RANS simulations of neutral atmospheric boundary layer flow over complex terrain with comparisons to field measurements

Micro‐scale Reynolds‐averaged Navier‐Stokes (RANS) simulations of the neutral atmospheric boundary layer (ABL) over complex terrain and a comparison of the results with conditionally averaged met‐tower data are presented. A robust conditional sampling procedure for the meteorological tower (met‐tower) data to identify near‐neutral conditions based on a criterion for the turbulence intensity is developed. The conditionally averaged wind data on 14 met‐towers are used for the model validation. The ABL flow simulations are conducted over complex terrain which includes a prominent hill using the OpenFOAM‐based simulator for on/offshore wind farm applications (SOWFA) with the k?? and the SST k?ω turbulence models. The discretization of the production term in the transport equation for the turbulent kinetic energy (TKE) is modified to greatly reduce the commonly observed nonphysical near surface TKE peak. The driving inflow is generated through an iterative approach using a precursor method to reproduce the measured wind statistics at the reference tower. Both of the RANS models are able to capture the flow behavior windward of the hill. The SST k?ω model predicts more intense flow separation than the k?? model downstream of the steepest sections of the hill. The wind statistics predicted at the location of the met‐towers by both of the RANS models are fairly consistent. Overall, the comparisons of the direction, mean, and standard deviation of the wind between the simulations and the tower data show reasonable agreement except for the differences of the mean wind speeds at four met‐towers located closer to the main ridge of the hill in a region of strong terrain variations.     

Evaluation of four numerical wind flow models for wind resource mapping

A wide range of numerical wind flow models are available to simulate atmospheric flows. For wind resource mapping, the traditional approach has been to rely on linear Jackson–Hunt type wind flow models. Mesoscale numerical weather prediction (NWP) models coupled to linear wind flow models have been in use since the end of the 1990s. In the last few years, computational fluid dynamics (CFD) methods, in particular Reynolds‐averaged Navier–Stokes (RANS) models, have entered the mainstream, whereas more advanced CFD models such as large‐eddy simulations (LES) have been explored in research but remain computationally intensive. The present study aims to evaluate the ability of four numerical models to predict the variation in mean wind speed across sites with a wide range of terrain complexities, surface characteristics and wind climates. The four are (1) Jackson–Hunt type model, (2) CFD/RANS model, (3) coupled NWP and mass‐consistent model and (4) coupled NWP and LES model. The wind flow model predictions are compared against high‐quality observations from a total of 26 meteorological masts in four project areas. The coupled NWP model and NWP‐LES model produced the lowest root mean square error (RMSE) as measured between the predicted and observed mean wind speeds. The RMSE for the linear Jackson‐Hunt type model was 29% greater than the coupled NWP models and for the RANS model 58% greater than the coupled NWP models. The key advantage of the coupled NWP models appears to be their ability to simulate the unsteadiness of the flow as well as phenomena due to atmospheric stability and other thermal effects. Copyright © 2012 John Wiley & Sons, Ltd.     

Evaluation of the effects of turbulence model enhancements on wind turbine wake predictions

The modelling of wind turbine wakes is investigated in this paper using a Navier–Stokes solver employing the k–ω turbulence model appropriately modified for atmospheric flows. It is common knowledge that even single‐wind turbine wake predictions with computational fluid dynamic methods underestimate the near wake deficit, directly contributing to the overestimation of the power of the downstream turbines. For a single‐wind turbine, alternative modelling enhancements under neutral and stable atmospheric conditions are tested in this paper to account for and eventually correct the turbulence overestimation that is responsible for the faster flow recovery that appears in the numerical predictions. Their effect on the power predictions is evaluated with comparison with existing wake measurements. A second issue addressed in this paper concerns multi‐wake predictions in wind farms, where the estimation of the reference wind speed that is required for the thrust calculation of a turbine located in the wake(s) of other turbines is not obvious. This is overcome by utilizing an induction factor‐based concept: According to it, the definition of the induction factor and its relationship with the thrust coefficient are employed to provide an average wind speed value across the rotor disk for the estimation of the axial force. Application is made on the case of five wind turbines in a row. Copyright © 2010 John Wiley & Sons, Ltd.     

Evaluating winds and vertical wind shear from Weather Research and Forecasting model forecasts using seven planetary boundary layer schemes

The existence of vertical wind shear in the atmosphere close to the ground requires that wind resource assessment and prediction with numerical weather prediction (NWP) models use wind forecasts at levels within the full rotor span of modern large wind turbines. The performance of NWP models regarding wind energy at these levels partly depends on the formulation and implementation of planetary boundary layer (PBL) parameterizations in these models. This study evaluates wind speeds and vertical wind shears simulated by the Weather Research and Forecasting model using seven sets of simulations with different PBL parameterizations at one coastal site over western Denmark. The evaluation focuses on determining which PBL parameterization performs best for wind energy forecasting, and presenting a validation methodology that takes into account wind speed at different heights. Winds speeds at heights ranging from 10 to 160 m, wind shears, temperatures and surface turbulent fluxes from seven sets of hindcasts are evaluated against observations at Høvsøre, Denmark. The ability of these hindcast sets to simulate mean wind speeds, wind shear, and their time variability strongly depends on atmospheric static stability. Wind speed hindcasts using the Yonsei University PBL scheme compared best with observations during unstable atmospheric conditions, whereas the Asymmetric Convective Model version 2 PBL scheme did so during near‐stable and neutral conditions, and the Mellor–Yamada–Janjic PBL scheme prevailed during stable and very stable conditions. The evaluation of the simulated wind speed errors and how these vary with height clearly indicates that for wind power forecasting and wind resource assessment, validation against 10 m wind speeds alone is not sufficient. Copyright © 2012 John Wiley & Sons, Ltd.     

Parabolic RANS solver for low‐computational‐cost simulations of wind turbine wakes

A numerical framework for simulations of wake interactions associated with a wind turbine column is presented. A Reynolds‐averaged Navier‐Stokes (RANS) solver is developed for axisymmetric wake flows using parabolic and boundary‐layer approximations to reduce computational cost while capturing the essential wake physics. Turbulence effects on downstream evolution of the time‐averaged wake velocity field are taken into account through Boussinesq hypothesis and a mixing length model, which is only a function of the streamwise location. The calibration of the turbulence closure model is performed through wake turbulence statistics obtained from large‐eddy simulations of wind turbine wakes. This strategy ensures capturing the proper wake mixing level for a given incoming turbulence and turbine operating condition and, thus, accurately estimating the wake velocity field. The power capture from turbines is mimicked as a forcing in the RANS equations through the actuator disk model with rotation. The RANS simulations of the wake velocity field associated with an isolated 5‐MW NREL wind turbine operating with different tip speed ratios and turbulence intensity of the incoming wind agree well with the analogous velocity data obtained through high‐fidelity large‐eddy simulations. Furthermore, different cases of columns of wind turbines operating with different tip speed ratios and downstream spacing are also simulated with great accuracy. Therefore, the proposed RANS solver is a powerful tool for simulations of wind turbine wakes tailored for optimization problems, where a good trade‐off between accuracy and low‐computational cost is desirable.     

De‐trending of wind speed variance based on first‐order and second‐order statistical moments only

The lack of efficient methods for de‐trending of wind speed resource data may lead to erroneous wind turbine fatigue and ultimate load predictions. The present paper presents two models, which quantify the effect of an assumed linear trend on wind speed standard deviations as based on available statistical data only. The first model is a pure time series analysis approach, which quantifies the effect of non‐stationary characteristics of ensemble mean wind speeds on the estimated wind speed standard deviations as based on mean wind speed statistics only. This model is applicable to statistics of arbitrary types of time series. The second model uses the full set of information and includes thus additionally observed wind speed standard deviations to estimate the effect of ensemble mean non‐stationarities on wind speed standard deviations. This model takes advantage of a simple physical relationship between first‐order and second‐order statistical moments of wind speeds in the atmospheric boundary layer and is therefore dedicated to wind speed time series but is not applicable to time series in general. The capabilities of the proposed models are discussed by comparing model predictions with conventionally de‐trended characteristics of measured wind speeds using data where high sampled time series are available, and a traditional de‐trending procedure therefore can be applied. This analysis shows that the second model performs significantly better than the first model, and thus in turn that the model constraint, introduced by the physical link between the first and second statistical moments, proves very efficient in the present context. © 2013 The Authors. Wind Energy Published by John Wiley & Sons Ltd.     

ENDOW (efficient development of offshore wind farms): modelling wake and boundary layer interactions

While experience gained through the offshore wind energy projects currently operating is valuable, a major uncertainty in estimating power production lies in the prediction of the dynamic links between the atmosphere and wind turbines in offshore regimes. The objective of the ENDOW project was to evaluate, enhance and interface wake and boundary layer models for utilization offshore. The project resulted in a significant advance in the state of the art in both wake and marine boundary layer models, leading to improved prediction of wind speed and turbulence profiles within large offshore wind farms. Use of new databases from existing offshore wind farms and detailed wake profiles collected using sodar provided a unique opportunity to undertake the first comprehensive evaluation of wake models in the offshore environment. The results of wake model performance in different wind speed, stability and roughness conditions relative to observations provided criteria for their improvement. Mesoscale model simulations were used to evaluate the impact of thermal flows, roughness and topography on offshore wind speeds. The model hierarchy developed under ENDOW forms the basis of design tools for use by wind energy developers and turbine manufacturers to optimize power output from offshore wind farms through minimized wake effects and optimal grid connections. The design tools are being built onto existing regional‐scale models and wind farm design software which was developed with EU funding and is in use currently by wind energy developers. Copyright © 2004 John Wiley & Sons, Ltd.     

Computational Fluid Dynamics model of stratified atmospheric boundary‐layer flow

For wind resource assessment, the wind industry is increasingly relying on computational fluid dynamics models of the neutrally stratified surface‐layer. So far, physical processes that are important to the whole atmospheric boundary‐layer, such as the Coriolis effect, buoyancy forces and heat transport, are mostly ignored. In order to decrease the uncertainty of wind resource assessment, the present work focuses on atmospheric flows that include stability and Coriolis effects. The influence of these effects on the whole atmospheric boundary‐layer are examined using a Reynolds‐averaged Navier–Stokes k‐ ε model. To validate the model implementations, results are compared against measurements from several large‐scale field campaigns, wind tunnel experiments, and previous simulations and are shown to significantly improve the predictions. Copyright © 2013 John Wiley & Sons, Ltd.     

Influence of atmospheric stability on wind turbine loads

Simulations of wind turbine loads for the NREL 5 MW reference wind turbine under diabatic conditions are performed. The diabatic conditions are incorporated in the input wind field in the form of wind profile and turbulence. The simulations are carried out for mean wind speeds between 3 and 16 m s ^{? 1} at the turbine hub height. The loads are quantified as the cumulative sum of the damage equivalent load for different wind speeds that are weighted according to the wind speed and stability distribution. Four sites with a different wind speed and stability distribution are used for comparison. The turbulence and wind profile from only one site is used in the load calculations, which are then weighted according to wind speed and stability distributions at different sites. It is observed that atmospheric stability influences the tower and rotor loads. The difference in the calculated tower loads using diabatic wind conditions and those obtained assuming neutral conditions only is up to 17%, whereas the difference for the rotor loads is up to 13%. The blade loads are hardly influenced by atmospheric stability, where the difference between the calculated loads using diabatic and neutral input wind conditions is up to 3% only. The wind profiles and turbulence under diabatic conditions have contrasting influences on the loads; for example, under stable conditions, loads induced by the wind profile are larger because of increased wind shear, whereas those induced by turbulence are lower because of less turbulent energy. The tower base loads are mainly influenced by diabatic turbulence, whereas the rotor loads are influenced by diabatic wind profiles. The blade loads are influenced by both, diabatic wind profile and turbulence, that leads to nullifying the contrasting influences on the loads. The importance of using a detailed boundary‐layer wind profile model is also demonstrated. The difference in the calculated blade and rotor loads is up to 6% and 8%, respectively, when only the surface‐layer wind profile model is used in comparison with those obtained using a boundary‐layer wind profile model. Finally, a comparison of the calculated loads obtained using site‐specific and International Electrotechnical Commission (IEC) wind conditions is carried out. It is observed that the IEC loads are up to 96% larger than those obtained using site‐specific wind conditions.Copyright © 2012 John Wiley & Sons, Ltd.     

Spectral tensor parameters for wind turbine load modeling from forested and agricultural landscapes

A velocity spectral tensor model was evaluated from the single‐point measurements of wind speed. The model contains three parameters representing the dissipation rate of specific turbulent kinetic energy, a turbulence length scale and the turbulence anisotropy. Sonic anemometer measurements taken over a forested and an agricultural landscape were used to calculate the model parameters for neutral, slightly stable and slightly unstable atmospheric conditions for a selected wind speed interval. The dissipation rate above the forest was nine times that at the agricultural site. No significant differences were observed in the turbulence length scales between the forested and agricultural areas. Only a small difference was observed in the turbulence anisotropy at the two sites, except near the surface, where the forest turbulence was more isotropic. The turbulence anisotropy remained more or less constant with height at the forest site, whereas the turbulence became more isotropic with height for the agricultural site. Using the three parameters as inputs, we quantified the performance of the model in coherence predictions for vertical separations. The model coherence of all the three velocity components was overestimated for the analyzed stability classes at both sites. As expected from the model approximations, the model performed better at both sites for neutral stability than slightly stable and unstable conditions. The model prediction of coherence of the along‐wind and vertical components was better than that of the cross‐wind component. No significant difference was found between the performance of the model at the forested and the agricultural areas. © 2014 The Authors. Wind Energy published by John Wiley & Sons, Ltd.     

Analytical model for predicting the performance of arbitrary size and layout wind farms

A simple engineering model for predicting wind farm performance is presented, which is applicable to wind farms of arbitrary size and turbine layout. For modeling the interaction of wind farm with the atmospheric boundary layer (ABL), the wind farm is represented as added roughness elements. The wind speed behind each turbine is calculated using a kinematic model, in which the friction velocity and the wind speed outside the turbine wake, constructed based on the wind farm‐ABL interaction model, are employed to estimate the wake expansion rate in the crosswind direction and the maximum wind speed that can be recovered within the turbine wake, respectively. Validation of the model is carried out by comparing the model predictions with the measurements from wind tunnel experiments and the Horns Rev wind farm. For all validation cases, satisfactory agreement is obtained between model predictions and experimental data. Copyright © 2015 John Wiley & Sons, Ltd.     

Aerodynamic structures and processes in rotationally augmented flow fields

Rotational augmentation of horizontal axis wind turbine blade aerodynamics currently remains incompletely characterized and understood. To address this, the present study concurrently analysed experimental measurements and computational predictions, both of which were unique and of high quality. Experimental measurements consisted of surface pressure data statistics used to infer sectional boundary layer state and to quantify normal force levels. Computed predictions included high‐resolution boundary layer topologies and detailed above‐surface flow field structures. This synergy was exploited to reliably identify and track pertinent features in the rotating blade boundary layer topology as they evolved in response to varying wind speed. Subsequently, boundary layer state was linked to above‐surface flow field structure and used to deduce mechanisms underlying augmented aerodynamic force production during rotating conditions. Copyright © 2007 John Wiley &Sons, Ltd.     

Diurnal cycle RANS simulations applied to wind resource assessment

Microscale computational fluid dynamics (CFD) models can be used for wind resource assessment on complex terrains. These models generally assume neutral atmospheric stratification, an assumption that can lead to inaccurate modeling results and to large uncertainties at certain sites. We propose a methodology for wind resource evaluation based on unsteady Reynolds averaged Navier‐Stokes (URANS) simulations of diurnal cycles including the effect of thermal stratification. Time‐dependent boundary conditions are generated by a 1D precursor to drive 3D diurnal cycle simulations for a given geostrophic wind direction sector. Time instants of the cycle representative of four thermal stability regimes are sampled within diurnal cycle simulations and combined with masts time series to obtain the wind power density (WPD). The methodology has been validated on a complex site instrumented with seven met masts. The WPD spatial distribution is in good agreement with observations with the mean absolute error improving 17.1% with respect to the neutral stratification assumption.     

基于分离涡方法的定日镜风效应研究

选用RANS湍流模型、大涡模拟与分离涡模型等计算流体动力学(CFD)方法,应用由新的湍流脉动流场产生方法DSRFG(discretizing and synthesizing random flow generation)模拟风场实际的湍流边界条件,对定日镜结构的风压分布及流场进行分析。将数值模拟结果与风洞试验数据进行对比,给出风向角为0°工况下定日镜结构的风压系数分布规律及特点,分析5种模型下定日镜周围的流场分布和涡量分布。结果表明,RANS模型虽然能够模拟出结构周围流场的基本规律,但却无法模拟出风场中的紊流和涡旋的分离扩散情况。大涡模拟及分离涡模型对风场中的紊流和涡旋的分离扩散有较好的模拟效果,在风压系数的分布上也与风洞试验数据拟合较好。在定日镜周围流场中脉动风压系数的分布上,分离涡模型的模拟结果较大涡模拟更为接近风洞试验值,且耗时更少。     

Atmospheric stability‐dependent infinite wind‐farm models and the wake‐decay coefficient

We extend the infinite wind‐farm boundary‐layer (IWFBL) model of Frandsen to take into account atmospheric static stability effects. This extended model is compared with the IWFBL model of Emeis and to the Park wake model used in Wind Atlas Analysis and Application Program (WAsP), which is computed for an infinite wind farm. The models show similar behavior for the wind‐speed reduction when accounting for a number of surface roughness lengths, turbine to turbine separations and wind speeds under neutral conditions. For a wide range of atmospheric stability and surface roughness length values, the extended IWFBL model of Frandsen shows a much higher wind‐speed reduction dependency on atmospheric stability than on roughness length (roughness has been generally thought to have a major effect on the wind‐speed reduction). We further adjust the wake‐decay coefficient of the Park wake model for an infinite wind farm to match the wind‐speed reduction estimated by the extended IWFBL model of Frandsen for different roughness lengths, turbine to turbine separations and atmospheric stability conditions. It is found that the WAsP‐recommended values for the wake‐decay coefficient of the Park wake model are (i) larger than the adjusted values for a wide range of neutral to stable atmospheric stability conditions, a number of roughness lengths and turbine separations lower than ～ 10 rotor diameters and (ii) too large compared with those obtained by a semiempirical formulation (relating the ratio of the friction to the hub‐height free velocity) for all types of roughness and atmospheric stability conditions. © 2013 The Authors. Wind Energy published by John Wiley & Sons, Ltd.     

A system for wind power estimation in mountainous terrain. Prediction of Askervein hill data

In mountainous terrain, where the wind power potential is largest, the estimation of the local wind power can be done rationally by means of available information about the large‐scale flow and the detailed terrain and numerical flow models for downscaling, provided that the numerical model estimates can be assigned sufficient confidence. In this study the confidence of a local model in such an estimation system is discussed. The model is based upon the Reynolds‐averaged Navier–Stokes equations with (K, ?) turbulence closure and integrated with finite element numerical techniques. The model has previously been validated relative to complicated laboratory‐scale flows and appears to predict some full‐scale geophysical flows plausibly. Here its predictions are compared quantitatively with the full‐scale Askervein hill experimental data. The model estimates the data to within the experimental uncertainty, which we judge to be comparable to 10%, as other comparable models also do. This contributes to assign confidence to the downscaling estimation system mentioned. Copyright © 2004 John Wiley & Sons, Ltd.     

An actuator sector method for efficient transient wind turbine simulation

This paper investigates a new method for transient simulation of flow through a wind turbine using an actuator technique. The aim, in the context of wind turbine wake simulation, is to develop an alternative to the widely used actuator disc model with an increased resolution and range of applications, for the same or less computational expense. In this new model, the actuator sector method, forces applied to the fluid are distributed azimuthally to maintain a continuous flow solution for increased time‐step intervals compared with the actuator line method. Actuator sector results are presented in comparison with actuator disc and actuator line models initially for a non‐dimensionalized turbine in laminar onset flow. Subsequent results are presented for a turbine operating in a turbulent atmospheric boundary layer. Results show significant increases in flow fidelity compared with actuator disc model results; this includes the resolution of diametric variation in rotor loading caused by horizontal or vertical wind shear and the helical vortex system shed from the turbine blade tips. Significant reductions in computational processing time were achieved with wake velocities and turbulence statistics comparable with actuator line model results. The actuator sector method offers an improved alternative to applications employing conventional actuator disc models, with little or no additional computational cost. This technique in conjunction with a Cartesian mesh‐based parallel flow solver leads to efficient simulation of turbines in atmospheric boundary layer flows. Copyright © 2014 John Wiley & Sons, Ltd.     

A linearized numerical model of wind‐farm flows

A fast and reasonably accurate numerical three‐dimensional wake model able to predict the flow behaviour of a wind farm over a flat terrain has been developed. The model is based on the boundary‐layer approximation of the Navier–Stokes equations, linearized around the incoming atmospheric boundary layer, with the assumption that the wind turbines provide a small perturbation to the velocity field. The linearization of the actuator‐disc theory brought additional insights that could be used to understand the behaviour, as well as the limitations, of a flow model based on linear methods: for instance, it is shown that an adjustment of the turbine's thrust coefficient is necessary in order to obtain the same wake velocity field provided by the actuator disc theory within the used linear framework. The model is here validated against two independent wind‐tunnel campaigns with a small and a large wind farm aimed at the characterization of the flow above and upstream of the farms, respectively. The developed model is, in contrary to current engineering wake models, able to account for effects occurring in the upstream flow region, thereby including more physical mechanisms than other simplified approaches. The conducted simulations (in agreement with the measurement results) show that the presence of a wind farm affects the approaching flow far more upstream than generally expected and definitely beyond the current industrial standards. Despite the model assumptions, several velocity statistics above wind farms have been properly estimated providing an insight into the transfer of momentum inside the turbine rows. Copyright © 2016 John Wiley & Sons, Ltd.     

Enhanced estimation of boundary layer advective properties to improve space‐to‐time conversion processes for wind energy applications

Remote sensing instruments that scan have the ability to provide high‐resolution spatial measurements of atmospheric boundary layer winds across a region. However, the ability to use these spatially distributed measurements to extract temporal variations in the flow at time scales less than the measurement revisit period is historically limited. As part of this work, the framework for an enhanced space‐to‐time conversion technique is established, allowing for time histories of atmospheric boundary layer wind characteristics to be reliably extracted for locations within the measurement domain. This space‐to‐time conversion technique is made possible by quantifying momentum advection within the measurement domain, rather than simply assuming a uniform advection based on a singular mean wind speed and direction. The use of this technique enables the extraction of long lead‐time (ie, upwards of 60 seconds) forecasts of wind speed and direction at individual locations within the measurement domain, thereby expanding the application and potential benefits of scanning instruments. For example, these long lead‐time forecasts can be used to enhance proactive wind turbine control and more accurately define wind turbine wake statistics.     

A comprehensive review on numerical approaches to simulate heat transfer of turbulent supercritical CO2 flows

Abstract

Extensive computational investigations have been performed to obtain more detailed information about the peculiar phenomena of turbulent supercritical carbon dioxide (sCO₂) flow as ideal heat transfer fluids in various thermal engineering applications. This paper reviews the simulation techniques used and discusses their advantages, shortcomings and applicability. Not only is a comprehensive inspection on various computational approaches provided, but also the model refinements are suggested. Direct Numerical Simulations (DNS) provides valuable and reliable information about the thermohydraulics of turbulent sCO₂ flows, in particular within the near-wall region, which well interprets the observed heat transfer enhancement and deterioration with property variations, flow acceleration and buoyancy discussed. However, DNS is not feasible when it comes to high Reynolds number flows with complex geometries encountered in practical applications because of the drastically increasing computational cost. Reynolds-Averaged Navier-Stokes (RANS) modeling is able to fill the gap with acceptable accuracy and becomes the mainstream for turbulent sCO₂ heat transfer simulations. The flow and heat transfer behaviors of turbulent sCO₂ can be simulated using RANS modeling leading to acceptable predictions. However, the performance variation is considerable for different models and for the same model of changing operating conditions, model generality is not reached. In addition, some treatments implemented into the RANS models for constant property fluids are not appropriate for variable-property sCO₂ flows, causing inconsistency on the mixed convection predictions. Variable turbulent Prandtl number and more advanced calculation schemes for buoyancy production of turbulent kinetic energy are strongly recommended. Also, more appropriate treatments for damping functions are demanded to enable the model properly respond to the local property changes, particularly near the wall. Much simpler models with far less computational cost based upon the two-layer theory are being developed to achieve the generality. While this is promising, the examinations are still limited to the certain conditions and some model parameters need to be calibrated against the DNS data, which definitely reduces the model universality since DNS only covers a limited range of operating conditions. Developing more generic and reliable RANS models is still the main focus of simulation techniques used for turbulent sCO₂ heat transfer.