Raul Bayoan Cal

Experimental study of the horizontally averaged flow structure in a model wind-turbine array boundary layer

When wind turbines are deployed in large arrays, their ability to extract kinetic energy from the flow decreases due to complex interactions among them, the terrain topography and the atmospheric boundary layer. In order to improve the understanding of the vertical transport of momentum and kinetic energy across a boundary layer flow with wind turbines, a wind-tunnel experiment is performed. The boundary layer flow includes a 3×3 array of model wind turbines. Particle-image-velocity measurements in a volume surrounding a target wind turbine are used to compute mean velocity and turbulence properties averaged on horizontal planes. Results are compared with simple momentum theory and with expressions for effective roughness length scales used to parametrize wind-turbine arrays in large-scale computer models. The impact of vertical transport of kinetic energy due to turbulence and mean flow correlations is quantified. It is found that the fluxes of kinetic energy associated with the Reynolds shear stresses a...

Influence of external conditions on transitionally rough favorable pressure gradient turbulent boundary layers

Laser Doppler anemometry measurements are carried out in order to investigate the influences of the external conditions on a transitionally rough favorable pressure gradient turbulent boundary layer. The acquired data is normalized using the scalings obtained by the means of equilibrium similarity of the outer flow. The point at hand is to not only understand the interaction between the rough surface and the outer flow but also to include the external pressure gradient as the flow evolves in the streamwise direction. It is found that the velocity profiles show the effects of the upstream conditions imposed on the flow when normalized with the free-stream velocity. However, the profiles do collapse when normalized with U ∞ δ*/δ, demonstrating that this scaling absorbs the roughness effects and upstream conditions. An augmentation in the Reynolds stresses occurs with an increase in the roughness parameter and a decrease due to the external favorable pressure gradient. However, close to the wall, there is an increase due to the favorable pressure gradient while on the outer part of the boundary layer there is a decrease in magnitude due to this imposed effect. The near-wall peak of the ⟨ u 2 ⟩ component is dampened by the surface roughness condition due to the destruction of the viscous sublayer. In addition, the shape of the profile in the inner region tends to flatten due to the surface roughness. The upstream wind-tunnel speed also plays an important role thus creating a Reynolds number dependence on the outer flow of the Reynolds stress components. Furthermore, through 11 consecutive downstream locations, the skin friction coefficient is obtained for smooth and rough favorable pressure gradient data. The skin friction shows dependencies on the Reynolds number, the roughness parameter, and the favorable pressure gradient condition in the transitionally rough regime; while for the fully rough regime, it becomes form drag and the dependencies are on the favorable pressure gradient and the Reynolds shear stress. The external condition effects are isolated with a fixed parameter comparison. Favorable pressure gradient effects slow down the growth of the boundary layer while the surface roughness promotes its growth.

Statistical analysis of kinetic energy entrainment in a model wind turbine array boundary layer

For large wind farms, kinetic energy must be entrained from the flow above the wind turbines to replenish wakes and enable power extraction in the array. Various statistical features of turbulence causing vertical entrainment of mean-flow kinetic energy are studied using hot-wire velocimetry data taken in a model wind farm in a scaled wind tunnel experiment. Conditional statistics and spectral decompositions are employed to characterize the most relevant turbulent flow structures and determine their length-scales. Sweep and ejection events are shown to be the largest contributors to the vertical kinetic energy flux, although their relative contribution depends upon the location in the wake. Sweeps are shown to be dominant in the region above the wind turbine array. A spectral analysis of the data shows that large scales of the flow, about the size of the rotor diameter in length or larger, dominate the vertical entrainment. The flow is less incoherent below the array, causing decreased vertical fluxes the...

Inner and outer scalings in rough surface zero pressure gradient turbulent boundary layers

A new set of experiments have been performed in order to study the effects of surface roughness and Reynolds number on a zero pressure gradient turbulent boundary layer. In order to properly capture the x dependence of the single point statistics, consecutive measurements of 11 streamwise locations were performed which enabled the use of the full boundary layer equations to calculate the skin friction. This quantity was obtained within 3% and 5% accuracy for smooth and rough surfaces, respectively. For the sand grain type roughnesses used, only the Zagarola and Smits scaling, U∞δ*∕δ, was able to remove the effects of roughness and Reynolds number from the velocity profiles in outer variables. However, each scaling used for the velocity deficit profiles resulted in self-similar solutions for fixed experimental conditions. When examining the Reynolds stresses in the inner region [i.e., 0<(y+ϵ)+<0.1δ+], the ⟨u2⟩ component showed the largest influence of roughness, where the high peak near the wall was decrea...

Interaction Between a Wind Turbine Array and a Turbulent Boundary Layer

This paper describes further data analysis and discussion of an experimental study discussed in reference [1], in which a scaled down wind farm is placed in a turbulent boundary layer in a wind-tunnel. A 3x3 array of wind turbine models were built and inflow conditions were tailored to reproduce conditions expected to hold in the field under neutral flow. Hot-wire anemometry was used to characterize the inflow properties. Measurements using Stereo-Particle Image Velocimetry (S-PIV) were performed in 18 planes surrounding the center wind turbine at the third downstream row. The gathered data was interpolated in the x and z directions to generate cross-stream planes used for the estimation of the wind turbine induction factor. Assuming an axisymmetric streamtube shape, the resulting induction factor is 0.087, which corresponds to a lightly loaded wind turbine. Results are then compared to direct mechanical power measurements. Moreover, the streamtube is visualized in order to gain insight into the flow and to test the axisymmetric assumption used for the calculation of the induction factor. Results show that the streamtube is indeed close to axisymmetric, but exhibits some slight distortions due to strong tower effects and shear from the wall.

Effects of free-stream turbulence on rough surface turbulent boundary layers

Several effects of nearly isotropic free-stream turbulence in transitionally rough turbulent boundary layers are studied using data obtained from laser Doppler anemometry measurements. The free-stream turbulence is generated with the use of an active grid, resulting in free-stream turbulence levels of up to 6.2 %. The rough surface is characterized by a roughness parameter k + ≈ 53, and measurements are performed at Reynolds numbers of up to Re θ = 11 300. It is confirmed that the free-stream turbulence significantly alters the mean velocity deficit profiles in the outer region of the boundary layer. Consequently, the previously observed ability of the Zagarola & Smits (J. Fluid Mech., vol. 373, 1998, p. 33) velocity scale U ∞ δ*/δ to collapse results from both smooth and rough surface boundary layers, no longer applies in this boundary layer subjected to high free-stream turbulence. In inner variables, the wake region is significantly reduced with increasing free-stream turbulence, leading to decreased mean velocity gradient and production of Reynolds stress components. The effects of free-stream turbulence are clearly identifiable and significant augmentation of the streamwise Reynolds stress profiles throughout the entire boundary layer are observed, all the way down to the inner region. In contrast, the Reynolds wall-normal and shear stress profiles increase due to free-stream turbulence only in the outer part of the boundary layer due to the blocking effect of the wall. As a consequence, there is a significant portion of the boundary layer in which the addition of nearly isotropic turbulence in the free-stream, results in significant increases in anisotropy of the turbulence. To quantify which turbulence length scales contribute to this trend, second-order structure functions are examined at various distances from the wall. Results show that the anisotropy created by adding nearly isotropic turbulence in the free-stream resides mostly in the larger scales of the flow. Furthermore, by analysing the streamwise Reynolds stress equation, it can be predicted that it is the wall-normal gradient of (u 2 v) term that is responsible for the increase in (u 2 ) profiles throughout the boundary layer (i.e. an efficient turbulent transport of turbulence away from the wall). Furthermore, a noticeable difference between the triple correlations for smooth and rough surfaces exists in the inner region, but no significant differences are seen due to free-stream turbulence. In addition, the boundary layer parameters δ*/δ 95 , H and c f are also evaluated from the experimental data. The flow parameters δ*/δ 95 and H are found to increase due to roughness, but decrease due to free-stream turbulence, which has significance for flow control, particularly in delaying separation. Increases in c f due to high free-stream turbulence are also observed, associated with increased momentum flux towards the wall.

Similarity analysis of favorable pressure gradient turbulent boundary layers with eventual quasilaminarization

Using similarity analysis, the scales and similarity constraints for a favorable pressure gradient (FPG) turbulent boundary layer with eventual quasilaminarization are obtained. In order to achieve equilibrium in the boundary layer, the pressure parameter Λ must be a constant; thus, a power relation between the boundary layer thickness δ and the free-stream velocity U∞ exists. Consequently, the power is given by the pressure parameter Λ as δ∼U∞−1/Λ. Through an analysis using the pressure parameter, two quadrants are found: quadrant I describes FPG turbulent flows and quadrant II corresponds to quasilaminar flows. Moreover, a horizontal line exists for zero pressure gradient flows. Different values of the pressure parameter are found for equilibrium FPG flows, contrary to the findings of Castillo and George [“Similarity analysis for turbulent boundary layer with pressure gradient: Outer flow,” AIAA J. 39, 41 (2001)]. In the case of strong FPG flows with quasilaminarization, the pressure parameter reaches a...

Upstream Condition Effects on Turbulent Boundary Layers Subject to Favorable Pressure Gradients

The effects of the upstream conditions in favorable pressure gradient boundary layers are studied by carrying out an experiment using laser-doppler anemometry over multiple traverses along a smooth plate. A set of upstream conditions composed of upstream wind tunnel speed, tripwire location, and the strength of the pressure gradient is analyzed. The similarity analysis of the equations of motion for pressure gradient flows is used to obtain the scales for the outer flow. For this study, the mean deficit profiles show a small dependence on the strength of the pressure gradient when scaled with the freestream velocity U ∞ . Second, the upstream conditions effects are removed from the velocity deficit profiles when normalized by the U ∞ δ*/δ scaling. However, the Reynolds stress profiles show the effects of upstream conditions and the strength of the pressure gradient. Finally, these favorable pressure gradient flows are found to be nonequilibrium flows because the pressure parameter A is not constant. In addition, three quadrants are found to describe all pressure gradient flows: one for adverse pressure gradient, one for favorable pressure gradient, and one for quasi-laminar flows, where different values are obtained and these are dependent on the experimental conditions. The quadrants are obtained by plotting log (U ∞ /U ∞i ;) versus log(δ/δ i ).

Low-order representations of the canonical wind turbine array boundary layer via double proper orthogonal decomposition

Wind turbine wakes are investigated in order to characterize the development of energetic turbulence structures. Experimental data from stereo particle image velocimetry render the full Reynolds stress tensor accessible in planes parallel to the swept area of the scale model turbine rotor. Proper orthogonal decomposition (POD) is applied to decompose and analyze structures in the wake. The modes resulting from the decomposition demonstrate that structures grow and develop along the streamwise direction. A second iteration of the snapshot POD, otherwise called double proper orthogonal decomposition (DPOD), is applied to modes of common rank from the span of measurement locations yielding an ordered set of projections. The DPOD describes the sub-modal organization in terms of largest common projection and a series of correction modes with coefficients that are functions of the streamwise coordinate. Sub-structures of POD modes that persist through the wake have a dominant projection that accounts for the ch...

Identification of Markov process within a wind turbine array boundary layer

The Markovian properties within a wind turbine array boundary layer are explored for data taken in a wind tunnel containing a model wind turbine array. A stochastic analysis of the data is carried out using the mathematics of Markov processes. The data were obtained using hot-wire anemometry thus providing point velocity statistics. The theory of Markov process is applied to obtain a statistical description of longitudinal velocity increments inside the turbine wake. Comparison of two- and three-scale conditional probability density functions indicates the existence of Markovian properties in longitudinal velocity increments for scale differences larger than the Taylor microscale. This result is quantified by use of the Wilcoxon rank-sum test which verifies that this relationship holds independent of initial scale selection outside of the near-wake region behind a wind turbine. Furthermore, at the locations which demonstrate Markovian properties, there appears to be a well defined inertial subrange which ...