A simplified model for transition prediction applicable to wind-turbine rotors

This work aims to develop a simple framework for transition prediction over wind-turbine blades, including effects of the blade rotation and spanwise velocity without requiring fully three-dimensional simulations. The framework is based on a set of boundary-layer equations (BLEs) and parabolized stability equations (PSEs), including rotation effects. An important element of the developed BL method is the modeling of the spanwise velocity at the boundary-layer edge. The two analyzed wind-turbine geometries correspond to a constant airfoil and the DTU 10-MW Reference Wind Turbine blades. The BL model allows an accurate prediction of the chordwise velocity profiles. Further, for regions not too close to the stagnation point and root of the blade, profiles of the spanwise velocity agree with those from Reynolds-averaged Navier–Stokes (RANS) simulations. The model also allows predicting inflectional velocity profiles for lower radial positions, which may allow crossflow transition. Transition prediction is performed at several radial positions through an “envelope-of-envelopes” methodology. The results are compared with the eN method of Drela and Giles, implemented in the EllipSys3D RANS code. The RANS transition locations closely agree with those from the PSE analysis of a 2D mean flow without rotation. These results also agree with those from the developed model for cases with low 3D and rotation effects, such as at higher radial positions and geometries with strong adverse pressure gradients where 2D Tollmien–Schlichting (TS) waves are dominant. However, the RANS and PSE 2D models predict a later transition in the regions where 3D and rotation effects are non-negligible. The developed method, which accounts for these effects, predicted earlier transition onsets in this region (e.g., 19 % earlier than RANS at 26 % of the radius for the constant-airfoil geometry) and shows that transition may occur via highly oblique modes. These modes differ from 2D TS waves and appear in locations with inflectional spanwise velocity. However, except close to the root of the blade, crossflow transition is unlikely since the crossflow velocity is too low. At higher radial positions, where 3D and rotation effects are weaker and the adverse pressure gradient is more significant, modes with small wave angles (close to 2D) are found to be dominant. Finally, it is observed that an increase in the rotation speed modifies the spanwise velocity and increases the Coriolis and centrifugal forces, shifting the transition location closer to the leading edge. This work highlights the importance of considering the blade rotation and the three-dimensional flow generated by that in transition prediction, especially in the inner part of the blade.

Experimental Study on Backflow Patterns Induced by a Bilateral Groin Pair with Different Spacing

Groins are one of the popular manmade structures to modify the hydraulic flow and sediment response in river training. The spacing between groins is a critical consideration to balance the channel-depth and the cost of construction, which is generally determined by the backflow formed downstream from groins. A series of experiments were conducted using Particle Image Velocimetry (PIV) to observe the influence of groin spacing on the backflow pattern of two bilateral groins. The spacing between groins has significant effect on the behavior of the large-scale recirculation cell behind groins. The magnitude of the wake flow induced by a groin was similar to that induced by another groin on the other side, but the flow direction is opposite. The spanwise velocity near the groin tip dictates the recirculation zone width behind the groins due to the strong links between the spanwise velocity and the contraction ratio of channel cross-sections between groins. Based on previous studies and present experimental results, quantitative empirical relationships are proposed to calculate the recirculation zone length behind groins alternately placed at different spacing along riverbanks. This study provides better understanding and a robust formula to assess the backflow extent of alternate groins and identify the optimum groins array configuration.

The meandering behaviour of large-scale structures in turbulent boundary layers

This paper quantifies the instantaneous form of large-scale turbulent structures in canonical smooth-wall boundary layers, demonstrating that they adhere to a form that is consistent with the self-sustaining streak instability model suggested by Flores & Jiménez (Phys. Fluids, vol. 22, 2010, 071704) and Hwang & Cossu (Phys. Fluids, vol. 23, 2011, 061702). Our motivation for this study stems from previous observations of large-scale streaks that have been spatially locked in position within spanwise-heterogeneous boundary layers. Here, using similar tools, we demonstrate that the randomly occurring large-scale structures in canonical layers show similar behaviour. Statistically, we show that the signature of large-scale coherent structures exhibits increasing meandering behaviour with distance from the wall. At the upper edge of the boundary layer, where these structures are severely misaligned from the main-flow direction, the induced velocities associated with the strongly yawed vortex packets/clusters yield a significant spanwise-velocity component leading to an apparent oblique coherence of spanwise-velocity fluctuations. This pronounced meandering behaviour also gives rise to a dominant streamwise periodicity at a wavelength of approximately $6\unicode[STIX]{x1D6FF}$. We further statistically show that the quasi-streamwise roll-modes formed adjacent to these very large wavy motions are often one-sided (spanwise asymmetric), in stark contrast to the counter-rotating form suggested by conventional conditionally averaged representations. To summarise, we sketch a representative picture of the typical large-scale structures based on the evidence gathered in this study.

Large coherence of spanwise velocity in turbulent boundary layers

The spatial signature of spanwise velocity coherence in turbulent boundary layers has been studied using a series of unique large-field-of-view multicamera particle image velocimetry experiments, which were configured to capture streamwise/spanwise slices of the boundary layer in both the logarithmic and the wake regions. The friction Reynolds number of $Re_{\unicode[STIX]{x1D70F}}\approx 2600$ was chosen to nominally match the simulation of Sillero et al. (Phys. Fluids, vol. 26 (10), 2014, 105109), who had previously reported oblique features of the spanwise coherence at the top edge of the boundary layer based on the sign of the spanwise velocity, and here we find consistent observations from experiments. In this work, we show that these oblique features in the spanwise coherence relate to the intermittent turbulent bulges at the edge of the layer, and thus the geometry of the turbulent/non-turbulent interface, with the clear appearance of two counter-oriented oblique features. Further, these features are shown to be also present in the logarithmic region once the velocity fields are deconstructed based on the sign of both the spanwise and the streamwise velocity, suggesting that the often-reported meandering of the streamwise-velocity coherence in the logarithmic region is associated with a more obvious diagonal pattern in the spanwise velocity coherence. Moreover, even though a purely visual inspection of the obliqueness in the spanwise coherence may suggest that it extends over a very large spatial extent (beyond many boundary layer thicknesses), through a conditional analysis, we show that this coherence is limited to distances nominally less than two boundary layer thicknesses. Interpretation of these findings is aided by employing synthetic velocity fields of a boundary layer constructed using the attached eddy model, where the range of eddy sizes can be prescribed. Comparisons between the model, which employs an array of self-similar packet-like eddies that are randomly distributed over the plane of the wall, and the experimental velocity fields reveal a good degree of agreement, with both exhibiting oblique features in the spanwise coherence over comparable spatial extents. These findings suggest that the oblique features in the spanwise coherence are likely to be associated with similar structures to those used in the model, providing one possible underpinning structural composition that leads to this behaviour. Further, these features appear to be limited in spatial extent to only the order of the large-scale motions in the flow.

Linearized simulation of flow over wind farms and complex terrains

The flow over complex terrains and wind farms is estimated here by numerically solving the linearized Navier–Stokes equations. The equations are linearized around the unperturbed incoming wind profile, here assumed logarithmic. The Boussinesq approximation is used to model the Reynolds stress with a prescribed turbulent eddy viscosity profile. Without requiring the boundary-layer approximation, two new linear equations are obtained for the vertical velocity and the wall-normal vorticity, with a reduction in the computational cost by a factor of 8 when compared with a primitive-variables formulation. The presence of terrain elevation is introduced as a vertical coordinate shift, while forestry or wind turbines are included as body forces, without any assumption about the wake structure for the turbines. The model is first validated against some available experiments and simulations, and then a simulation of a wind farm over a Gaussian hill is performed. The speed-up effect of the hill is clearly beneficial in terms of the available momentum upstream of the crest, while downstream of it the opposite can be said as the turbines face a decreased wind speed. Also, the presence of the hill introduces an additional spanwise velocity component that may also affect the turbines’ operations. The linear superposition of the flow over the hill and the flow over the farm alone provided a first estimation of the wind speed along the farm, with discrepancies of the same order of magnitude for the spanwise velocity. Finally, the possibility of using a parabolic set of equations to obtain the turbulent kinetic energy after the linearized model is investigated with promising results. This article is part of the themed issue ‘Wind energy in complex terrains’.