Impact of Neutral Boundary-Layer Turbulence on Wind-Turbine Wakes: A Numerical Modelling Study

The wake characteristics of a wind turbine in a turbulent boundary layer under neutral stratification are investigated systematically by means of large-eddy simulations. A methodology to maintain the turbulence of the background flow for simulations with open horizontal boundaries, without the necessity of the permanent import of turbulence data from a precursor simulation, was implemented in the geophysical flow solver EULAG. These requirements are fulfilled by applying the spectral energy distribution of a neutral boundary layer in the wind-turbine simulations. A detailed analysis of the wake response towards different turbulence levels of the background flow results in a more rapid recovery of the wake for a higher level of turbulence. A modified version of the Rankine–Froude actuator disc model and the blade element momentum method are tested as wind-turbine parametrizations resulting in a strong dependence of the near-wake wind field on the parametrization, whereas the far-wake flow is fairly insensitive to it. The wake characteristics are influenced by the two considered airfoils in the blade element momentum method up to a streamwise distance of 14D (D = rotor diameter). In addition, the swirl induced by the rotation has an impact on the velocity field of the wind turbine even in the far wake. Further, a wake response study reveals a considerable effect of different subgrid-scale closure models on the streamwise turbulent intensity.     

Observations of turbulent boundary-layer interaction with a thunderstorm outflow — A possible wake region energy source

Laboratory and numerical model simulations of turbulent circulations within the wake regions of thunderstorm outflows have been done with the assumption that there is no turbulence within the ambient airmass. Furthermore, many observational studies have used Doppler radar data that have been filtered so that turbulent structures are reduced in amplitude or eliminated altogether. This study presents unique Doppler radar observations of the collision of a roll-like boundary-layer circulation with a gust flow. The boundary-layer circulation is seen to interact with the circulation within the gust flow head and to reappear within the wake region. It is suggested that the ambient boundary layer may be an energy source for the generation and/or maintenance of turbulence in the wake region.     

On the Velocity Gradient in Stably Stratified Sheared Flows. Part 1: Asymptotic Analysis and Applications

We give a new derivation of the familiar linear relation for the dimensionless velocity gradient in the stably stratified surface layer and provide physical and empirical grounds for its universal applicability in stationary homogeneous turbulence over the whole range of static stabilities from Ri =  0 to very large Ri. Combining this relation with the budget equation for the turbulent kinetic energy we obtain the “equilibrium formulation” of the turbulent dissipation length scale, and recommend it for use in turbulence closure models.     

A Hierarchy of Energy- and Flux-Budget (EFB) Turbulence Closure Models for Stably-Stratified Geophysical Flows

Here we advance the physical background of the energy- and flux-budget turbulence closures based on the budget equations for the turbulent kinetic and potential energies and turbulent fluxes of momentum and buoyancy, and a new relaxation equation for the turbulent dissipation time scale. The closure is designed for stratified geophysical flows from neutral to very stable and accounts for the Earth’s rotation. In accordance with modern experimental evidence, the closure implies the maintaining of turbulence by the velocity shear at any gradient Richardson number Ri, and distinguishes between the two principally different regimes: “strong turbulence” at ${Ri \ll 1}$ typical of boundary-layer flows and characterized by the practically constant turbulent Prandtl number Pr _T; and “weak turbulence” at Ri > 1 typical of the free atmosphere or deep ocean, where Pr _T asymptotically linearly increases with increasing Ri (which implies very strong suppression of the heat transfer compared to the momentum transfer). For use in different applications, the closure is formulated at different levels of complexity, from the local algebraic model relevant to the steady-state regime of turbulence to a hierarchy of non-local closures including simpler down-gradient models, presented in terms of the eddy viscosity and eddy conductivity, and a general non-gradient model based on prognostic equations for all the basic parameters of turbulence including turbulent fluxes.     

A Note on k - ε Modelling of Vegetation Canopy Air-Flows

The k - turbulence model is a standard of computational software packages for engineering, yet its application to canopy turbulence has not received comparable attention. This is probably due to the additional source (and/or sink) terms, whose parameterization remained uncertain. This model must include source terms for both turbulent kinetic energy (k) and the viscous dissipation rate (), to account for vegetation wake turbulence budget. In this note, we show how Kolmogorov's relation allows for an analytical solution to be calculated within the portion of a dense and homogeneous canopy where the mixing length does not vary. By substitution within model equations, this solution allows for a set of constraints on source term model coefficients to be derived.Those constraints should meet both Reynolds averaged Navier–Stokes equationsand large-eddy simulation sub-grid scale turbulence modelling requirements.Although originating from within a limited portion of the canopy, the predictedcoefficients values must be valid elsewhere in order to make the model capable of predicting the whole canopy-layer flow with a single set of constants.     

Experiments on scalar dispersion within a model plant canopy part I: The turbulence structure

This is the first of a series of three papers describing experiments on the dispersion of trace heat from elevated line and plane sources within a model plant canopy in a wind tunnel. Here we consider the wind field and turbulence structure. The model canopy consisted of bluff elements 60 mm high and 10 mm wide in a diamond array with frontal area index 0.23; streamwise and vertical velocity components were measured with a special three-hot-wire anemometer designed for optimum performance in flows of high turbulence intensity. We found that:

1. The momentum flux due to spatial correlations between time-averaged streamwise and vertical velocity components (the dispersive flux) was negligible, at heights near and above the top of the canopy.
2. In the turbulent energy budget, turbulent transport was a major loss (of about one-third of local production) near the top of the canopy, and was the principal gain mechanism lower down. Wake production was greater than shear production throughout the canopy. Pressure transport just above the canopy, inferred by difference, appeared to be a gain in approximate balance with the turbulent transport loss.
3. In the shear stress budget, wake production was negligible. The role of turbulent transport was equivalent to that in the turbulent energy budget, though smaller.
4. Velocity spectra above and within the canopy showed the dominance of large eddies occupying much of the boundary layer and moving downstream with a height-independent convection velocity. Within the canopy, much of the vertical but relatively little of the streamwise variance occurred at frequencies characteristic of wake turbulence.
5. Quadrant analysis of the shear stress showed only a slight excess of sweeps over ejections near the top of the canopy, in contrast with previous studies. This is a result of improved measurement techniques; it suggests some reappraisal of inferences previously drawn from quadrant analysis.

     

Effects of Thermal Stability and Incoming Boundary-Layer Flow Characteristics on Wind-Turbine Wakes: A Wind-Tunnel Study

Wind-tunnel experiments were carried out to study turbulence statistics in the wake of a model wind turbine placed in a boundary-layer flow under both neutral and stably stratified conditions. High-resolution velocity and temperature measurements, obtained using a customized triple wire (cross-wire and cold wire) anemometer, were used to characterize the mean velocity, turbulence intensity, turbulent fluxes, and spectra at different locations in the wake. The effect of the wake on the turbulence statistics is found to extend as far as 20 rotor diameters downwind of the turbine. The velocity deficit has a nearly axisymmetric shape, which can be approximated by a Gaussian distribution and a power-law decay with distance. This decay in the near-wake region is found to be faster in the stable case. Turbulence intensity distribution is clearly non-axisymmetric due to the non-uniform distribution of the incoming velocity in the boundary layer. In the neutral case, the maximum turbulence intensity is located above the hub height, around the rotor tip location and at a distance of about 4–5.5 rotor diameters, which are common separations between wind turbines in wind farms. The enhancement of turbulence intensity is associated with strong shear and turbulent kinetic energy production in that region. In the stable case, the stronger shear in the incoming flow leads to a slightly stronger and larger region of enhanced turbulence intensity, which extends between 3 and 6 rotor diameters downwind of the turbine location. Power spectra of the streamwise and vertical velocities show a strong signature of the turbine blade tip vortices at the top tip height up to a distance of about 1–2 rotor diameters. This spectral signature is stronger in the vertical velocity component. At longer downwind distances, tip vortices are not evident and the von Kármán formulation agrees well with the measured velocity spectra.     

A Wind-Tunnel Investigation of Wind-Turbine Wakes: Boundary-Layer Turbulence Effects

Wind-tunnel experiments were performed to study turbulence in the wake of a model wind turbine placed in a boundary layer developed over rough and smooth surfaces. Hot-wire anemometry was used to characterize the cross-sectional distribution of mean velocity, turbulence intensity and kinematic shear stress at different locations downwind of the turbine for both surface roughness cases. Special emphasis was placed on the spatial distribution of the velocity deficit and the turbulence intensity, which are important factors affecting turbine power generation and fatigue loads in wind energy parks. Non-axisymmetric behaviour of the wake is observed over both roughness types in response to the non-uniform incoming boundary-layer flow and the effect of the surface. Nonetheless, the velocity deficit with respect to the incoming velocity profile is nearly axisymmetric, except near the ground in the far wake where the wake interacts with the surface. It is found that the wind turbine induces a large enhancement of turbulence levels (positive added turbulence intensity) in the upper part of the wake. This is due to the effect of relatively large velocity fluctuations associated with helicoidal tip vortices near the wake edge, where the mean shear is strong. In the lower part of the wake, the mean shear and turbulence intensity are reduced with respect to the incoming flow. The non-axisymmetry of the turbulence intensity distribution of the wake is found to be stronger over the rough surface, where the incoming flow is less uniform at the turbine level. In the far wake the added turbulent intensity, its positive and negative contributions and its local maximum decay as a power law of downwind distance (with an exponent ranging from −0.3 to −0.5 for the rough surface, and with a wider variation for the smooth surface). Nevertheless, the effect of the turbine on the velocity defect and added turbulence intensity is not negligible even in the very far wake, at a distance of fifteen times the rotor diameter.     

Wind-Turbine Wakes in a Convective Boundary Layer: A Wind-Tunnel Study

Thermal stability changes the properties of the turbulent atmospheric boundary layer, and in turn affects the behaviour of wind-turbine wakes. To better understand the effects of thermal stability on the wind-turbine wake structure, wind-tunnel experiments were carried out with a simulated convective boundary layer (CBL) and a neutral boundary layer. The CBL was generated by cooling the airflow to 12–15 °C and heating up the test section floor to 73–75 °C. The freestream wind speed was set at about 2.5 m s^?1, resulting in a bulk Richardson number of ?0.13. The wake of a horizontal-axis 3-blade wind-turbine model, whose height was within the lowest one third of the boundary layer, was studied using stereoscopic particle image velocimetry (S-PIV) and triple-wire (x-wire/cold-wire) anemometry. Data acquired with the S-PIV were analyzed to characterize the highly three-dimensional turbulent flow in the near wake (0.2–3.2 rotor diameters) as well as to visualize the shedding of tip vortices. Profiles of the mean flow, turbulence intensity, and turbulent momentum and heat fluxes were measured with the triple-wire anemometer at downwind locations from 2–20 rotor diameters in the centre plane of the wake. In comparison with the wake of the same wind turbine in a neutral boundary layer, a smaller velocity deficit (about 15 % at the wake centre) is observed in the CBL, where an enhanced radial momentum transport leads to a more rapid momentum recovery, particularly in the lower part of the wake. The velocity deficit at the wake centre decays following a power law regardless of the thermal stability. While the peak turbulence intensity (and the maximum added turbulence) occurs at the top-tip height at a downwind distance of about three rotor diameters in both cases, the magnitude is about 20 % higher in the CBL than in the neutral boundary layer. Correspondingly, the turbulent heat flux is also enhanced by approximately 25 % in the lower part of the wake, compared to that in the undisturbed CBL inflow. This study represents the first controlled wind-tunnel experiment to study the effects of the CBL on wind-turbine wakes. The results on decreased velocity deficit and increased turbulence in wind-turbine wakes associated with atmospheric thermal stability are important to be taken into account in the design of wind farms, in order to reduce the impact of wakes on power output and fatigue loads on downwind wind turbines.     

Fractional Flow Speed-Up from Porous Windbreaks for Enhanced Wind-Turbine Power

The potential for porous windbreaks to enhance wind-turbine power production is studied using linearized theory and wind-tunnel experiments. Results suggest that windbreaks have the potential to substantially increase power production, while lowering mean shear, and leading to negligible changes in turbulence intensity. The fractional increase in turbine power output is found to vary roughly linearly with windbreak height, where a windbreak 10% the height of the turbine hub increases power by around 10%. Wind-tunnel experiments with a windbreak imposed beneath a turbulent boundary layer show the linearized predictions to be in good agreement with particle-image-velocimetry data. Power measurements from a model turbine further corroborate predictions in power increase. Moreover, the wake of the windbreak showed a significant interaction with the turbine wake, which may inform windbreak use in large wind farms. Power measurements from a second turbine downwind of the first with its own windbreak show that the net effect for multiple turbines is dependent on windbreak height.     

Turbulence Structure Within and Above a Canopy of Bluff Elements

Measurements of turbulence structure in a wind-tunnel model canopy of bluff elements show many of the features associated with vegetation canopies and roughness sublayers but also display features more characteristic of the inertial sublayer (ISL). Points of similarity include the existence of an inflexion point in the space-time averaged streamwise velocity at the canopy top, the variation with height of turbulent second moments and the departure of the turbulent kinetic energy budget from local equilibrium in and just above the canopy. Quadrant analysis shows characteristic dominance of sweep over ejection events within the canopy although sweeps are more frequent than usually seen in vegetation canopies. Points of difference are a u′, w′ correlation coefficient that is closer to the ISL value than to most canopy data, and a turbulent Prandtl number midway between canopy and ISL values. Within the canopy there is distinct spatial partitioning into two flow regimes, the wake and non-wake regions. Both time-mean and conditional statistics take different values in these different regions of the canopy flow. We explain many of these features by appealing to a modified version of the mixing-layer hypothesis that links the dominant turbulent eddies to the instability of the inflexion point at canopy top. However, it is evident that these eddies are perturbed by the quasi-coherent wakes of the bluff canopy elements. Based upon an equation for the instantaneous velocity perturbation, we propose a criterion for deciding when the eddies linked to the inflexion point will dominate flow structure and when that structure will be replaced by an array of superimposed element wakes. In particular, we show that the resemblance of some features of the flow to the ISL does not mean that ISL dynamics operate within bluff-body canopies in any sense.     

Turbulent Mechanical Energy Budget in Stably Stratified Baroclinic Flows over Sloping Terrain

Analysis of second-moment budget equations in a slope-oriented coordinate frame exhibits the pathways of exchange between the potential energy of mean flow and the total turbulent mechanical energy. It is shown that this process is controlled by the inclination of the potential temperature gradient. Hence, this parameter should be considered in studies of turbulence in slope flows as well as the slope inclination. The concept of turbulent potential energy is generalized to include baroclinicity, and is used to explain the role of along-slope turbulent heat flux in energy conversions. A generalization of static stability criteria for baroclinic conditions is also proposed. In addition, the presence of feedback between the turbulent heat flux and the temperature variance in stably-stratified flows is identified, which implies the existence of oscillatory modes characterized by the Brunt–Väisäla frequency.     

湍流的粘性和频散效应

本文应用Prandtl混合长理论导得了既包含湍流粘性又包含湍流频散的新的Reynolds平均运动方程组.分析指出:(1)湍流不仅存在粘性效应,而且存在频散效应;(2)正是湍流的频散效应可能导致能量逆转(即常说的负粘性现象,实质为一定条件下的负频散现象),并给出了能量逆转的必要条件和充分条件;(3)给出了湍流的KdV-Burgers方程模型.     

Wind Conditions in Idealized Building Clusters: Macroscopic Simulations Using a Porous Turbulence Model

Simulating turbulent flows in a city of many thousands of buildings using general high-resolution microscopic simulations requires a grid number that is beyond present computer resources. We thus regard a city as porous media and divide the whole hybrid domain into a porous city region and a clear fluid region, which are represented by a macroscopic k–e{\varepsilon} model. Some microscopic information is neglected by the volume-averaging technique in the porous city to reduce the calculation load. A single domain approach is used to account for the interface conditions. We investigated the turbulent airflow through aligned cube arrays (with 7, 14 or 21 rows). The building height H, the street width W, and the building width B are the same (0.15 m), and the fraction of the volume occupied by fluid (i.e. the porosity) is 0.75; the approaching flow is parallel to the main streets. There are both microscopic and macroscopic simulations, with microscopic simulations being well validated by experimental data. We analysed microscopic wind conditions and the ventilation capacity in such cube arrays, and then calculated macroscopic time-averaged properties to provide a comparison for macroscopic simulations. We found that the macroscopic k–e{\varepsilon} turbulence model predicted the macroscopic flow reduction through porous cube clusters relatively well, but under-predicted the macroscopic turbulent kinetic energy (TKE) near the windward edge of the porous region. For a sufficiently long porous cube array, macroscopic flow quantities maintain constant conditions in a fully developed region.     

A Comprehensive Modelling Approach for the Neutral Atmospheric Boundary Layer: Consistent Inflow Conditions, Wall Function and Turbulence Model

We report on a novel approach for the Reynolds-averaged Navier-Stokes (RANS) modelling of the neutral atmospheric boundary layer (ABL), using the standard k-ek-{\varepsilon} turbulence model. A new inlet condition for turbulent kinetic energy is analytically derived from the solution of the k-ek-{\varepsilon} model transport equations, resulting in a consistent set of fully developed inlet conditions for the neutral ABL. A modification of the standard k-ek-{\varepsilon} model is also employed to ensure consistency between the inlet conditions and the turbulence model. In particular, the turbulence model constant C _μ is generalized as a location-dependent parameter, and a source term is introduced in the transport equation for the turbulent dissipation rate. The application of the proposed methodology to cases involving obstacles in the flow is made possible through the implementation of an algorithm, which automatically switches the turbulence model formulation when going from the region where the ABL is undisturbed to the region directly affected by the building. Finally, the model is completed with a slightly modified version of the Richards and Hoxey rough-wall boundary condition. The methodology is implemented and tested in the commercial code Ansys Fluent 12.1. Results are presented for a neutral boundary layer over flat terrain and for the flow around a single building immersed in an ABL.     

Applied model for the growth of the daytime mixed layer

A slab model is proposed for developing the height of the mixed layer capped by stable air aloft. The model equations are closed by relating the consumption of energy (potential and kinetic) at the top of the mixed layer to the production of convective and mechanical turbulent kinetic energy within the mixed layer. By assuming that the temperature difference at the top of the mixed layer instantaneously adjusts to the actual meteorological conditions without regard to the initial temperature difference that prevailed, the model is reduced to a single differential equation which easily can be solved numerically. When the mixed layer is shallow or the atmosphere nearly neutrally stratified, the growth is controlled mainly by mechanical turbulence. When the layer is deep, its growth is controlled mainly by convective turbulence. The model is applied on a data set of the evolution of the height of the mixed layer in the morning hours, when both mechanical and convective turbulence contribute to the growth process. Realistic mixed-layer developments are obtained.     

Application of transilient turbulent theory to study interactions between the atmospheric boundary layer and forest canopies

The new Forest-Land-Atmosphere ModEl called FLAME is presented. The first-order, nonlocal turbulence closure called transilient turbulence theory (Stull, 1993) is applied to study the interactions between a forested land-surface and the atmospheric boundary layer (ABL). The transilient scheme is used for unequal vertical grid spacing and includes the effects of drag, wake turbulence, and interference to vertical mixing by plant elements. Radiation transfer within the vegetation and the equations for the energy balance at the leaf surface have been taken from Norman (1979). Among others, the model predicts profiles of air temperature, humidity and wind velocity within the ABL, sensible and latent heat fluxes from the soil and the vegetation, the stomata and aerodynamic resistances, as well as profiles of temperature and water content in the soil. Preliminary studies carried out for a cloud free day and idealized initial conditions are presented. The canopy height is 30 m within a vertical domain of 3 km. The model is able to capture some of the effects usually observed within and above forested areas, including the relative wind speed maximum in the trunk space and the counter gradient-fluxes in the lower part of the plant stand. Of special interest is the determination of the location and magnitude of the turbulent mixing between model layers, which permits one to identify the effects of large eddies transporting momentum and scalar quantities into the canopy. A comparison between model simulations and field measurements will be presented in a future paper.     

An application of the E-ε turbulence model for studying coupled air-sea boundary-layer structure

An E- turbulence model is used to study air-sea interaction characteristics and turbulence structure using a coupled model for air-sea boundary layers. The E- turbulence model consists of equations for the turbulent kinetic energy, the energy-dissipation, and for the turbulent exchange coefficient expressed in terms of turbulent kinetic energy and energy-dissipation. The energy-dissipation equations for the air-sea interface are solved analytically to obtain boundary conditions for energy-dissipation at the interface. The air-sea interaction and turbulence characteristics of the E- model are compared with those of the mixing-length model and with available observations.The simulations demonstrate that the air-sea interaction parameters obtained by the E- model agree well with observations. The numerical studies also show that the E- turbulence model with appropriate constants can give good results in modeling coupled air-sea boundary-layer flows.     

On the initiation of surface waves by turbulent shear flow

An analytical model is developed for the initial stage of surface wave generation at an air–water interface by a turbulent shear flow in either the air or in the water. The model treats the problem of wave growth departing from a flat interface and is relevant for small waves whose forcing is dominated by turbulent pressure fluctuations. The wave growth is predicted using the linearised and inviscid equations of motion, essentially following Phillips [Phillips, O.M., 1957. On the generation of waves by turbulent wind. J. Fluid Mech. 2, 417–445], but the pressure fluctuations that generate the waves are treated as unsteady and related to the turbulent velocity field using the rapid-distortion treatment of Durbin [Durbin, P.A., 1978. Rapid distortion theory of turbulent flows. PhD thesis, University of Cambridge]. This model, which assumes a constant mean shear rate Γ, can be viewed as the simplest representation of an oceanic or atmospheric boundary layer.For turbulent flows in the air and in the water producing pressure fluctuations of similar magnitude, the waves generated by turbulence in the water are found to be considerably steeper than those generated by turbulence in the air. For resonant waves, this is shown to be due to the shorter decorrelation time of turbulent pressure in the air (estimated as ∝ 1/Γ), because of the higher shear rate existing in the air flow, and due to the smaller length scale of the turbulence in the water. Non-resonant waves generated by turbulence in the water, although being somewhat gentler, are still steeper than resonant waves generated by turbulence in the air. Hence, it is suggested that turbulence in the water may have a more important role than previously thought in the initiation of the surface waves that are subsequently amplified by feedback instability mechanisms.     

The Effect of Wind-Turbine Wakes on Summertime US Midwest Atmospheric Wind Profiles as Observed with Ground-Based Doppler Lidar

We examine the influence of a modern multi-megawatt wind turbine on wind and turbulence profiles three rotor diameters ( $D$ D ) downwind of the turbine. Light detection and ranging (lidar) wind-profile observations were collected during summer 2011 in an operating wind farm in central Iowa at 20-m vertical intervals from 40 to 220 m above the surface. After a calibration period during which two lidars were operated next to each other, one lidar was located approximately $2D$ 2 D directly south of a wind turbine; the other lidar was moved approximately $3D$ 3 D north of the same wind turbine. Data from the two lidars during southerly flow conditions enabled the simultaneous capture of inflow and wake conditions. The inflow wind and turbulence profiles exhibit strong variability with atmospheric stability: daytime profiles are well-mixed with little shear and strong turbulence, while nighttime profiles exhibit minimal turbulence and considerable shear across the rotor disk region and above. Consistent with the observations available from other studies and with wind-tunnel and large-eddy simulation studies, measurable reductions in wake wind-speeds occur at heights spanning the wind turbine rotor (43–117 m), and turbulent quantities increase in the wake. In generalizing these results as a function of inflow wind speed, we find the wind-speed deficit in the wake is largest at hub height or just above, and the maximum deficit occurs when wind speeds are below the rated speed for the turbine. Similarly, the maximum enhancement of turbulence kinetic energy and turbulence intensity occurs at hub height, although observations at the top of the rotor disk do not allow assessment of turbulence in that region. The wind shear below turbine hub height (quantified here with the power-law coefficient) is found to be a useful parameter to identify whether a downwind lidar observes turbine wake or free-flow conditions. These field observations provide data for validating turbine-wake models and wind-tunnel observations, and for guiding assessments of the impacts of wakes on surface turbulent fluxes or surface temperatures downwind of turbines.