18 results
Deep reinforcement transfer learning of active control for bluff body flows at high Reynolds number
- Zhicheng Wang, Dixia Fan, Xiaomo Jiang, Michael S. Triantafyllou, George Em Karniadakis
-
- Journal:
- Journal of Fluid Mechanics / Volume 973 / 25 October 2023
- Published online by Cambridge University Press:
- 20 October 2023, A32
-
- Article
- Export citation
-
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.
Mapping the properties of the vortex-induced vibrations of flexible cylinders in uniform oncoming flow
- Dixia Fan, Zhicheng Wang, Michael S. Triantafyllou, George Em Karniadakis
-
- Journal:
- Journal of Fluid Mechanics / Volume 881 / 25 December 2019
- Published online by Cambridge University Press:
- 25 October 2019, pp. 815-858
-
- Article
- Export citation
-
Flexible structures placed within an oncoming flow exhibit far more complex vortex-induced dynamics than flexibly mounted rigid cylinders, because they involve the distributed interaction between the structural and wake dynamics along the entire span. Hence, mapping the well-understood properties of rigid cylinder vibrations to those of strings and beams has been elusive. We show here with a combination of experiments, conducted at Reynolds number, $Re$ from 250 to 2300, and computational fluid dynamics that such a mapping is possible for flexible structures in uniform flow undergoing combined cross-flow and in-line oscillations, but only when additional concepts are introduced to model the extended coupling of the flow and the structure. The in-line response consists of largely standing waves that define cells, each cell spanning the distance between adjacent nodes, over which stable vortical patterns form, whose features (‘2S’ versus ‘P$+$S’) depend strongly on the true reduced velocity, $V_{r}=U/f_{y}d$, where $U$ is the inflow velocity, $f_{y}$ is the cross-flow vibration frequency and $d$ is the cylinder diameter, and the phase angle between in-line and cross-flow response; while the cross-flow response may contain travelling waves, breaking the symmetry of the problem. The axial distribution of the highly variable effective added masses in the cross-flow and in-line directions, and the local phase angle between in-line and cross-flow motion determine the single frequency of cross-flow response, while the in-line response vibrates at twice the cross-flow frequency. The cross-flow and in-line lift coefficients in phase with velocity depend strongly on the true reduced velocity but also on the local phase angle between in-line and cross-flow motions. Modal shapes can be defined for in-line and cross-flow, based on the resemblance of the response to conventional modes, which can be in the ratio of either ‘$2n/n$’ or ‘$(2n-1)/n$’, where $n$ is the order of the cross-flow response mode. We use an underwater optical tracking system to reconstruct the sectional fluid forces in a flexible structure and show that, once the cross-flow and in-line motion features are known, employing strip theory and the hydrodynamic coefficients obtained from forced rigid cylinder experiments allows us to predict the distributed forces accurately.
Deep learning of vortex-induced vibrations
- Maziar Raissi, Zhicheng Wang, Michael S. Triantafyllou, George Em Karniadakis
-
- Journal:
- Journal of Fluid Mechanics / Volume 861 / 25 February 2019
- Published online by Cambridge University Press:
- 19 December 2018, pp. 119-137
-
- Article
- Export citation
-
Vortex-induced vibrations of bluff bodies occur when the vortex shedding frequency is close to the natural frequency of the structure. Of interest is the prediction of the lift and drag forces on the structure given some limited and scattered information on the velocity field. This is an inverse problem that is not straightforward to solve using standard computational fluid dynamics methods, especially since no information is provided for the pressure. An even greater challenge is to infer the lift and drag forces given some dye or smoke visualizations of the flow field. Here we employ deep neural networks that are extended to encode the incompressible Navier–Stokes equations coupled with the structure’s dynamic motion equation. In the first case, given scattered data in space–time on the velocity field and the structure’s motion, we use four coupled deep neural networks to infer very accurately the structural parameters, the entire time-dependent pressure field (with no prior training data), and reconstruct the velocity vector field and the structure’s dynamic motion. In the second case, given scattered data in space–time on a concentration field only, we use five coupled deep neural networks to infer very accurately the vector velocity field and all other quantities of interest as before. This new paradigm of inference in fluid mechanics for coupled multi-physics problems enables velocity and pressure quantification from flow snapshots in small subdomains and can be exploited for flow control applications and also for system identification.
An entropy-viscosity large eddy simulation study of turbulent flow in a flexible pipe
- Zhicheng Wang, Michael S. Triantafyllou, Yiannis Constantinides, George Em Karniadakis
-
- Journal:
- Journal of Fluid Mechanics / Volume 859 / 25 January 2019
- Published online by Cambridge University Press:
- 23 November 2018, pp. 691-730
-
- Article
- Export citation
-
We present a new approach – the entropy-viscosity method (EVM) – for numerical modelling of high Reynolds number flows and investigate its potential by simulating fully developed incompressible turbulent flow, first in a stationary pipe and subsequently in a flexible pipe. This method, which was first proposed by Guermond et al. (J. Comput. Phys., vol. 230 (11), 2011, pp. 4248–4267), introduces the concept of entropy viscosity, computed based on the nonlinear localized residual obtained from the energy equation. Specifically, this nonlinear viscosity based on the local size of entropy production is added to the spectral element discretization employed in our work for stabilization at insufficient resolution. Unlike its original formulation, which includes an ad hoc tuneable parameter $\unicode[STIX]{x1D6FC}$, here, we determine the value of $\unicode[STIX]{x1D6FC}$ by assuming that the entropy viscosity is analogous to the eddy viscosity of the Smagorinsky model. However, the overall approach has the flavour of the implicit large eddy simulation (ILES) instead of the standard large eddy simulation (LES). Given the empiricism of our approach, we have performed systematic studies of homogeneous isotropic turbulence for validation (see appendix A). We have also carried out a more complete numerical simulation study to investigate incompressible turbulent flow in a stationary pipe at $Re_{D}=5300$ and $Re_{D}=44\,000$, following the work of Wu & Moin (J. Fluid Mech., vol. 608, 2008, pp. 81–112) who performed very accurate direct numerical simulations (DNS) of these two cases. We found that the mean flow, turbulence fluctuations, and two-point correlations of the EVM-based LES are in good agreement with the DNS of Wu & Moin despite the fact that we employed grids with resolution two orders of magnitude smaller. If we instead use the standard Smagorinsky model in our simulations, the computations become unstable due to insufficient resolution of the smaller scales. Another important difference is that the entropy-viscosity model scales with the cube of the distance from the wall and approaches zero at the wall, which is theoretically correct, as shown by our a posteriori tests. Based on the validated EVM approach, we then simulated fully developed turbulent flow at $Re_{D}=5300$ in a flexible pipe subject to prescribed vibrations in the cross-flow plane corresponding to a standing wave of amplitude $A$ and wavelength $\unicode[STIX]{x1D706}=3D$, where $D=2R$ is the pipe diameter and $R$ is the radius. We have simulated 11 cases corresponding to increasing values of wave steepness $s_{o}=2A/\unicode[STIX]{x1D706}$, with $s_{o}\in [0,0.067]$. We found a quadratic dependence of the friction factor on $s_{o}$ with the minimum at approximately $s_{o}\approx 0.01$, so, surprisingly, we have a slight decrease in drag at first and then a substantial increase compared to the stationary pipe. To obtain the turbulence statistics, we averaged the simulated flow over twenty time periods at the nodes and anti-nodes separately. We found substantial changes in the mean velocity profile at distances $(1-r)^{+}>5$ while the peaks of turbulent intensities were amplified by 50 % in the axial direction and by 200 % in the normal and azimuthal directions at $s_{o}=0.067$. The peak shear stress at the node increased by more than 200 % whereas at the anti-node it attained negative values. Turbulent budgets revealed large changes close to the wall at $(1-r)^{+}<50$ while flow visualizations showed that many more strong worm-like vortices were generated in the near-wall regions compared to the stationary pipe. We have also computed various spatio-temporal correlations that show that the pressure fluctuations are very sensitive to the pipe vibration and scale quadratically with $s_{o}$. Both pressure and velocity correlations exhibit cellular patterns consistent with the standing-wave pipe motion.
Independent caudal fin actuation enables high energy extraction and control in two-dimensional fish-like group swimming
- Amy Gao, Michael S. Triantafyllou
-
- Journal:
- Journal of Fluid Mechanics / Volume 850 / 10 September 2018
- Published online by Cambridge University Press:
- 04 July 2018, pp. 304-335
-
- Article
- Export citation
-
We study through numerical simulation the optimal hydrodynamic interactions and basic vorticity control mechanisms for two fish-like bodies swimming in tandem. We show that for a fish swimming in the wake of an upstream fish, using independent pitch control of its caudal fin, in addition to optimized body motion, results in reduction of the energy needed for self-propulsion by more than 50 %, providing a quasi-propulsive efficiency of 90 %, up from 60 % without independent caudal fin control. Such high efficiency is found over a narrow parametric range and is possible only when the caudal fin is allowed to pitch independently from the motion of the main body. We identify the vorticity control mechanisms employed by the body and tail to achieve this remarkable performance through thrust augmentation and destructive interference with the upstream fish-generated vortices. A high sensitivity of the propulsive performance to small variations in caudal fin parameters is found, underlying the importance of accurate flow sensing and feedback control. We further demonstrate that using lateral line-like flow measurements to drive an unscented Kalman filter, the near-field vortices can be localized within 1 % of the body length, and be used with a phase-lock controller to drive the body and tail undulation of a self-propelled fish, moving within the wake of an upstream fish, to stably reach the optimal gait and fully achieve maximum energy extraction.
Direct numerical simulations of two-phase flow in an inclined pipe
- Fangfang Xie, Xiaoning Zheng, Michael S. Triantafyllou, Yiannis Constantinides, Yao Zheng, George Em Karniadakis
-
- Journal:
- Journal of Fluid Mechanics / Volume 825 / 25 August 2017
- Published online by Cambridge University Press:
- 20 July 2017, pp. 189-207
-
- Article
- Export citation
-
We study the instability mechanisms leading to slug flow formation in an inclined pipe subject to gravity forces. We use a phase-field approach, where the Cahn–Hillard model is used to model the interface. At the inlet, a stratified flow is imposed with a specified velocity profile. We validate our numerical results by comparing against previous theoretical models and by predicting the various flow regimes for horizontal and inclined pipes, including stratified flow, slug flow, dispersed bubble flow and annular flow. Subsequently, we focus on slug formation in an inclined pipe and connect its appearance with specific vortical dynamics. A two-dimensional channel geometry is first considered. When the heavy fluid is injected as the top layer, inverted vortex shedding emerges, which periodically impacts on the bottom wall, as it develops further downstream. The accumulation of heavy fluid in the bottom wall causes a back flow that induces rolling waves and interacts with the upstream jet. When the heavy fluid is placed as the bottom layer, the heavy fluid accumulates and initially forms a massive slug at the bottom region, close to the inlet. Subsequently, the heavy fluid slug starts to break into smaller pieces, some of which translate along the pipe. During the accumulation phase, a back flow forms also generating rolling waves. Occasionally, a rolling wave can reach the top of the pipe and form a new slug. To describe the generation of vorticity from the two-phase interface and pipe walls in the slug formation, we study the circulation dynamics and connect it with the resulting two-phase flow patterns. Finally, we conduct three-dimensional (3-D) simulations in a circular pipe and compare the differences between the 3-D flow patterns and its circulation dynamics against the 2-D simulation results.
Optimal undulatory swimming for a single fish-like body and for a pair of interacting swimmers
- Audrey P. Maertens, Amy Gao, Michael S. Triantafyllou
-
- Journal:
- Journal of Fluid Mechanics / Volume 813 / 25 February 2017
- Published online by Cambridge University Press:
- 20 January 2017, pp. 301-345
-
- Article
- Export citation
-
We establish through numerical simulation conditions for optimal undulatory propulsion for a single fish, and for a pair of hydrodynamically interacting fish, accounting for linear and angular recoil. We first employ systematic two-dimensional (2-D) simulations to identify conditions for minimal propulsive power of a self-propelled fish, and continue with targeted 3-D simulations for a danio-like fish; all at Reynolds number 5000. We find that the Strouhal number, phase angle between heave and pitch at the trailing edge, and angle of attack are principal parameters. For 2-D simulations, imposing a deformation based on measured displacement for carangiform swimming provides, at best, efficiency of 35 %, which increases to 50 % for an optimized motion; for a 3-D fish, the efficiency increases from 22 % to 34 %. Indeed, angular recoil has significant impact on efficiency, and optimized body bending requires maximum bending amplitude upstream of the trailing edge. Next, we turn to 2-D simulation of two hydrodynamically interacting fish. We find that the upstream fish benefits energetically only for small distances. In contrast, the downstream fish can benefit at any position that allows interaction with the upstream wake, provided its body motion is timed appropriately with respect to the oncoming vortices. For an in-line configuration, one body length apart, the efficiency of the downstream fish can increase from 50 % to 60 %; for an offset arrangement it can reach 80 %. This proves that in groups of fish, energy savings can be achieved for downstream fish through interaction with oncoming vortices, even when the downstream fish lies directly inside the jet-like flow of an upstream fish.
The onset of vortex-induced vibrations of a flexible cylinder at large inclination angle
- Rémi Bourguet, Michael S. Triantafyllou
-
- Journal:
- Journal of Fluid Mechanics / Volume 809 / 25 December 2016
- Published online by Cambridge University Press:
- 09 November 2016, pp. 111-134
-
- Article
- Export citation
-
The onset of the vortex-induced vibration (VIV) regime of a flexible cylinder inclined at $80^{\circ }$ within a uniform current is studied by means of direct numerical simulations, at Reynolds number $500$ based on the body diameter and inflow velocity magnitude. A range of values of the reduced velocity, defined as the inverse of the fundamental natural frequency, is examined in order to capture the emergence of the body responses and explore the concomitant reorganization of the flow and fluid forcing. Additional simulations at normal incidence confirm that the independence principle, which states that the system behaviour is determined by the normal inflow component, does not apply at such large inclination angle. Contrary to the normal incidence case, the free vibrations of the inclined cylinder arise far from the Strouhal frequency, i.e. the vortex shedding frequency downstream of a fixed rigid cylinder. The trace of the stationary body wake is found to persist beyond the vibration onset: the flow may still exhibit an oblique component that relates to the slanted vortex shedding pattern observed in the absence of vibration. This flow component which occurs close to the Strouhal frequency, at a high and incommensurable frequency compared to the vibration frequency, is referred to as Strouhal component; it induces a high-frequency component in fluid forcing. The vibration onset is accompanied by the appearance of novel, low-frequency components of the flow and fluid forcing which are synchronized with body motion. This second dominant flow component, referred to as lock-in component, is characterized by a parallel spatial pattern. The Strouhal and lock-in components of the flow coexist over a range of reduced velocities, with variable contributions, which results in a variety of mixed wake patterns. The transition from oblique to parallel vortex shedding that occurs during the amplification of the structural responses, is driven by the opposite trends of these two component contributions: the decrease of the Strouhal component magnitude associated with the progressive disappearance of the high-frequency force component, and simultaneously, the increase of the lock-in component magnitude, which dominates once the fully developed VIV regime is reached and the flow dynamics is entirely governed by wake–body synchronization.
The flow dynamics of the garden-hose instability
- Fangfang Xie, Xiaoning Zheng, Michael S. Triantafyllou, Yiannis Constantinides, George Em Karniadakis
-
- Journal:
- Journal of Fluid Mechanics / Volume 800 / 10 August 2016
- Published online by Cambridge University Press:
- 12 July 2016, pp. 595-612
-
- Article
- Export citation
-
We present fully resolved simulations of the flow–structure interaction in a flexible pipe conveying incompressible fluid. It is shown that the Reynolds number plays a significant role in the onset of flutter for a fluid-conveying pipe modelled through the classic garden-hose problem. We investigate the complex interaction between structural and internal flow dynamics and obtain a phase diagram of the transition between states as function of three non-dimensional quantities: the fluid-tension parameter, the dimensionless fluid velocity and the Reynolds number. We find that the flow patterns inside the pipe strongly affect the type of induced motion. For unsteady flow, if there is symmetry along a direction, this leads to in-plane motion whereas breaking of the flow symmetry results in both in-plane and out-of-plane motions. Hence, above a critical Reynolds number, complex flow patterns result for the vibrating pipe as there is continuous generation of new vorticity due to the pipe wall acceleration, which is subsequently shed in the confined space of the interior of the pipe.
Wake-induced ‘slaloming’ response explains exquisite sensitivity of seal whisker-like sensors
- Heather R. Beem, Michael S. Triantafyllou
-
- Journal:
- Journal of Fluid Mechanics / Volume 783 / 25 November 2015
- Published online by Cambridge University Press:
- 16 October 2015, pp. 306-322
-
- Article
- Export citation
-
Blindfolded harbour seals are able to use their uniquely shaped whiskers to track vortex wakes left by moving animals and identify objects that passed by 30 s earlier, an impressive feat, as the flow features have velocities as low as $1~\text{mm}~\text{s}^{-1}$. The seals sense while swimming, hence their whiskers are sensitive enough to detect small-scale changes in the flow, while rejecting self-generated flow noise. Here we identify and illustrate a novel flow mechanism, causing a large-amplitude ‘slaloming’ whisker response, which allows artificial whiskers with the identical unique undulatory geometry as those of the harbour seal to detect the features of minute flow fluctuations when placed within wakes. Whereas in open water the whisker responds with very low-amplitude vibration, once within a wake, it oscillates with large amplitude and, importantly, its response frequency coincides with the Strouhal frequency of the upstream cylinder, making the detection of an upstream wake and an estimation of the size and shape of the wake-generating body possible. This mechanism has some similarities with the flow mechanisms observed in actively controlled propulsive foils within upstream wakes and trout swimming behind bluff cylinders in a stream, but there are also differences caused by the unique whisker morphology, which enables it to respond passively and within a much wider parametric range.
U-shaped fairings suppress vortex-induced vibrations for cylinders in cross-flow
- Fangfang Xie, Yue Yu, Yiannis Constantinides, Michael S. Triantafyllou, George Em Karniadakis
-
- Journal:
- Journal of Fluid Mechanics / Volume 782 / 10 November 2015
- Published online by Cambridge University Press:
- 09 October 2015, pp. 300-332
-
- Article
- Export citation
-
We employ three-dimensional direct and large-eddy numerical simulations of the vibrations and flow past cylinders fitted with free-to-rotate U-shaped fairings placed in a cross-flow at Reynolds number $100\leqslant \mathit{Re}\leqslant 10\,000$. Such fairings are nearly neutrally buoyant devices fitted along the axis of long circular risers to suppress vortex-induced vibrations (VIVs). We consider three different geometric configurations: a homogeneous fairing, and two configurations (denoted A and AB) involving a gap between adjacent segments. For the latter two cases, we investigate the effect of the gap on the hydrodynamic force coefficients and the translational and rotational motions of the system. For all configurations, as the Reynolds number increases beyond 500, both the lift and drag coefficients decrease. Compared to a plain cylinder, a homogeneous fairing system (no gaps) can help reduce the drag force coefficient by 15 % for reduced velocity $U^{\ast }=4.65$, while a type A gap system can reduce the drag force coefficient by almost 50 % for reduced velocity $U^{\ast }=3.5,4.65,6$, and, correspondingly, the vibration response of the combined system, as well as the fairing rotation amplitude, are substantially reduced. For a homogeneous fairing, the cross-flow amplitude is reduced by about 80 %, whereas for fairings with a gap longer than half a cylinder diameter, VIVs are completely eliminated, resulting in additional reduction in the drag coefficient. We have related such VIV suppression or elimination to the features of the wake flow structure. We find that a gap causes the generation of strong streamwise vorticity in the gap region that interferes destructively with the vorticity generated by the fairings, hence disorganizing the formation of coherent spanwise cortical patterns. We provide visualization of the incoherent wake flow that leads to total elimination of the vibration and rotation of the fairing–cylinder system. Finally, we investigate the effect of the friction coefficient between cylinder and fairing. The effect overall is small, even when the friction coefficients of adjacent segments are different. In some cases the equilibrium positions of the fairings are rotated by a small angle on either side of the centreline, in a symmetry-breaking bifurcation, which depends strongly on Reynolds number.
The boundary layer instability of a gliding fish helps rather than prevents object identification
- Audrey P. Maertens, Michael S. Triantafyllou
-
- Journal:
- Journal of Fluid Mechanics / Volume 757 / 25 October 2014
- Published online by Cambridge University Press:
- 19 September 2014, pp. 179-207
-
- Article
- Export citation
-
Inspired by the function of the lateral line in aquatic animals, we study the shape identification of a stationary cylinder through pressure measurements made by sensors located on the surface of a steadily moving foil, modelling a fish gliding in close proximity to an object. Comparing experimental results, potential flow predictions and viscous simulations, we first show that the pressure in the boundary layer of the foil is significantly affected by unsteady viscous effects, especially in the posterior half of the foil. Therefore, even after the effects of the boundary layer thickness are accounted for, potential flow predictions are inaccurate. Subsequently, we show that the spatial features of the unsteady patterns developing when the foil is moving near a cylinder can be predicted accurately through linear stability analysis of the average boundary layer velocity profile under open water conditions. Because these unsteady patterns result from amplification of the potential flow-like disturbance caused in the front part of the foil, they are specific to the cylinder that generated them and could be used to identify its shape. We develop and demonstrate a methodology to calculate the unsteady pressure based on combining potential flow predictions with results from linear stability analysis of the boundary layer. The findings can be useful for object identification in underwater vehicles, and support the intriguing possibility that the significant viscous effects caused by nearby bodies on the fish boundary layer, far from preventing detection, could actually be used by animals to identify objects.
Adding in-line motion and model-based optimization offers exceptional force control authority in flapping foils
- Jacob S. Izraelevitz, Michael S. Triantafyllou
-
- Journal:
- Journal of Fluid Mechanics / Volume 742 / 10 March 2014
- Published online by Cambridge University Press:
- 21 February 2014, pp. 5-34
-
- Article
- Export citation
-
We study experimentally the effect of adding an in-line oscillatory motion to the oscillatory heaving and pitching motion of flapping foils that use a power downstroke. We show that far from being a limitation imposed by the muscular structure of certain animals, in-line motion can be a powerful means to either substantially augment the mean lift, or reduce oscillatory lift and increase thrust; propulsive efficiency can also be increased. We also show that a model-based optimization scheme that is used to drive an iterative sequence of experimental runs provides exceptional ability for flapping foils to tightly vector and keep the force in a desired direction, hence improving performance in locomotion and manoeuvring. Flow visualization results, using particle image velocimetry, establish the connection of distinct wake patterns with flapping modes associated with high lift forces, or modes of high thrust and low lift forces.
Distributed lock-in drives broadband vortex-induced vibrations of a long flexible cylinder in shear flow
- Rémi Bourguet, George Em Karniadakis, Michael S. Triantafyllou
-
- Journal:
- Journal of Fluid Mechanics / Volume 717 / 25 February 2013
- Published online by Cambridge University Press:
- 01 February 2013, pp. 361-375
-
- Article
- Export citation
-
A slender flexible body immersed in sheared cross-flow may exhibit vortex-induced vibrations (VIVs) involving a wide range of excited frequencies and structural wavenumbers. The mechanisms of broadband VIVs of a cylindrical tensioned beam of length-to-diameter aspect ratio 200 placed in shear flow, with an exponentially varying profile along the span, are investigated by means of direct numerical simulation. The Reynolds number is equal to 330 based on the maximum velocity, for comparison with previous work on narrowband vibrations in linear shear flow. The flow is found to excite the structure at a number of different locations under a condition of wake–body synchronization, or lock-in. Broadband responses are associated with a distributed occurrence of the lock-in condition along the span, as opposed to the localized lock-in regions limited to the high inflow velocity zone, reported for narrowband vibrations in sheared current. Despite the instantaneously multi-frequency nature of broadband responses, the lock-in phenomenon remains a locally mono-frequency event, since the vortex formation is generally synchronized with a single vibration frequency at a given location. The spanwise distribution of the excitation zones induces travelling structural waves moving in both directions; this contrasts with the narrowband case where the direction of propagation toward decreasing inflow velocity is preferred. A generalization of the mechanism of phase-locking between the in-line and cross-flow responses is proposed for broadband VIVs under the lock-in condition. A spanwise drift of the in-line/cross-flow phase difference is identified for the high-wavenumber vibration components; this drift is related to the strong travelling wave character of the corresponding structural waves.
Vortex-induced vibrations of a long flexible cylinder in shear flow
- REMI BOURGUET, GEORGE E. KARNIADAKIS, MICHAEL S. TRIANTAFYLLOU
-
- Journal:
- Journal of Fluid Mechanics / Volume 677 / 25 June 2011
- Published online by Cambridge University Press:
- 27 April 2011, pp. 342-382
-
- Article
- Export citation
-
We investigate the in-line and cross-flow vortex-induced vibrations of a long cylindrical tensioned beam, with length to diameter ratio L/D = 200, placed within a linearly sheared oncoming flow, using three-dimensional direct numerical simulation. The study is conducted at three Reynolds numbers, from 110 to 1100 based on maximum velocity, so as to include the transition to turbulence in the wake. The selected tension and bending stiffness lead to high-wavenumber vibrations, similar to those encountered in long ocean structures. The resulting vortex-induced vibrations consist of a mixture of standing and travelling wave patterns in both the in-line and cross-flow directions; the travelling wave component is preferentially oriented from high to low velocity regions. The in-line and cross-flow vibrations have a frequency ratio approximately equal to 2. Lock-in, the phenomenon of self-excited vibrations accompanied by synchronization between the vortex shedding and cross-flow vibration frequencies, occurs in the high-velocity region, extending across 30% or more of the beam length. The occurrence of lock-in disrupts the spanwise regularity of the cellular patterns observed in the wake of stationary cylinders in shear flow. The wake exhibits an oblique vortex shedding pattern, inclined in the direction of the travelling wave component of the cylinder vibrations. Vortex splittings occur between spanwise cells of constant vortex shedding frequency. The flow excites the cylinder under the lock-in condition with a preferential in-line versus cross-flow motion phase difference corresponding to counter-clockwise, figure-eight orbits; but it damps cylinder vibrations in the non-lock-in region. Both mono-frequency and multi-frequency responses may be excited. In the case of multi-frequency response and within the lock-in region, the wake can lock in to different frequencies at various spanwise locations; however, lock-in is a locally mono-frequency event, and hence the flow supplies energy to the structure mainly at the local lock-in frequency.
Three-dimensionality effects in flow around two tandem cylinders
- GEORGIOS V. PAPAIOANNOU, DICK K. P. YUE, MICHAEL S. TRIANTAFYLLOU, GEORGE E. KARNIADAKIS
-
- Journal:
- Journal of Fluid Mechanics / Volume 558 / 10 July 2006
- Published online by Cambridge University Press:
- 04 July 2006, pp. 387-413
-
- Article
- Export citation
-
The flow around two stationary cylinders in tandem arrangement at the laminar and early turbulent regime, ($\hbox{\it Re}\,{=}\,10^2$–$10^3$), is studied using two- and three-dimensional direct numerical simulations. A range of spacings between the cylinders from 1.1 to 5.0 diameters is considered with emphasis on identifying the effects of three-dimensionality and cylinder spacing as well as their coupling. To achieve this, we compare the two-dimensional with corresponding three-dimensional results as well as the tandem cylinder system results with those of a single cylinder. The critical spacing for vortex formation and shedding in the gap region depends on the Reynolds number. This dependence is associated with the formation length and base pressure suction variations of a single cylinder with Reynolds number. This association is useful in explaining some of the discrepancies between the two-dimensional and three-dimensional results. A major effect of three-dimensionality is in the exact value of the critical spacing, resulting in deviations from the two-dimensional predictions for the vorticity fields, the forces on the downstream cylinder, and the shedding frequency of the tandem system. Two-dimensional simulations under-predict the critical spacing, leading to erroneous results for the forces and shedding frequencies over a range of spacings where the flow is qualitatively different. To quantify the three-dimensional effects we first employ enstrophy, decomposed into a primary and a secondary component. The primary component involves the vorticity parallel to the cylinder axis, while the secondary component incorporates the streamwise and transverse components of the vorticity vector. Comparison with the single cylinder case reveals that the presence of the downstream cylinder at spacings lower than the critical value has a stabilizing effect on both the primary and secondary enstrophy. Systematic quantification of three-dimensionalities involves finding measures for the intensity of the spanwise fluctuations of the forces. This also verifies the stabilization scenario, suggesting that when the second cylinder is placed at a distance smaller than the critical one, three-dimensional effects are suppressed compared to the single-cylinder case. However, when the spacing exceeds the critical value, the upstream cylinder tends to behave like a single cylinder, but three-dimensionality in the flow generally increases.
On the formation of vortex streets behind stationary cylinders
- George S. Triantafyllou, Michael S. Triantafyllou, C. Chryssostomidis
-
- Journal:
- Journal of Fluid Mechanics / Volume 170 / September 1986
- Published online by Cambridge University Press:
- 21 April 2006, pp. 461-477
-
- Article
- Export citation
-
The formation of vortex streets behind stationary cylinders is found to be caused by an absolute instability in the wake immediately behind the cylinder. The inviscid Orr–Sommerfeld equation is used together with measured profiles at Reynolds numbers of (a) Re = 56 when the absolute instability provides a Strouhal number of 0.13; and (b) Re = 140000 providing a Strouhal number of 0.21, both in agreement with experimental values. At the subcritical Re = 34 the instability is of the convective type; i.e. the disturbance decays, being convected away once the external disturbance is removed, in agreement with experimental observations. Finally, the instability of the mode which causes a symmetric array of vortices is shown to be always of the convective type.
Turbulent flow over a flexible wall undergoing a streamwise travelling wave motion
- LIAN SHEN, XIANG ZHANG, DICK K. P. YUE, MICHAEL S. TRIANTAFYLLOU
-
- Journal:
- Journal of Fluid Mechanics / Volume 484 / 10 June 2003
- Published online by Cambridge University Press:
- 20 May 2003, pp. 197-221
-
- Article
- Export citation
-
Direct numerical simulation is used to study the turbulent flow over a smooth wavy wall undergoing transverse motion in the form of a streamwise travelling wave. The Reynolds number based on the mean velocity $U$ of the external flow and wall motion wavelength $\lambda$ is 10 170; the wave steepness is $2\pi a/\lambda=0.25$ where $a$ is the travelling wave amplitude. A key parameter for this problem is the ratio of the wall motion phase speed $c$ to $U$, and results are obtained for $c/U$ in the range of $-1.0$ to $2.0$ at $0.2$ intervals. For negative $c/U$, we find that flow separation is enhanced and a large drag force is produced. For positive $c/U$, the results show that as $c/U$ increases from zero, the separation bubble moves further upstream and away from the wall, and is reduced in strength. Above a threshold value of $c/U\approx 1$, separation is eliminated; and, relative to small- $c/U$ cases, turbulence intensity and turbulent shear stress are reduced significantly. The drag force decreases monotonically as $c/U$ increases while the power required for the transverse motion generally increases for large $c/U$; the net power input is found to reach a minimum at $c/U\approx 1.2$ (for fixed $U$). The results obtained in this study provide physical insight into the study of fish-like swimming mechanisms in terms of drag reduction and optimal propulsive efficiency.