Vortex Shedding Patterns Research Articles

Numerical assessment of RANS turbulence models for the development of data driven Reduced Order Models

The ability to accurately predict vortex shedding around wind turbine blades is paramount, particularly at high Reynolds number. Turbulence models employed in the numerical studies strongly influence flow separation and the aerodynamic loading, thus affecting the overall accuracy of numerical simulations. In this manuscript, three turbulence models (Spalart–Allmaras, k−ϵ and k−ω Shear Stress Transport model) are investigated in two and three-dimensional configurations using standard Reynolds Average Navier–Stokes equations. The focus is on the NACA0015 airfoil, and the simulations are conducted at a Reynolds number of 1.96×106 to match the experimental data in the literature. The effect of flow separation and vortex shedding pattern is investigated at different angles of attack (0∘≤α≤ 17∘) along with the prediction ability of the turbulence models. Spectral analysis is performed over the time history of aerodynamic coefficients to identify the dominant frequencies along with their even and odd harmonics. A reduced-order model based on the van der Pol equation is proposed for the aerodynamic lift calculation. The method of multiple scales (a perturbation approach) is adapted to compute the coefficients of the proposed model consisting of quadratic and cubic nonlinearities at the various angle of attacks (α). The model is also tested in a predictive setting, and the results are compared against the full order model solution.

Large-eddy simulation of the near wake of a 5:1 rectangular cylinder in oscillating flows at Re=670

In this study, three-dimensional Large-Eddy Simulations (3D LES) are conducted to investigate the near-wake characteristics of a 5:1 rectangular cylinder in oscillating flow. The oscillating flow is generated by introducing a sinusoidal velocity perturbation to the smooth flow at a low Reynolds number. It is observed that the dynamics of the vortices on the upper and lower surfaces are synchronously affected by the oscillating flow, and thus interact with the wake flow. Consequently, the vortex shedding patterns that appear are less regular than those in uniform flow, resulting in a non-synchronous phenomenon between the shedding of the wake vortices and the leading-edge vortices. Interestingly, the complex near-wake dynamics in the oscillating flow are characterized by multiple peaks of the wake velocity in the frequency domain. The energy contributions of each frequency component are studied through POD analysis. The results indicate that the flow structures of Modes 1 and 2 are of Kármán vortices which dominate the velocity fluctuations in the wake and exhibit the most prominent peak in the velocity spectra. In contrast, Modes 3 and 4 are controlled by the inflow oscillations. The higher modes result from the interactions between the above two patterns. It is worth noting that the shedding frequency, longitudinal spacing and convective speed of the Kármán vortices are synchronously influenced by the inflow frequency and amplitude.

Simultaneous vortex- and wake-induced vibration suppression of tandem-arranged circular cylinders using active feedback control system

This paper deals with the active flow-induced vibration (FIV) suppression of two identical tandem-arranged circular cylinders at a low Reynolds number of Re=100. The adopted control system employs fuzzy PID controller in which the desired control force is computed based on the cylinder displacement amplitude, and applied transversely for effective attenuation of flow-induced instabilities in both transverse and streamwise directions. Moreover, the effect of FIV suppression of each cylinder on the response amplitude of other one, and the simultaneous vibration reduction of both cylinders are investigated based on fully-coupled fluid-structure interaction (FSI) simulations. The rigid body motion equations in streamwise and transverse directions are incorporated into the computational fluid dynamics solver to treat the coupling which exists between the fluid flow and cylinders movement. Next, in the utilized co-simulations, the active fuzzy PID controller implemented in Matlab/Simulink is coupled with the FSI oscillator model constructed in computational fluid dynamics solver package. It was shown that, the sudden suppression of the upstream cylinder vibration causes quick distortion in the flow field around the rear cylinder, and consequently, its steady-state response amplitude is destabilized and experiences transient fluctuations once again. On the contrary, the decrease in the transverse oscillation of the downstream cylinder leaves no sensible effect on the vibration of upstream cylinder. In particular, the active control system effectively reduces the transverse displacement amplitudes of upstream and downstream cylinders by as much as 99.9% and 98.7%, respectively, for Vr=5.5, while the corresponding values are 99.8% and 99.7% for Vr=7.5. This superb performance of active FIV control systems is mainly due to de-synchronization-type action in which the vortex shedding frequency is deviated from the oscillator natural frequency. Lastly, it is demonstrated that the vortex shedding patterns for uncontrolled cylinders, which primarily depend on reduced velocity, are turned very similar to that of the stationary cylinders after adopting the fully active control systems.

Analysis of a channel-confined non-Newtonian shear-thinning flow past a pair of mildly heated side-by-side square cylinders

The dynamics of a shear-thinning fluid flowing past a pair of mildly heated side-by-side square cylinders, in a confined horizontal flow channel at low Reynolds number (Re), has been investigated. A detailed probe for flow physics in terms of vortex shedding patterns, near-wake streamlines and stretch of isotherms are carried out at Re = 1 and 100 (signifying two-dimensional unseparated steady flow and transient flow). The power-law index (n) is varied from 0.4 to 1 and the side-by-side transverse gap ratio (s/d) ranges from 1 (pressure-driven flow regime) to 5 (momentum-driven flow regime) at a constant value of Prandtl number (Pr) = 50. When the shear-thinning effects in the flow are increased (in the present numerical framework) at Re = 100, the time-averaged streamlines depict an early onset of leading edge flow separations from the pair of side-by-side square cylinders. One can infer from the phase space plots that the flow becomes chaotic with the increase in shear-thinning effect from n = 0.8 to 0.4 and decrease in s/d from 5 to 1. An anti-phase vortex shedding can be characterized by the occurrences of symmetrical structures of negative ζ (where ζ quantifies the accumulation and propagation of the vortices) contours in the downstream and this is realized at Re = 100, n = 0.8 and s/d ≥ 1.7. An in-phase vortex shedding (which occurs at Re = 100, n = 0.4 and all values of s/d) is characterized by asymmetrical occurrences of negative ζ contours which have a tendency of dying down early in the downstream with the increase in the nearness of the side-by-side square cylinders. This is more clearly realized at enhanced shear-thinning effects in the flow. Finally, the variation of time and space-averaged drag flow parameter (CD) and Nusselt number (Nu) with respect to shear-thinning effects in the flow has been extensively determined.

Vortex-induced vibration of a cylinder in pulsating nanofluid flow

In this paper, vortex-induced vibration of a circular cylinder with forced convection heat transfer and entropy generation in pulsating alumina–water nanofluid flow is investigated numerically. Numerical simulation is carried out for a constant mass ratio of 2 and damping ratio of 0.01 at a fixed Reynolds number of 150. The ranges of reduced velocity, particle volume fraction and inlet velocity oscillation amplitude are 3–8, 0–5% and 0–1, respectively. It was found that the lock-in phenomenon, nanofluid concentration and inlet velocity oscillation amplitude have an effective role in increasing heat transfer and decreasing entropy generation. Two wake patterns (2S and 2P) were observed in the present simulation. For velocity oscillation amplitude of 1, the transition from 2S to 2P modes occurs in vortex shedding pattern.

Vortex shedding patterns in flow past a streamwise oscillating square cylinder at low Reynolds number using dynamic meshing

We present a two-dimensional numerical study for uniform flow past a streamwise oscillating square cylinder at a Reynolds number of 200. To overcome the limitations with an oscillating inlet flow as used in earlier studies, a dynamic meshing feature is used to oscillate the cylinder. A parametric study is carried out by varying amplitude and frequency of cylinder oscillation. Two symmetric modes, named here as S-II-I and S-IV-D, have been found. In S-II-I mode, a pair of vortices are shed symmetrically on each side of the cylinder in one cycle (S-II mode), and in S-IV-D mode, two pairs of vortices of opposite sense are shed on each side of the cylinder. A vortex flapping mode has also been obtained for low to moderate amplitude and frequency ratios. A new mode of vortex shedding termed the “vortex dipole” mode is found and involves the alternate arrangement of vortex pairs unlike the zigzag arrangement of single vortices in a Kármán vortex street. As in most nonlinear oscillators, vortex shedding becomes chaotic when forced sufficiently strongly and is usually associated with nonlinear interactions between competing frequencies. Many modes observed in the current study become chaotic when the peak cylinder velocity becomes comparable with the inlet velocity. The 0-1 test for chaos is applied to the time series of lift coefficient to show that the signals are truly chaotic. We also observe chaos due to mode competition when shedding transitions from an antisymmetric to symmetric modes.

CFD evaluation and experimental comparison on the flow around fixed multi-column configurations

The flow-induced motion (FIM) of platforms is a vital phenomenon issue to be investigated to help the designers and to decrease the costs related to the mooring and/or riser systems. On this matter, when talking about multi-column configurations, captive tests (also called fixed or stationary tests) can be a methodology worth of examining the vortex detachments, the source for the oscillatory lift, the drag force, and the interference of the wake of the upstream column on the downstream ones. Computational fluid dynamics (CFD) evaluations on the flow around a fixed array of one, three, and four columns with low aspect ratio, $${\text{AR}} = H/L = 1.5$$ (the ratio between the column draft, $$H$$, and the column face dimension, $$L$$) were conducted. Three different shapes of the column sections were tested, namely, circular, square, and diamond. For the multi-column configurations, the spacing ratio tested was $$S/L$$ (where $$S$$ is the distance from center to center of each column). The Reynolds number tested was 100,000. Lift and drag forces were monitored in each column aiming at the integral quantities of the hydrodynamic to compare with the experimental results. Time averages of velocities and vorticity fields were also observed. The calculations were performed with the flow solver StarCCM+; the code solves the multi-phase incompressible Unsteady Reynolds-Averaged Navier–Stokes (URANS) equations. Simulations were carried out with the Improved Delayed Detached Eddy Simulation (IDDES) method. The IDDES estimates the small turbulence scales near the body boundary with the Reynolds-Averaged Navier–Stokes (RANS) model and the large scales with the Large Eddy Simulation (LES) model. For the volume of fluid (VoF), an interface-capturing approach was used. The multi-column arrays presented no regular vortex shedding pattern when compared with the single-column case. The vortex shedding behavior was mainly determined by the column section. For the multi-column configurations, the number of columns, 3 or 4, was not the main issue. CFD calculations compared with the experiments showed good agreement for the circular and square cases and a significant difference for the diamond cases, which need to be further investigated.

Kármán vortex street in a two-component Bose–Einstein condensate

Vortex shedding from a moving obstacle potential in a two-component Bose–Einstein condensate is investigated numerically. For a miscible two-component condensate composed of 23Na and 87Rb atoms, in the wake of obstacle, the Kármán vortex street is discovered in one component, while the Kármán-like vortex street named ‘half-quantum vortex street’ is formed in another component. The other patterns of vortex shedding, such as the vortex dipoles, V-shaped vortex pairs and corresponding ‘half-quantum vortex shedding’, can also be found. The drag force acting on obstacle potential is calculated and discussed. The parameter region for various vortex patterns and critical velocity for vortex emission are presented. In addition, a 85Rb–87Rb mixture is also considered, where the Kármán vortex street and other typical patterns exist in both components. Finally, we provide an experimental protocol for the above realization and observation.

Numerical prediction of hydrodynamic coefficients for a semi-sub platform by using large eddy simulation with volume of fluid method and Richardson extrapolation

Hydrodynamic coefficients for predicting hydrodynamic loading is significant for the design of offshore wind turbine floaters. In this paper, hydrodynamic coefficients for a semi-submersible floating offshore wind turbine are investigated experimentally and numerically. In the water tank test, added mass and drag coefficients of the semi-submersible model are identified by the forced oscillation tests. In numerical simulation, large eddy simulation (LES) with volume of fluid method (VOF) is adopted to predict added mass and drag coefficients. Firstly, numerical errors in the predicted hydrodynamic coefficients are systematically studied, and Richardson extrapolation is employed to obtain the grid independent solution. The predicted added mass and drag coefficients varying with KC number are then validated by the water tank tests and the mechanism of the hydrodynamic force are clarified by vortex shedding patterns. The hydrodynamic coefficients for each element are also investigated. Finally, effect of free surface on the hydrodynamic forces is discussed and the predicted added mass and drag coefficients are compared with those obtained from the water tank tests.

Self-propelled plate in wakes behind tandem cylinders.

Fish may take advantage of environmental vortices to save the cost of locomotion. The complex hydrodynamics shed from multiple physical objects may significantly affect fish refuging (holding stationary). Taking a model of a self-propelled flapping plate, we numerically studied the locomotion of the plate in wakes of two tandem cylinders. In most simulations, the plate heaves at its initial position G_{0} before the flow comes (releasing Style I). In the typical wake patterns, the plate may hold stationary, drift upstream, or drift downstream. The phase diagrams of these modes in the G_{0}-A plane for the vortex shedding patterns were obtained, where A is the flapping amplitude. It is observed that the plate is able to hold stationary at multiple equilibrium locations after it is released. Meanwhile, the minimum amplitude and the input power required for the plate seem inversely proportional to the shedding vortex strength. The effect of releasing style was also investigated. If the plate keeps stationary and does not flap until the vortex shedding is fully developed (releasing Style II), then the plate is able to hold stationary at some equilibrium locations but the flapping plate has a very minor effect on the shedding vortices. However, in Style I, the released plate is able to achieve more equilibrium locations through adjusting the phase of vortex shedding. The effort of the preflapping in Style I is not in vain, because although it consumes more energy, it becomes easier to hold stationary later. The relevant mechanism is explored.

Effect of vortex-induced vibration of finned cylinders on heat transfer enhancement

Two-degree-of-freedom vortex-induced vibration (VIV) of a finned cylinder with heat transfer is studied numerically at the Reynolds number Re = 150. The governing equations in the Arbitrary Lagrangian-Eulerian frame are solved by the finite volume method. The dynamics of the oscillating cylinder (with or without fins) in the fluid flow was approximated as a mass-spring system. The effects of the number and arrangement of the fins (14 different cases) on the vortex shedding pattern, vibration amplitude, and frequency and heat transfer of the cylinder are investigated and discussed. The results indicate that in comparison with the stationary state, the effects of the number and arrangement of the fins on the wake pattern and the heat transfer enhancement in the VIV state are significant. Different vortex shedding pattern like 2S, P, 2P, S + P and combination of them with stable or unstable interactions between vortices and cylinders are observed in an oscillating cylinder. In the vibration state of finned cylinders, the heat transfer enhances up to 50.4% with respect to the stationary state and increases up to 64% with respect to the stationary smooth cylinder.

Experimental study on aerodynamic characteristics of two square cylinders at various incidence angles

Wind tunnel tests are conducted to study the aerodynamic characteristics of two identical square cylinders with variations in the incidence angle at a Reynolds number of Re = 8.0 × 104. The center-to-center spacing (P) ranges from 1.25 to 5.0 times the width of the cylinders (B), and the incidence angle (α) varies from 0° to 90°. The spacing ratio significantly influences the aerodynamics. When the two cylinders are very close, they can be treated as one bluff body for which the vortex sheds only at the wake of the downstream cylinder. With an increasing spacing ratio, the flow finally separates individually from the two cylinders and creates two related vortex shedding patterns. The interference effects of the two cylinders on the aerodynamics changes with an increasing spacing ratio. According to the aerodynamics, the arrangement of two identical square cylinders can be classified by the spacing ratio into three states: closely spaced (P/B < 1.5), moderately spaced (1.5 ≤ P/B ≤ 3) and widely spaced (3 < P/B ≤ 5). The characteristics of the aerodynamics and mechanism of interference effects in the three states are discussed, considering the influence of the incidence angles.

Active control of vortex shedding from a blunt trailing edge using oscillating piezoelectric flaps

Active control of vortex shedding from a blunt trailing edge is achieved experimentally using piezoelectric actuators. The system can suppress and amplify the vortex shedding pattern in the wake, as well as force near-wake symmetry. An application of closed-loop control is also demonstrated.

Measurements on a yawed rotor blade pitching in reverse flow

Vortex shedding patterns are examined on a yawed wing pitching in reverse flow. The yawed wing exhibits suppression of its secondary flow structures compared to an unyawed wing. Various physical mechanisms, particularly spanwise flow, are evaluated to explain the shedding pattern of the yawed wing.

Cost-effective CFD for vortex shedding from a trailing edge of hydraulic turbine blade

This paper describes the method for analysing the vortex from a trailing edge of the blade with high accuracy using CFD. As for the analysis method, RANS and LES hybrid model, which is a combination of RANS with a low calculation load and LES with a high calculation load, was used on understanding the turbine-scale phenomenon with a relatively low calculation load. As for the first step its application as a turbine runner, we conducted the case study in which the blade model was fixed in a uniform and we confirmed that the present CFD could be predicted the vortex shedding phenomena, such as power spectra of velocity fluctuations, wake fluctuation, vortex shedding pattern and hydraulic force acting on the blade etc.

Surface temperature effects on the compressible flow past a rotating cylinder

Spinning cylinders have been the subject of numerous studies because of not only their interesting flow patterns but also their widespread applications. In this study, the effects of the surface temperature of a spinning cylinder on the compressible flow characteristics have been studied numerically. Simulations are performed in the laminar flow regime at Re = 200, M∞ = 0.1-0.4, and Pr = 0.7. The dimensionless cylinder surface velocity is considered from 0 to 7 for a wide range of cylinder surface temperatures. Results show that increasing the cylinder surface temperature leads to a considerable reduction in the lift coefficient. However, surface temperature effects on the drag coefficient do not follow a regular trend due to various vortex shedding patterns. The results also reveal that the vortex shedding pattern and the position of the stagnation points not only depend on the speed ratio but also depend on the surface temperature. Furthermore, at a narrow band of speed and temperature ratios, an oscillatory flow without vortex shedding occurs which has not been reported in previous studies. The heat transfer analysis shows that the cylinder mean surface Nusselt number decreases as the surface temperature increases at both Mach numbers and all speed ratios. Moreover, increasing the speed ratios increases the mean Nusselt number at M∞ = 0.3; however, there is no such trend at M∞ = 0.2. Investigating the compressibility effects also shows that the lift coefficient decreases with increasing Mach number, while the drag coefficient and Nusselt number increase.

Analysis of sound generation by flow past a circular cylinder performing rotary oscillations using direct simulation approach

Generation of sound due to laminar flow past a circular cylinder performing rotary oscillations has been studied using a direct numerical simulation approach. Two-dimensional, unsteady, compressible Navier-Stokes equations are directly solved using high resolution, physical dispersion relation preserving schemes. In this work, modifications in the flow induced acoustic noise due to imposed rotary oscillations have been discussed in detail. Simulations have been performed for a Reynolds number Re = 150 and a Mach number M = 0.2 over a wide range of forcing frequencies and amplitudes of rotary oscillation, specifically in the synchronization region. Rotary oscillating motion of a cylinder modifies the vortex shedding patterns in the wake region as compared to the case of flow past a stationary cylinder. The frequency and strength of shed vortices determine the nature of aerodynamic forces acting on the cylinder as well as sound generation. Reduction in sound generation has been observed for some of the forced oscillation cases as compared to the flow past a stationary cylinder case. The Doak’s decomposition methodology has been used to segregate the acoustic and hydrodynamic modes from the momentum density field to understand changes in the radiated sound field for different forcing conditions. Furthermore, disturbance pressure fields have been decomposed into a number of modes based on their significance, using a proper orthogonal decomposition (POD) technique in order to identify and quantify the contribution of the lift and drag dipoles to the sound field. In addition, POD modes of disturbance vorticity fields as well as noise source structures based on approximate Lighthill’s stress tensor are also obtained and related to the generated sound fields. This analysis concludes that the frequency of rotary oscillation dictates the frequency content of the flow induced sound field. Low frequency rotary oscillations trigger sound waves with low frequencies and large wavelengths. As the forcing frequency increases, the corresponding sound field displays shorter wavelengths. Directivity of the sound field is affected by the amplitude of rotary oscillation. A case with higher forcing amplitude distributes sound energy more evenly in all directions as compared to a lower forcing amplitude case. Prescription of rotary oscillations to the circular cylinder significantly alters the frequency, amplitude, and directivity of the generated sound field.

Effects of steady wake-jets on subcritical cylinder flow

We investigate the effects of active wake-jets (characterized by a dimensionless jet momentum coefficient Cμ) on the suppression of aerodynamic forces and the manipulation of wake flow topology behind a cylindrical model through wind tunnel tests. The active jets are positioned at the rear stagnation points of the cylindrical test model. The experimental campaign is conducted at a subcritical Reynolds number of Re=3.33×104. The surface pressure distributions around the bare and controlled cylinders are obtained by using a pressure measurement system. Apart from pressure measurements, we also obtain the streamwise and spanwise flow structures around the circular cylinder with different Cμ (including Cμ=0) by employing the particle image velocimetry (PIV) technique. Pressure measurement results demonstrate that the lift force acting on the cylindrical test model is greatly reduced and drag decreased with the implementation of active wake-jets. Besides, it is found that a higher Cμ contributes to a better control effectiveness in unsteady lift forces but not necessarily a better drag reduction. PIV measurement results indicate that the mechanism of the active jet control scheme is to impose steady and symmetric perturbations into the unsteady and asymmetric flows in the cylinder wake. Owing to the dynamic competition of the wake-jet flow and shear layer flows, the vortex shedding pattern behind the controlled cylinder is greatly modified, vortex formation length significantly elongated and the fluctuations of aerodynamic forces conceivably suppressed.

Numerical simulation of vortex-induced vibration of long flexible risers using a SDVM-FEM coupled method

This paper presents a grid-independent numerical methodology that couples the strip theory based discrete vortex method (SDVM) with the finite element method (FEM) to simulate the vortex-induced vibration (VIV) of a long flexible vertical riser. Based on the strip theory, a three-dimensional flow filed is approximately simulated by a series of computational ‘flow strips’. A Lagrangian discrete vortex method is employed to numerically solve the unsteady vorticity transport equations of each ‘flow strip’. The flexible riser is modelled as a tensioned Bernoulli-Euler beam with the dynamical equation solved by the finite element method in time domain. The two-dimensional DVM code is firstly validated for the VIV simulation of a rigid cylinder that was experimentally studied by Khalak and Williamson (1996). Referring to two typical experimental configurations of Lehn (2003) and Chaplin et al. (2005), the VIV of a long flexible riser immersed in a uniform and stepped incoming flow are numerically simulated, respectively. A good agreement was achieved through detailed comparisons between the present numerical prediction and the experimental data, including the structural in-line and cross-flow VIV response modes, root mean square amplitudes and the dominant frequency. The occurrence of standing and travelling wave responses, dual resonance between in-line and cross-flow motions and figure-eight trajectory are reported. The wake patterns corresponding to two response waves are also presented and investigated. Related to structural local vibration amplitude, two principle vortex patterns resembling the ‘2S’ and ‘2P’ modes are identified in the wake. The standing wave component of structural response determines the vortex shedding pattern. The travelling wave component affects the spanwise vortices shedding at different phases.

A parametric study of energy extraction from vortex-induced vibrations

This paper presents a parametric investigation of an oscillating-cylinder turbine concept based on vortex-induced vibrations. The parametric space includes four parameters: the Reynolds number, the mass ratio, the dimensionless stiffness, and the dimensionless damping. The damping–stiffness space is explored for four different mass ratios at a fixed Reynolds number of 200. Also, the influence of the parameters on the amplitude of cylinder displacement and on the efficiency of power harnessing is discussed. Vortex-shedding patterns observed within the parametric space are investigated. The 2S, 2P, and C(2S) wake modes are observed and are related to turbine performance. Preliminary results show a maximum efficiency of 10.6%, which is obtained with low mass ratios.