Power-law Wind Research Articles

Performance of a Savonius vertical axis wind turbine installed on a forward facing step

This study investigates the effects of installing a Savonius turbine on a forward-facing step to increase the power efficiency. Since the flow is disturbed by the step, the turbine may benefit from the accelerated flow found on top of the step. The flow field is solved using computational fluid dynamics in a 3D computational domain. The finite volume method is used to solve the Reynolds average Navier–Stokes governing equations and the SST k-ω turbulence equations. This simulation includes both rotating turbine and the step. The novelty of this work is to study this configuration with a power law wind velocity distribution as inlet velocity, which is more realistic in common applications, and to investigate a different turbine. The study shows that the Savonius turbine generates up to 73% more power when installed on a 5 m step. However, in case of a very high step, or a different turbine no improvement has been observed.

A Comparative Study on Wind Profiles and Surface Aerodynamic Parameters of Typhoons Over Coastland and Coastal Sea

AbstractUnderstanding the aerodynamic characteristics of landfalling typhoons is of great importance for both wind engineering and meteorology. This study comparatively investigated the near‐surface wind profiles and aerodynamic parameters over coastland and coastal sea areas using typhoon observational data collected by Doppler wind lidars and wind tower anemometers during the passage of 15 typhoons that made landfall over China during 2009–2020. Specifically, the three surface aerodynamic parameters of roughness length, friction velocity, and drag coefficient (Cd) were obtained using the logarithmic law wind profile method. Results showed that the near‐surface wind profiles became much closer to the power law wind profile with increase in wind speed. The values of roughness length and friction velocity over the coastal sea were found to exceed those over coastland areas when the 10‐m wind speed (U(10)) was larger than 18 m s−1. The critical wind speed at which Cd peaks over the coastal sea was found to be 24 m s−1. There are two peaks in the variation of Cd with U(10) under the condition of onshore wind over the sea, which has never been reported in previous observational studies. Finally, a formula for Cd was proposed to describe the variation in Cd with U(10) under the condition of onshore wind over land, which is expected to be applied in the typhoon surface layer scheme to improve numerical simulation of landfalling typhoons.

Modeling the effect of wind speed and direction shear on utility‐scale wind turbine power production

AbstractWind speed and direction variations across the rotor affect power production. As utility‐scale turbines extend higher into the atmospheric boundary layer (ABL) with larger rotor diameters and hub heights, they increasingly encounter more complex wind speed and direction variations. We assess three models for power production that account for wind speed and direction shear. Two are based on actuator disc representations, and the third is a blade element representation. We also evaluate the predictions from a standard power curve model that has no knowledge of wind shear. The predictions from each model, driven by wind profile measurements from a profiling LiDAR, are compared to concurrent power measurements from an adjacent utility‐scale wind turbine. In the field measurements of the utility‐scale turbine, discrete combinations of speed and direction shear induce changes in power production of −19% to +34% relative to the turbine power curve for a given hub height wind speed. Positive speed shear generally corresponds to over‐performance and increasing magnitudes of direction shear to greater under‐performance, relative to the power curve. Overall, the blade element model produces both higher correlation and lower error relative to the other models, but its quantitative accuracy depends on induction and controller sub‐models. To further assess the influence of complex, non‐monotonic wind profiles, we also drive the models with best‐fit power law wind speed profiles and linear wind direction profiles. These idealized inputs produce qualitative and quantitative differences in power predictions from each model, demonstrating that time‐varying, non‐monotonic wind shear affects wind power production.

Towards urban wind utilization: The spatial characteristics of wind energy in urban areas

Urban wind energy is gaining increasing recognition for its environmentally friendly nature, particularly in the context of energy shortages. Predicting wind speed in urban environments is challenging due to the varying roughness and drag caused by obstacles on the ground. The complexity of urban morphology significantly disrupts the wind field and hampers the utilization of wind energy. This study aimed to investigate the diverse impacts of highly heterogeneous urban environment on the urban wind energy by innovatively establishing spatially varying power law wind profiles. Firstly, long-term LIDAR observations were conducted to measure the vertical wind profile in the study area. Then, a high-resolution LCZ map was created and integrated into the Weather Research and Forecasting (WRF) model to reproduce the urban wind field, which was validated using the observational data. Finally, the spatial characteristics of the urban wind field and wind energy were analyzed based on 3 representative points and the urban LCZ categories. The results show that the average power law exponents of each LCZ classification ranges from 0.29 to 0.75, with the average power law exponent of the high-volume building area being larger than 0.6. The highest wind power density in the study area can reach 343.3W/m2 at 200m height. Further, significant negative correlation coefficients were found between wind power density and building height, as well as building density, with values of approximately −0.6 and −0.35, respectively. Overall, the high-volume-ratio built-up areas with higher roughness had a notable impact on the wind speed by increasing the power law exponents. These spatially varying wind profiles are expected to provide technical support for the utilization of urban wind energy.

Wind Resource Assessment: Optimizing the Weibull Distribution Curve

Abstract: In this paper, it was analyze the wind speed characteristics and provide projections of optimal wind resources by comparing data at different hub heights using wind power law. We have acquired data from an operational project site in the western part of India using data points acquired from the site from August 2017 to February 2018.Weibull distribution probability distribution function and cumulative distribution function for wind speed and other parameters involved in an accurate wind resource assessment methodology. To predict wind regimes, the Weibull probability function is commonly used. A comparison of alternative methods for estimating Weibull parameters of a wind regime is presented in this research. For the estimation, five alternative methods are discussed and employed. The study examined wind speed time series data at two sites over the course of a year. Although all five methods produce similar results when plotting error versus wind speed, the standard deviation method produces the best results.

Measurements on the surface wind pressure characteristics of a thousand-meter scale megatall building by wind tunnel test

This paper investigates the wind pressure distribution of a thousand-meter scale megatall building through a wind tunnel test. One key challenge is that the power-law wind profiles are not applicable due to the height limitation. Therefore, a mesoscale meteorological model WRFv3.4 (Weather Research & Forecasting Model) was used to explore the wind profile covering the height of the thousand-meter scale megatall building. Then the wind profile was reproduced in the wind tunnel representing the actual vertical distribution of wind speed by a passive simulation method, and thereby the wind pressure test was conducted in the wind tunnel. Moreover, to investigate the effect of the inlet wind profile on the wind pressure, a wind tunnel test using the power-law wind profile was carried out for comparison as well. It was revealed that the wind pressure distribution was greatly influenced by the inlet wind profile, which should be investigated with accuracy in the wind tunnel.

Development of a simple equivalent tornado wind profile for structural design and evaluation

Tornadoes cause damage to buildings and infrastructure. Providing the spatially varying tornado activities or tornado occurrence rate alone does not facilitate the tasks of checking and evaluating structures subjected to the tornado wind velocity hazard. In the present study, the estimation of the quantile of the tornado wind velocity hazard along the height for southern Ontario – a tornado-prone region in Canada – is carried out. For the assessment, a tornado occurrence rate model is developed by considering the reporting bias due to population density and by using the cloud-to-ground lightning flash density and thunderstorm days per year as the explanatory variables. Also, a simple equivalent along height tornado design wind profile for a vertical line-like structure is proposed by considering the bending moment and shear force along the height of the structure. Moreover, the concept of disaggregation analysis is employed to identify the scenario tornado wind profiles. The results indicate that the identified scenario wind profiles could be crudely bounded by using the rectangular wind profile and the power-law wind profile for synoptic winds, which are all hinged at the return period value of the tornado wind velocity at 10 ​m height. • A systematic modeling of tornado occurrence for southern Ontario is presented. • The cloud-to-ground lightning flash density and thunderstorm days are used as explanatory variables. • Tornado wind profile based on quantiles of tornado wind speed is presented. • Simple equivalent tornado design wind profiles are developed or point-like and line like structures.

A Perspective on the Scaling of Magnetosheath Turbulence and Effects of Bow Shock Properties

Abstract We analyze magnetic field data from two magnetosheath crossings, representative of a larger collection of similar cases in the database of the Cluster spacecraft. We apply a novel data analysis method to identify the power-law behavior of the structure functions and to find the validity range of the power-law scaling. We validate the technique with solar wind magnetic field data and a synthetic magnetic field signal. This approach grants a rigorous determination of the scale range for a linear fit of the structure function in the log–log representation, which most often is chosen arbitrarily. The fitting allows an estimation of the power spectral index from the scale variation of the second-order structure function exponent. Data recorded during the first Cluster magnetosheath crossing, called Event 1, indicate three different power-law scaling regimes (injection, inertial, and kinetic) separated by two spectral breaks, consistent with the scenario of fully developed turbulence. However, data from the second Cluster magnetosheath crossing, called Event 2, depict a different scenario with only two power-law scaling regimes determined from the fit. A spectral slope shallower than the Kolmogorovian solar wind power-law index is determined at magnetohydrodynamic scales, spanning more than three frequency decades, which is separated by a spectral break from the kinetic regime. An analysis of simultaneous solar wind data from the Advanced Composition Explorer suggests that the scale behavior of the magnetosheath fluctuations might be controlled by the structure of the bow shock; solar wind turbulent fluctuations are only partially destroyed while they are carried across the bow shock. Both events are recorded in a quasi-perpendicular magnetosheath.

Extrapolation of wind data using generalized versus site-specific wind power law for wind power production prospective at Shahbandar- a coastal site in Pakistan

The aim of this work is to compare the wind data extrapolated by 1/7th wind power law and site-specific wind power law for wind power potential estimation at Shahbandar. Both the Wind shear exponents (WSE) and local air density values were calculated using measured wind data at 10 and 30 m heights and they were found minimum in summer and maximum in winter. Weibull distribution was applied with a newly developed method to estimate the Weibull parameters whose accuracy was tested using coefficient of determination which was more than 95%. Technical analysis of energy generation was conducted which showed that GE1 and GE2 turbines have highest yield and capacity factors respectively while B3 and V5 has corresponding minimum values. Comparison showed that 1/7th wind power estimates lower values of wind potential than site-specific wind power law. Moreover, comparison of predicted data with measured data shows that site-specific wind power law estimates data more accurately.

Suitability of power-law extrapolation for wind speed estimation on a tropical island

In this study, the ability of the power-law wind model to reproduce a tropical vertical wind profile is investigated. Data from a one-year observation on an offshore island of Singapore, obtained using a lidar, are used to show that the power-law model profiles are unable to capture the pertinent features of the observed wind profiles. Two alternative profile models, one based on the free convection limit scaling and the other based on the arctangent function, are introduced and tested. The latter model, although lacking physical basis, is found to be superior in predicting the measured profiles. A systematic study of the seasonal and diurnal variations of the model parameters is presented and some practical implications of the results are also discussed.

An analytical model for rapid estimation of hurricane supergradient winds

The supergradient winds that may have severe implications on the wind design of high-rise buildings have been commonly observed in the hurricane boundary layer. However, the widely-used log-law or power-law wind profile excludes the supergradient-wind region in which the tangential winds are larger than the gradient winds. Although high-fidelity, nonlinear hurricane wind models may well capture the supergradient winds, high computational demand is needed for each simulation. Recently developed linear, height-resolving hurricane wind models, while can efficiently consider the existence of supergradient winds, significantly underestimate them due essentially to the ignorance of vertical advection term in the governing equations. A number of studies have actually demonstrated that the vertical advection is a major contributor to the transfer of horizontal momentum to the supergradient region. To this end, a refined analytical model that simultaneously integrates the horizontal advection, vertical advection and vertical diffusion terms into the governing equations is developed for accurately and efficiently estimating the hurricane supergradient winds. The important role of the vertical wind speed in determining the horizontal wind speeds (including supergradient winds) in the hurricane boundary layer is highlighted. Since the horizontal and vertical wind components are mutually dependent, the iteration technique is utilized to solve the proposed analytical model. The consideration of the vertical advection results in intensified supergradient winds that are consistent with the observations. Furthermore, a strong outflow region in the vicinity of the radius of maximum winds due to the supergradient winds can be obtained. Due to its simplicity and computational efficiency, the developed analytical model can be easily implemented in the Monte Carlo simulations for the rapid assessment of hurricane wind risk to coastal structures, especially to high-rise buildings.

Drivers of diffusive CH<sub>4</sub> emissions from shallow subarctic lakes on daily to multi-year timescales

Abstract. Lakes and reservoirs contribute to regional carbon budgets via significant emissions of climate forcing trace gases. Here, for improved modelling, we use 8 years of floating chamber measurements from three small, shallow subarctic lakes (2010–2017, n=1306) to separate the contribution of physical and biogeochemical processes to the turbulence-driven, diffusion-limited flux of methane (CH4) on daily to multi-year timescales. Correlative data include surface water concentration measurements (2009–2017, n=606), total water column storage (2010–2017, n=237), and in situ meteorological observations. We used the last to compute near-surface turbulence based on similarity scaling and then applied the surface renewal model to compute gas transfer velocities. Chamber fluxes averaged 6.9±0.3 mg CH4 m−2 d−1 and gas transfer velocities (k600) averaged 4.0±0.1 cm h−1. Chamber-derived gas transfer velocities tracked the power-law wind speed relation of the model. Coefficients for the model and dissipation rates depended on shear production of turbulence, atmospheric stability, and exposure to wind. Fluxes increased with wind speed until daily average values exceeded 6.5 m s−1, at which point emissions were suppressed due to rapid water column degassing reducing the water–air concentration gradient. Arrhenius-type temperature functions of the CH4 flux (Ea′=0.90±0.14 eV) were robust (R2≥0.93, p<0.01) and also applied to the surface CH4 concentration (Ea′=0.88±0.09 eV). These results imply that emissions were strongly coupled to production and supply to the water column. Spectral analysis indicated that on timescales shorter than a month, emissions were driven by wind shear whereas on longer timescales variations in water temperature governed the flux. Long-term monitoring efforts are essential to identify distinct functional relations that govern flux variability on timescales of weather and climate change.

A semi-empirical model for mean wind velocity profile of landfalling hurricane boundary layers

The existence of the super-gradient-wind region, where the tangential winds are larger than the gradient wind, has been widely observed inside the hurricane boundary layer. Hence, the extensively used log-law or power-law wind profiles under near-neutral conditions may be inappropriate to characterize the boundary layer winds associated with hurricanes. Recent development in the wind measurement techniques overland together with the abundance of data over ocean enabled a further investigation on the boundary layer wind structure of hurricanes before/after landfall. In this study, a semi-empirical model for mean wind velocity profile of landfalling hurricanes has been developed based on the data from the Weather Surveillance Radar-1988 Doppler (WSR-88D) network operated by the National Weather Service and the Global Positioning System (GPS) dropsondes collected by the National Hurricane Center and Hurricane Research Division. The proposed mathematical representation of engineering wind profile consists of a logarithmic function of the height z normalized by surface roughness z0 (z/z0) and an empirical function of z normalized by the height of maximum wind δ (z/δ). In addition, the consideration of wind direction in terms of the inflow angle is integrated in the boundary layer wind profile. Field-measurement wind data for both overland and over-ocean conditions have been employed to demonstrate the accuracy of simulation and convenience in use of the developed semi-empirical model for mean wind velocity profile of landfalling hurricanes.

Comparison of RANS and LES in the Prediction of Airflow Field over Steep Complex Terrain

The present study compared the prediction accuracy of the three CFD software packages for simulating airflow around a three-dimensional, isolated hill with a steep slope: 1) WindSim (turbulence model: RNG k-e RANS), 2) Meteodyn WT (turbulence model: k-L RANS), which are the leading commercially available CFD software packages in the wind power industry and 3) RIAM-COMPACT (turbulence model: standard Smagorinsky LES), which has been developed by the lead author of the present paper. Distinct differences in the airflow patterns were identified in the vicinity of the isolated hill (especially downstream of the hill) between the RANS results and the LES results. No reverse flow region (vortex region) characterized by negative wind velocities was identified downstream of the isolated hill in the result from the simulation with WindSim (RNG k-e RANS) and Meteodyn WT (k-L RANS). In the case of the simulation with RIAM-COMPACT natural terrain version (standard Smagorinsky LES), a reverse flow region (vortex region) characterized by negative wind velocities clearly forms. Next, an example of wind risk (terrain-induced turbulence) diagnostics was presented for a large-scale wind farm in China. The vertical profiles of the streamwise (x) wind velocity do not follow the so-called power law wind profile; a large velocity deficit can be seen between the hub center and the lower end of the swept area in the case of the LES calculation (RIAM-COMPACT).

Evolution of clustered supernovae

We study the merging and evolution of isolated supernovae (SNe) remnants in a stellar cluster into a collective superbubble, with the help of 3-D hydrodynamic simulations. We particularly focus on the transition stage when the isolated SNe remnants gradually combine to form a superbubble. We find that when the SN rate is high ($\nu_{\rm sn}\sim 10^{-9}$ pc$^{-3}$ yr$^{-1}$), the merging phase lasts for $\sim 10^4$ yr, for $n=1\hbox{--}10$ cm$^{-3}$, and the merging phase lasts for a longer time ($\sim 0.1$ Myr or more) for lower SN rates ($\nu_{\rm sn}\le 10^{-10}$ pc$^{-3}$ yr$^{-1}$). During this transition phase, the growing superbubble is filled with dense and cool fragments of shells and most of the energy is radiated away during this merging process. After passing through the intermediate phase, the superbubble eventually settles on to a new power-law wind asymptote that is smaller than estimated in a continuous wind model. This results in a significant (more than {\it several times}) underestimation of the mechanical luminosity needed to feed the bubble. We determine the X-ray and H$\alpha$ surface brightnesses as functions of time for such merging SNe in a stellar cluster and find that clusters with high SN rate shine predominantly in soft X-rays and H$\alpha$. In particular, a low value of the volume averaged H$\alpha$ to H$\beta$ ratio and its large spread can be a good indicator of the transition phase of merging SNe.

Feasibility Investigation of a Hybrid On-Grid Wind Photovoltaic Retrofitting System

This paper investigates the feasibility of wind–photovoltaic (PV) penetration into an existing utility grid system for the city of Ibrahimyya in Jordan. Ibrahimyya is selected because it enjoys both high annual wind speed of 7.27 m/s and high annual solar radiation of $\text{6.05}\;{\text{kWh}}/{\text{m}}^2/{\text{day}}$ . Two sizing methods are presented using MATLAB and hybrid optimization multiple energy resources software. Thousands of iterations have been carried out in order to get the global autonomous sizing solution that is used for economic analysis. Results show that three CS6X-310 PV panels and eight GE1.5sle-77 wind turbines are the optimal choice. A step-by-step analysis of the proposed system is presented. The net present cost (NPC) is 65 069 349$. The cost of energy (COE) is 0.0817$/kWh. A sensitivity analysis on interest rate, inflation rate, wind power law exponent, annual average daily energy demand, and fuel price is implemented to assess the robustness of the system. The results prove the feasibility to apply the proposed hybrid wind–PV system for this city. The same procedure can be applied anywhere.

A method to correct the flow distortion of offshore wind data using CFD simulation and experimental wind tunnel tests

The assessment of wind energy resource for the development of deep offshore wind plants requires the use of every possible source of data and, in many cases, includes data gathered at meteorological stations installed at islands, islets or even oil platforms—all structures that interfere with, and change, the flow characteristics. This work aims to contribute to the evaluation of such changes in the flow by developing a correction methodology and applying it to the case of Berlenga island, Portugal. The study is performed using computational fluid dynamic simulations (CFD) validated by wind tunnel tests. In order to simulate the incoming offshore flow with CFD models a wind profile, unknown a priori, was established using observations from two coastal wind stations and a power law wind profile was fitted to the existing data (α=0.165). The results show that the resulting horizontal wind speed at 80m above sea level is 16% lower than the wind speed at 80m above the island for the dominant wind direction sector.

Research on the Inflow Boundary Condition of $k-\varepsilon$ Model for the Simulation of Atmospheric Boundary Layer Flow

Choosing proper inlet boundary conditions is an important issue for modeling the wind field using CFD. Studies have shown that the profile of turbulent kinetic energy, k, can be considered as the function of the shear stress. Based on this assumption, four sets of inlet boundary conditions were derived first into two kinds of situations, logarithm-law and power-law wind velocity profile, as analytic solutions of standard k−e model. Then the performances of these four cases for three different roughness types were modeled by commercial CFD software FLUENT 6.3. Finally, some significant results were obtained and conclusions were discussed. The results show that using Power-Logarithm sets model are more proper and convenient.

The iteration method for tower height matching in wind farm design

This paper studies the tower height matching problem in wind turbine positioning optimization. Various models are introduced, including the power law wind speed model with height in the wind farm, the linear wake flow model for flat terrain, the particle wake flow model for complex terrain and the power curve model with power control mechanisms. The greedy algorithm is employed to solve the wind turbine positioning optimization at a specified tower height. The optimization objective is to maximize the Turbine-Site Matching Index (TSMI), which includes both the production and the cost of wind farm. Assuming that the optimized layout for each tower height is the same, an iteration method is developed to obtain the approximated optimal height. The convergence of the proposed iteration method is discussed through the mathematical analysis. The proposed iteration method is validated through the numerical cases over both flat terrain and complex terrain. The results indicate that the proposed method can obtain better optimized height in shorter computational time than previous studies.

Validation of boundary layer parameterization schemes in the weather research and forecasting model under the aspect of offshore wind energy applications— Part I: Average wind speed and wind shear

AbstractFive different planetary boundary layer (PBL) schemes in the weather research and forecasting model have been tested with respect to their capability to model boundary layer parameters relevant for offshore wind deployments. For the year 2005 model simulations based on the Yonsei University, asymmetric convection model version 2, quasi‐normal scale elimination, Mellor–Yamada–Janjic and Mellor–Yamada–Nakanishi–Niino PBL schemes with weather research and forecasting have been performed for the North Sea and validated against measurements of the Forschungsplattformen in Nord‐ und Ostsee Nr.1 platform. The investigations have been focused on the key parameters 100 m mean wind speed and wind shear expressed by the power law exponent α. All PBL‐schemes are doing well in reproducing averages and average annual statistics of the 100 m wind speed. However, two of the schemes (Yonsei University and Mellor–Yamada–Nakanishi–Niino) overestimate the wind speed above 15 m s−1 systematically. The results for the power law wind profile show a large variability between the models and the observations for different atmospheric stability conditions and also differ a lot from the industry standards. Overall, the Mellor–Yamada–Janjic scheme performs slightly better than the others and is suggested as first choice for marine atmospheric boundary layer simulations without apriori information of atmospheric stability in the region of interest. Copyright © 2014 John Wiley & Sons, Ltd.