous wake structure. In the second part of the flapping work we investigate the absolute or convective nature of the instability of a two-dimensional flapping filament submerged in a uniform fluid inflow. When the structure-to-fluid mass ratio is zero, we show that two families of flapping waves exist, with phase velocities that are equal in magnitude and have opposite signs, increasing the mass ratio for a given Reynolds number increases the phase velocity of the waves propagating in the same direction as the flow, and decreases the phase velocity of the waves propagating opposite to the flow. Using a linearized energy conservation law we show that after a critical value of mass ratio is exceeded the flapping instability is sustained when the fast (positive energy) and the slow (negative energy) waves coalesce creating waves with zero energy which do not require an energy source or a sink to be sustained, and grow exponentially in time. Under such conditions an analytical condition for absolute instability is derived. We further show based on a group velocity criterion, that when the two characteristic speeds have opposite signs the instability is absolute, where as if they have the same sign the instability is convective. A range of mass ratio regimes is found where the instability is absolute and where it is convective; with the unstable flapping amplitude at the instability threshold, satisfying the Klein-Gordon equation. Part II: Accurate prediction of the highly mixed flow in the near field of a surface ship is a challenging and active research topic in Computational Ship Hydrodynamics. The disparity in length and time scales recognizes the importance of accurate bubble source and mixed-phase flow models; whereas the current state of the art models are adhoc at best. Second part of the thesis details the air entrainment characteristics in the incompressible highly variable density turbulent flow-field behind a canonical stern with the inclusion of simple speed/geometry/Reynolds number effects. Using high-resolution two-phase flow data sets generated from high fidelity simulations of a canonical stern simulated down to the scales of bubble entrainment. The study details key variables for: (i) characterization of wake structure, near-wake air entrainment and the nature of incompressible variable density turbulence, underlining the major implications and dominant terms by studying the dynamics of the continuity equation, the momentum equation, the density variance equation, the turbulent mass flux and the turbulent kinetic energy; (ii) the role of non-Boussinesq effects and turbulent mass flux in the wake of the stern, identifying the breaking event to be related to the air-entrainment and subsequent generation of turbulent mass flux and establishing the density intensity as an effective metric; (iii) develop and a priori validate novel multiphase models for turbulent mass flux and turbulent kinetic energy using gradient hypothesis and measuring the model performance for varied geometry/speed/Reynolds number effects. The first part of the thesis advances our understanding in varying applications ranging from the biomechanics of snoring, to improving novel designs for flow energy harvesters. The second part presents a methodology, using high-fidelity simulations coupled to physics-based parameterization of near-field air entrainment about surface ships to help improve mixed-phase turbulent flow models in Computational Ship Hydrodynamics.

##### Description

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2013. Cataloged from PDF version of thesis. Includes bibliographical references (p. 309-328).

##### Date issued

2013##### Department

Massachusetts Institute of Technology. Department of Mechanical Engineering.##### Publisher

Massachusetts Institute of Technology

##### Keywords

Mechanical Engineering.