4 results
A point vortex transportation model for yawed wind turbine wakes
- Haohua Zong, Fernando Porté-Agel
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- Journal:
- Journal of Fluid Mechanics / Volume 890 / 10 May 2020
- Published online by Cambridge University Press:
- 11 March 2020, A8
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In this study, stereo particle imaging velocimetry measurements are performed at multiple streamwise locations behind a yawed wind turbine to reveal the formation mechanisms of the counter-rotating vortex pair (CVP), and a point vortex transportation (PVT) model is proposed to reproduce the top–down asymmetric kidney-shaped wake (also referred to as a curled wake). Results indicate that the CVP formed behind a yawed wind turbine originates from the complex interactions between the hub vortex and the streamwise components of the blade tip vortices, which is fundamentally different from the case of a yawed drag disk where the hub vortex is absent. Specifically, when the yaw angle exceeds a critical value, a small part of the streamwise vorticity shed from the rotor disk edge switches its sign from negative to positive and subsequently merges with the concentrated hub vortex under mutual induction, creating a patch of positive vorticity; meanwhile, the remaining streamwise vorticity distributed along the rotor edge curls and evolves into another patch of negative vorticity. These two patches of streamwise vorticity essentially constitute the CVP. Based on the physics learnt from the experiments, the non-uniform cross-stream velocity fields are first reconstructed by a cloud of point vortices distributed along the rotor edge and a hub vortex located in the rotor centre, and subsequently used to numerically solve a simplified transportation–diffusion equation of the wake velocity deficit, which altogether constitute the PVT model. This physics-based reduced-order model is the first model capable of accurately reproducing the wake deformation behind a yawed wind turbine.
A momentum-conserving wake superposition method for wind farm power prediction
- Haohua Zong, Fernando Porté-Agel
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- Journal:
- Journal of Fluid Mechanics / Volume 889 / 25 April 2020
- Published online by Cambridge University Press:
- 24 February 2020, A8
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Analytical wind turbine wake models and wake superposition methods are prevailing tools widely adopted by the wind energy community to predict the power production of wind farms. However, none of the existing wake superposition methods conserve the streamwise momentum. In this study, a novel wake superposition method capable of conserving the total momentum deficit in the streamwise direction is derived theoretically, and its performance is validated with both particle imaging velocimetry measurements and large-eddy simulation results. Detailed inter-method comparisons show that the novel wake superposition method outperforms all the existing methods by delivering an accurate prediction of the power production and the centreline wake velocity deficit, with a typical error of less than 5 % (excluding the near-wake region). Additionally, the momentum-conserving wake superposition method is extended to combine the transverse velocities induced by yawed wind turbines, and the secondary wake steering effect crucial to the power optimization in active wake control is well reproduced.
Effect of velocity ratio on the interaction between plasma synthetic jets and turbulent cross-flow
- Haohua Zong, Marios Kotsonis
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- Journal:
- Journal of Fluid Mechanics / Volume 865 / 25 April 2019
- Published online by Cambridge University Press:
- 28 February 2019, pp. 928-962
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Plasma synthetic jet actuators (PSJAs) are particularly suited for high-Reynolds-number, high-speed flow control due to their unique capability of generating supersonic pulsed jets at high frequency (${>}5$ kHz). Different from conventional synthetic jets driven by oscillating piezoelectric diaphragms, the exit-velocity variation of plasma synthetic jets (PSJs) within one period is significantly asymmetric, with ingestion being relatively weaker (less than $20~\text{m}~\text{s}^{-1}$) and longer than ejection. In this study, high-speed phase-locked particle image velocimetry is employed to investigate the interaction between PSJAs (round exit orifice, diameter 2 mm) and a turbulent boundary layer at constant Strouhal number (0.02) and increasing mean velocity ratio ($r$, defined as the ratio of the time-mean velocity over the ejection phase to the free-stream velocity). Two distinct operational regimes are identified for all the tested cases, separated by a transition velocity ratio, lying between $r=0.7$ and $r=1.0$. At large velocity and stroke ratios (first regime, representative case $r=1.6$), vortex rings are followed by a trailing jet column and tilt downstream initially. This downstream tilting is transformed into upstream tilting after the pinch-off of the trailing jet column. The moment of this transformation relative to the discharge advances with decreasing velocity ratio. Shear-layer vortices (SVs) and a hanging vortex pair (HVP) are identified in the windward and leeward sides of the jet body, respectively. The HVP is initially erect and evolves into an inclined primary counter-rotating vortex pair ($p$-CVP) which branches from the middle of the front vortex ring and extends to the near-wall region. The two legs of the $p$-CVP are bridged by SVs, and a secondary counter-rotating vortex pair ($s$-CVP) is induced underneath these two legs. At low velocity and stroke ratios (second regime, representative case $r=0.7$), the trailing jet column and $p$-CVP are absent. Vortex rings always tilt upstream, and the pitching angle increases monotonically with time. An $s$-CVP in the near-wall region is induced directly by the two longitudinal edges of the ring. Inspection of spanwise planes ($yz$-plane) reveals that boundary-layer energization is realized by the downwash effect of either vortex rings or $p$-CVP. In addition, in the streamwise symmetry plane, the increasing wall shear stress is attributed to the removal of low-energy flow by ingestion. The downwash effect of the $s$-CVP does not benefit boundary-layer energization, as the flow swept to the wall is of low energy.
Formation, evolution and scaling of plasma synthetic jets
- Haohua Zong, Marios Kotsonis
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- Journal:
- Journal of Fluid Mechanics / Volume 837 / 25 February 2018
- Published online by Cambridge University Press:
- 20 December 2017, pp. 147-181
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Plasma synthetic jet actuators (PSJAs), capable of producing high-velocity pulsed jets at high frequency, are well suited for high-Reynolds-number subsonic and supersonic flow control. The effects of energy deposition and actuation frequency on the formation and evolution characteristics of plasma synthetic jets (PSJs) are investigated in detail by high-speed phase-locked particle imaging velocimetry (PIV). Increasing jet intensity with energy deposition is mainly contributed by the increasing peak jet velocity ($U_{p}$), while decreasing jet intensity with actuation frequency is attributed to both the reduced cavity density (primary factor) and the shortened jet duration (secondary factor). The total energy efficiency of the considered PSJA ($O(0.01\,\%)$) reduces monotonically with increasing frequency, while the time-averaged thrust produced by the PSJA is positively proportional to both the deposition energy and the frequency. A simplified theoretical model is derived and reveals a scaling power law between the peak jet velocity and the non-dimensional deposition energy (exponent $1/3$). The propagation velocity of the vortex ring attached at the jet front shows a non-monotonic behaviour of initial sharp increase and subsequent mild decay. The peak values for both the propagation velocity and the circulation of the front vortex ring are reached approximately two exit diameters away from the exit. Finally, analysis of the time-averaged flow fields of the issuing PSJ indicates that the axial decay rate of the centreline velocity is proportional to the actuation frequency whereas it is invariant with the energy deposition. The jet spreading rate of the PSJ is found to be higher than steady jets but lower than piezoelectric synthetic jets. Similarly, the entrainment coefficients of the PSJ are found to be twice as high as the values for comparable steady jets.