Wake Instability Research Articles

Modal decomposition of fluid–structure interaction with application to flag flapping

Modal decompositions such as proper orthogonal decomposition (POD), dynamic mode decomposition (DMD) and their variants are regularly used to educe physical mechanisms of nonlinear flow phenomena that cannot be easily understood through direct inspection. In fluid–structure interaction (FSI) systems, fluid motion is coupled to vibration and/or deformation of an immersed structure. Despite this coupling, data analysis is often performed using only fluid or structure variables, rather than incorporating both. This approach does not provide information about the manner in which fluid and structure modes are correlated. We present a framework for performing POD and DMD where the fluid and structure are treated together. As part of this framework, we introduce a physically meaningful norm for FSI systems. We first use this combined fluid–structure formulation to identify correlated flow features and structural motions in limit-cycle flag flapping. We then investigate the transition from limit-cycle flapping to chaotic flapping, which can be initiated by increasing the flag mass. Our modal decomposition reveals that at the onset of chaos, the dominant flapping motion increases in amplitude and leads to a bluff-body wake instability. This new bluff-body mode interacts triadically with the dominant flapping motion to produce flapping at the non-integer harmonic frequencies previously reported by Connell and Yue (2007). While our formulation is presented for POD and DMD, there are natural extensions to other data-analysis techniques.

Wake Instability Behind Low-Profile “Convergent Riblet” Vortex Generators in Incompressible Laminar Flow

Vane-type vortex generators have proven to be well suited for passive aerodynamic control through their substantial increase in near-wall momentum. As a structurally strong variance for durable use in low-speed airfoil and turbine applications, this study looks experimentally into the low-profile triangular convergent riblet element (consisting of two short convergent vanes of triangular cross sections with 30 deg half-intervane angles) in incompressible laminar flow. The flow organization and instability within the wake of isolated vortex generators are thus investigated using hot-wire measurements over a length of downstream of the element, where is the local boundary-layer thickness. A preliminary analysis serves first to characterize the effect of the isolated element height across height adjustments for rectangular cross-section elements. A selection of three triangular element heights is subsequently investigated in detail, undergoing the following: 1) with , longitudinal vortices are found to remain quasi steady and with eventual disturbance attenuation; 2) with , the wake starts exhibiting strong fluctuations as it approaches critical conditions; and 3) with , transition to turbulence takes place close behind the element. The switch from a varicose to a sinuous wake instability for low-profile (near-critical) configurations places the transition onset within the region of strong lateral shear.

Propeller wake evolution mechanisms in oblique flow conditions

In the present study the wake flow past an isolated propeller operating in oblique flow conditions is investigated experimentally. In particular, the investigation concerns a systematic topological comparison of the wake behaviour in axisymmetric and in oblique inflow conditions, for three inclination angles, and is focused on an analysis of the underlying mechanisms of wake evolution and instability. To this end, the experiment has been designed to investigate the dynamics of propeller vortical structures over a wide spatial extent covering the wake region from the propeller disk up to 4.5 diameters in the streamwise direction. Detailed flow measurements have been undertaken by particle image velocimetry (PIV), using a multicamera configuration with three cameras arranged side by side. This allowed simultaneous acquisition of a large flow extent at a spatial resolution adequate to resolve the smallest vortical structures involved in the process of propeller wake instability. The analysis has been based on both phase-locked averaged and instantaneous flow fields. The study extends the knowledge on the subject of propeller wake dynamics, highlighting the major hydrodynamic effects that non-axisymmetric propeller operating conditions exert on the mechanisms of wake evolution, instability and breakdown, such as asymmetric destabilization of the tip vortices on the leeward and windward sides of the wake, and the interference between the tip and the junction vortices, as well as the cause–effect relation between the breakdown of the blade trailing wake and the instability of the tip and hub vortices.

The unsteady aerodynamics of floating wind turbine under platform pitch motion

The aerodynamic performance of floating platform wind turbines is much more complex than fixed-base wind turbines because of the flexibility of the floating platform. Due to the extra six degrees-of-freedom of the floating platform, the inflow of the wind turbine rotors is highly influenced by the motions of the floating platform. It is therefore of interest to study the unsteady aerodynamics of the wind turbine rotors involved with the interaction of the floating platform induced motions. In the present work, a lifting surface method with a free wake model is developed for analysis of the unsteady aerodynamics of wind turbines. The aerodynamic performance of the NREL 5 MW floating wind turbine under the prescribed floating platform pitch motion is studied. The unsteady aerodynamic loads, the transient of wind turbine states, and the instability of the wind turbine wakes are discussed in detail.

High-resolution simulation for rotorcraft aerodynamics in hovering and vertical descending flight using a hybrid method

A high-resolution simulation tool for rotorcraft aerodynamics is developed by coupling CFD with a Vorticity Transport Model (VTM). An Eulerian-based CFD module is used to model the blade near body flowfield, and a Lagrangian-based VTM module is employed for vortex tracking in the far wake. The coupling procedure is implemented by transmitting vortex sources to the VTM module and feeding boundary conditions back to the CFD module. The presented CFD/VTM hybrid solver is firstly validated by hover cases of three different rotor configurations. Simulation results, including the blade surface pressure distribution, rotor downwash, and hover figure of merit, exhibit favorable correlations with available experimental data. Then, a rotor operated in vertical descending flight with a fixed collective pitch is investigated. It is shown that the CFD/VTM coupling method is suitable for rotor wake simulation. Wake instabilities (far wake breakdown in hover and toroidal wake pattern in the vortex ring state) are successfully demonstrated with a moderate computational cost.

Three-dimensional wake transition of a square cylinder

Three-dimensional (3-D) wake transition for flow past a square cylinder aligned with sides perpendicular and parallel to the approaching flow is investigated using direct numerical simulation. The secondary wake instability, namely a Mode A instability, occurs at a Reynolds number ($Re$) of 165.7. A gradual wake transition from Mode A* (i.e. Mode A with vortex dislocations) to Mode B is observed over a range of $Re$ from 185 to 210, within which the probability of occurrence of vortex dislocations decreases monotonically with increasing $Re$. The characteristics of the Strouhal–Reynolds number relationship are analysed. At the onset of Mode A*, a sudden drop of the 3-D Strouhal number from its two-dimensional counterpart is observed, which is due to the subcritical nature of the Mode A* instability. A continuous 3-D Strouhal–Reynolds number curve is observed over the mode swapping regime, since Mode A* and Mode B have extremely close vortex shedding frequencies and therefore only a single merged peak is observed in the frequency spectrum. The existence of hysteresis for the Mode A and Mode B wake instabilities is examined. The unconfined Mode A and Mode B wake instabilities are hysteretic and non-hysteretic, respectively. However, a spanwise confined Mode A could be non-hysteretic. It is proposed that the existence of hysteresis at a wake instability can be identified by examining the sudden/gradual variation of the 3-D flow properties at the onset of the wake instability, with sudden and gradual variations corresponding to hysteretic (subcritical) and non-hysteretic (supercritical) flows, respectively.

Experimental study on mitigating vortex-induced vibration of a bridge by using passive vortex generators

It has been reported that three-dimensional spanwise-varying control is very efficient in suppressing vortex shedding behind bluff bodies. Therefore, a new passive control method, spanwise-varying passive vortex generator (PVG), was proposed to mitigate the vortex-induced-vibration (VIV) of a bridge. The PVGs can directly generate streamwise vortices, which behave like secondary wake instability modes (3D instability modes). Therefore, the PVGs can cause 3D instability of spanwise vortex shedding and suppress VIV. In this study, isolated PVGs were arranged on the lower surface of the bridge in spanwise direction, and their control effects on mitigating VIV were investigated through wind tunnel tests. The results show that as PVGs are arranged with spanwise distance of 1–3H (H is the height of the bridge) and the PVG height is 0.1–0.25H, both vertical and torsional VIV can be completely suppressed, and the trailing edge is the key region to suppress VIV. Further, the control effects of PVG are barely influenced by the boundary layer of the bridge. The spectrum analysis of the wake velocity shows that the PVG can completely suppress the vortex shedding near a wake, and thereby resulting in the vanishing of VIV.

A parallel stability analysis of a trailing vortex wake

Trailing vortices are generated in aeronautical and maritime applications and produce a variety of adverse effects that remain difficult to control. A stability analysis can direct flow control designers towards pertinent frequencies, wavelengths and locations that may lead to the excitation of instabilities, resulting in the eventual breakup of the vortex. Most models for trailing vortices, however, are far-field models, making implementation of the findings from stability analyses challenging. As such, we perform a stability analysis in the formative region where the numerically computed base flow contains both a two-dimensional wake and a tip vortex generated from a NACA0012 at a$5^{\circ }$angle of attack and a chord-based Reynolds number of$Re_{c}=1000$. The parallel temporal and spatial analyses show that at three chord lengths downstream of the trailing edge, seven unstable modes are present: three stemming from the temporal analysis and four arising in the spatial analysis. The three temporal instabilities are analogues to three unstable modes in the spatial analysis, with the wake instability dominating in both analyses. The helical mode localized to the vortex co-rotates with the base flow, which is converse with the counter-rotating$m=-1$instabilities of a Batchelor vortex model, which may be a result of the formative nature of the base-flow vortex. The fourth spatial mode is localized to the tip vortex region. The continuous part of the spectrum contains oscillatory and wavepacket solutions prompting the utilization of a wavepacket analysis to analyse the flow field and group velocity. The structure and details of the full bi-global spectrum will help navigate the design space of effective control strategies to hasten decay of persistent wingtip vortices.

Wake Instability of Stator Blade Row with Large Separation

Wake Instability of Stator Blade Row with Large Separation

Trajectory modes and wake patterns of freely falling plates

The free falling of a plate is an interesting and canonical problem in the study of fluid–body interactions. In this paper, experiments with a wide range of the dimensionless moment of inertia ( $$I^*=0.05{-}1.6$$ ) and the Reynolds numbers ( $$Re=10{-}350$$ ) were conducted to investigate the trajectory modes and the corresponding wake patterns of freely falling plates. Experimental results show that the freely falling plates exhibit four trajectory modes including vertical falling, fluttering, tumbling, and chaotic motions. Based on massive experiments, a detailed $$Re{-}I^*$$ phase diagram is given and shows different trajectory regimes, which are distinguished by clear boundaries. Then, the wake patterns corresponding to different trajectory modes are investigated. When Re is rather small, plates fall vertically and the corresponding wake exhibits a stable and symmetrical pattern. With increasing Re, it is found that the plate falls vertically, whereas the corresponding wake has developed to be similar to the Karman vortex street, thereby indicating that wake instability should be prior to the path instability. As Re and $$I^*$$ further increase, both trajectory mode and wake pattern are unstable. The trajectory modes and the wake patterns of the freely falling plates are summarized in one $$Re{-}I^*$$ phase diagram, and the onset of the wake instability is found to occur when Re is approximately 30.

Secondary wake instability of a bridge model and its application in wake control

Three-dimensional spanwise-varying control, which is known to be related to secondary wake instability, has recently been reported as a highly efficient method to control vortex shedding. With the aim of suppressing Kármán vortex shedding and the underlying aerodynamic forces in a bridge model using three-dimensional spanwise-varying control, Floquet stability analysis was applied to determine the most unstable secondary instability of a period vortex shedding wake at low Reynolds numbers (i.e. Re = 516, 774, and 1032). The numerical results showed that there was only a single peak of Floquet multipliers ranging from 1H to 6H, with H being the height of the bridge model; additionally, all Floquet modes were found to be analogous to the Mode-A type. Subsequently, spanwise-varying passive vortex generators (PVGs), which can trigger secondary instability of a wake by activating pairs of streamwise counter-rotating vortical structures, were applied to implement wake control. Large eddy simulation was used to verify the wake control effects with PVGs arranged on the lower surface of the bridge model. The results showed that, overall, the case of λ/H = 2 yields improved control effects on the fluctuating aerodynamic forces (an approximately 60% reduction in fluctuating lift and moment, 10% reduction in fluctuating drag). In addition, the PVG could effectively trigger and enhance the Mode-A-like flow pattern and suppress spanwise vortices.

Open-loop and closed-loop flow control based on Van der Pol modeling

A real-time modeling and control architecture for coupled shear layer von Karman instabilities on a wing section wake is developed. Previous wind tunnel experiments highlighted that these wake instabilities give rise to limit cycles on both local and resulting airloads. The two-state Van der Pol system is employed to model the self-sustained oscillations exhibited by the actual flow. Schemes featuring either one or two coupled Van der Pol oscillators in parallel are taken under consideration. Open-loop and closed-loop control laws to manipulate and reduce the self-sustained oscillations are extensively studied. An adaptive control scheme is developed to optimize the performance of the controller, according to the flow conditions. For the open-loop control scheme, the consistency with experimental tests performed on a wind tunnel model is shown.

Stability and Sensitivity Analysis of the Secondary Instability in the Sphere Wake

The three-dimensional flow past a fixed sphere placed within a uniform stream is investigated. This paper focuses on the second bifurcation, which is responsible for the onset of the unsteadiness. Using the highly efficient Nek5000 parallel solver together with a recently developed numerical algorithm to stabilize and accelerate the numerical solution, it was possible to identify the three-dimensional eigenmode responsible for the second bifurcation. The characteristics of this eigenmode are analyzed in detail. The value of the critical Reynolds number , as well as the Strouhal number of the arising limit cycle, agree well with previous experimental and numerical investigations. To further assess the nature of the instability, an adjoint-based sensitivity analysis is carried out. The structure of the direct and adjoint modes are discussed, and then the core of the instability is localized. Finally, the sensitivity of the instability to a generic base flow modification is investigated.

Influence of synthetic jet location on active control of an airfoil at low Reynolds number

The reattachment of post-stall separated flow on a NACA 0025 airfoil at a Reynolds number of 100,000 and angle-of-attack of 12 $$^\circ$$ using synthetic jet control was studied experimentally. The goal of this work was to study the effect of control parameters including blowing ratio, frequency, and in particular, slot location, on aerodynamic performance. Slot locations both upstream and downstream of the mean separation point were tested. The results showed that for both drag reduction and lift increase, once a particular blowing ratio was met, the benefits of control saturated. Positioning the slot at the most upstream location was found to be the most effective, both in terms of having the lowest threshold blowing ratio and producing the largest lift-to-drag ratios. A monotonic increase in threshold blowing ratio (defined as being the blowing ratio required for fully attached flow) and decrease in lift-to-drag was observed as the slot location moved downstream. It was also found that while forcing at a frequency corresponding to the wake instability led to maximum lift increase, forcing in the range of the separated shear layer instability (frequencies an order of magnitude larger) led to maximum drag reduction.

Wake mode sidebands and instability in mode-locked lasers with slow saturable absorbers.

Passively mode-locked lasers with semiconductor saturable absorption mirrors are attractive comb sources due to their simplicity, excellent self-starting properties, and their environmental robustness. These lasers, however, can have an increased noise level and wake mode instabilities. Here, we investigate the wake mode dynamics in detail using a combination of evolutionary and dynamical methods. We describe the mode-locked pulse generation from noise when a stable pulse exists and the evolution of the wake mode instability when no stable pulse exists. We then calculate the dynamical spectrum of the mode-locked pulse, and we show that it has six discrete eigenmodes, two of which correspond to wake modes. The wake modes are unstable when the wake mode eigenvalues have a positive real part. We also show that even when the laser is stable, the wake modes lead to experimentally observed sidebands.

Elastic wake instabilities in a creeping flow between two obstacles

It is shown that a channel flow of a dilute polymer solution between two widely spaced cylinders hindering the flow is an important paradigm of an unbounded flow in the case in which the channel wall is located sufficiently far from the cylinders. The quantitative characterization of instabilities in a creeping viscoelastic channel flow between two widely spaced cylinders reveals two elastically driven transitions, which are associated with the breaking of time-reversal and mirror symmetries: Hopf and forward bifurcations described by two order parameters $\mbox{v}_{rms}$ and $\bar{\omega}$, respectively. We suggest that a decrease of the normalized distance between the obstacles leads to a collapse of the two bifurcations into a codimension-2 point, a situation general for many non-equilibrium systems. However, the striking and unexpected result is the discovery of a mechanism of the vorticity growth via an increase of a vortex length at the preserved streamline curvature in a viscoelastic flow, which is in sharp contrast to the well-known suppression of the vorticity in a Newtonian flow by polymer additives.

Power Properties of Two Interacting Wind Turbine Rotors

In the current experiments, two identical wind turbine models were placed in uniform flow conditions in a water flume. The initial flow in the flume was subject to a very low turbulence level, limiting the influence of external disturbances on the development of the inherent wake instability. Both rotors are three-bladed and designed using blade element/lifting line (BE/LL) optimum theory at a tip-speed ratio, λ, of 5 with a constant design lift coefficient along the span, CL = 0.8. Measurements of the rotor characteristics were conducted by strain sensors installed in the rotor mounting. The resulting power capacity has been studied and analyzed at different rotor positions and a range of tip-speed ratios from 2 to 8, and a simple algebraic relationship between the velocity deficit in the wake of the front turbine and the power of the second turbine was found, when both rotors have the coaxial position.

A numerical assessment of the interaction of a supercavitating flow with a gas jet

In this work, the interaction between a ventilated supercavity and a jet are examined using computational fluid dynamics (CFD). CFD results compare favorably to experimental data describing bulk cavity behavior. These validated models are used to develop a number of novel insights into the physical characteristics of the interaction. These interactions are described by: (1) the jet ventilation gas appears to dominate the gas attached to the cavity shear layer, (2) the jet appears to cause additional gas leakage by transitioning the cavity from a recirculating flow to an axial flow, (3) the jet creates more slender cavities, and (4) with sufficient momentum, the jet invokes wake instabilities that drive cavity pulsation.

On numerical aspects of simulating flow past a circular cylinder

AbstractThree‐dimensional direct numerical simulation results of flow past a circular cylinder are influenced by numerical aspects, for example the spanwise domain length and the lateral boundary condition adopted for the simulation. It is found that inappropriate numerical set‐up, which restricts the development of intrinsic wake structure, leads to an over‐prediction of the onset point of the secondary wake instability (Recr). A best practice of the numerical set‐up is presented for the accurate prediction of Recr by direct numerical simulation while minimizing the computational cost. The cylinder span length should be chosen on the basis of the intrinsic wavelength of the wake structure to be simulated, whereas a long span length is not necessary. For the wake transitions above Recr, because the wake structures no longer follow particular wavelengths but become disordered and chaotic, a span length of more than 10 cylinder diameters (approximately three times the intrinsic wavelength) is recommended for the simulations to obtain wake structures and hydrodynamic forces that are not strongly restricted by the numerical set‐up. The performances of the periodic and symmetry lateral boundary conditions are compared and discussed. The symmetry boundary condition is recommended for predicting Recr, while the periodic boundary condition is recommended for simulating the wake structures above Recr. The general conclusions drawn through a circular cylinder are expected to be applicable to other bluff body configurations. Copyright © 2017 John Wiley & Sons, Ltd.

Prediction of the secondary wake instability of a circular cylinder with direct numerical simulation

Abstract This paper presents an improved method for the prediction of the critical Reynolds number Recr for the secondary wake instability of flow past a circular cylinder based on three-dimensional (3D) direct numerical simulations (DNS). It is also found that insufficient mesh resolution in the plane perpendicular to the cylinder axis is a major cause for the over-prediction of Recr (∼ 200) reported in the literature using 3D DNS. It is demonstrated that the use of an optimized computational domain and mesh resolution (10 spanwise mesh layers to resolve only a half of a pair of the 3D mode) can reduce the computational cost significantly and yet retain adequate accuracy. The most accurate Recr predicted by the present DNS reduces to 190.74, which is consistent with independent linear stability analysis results of Recr ∼ 190. It is also demonstrated that 3D DNS is capable of accurately predicting the neutral curve for the secondary wake instability with a reasonable computational cost. The general conclusions drawn through a circular cylinder are expected to provide guidance on the prediction of Recr and neutral instability curve for other cylindrical objects.