Determination of Wind Turbine Near-Wake Length Based on Stability Analysis

A numerical study on the wake behind a wind turbine is carried outfocusing on determining the length of the near-wake based on the instability onset ofthe trailing tip vortices shed from the turbine blades. The numerical model is based onlarge-eddy simulations (LES) of the Navier-Stokes equations using the actuator line(ACL) method. The wake is perturbed by applying stochastic or harmonic excitations inthe neighborhood of the tips of the blades. The flow field is then analyzed to obtain thestability properties of the tip vortices in the wake of the wind turbine. As a mainoutcome of the study it is found that the amplification of specific waves (travelingstructures) along the tip vortex spirals is responsible for triggering the instabilityleading to wake breakdown. The presence of unstable modes in the wake is related tothe mutual inductance (vortex pairing) instability where there is an out-of-phasedisplacement of successive helix turns. Furthermore, using the non-dimensional growthrate, it is found that the pairing instability has a universal growth rate equal to π/2.Using this relationship, and the assumption that breakdown to turbulence occurs once avortex has experienced sufficient growth, we provide an analytical relationship betweenthe turbulence intensity and the stable wake length. The analysis leads to a simpleexpression for determining the length of the near wake. This expression shows that thenear wake length is inversely proportional to thrust, tip speed ratio and the logarithmicof the turbulence intensit

Extension of the law of the wall exploiting the concepts of strong and weak universality of velocity fluctuations in a channel

This paper explores the universality of the instantaneous velocity profiles in a channel, which, despite the equilibrium nature of a channel flow, are subjected to strong non-equilibrium effects. In the analysis, we employ a one-dimensional scalar variant of the proper orthogonal decomposition (POD) and exploit the concepts of strong and weak universalities. Strong universality requires that all POD modes are universal with respect to the Reynolds number, while weak universality only requires that the first few POD modes are universal. As POD analysis concerns information at more than one location, these universalities are more general than various similarities and universality in the literature concerning single-point flow statistics, e.g., outer layer similarity or universality of the log law. We examine flows at $Re_\tau=$180, 540, 1000, and 5200. Strong universality is observed in the outer layer, and weak universality is found in both the inner layer and the outer part of the logarithmic layer. The presence of weak universality suggests the existence of an extension to the law of the wall (LoW). Here, we propose such an extension based on the results from one-dimensional POD analysis. The usefulness of the LoW extension is assessed by comparing flow reconstructions according to the extended LoW and the equilibrium LoW. We show that the extended LoW provides strikingly accurate flow reconstruction in the wall layer across a wide range of Reynolds numbers, capturing fine-scale motions that are entirely missed by the equilibrium LoW.Comment: 20 pages, 16 figure

Proton Pump Activity of Mitochondria-rich Cells : The Interpretation of External Proton-concentration Gradients

We have hypothesized that a major role of the apical H+-pump in mitochondria-rich (MR) cells of amphibian skin is to energize active uptake of Cl− via an apical Cl−/HCO3−-exchanger. The activity of the H+ pump was studied by monitoring mucosal [H+]-profiles with a pH-sensitive microelectrode. With gluconate as mucosal anion, pH adjacent to the cornified cell layer was 0.98 ± 0.07 (mean ± SEM) pH-units below that of the lightly buffered bulk solution (pH = 7.40). The average distance at which the pH-gradient is dissipated was 382 ± 18 μm, corresponding to an estimated “unstirred layer” thickness of 329 ± 29 μm. Mucosal acidification was dependent on serosal pCO2, and abolished after depression of cellular energy metabolism, confirming that mucosal acidification results from active transport of H+. The [H+] was practically similar adjacent to all cells and independent of whether the microelectrode tip was positioned near an MR-cell or a principal cell. To evaluate [H+]-profiles created by a multitude of MR-cells, a mathematical model is proposed which assumes that the H+ distribution is governed by steady diffusion from a number of point sources defining a set of particular solutions to Laplace's equation. Model calculations predicted that with a physiological density of MR cells, the [H+] profile would be governed by so many sources that their individual contributions could not be experimentally resolved. The flux equation was integrated to provide a general mathematical expression for an external standing [H+]–gradient in the unstirred layer. This case was treated as free diffusion of protons and proton-loaded buffer molecules carrying away the protons extruded by the pump into the unstirred layer; the expression derived was used for estimating stationary proton-fluxes. The external [H+]-gradient depended on the mucosal anion such as to indicate that base (HCO3−) is excreted in exchange not only for Cl −, but also for Br− and I−, indicating that the active fluxes of these anions can be attributed to mitochondria-rich cells

Wind power variability and power system reserves in South Africa

Variable renewable generation, primarily from wind and solar, introduces new uncertainties in the operation of power systems. This paper describes and applies a method to quantify how wind power development will affect the use of short-term automatic reserves in the future South African power system. The study uses a scenario for wind power development in South Africa, based on information from the South African transmission system operator (Eskom) and the Department of Energy. The scenario foresees 5% wind power penetration by 2025. Time series for wind power production and forecasts are simulated, and the duration curves for wind power ramp rates and wind power forecast errors are applied to assess the use of reserves due to wind power variability. The main finding is that the 5% wind power penetration in 2025 will increase the use of short-term automatic reserves by approximately 2%