An experimental investigation of instabilities and transition in the boundary layer on a rotating broad (120 degrees apex angle) cone through hot-wire measurements combined with local linear stability analysis (LLSA) has been undertaken. The rotating-cone flow is susceptible to both cross-flow and centrifugal instabilities. For broad cones, the cross-flow instability dominates over the centrifugal instability, and vice versa for slender cones. Although stationary vortical disturbances from the cross-flow instability are dominant on the broad cone (in this case 24-26 vortices develop), we have identified an initially slowly growing nonstationary mode with a much smaller wavenumber, which close to transition increases its growth rate dramatically. We report on a detailed process to identify the wavenumber of the measured nonstationary disturbance, as well as quantitative comparisons between experimental results and LLSA.

Planar particle image velocimetry was conducted upstream and in the near-wake of a lab-scale free-rotating wind turbine model and compared to several actuator disks with the same dimensions. The Reynolds number of the incoming flow is order 10(4). Actuator disks with different designs and solidities were tested, and the process of actuator disk selection is explicitly shown. The drag, mean velocity and mean vorticity in the wake of the disks were compared to that of the rotating model. For the disk that was the best match, the Reynolds stresses and swirling strength are also presented. The instantaneous swirling strength illustrated that despite similar mean fields, the instantaneous phenomena were significantly different. Distinct tip vortices were present in the wake of the rotating model but were absent from the wake of the actuator disk. Proper orthogonal decomposition was used to further investigate the underlying phenomena in the two flows, again demonstrating the importance of tip vortices when studying the rotating model and the lack of such distinct vortices when using the actuator disk. Hence, despite well-matched mean characteristics, the instantaneous structures in the two flows remain distinct.

The aerodynamics of a rotor with pitch imbalance has been investigated experimentally and numerically in the present work. The comparison of mean velocity and turbulence intensity in the balanced and unbalanced cases indicated that a pitch imbalance modifies both the mean velocity and the turbulent activity; the latter is weakly increased by the imbalance. Spectral analysis indicated that the dynamics of the wake is also affected by the pitch imbalance since the tip vortices loose strength and disorganise more quickly than in the balanced case. The pitch imbalance has, however, a detrimental effect on the power coefficient and it affects the thrust coefficient as well. Only the blade affected by the imbalance shows significant modifications of the applied load, while the other blades operate with the same loading conditions.

Wind-farm blockage is investigated by means of an analytical model based on the linearized Reynolds-averaged Navier-Stokes equation. Despite the simplifications, useful insight is obtained about the induction region upstream of a single wind turbine and of a cluster of turbines. Since the model is linearized, superposition methods are allowed and the farm blockage is obtained as a linear superposition of all the induction zones of each turbine present in the farm, including the mirrored ones due to the presence of the ground. The model is validated against data from wind tunnel experiments, and it is later used to assess blockage in velocity and power for wind farms with different layouts and from several wind directions.

The structure of the internal boundary layer above long wind farms is investigated experimentally. The transfer of kinetic energy from the region above the farm is dominated by the turbulent flux of momentum together with the displacement of kinetic energy operated by the mean vertical velocity: these two have comparable magnitude along the farm opposite to the infinite-farm case. The integration of the energy equation in the vertical highlighted the key role of the energy flux, and how that is balanced by the growth of the internal boundary layer in terms of energy thickness with a small role of the dissipation. The mean velocity profiles seem to follow a universal structure in terms of velocity deficit, while the Reynolds stress does not follow the same scaling structure. Finally, a spectral analysis along the farm identified the leading dynamics determining the turbulent activity: while behind the first row the signature of the tip vortices is dominant, already after the second row their coherency is lost and a single broadband peak, associated with wake meandering, is present until the end of the farm. The streamwise velocity peak is associated with a nearly constant Strouhal number weakly dependent on the farm layout and free stream turbulence condition. A reasonable agreement of the velocity spectra is observed when the latter are normalised by the velocity variance and integral time scale: nevertheless the spectra show clear anisotropy at the large scales and even the small scales remain anisotropic in the inertial subrange.

The power production of the Lillgrund wind farm has been investigated by means of SCADA data covering almost 10 years of operation, wake models and numerical simulation tools, such as WindSim, OpenFOAM and ORFEUS. The analysis of the SCADA data provided the quantification of wake losses and of blockage effects, results that enable a benchmark to assess the uncertainty of other numerical methods of industrial use. The results have been analysed in terms of global array efficiency for different wind directions, wind velocity and stratification conditions. A comparison of the present results with the Jensen and Ainsle models indicated that the two used wake models are affected by an error of about 8–10% in the estimation of the array efficiency, while the error does not vary significantly when using numerical tools such as ORFEUS, WindSim and OpenFOAM. By comparing wind statistics available before the park construction, an assessment of the blockage of the Lillgrund farm was performed with contrasting results from the other numerical tools, highlighting how challenging is to assess farm blockage with current industrial settings.

Instability and transition in the boundary layer on a slender cone (600 apex angle) rotating in still fluid are investigated using hot-wire anemometry as well as through linear stability analysis. In contrast to broad cones (including the disk), where a cross-flow instability dominates the transition and different studies report similar transition Reynolds numbers, the reported transition Reynolds numbers on slender cones are scattered. The present experiments provide quantitative experimental datasets and the stability and transition are evaluated based on both the Reynolds number and a Girder number. The results consistently show that the instability development depends on the Gortler number rather than the Reynolds number and that transition starts at a well-defined Gortler number, whereas the transition Reynolds number depends on the rotational rate. The measured disturbance that first grows in the laminar region has a frequency approximately the same as or twice the rotational rate of the cone, which according to the stability analysis corresponds to the critical frequency of a slightly inclined vortex structure with respect to the cone axis or an axisymmetric vortex structure. These structures are similar to those observed in the flow visualisations of Kobayashi & Izumi (J. Fluid Mech., vol. 127, 1983, pp. 353-364) and considered as being due to a centrifugal instability.

The pressure gradient in a jet is usually regarded as negligibly small when deriving the streamwise velocity profile from the momentum equations. In addition one assumes that the bulk streamwise momentum is conserved in the streamwise direction. On the other hand, it is known that the pressure distribution in the jet is well balanced with the square of the lateral velocity fluctuation, indicating that pressure is not negligible in the lateral momentum equation. The purpose of this study is to determine the importance of the pressure in the jet by evaluating balances in the streamwise and lateral momentum equations from experimental data measured by a static pressure tube and an X-probe. The turbulence fluctuations and the static pressure indicate similarities in their lateral distributions and are well balanced in the streamwise and lateral momentum equations. Although the contribution of the static pressure to the streamwise momentum is small, it is of the same order as that of the turbulent statistics in the lateral momentum equation.

The diagnostic plot was introduced in 2010 (Eur. J. Mech. B/Fluids 29: 403–406) but was used already in 2008 during a large measurement campaign as a litmus test to determine if tripped zero-pressure gradient turbulent boundary layers fulfilled basic criteria of being canonical. It used the rms-level of streamwise velocity (urms ) in the outer part of the boundary layer, a region where urms can give clear indications if insufficient or too tough tripping has been used. In standard plots one needs both the friction velocity and measurement of the full velocity and turbulence profiles. By instead plotting urms/ U∞ as a function of U/ U∞, it was found that this gives rise to a well-defined distribution that could be used as a canonical measure. It was later discovered that it is possible to extend the description to the near wall region. It has also been extended to boundary layers over rough surfaces and with pressure gradients, and some further uses. This paper aims to be both a review of the development of the method during the last 10+ years and a tutorial for those who want to employ it in their research and maybe also find new uses of the methodology.

The effect of surface roughness on the steady laminar flow induced by a rotating disk submerged by fluid otherwise at rest is investigated here theoretically and numerically. A theory is proposed where a triple-deck analysis is applied leading to a fast evaluation of the steady-flow modification due to the rough surface. The theory assumes that the roughness is much smaller than the boundary-layer height and is characterized by a significantly longer length scale (slender roughness). Only the leading-order correction is developed here, corresponding to a velocity-field correction that is linear with the roughness height. The proposed theory neglects some curvature terms (here partially accounted by means of a stretching of the radial coordinate and of a scaling of the dependent variables). Numerical simulations performed with different roughness geometries (axisymmetric roughness, radial grooves, and localized bumps) have been used to validate the theory. Results indicate that the proposed theory leads to a good quantification of the flow modifications due to surface roughness at a very low computational cost. A demonstration of the capabilities of the theory is finally proposed where the statistical effects on the flow due to a random (but statistically known) roughness distributed on the surface of a rotating disk are characterized.