New dynamic‐inflow engineering models based on linear and nonlinear actuator disc vortex models

Two new engineering models are presented for the aerodynamic induction of a wind turbine under dynamic thrust. The models are developed using the differential form of Duhamel integrals of indicial responses of actuator disc type vortex models. The time constants of the indicial functions are obtained by the indicial responses of a linear and a nonlinear actuator disc model. The new dynamic‐inflow engineering models are verified against the results of a Computational Fluid Dynamics (CFD) model and compared against the dynamic‐inflow engineering models of Pitt‐Peters, Øye, and Energy Research Center of the Netherlands (ECN), for several load cases. Comparisons of all models show that two time constants are necessary to predict the dynamic induction. The amplitude and phase delay of the velocity distribution shows a strong radial dependency. Verifying the models against results from the CFD model shows that the model based on the linear actuator disc vortex model predicts a similar performance as the Øye model. The model based on the nonlinear actuator disc vortex model predicts the dynamic induction better than the other models concerning both phase delay and amplitude, especially at high load.     

A new dynamic inflow model for vertical‐axis wind turbines

This paper presents a new dynamic inflow model for vertical‐axis wind turbines (VAWTs). The model uses the principle of Duhamel's integral. The indicial function of the inflow‐ and crossflow‐induction required to apply Duhamel's integral is represented by an exponential function depending on the thrust coefficient and the azimuthal position. The parameters of this approximation are calibrated using a free wake vortex model. The model is compared with the results of a vortex model and higher fidelity computational fluid dynamic (CFD) simulations for the response of an actuator cylinder to a step input of the thrust and to a cyclic thrust. It is found that the discrepancies of the dynamic inflow model increase with increasing reduced frequency and baseline thrust. However, the deviations remain small. Analysing the application of a finite‐bladed floating VAWT with non‐uniform loading and validating it against actuator line CFD results that intrinsically include dynamic inflow shows that the new dynamic inflow model significantly outperforms the Larsen and Madsen model (which is the current standard in fully coupled VAWT models) and enhances the modelling of VAWTs.     

Streamwise Vortex Interaction with a Horseshoe Vortex

How control in turbomachinery is very difficult because of the complexity of its fully 3-D flow structure. The authors propose to introduce streamwise vortices into the control of internal flows. A simple configuration of vortices was investigated in order to better understand the flow control methods by means of streamwise vortices. The research presented here concerns streamwise vortex interaction with a horseshoe vortex. The effects of such an interaction are significantly dependent on the relative location of the streamwise vortex in respect to the leading edge of the profile. The streamwise vortex is induced by an air jet. The horseshoe vortex is generated by the leading edge of a symmetric profile. Such a configuration gives possibility to investigate the interaction of these two vortices alone. The presented analysis is based on numerical simulations by means of N-S compressible solver with a two-equation turbulence model.     

Helical vortex theory and blade element analysis of multi-bladed windmills

Multi-bladed windmills usually pump water for agriculture and domestic consumption, often in remote locations. Although they have been around for over 150 years, their aerodynamic performance is still poorly understood. This paper describes the use of helical vortex theory (HVT) and blade element momentum (BEM) analysis to predict windmill thrust, torque, and extracted power. We emphasize the unusual features of windmills: low Reynolds numbers and tip speed ratios and high solidity, all related to the generation of high torque at low wind speeds. Wind tunnel tests on a model rotor with 3, 6, 12, and 24 circular-arc, constant-chord blades determined the thrust, torque, and extracted power over a range of tip speed ratio that extended to runaway. For comparison, BEM was implemented with a correction for finite blade number derived from HVT, as well as the classical Prandtl tip loss factor. The HVT correction predicted the rotor power coefficient to within 3% of the test data on the average. At low tip speed ratios and smaller blade numbers, HVT was consistently more accurate than the Prandtl factor. At all blade numbers, the measured rotor torque exceeded the BEM predictions at the lowest tip speed ratios indicating stall delay which became more important (and more beneficial for windmill performance) as the blade number increased. The Prandtl formulation predicted the thrust to within a mean accuracy of 13% and was more accurate than the HVT method.     

涡流管非稳态旋流流场数值模拟研究

旋流主导着涡流管的内部流动,在有旋流的设备当中,高强度旋流由于涡旋破碎诱导产生的位于中央回流面附近的进动涡核被认为是旋流中的一种拟序结构,可以在一个峰值频率下偏离管道中心并绕着轴线做周期性运动,这种流动结构的产生对旋流本身产生了极大的影响。采用非定常求解模式计算三维涡流管内的内部流场,雷诺应力模型用于封闭Navier-Stokes输运方程,在FLUENT 15.0中数值模拟计算涡流管的内部旋流。结果显示了涡流管瞬态旋流速度场中的周期性振荡,以及非对称大尺度涡结构。     

An actuator disk method with tip‐loss correction based on local effective upstream velocities

This work aims at assessing the performance of a tip‐loss correction for advanced actuator disk (AD) methods coupled to large eddy simulation and making this correction possible in a wind farm configuration. The classical Glauert tip‐loss factor, commonly used in the blade element momentum method, is added here to correct the tip and the root induced velocities at the rotor. However, it requires a reference upstream velocity, which is problematic to define in complex flows, such as in wind farms. A methodology is proposed here to infer an effective upstream velocity local to each disk element, based on the one‐dimensional momentum theory and using only the local data at the rotor. This estimation is verified through a set of simulations, leading to good results in spite of the crude assumptions of the one‐dimensional momentum theory. This AD supplemented with the tip‐loss correction is compared with a high fidelity vortex particle‐mesh method, through the simulations in uniform wind of a constant circulation wind turbine and of a more realistic machine, the NREL‐5MW rotor. The results show that the AD behavior is clearly improved by the addition of a tip‐loss factor and the potential errors on the effective upstream velocity estimation have a moderate impact on the tip‐loss correction.     

Stochastic modeling of lift and drag dynamics under turbulent wind inflow conditions

We present a new approach to model the complex dynamics of aerodynamic forces on an airfoil in turbulent inflow conditions. Our ansatz is based on stochastic differential equations and aims at replacing traditional look‐up table methods used in wind turbine simulation systems by the effective response dynamics of lift and drag forces. The parameters of the model are derived directly from empirical data. Measurements were taken in the closed loop wind tunnel of the University of Oldenburg for an airfoil FX 79‐W‐151A. The turbulent inflow was generated using a fractal square grid as it is possible to generate in this way wind speed fluctuations with similar statistics as observed in nature. Forces were measured using two strain gauge force sensors at two end points of the vertically installed airfoil. The modeling is performed by applying a stochastic approach on the measured data. By estimating the first two Kramers–Moyal coefficients, a first‐order stochastic differential equation called the Langevin equation is obtained. The stochastic model achieved through this approach is extended to account for oscillation effects contained in lift and drag dynamics that probably stem from unsteady aerodynamic effects. The results are optimized by applying a χ² test on the probability density functions (PDFs) of model and measurements. With the knowledge of the Langevin equation, synthetic time series are generated. Their stationary PDFs as well as conditional PDFs show good agreement with the actual measurements. A comparison of classical averaging and the stochastic approach shows that stochastic analysis achieves additional insight into the local dynamics of lift and drag forces. Copyright © 2014 John Wiley & Sons, Ltd.     

Verifying the Blade Element Momentum Method in unsteady,radially varied,axisymmetric loading using a vortex ring model

Although the Blade Element Momentum method has been derived for the steady conditions, it is used for unsteady conditions by using corrections of engineering dynamic inflow models. Its applicability in these cases is not yet fully verified. In this paper, the validity of the assumptions of quasi‐steady state and annuli independence of the blade element momentum theory for unsteady, radially varied, axi‐symmetric load cases is investigated. Firstly, a free wake model that combines a vortex ring model with a semi‐infinite cylindrical vortex tube was developed and applied to an actuator disc in three load cases: (i) steady uniform and radially varied, (ii) two types of unsteady uniform load and (iii) unsteady radially varied load. Results from the three cases were compared with Momentum Theory and also with two widely used engineering dynamic inflow models—the Pitt‐Peters and the Øye for the unsteady load cases. For unsteady load, the free wake vortex ring model predicts different hysteresis loops of the velocity at the disc or local annuli, and different aerodynamic work from the engineering dynamic inflow models. Given that the free wake vortex ring model is more physically representative, the results indicate that the engineering dynamic inflow models should be improved for unsteady loaded rotor, especially for radially varied unsteady loads. © 2016 The Authors. Wind Energy Published by John Wiley & Sons, Ltd.     

通道内设置涡发生器时的强化传热研究现状与展望

随着强化传热技术的研究发展，各种形式的涡发生器的强化传热效果日益受到国内外的重视。文章比较全面地介绍了近年来国内外关于通道内布置各类涡发生器时的强化传热研究状况，并提出了有待进一步开展的研究内容。     

Characteristics of transient vortices in the boundary layer on a rotating disk under orbital motion

The objective of this study is to experimentally examine the characteristics of transient vortices in the boundary layer on a disk undergoing both rotation and orbital motion. The velocity fluctuations on a rotating, orbiting disk （disk radius equal to orbital radius） are measured by the hot-wire method, and the effects of orbital motion on the transient vortices in the boundary layer are examined. When the ratio of the orbital speed to the speed of rotation is i-0.025, the interval of transient vortices depends on only the orbital radius, regardless of the directions of rota- tion and orbital motion. The rate of low-frequency disturbances increases as the orbital speed increases, and the vortices induced by these low-frequency disturbances travel over the disk and then develop in the region of in- creased velocity. Consequently, no vortices generated on a rotating disk under orbital motion are stationary rela- tive to the disk.     

Investigation of flow dynamics and decrease of vortex noise inside volute of centrifugal fans

The characteristics of three-dimension flow dynamics inside the volute of a G4-73No.8D centrifugal fan was simulated numerically using a computational fluid dynamics(CFD) technique. The generation, evolution, and noise of the vortex were investigated when cylinder-shaped and cone-cylinder-shaped anti-vortex rings were added separately. Numerical results showed that large-scale vortices were broken effectively and the flow fields inside the fan were more uniform with the two anti-vortex rings installed. Experimental results indicated A-sound level and spectrum noise of the refitted fan decreased and the two anti-vortex rings were effective in decreasing vortex noise. The cone-cylinder-shaped anti-vortex ring was more effective than the cylinder-shaped one in breaking large-scale vortexes and decreasing vortex noise. __________ Translated from Proceedings of the CSEE, 2006, 26(17): 117–121 [译自: 中国电机工程学报]     

A 2-D DNS investigation of extinction and reignition dynamics in nonpremixed flame–vortex interactions

Two-dimensional (2-D) DNS investigations of extinction and reignition dynamics during interactions of laminar nonpremixed flames with counterrotating vortex pairs are performed. The length and velocity scales chosen for the vortices are representative of those in the near fields of high-Reynolds-number jets such as those occurring in Diesel engines. The governing equations are solved with sixth-order spatial discretization and fourth-order time integration. Chemistry is modeled as an irreversible single-step reaction. Local extinction along the symmetry axis, followed by reignition, is observed. The extinction is characterized by strong unsteady effects, which are captured well by 1-D transient diffusion flamelet libraries, provided the time-history of the instantaneous scalar dissipation rate is taken into account. On the other hand, reignition is essentially a 2-D phenomenon involving flame–flame interactions, which are favored for smaller vortices and increasing flame curvature. The effects of unsteadiness and curvature on extinction and reignition are carefully assessed through parametric studies involving a range of vortex and flame characteristics. The interaction outcomes are summarized on Reynolds–Damköhler number (Re–Da) diagrams, which show the combined effects of unsteadiness and curvature on extinction and reignition. The implications of the observed interaction outcomes for turbulent combustion modeling in the near fields of jet diffusion flames are discussed.     

Overcoming fundamental limitations of wind turbine individual blade pitch control with inflow sensors

Individual pitch control (IPC) provides an important means of attenuating harmful fatigue and extreme loads upon the load bearing structures of a wind turbine. Conventional IPC architectures determine the additional pitch demand signals required for load mitigation in response to measurements of the flap‐wise blade‐root bending moments. However, the performance of such architectures is fundamentally limited by bandwidth constraints imposed by the blade dynamics. Seeking to overcome this problem, we present a simple solution based upon a local blade inflow measurement on each blade. Importantly, this extra measurement enables the implementation of an additional cascaded feedback controller that overcomes the existing IPC performance limitation and hence yields significantly improved load reductions. Numerical demonstration upon a high‐fidelity and nonlinear wind turbine model reveals (1) 60% reduction in the amplitude of the dominant 1P fatigue loads and (2) 59% reduction in the amplitude of extreme wind shear‐induced blade loads, compared with a conventional IPC controller with the same robust stability margin. This paper therefore represents a significant alternative to wind turbine IPC load mitigation as compared with light detection and ranging‐based feedforward control approaches.     

内置扰流器驻涡燃烧室燃烧流动分析

为了研究内置导流片与扰流板等扰流器驻涡燃烧室的燃烧流动性能,对不同导流片结构参数下的燃烧室总压损失、燃烧效率、速度温度分布及污染物排放进行了数值分析.结果 表明:内置导流片与扰流板的驻涡燃烧室性能更加优于仅存在导流片时的性能,会进一步增强凹腔内的燃气掺混、提高燃烧效率、改善出口温度分布、降低NO排放.当导流片伸入凹腔的...     

纵向涡发生器强化传热管的实验研究

介绍了一种高效强化传热管,沿传热管内壁轴向均匀排布三列成对的纵向涡发生器,在常壁温条件下进行加热空气在管内流动的冷却实验,研究强化传热管的传热和阻力特性。结果表明,在过渡流区管内置纵向涡发生器的强化传热大大增强,Nu增大为光管的2.02.3倍,阻力损失也相应有所增加,提出一种比较优化的发生器的形状设计,探讨了传热和阻力随设置间距变化的规律。     

Generalized thermo-electro-elasticity of a piezoelectric disk using Lord-Shulman theory

Abstract

Current investigation deals with the generalized thermoelastic response of a finite hollow disk made of a piezoelectric material. The constitutive equations of the piezoelectric media are reduced to a two dimensional plane-stress state. To capture the finite speed of temperature wave, the single relaxation time theory of Lord and Shulman is used. Three coupled differential equations in terms of radial displacement, electric potential, and temperature change are obtained. These equations are written in a dimensionless presentation. With the aid of the differential quadrature method (DQM) a time-dependent algebraic system of equations is extracted. The Newmark time marching scheme is applied to trace the temporal evolution of temperature change, electric potential, radial displacement, stresses, and electric displacement. Numerical results demonstrate that radial displacement and temperature waves propagate with finite speed while the electric potential propagates with infinite speed.     

A general momentum theory applied to an energy‐extracting actuator disc

A general momentum theory for an energy‐extracting actuator disc modelling a rotor with a multiplicity of blades having radially uniform circulation is presented that includes the effects of wake rotation and expansion. A parallel theory directed at the propeller has been published elsewhere, but not one intended for the wind turbine. The rotation of the wake is shown to be accompanied by a fall in static pressure that is additional to that which occurs across the actuator disc and accounts for the energy extraction from the wind. Energy extraction is recognized in the fully developed wake by the flow regaining the static pressure of the undisturbed wind at the expense of the kinetic energy in the wake. Because the wake is still rotating in the fully developed wake, the additional fall in static pressure appears there also and so does not augment the energy extraction. However, the additional fall in pressure would cause a discontinuity in pressure across the fully developed wake but is prevented by a further slowing down of the wake. The additional slowing down extracts a little more energy from the flow than that predicted by the simple momentum theory, which does not include wake rotation. The overall effect of wake rotation on energy extraction is very small for wind turbines operating at high tip speed ratios but can significantly increase the predicted power output for turbines operating at low tip speed ratios. Copyright © 2004 John Wiley & Sons, Ltd.     

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.