The Structure of Turbulent Shear Flow By Dr. A. A. Townsend. Pp. xii + 315. 8¾ in. × 5½ in. (Cambridge: At the University Press.) 40s.

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The Structure of Turbulent Shear Flow

Wind energy, together with other renewable energy sources, are expected to grow substantially in the coming decades and play a key role in mitigating climate change and achieving energy sustainability. One of the main challenges in optimizing the design, operation, control, and grid integration of wind farms is the prediction of their performance, owing to the complex multiscale two-way interactions between wind farms and the turbulent atmospheric boundary layer (ABL). From a fluid mechanical perspective, these interactions are complicated by the high Reynolds number of the ABL flow, its inherent unsteadiness due to the diurnal cycle and synoptic-forcing variability, the ubiquitous nature of thermal effects, and the heterogeneity of the terrain. Particularly important is the effect of ABL turbulence on wind-turbine wake flows and their superposition, as they are responsible for considerable turbine power losses and fatigue loads in wind farms. These flow interactions affect, in turn, the structure of the ABL and the turbulent fluxes of momentum and scalars. This review summarizes recent experimental, computational, and theoretical research efforts that have contributed to improving our understanding and ability to predict the interactions of ABL flow with wind turbines and wind farms.

https://link.springer.com/content/pdf/10.1007/s10546-019-00473-0.pdf

Wind-Turbine and Wind-Farm Flows: A Review

http://www.urbanphysics.net/2016_BAE_BB_TS_JvB__PLW_review.pdf

Pedestrian-level wind conditions around buildings: Review of wind-tunnel and CFD techniques and their accuracy for wind comfort assessment

In this study, large-eddy simulation is combined with a turbine model to investigate the influence of atmospheric thermal stability on wind-turbine wakes. The simulation results show that atmospheric stability has a significant effect on the spatial distribution of the mean velocity deficit and turbulence statistics in the wake region as well as the wake meandering characteristics downwind of the turbine. In particular, the enhanced turbulence level associated with positive buoyancy under the convective condition leads to a relatively larger flow entrainment and, thus, a faster wake recovery. For the particular cases considered in this study, the growth rate of the wake is about 2.4 times larger for the convective case than for the stable one. Consistent with this result, for a given distance downwind of the turbine, wake meandering is also stronger under the convective condition compared with the neutral and stable cases. It is also shown that, for all the stability cases, the growth rate of the wake and wake meandering in the vertical direction is smaller compared with the ones in the lateral direction. This is mainly related to the different turbulence levels of the incoming wind in the different directions, together with the anisotropy imposed by the presence of the ground. It is also found that the wake velocity deficit is well characterized by a modified version of a recently proposed analytical model that is based on mass and momentum conservation and the assumption of a self-similar Gaussian distribution of the velocity deficit. Specifically, using a two-dimensional elliptical (instead of axisymmetric) Gaussian distribution allows to account for the different lateral and vertical growth rates, particularly in the convective case, where the non-axisymmetry of the wake is stronger. Detailed analysis of the resolved turbulent kinetic energy budget in the wake reveals also that thermal stratification considerably affects the magnitude and spatial distribution of the turbulence production, dissipation, and transport terms.

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Influence of atmospheric stability on wind-turbine wakes: A large-eddy simulation study

Direct numerical simulation of two turbulent boundary layer flows has been performed. The boundary layers are both subject to a strong adverse pressure gradient. In one case a separation bubble is created while in the other the boundary layer is everywhere attached. The data from the simulations are used to investigate scaling laws near the wall, a crucial concept in turbulence models. Theoretical work concerning the inner region in a boundary layer under an adverse pressure gradient is reviewed and extended to the case of separation. Excellent agreement between theory and data from the direct numerical simulation is found in the viscous sub-layer, while a qualitative agreement is obtained for the overlap region.

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Direct numerical simulation of a separated turbulent boundary layer

Wind turbine wake properties: Comparison between a non-rotating simplified wind turbine model and a rotating model

Measurements have been made in the wake of a model wind turbine in both a neutral and a stable atmospheric boundary layer, in the EnFlo stratified-flow wind tunnel, between 05 and 10 rotor diameters from the turbine, as part of an investigation of wakes in offshore winds In the stable case the velocity deficit decreased more slowly than in the neutral case, partly because the boundary-layer turbulence levels are lower and the consequentially reduced level of mixing, an ‘indirect’ effect of stratification A correlation for velocity deficit showed the effect of stratification to be the same over the whole of the measured extent, following a polynomial form from about five diameters After about this distance (for the present stratification) the vertical growth of the wake became almost completely suppressed, though with an increased lateral growth; the wake in effect became ‘squashed’, with peaks of quantities occurring at a lower height, a ‘direct’ effect of stratification Generally, the Reynolds stresses were lower in magnitude, though the effect of stratification was larger in the streamwise fluctuation than on the vertical fluctuations The vertical heat flux did not change much from the undisturbed level in the first part of the wake, but became much larger in the later part, from about five diameters onwards, and exceeded the surface level at a point above hub height

Wind-Tunnel Simulation of the Wake of a Large Wind Turbine in a Stable Boundary Layer: Part 2, the Wake Flow

Pulsed-wire measurements of the streamwise mean velocity and Reynolds stress, mean and fluctuating surface shear stress, and other statistics have been made in a sharp-
 edged turbulent separation bubble formed behind a normal flat plate mounted on the front of a long splitter plate, covering nearly a decade range of low Reynolds number. The streamwise Reynolds stress increases appreciably with Reynolds number, from a level comparable with that in an isolated plane mixing layer to more than twice that level, while the change in the mean flow is at most slight. It is inferred using previous measurements that the other stresses do not change as much, thereby leaving the mean flow relatively unaffected. The mean wall shear stress and the r.m.s. of the (streamwise) fluctuations decrease in fixed proportion with increasing Reynolds number. Normalized p.d.f. distributions of velocity and wall shear stress do not change, except in the vicinity of the secondary separation bubble. At low Reynolds number the development length of the overlying mixing layer is an appreciable proportion of the bubble length, the development length being a function of the momentum thickness at separation. It is argued that the observed changes with Reynolds number in the bulk of the flow arise primarily as a result of a change in response of this layer to the fluctuating rates of strain imposed by the recirculating flow; at a low Reynolds number the response of the shear layer structures to the fluctuating rates of strain is less than it is at a high Reynolds number. As a consequence of the sensitivity to fluctuating strain rates the structure of the layer differs fundamentally from that of an isolated mixing layer.The measurements help to reconcile previous measurements in this flow geometry which otherwise appear to be inconsistent. Moreover, in most of the previous measurements the flow width was not sufficient for end effects to have been negligible, most noticeably in the near-wall flow, where such effects are largest.

Low Reynolds number two-dimensional separated and reattaching turbulent shear flow

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.

A Wind-Tunnel Simulation of the Wake of a Large Wind Turbine in a Weakly Unstable Boundary Layer

Pulsed-wire measurements of wall shear stress have been made beneath two separation bubbles. In one a cross flow was generated by means of a (25°) swept separation line. Fluctuating stresses in orthogonal “streamwise” and cross-flow directions are very nearly equal and independent of at least moderate cross flow velocity. These fluctuations are largely determined by large-scale motions in the outer flow, whereas the mean shear stresses are not. The pdf of the “streamwise” fluctuations is unchanged by the cross flow. When a cross flow is present the pdf of the cross-flow stresses is similar to the “streamwise” pdf. Dependence on Reynolds number is the same in both flows.

P. E. Hancock

Papers

Wind turbine wake properties: Comparison between a non-rotating simplified wind turbine model and a rotating model

Wind-Tunnel Simulation of the Wake of a Large Wind Turbine in a Stable Boundary Layer: Part 2, the Wake Flow

Low Reynolds number two-dimensional separated and reattaching turbulent shear flow

A Wind-Tunnel Simulation of the Wake of a Large Wind Turbine in a Weakly Unstable Boundary Layer

Measurements of mean and fluctuating wall shear stress beneath spanwise-invariant separation bubbles