Vortex Instability Research Articles

Stability of Floating Wind Turbine Wakes

Floating offshore wind turbines (FOWTs) are the next frontier in offshore wind energy, allowing exploration of deep-water regions previously unavailable to fixed-foundation turbines. Since offshore turbines operate in lower turbulence levels, the intrinsic hydrodynamic unstable modes of the tip vortices can have even more relevance than in onshore turbines. For floating turbines, platform motion induced by wind and wave loads can trigger vortex instabilities, modifying the wake structure, possibly influencing the flow reaching downstream wind turbines. In the present paper, we study those effects by the means of numerical simulations and their comparison with analytical studies. In our simulations, the wind turbine blades are modeled as actuator lines in the incompressible Navier–Stokes equations. Heave motion with different amplitudes and frequencies are studied. The effect of increasing amplitude is to advance the onset of vortex interaction. For the lower frequency of heave motion, several vortices coalesce to form a large flow structure. High amplitude of oscillations in the streamwise velocity were observed due to these flow structures, which may increase fatigue or induce high amplitude motion on downstream turbines. The number of vortices that interact, as other qualitative phenomena of the numerical simulation, were well predicted by a simple stability model of two-dimensional row of vortices. The disturbances imposed by the heave motion were also compared to the eigenvectors resulting from linear stability theory for helical vortices and the predicted growth rates for the wavenumbers resulting from this comparison were consistent with the model of a row of vortices. These results motivate further studies to understand the impact of the larger flow structures on downstream turbines.

Theoretical, numerical and experimental study of hypersonic boundary layer transition: Blunt circular cone

• Hypersonic boundary layer transition is studied using various approaches. • Leading edge receptivity is crucial for understanding “transition reversal”. • Centreline and crossflow vortices significantly promote transition on a yawed cone. • The newly proposed C - γ - Re θ transition model works well at various flow conditions. • Valuable transition data is acquired in real flight test for a cone model. This article reviews the hypersonic laminar-turbulent boundary layer transition over a blunt circular cone under support of the National Key Research and Development Program of China (contract No. 2016YFA0401200). Various approaches, including theoretical, numerical, experimental and flight test, are combined to obtain a complete perspective of the transition process as well as some fundamental issues for this kind of flow. The interaction between freestream disturbances and the front shock wave is analysed theoretically, and multiple receptivity routes are unveiled using a sub-zone analysis technique. The entire transition process is captured using high-resolution nano-tracer-based planar laser scattering technique in a quiet windtunnel as well as large-scale high-fidelity direct numerical simulations. Using dynamic mode decomposition, the relationship between the second Mach mode and the low-frequency mode in the late stage of the transition is revealed. The “transition reversal” phenomenon is recovered in two of our conventional windtunnels. The numerical results show that leading-edge receptivity varies significantly for different cone bluntness, which might be responsible for the “transition reversal” phenomenon. For the cone at angles of attack, new instabilities including the leeward centerline vortex instability and the crossflow instability, occur and can significantly promote the transition process. A newly developed C - γ - Re θ transition model can give a good transition front prediction compared to the experimental data. The flight test for a cone model conducted within this project is reviewed, and the correlation between the ground experimental data and the flight data is established.

Turbulence Structure and Momentum Exchange in Compound Channel Flows With Shore Ice Covered on the Floodplains

AbstractIce cover formed on a river surface is a common natural phenomenon during the winter season in cold high latitude northern regions. For the ice‐covered river with compound cross‐section, the interaction of the turbulence caused by the ice cover and the channel bed bottom affects the transverse mass and momentum exchange between the main channel and floodplains. In this study, laboratory experiments are performed to investigate the turbulent flow of a compound channel with shore ice covered on the floodplains. Results show that the shore ice resistance restricts the development of the water flow and creates a relatively strong shear layer near the edge of the ice‐covered floodplain. The mean streamwise velocity in the main channel and on the ice‐covered floodplains shows an opposite variation pattern along with the longitudinal distance and finally reaches the longitudinal uniformity. The mixing layer bounded by the velocity inflection point consists of two layers that evolve downstream to their respective fully developed states. The velocity inflection point and strong transverse shear near the interface in the fully developed profile generate the Kelvin‐Helmholtz instability and horizontal coherent vortices. These coherent vortices induce quasi‐periodic velocity oscillations, while the dominant frequency of the vortical energy is determined through the power spectral analysis. Subsequently, quadrant analysis is used in ascertaining the mechanism for the lateral momentum exchange, which exhibits the governing contributions of sweeps and ejections within the vortex center. Finally, an eddy viscosity model is presented to investigate the transverse momentum exchange. The presented model is well validated through comparison with measurements, whereas the constants α and β appeared in the model need to be further investigated.

Investigation of the near wake of a horizontal-axis wind turbine model by dynamic mode decomposition

The wake flow of a horizontal-axis wind turbine has an important effect on the energy extraction and downstream turbulent flow. In this paper, large eddy simulation is employed to obtain the unsteady flow over a two-blade wind turbine model. The detailed geometry of the blade is resolved in the computational mesh. The wake flow is analyzed using dynamic mode decomposition (DMD). The DMD results for the wake flow in the absolute reference frame indicate that the tip vortices are the dominant unsteady flow features in the near wake. The leading energetic modes illustrate the downstream, swing and rotating motion of the tip vortices. The wake flow in a relative reference frame static to the rotor is also analyzed by DMD. The decomposition results illustrate the traveling wave structures and spatial-growth disturbances on the helical vortex filaments. The mode results suggest that the disturbances are gradually formed from the small-scale turbulences, grow rapidly on the helical vortex filament and eventually contribute to the mutual instability of the tip vortices. The breakdown of the tip vortices will lead to the wake recovery and affect the energy extraction of downstream turbines.

Modelling the nacelle wake of a horizontal-axis wind turbine under different yaw conditions

Recently, actuator line model become popular in studying wind-turbine wakes. However, existing models ignore or inaccurately describe nacelle effects, which have been shown to pose significantly impact on wakes. To address the physics underlying here, we develop the actuator line model with large-eddy simulation by introducing a new anisotropic body-force projection model. We validate the new model against a field experiment and the validation indicates that the new anisotropic model can predict the wake more precise than the existing isotropic model. Furthermore, we extend the study to wake characteristics under various yaw conditions. The results show that the thrust component normal to the flow direction creates a skewed wake behind the turbine, which in turn promotes the wake transition from the two-peak profile to the one-peak profile. The wake skew exacerbates the instability of the tip vortex and causes the wake region to narrow. At small yaw angles, the nacelle vortex radially diffuses and blends with the tip vortex in the far wake. At large yaw angles, the nacelle vortex intercepts the tip vortex in the near wake due to the different spatial distribution of thrust. It is concluded that the nacelle significantly affects wind-turbine wakes especially during yaw condition.

Flow behavior of skewed vortex generators on a backward-facing ramp

The impact of skewness angle on the effectiveness of vortex generators (VGs) and the behavior of streamwise vortices on flow separation behind a backward-facing ramp (BFR) with a sharp transition were experimentally investigated using surface oil flow visualizations, planar and stereoscopic particle image velocimetry measurements. Counter/corotating streamwise vortices were generated by a set of boundary layer-type rectangular VG located upstream of the BFR that comprised a flat- and 30-inclined sections with different skewness angles of 10°, 20°, and 30°. Local Reynolds number based on the VG location was Rex ≈ 3 × 106. Results show that the reattachment length was reduced by ∼45% when the VG was located five times its height ahead of the transition. Additionally, the behavior of the vortex core generated by the left vane displayed strong dependence on the skewness angle, whereby its vorticity magnitude and vortex instability increase with the skewness angle. Circulation magnitude and vortex radius of the left vortex core are also observed to be physically larger and less stable. In contrast, the vortex core produced by the right vane displays opposite behavior as the skewness angle increases. Lastly, the vortex core location is observed to fluctuate more in the vertical direction than horizontal direction.

Interactions between Water Vapor, Potential Vorticity, and Vertical Wind Shear in Quasi-Geostrophic Motions: Implications for Rotational Tropical Motion Systems

AbstractA linear two-layer model is used to elucidate the role of prognostic moisture on quasigeostrophic (QG) motions in the presence of a mean thermal wind (). Solutions to the basic equations reveal two instabilities that can explain the growth of moist QG systems. The well-documented baroclinic instability is characterized by growth at the synoptic scale (horizontal scale of ~1000 km) and systems that grow from this instability tilt against the shear. Moisture–vortex instability—an instability that occurs when moisture and lower-tropospheric vorticity exhibit an in-phase component—exists only when moisture is prognostic. The instability is also strongest at the synoptic scale, but systems that grow from it exhibit a vertically stacked structure. When moisture is prognostic and is easterly, baroclinic instability exhibits a pronounced weakening while moisture vortex instability is amplified. The strengthening of moisture–vortex instability at the expense of baroclinic instability is due to the baroclinic () component of the lower-tropospheric flow. In westward-propagating systems, lower-tropospheric westerlies associated with an easterly advect anomalous moisture and the associated convection toward the low-level vortex. The advected convection causes the vertical structure of the wave to shift away from one that favors baroclinic instability to one that favors moisture–vortex instability. On the other hand, a westerly reinforces the phasing between moisture and vorticity necessary for baroclinic instability to occur. Based on these results, it is hypothesized that moisture–vortex instability is an important instability in humid regions of easterly such as the South Asian and West African monsoons.

Density and surface tension effects on vortex stability. Part 2. Moore–Saffman–Tsai–Widnall instability

Abstract

Comparison of hydrodynamic performance and wake vortices of two typical types of pumpjet propulsor

Pumpjet propulsor (PJP) is widely used in various underwater vehicles recently. Two types of PJP, the stator-rotor PJP (the rotor is behind the stator) and the rotor-stator PJP (the rotor is in front of the stator), are designed to investigate the difference of the hydrodynamic performance between those two PJPs. Numerical simulations based on the Improved Delayed Detached Eddy Simulation (IDDES) model are carried out. Results show that the rotor-stator PJP has a better balanced torque character than that of the stator-rotor PJP. In addition, the characteristic frequency of unsteady forces acting on each rotor blade is the stator blade passage frequency and its harmonics, while that of each stator blade is the rotor blade passage frequency and its harmonics. The wake vortex structure and the evolution mechanism of both PJPs are discussed and compared. Spiral precession and double-helix breakdown of hub vortex are observed for the stator-rotor PJP. The roll-up process of rotor blade trailing edge vortex sheet for both PJPs is discussed. The short-wave instability and the mutual-inductance instability of tip vortices for PJPs are discussed. The instability of tip and hub vortices of the rotor-stator PJP is more likely to occur.

Mathematical formulation for the analysis of the periodic convergence during co-processing routines in long-run, scale-resolving simulations of turbomachinery

Scale-resolving simulations, like LES modelling, are recent CFD techniques to analyse numerically unsteady flows and turbulence in turbomachinery. Despite their high computational costs, they provide an unsteady, time-resolved solution of the flow with embedded turbulent scales that requires an additional statistical description. This paper provides the mathematical formulation required to compute and assure its periodic convergence, updating the phase-averaged values and the residual on the run, so the amount of data to be stored is extremely reduced. The formulation, applied over a numerical database of a wall-modelled LES simulation of the rotor-stator interaction in a low-speed axial fan using a 3D linear cascade model, reveals that primary flow variables converge faster than turbulent structures due to inherent instabilities of the coherent flow vortices. This work forms part of the concept of co-processing, where some post-processing routines are resolved during the iterative process of CFD simulations to save computational costs.

Mathematical formulation for the analysis of the periodic convergence during co-processing routines in long-run, scale-resolving simulations of turbomachinery

Scale-resolving simulations, like LES modelling, are recent CFD techniques to analyse numerically unsteady flows and turbulence in turbomachinery. Despite their high computational costs, they provide an unsteady, time-resolved solution of the flow with embedded turbulent scales that requires an additional statistical description. This paper provides the mathematical formulation required to compute and assure its periodic convergence, updating the phase-averaged values and the residual on the run, so the amount of data to be stored is extremely reduced. The formulation, applied over a numerical database of a wall-modelled LES simulation of the rotor-stator interaction in a low-speed axial fan using a 3D linear cascade model, reveals that primary flow variables converge faster than turbulent structures due to inherent instabilities of the coherent flow vortices. This work forms part of the concept of co-processing, where some post-processing routines are resolved during the iterative process of CFD simulations to save computational costs.

Numerical investigation of marine propeller underwater radiated noise using acoustic analogy Part 2: The influence of eddy viscosity turbulence models

The present study focuses on the impact of eddy viscosity turbulence models on the benchmark INSEAN E779A marine propeller hydroacoustic performance under non-cavitating and open water conditions. In the numerical calculations, Realisable k-epsilon (k-ε), k-ω Shear Stress Transport (k-ω SST) and Spalart-Allmaras turbulence models, which are widely used in hydrodynamic fields, are selected. Hydroacoustic performance of the model propeller is predicted with the porous FW-H formulation coupled with Reynolds-averaged Navier Stokes (RANS) solver. This study aims to show the effects of different turbulence models on marine propeller hydroacoustic performance at high and low blade loading conditions both in the near and far-fields. The numerical results show that the underwater radiated noise (URN) levels, which are predicted by using different eddy viscosity turbulence models together with the porous FW-H formulation, are found to be similar at low blade loading conditions. The reason behind this similarity is due to the analogous wake structure and hydrodynamic field. However, when the propeller loading is high, the propeller's wake loses its stability; hence, the coherent vortex structures break-up and evolve into the far-field of the propeller's slipstream. The instability process of the propeller's wake is predicted in a different manner by eddy viscosity turbulence models, and these differences cause dissimilar prediction of the URN in the far-field. Consequently, the underwater pressure field is considerably affected by the instability of the vortex structures (as a non-linear noise source) for far-field noise estimations. As a result, vortex instability in the propeller's slipstream might be the main noise source of the URN for far-field noise estimations under non-cavitating and high blade loading conditions.

Stability analysis and transition prediction of streamwise vortices over a yawed cone at Mach 6

An investigation into the linear instability of streamwise vortices over a yawed blunt cone with a half-angle of 7° at 6° angle of attack, a free-stream Mach number of 6, and a Reynolds number of 1.0 × 107/m was performed. The steady laminar base flow obtained using direct numerical simulation (DNS) has a mushroom structure. Three classes of unstable modes (inner mode, outer mode, and Mack mode modified by the streamwise vortices) were identified using a two-dimensional spatial global stability analysis (bi-global). Among them, the inner mode and the modified Mack mode were discovered for the first time for such a configuration. Notably, the inner mode appears only over a short distance upstream of the cone, and its energy is mainly in the vicinity of the symmetry plane of the mushroom structure. By comparing with DNS results, it was shown that multiple instability modes can coexist physically during the transition in the leeward plane. In addition, the eN method based on global stability theory was used to predict the location of the transition along the centerline on the leeward side of the cone. It was found that the inner modes grow rapidly in the upstream region, while the outer mode near the stem of the mushroom structure dominates the transition in the downstream region. Further analysis suggests that the inner modes dominate the transition only in a noisy environment, whereas the traditional centerline modes dominate the transition in quiet free-stream conditions.

POD‐based analysis of a wind turbine wake under the influence of tower and nacelle

AbstractThe wake produced by a model wind turbine is investigated using proper orthogonal decomposition (POD) of numerical data obtained by large eddy simulations at a diameter‐based Reynolds number . The blades are modeled employing the actuator line method and an immersed boundary method is used to simulate tower and nacelle. Two simulations are performed: one accounts only for the blades effect; the other includes also tower and nacelle. The two simulations are analyzed and compared in terms of mean flow fields and POD modes that mainly characterize the wake dynamics. In the rotor‐only case, the most energetic modes in the near wake are composed of high‐frequency tip and root vortices, whereas in the far wake, low‐frequency modes accounting for mutual inductance instability of tip vortices are found. When tower and nacelle are included, low‐frequency POD modes are present already in the near wake, linked to the von Karman vortices shed by the tower. These modes interact nonlinearly with the tip vortices in the far wake, generating new low‐frequency POD modes, some of them lying in the frequency range of wake meandering. An analysis of the mean kinetic energy (MKE) entrainment of each POD mode shows that tip vortices sustain the wake mean shear, whereas low‐frequency modes contribute to wake recovery. This explains why tower and nacelle induce a faster wake recovery.

Dynamical analysis of submesoscale fronts associated with wind-forced offshore jet in the western South China Sea

This study investigates the submesoscale fronts and their dynamic effects on the mean flow due to frontal instabilities in the wind-driven summer offshore jet of the western South China Sea (WSCS), using satellite observations, a 500 m-resolution numerical simulation, and diagnostic analysis. Both satellite measurements and simulation results show that the submesoscale fronts occupying a typical lateral scale of O(∼10) km are characterized with one order of Rossby (Ro) and Richardson (Ri) numbers in the WSCS. This result implies that both geostrophic and ageostrophic motions feature in these submesoscale fronts. The diagnostic results indicate that a net cross-frontal Ekman transport driven by down-front wind forcing effectively advects cold water over warm water. By this way, the weakened local stratification and strong lateral buoyancy gradients are conducive to a negative Ertel potential vorticity (PV) and triggering frontal symmetric instability (SI) at the submesoscale density front. The cross-front ageostrophic secondary circulation caused by frontal instabilities is found to drive an enhanced vertical velocity reaching O(100) m/d. Additionally, the estimate of the down-front wind forcing the Ekman buoyancy flux (EBF) is found to be scaled with the geostrophic shear production (GSP) and buoyancy flux (BFLUX), which are the two primary energy sources for submesoscale turbulence. The large values of GSP and BFLUX at the fronts suggest an efficient downscale energy transfer from larger-scale geostrophic flows to the submesoscale turbulence owing to down-front wind forcing and frontal instabilities. In this content, submesoscale fronts and their instabilities substantially enhance the local vertical exchanges and geostrophic energy cascade towards smaller-scale. These active submesoscale processes associated density fronts and filaments likely provide new physical interpretations for the filamentary high chlorophyll concentration and frontal downscale energy transfer in the WSCS.

Double-layer Bose-Einstein condensates: A quantum phase transition in the transverse direction, and reduction to two dimensions.

We revisit the problem of the reduction of the three-dimensional (3D) dynamics of Bose-Einstein condensates, under the action of strong confinement in one direction (z), to a 2D mean-field equation. We address this problem for the confining potential with a singular term, viz., V_{z}(z)=2z^{2}+ζ^{2}/z^{2}, with constant ζ. A quantum phase transition is induced by the latter term, between the ground state (GS) of the harmonic oscillator and the 3D condensate split in two parallel noninteracting layers, which is a manifestation of the "superselection" effect. A realization of the respective physical setting is proposed, making use of resonant coupling to an optical field, with the resonance detuning modulated along z. The reduction of the full 3D Gross-Pitaevskii equation (GPE) to the 2D nonpolynomial Schrödinger equation (NPSE) is based on the factorized ansatz, with the z -dependent multiplier represented by an exact GS solution of the 1D Schrödinger equation with potential V_{z}(z). For both repulsive and attractive signs of the nonlinearity, the 2D NPSE produces GS and vortex states, that are virtually indistinguishable from the respective numerical solutions provided by full 3D GPE. In the case of the self-attraction, the threshold for the onset of the collapse, predicted by the 2D NPSE, is also virtually identical to its counterpart obtained from the 3D equation. In the same case, stability and instability of vortices with topological charge S=1, 2, and 3 are considered in detail. Thus, the procedure of the spatial-dimension reduction, 3D → 2D, produces very accurate results, and it may be used in other settings.

Birth of a hurricane: early detection of large-scale vortex instability

A way is substantiated for detecting new large-scale vortex instability in the tropical atmosphere. The instability may occur several hours or even several dozens of hours before the formation of a tropical depression or tropical storm. The diagnosis of instability was developed on the basis of data from idealized cloud-resolving atmospheric simulation for tropical cyclogenesis. It is suggested how the evolving instability may be traced by combining high-resolution numerical modeling and GOES Imagery. As an illustration, it is speculated and discussed that the instability may have emerged in future Hurricane Isaias (2020) when it had a status of Potential Tropical Cyclone for 36 hours before it was diagnosed as Tropical Storm.

Three-Dimensional Effects on Plunging Airfoils at Low Reynolds Numbers

We present two-dimensional and three-dimensional (3-D) direct numerical simulations of large-amplitude plunging maneuvers at Reynolds numbers of and 5000, with velocity ratios of , 1, and 2. For all cases, the evolution of the force coefficients is qualitatively similar. The lift coefficient presents a pronounced peak toward the end of the acceleration phase of the maneuver, a local minimum in the deceleration phase, and a second peak at the end of the maneuver. The amplitude of the main peak increases linearly with , with limited effect of the Reynolds number and a negligible effect of the three-dimensionality of the flow. On the other hand, both the Reynolds number and three-dimensionality have a stronger effect on the amplitude of the maximum value of the lift coefficient at the end of the maneuver, as well as on the subsequent transient decay toward the static values. The comparison of the evolution of the flow structures near the airfoil shows that these differences in the force coefficients are due to subtle interactions between the various vortices generated during the maneuver, as well as to the development of a 3-D boundary layer on the suction side of the airfoil triggered by the instability of the trailing-edge vortices.

Evolution, propagation and interactions with topography of hurricane-like vortices in a moist-convective rotating shallow-water model

Abstract

A new LES approach to trans-critical mixing and combustion processes in high-pressure liquid-injectant engines

The understanding of flame holding mechanism is very important for combustor design. To elucidate the flame holding mechanism at the injector exit in liquid rocket engines, it is indispensable to know the underlying physics of trans-critical mixing process, because the flame holding location is exactly where trans-critical mixing process, which is still veiled, takes place. In the present paper, a new Large Eddy Simulation (LES) method is developed by gaining deeper physical insights into possible sub-grid-scale (SGS) thermodynamic and fluid dynamic instabilities excitable at thin large-density-gradient-magnitude portions to describe trans-critical processes. The presence of thin large-density-gradient-magnitude portions in trans-critical mixing process is troublesome for numerical stability of supercritical fluid flow LES from various points of view. Our idea is to utilize an SGS model functioning at the crossover between the liquid-like and gas-like supercritical fluids in a hybrid scheme of Lagrangian particle tracking and two-phase flow LES. Reduced dynamic viscosity at high pressure may cause SGS thermodynamic and hydrodynamic instabilities in the trans-critical mixing flow field. They are (1) phase separation due to thermodynamic instability, (2) Landau's hydrodynamic instability occurring at the pseudo-boiling location within a heated injector, and (3) Rayleigh–Taylor instability at the pseudo-boiling location, which is induced by Kelvin–Helmholtz instability vortices. These are analyzed and organized into new SGS models characterizing the trans-critical jet mixing process.