Three-dimensional Wake Research Articles

Comparison of Experimental and Numerically Predicted Three-Dimensional Wake Behavior of Vertical Axis Wind Turbines

The evolution of the wake of a wind turbine contributes significantly to its operation and performance, as well as to those of machines installed in the vicinity. The inherent unsteady and three-dimensional (3D) aerodynamics of vertical axis wind turbines (VAWT) have hitherto limited the research on wake evolution. In this paper, the wakes of both a troposkien and a H-type VAWT rotor are investigated by comparing experiments and calculations. Experiments were carried out in the large-scale wind tunnel of the Politecnico di Milano, where unsteady velocity measurements in the wake were performed by means of hot wire anemometry. The geometry of the rotors was reconstructed in the open-source wind-turbine software QBlade, developed at the TU Berlin. The aerodynamic model makes use of a lifting line free-vortex wake (LLFVW) formulation, including an adapted Beddoes-Leishman unsteady aerodynamic model; airfoil polars are introduced to assign sectional lift and drag coefficients. A wake sensitivity analysis was carried out to maximize the reliability of wake predictions. The calculations are shown to reproduce several wake features observed in the experiments, including blade-tip vortex, dominant and minor vortical structures, and periodic unsteadiness caused by sectional dynamic stall. The experimental assessment of the simulations illustrates that the LLFVW model is capable of predicting the unsteady wake development with very limited computational cost, thus making the model ideal for the design and optimization of VAWTs.

Spatio-temporal flow structures in the three-dimensional wake of a circular cylinder

A new method to analyze spatio-temporal flow structures is presented. It consists on applying a higher order dynamic mode decomposition sequentially, in time and space. The method is successfully applied to analyze the three-dimensional wake of a circular cylinder. The results obtained are in good agreement with their counterparts predicted by the linear theory (Floquet stability analysis), although the data analyzed are nonlinear. This sequential spatio-temporal method provides a more detailed description of the flow physics, since the dominant frequencies, wavenumbers and their harmonics are accurately calculated. This method is a promising tool, suitable to uncover spatio-temporal flow structures that could be used to study global instabilities in complex nonlinear flows.

Study on an innovative three-dimensional wind turbine wake model

In this paper, to help handle wind farm optimization problems, an original analytical three-dimensional wind turbine wake model is presented and validated. Compared with existing analytical wake models, the presented wake model also considers the wind variation in the height direction, which is more accurate and closer to the reality. The wake model is based on the flow flux conservation law, and it assumes that the wind deficit downstream of a wind turbine is Gaussian-shaped. The derivation process is described in detail. The wake model is validated by published wind tunnel measurement data at both horizontal and vertical sections. Detailed relative errors are analyzed: the relative errors are mostly within 5% in the horizontal profile validation and within 3% in the vertical profile validation. Based on the wake model, a series of prediction results from multiple views and at different positions are demonstrated. From the predictions, the three-dimensional wake model is effective in describing the spatial distribution of wind velocity. It makes a theoretical contribution to the single wake study, and it is also meaningful to the further study of multiple wakes. Because height is considered in the three-dimensional wake model, the model can be used to optimize wind turbine hub heights and to solve more wind farm layout optimization problems, which will further contribute to increasing the energy output and decreasing the cost of energy.

Stabilization of a multi-tethered lighter-than-air rigid-body sphere undergoing vortex-induced vibrations in uniform flow

We consider the stabilization of a multi-tethered lighter-than-air sphere undergoing vortex-induced vibrations in uniform flow. Motivated by recent engineering applications, we extend a single-tether model coupled with a three-dimensional wake oscillator to incorporate a four-tether configuration with general rigid-body rotations for the light sphere. The fundamental bifurcation structure of the coupled model includes periodic self-excited limit cycles, which culminate with quasiperiodic solutions with increased reduced velocity. Stabilization of limit-cycle oscillations is achieved for optimal mass ratio and tether length parameters which are obtained by asymptotic analysis of reduced-order models. The resulting reduction in transverse and rotational amplitudes is at the expense of a decreasing range of the periodic bifurcation region for large tether inclination angles, whereas in addition to rotational amplitude reduction, regularization of nonstationary solutions occurred for a medium inclination angle.

Modelling and feedback control of vortex shedding for drag reduction of a turbulent bluff body wake

Three-dimensional bluff body wakes are of key importance due to their relevance to the automotive industry. Such wakes have both large pressure drag and a number of coherent flow structures associated with them. Depending on the geometry, these structures may include both a bistability resulting from a spatial symmetry breaking (SB), and a quasi-periodic vortex shedding. The authors have recently shown that the bistability may be modelled by a Langevin equation and that this model enables the design of a feedback control strategy that efficiently reduces the drag through suppression of asymmetry. In this work the stochastic modelling approach is extended to the vortex shedding, capturing qualitatively both the forced and unforced behaviour. A control strategy is then presented that makes use of the frequency response of the wake, and aims to reduce the measured fluctuations associated with the vortex shedding. The strategy proves to be effective at suppressing fluctuations within specific frequency ranges but, due to amplification of disturbances at other frequencies, is unable to give drag reduction.

Three-Dimensional Pitching Panel Wake: Lagrangian Analysis and Momentum Distribution from Experiments

A majority of fish and other aquatic animals generate thrust by oscillating their fins and flukes, which creates a highly three-dimensional and complex wake that is characterized by spanwise compression, transverse expansion, wake breakdown, etc. The interaction between the oscillating fins and the surrounding fluid creates a complex system of wake structures that is a signature of what can be an animal’s markedly efficient swimming abilities. To interrogate the evolution of these flowfields, Lagrangian analysis using the finite-time Lyapunov exponent field was carried out on experimentally recorded three-dimensional velocity data in the wake of an oscillating trapezoidal panel that models a fish caudal fin in a Strouhal number range of 0.17–0.56. The release of bounding Lagrangian saddles, identified as intersections of positive- and negative-time finite-time Lyapunov exponent ridges, from the panel trailing edge is shown to be related to the extrema of thrust and the evolution of the streamwise momentum field during an oscillation period. The location of vortex disintegration, which is observed downstream of the panel–fluid interaction, was observed to correspond with regions of low streamwise momentum, bifurcated wake structure, and the merger of Lagrangian saddles from two consecutive spanwise structures.

Experimental observations of the three-dimensional wake structures and dynamics generated by a rigid, bioinspired pitching panel

The wake created by a trapezoidal pitching panel displays a variety of dynamics and behaviors. Results show that a chain of highly three-dimensional, alternating vortex rings is shed from the trailing edge. These rings interact with each other in a manner that is dependent on Strouhal number.

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.

Theoretical Acoustic Prediction of the Aerodynamic Interaction for Contra-Rotating Fans

The theoretical prediction formula of far-field interaction tonal noise radiation by contra-rotating fans in free space with point force approximation is derived as the extension of the method of William K. Blake for the conventional stator–rotor interaction. Two primary mechanisms for interaction noise reduction are easily found based on a simple analysis of the formula, which are either to increase the order of the Bessel function of the first kind or to reduce the unsteady lift force. The latter can be realized by reducing the magnitude of the wake centerline velocity deficit or broadening the wake width, which are both related to the interstage separation distance. The aerodynamic and acoustic effects of inter-rotor axial spacing are studied experimentally. It is found that the axial spacing has little effect on aerodynamic performance of the contra-rotating fan, when the nondimensional inter-rotor axial gap based on the axial rotor chord varies in the measured range of 0.18–1.36. Sound pressure level follows an exponential decay law with interstage spacing, from which it is predicted that the three-dimensional rotor wake follows an exponential decay law as well and it decays much faster than the two-dimensional cascade wake. When the nondimensional inter-rotor axial gap is larger than 0.41, it has little effect on the noise level. On the contrary, the interaction noise is very sensitive to the axial spacing in the range below 0.41.

Multi-camera volumetric PIV for the study of jumping fish

Archer fish accurately jump multiple body lengths for aerial prey from directly below the free surface. Multiple fins provide combinations of propulsion and stabilization, enabling prey capture success. Volumetric flow field measurements are crucial to characterizing multi-propulsor interactions during this highly three-dimensional maneuver; however, the fish’s behavior also drives unique experimental constraints. Measurements must be obtained in close proximity to the water’s surface and in regions of the flow field which are partially-occluded by the fish body. Aerial jump trajectories must also be known to assess performance. This article describes experiment setup and processing modifications to the three-dimensional synthetic aperture particle image velocimetry (SAPIV) technique to address these challenges and facilitate experimental measurements on live jumping fish. The performance of traditional SAPIV algorithms in partially-occluded regions is characterized, and an improved non-iterative reconstruction routine for SAPIV around bodies is introduced. This reconstruction procedure is combined with three-dimensional imaging on both sides of the free surface to reveal the fish’s three-dimensional wake, including a series of propulsive vortex rings generated by the tail. In addition, wake measurements from the anal and dorsal fins indicate their stabilizing and thrust-producing contributions as the archer fish jumps.

Two- and three-dimensional wake transitions of an impulsively started uniformly rolling circular cylinder

This paper presents the characteristics of the different stages in the evolution of the wake of a circular cylinder rolling without slipping along a wall at constant speed, acquired through numerical stability analysis and two- and three-dimensional numerical simulations. Reynolds numbers between 30 and 300 are considered. Of importance in this study is the transition to three-dimensionality from the underlying two-dimensional periodic flow and, in particular, the way that the associated transitions influence the fluid forces exerted on the cylinder and the development and the structure of the wake. It is found that the steady two-dimensional flow becomes unstable to three-dimensional perturbations at $Re_{c,3D}=37$, and that the transition to unsteady two-dimensional flow – or periodic vortex shedding – occurs at $Re_{c,2D}=88$, thus validating and refining the results of Stewart et al. (J. Fluid Mech. vol. 648, 2010, pp. 225–256). The main focus here is on Reynolds numbers beyond the transition to unsteady flow at $Re_{c,2D}=88$. From impulsive start up, the wake almost immediately undergoes transition to a periodic two-dimensional wake state, which, in turn, is three-dimensionally unstable. Thus, the previous three-dimensional stability analysis based on the two-dimensional steady flow provides only an element of the full story. Floquet analysis based on the periodic two-dimensional flow was undertaken and new three-dimensional instability modes were revealed. The results suggest that an impulsively started cylinder rolling along a surface at constant velocity for $Re\gtrsim 90$ will result in the rapid development of a periodic two-dimensional wake that will be maintained for a considerable time prior to the wake undergoing three-dimensional transition. Of interest, the mean lift and drag coefficients obtained from full three-dimensional simulations match predictions from two-dimensional simulations to within a few per cent.

Flow control with rotating cylinders

We study the use of small counter-rotating cylinders to control the streaming flow past a larger main cylinder for drag reduction. In a water tunnel experiment at a Reynolds number of 47 000 with a three-dimensional and turbulent wake, particle image velocimetry (PIV) measurements show that rotating cylinders narrow the mean wake and shorten the recirculation length. The drag of the main cylinder was measured to reduce by up to 45 %. To examine the physical mechanism of the flow control in detail, a series of two-dimensional numerical simulations at a Reynolds number equal to 500 were conducted. These simulations investigated a range of control cylinder diameters in addition to rotation rates and gaps to the main cylinder. Effectively controlled simulated flows present a streamline that separates from the main cylinder, passes around the control cylinder, and reattaches to the main cylinder at a higher pressure. The computed pressure recovery from the separation to reattachment points collapses with respect to a new scaling, which indicates that the control mechanism is viscous.

Experimental and numerical analysis of the performance and wake of a scale–model horizontal axis marine hydrokinetic turbine

This paper presents an experimental and numerical study of a scale-model Horizontal Axis Hydrokinetic Turbine (HAHT). The model turbine is based on the U.S. Department of Energy Reference Model 1 (RM1), with the blade geometry modified to reproduce the design Cp–TSR performance curve of the RM1 at the flume scale Reynolds numbers (5 × 104–10 × 105). The performance and wake structure of a 45:1 scale turbine were measured using a load cell (torque applied on shaft) and a magnetic angular encoder (rotor rpm), and by planar particle image velocimetry, respectively. The details of the rotor flow field and three-dimensional wake evolution are analyzed from the numerical solution of the RANS equations solved around a computational model of the turbine. The comparison of experimental and numerical results highlights the strengths and limitations of the experimental and numerical analyses in the characterization of HAHT. Useful guidelines for developing experimental flume scale data and using them for validating numerical tools, as well as for performing a similar type of analysis and design validation of full scale devices as pilot projects start to go in the water in the United States, are provided.

Three-dimensional wake transition for a circular cylinder near a moving wall

Three-dimensional (3D) wake transition for a circular cylinder placed near to a moving wall is investigated using direct numerical simulation (DNS). The study covers a parameter space spanning a gap ratio $(G/D)\geqslant 0.3$ and Reynolds number ($Re$) up to 325. The wake transition regimes in the parameter space are mapped out. It is found that vortex dislocation associated with Mode A is completely suppressed at $G/D$ smaller than approximately 1.0. The suppression of vortex dislocation is believed to be due to the confinement of the Mode A streamwise vortices by the plane wall, which suppresses the excess growth and local dislocation of any Mode A vortex loop. Detailed wake transition is examined at $G/D=0.4$, where the wake transition sequence is ‘two-dimensional (2D) $\rightarrow$ ordered Mode A $\rightarrow$ mode swapping (without dislocations) $\rightarrow$ Mode B’. Relatively strong three-dimensionality is found at $Re=160{-}220$ as the wake is dominated by large-scale structure of ordered Mode A, and also at $Re\geqslant 285$, where Mode B becomes increasingly disordered. A local reduction in three-dimensionality is observed at $Re=225{-}275$, where the wake is dominated by finer-scale structure of a mixture of ordered Modes A and B. Corresponding variations in the vortex shedding frequency and hydrodynamic forces are also investigated.

Discussion about the differences in mass transfer, bubble motion and surrounding liquid motion between a contaminated system and a clean system based on consideration of three-dimensional wake structure obtained from LIF visualization

Mass transfer from a bubble to the surrounding liquid plays an important role in industry processes. To improve the efficiency of the industrial processes, a deep understanding of the mass transfer mechanism is essential. In the present study, the relationship between the instantaneous mass transfer and the motions of the bubble and three-dimensional bubble wakes is discussed, on the basis of precise measurement. Moreover, since some industrial applications are contaminated system, the authors consider influences of bubble-surface contamination on the above. In the present experiments, purified water, and water contaminated with a very small amount of surfactant (1-pentanol) were employed. LIF (Laser Induced Fluorescence) technique and HPTS (a pH-sensitive dye) that was calibrated through a photoelectric optical fiber probe in advance were employed to visualize the mass transfer of the bubble and the wake structure of the bubble. The authors investigated highly reproducible single bubbles (considered to be almost the same bubble) launched from a special bubble-launch device; successfully they acquired pseudo-time-series sliced bubble wakes' images from every y-z plane at an equidistant interval. By processing the pseudo-time-series images through their own new image-processing, they challengingly reconstructed three-dimensional bubble wakes. From careful observations on the three-dimensional bubble wakes’ structure, they indirectly found out that the Marangoni convection, which was induced by the non-uniform distribution of surfactants desorption on the bubble surface, raised changes in the boundary layers in the contaminated water. The authors discussed the influences of gas-liquid interface contamination on the bubble motions, bubble wakes, and mass transfer process based on the reconstruction of three-dimensional bubble wakes in the purified water and contaminated water.

Influence of hydrodynamic slip on convective transport in flow past a circular cylinder

The presence of a finite tangential velocity on a hydrodynamically slipping surface is known to reduce vorticity production in bluff body flows substantially while at the same time enhancing its convection downstream and into the wake. Here, we investigate the effect of hydrodynamic slippage on the convective heat transfer (scalar transport) from a heated isothermal circular cylinder placed in a uniform cross-flow of an incompressible fluid through analytical and simulation techniques. At low Reynolds (Re > 1) numbers, our theoretical analysis based on Oseen and thermal boundary layer equations allows for an explicit determination of the dependence of the thermal transport on the non-dimensional slip length l(s). In this case, the surface-averaged Nusselt number, Nu transitions gradually between the asymptotic limits of Nu similar to Pe(1/3) and Nu similar to Pe(1/2) for no-slip (l(s) -> 0) and shear-free (l(s) -> infinity) boundaries, respectively. Boundary layer analysis also shows that the scaling Nu similar to Pe(1/2) holds for a shear-free cylinder surface in the asymptotic limit of Re >> 1 so that the corresponding heat transfer rate becomes independent of the fluid viscosity. At finite Re, results from our two-dimensional simulations confirm the scaling Nu similar to Pe(1/2) for a shear-free boundary over the range 0.1 <= Re <= 10(3) and 0.1 <= Pr <= 10. A gradual transition from the lower asymptotic limit corresponding to a no-slip surface, to the upper limit for a shear-free boundary, with l(s), is observed in both the maximum slip velocity and the Nu. The local time-averaged Nusselt number Nu(theta) for a shear-free surface exceeds the one for a no-slip surface all along the cylinder boundary except over the downstream portion where unsteady separation and flow reversal lead to an appreciable rise in the local heat transfer rates, especially at high Re and Pr. At a Reynolds number of 10(3), the formation of secondary recirculating eddy pairs results in appearance of additional local maxima in Nu(theta) at locations that are in close proximity to the mean secondary stagnation points. As a consequence, Nu exhibits a non-monotonic variationwith l(s) increasing initially from its lowermost value for a no-slip surface and then decreasing before rising gradually toward the upper asymptotic limit for a shear-free cylinder. A non-monotonic dependence of the spanwise-averaged Nu on l(s) is observed in three dimensions as well with the three-dimensional wake instabilities that appear at sufficiently low l(s), strongly influencing the convective thermal transport from the cylinder. The analogy between heat transfer and single-component mass transfer implies that our results can directly be applied to determine the dependency of convective mass transfer of a single solute on hydrodynamic slip length in similar configurations through straightforward replacement of Nu and Pr with Sherwood and Schmidt numbers, respectively.

Instability of cylinder wake under open-loop active control

Instability of a wake controlled by a streamwise Lorentz force is investigated through a Floquet stability analysis. The streamwise Lorentz force, which is a two-dimens- ional control input created by an electromagnetic actuator located on the cylinder surface, adjusts the base flow to affect the three-dimensional wake instability and achieve wake stabilization and transition delay. The instability mode at a Reynolds number Re = 300 can be transformed from B to A with N = 1.0, where N is an interaction number repre- senting the strength of the Lorentz force relative to the inertial force in the fluid. The wake flow is Floquet stable when N increases to 1.3. The spanwise perturbation wavelengths are 3.926D and 0.822D in the modes A and B, respectively, where D is the cylinder diameter. In addition, the oscillating amplitudes of drag and lift are reduced with the increase in the interaction number. Particle tracing is used to explore the essential physical mechanism for mode transformation. The path lines show that suppression of flow separation hinders the fluid deformation and rotation, leading to the decrease in elliptic and hyperbolic instability regions, which is the material cause of mode transformation. All of the results indicate that wake stabilization and transition delay can be achieved under open-loop active control via the streamwise Lorentz force.

A linearized numerical model of wind-farm flows

A fast and reasonably accurate numerical three-dimensional wake model able to predict the flow behaviour of a wind farm over a flat terrain has been developed. The model is based on the boundary-la ...

Stable state of Mode A for flow past a circular cylinder

A stable three-dimensional (3D) wake structure for flow past a circular cylinder has been discovered through 3D direct numerical simulations (DNS). The stable 3D wake structure occurs over a small range of Reynolds number (Re) below the critical Re for Mode A∗ (i.e., Mode A with large-scale vortex dislocations, where Mode A is the first 3D instability mode which will evolve into Mode A∗) instability. It is believed that the stable 3D wake structure discovered in this study is the stable state of Mode A wake structure inferred by Williamson [“Three-dimensional wake transition,” J. Fluid Mech. 328, 345–407 (1996)]. This confirms the wake transition sequence of 2D → A → A∗ → B suggested by Williamson. Compared with conventional Mode A structure, the stable state of Mode A structure has much weaker amplitude and does not evolve into large-scale vortex dislocations. The stable state of Mode A structure is triggered by small-scale spanwise disturbance introduced upstream of the cylinder, due to energy amplification through convective instability of the flow. The stable state of Mode A is transient and is damped out eventually under a transient initial disturbance condition, but is sustained throughout under a persistent disturbance condition. The emergence of the stable state of Mode A structure is correlated with both Re and the disturbance level. With the decrease of Re, the stable state of Mode A structure gradually becomes less well-defined and eventually disappears. With the decrease of the disturbance level, the stable state of Mode A structure emerges at a higher Re.

Turbulent wake behind two intersecting flat plates

We have considered the three-dimensional wake behind a cross formed by two intersecting flat plates using direct numerical simulations. The Reynolds number based on the uniform inflow velocity U0 and the plate width d was 1000. The vortex shedding in the wake was totally suppressed in a 4d wide intersection region and this gave rise to a massive zone of recirculating flow. Quasi two-dimensional vortex shedding with a primary frequency 0.165 U0/d occurred behind the outer branches more than 7d from the intersection. The wake behind the outer branches of the crossing plates closely resembled the wake behind a single flat plate. However, the wake flow in an intermediate region (located between the intersection region and the outer branches) was affected by persistent secondary flows. Further, shear-layer (K-H) instabilities have been observed in this region. The mean wake structure revealed the formation of four symmetrically positioned pairs of swirling vortices close to the intersection corner next to the plate's edges.