Rajeev Jaiman

In this work, we present the development of a new computational framework based on the stabilized variational finite element methods for unsteady cavitating flows and application to flow-induced vibrations of freely oscillating hydrofoils. The ultimate goal is to build a robust and accurate high-fidelity framework for the computational study of the coupled multiphase fluid-structure dynamics and noise reduction of marine propellers. The first part of this work involves a delineation of the systematic development and testing of the new computational framework. We propose novel linearizations of the governing cavitation partial differential equations (PDEs) for numerical modeling. Numerical challenges arising due to the particular characteristics of two-phase cavitating flows and fluid-structure interaction are addressed. We demonstrate the ability of the numerical implementation to accurately capture prominent features of cavitating flows such as bubble collapse, steady and unsteady partial cavitation, cavity shedding, and re-entrant jet formation. The second part focuses on the application of the developed computational framework for flow-induced vibrations of freely oscillating hydrofoils with unsteady partial cavitating conditions. The interaction dynamics of the hydrofoil with the fluid forces are represented as an elastically mounted rigid body. A frequency lock-in mechanism of the unsteady cavity and vortex shedding to a sub-harmonic of the structural natural frequency is observed to sustain high-amplitude transverse oscillations of the hydrofoil. This exploratory work paves the way for the coupled multiphase hydroelastic interaction of propellers with the target of noise mitigation by active or passive control mechanisms.

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This work presents data-driven predictions of nonlinear dynamical systems involving unsteady flow and fluid-structure interaction. Of particular interest is to develop a new simulation framework integrating high-fidelity models with deep learning towards Digital Twin. The final goal is to learn and predict the coupled dynamics via the digital twin of ship vessels and propellers. End-to-end deep learning-based reduced order models (DL-ROMs) are presented for digital twin development.The first part of this study develops an overall framework for DL-ROMs. The emphasis is to investigate the predictive performance of the hybrid DL-ROMs, which vary in obtaining the low-dimensional features, i.e., proper orthogonal decomposition (POD) and convolutional autoencoders. The low-dimensional features are evolved in time using recurrent neural networks (RNNs). This leads to the formulation of two DL-ROM frameworks: the POD-RNN and the convolutional recurrent autoencoder network (CRAN). To assess data-driven predictions, POD-RNN and CRAN are applied to predict unsteady flows and instantaneous forces for flow past static bluff bodies. We perform flow prediction analysis for a configuration of side-by-side cylinders with wake interference. For systems with moving interfaces and three-dimensional (3D) geometries, we develop modular DL-ROM techniques.The second part of this study includes model reduction strategies to predict vortex-induced vibration and 3D unsteady flows. The knowledge gained in the previous parts is utilized to develop partitioned and scalable DL-ROMs for unsteady flows with moving interfaces and parametric effects. We first develop a partitioned DL-ROM framework for fluid-structure interaction. The novel multi-level DL-ROM combines the effect of POD-RNN and CRAN by modular learning of two physical fields independently. While POD-RNN provides extraction of the fluid-structure interface, the CRAN enables the prediction of flow fields. For time series prediction of 3D flows, we present a 3D CRAN-based framework for predicting the fluid forces and vortex shedding patterns. We provide an assessment of improving learning capabilities using transfer learning for complex 3D flows with variable Reynolds numbers. The simplicity and computational efficiency of the proposed DL-ROMs allow investigation for various geometries and physical parameters. This research opens ways for digital twin development for near real-time prediction of unsteady flows and fluid-structure interaction.

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Whiskers in some mammals, such as rats and seals, have a mysterious level of sensing ability. A whisker interacting with the fluid flow can sense minuscule aero/hydrodynamic information and turn this information into an understanding of the environment. Our present work investigates the fluid-structure interaction of a flexible cantilever cylinder, as a canonical model of a whisker, to help understand how a rat or a seal whisker vibrates in response to low-speed air or water flow. We employ a fully-coupled fluid-structure solver based on the three-dimensional Navier-Stokes and structural equations to examine the dynamics of the cylinder. Of particular interest is to explore the possibility of flow-induced vibrations at laminar subcritical Reynolds numbers, where no periodic vortex shedding pattern is present. We show that the flexible cantilever cylinder could undergo sustained oscillations in this Reynolds regime when certain conditions are satisfied. The vibration frequencies are shown to match the cylinder's first- or second-mode natural frequency. The range of the frequency match, known as the lock-in regime, is found to have a strong dependence on the Reynolds number and mass ratio. Unlike the steady wake behind a stationary rigid cylinder, the wake of the flexible cantilever cylinder in the water flow is shown to become unstable at Reynolds numbers as low as 22 for a particular range of system parameters. We find that the cylinder could also experience sustained oscillations when positioned in the wake of a rigid stationary cylinder in a tandem configuration. For the cylinder in airflow, we show that a wavy pattern in the shear layer is the dominant feature of the wake. These findings provide a unified understanding of the flow-induced vibration phenomenon in flexible cantilever cylinders and lay the foundation for designing novel flow-measurement sensors for the next-generation underwater and aerial vehicles.

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In this work, we present the coupled dynamics and stability predictions of marine vessels in the ocean environment, with particular focus on the synergy of physics-based and data-driven models towards Digital Twin. The ultimate goal is to predict and control the coupled dynamics and stability in normal and extreme conditions via the digital twin of marine vessels and propellers.The first part of this study includes a high-dimensional representation of multiphase fluid-structure interaction via the nonlinear system of partial differential equations. The second part of this study includes the model reduction of flow-induced vibrations (FIV) and the application of the knowledge gained in the previous parts in efficient parametric design optimization and control of marine tugboats. Towards this goal, two advanced physics-based system identification approaches are considered via projection-based and deep-learning-based reduced-order models. The projection-based approach includes a linear reduced-order model (ROM) for stability prediction using the eigensystem realization algorithm (ERA), which provides a low-order approximation of unsteady flow dynamics in the neighbourhood of equilibrium steady state. We perform a systematic ROM-based stability analysis to understand the frequency lock-in mechanism and self-sustained FIV phenomenon by examining eigenvalue trajectories.However, for high Reynolds number flows and near real-time feedback control, this goal can only be achieved through the recent advances in nonlinear model reduction and deep learning (DL) algorithms. To demonstrate this idea, we have developed a data-driven coupling for predicting unsteady forces and vortex-induced vibration (VIV) lock-in by using a long short-term memory network (LSTM) as a DL-based ROM technique. The structure of the LSTM has the format of a nonlinear state-space model (NLSS) and provides a nonlinear mapping of input-output dynamics that can potentially predict the dynamics for a longer horizon utilized for the stability predictions. The simplicity and computational efficiency of the proposed ROMs allow investigation of the FIV mechanism for a variety of geometries and parameters, and open ways for the development of control devices and on-board and in real-time predictions.

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