Aerodynamic analysis of HAWTs operating in unsteady conditions

This article presents a numerical method for predicting unsteady aerodynamics of horizontal axis wind turbines (HAWTs). In this method the flow field is described by the unsteady incompressible Navier–Stokes equations. The rotor and tower are idealized respectively as actuator disc and flat plate permeable surfaces on which external normal surficial forces are balanced by fluid pressure discontinuities. The external forces exerted by the rotor and tower on the flow are prescribed according to blade element theory. Dynamic behaviour of the rotor aerodynamic characteristics is simulated using either the Gormont or the Beddoes–Leishman model. The resulting mathematical formulation is solved using a control volume finite element method. The fully implicit scheme is used for time discretization. In general, the proposed method has demonstrated its capability to adequately represent the field data. It has been demonstrated that the accuracy of the predicted results depends primarily on the dynamic stall model as well as on the turbulence model employed. Copyright © 2001 John Wiley & Sons, Ltd.     

The analytical solution of natural convection in a micro size horizontal cylindrical annulus with periodic volumetric heat flux

We consider the two‐dimensional problem of steady natural convection in a narrow (micro size) horizontal cylindrical annulus filled with viscous fluid and periodic volumetric heat flux. The solution is expanded in powers of a single combined similarity parameter, which is the product of the gap ratio to the power of four, and Rayleigh number and the series extended by means of symbolic calculation up to 16 terms. Analysis of these expansions allows the exact computation for arbitrary accuracy up to 50,000 figures. Although the range of the radius of convergence is small, the Pade approximation leads our result to be good even for much higher values of the similarity parameter. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20323     

Characterization of the unsteady flow in the nacelle region of a modern wind turbine

A three‐dimensional Navier–Stokes solver has been used to investigate the flow in the nacelle region of a wind turbine where anemometers are typically placed to measure the flow speed and the turbine yaw angle. A 500 kW turbine was modelled with rotor and nacelle geometry in order to capture the complex separated flow in the blade root region of the rotor. A number of steady state and unsteady simulations were carried out for wind speeds ranging from 6 m s^?1 to 16 m s^?1 as well as two yaw and tilt angles. The flow in the nacelle region was found to be highly unsteady, dominated by unsteady vortex shedding from the cylindrical part of the blades, which interacted with the root vortices from each blade, generating high‐velocity gradients. As a consequence, the nacelle wind speed and the nacelle flow angle were found to vary significantly with the height above the nacelle surface. The nacelle anemometry showed significant dependence on both yaw and tilt angles with yaw errors of up to 10 degrees when operating in a tilted inflow. Copyright © 2010 John Wiley & Sons, Ltd.     

Effect of Placing a Diffuser around a Wind Turbine

An actuator disc CFD model of the flow through a wind turbine in a diffuser is developed and validated. Further, it is shown theoretically from a 1D analysis that the Betz limit can be exceeded by a factor proportional to the relative increase in mass flow through the rotor induced by the diffuser. The theoretical 1D result is verified by the CFD model. Copyright © 2000 John Wiley & Sons, Ltd.     

Verification and validation of an actuator disc model

Wind turbine wake can be studied in computational fluid dynamics with the use of permeable body forces (e.g. actuator disc, line and surface). This paper presents a general flexible method to redistribute wind turbine blade forces as permeable body forces in a computational domain. The method can take any kind of shape discretization, determine the intersectional elements with the computational grid and use the size of these elements to redistribute proportionally the forces. This method can potentially reduce the need for mesh refinement in the region surrounding the rotor and, therefore, also reduce the computational cost of large wind farm wake simulations. The special case of the actuator disc is successfully validated with an analytical solution for heavily loaded turbines and with a full‐rotor computation in computational fluid dynamics. Copyright © 2013 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.     

Transition prediction for a two‐dimensional reynolds‐averaged navier–stokes method applied to wind turbine airfoils

Boundary layer transition is significant to many flow fields that include both laminar and turbulent regions. Accurate prediction of transition onset is fundamental to the modelling of these flows. In most flow solvers based on the Reynolds‐averaged Navier–Stokes equations, transition onset must be specified manually. To overcome this weakness and to more accurately predict aerodynamic flow fields, a boundary layer transition prediction methodology is presented. This methodology, which has been applied to a Navier–Stokes solver, dynamically locates transition onset as the flow solution is converging. The prediction methodology identifies several boundary layer transition mechanisms, including Tollmien–Schlichting instability, laminar separation and turbulence contamination. Where possible, the implementation utilizes the calculated boundary layer velocity profiles to strongly couple the predicted transition locations and the flow solution. The transition prediction methodology was used to predicted transition onset for the NLF(1)‐0416 and S809 single‐element wind turbine airfoils. Results obtained with numerical calculations are found to agree well with experimental observations. Copyright © 2001 John Wiley & Sons, Ltd.     

Comparative study of a three-bucket Savonius rotor with a combined three-bucket Savonius–three-bladed Darrieus rotor

The vertical axis wind turbines are simple in construction, self-starting, inexpensive and can accept wind from any direction without orientation. A combined Savonius–Darrieus type vertical axis wind rotor has got many advantages over individual Savonius or individual Darrieus wind rotor, such as better efficiency than Savonius rotor and high starting torque than Darrieus rotor. But works on the combined Savonius–Darrieus wind rotor are very scare. In view of the above, two types of models, one simple Savonius and the other combined Savonius–Darrieus wind rotors were designed and fabricated. The Savonius rotor was a three-bucket system having provisions for overlap variations. The Savonius–Darrieus rotor was a combination of three-bucket Savonius and three-bladed Darrieus rotors with the Savonius placed on top of the Darrieus rotor. The overlap variation was made in the upper part, i.e. the Savonius rotor only. These were tested in a subsonic wind tunnel available in the department. The various parameters namely, power coefficients and torque coefficients were calculated for both overlap and without overlap conditions. From the present investigation, it is seen that with the increase of overlap, the power coefficients start decreasing. The maximum power coefficient of 51% is obtained at no overlap condition. However, while comparing the power coefficients (C_p) for simple Savonius-rotor with that of the combined configuration of Savonius–Darrieus rotor, it is observed that there is a definite improvement in the power coefficient for the combined Savonius–Darrieus rotor without overlap condition. Combined rotor without overlap condition provided an efficiency of 0.51, which is higher than the efficiency of the Savonius rotor at any overlap positions under the same test conditions.     

Viscous and Aeroelastic Effects on Wind Turbine Blades. The VISCEL Project. Part II: Aeroelastic Stability Investigations

The recent introduction of ever larger wind turbines poses new challenges with regard to understanding the mechanisms of unsteady flow–structure interaction. An important aspect of the problem is the aeroelastic stability of the wind turbine blades, especially in the case of combined flap/lead–lag vibrations in the stall regime. Given the limited experimental information available in this field, the use of CFD techniques and state‐of‐the‐art viscous flow solvers provides an invaluable alternative towards the identification of the underlying physics and the development and validation of sound engineering‐type aeroelastic models. Navier–Stokes‐based aeroelastic stability analysis of individual blade sections subjected to combined pitch/flap or flap/lead–lag motion has been attempted by the present consortium in the framework of the concluded VISCEL JOR3‐CT98‐0208 Joule III project. Copyright © 2003 John Wiley & Sons, Ltd.     

A simple improvement of a tip loss model for actuator disc simulations

The loading of a wind turbine decreases towards the blade tip because of the velocities induced by the tip vortex. This tip loss effect has to be taken into account when performing actuator disc simulations, where the single blades of the turbine are not modeled. A widely used method applies a factor on the axial and tangential loading of the turbine. This factor decreases when approaching the blade tip. It has been shown that the factor should be different for the axial and tangential loading of the turbine to model the rotation of the resulting force vector at the airfoil sections caused by the induced velocity. The present article contains the derivation of a simple correction for the tangential load factor that takes this rotation into account. The correction does not need any additional curve fitting but just depends on the local airfoil characteristics and angle of attack. Actuator disc computations with the modified tip loss correction show improved agreement with results from actuator line, free wake lifting line, and blade element momentum simulations.     

Validation and modification of the Blade Element Momentum theory based on comparisons with actuator disc simulations

A comprehensive investigation of the Blade Element Momentum (BEM) model using detailed numerical simulations with an axis symmetric actuator disc (AD) model has been carried out. The present implementation of the BEM model is in a version where exactly the same input in the form of non‐dimensional axial and tangential load coefficients can be used for the BEM model as for the numerical AD model. At a rotor disc loading corresponding to maximum power coefficient, we found close correlation between the AD and BEM model as concerns the integral value of the power coefficient. However, locally along the blade radius, we found considerable deviations with the general tendency, that the BEM model underestimates the power coefficient on the inboard part of the rotor and overestimates the coefficient on the outboard part. A closer investigation of the deviations showed that underestimation of the power coefficient on the inboard part could be ascribed to the pressure variation in the rotating wake not taken into account in the BEM model. We further found that the overestimation of the power coefficient on the outboard part of the rotor is due to the expansion of the flow causing a non‐uniform induction although the loading is uniform. Based on the findings we derived two small engineering sub‐models to be included in the BEM model to account for the physical mechanisms causing the deviations. Finally, the influence of using the corrected BEM model, BEM_cor on two rotor designs is presented. Copyright © 2009 John Wiley & Sons, Ltd.     

大型核电汽轮发电机转子通风系统 流动特性数值模拟

核电汽轮发电机是核能发电的主要设备之一,其通风冷却性能是影响核电机组安全运行的重要因素。转子采用轴向—径向通风是大型核电汽轮发电机常用的通风系统之一。根据计算流体力学（CFD）的基本原理,对大型核电汽轮发电机转子通风系统的通风结构和性能进行了分析,建立了转子通风系统内冷却气体流动的三维计算模型,确定了相应的边界条件,进行了数值计算和分析,得到了该汽轮发电机转子线圈直线段各通风沟内冷却气体的流量分配规律,气隙内的流场及静压分布规律。研究结果可为汽轮发电机转子通风系统结构优化及温升计算提供参考。     

Viscous and Aeroelastic Effects on Wind Turbine Blades. The VISCEL project. Part I: 3D Navier–Stokes Rotor simulations

Aerodynamic modelling of HAWT rotors by means of “engineering methods” has reached a saddle point, where no further development can be expected without a breakthrough in understanding the physics of unsteady, rotating three‐dimensional flows. However, such a breakthrough becomes ever more necessary, as the size of the wind turbines increases. With the experimental work in that direction being mostly limited to observing the phenomena and interpreting the associated mechanisms, and its increased cost, alternatives are being sought. The use of CFD techniques and state‐of‐the‐art Navier–Stokes solvers is considered a very serious contender, a belief shared by the members of the present consortium, which has worked on the VISCEL JOR3‐CT98‐0208 Joule III project. This project's goal was to determine the aerodynamic characteristics as well as the aeroelastic behaviour of wind turbine blades across their broad range of operational conditions, from attached to highly separated flow regimes. The work programme included specific tasks for the validation and assessment of existing 3D solvers, for the parametric study of 3D flow around realistic blades and for the investigation of aeroelastic stability, at the blade section level. Copyright © 2003 John Wiley & Sons, Ltd.     

Analysis of wake states by a full-field actuator disc model

Various wake status have been analysed by a numerical method that combines the actuator disc principle with the Navier–Stokes equations. Results are compared with one-dimensional momentum theory and experiments. The computations are in excellent agreement with one-dimensional momentum theory for rotors working in the windmill brake state as well as in the propeller and hover states. The computations demonstrate that the turbulent wake and vortex ring states are unstable regimes for a rotor with constant loading and that these states, after a complicated transient phase, settle to a steady state. Copyright © 1998 John Wiley & Sons, Ltd.     

Numerical study of turbulent flow around a wind turbine nacelle

This article presents a numerical method for the simulation of turbulent flow around the nacelle of a horizontal axis wind turbine. The flow field around the turbine and nacelle is described by the Reynolds‐averaged Navier–Stokes equations. The k–? model has been chosen for closure of the time‐averaged turbulent flow equations. The rotor disc is modelled using the actuator disc concept. The main purpose of this article is to assess the impacts of the variation of some operational parameters (e.g. blade pitch angle changes) and atmospheric turbulence upon the relationship between wind speed measured near the nacelle and freestream wind speed established for an isolated turbine. Simulation results were compared with experimental data (from a typical stall‐controlled, commercially available wind turbine rated higher than 600 kW). In general, good qualitative agreements have been found that validate the proposed method. It has been shown that a level of accuracy sufficient for use in power performance testing can be obtained only when a proper aerodynamic analysis of the inboard non‐lifting cylindrical sections of the blade is included. Furthermore, the numerical method has proven to be a useful tool for locating nacelle anemometers. Copyright © 2005 John Wiley & Sons, Ltd.     

Effect of wind turbine surge motion on rotor thrust and induced velocity

Offshore wind turbines on floating platforms will experience larger motions than comparable bottom fixed wind turbines—for which the majority of industry standard design codes have been developed and validated. In this paper, the effect of a periodic surge motion on the integrated loads and induced velocity on a wind turbine rotor is investigated. Specifically, the performance of blade element momentum theory with a quasisteady wake as well as two widely used engineering dynamic inflow models is evaluated. A moving actuator disc model is used as reference, since the dynamics associated with the wake will be inherently included in the solution of the associated fluid dynamic problem. Through analysis of integrated rotor loads, induced velocities and aerodynamic damping, it is concluded that typical surge motions are sufficiently slow to not affect the wake dynamics predicted by engineering models significantly. Copyright © 2012 John Wiley & Sons, Ltd.     

The Betz–Joukowsky limit: on the contribution to rotor aerodynamics by the British,German and Russian scientific schools

The derivation of the efficiency of an ideal wind turbine has been attributed to the three famous scientists of the three aerodynamic research schools in Europe during the first decades of the previous century: Lanchester, Betz and Joukowsky. However, detailed reading of their classical papers has shown that Lanchester did not accept Froude's result that the velocity through the disc is the average of the velocities far upstream and far downstream, by which his solution is not determined. Betz and Joukowsky used vortex theory to support Froude's result and derived the ideal efficiency of a wind turbine at the same time. This efficiency has been known as the Joukowsky limit in Russia and as the Betz limit everywhere else. Because of the contribution of both scientists, this result should be called the Betz–Joukowsky limit everywhere. Copyright © 2011 John Wiley & Sons, Ltd.     

Modelling of the flow at the rotor disc in a geothermal turbine of 110 MW

To elucidate an excessive erosion damage produced by solid particles in the fourth stage rotor disc of a 110 MW double flow geothermal turbine, a bi-dimensional modelling investigation has been conducted. The study was based on a set of results from a computational model using a Reynolds stress, RSM, turbulence model. The predicted results confirmed characteristic flow conditions that may play a main role in the serious erosion of the fourth stage rotor disc governor side, which has been detected in periodic overhauls. The results show a jet of vapour that hits the disc transition radius surface at velocities around 112 m/s. These conditions are produced by the flow outgoing from the labyrinth seal, which passes through a drastic cross-section reduction in the last seal strip. The flow was then simulated introducing specific changes to the geometry and the grid in order to modify the flow patterns favourably. Actually, the suggested changes have been envisaged indeed to be practically feasible of being implemented. The new results showed that it is possible to reduce the erosion process up to 86% by increasing the distance from the labyrinth seal to the rotor disc, which produces a 38% velocity reduction of the vapour flow in that zone. The design proposed in this work produces a flow pattern of a lower velocity on disc surface together with a modified angle of flow incidence. Furthermore, the proposed design also reduces a recirculating flow at the exit of the last seal strip. Based on these results, an analysis of erosion against velocity demonstrates that the redesigned rotor disc proposed here leads to the duplication of the time period used at present between maintenance repairs.     

A study on rotational augmentation using CFD analysis of flow in the inboard region of the MEXICO rotor blades

This work presents an analysis of data from existing as well as new full‐rotor computational fluid dynamics computations on the MEXICO rotor, with focus on the flow around the inboard parts of the blades. The boundary layer separation characteristics on the airfoil sections in the inboard parts of the rotor are analysed using the pressure and the skin friction data at a range of angles of attack. These data are used to gain insight on the relative behaviour of separated boundary layers in 3D flow compared with 2D flow. It has been found that separation on airfoils in rotating flows is different from that in 2D flows in two respects: (i) there is a chord‐wise postponement (or delay) of the separation point, and (ii) the angle of attack at which separation is initiated is higher in 3D compared with 2D. Comments are made on the mechanism of stall delay, and the main differences between the skin friction and pressure distribution behaviours in 2D and 3D rotating flows are highlighted. Copyright © 2014 John Wiley & Sons, Ltd.     

Estimation of power performances and flow characteristics for a Savonius rotor by vortex particle method

This study investigates the implementation of the vortex particle method (VPM) with the goal of efficiently and accurately estimating the power performances and flow characteristics for a Savonius rotor. The accuracy and efficiency of simulation methods are critical for the reliable design of Savonius rotors. Among various approaches, VPM is chosen because it can be flexibly incorporated with self-correction techniques, and the distribution of bound vortex particles can effectively represent complex geometries. In this work, a double-trailing-edge-wake-modeling vortex particle method (DTVPM) is presented to extend the working range of VPM for dealing with large rotating amplitudes and high tip speed ratios (TSRs). DTVPM addresses asymmetrical torque predictions for a Savonius rotor without gap width. However, DTVPM performs poorly at high TSRs due to the absence of viscous effects near the surface. To capture complex wake structures, such as reverse flow structures, the viscous correction for tip vortices is suggested. The current research focuses on the implementation and validation of DTVPM for predicting torque coefficients and wake patterns, as well as comparisons to OpenFOAM results. Two-dimensional and incompressible flow is estimated at $\lambda$ = 0.2–1.2. For the studied cases, a maximum power coefficient is obtained at $\lambda \approx 0.8$, consistent with published experimental data. In addition, the process of trailing-edge vortices generation and detachment is captured by DTVPM. The comparison results between OpenFOAM and DTVPM show that DTVPM allows to efficiently simulate a Savonius rotor without any empirical parameters. DTVPM will help to improve existing engineering models for wind energy fields.