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"Cylinders"
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Near-Perfect Matchings on Cylinders Cm × Pn of Odd Order
A close relationship was established between the number of perfect and nearperfect matchings on cylinders Cm×Pn. Generating functions are obtained for the number of near-perfect matchings in these graphs for fixed odd m ≤ 13. A conjecture is put forth on the properties of the denominators of generating functions for arbitrary odd m.
Conference Proceeding
Experimental investigation of three-dimensional modes in the wake of a rotationally oscillating cylinder
Three-dimensionalities in the wake of flow past a circular cylinder executing sinusoidal rotary oscillations about its axis is studied experimentally. The results of water tunnel experiments on a rotationally oscillating cylinder for Reynolds number of 250 with varying amplitude and forcing frequency are discussed. Qualitative studies using hydrogen bubble and laser-induced fluorescence flow visualisation techniques are performed. Observation made for oscillating amplitude, $\\theta _{0} = {\\rm \\pi}/4$ and $\\theta _{0}=3{\\rm \\pi} /4$, and a low normalised forcing frequency, $FR$, of 0.75 and 0.5, respectively, confirmed a mode having a spanwise non-dimensional wavelength of $\\sim$1.8 which is also observed for a rotating cylinder. On increasing forcing frequency this mode disappears and a new mode with a bean-shaped structure and a much smaller spanwise normalised wavelength of $\\sim$0.8 appears at an $FR$ of 1 and an oscillation amplitude of ${\\rm \\pi} /2$. This mode remains almost stable until a forcing frequency of $FR=1.4$. At higher forcing frequency, $FR=2.75$, and oscillation amplitude of $3{\\rm \\pi} /4$, a mode with cellular structure and a normalised spanwise wavelength of $\\sim$1.6 is identified. The cells in this mode flatten up with increasing downstream distance and are shed alternately with respect to the adjacent cell. Certain combinations of forcing parameters resulted in a forced two-dimensionality of the wake. Quantitative studies using hot-wire measurements and particle image velocimetry confirm the presence of these modes and wake characteristics. Wake mode map in the forcing frequency and amplitude plane is presented showing regions of newly discovered modes and wake lock-on boundaries.
Journal Article
Experimental investigation of flow-induced vibration of a rotating circular cylinder
While flow-induced vibration of bluff bodies has been extensively studied over the last half-century, only limited attention has been given to flow-induced vibration of elastically mounted rotating cylinders. Since recent low-Reynolds-number numerical work suggests that rotation can enhance or suppress the natural oscillatory response, the former could find applications in energy harvesting and the latter in vibration control. The present experimental investigation characterises the dynamic response and wake structure of a rotating circular cylinder undergoing vortex-induced vibration at a low mass ratio (
$m^{\\ast }=5.78$
) over the reduced velocity range leading to strong oscillations. The experiments were conducted in a free-surface water channel with the cylinder vertically mounted and attached to a motor that provided constant rotation. Springs and an air-bearing system allow the cylinder to undertake low-damped transverse oscillations. Under cylinder rotation, the normalised frequency response was found to be comparable to that of a freely vibrating non-rotating cylinder. At reduced velocities consistent with the upper branch of a non-rotating transversely oscillating cylinder, the maximum oscillation amplitude increased with non-dimensional rotation rate up to
$\\unicode[STIX]{x1D6FC}\\approx 2$
. Beyond this, there was a sharp decrease in amplitude. Notably, this critical value corresponds approximately to the rotation rate at which vortex shedding ceases for a non-oscillating rotating cylinder. Remarkably, at
$\\unicode[STIX]{x1D6FC}=2$
there was approximately an 80 % increase in the peak amplitude response compared to that of a non-rotating cylinder. The observed amplitude response measured over the Reynolds-number range of (
$1100\\lesssim Re\\lesssim 6300$
) is significantly different from numerical predictions and other experimental results recorded at significantly lower Reynolds numbers.
Journal Article
Mapping the properties of wake-induced vibration on a circular cylinder
This study conducts experimental investigations into wake-induced vibration (WIV) of a circular cylinder placed downstream of an oscillating cylinder. Surprisingly, it is observed that the previously identified WIV phenomenon, characterized by a sustained increase in amplitude at higher reduced velocities, does not occur when the upstream cylinder oscillates at large amplitudes. Instead, a different phenomenon, which we refer to as the ‘wake-captured vibration’, becomes dominant. The experiments reveal a negative correlation between the vortex-induced vibration amplitude response of the upstream cylinder and the WIV amplitude response of the downstream cylinder. Through a quasi-steady and linear instability analysis, the study demonstrates that the previously proposed wake-displacement mechanism may not be applicable for predicting the cylinder WIV response in the wake of an oscillating body. This is because the lift force gradients across the wake, measured through stationary cylinder experiments, decrease significantly when the upstream cylinder vibrates at higher amplitudes. Consequently, actively controlled vibration experiments are conducted to systematically map the hydrodynamic properties of the downstream cylinder vibrating in the wake of an oscillating cylinder. The findings align with observations from free-vibration experiments, and help to explain the amplitude and frequency response of WIV. Additionally, wake visualization through particle image velocimetry is conducted to provide further insights into the complex wake and vortex–body interactions.
Journal Article
Nonlinear mode decomposition with convolutional neural networks for fluid dynamics
We present a new nonlinear mode decomposition method to visualize decomposed flow fields, named the mode decomposing convolutional neural network autoencoder (MD-CNN-AE). The proposed method is applied to a flow around a circular cylinder at the Reynolds number$Re_{D}=100$as a test case. The flow attributes are mapped into two modes in the latent space and then these two modes are visualized in the physical space. Because the MD-CNN-AEs with nonlinear activation functions show lower reconstruction errors than the proper orthogonal decomposition (POD), the nonlinearity contained in the activation function is considered the key to improving the capability of the model. It is found by applying POD to each field decomposed using the MD-CNN-AE with hyperbolic tangent activation such that a single nonlinear MD-CNN-AE mode contains multiple orthogonal bases, in contrast to the linear methods, i.e. POD and MD-CNN-AE with linear activation. We further assess the proposed MD-CNN-AE by applying it to a transient process of a circular cylinder wake in order to examine its capability for flows containing high-order spatial modes. The present results suggest a great potential for the nonlinear MD-CNN-AE to be used for feature extraction of flow fields in lower dimensions than POD, while retaining interpretable relationships with the conventional POD modes.
Journal Article
Deep reinforcement transfer learning of active control for bluff body flows at high Reynolds number
We demonstrate how to accelerate the computationally taxing process of deep reinforcement learning (DRL) in numerical simulations for active control of bluff body flows at high Reynolds number ($Re$) using transfer learning. We consider the canonical flow past a circular cylinder whose wake is controlled by two small rotating cylinders. We first pre-train the DRL agent using data from inexpensive simulations at low $Re$, and subsequently we train the agent with small data from the simulation at high $Re$ (up to $Re=1.4\\times 10^5$). We apply transfer learning (TL) to three different tasks, the results of which show that TL can greatly reduce the training episodes, while the control method selected by TL is more stable compared with training DRL from scratch. We analyse for the first time the wake flow at $Re=1.4\\times 10^5$ in detail and discover that the hydrodynamic forces on the two rotating control cylinders are not symmetric.
Journal Article
Deep reinforcement learning finds a new strategy for vortex-induced vibration control
As a promising machine learning method for active flow control (AFC), deep reinforcement learning (DRL) has been successfully applied in various scenarios, such as the drag reduction for stationary cylinders under both laminar and weakly turbulent conditions. However, current applications of DRL in AFC still suffer from drawbacks including excessive sensor usage, unclear search paths and insufficient robustness tests. In this study, we aim to tackle these issues by applying DRL-guided self-rotation to suppress the vortex-induced vibration (VIV) of a circular cylinder under the lock-in condition. With a state space consisting only of the acceleration, velocity and displacement of the cylinder, the DRL agent learns an effective control strategy that successfully suppresses the VIV amplitude by $99.6\\,\\%$. Through systematic comparisons between different combinations of sensory-motor cues as well as sensitivity analysis, we identify three distinct stages of the search path related to the flow physics, in which the DRL agent adjusts the amplitude, frequency and phase lag of the actions. Under the deterministic control, only a little forcing is required to maintain the control performance, and the VIV frequency is only slightly affected, showing that the present control strategy is distinct from those utilizing the lock-on effect. Through dynamic mode decomposition analysis, we observe that the growth rates of the dominant modes in the controlled case all become negative, indicating that DRL remarkably enhances the system stability. Furthermore, tests involving various Reynolds numbers and upstream perturbations confirm that the learned control strategy is robust. Finally, the present study shows that DRL is capable of controlling VIV with a very small number of sensors, making it effective, efficient, interpretable and robust. We anticipate that DRL could provide a general framework for AFC and a deeper understanding of the underlying physics.
Journal Article
Data-driven prediction of unsteady flow over a circular cylinder using deep learning
Unsteady flow fields over a circular cylinder are used for training and then prediction using four different deep learning networks: generative adversarial networks with and without consideration of conservation laws; and convolutional neural networks with and without consideration of conservation laws. Flow fields at future occasions are predicted based on information on flow fields at previous occasions. Predictions of deep learning networks are made for flow fields at Reynolds numbers that were not used during training. Physical loss functions are proposed to explicitly provide information on conservation of mass and momentum to deep learning networks. An adversarial training is applied to extract features of flow dynamics in an unsupervised manner. Effects of the proposed physical loss functions and adversarial training on predicted results are analysed. Captured and missed flow physics from predictions are also analysed. Predicted flow fields using deep learning networks are in good agreement with flow fields computed by numerical simulations.
Journal Article
Numerical analyses of the flow past a short rotating cylinder
This work studies the three-dimensional flow dynamics around a rotating circular cylinder of finite length, whose axis is positioned perpendicular to the streamwise direction. Direct numerical simulations and global stability analyses are performed within a parameter range of Reynolds number $Re=DU_\\infty /\\nu <500$ (based on cylinder diameter $D$, uniform incoming flow velocity $U_\\infty$), length-to-diameter ratio ${\\small \\text{AR}}=L/D\\leq 2$ and dimensionless rotation rate $\\alpha =D\\varOmega /2U_\\infty \\leq 2$ (where $\\varOmega$ is rotation rate). By solving Navier–Stokes equations, we investigated the wake patterns and explored the phase diagrams of the lift and drag coefficients. For a cylinder with ${\\small \\text{AR}}=1$, we found that when the rotation effect is weak ($0\\leq \\alpha \\lesssim 0.3$), the wake pattern is similar to the unsteady wake past the non-rotating finite-length cylinder, but with a new linear unstable mode competing to dominate the saturation state of the wake. The flow becomes stable for $0.3\\lesssim \\alpha \\lesssim 0.9$ when $Re<360$. When the rotation effect is strong ($\\alpha \\gtrsim 0.9$), new low-frequency wake patterns with stronger oscillations emerge. Generally, the rotation effect first slightly decreases and then sharply increases the $Re$ threshold of the flow instability when $\\alpha$ is relatively small, but significantly decreases the threshold at high $\\alpha$ ($0.9<\\alpha \\leq 2$). Furthermore, the stability analyses based on the time-averaged flows and on the steady solutions demonstrate the existence of multiple unstable modes undergoing Hopf bifurcation, greatly influenced by the rotation effect. The shapes of these global eigenmodes are presented and compared, as well as their structural sensitivity, visualising the flow region important for the disturbance development with rotation. This research contributes to our understanding of the complex bluff-body wake dynamics past this critical configuration.
Journal Article