Philip Hancock

Wind tunnel experiments are performed in both neutral and stable boundary layers to study the effect of thermal stability on the wake of a single turbine and on the wakes of two axially aligned turbines, thereby also showing the influence of the second turbine on the impinging wake. In the undisturbed stable boundary layers, the turbulence length scales are significantly smaller in the vertical and longitudinal directions (up to 50 % and ≈≈40 %, respectively), compared with the neutral flow, while the lateral length scale is unaffected. The reductions are larger with the imposed inversion of a second stable case, except in the near-wall region. In the neutral case, the length scales in the wake flow of the single turbine are reduced both vertically and laterally (up to 50 % and nearly 40 %, respectively). While there is significant upstream influence of a second turbine (on mean and turbulence quantities), there is virtually no upstream effect on vertical length scales. However, curiously, the presence of the second turbine aids length-scale recovery in both directions. Longitudinally, each turbine contributes to successive reduction in coherence. The effect of stability on the turbulence length scales in the wake flows is non-trivial: at the top of the boundary layer, the reduction in the wall-normal length scale is dominated by the thermal effect, while closer to the wall, the wake processes strongly modulate this reduction. Laterally, the turbines’ rotation promotes asymmetry, while stability opposes this tendency. The longitudinal coherence, significantly reduced by the wake flows, is less affected by the boundary layer's thermal stability.

A series of experiments have been conducted in a stratifiable Atmospheric Boundary Layer (ABL) wind tunnel, using neutral and stable conditions, in which a forest canopy has been represented by use of architectural model trees. These experiments have been replicated in Computation Fluid Dynamic (CFD) simulations using a previously validated methodology. Both the numerical simulations and the experimental data show that atmospheric stability has a significant effect on the development and extent of the forest wake and on the prevalence of the canopy flow features such as the sub-canopy jet. The analysis shows that it is possible to include both forestry and buoyancy effects in numerical simulations using two sets of source and sink terms and achieve satisfactory convergence. However, it is shown that the numerical simulations overestimate the effects of thermal stratification when using the standard configuration.

In order to study the wind turbine wake and its eventual interactions with neighbouring wind turbines, several numerical and physical modelling approaches are used. Some model the wind turbine with the simplest model, that is the actuator disc concept, adding a drag source (i.e. pressure loss) within the surface swept by the blades (numerical [2], physical [1]). Some use the Blade Element Momentum Theory, which takes into account the blade rotation effect on the wake and the aerodynamic features of the blades [3]. Some use Large Eddy Simulation to compute the unsteady flow around the entire rotor [5]. In a wind resource assessment context, the latter one is not practical enough to be used since the computation times are extremely long.

A second programme of work is about to commence as part of a further four years of funding for the UK-EPSRC SUPERGEN-Wind large-wind-farm consortium. The first part of the initial programme at Surrey was to establish and set up appropriate techniques for both on- and off-shore boundary layers (though with an emphasis on the latter) at a suitable scale, and to build suitable rotating model wind turbines. The EnFlo wind tunnel, a UK-NCAS special facility, is capable of creating scaled neutral, stable and unstable boundary layers in its 20m long working section. The model turbines are 1/300-scale of 5MW-size, speed controlled with phase-lock measurement capability, and the blade design takes into account low Reynolds-number effects. Velocity measurements are primarily made using two-component LDA, combined with a ‘cold-wire' probe in order to measure the local turbulent heat flux. Simulation of off-shore wakes is particularly constrained because i) at wind tunnel scale the inherently low surface roughness can be below that for fully rough conditions, ii) the power required to stratify the flow varies as the square of the flow speed, and could easily be impractically large, iii) low blade Reynolds number. The boundary layer simulations, set up to give near-equilibrium conditions in terms of streamwise development, and the model turbines have been designed against these constraints, but not all constraints can be always met simultaneously in practice. Most measurements so far have been made behind just one or two turbines in neutral off- and on-shore boundary layers, at stations up to 12 disk diameters downstream. These show how, for example, the wake of a turbine affects the development of the wake of a downwind turbine that is laterally off-set by say half or one diameter, and how the unaffected part from the first turbine merges with the affected wake of the second. As expected a lower level of atmospheric turbulence causes the wakes to develop and fill-in more slowly compared with the on-shore case. A turbine can also suppress the level of atmospheric turbulence below hub height. In neutral flow, the wakes grow in width and height. However, even in mild stable stratification the vertical development of the wake deficit can be completely inhibited; at least some reduction would be expected arising from the stabilizing influence on vertical fluctuations. The width in contrast develops at about the same rate. As anticipated, the wake development is slower still in the stable case because of the lower level ambient turbulence. The maximum deficit is at a lower height than it is for neutral flow. Various aspects of the turbulence in the wake have been investigated. Second-phase work will examine a larger number of wake-turbine and wake-wake interactions, make a more detailed study of how turbines alter the atmospheric turbulence, and examine more cases of stratification. Work is also in hand related to turbines in or near forested regions, and it is expected that aspects of the physics will have links with the effect a large wind farm will have on the ABL and on the wind resource for a downwind farm. The work will produce a series of test cases to assist in the development of better wake and wind resource prediction models as well as a better understanding of wake physics.

Comparisons are made between Meteodyn WT (MWT) and wind tunnel measurements from the three RUSHIL test cases that represent hills of increasing steepness. The two steeper cases are of interest; in one the flow on the lee side is close to separation (Hill 5), for the other the flow has clearly separated (Hill 3). Although it is well known that WAsP 8.3 (WP) cannot predict separation, its predictions are included to represent the current industry standard. Both models agree well with mean wind speeds measured upstream of the Hill 5 crest. MWT gives significantly better but not good agreement upstream of the Hill 3 crest, where WP significantly over-predicts the speed-up. Downstream, MWT predictions are closer to measurements, but predict a smaller separation bubble on Hill 3, due to limitations of the turbulence model. A practical viewpoint requires improved modelling to have only a minimal impact on computational resource requirements.

Measurements have been made in the turbulent boundary layer on a flat plate in the presence of grid-generated free-stream, turbulence with a wide range of lengthscales. The data include conditionally sampled averages in which free-stream fluid was distinguished from boundary-layer fluid by heating the latter. Free-stream turbulence increases the standard deviation of the hot–cold interface as a proportion of the boundary-layer thickness, whilst the average position is mainly dependent upon the lengthscale. The shear correlation coefficient of the boundary-layer fluid decreases, and it is shown that the change in structure is directly related to the fluctuating-strain rate. Transport velocities representing the diffusion of turbulent kinetic energy and shear stress have opposite signs in the boundary-layer fluid to those in the free-stream fluid, and it is shown that they are also related to the fluctuating-strain rate. Complete balances of turbulent kinetic energy and shear stress have been evaluated, dissipation and pressure–strain redistribution having been deduced by difference. The dissipation length scale $L\tau = (-\overline{uv})^{\frac{3}{2}}/\epsilon $ is little affected by free-stream turbulence, whereas the corresponding parameter based on turbulent energy instead of shear stress is strongly affected.

Mean flow measurements, and some turbulence measurements, have been made in a two-dimensional incompressible constant-pressure (“flat plate”) turbulent boundary layer beneath a nearly homogeneous nearly-isotropic (grid-generated) turbulent free stream. An appreciably nonlinear dependence of the skin-friction coefficient and other boundary layer parameters on rms free-stream turbulence intensity has been confirmed. A much wider range of free-stream length scales has been studied than in previous work, and the results (which agree well with previous data where they overlap) clearly indicate the large effect of free-stream length scale on the response of the boundary layer. The decrease of free-stream turbulence effect with increasing length scale is at least partly attributable to simple reduction of normal-component velocity fluctuations by the solid surface; this would not be the case in free shear layers.

Decaying grid turbulence was passed over a wall moving at the stream speed. For the high Reynolds number of the experiment, the field due to the wall constraint on the normal component of the velocity fluctuations is found to extend further into the flow than the influence of the viscous boundary condition on the tangential-component fluctuations. Measurements of the variances, length scales and spectra of the three velocity components of the turbulence are compared with the results of a previous experiment and with the theoretical predictions for an idealization of the flow. A simple model for some departures from the theory is proposed.

A series of numerical simulations of the flow over a forest stand have been conducted using two different turbulence closure models along with various levels of canopy morphology data. Simulations have been validated against Stereoscopic Particle Image Velocimetry measurements from a wind tunnel study using one hundred architectural model trees, the porosities of which have been assessed using a photographic technique. It has been found that an accurate assessment of the porosity of the canopy, and specifically the variability with height, improves simulation quality regardless of the turbulence closure model used or the level of canopy geometry included. The observed flow field and recovery of the wake is in line with characteristic canopy flows published in the literature and it wasfound that the shear stress transport turbulence model was best able to capture this detail numerically.

© 2015 Springer Science+Business Media Dordrecht Measurements have been made in the wake of a model wind turbine in both a weakly unstable and a baseline neutral atmospheric boundary layer, in the EnFlo stratified-flow wind tunnel, between 0.5 and 10 rotor diameters from the turbine, as part of an investigation of wakes in offshore winds. In the unstable case the velocity deficit decreases more rapidly than in the neutral case, largely because the boundary-layer turbulence levels are higher with consequent increased mixing. The height and width increase more rapidly in the unstable case, though still in a linear manner. The vertical heat flux decreases rapidly through the turbine, recovering to the undisturbed level first in the lower part of the wake, and later in the upper part, through the growth of an internal layer. At 10 rotor diameters from the turbine, the wake has strong features associated with the surrounding atmospheric boundary layer. A distinction is drawn between direct effects of stratification, as necessarily arising from buoyant production, and indirect effects, which arise only because the mean shear and turbulence levels are altered. Some aspects of the wake follow a similarity-like behaviour. Sufficiently far downstream, the decay of the velocity deficit follows a power law in the unstable case as well as the neutral case, but does so after a shorter distance from the turbine. Tentatively, this distance is also shorter for a higher loading on the turbine, while the power law itself is unaffected by turbine loading.

Two cases of an overlying inversion imposed on a stable boundary layer are investigated, extending the work of Hancock and Hayden (Boundary-Layer Meteorol 168:29-57, 2018; 175:93-112, 2020). Vertical profiles of Reynolds stresses and heat flux show closely horizontally homogeneous behaviour over a streamwise fetch of more than eight boundary-layer heights. However, profiles of mean temperature and velocity show closely horizontally homogeneous behaviour only in the top two-thirds of the boundary layer. In the lower one-third the temperature decreases with fetch, directly as a consequence of heat transfer to the surface. A weaker effect is seen in the mean velocity profiles, curiously, such that the gradient Richardson number is invariant with fetch, while various other quantities are not. Stability leads to a 'blocking' of vertical influence. Inferred aerodynamic and thermal roughness lengths increase with fetch, while the former is constant in the neutral case, as expected. Favourable validation comparisons are made against two sets of local-scaling systems over the full depth of the boundary layer. Close concurrence is seen for all stable cases for z/L < 0.2, where z and L are the vertical height and local Obukhov length, respectively, and over most of the layer for some quantities.

It is demonstrated that the vertical profile of gradient Richardson number, Ri , can be shaped by control of the working-section inlet temperature profile. In previous work (Hancock and Hayden in Boundary-Layer Meteorol 168:20–57, 2018; 175:93–112, 2020; 180:5–26, 2021) the inlet temperature profile had been specified but without control of the profile of Ri in the developed-flow region of the working section. Control of the inlet temperature profile is provided by 15 inlet heaters (spread uniformly across the height of the working section), allowing control of the temperature gradient over the bulk of the boundary layer, and the overall temperature level above that of the surface. The bulk Richardson number for the 11 cases covers the range 0.01–0.17 (there is no overlying inversion). In the upper ≈ 2/3 of the boundary layer the Reynolds stresses and turbulent heat flux are controlled by the gradient in mean temperature, while in the lower ≈ 1/3 they are controlled both by this gradient and by the level above the surface temperature. In three examples, Ri is approximately constant at 0.07, 0.10 and 0.13 across the bulk of the layer. The previous observation of horizontally homogenous behaviour in the temperature profiles in the top ≈ 2/3 of the boundary layer but not in the lower ≈ 1/3 is repeated here, except when, tentatively, Ri does not exceed 0.05 over the bulk of the boundary layer. Favourable validation comparisons are made against two sets of local scaling systems and field data over the full depth of the boundary layer, over the range 0.006 ≤ R i ≤ 0.3, or, in terms of height and local Obukhov length, 0.005 ≤ z / L ≤ 1.

Abstract from manuscript: "Wind tunnel experiments are performed in both neutrally and stable boundary layers in order to study the effect of thermal stability on the wake of a single turbine and on the wakes of two axially aligned turbines, thereby also showing the influence of the second turbine on the impinging wake. In the undisturbed stable boundary layer, the turbulence length scales are significantly smaller in the vertical and longitudinal directions (up to 50% and 30%, respectively), compared with the neutral flow, while the lateral length scale is unaffected. The reductions are larger still with the imposed inversion of a second stable case, except in the near-wall region. In the neutral case, the length scales in the wake flow of the single turbine are reduced both vertically and laterally (up to 50% and 40% respectively). While there is significant upstream influence of a second turbine (on mean and turbulence quantities), there is virtually no upstream effect on vertical length scales. However, curiously, the presence of the second turbine aids length-scale recovery in both directions. Longitudinally, each turbine contributes to successive reduction in coherence. The effect of stability on the turbulence length scales in the wake flows is non-trivial: at the top of the boundary layer, the reduction in the wall-normal length scale is dominated by the thermal effect, while closer to the wall, the wake processes strongly modulate this reduction. Laterally, the turbines’ rotation promotes asymmetry, while stability opposes this tendency. The longitudinal coherence, significantly reduced by the wake flows, is less affected by the boundary layer’s thermal stability.

A wind-tunnel simulation of an atmospheric boundary layer, artificially thickened as is often used in neutral flow wind-loading studies, has been investigated for weakly unstable stratification, including the effect of an overlying inversion. Rather than using a uniform inlet temperature profile, the inlet profile was adjusted iteratively by using measured downstream profiles. It was found that three cycles are sufficient for there to be no significant further change in profiles of temperature and other quantities. Development to nearly horizontally-homogeneous flow took a longer distance than in the neutral case because the simulated layer was deeper and therefore the length scales larger. Comparisons show first-order and second-order moments quantities are substantially larger than given by 'standard forms' in the mixed layer but are close in the surface layer. Modified functions, obtained by matching one to the other, are suggested that amount to an interpolation in the mixed layer between the strongly unstable and the weakly unstable cases.

Experimental results on the wake properties of a non-rotating simplified wind turbine model, based on the actuator disc concept, and a rotating model, a three-blade wind turbine, are presented. Tests were performed in two different test sections, one providing a nominally decaying isotropic turbulent inflow (turbulence intensity of 4% at rotor disc location) and one providing a neutral atmospheric boundary layer above a moderately rough terrain at a geometric scale of 1:300 (determined from the combination of several indicators), with 13% of turbulence intensity at hub height. The objective is to determine the limits of the simplified wind turbine model to reproduce a realistic wind turbine wake. Pressure and high-order velocity statistics are therefore compared in the wake of both rotor discs for two different inflow conditions in order to quantify the influence of the ambient turbulence. It has been shown that wakes of rotating model and porous disc developing in the modeled atmospheric boundary layer are indistinguishable after 3 rotor diameters downstream of the rotor discs, whereas few discrepancies are still visible at the same distance with the decaying isotropic turbulent inflow.

The simulation of horizontally homogeneous boundary layers that have characteristics of weakly and moderately stable atmospheric flow is investigated, where the well-established wind engineering practice of using ‘flow generators’ to provide a deep boundary layer is employed. Primary attention is given to the flow above the surface layer, in the absence of an overlying inversion, as assessed from first- and second-order moments of velocity and temperature. A uniform inlet temperature profile ahead of a deep layer, allowing initially neutral flow, results in the upper part of the boundary layer remaining neutral. A non-uniform inlet temperature profile is required but needs careful specification if odd characteristics are to be avoided, attributed to long-lasting effects inherent of stability, and to a reduced level of turbulent mixing. The first part of the wind-tunnel floor must not be cooled if turbulence quantities are to vary smoothly with height. Closely horizontally homogeneous flow is demonstrated, where profiles are comparable or closely comparable with atmospheric data in terms of local similarity and functions of normalized height. The ratio of boundary-layer height to surface Obukhov length, and the surface heat flux, are functions of the bulk Richardson number, independent of horizontal homogeneity. Surface heat flux rises to a maximum and then decreases.

An analysis is made of wind turbines in a row by means of an extension to actuator disk theory and a representation of the turbulent diffusion in the wake by a velocity deficit scale and a single free parameter. Beyond this, no wake model is used. It is shown that when the thrust coefficient is 'high' a maximisation of overall power output leads to a large drop in power after the first turbine, followed by a fairly constant level and a rise at the end of the row; this behaviour is a natural consequence of optimisation, and on this basis a 'deep array effect' is to be expected. A variation of turbine size and the effect of impaired turbine performance are examined. The approach can also be used to calculate the turbine upstream velocity (with respect to a reference) from a distribution of measured power output and to make inferences about wake development. The approach could be useful in the assessment of wake models as well as turbine operation.

Four cases of an overlying inversion imposed on a stable boundary layer are investigated, extending the earlier work of Hancock and Hayden (Boundary-Layer Meteorol 168:29–57, 2018), where no inversion was imposed. The inversion is imposed to one or other of two depths within the layer: midway or deep. Four cases of changed surface condition are also investigated, and it is seen that the surface and imposed conditions behave independently. A change of imposed inversion condition leaves the bottom 1/3 of the layer almost completely unaffected; a change of the surface condition leaves the top 2/3 unaffected. Comparisons are made against two sets of local-scaling systems over the full height of the boundary layer. Both show some influence of the inversion condition. The surface heat flux and the reduction in surface shear stress, and hence the ratio of the boundary-layer height to surface Obukhov length, are determined by the temperature difference across the surface layer (not the whole layer), bringing all cases together in single correlations as functions of a surface-layer bulk Richardson number.

It is demonstrated that the vertical profile of gradient Richardson number, Ri, can be shaped by control of the working-section inlet temperature profile. In previous work (Hancock and Hayden in Boundary-LayerMeteorol 168:20–57, 2018; 175:93–112, 2020; 180:5–26, 2021) the inlet temperature profile had been specified but without control of the profile of Ri in the developed-flow region of the working section. Control of the inlet temperature profile is provided by 15 inlet heaters (spread uniformly across the height of the working section), allowing control of the temperature gradient over the bulk of the boundary layer, and the overall temperature level above that of the surface. The bulk Richardson number for the 11 cases covers the range 0.01–0.17 (there is no overlying inversion). In the upper ≈ 2/3 of the boundary layer, the Reynolds stresses and turbulent heat flux are controlled by the gradient in mean temperature, while in the lower ≈ 1/3 they are controlled both by this gradient and by the level above the surface temperature. In three examples, Ri is approximately constant at 0.07, 0.10 and 0.13 across the bulk of the layer. The previous observation of horizontally homogenous behaviour in the temperature profiles in the top ≈ 2/3 of the boundary layer but not in the lower ≈ 1/3 is repeated here, except when, tentatively, Ri does not exceed 0.05 over the bulk of the boundary layer. Favourable validation comparisons are made against two sets of local scaling systems and field data over the full depth of the boundary layer, over the range 0.006 ≤ Ri ≤ 0.3, or, in terms of height and local Obukhov length, 0.005 ≤ z/L ≤ 1.

This chapter considers the offshore wind resource and how it is likely to be translated into power production by large arrays of offshore wind turbines. Firstly, the characteristics of the offshore wind resource were studied using long-term reanalysis data from the ERA–40 dataset. For two offshore sites, a more in-depth prediction of the wind resource was made using a mesoscale model. Finally, the results of two studies of the characteristics of offshore wind farm wakes is presented, using a computational fluid dynamics (CFD) model and then inferred from scale model measurements in a meteorological wind tunnel.

This paper presents first test results from wind tunnel studies of mean and turbulent wake characteristics within an array of large wind turbines. Up to now, a single rotating speed controlled 1:300 scale model of a 5MW-rated machine with a rotor diameter of 126m and a hub height of 90m is tested in a realistic model off-shore atmospheric boundary layer. The blade design is based on blade-element theory for low Reynolds number blade aerodynamics to comply with modelling requirements. Preliminary tests in a low-turbulence flow at a tip speed ratio of TSR=6 yielded a thrust coefficient of CT=0.52 which is within 5% of the predicted value of the theoretical design case with a lift coefficient of C= 0.6 (but a larger blade chord to mimic a higher C). Velocity measurements in the modelled off-shore boundary layer at several downstream positions suggest a transition from near to far wake at a downstream distance of approximately 4 rotor diameters D. At a downstream distance of 10D turbulence intensities in the wake of the single model turbine are still approximately twice as large as in the undisturbed boundary layer. Along with the high turbulence levels a velocity deficit of about 25% is found. Time averaged flow fields and lateral profiles of the vertical velocity clearly illustrate the characteristic swirl generated by the blade rotation, which persists until about a downstream distance of 7D.

This work was presented at WESC 2019 in Cork.