Large Velocity Fluctuations Research Articles

Measurement of flow structures and heat transfer behind a wall-proximity square rib using TSP, PIV and split-fiber film

In the present study, complementary measurement techniques—temperature sensitive paint (TSP), planar particle image velocimetry (planar PIV) and a split-fiber film probe—were used to investigate the effects of a “wall-proximity square rib” on flow structure and surface heat transfer augmentation. TSP was used to measure the time-averaged wall temperature field at three different Reynolds numbers ( $$ Re_{d} $$ = 3800, 7600 and 11,400) based on the rib height d and the mainstream velocity $$ U_{o} $$ , and wall-proximity configurations with four different gap ratios (gap size $$ G $$ over rib height d), G/d = 0, 0.25, 0.50 and 0.75. The two-dimensional distribution of the normalized Nusselt number convincingly demonstrated the existence of a hot spot immediately behind the rib in the attached rib configuration (G/d = 0) and surface heat transfer augmentation in the reattachment zone. Among the three wall-proximity configurations, G/d = 0.25 resulted in maximum heat transfer augmentation immediately behind the rib and overall improvement in surface heat removal. However, no distinctly different spatial patterns of the normalized Nusselt number distribution were found at the three different Reynolds numbers. A subsequent experiment examined the flow pattern and flow structures at $$ Re_{d} $$ = 7600 and three wall-proximity configurations (G/d = 0, 0.25 and 0.50). Velocity field measurements using PIV, along with complementary measurements using split-fiber film, gave a clear view of the flow pattern behind the rib; a very slender separation bubble with highly unsteady flow reversal was found close to the surface when G/d = 0.25. For configurations with G/d = 0.25 and 0.50, the high-speed jet issuing from the gap had a complicated influence on the interaction between the upper free shear layer and lower strong shear layer, resulting in slanted movement of the coupled wake flow. Proper orthogonal decomposition was used to identify the spatial characteristics of the superimposed flow structures. In the configuration G/d = 0.25, coherent structures were found throughout most of the wake region, beginning roughly 1.2d behind the rib. Fluid flow in the region near the wall was strongly influenced by the dominant coherent structures, which were evidently the main mechanism for surface heat removal. In the configuration with G/d = 0.50, the area with large velocity fluctuation intensity shifted away from the wall toward the mainstream due to rapid expansion of the wall jet. This, in combination with large-scale coherent structures from the surface, meant a much reduced influence on the fluid near the wall and a corresponding deterioration of surface heat transfer beyond the station x/d = 4 (x being the downstream distance from the rib’s trailing edge).

Large-scale numerical simulations of polydisperse particle flow in a silo

Very recently, we have examined experimentally and numerically the micro-mechanical details of monodisperse particle flows through an orifice placed at the bottom of a silo (Rubio-Largo et al. in Phys Rev Lett 114:238002, 2015). Our findings disentangled the paradoxical ideas associated to the free-fall arch concept, which has historically served to justify the dependence of the flow rate on the outlet size. In this work, we generalize those findings examining large-scale polydisperse particle flows in silos. In the range of studied apertures, both velocity and density profiles at the aperture are self-similar, and the obtained scaling functions confirm that the relevant scale of the problem is the size of the aperture. Moreover, we find that the contact stress monotonically decreases when the particles approach the exit and vanish at the outlet. The behavior of this magnitude is practically independent of the size of the orifice. However, the total and partial kinetic stress profiles suggest that the outlet size controls the propagation of the velocity fluctuations inside the silo. Examining this magnitude, we conclusively argue that indeed there is a well-defined transition region where the particle flow changes its nature. The general trend of the partial kinetic pressure profiles and the location of the transition region results the same for all particle types. We find that the partial kinetic stress is larger for bigger particles. However, the small particles carry a higher fraction of kinetic stress respect to their concentration, which suggest that the small particles have larger velocity fluctuations than the large ones and showing lower strength of correlation with the global flow. Our outcomes explain why the free-fall arch picture has served to describe the polydisperse flow rate in the discharge of silos.

A comprehensive numerical investigation on the hydrodynamics and erosion characteristics in a pressurized fluidized bed with dense immersed tube bundles

Based on the coupling method of computational fluid dynamics (CFD) with discrete element method (DEM), numerical investigation on the gas-solid hydrodynamics and erosion characteristics is conducted in a 3-D pressurized fluidized bed with immersed tube bundles. The effects of operating pressure on time-averaged solid-phase characteristics, solid circulation features, granular temperature and tube erosion patterns are analyzed. Elevated pressure accelerates both upward and downward particle flows, resulting in a lower solid concentration in the bottom part compared to the upper part. A theory is proposed to explain the occurrence of large solid velocity fluctuation. The distinct erosion distribution of each tube is found to be strongly related to solid flux distribution. The mechanism of bubble-induced tube erosion is represented and validated by simulation result.

The effects of bar–spiral coupling on stellar kinematics in the Galaxy

We investigate models of the Milky Way disc taking into account simultaneously the bar and a two-armed quasi-static spiral pattern. Away from major resonance overlaps, the mean stellar radial motions in the plane are essentially a linear superposition of the isolated effects of the bar and spirals. Thus, provided the bar is strong enough, even in the presence of spiral arms, these mean radial motions are predominantly affected by the Galactic bar for large scale velocity fluctuations. This is evident when comparing the peculiar line-of-sight velocity power spectrum of our coupled models with bar-only models. However, we show how forthcoming spectroscopic surveys could disentangle bar-only non-axisymmetric models of the Galaxy from models in which spiral arms have a significant amplitude. We also point out that overlaps of low-order resonances are sufficient to enhance stellar churning within the disc, even when the spirals amplitude is kept constant. Nevertheless, for churning to be truly non-local, stronger or (more likely) transient amplitudes would be needed: otherwise the disc is actually mostly unaffected by churning in the present models. Finally, regarding vertical breathing modes, the combined effect of the bar and spirals on vertical motions is a clear non-linear superposition of the isolated effects of both components, significantly superseding the linear superposition of modes produced by each perturber separately, thereby providing an additional effect to consider when analysing the observed breathing mode of the Galactic disc in the extended Solar neighbourhood.

The flow inside shaking flasks and its implication for mycelial cultures

Several parameters such as mixing time, power consumption and deformation rates have been commonly reported in the literature for the hydrodynamic characterization of shaken flasks. In the present work, flow fields of orbital shaken flasks having different geometries have been experimentally obtained. Conventional, baffled and coiled flasks were tested at constant shaking speed of 150rpm at which the cultures are grown. Flow fields in terms of turbulence intensity and deformation rate were both determined by means of the Particle Image Velocimetry (PIV) technique. Velocity fields are strongly dependent on the flask geometry; in particular, the main flow is confined near the wall for the conventional geometry. In general, large velocity fluctuations are found in the whole flask for the baffled and coiled geometries, while the turbulence intensity is virtually zero at the center region for the conventional flask. The measurement of the average deformation rate indicates that flow obstacles, such as indentations and coiled springs, generate regions with high hydrodynamic stresses promoting the elongation and breakup of bubbles and biomass. Results from this study have been compared with previous studies finding good agreement for the same flask configurations at similar experimental conditions.

Characterization of Transition to Turbulence for Blood in a Straight Pipe Under Steady Flow Conditions.

Blood is a complex fluid that, among other things, has been established to behave as a shear thinning, non-Newtonian fluid when exposed to low shear rates (SR). Many hemodynamic investigations use a Newtonian fluid to represent blood when the flow field of study has relatively high SR (>200 s-1). Shear thinning fluids have been shown to exhibit differences in transition to turbulence (TT) compared to that of Newtonian fluids. Incorrect prediction of the transition point in a simulation could result in erroneous hemodynamic force predictions. The goal of the present study was to compare velocity profiles near TT of whole blood and Newtonian blood analogs in a straight rigid pipe with a diameter 6.35 mm under steady flow conditions. Rheology was measured for six samples of whole porcine blood and three samples of a Newtonian fluid, and the results show blood acts as a shear thinning non-Newtonian fluid. Measurements also revealed that blood viscosity at SR = 200 s-1 is significantly larger than at SR = 1000 s-1 (13.8%, p < 0.001). Doppler ultrasound (DUS) was used to measure velocity profiles for blood and Newtonian samples at different flow rates to produce Reynolds numbers (Re) ranging from 1000 to 3300 (based on viscosity at SR = 1000 s-1). Two mathematically defined methods, based on the velocity profile shape change and turbulent kinetic energy (TKE), were used to detect TT. Results show similar parabolic velocity profiles for both blood and the Newtonian fluid for Re < 2200. However, differences were observed between blood and Newtonian fluid velocity profiles for larger Re. The Newtonian fluid had blunt-like velocity profiles starting at Re = 2403 ± 8 which indicated transition. In contrast, blood did not show this velocity profile change until Re = 2871 ± 104. The Newtonian fluid had large velocity fluctuations (root mean square (RMS) > 20%) with a maximum TKE near the pipe center at Re = 2316 ± 34 which indicated transition. In contrast, blood results showed the maximum TKE at Re = 2806 ± 109. Overall, the critical Re was delayed by ∼20% (p < 0.001) for blood compared to the Newtonian fluid. Thus, a Newtonian assumption for blood at flow conditions near transition could lead to large errors in velocity prediction for steady flow in a straight pipe. However, these results are specific to this pipe diameter and not generalizable since SR is highly dependent on pipe diameter. Further research is necessary to understand this relation in different pipe sizes, more complex geometries, and under pulsatile flow conditions.

Instabilities due to turbulence through inlet jet in plunging jet bubble column

Bubble columns, where the liquid is in the continuous phase and the gas phase is on the form of dispersed bubbles, are widely utilised in many industrial applications. When designing these bubble columns it is important to be able to predict the conditions that mark the transition from homogeneous (bubbly) to heterogeneous (churn-turbulent) flow. The transition is a function of many variables, including: liquid and gas superficial velocities, bubble diameter, and liquid and gas physical properties. Linear stability analysis (LSA) has been successfully applied by many researchers to determine the gas volume fraction at which the instability takes place; and correspondingly a one dimensional stability factor, f1, has been proposed (see for example Joshi et al. (2001)). Briefly, the LSA analysis utilises the velocity fluctuations of both the dispersed and continuous phases associated with the specific energy dissipation rate of the two phase mixture. Typically, the specific energy dissipation rate is correlated with the density of the bed. The previous analysis, however, does not consider the energy input which associated with the turbulence intensity (velocity fluctuations) of the incoming liquid stream. Usually, this component can be ignored in sparged bubble columns because its magnitude is relatively small and it also decays in the axial direction. In plunging liquid jet bubble columns the liquid is introduced as a high speed jet that entrains gas which is then broken into fine bubbles in the Mixing Zone. The bubby mixture then passes into the Two Phase Flow Zone where instabilities can be generated. The Mixing Zone is a region of high energy dissipation resulting in relatively large liquid velocity fluctuations, which can directly influence the instability of the Two Phase Flow Zone.In this study the existing linear stability analysis is modified to include the influence of inlet liquid velocity fluctuations on the stability parameter, f1. The modified theory is applied to the previous work of Evans (1990) for a plunging liquid jet bubble column to determine the critical gas volume fraction at which transition takes place in the Two Phase Flow Zone. In order to apply the model, drift-flux analysis has been used to obtain bubble diameter as a function of gas and liquid superficial velocities, and computational fluid dynamics has been utilised to quantify the velocity fluctuations of the liquid exiting the Mixing Zone.

Gauge condition for studying intrinsic magnetospheres

We propose an analytical model based on the solution of the magnetohydrodynamics (MHD) equations for studying intrinsic magnetospheres. For this purpose, we introduce a new gauge condition for the electromagnetic vector potential, which simplifies the solution of this complex system of nonlinear equations. Using this model, we analyse the deformation of the terrestrial magnetic field due to the presence of the solar wind. By comparing the results with experimental observations, we find that our model reproduces with good agreement the geometrical configuration of the magnetosphere, and that the solar wind should have a finite conductivity. This model could also be used to perform linear stability analysis of fluid and magnetic instabilities. Finally, our solution is not limited to magnetospheric configurations but also applies to a steady-state incompressible and irrotational flow with large plasma parameter and small velocity fluctuations.

Coupling between free-surface fluctuations, velocity fluctuations and turbulent Reynolds stresses during the upstream propagation of positive surges, bores and compression waves

In open channel, canals and rivers, a rapid increase in flow depth will induce a positive surge, also called bore or compression wave. The positive surge is a translating hydraulic jump. Herein new experiments were conducted in a large-size rectangular channel to characterise the unsteady turbulent properties, including the coupling between free-surface and velocity fluctuations. Experiments were repeated 25 times and the data analyses yielded the instantaneous median and instantaneous fluctuations of free-surface elevation, velocities and turbulent Reynolds stresses. The passage of the surge front was associated with large free-surface fluctuations, comparable to those observed in stationary hydraulic jumps, coupled with large instantaneous velocity fluctuations. The bore propagation was associated with large turbulent Reynolds stresses and instantaneous shear stress fluctuations, during the passage of the surge. A broad range of shear stress levels was observed underneath the bore front, with the probability density of the tangential stresses distributed normally and the normal stresses distributed in a skewed single-mode fashion. Maxima in normal and tangential stresses were observed shortly after the passage of a breaking bore roller toe. The maximum Reynolds stresses occurred after the occurrence of the maximum free-surface fluctuations, and this time lag implied some interaction between the free-surface fluctuations and shear stress fluctuations beneath the surge front, and possibly some causal effect.

LES Predictions of Self-Sustained Oscillations in Homogeneous Density Round Free Jet

The paper presents a detailed LES analysis of turbulent round jets dominated by the mechanism of Kelvin-Helmholtz (K-H) instability and the so-called self-sustained regime, which is characterised by large velocity fluctuations, reminiscent of the behaviour of excited jets. It is shown that the occurrence of this regime is largely conditioned by the type and parameters of the inlet jet velocity profile, i.e., the shear layer momentum thickness 𝜃, turbulence intensity Ti. A high order numerical code based on the combined pseudo-spectral / compact difference methods is used in the simulations. Analysis is performed for the Reynolds number Re = 1 × 104 with 𝜃 characterised by R/𝜃 = 16, 20, 24, 28 and 32 (with R - jet radius) and for Ti = 10−2, 10−3, 10−4. Two inlet velocity profiles are used in the simulations: hyperbolic tangent and Blasius. Comparisons focus on the axial velocity profiles and the spectra of the velocity signals. It is shown that in the self-sustained regime the results obtained with the Blasius profile are significantly closer to the experimental data. Sensitivity tests of the self-sustained regime on the sub-grid modelling are performed based on four well known models: classical and dynamic Smagorinsky, the filtered structure function model of Ducros et al. (JFM, 1996) and the relatively new model proposed by Vreman (PoF, 2004). It is shown that in the case of the classical Smagorinsky model an excess of sub-grid dissipation prevents the appearance of self-sustained velocity oscillations and in effect gives results significantly different from the remaining models. On the other hand, when the jets are dominated by K-H instability all the models lead to very similar solutions.

Modulation of homogeneous shear turbulence laden with finite-size particles

The dynamics of homogeneous shear turbulence laden with spherical finite-size particles is investigated using fully resolved numerical simulations to understand how the presence of particles modulates turbulent shear flows. We focus on a dilute flow laden with non-sedimenting particles whose diameter is slightly smaller than or comparable with those of vortex cores in turbulence. An immersed boundary method is adopted to represent a spherical finite-size particle. Numerical results show that the presence of particles augments the viscous dissipation of turbulence kinetic energy, which leads to a slower increase in the turbulence energy. Although the augmentation of energy dissipation occurs predominantly inside viscous layers surrounding particles in an initial period, the contribution from their outside becomes more significant due to the modification of turbulence structures as turbulence develops. It is found that the particles exhibit weak tendency to accumulate in vortex layers. The particles approaching and colliding with vortex layers induce large velocity fluctuations, which leads to the generation and shedding of thin vortex tubes. Newly generated vortex tubes interact with developed vortex tubes and layers, and modify the entire structure of the vorticity field.

Velocity of DNA during translocation through a solid-state nanopore.

While understanding translocation of DNA through a solid-state nanopore is vital for exploiting its potential for sensing and sequencing at the single-molecule level, surprisingly little is known about the dynamics of the propagation of DNA through the nanopore. Here we use linear double-stranded DNA molecules, assembled by the DNA origami technique, with markers at known positions in order to determine for the first time the local velocity of different segments along the length of the molecule. We observe large intramolecular velocity fluctuations, likely related to changes in the drag force as the DNA blob unfolds. Furthermore, we observe an increase in the local translocation velocity toward the end of the translocation process, consistent with a speeding up due to unfolding of the last part of the DNA blob. We use the velocity profile to estimate the uncertainty in determining the position of a feature along the DNA given its temporal location and demonstrate the error introduced by assuming a constant translocation velocity.

Unsteady turbulence in expansion waves in rivers and estuaries: an experimental study

A sudden decrease in water depth, called a negative surge or expansion wave, is characterised by a gentle change in free-surface elevation. Some geophysical applications include the ebb tide flow in macro-tidal estuaries, the rundown of swash waters and the retreating waters after maximum tsunami runup in a river channel. The upstream propagation of expansion waves against an initially steady flow was investigated in laboratory under controlled flow conditions including detailed free-surface velocity and Reynolds stress measurements. Both non-intrusive free-surface measurements and intrusive velocity measurements were conducted for relatively large Reynolds numbers with two types of bed roughness. The data showed that the propagation of expansion waves appeared to be a relatively smooth lowering to the water surface. The wave leading edge celerity data showed a characteristic trend, with a rapid acceleration immediately following the surge generation, followed by a deceleration of the leading edge surge towards an asymptotical value: $$(\mathrm{U}+\mathrm{V}_\mathrm{o})/(\mathrm{g}\times \mathrm{d}_\mathrm{o})^{1/2}=1$$ for both smooth and rough bed experiments. The results indicated that the bed roughness had little to no effect, within the experimental flow conditions. Relatively large fluctuations in free-surface elevation, velocity and turbulent shear stress were recorded beneath the leading edge of the negative surge for all flow conditions. The instantaneous turbulent shear stress levels were significantly larger than the critical shear stress for sediment erosion. The present results implied a substantial bed erosion during an expansion wave motion.

POD analysis of the unsteady behavior of a laminar separation bubble

Particle Image Velocimetry (PIV) measurements have been performed in order to analyze the unsteady flow field developing along the separated flow region of a laminar separation bubble. Data have been post-processed by means of Proper Orthogonal Decomposition (POD) to improve the understanding of the physics of this complex phenomenon. The paper shows that the first two POD modes of the normal to the wall velocity component are coupled. Thus, they are representative of a vortex shedding phenomenon which is identified to be induced by Kelvin–Helmholtz instability. The POD allows the phase identification of each PIV image within the vortex shedding cycle. The computed eigenvectors are used to sort the experimental snapshots and then reconstruct a phase-averaged velocity field which highlighted the motion of vortices shed close to the bubble maximum displacement. Moreover, other sources of deterministic fluctuations characterized by frequencies which are different from the one induced by the Kelvin–Helmholtz instability are also revealed. Indeed, the most energetic POD mode of the streamwise velocity component is not related to the shedding frequency, while it describes large velocity fluctuations in the shear layer region upstream of the bubble maximum displacement, where the turbulent activity is not yet present. The POD decomposition presented here identifies the large scale structures within the flow, thus separately accounts for both coherent and stochastic contributions to the overall energy of the velocity fluctuations.

Visualization experiment of complex flow field in a sphere-packed pipe by detailed PIV measurement

A sphere-packed pipe has been proposed as a heat transfer promoter for the first wall cooling in a Flibe blanket. In this study, the flow field in a sphere-packed pipe was well investigated by means of two-dimensional PIV method by matching refractive index of a channel material and working fluid. Three-dimensional flow structure was clarified by integrating the obtained data. The feature of the flow was tortuous high-velocity region formed near pebbles and large velocity fluctuation in the vicinity of the channel wall. And, to apply this flow structure to the actual first wall cooling, a new cooling system using finger-stacked structure was proposed and discussed.

Capture-induced transition in foamy suspensions.

We investigate the drainage behaviour of foamy granular suspensions. Results reveal large fluctuations in the drainage velocity as bubble size, particle size and gas volume fraction are varied for a given particle volume fraction. Particle capture is proved to control the overall drainage behaviour through the parameter λ, which compares the particle size to the size of passage through constrictions within the foam pore space. λ highlights a sharp transition: for λ < 1 particles are free to drain with the liquid, which involves the shear of the suspension in foam interstices, for λ > 1 particles are trapped and the resulting drainage velocity is strongly reduced. A phenomenological model is proposed to describe this behaviour.

GS43 単純形状モデルを用いた鉄道車両床下流れの数値シミュレーション

Large-eddy simulation of flow around a train was conducted to investigate unsteady under body flows. The results of this study showed that large lateral velocity fluctuations were generated by two vortex streets along the train and that they propagated along the streamwise direction under the train.

The convection of large and intermediate scale fluctuations in a turbulent mixing layer

The convection velocity of large and intermediate scale velocity fluctuations in a nominally two-dimensional planar mixing layer, and its dependence upon the length scale, is explored by carrying out particle image velocimetry (PIV) experiments. A “global” convection velocity, containing the convection of all the length scales present in the flow, is produced by examining the autocorrelation functions between velocity fluctuations in successive PIV records across the mixing layer. This “global” convection velocity is found to be similar to the mean flow, although fluctuations on the low speed side of the mixing layer on average convect at speeds greater than the mean and fluctuations on the high speed side of the mixing layer are observed to convect at speeds less than the mean. Scale specific convection velocity profiles are then produced by examining the phase difference between the spectral content specific to one wavenumber in streamwise velocity fluctuation traces in successive PIV records, offset by time τ. Probability density functions (pdfs) are produced of this phase difference, which is subsequently converted into a convection displacement, and these show that the convection of single length scale fluctuations exhibits a significant variance, particularly so for larger scale fluctuations and in the high speed side of the mixing layer. Convection velocity profiles are produced from these pdfs using both the mean convection distance and the modal convection distance. It is observed that the convection velocity is relatively insensitive to the length scale of the fluctuations considered, particularly when the mean convection distance is used. A slight sensitivity to length scale is, however, observed for convection velocities based on the modal convection distance. This dependence is primarily observed in the high speed side of the mixing layer, in which smaller length-scale fluctuations convect more quickly than larger length-scale fluctuations. It is also observed that the magnitude of the fluctuation itself affects the convection velocity with larger magnitude fluctuations convecting less rapidly than lower magnitude ones at the largest length scales investigated with this behaviour being reversed at more intermediate length scales.

Seismic energy envelopes in volcanic media: in need of boundary conditions

Seismogram envelopes recorded at Campi Flegrei caldera show diffusive characteristics as well as steep amplitude increases in the intermediate and late coda, which can be related to the presence of a non-uniformly scattering medium. In this paper, we first show the results of a simulation with a statistical model considering anisotropic scattering interactions, in order to match coda-envelope duration and shape. We consider as realistic parameters for a volcanic caldera the presence of large square root velocity fluctuations (10 per cent) and two typical correlation lengths for such an heterogeneous crust, a = 0.1 and 1 km. Then, we propose the inclusion of a diffusive boundary condition in the stochastic description of multiple scattering, in order to model intermediate and late coda intensities, and particularly the sharp intensity peaks at some stations in the caldera. Finally, we show that a reliable 2-D synthetic model of the envelopes produced by earthquakes vertically sampling a small region can be obtained including a single drastic change of the scattering properties of the volcano, that is, a caldera rim of radius 3 km, and sections varying between 2 and 3 km. These boundary conditions are diffusive, which signifies that the rim must have more scattering potential than the rest of the medium, with its diffusivity 2–3 orders of magnitude lower than the one of the background medium, so that the secondary sources on its interface(s) could enhance coda intensities. We achieve a good first-order model of high-frequency (18 Hz) envelope broadening adding to the Monte Carlo solution for the incident flux the secondary source effects produced by a closed annular boundary, designed on the caldera rim signature at 1.5 km depth. At lower frequencies (3 Hz) the annular boundary controls the intermediate and late coda envelope behaviour, in a way similar to an extended diffusive source. In our interpretation, the anomalous intensities observed at several stations and predicted by the final Monte Carlo solutions are mainly due to the diffusive transmission reflection from a scattering object of increased scattering power, and are controlled by its varying thickness.

An adaptive control scheme for doubly fed induction generators – wind turbine implementation

This paper presents a new adaptive scheme for doubly fed induction generators (DFIGs) in order to augment their flexibility confronting with unpredicted operational conditions. Due to large fluctuations in the wind velocity, the proposed scheme would handle system unreliable operational conditions. In such system, which has multi-input, multi-output and is also represented as a nonlinear control system, the uncertain parameters would affect the operational conditions. So, in order to have a robust controlling scheme, the mentioned characteristics should be considered in the proposed method. The adaptive control scheme proposed in this paper satisfies the expected constraints and could also be implemented in real-world platforms, especially in large-scale wind farms with DFIG turbines.