Numerical analysis of the effect of boundary layer thickness on vortex structures and heat transfer in the wake behind a hill

This study presents a three‐dimensional numerical analysis of the effect of boundary layer thickness on vortex structures and heat transfer behind a hill mounted in a laminar boundary layer. When the thickness of the velocity boundary layer is comparable to the hill height, a hairpin vortex is formed symmetrically to the center of the spanwise direction in the wake. A secondary vortex is formed between the legs, and horn‐shaped secondary vortices appear under the concave parts of the hairpin vortex. When the boundary layer thickness increases, the legs and horn‐shaped secondary vortices move toward the center of the spanwise direction, and thus heat transport and heat transfer increase there. At this time, high‐turbulence areas generated locally move toward the center of the spanwise direction with an increase in the boundary layer thickness. With a further increase in the boundary layer thickness, steady streamwise vortices are formed downstream of the hill, but the heat transfer decreases. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20261     

Geometrical characterization of stall cells on rectangular wings

The onset of stall cells (SCs) is experimentally investigated on a flattop loaded 18% thick airfoil optimized for use on wind turbine blades, exhibiting trailing edge separation. SCs are dynamic coherent vortical structures that appear on wings under separated flow conditions. Although SCs have been known for long, neither are their characteristics completely documented nor their generating mechanisms fully understood. The present investigation aims at providing additional information on the geometric characteristics in terms of width, length and occupied area. The relevant data are presented as functions of Reynolds (Re) number, angle of attack and aspect ratio (AR) of the model. In the tests reported, the dynamic character of SCs is suppressed by imposing a localized flow disturbance. For the specific airfoil and for the Re and AR range tested, it is found that: the angle of attack at which SCs are initially formed decreases linearly with Re number and independently of the AR; unlike two‐dimensional separation, their chordwise length increases with Re; the SC area relative to the wing planform area (defined as the relative SC area) grows asymptotically with angle of attack and Re number reaching an upper bound, which is independent of the AR; at intermediate angles of attack, the SC relative area is higher for the lower AR wing; for a fixed increment in Re number, the growth of the SC relative area is independent of the initial Re number; at lower angles of attack, the actual SC area is independent of the wing span. Copyright © 2013 John Wiley & Sons, Ltd.     

Large eddy simulation of flow over square cylinder arrays in an octagonal configuration at subcritical Reynolds numbers

In this study, fluid flow over an array of eight, 0.029 m × 0.029 m, square cross‐section cylinders in an octagonal configuration is studied numerically. The mean force coefficients (drag and lift) and the vortex formation characteristics of the array are calculated numerically by utilizing a three‐dimensional large eddy simulation mathematical model for turbulence. The numerical simulation is performed with commercial software ANSYS Fluent 19R1. To investigate the parametric influences, three spacings between the cylinders (0.07, 0.14, and 0.2 m), two array attack angles (0° and 15°), and two Reynolds numbers (4060 and 45 800) are considered. The results comprise flow patterns and force coefficients' variations with Reynolds numbers. The lift force of the downstream cylinder reaches its maximum at α = 15°, and the drag force of the upstream cylinders finds its peak at α = 0°. It is observed through velocity and viscosity contour plots that vortex formation length near the cylinder increases at higher Reynolds number. Velocity vector plots are also presented to show fluid flow behavior near the cylinder. Furthermore, the predicted mean forces on the cylinders are slightly different for different Reynolds numbers, spacings, and angles of attack.     

Analysis on the mechanism of evolutionary process of counter-rotating vortex pair in film cooling based on hybrid thermal lattice Boltzmann method

Massively parallel simulation applying multiple graphic processing units (multi-GPUs) is carried out to perform a deep going investigation on the counter-rotating vortex pair (CVP) in single-jet film cooling based on hybrid thermal lattice Boltzmann method (HTLBM) and large eddy simulation (LES). The mechanism of evolutionary process of CVP and its influence on the Reynolds shear stress and cooling performance are studied in detail. In the simulation, the blowing ratio of coolant jet is kept to BR = 0.5 and the inclined angle is α = 30^°. The Reynolds number based on the crossflow velocity and diameter of the jet hole is Re = 4000. The secondary anti-kidney vortices, tertiary kidney vortices and quaternary anti-kidney vortices are captured, which increase the spanwise coolant-film coverage on the surface of the bottom wall. The size of the primary CVP significantly influences the distribution of Reynolds shear stress R_uv and R_uw. The vortex strength of the primary CVP and the characteristics of minor counter-rotating vortices mainly impact on the streamwise and spanwise distribution of film cooling effectiveness, respectively.     

Numerical simulation of asymmetrical flow and heat transfer behind a hill in shear flows

Three‐dimensional numerical simulations of asymmetrical flows and heat transfer around a hill in shear flows were performed. When shear velocity distributions are introduced at the inlet, a vortex pair is formed asymmetrically to the spanwise direction behind the hill. Further, an asymmetrical hairpin vortex is periodically generated downstream. The leg of the asymmetrical hairpin vortex on the high‐speed side collapses first. Further downstream, the asymmetrical hairpin vortex breaks down earlier than the symmetrical hairpin vortex, and streamwise vortices appear on the high‐speed side. These streamwise vortices increase the heat transfer downstream. In contrast, no hairpin vortex appears in the case of a strong shear velocity distribution, but instead a streamwise vortex appears. The heat transfer decreases downstream since the turbulence generated by streamwise vortices is weak. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20223     

Numerical simulation of vortex structures and heat transfer behind a hill in a laminar boundary layer

The present study examines a three‐dimensional numerical simulation of vortex structures and heat transfer behind a hill mounted in a laminar boundary layer. A vortex pair is formed symmetrically in the separation bubble behind the hill, and a hairpin vortex is periodically shed in the wake. The hairpin vortex moves downstream with time, and the gradient of the head of the hairpin vortex increases. Further downstream, the hairpin vortex is deformed to an Ω‐shaped structure. In the growth process of the hairpin vortex, horn‐shaped secondary vortices grow near the wall. The dissipation rate of the temperature fluctuation around the hairpin vortex increases because the heated fluid near the wall is removed to the free stream by Q2 ejection. Heat transfer increases due to the legs of the hairpin vortex and secondary vortices. These vortices generate high turbulence in the flow field and also contribute to an increase in Reynolds shear stress and turbulent heat flux. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(7): 398–411, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20217     

Heat transfer enhancement by using a rectangular wing vortex generator on the triangular shaped fins of a plate‐fin heat exchanger

The present numerical analysis pertains to the heat transfer enhancement in a plate‐fin heat exchanger employing triangular shaped fins with a rectangular wing vortex generator on its slant surfaces. The study has been carried out for three different angles of attack of the wing, i.e., 15°, 20° and 26°. The aspect ratio of the wing is not varied with its angle of attack. The flow considered herein is laminar, incompressible, and viscous with the Reynolds number not exceeding 200. The pressure and the velocity components are obtained by solving the continuity and the Navier– Stokes equations by the Marker and Cell method. The present analysis reveals that the use of a rectangular wing vortex generator at an attack angle of 26° results in about a 35% increase in the combined spanwise average Nusselt number as compared to the plate‐triangular fin heat exchanger without any vortex generator. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20285     

Analysis of vortex‐induced and stall‐induced vibrations at standstill conditions using a free wake aerodynamic code

Vortex‐induced and stall‐induced vibrations of a 2D elastically mounted airfoil at high angles of attack in the vicinity of 90° are investigated using a vortex type model. Such conditions are encountered in parked or idling operation at extreme yaw angles provoked by control system failures. At very high angles of attack, massive flow separation takes place over the entire blade span, and vortex shedding evolves downstream of the blade giving rise to periodically varying loads at frequencies corresponding to the Strouhal number of the vortices shed in the wake. As a result, vortex‐induced vibrations may occur when the shedding frequency matches the natural frequency of the blade. A vortex type model formulated on the basis of the ‘double wake’ concept is employed for the modelling of the stalled flow past a 2D airfoil. By tuning the core size of the vortex particles in the wake, the model predictions are successfully validated against averaged 2D measurements on a DU‐96‐W‐180 airfoil at high angles of attack. In order to assess the energy fed to the airfoil by the aerodynamic loads, the behaviour under imposed sinusoidal edgewise motions is analysed for various oscillation frequencies and amplitudes. Moreover, stall‐induced and vortex‐induced vibrations of an elastically mounted airfoil section are assessed. The vortex model predicts higher aeroelastic damping as compared with that obtained using steady‐state aerodynamics. Excessive combined vortex‐induced and stall‐induced edgewise vibrations are obtained beyond the wind speed of 30 m s^?1. Copyright © 2014 John Wiley & Sons, Ltd.     

Near wake flow analysis of a vertical axis wind turbine by stereoscopic particle image velocimetry

The development of the near wake of a vertical axis wind turbine is investigated by stereoscopic particle image velocimetry. The experiments are conducted in an open-jet wind tunnel on an H-shaped rotor, operated at a tip speed ratio of 4.5 and at an average chord-based Reynolds number of 1.7 × 10⁵. Phase-locked measurements are acquired at the turbine mid span in order to study the horizontal wake dynamics at the symmetry plane. Results show the evolution of the vorticity shed by the blade, how it organizes in large scale vortical structures at the edges of the wake and the resulting asymmetric induction field in the wake. The evolution of the blade tip vortices and the 3D wake geometry are detailed by a second set of measurements acquired at several vertical planes aligned with the free stream. The dynamics of the system of tip vortices, their vertical motion and interactions are discussed and related to the geometry and the recovery of the wind turbine wake. The experimental data are made publicly available for research purposes.     

Computational fluid dynamics simulation of the aerodynamics of a high solidity,small‐scale vertical axis wind turbine

A computational fluid dynamics simulation was performed for a small‐scale, high solidity (σ = 0.48) H‐type Darrieus vertical axis wind turbine. Two‐dimensional unsteady Reynolds‐averaged Navier–Stokes equations were solved for the turbine numerical model, which has a large stationary domain and smaller rotating subdomain connected by a sliding mesh interface. The simulation results were first validated against steady‐state airfoil data. The model was then used to solve for three rotating blades with constant ambient flow velocity (Re = 360,000) over numerous blade speed ratios. The high solidity and the associated low blade speed ratio and rotational speed of the turbine result in complex flow–blade interaction mechanisms. These include dynamic stall resulting in vortex shedding, vortex impingement on the source blade and significant flow momentum extraction causing reduced power production from the downstream blade pass. Copyright © 2011 John Wiley & Sons, Ltd.     

大尺度展向波形圆柱绕流流场结构的数值研究

针对大尺度展向波形圆柱绕流的减阻特性,通过大涡模拟（LES）研究波形振幅对圆柱体绕流流场结构的影响,获得波形圆柱体绕流气动性能曲线、尾迹时均流速分布和非定常涡量场分布,最后与直圆柱绕流的流场结构进行对比分析。结果表明,波形圆柱绕流的平均阻力系数小于直圆柱体绕流,流向涡的形成改变了圆柱近尾迹区的流场结构,因此,波形圆柱体尾迹涡系表现得更为紧凑,尾迹涡流得到拉伸与破裂。在亚临界雷诺数为3000时,最大阻力系数减少18.3%,最优振幅比为0.152;且波形圆柱体的升力波动大大减少,甚至得到抑制。由于波形表面会形成更稳定的三维自由剪切层,这样的自由剪切层在下游位置卷起漩涡,大大地改变了圆柱周围的流场结构。研究表明振幅比在确定波形圆柱后面的三维涡旋结构中起着至关重要的作用,并对升力波动和流动阻力的降低有着显著的影响。     

Vortex‐induced vibrations on a modern wind turbine blade

This article investigates the aero‐elastic response of the DTU 10‐MW RWT blade in deep stall conditions with angles of attack in the vicinity of 90 degrees. The simulations were conducted with the high‐fidelity fluid–structure interaction simulation tool HAWC2CFD employing the multi‐body‐based structural model of HAWC2 and the incompressible computational fluid dynamics solver EllipSys3D. The study utilizes detached eddy simulation computations and considers the three‐dimensional blade geometry including blade twist and taper. A preliminary frequency analysis of the load variations on a stiff blade showed that an inclined inflow with a velocity component along the blade axis can trigger a spanwise correlated vortex shedding over large parts of the blade. Moderate wind speeds were sufficient to generate vortex shedding with frequencies close to the first edgewise eigenfrequency of the blade. Aero‐elastic computations of the elastic blade confirmed the findings of the frequency analysis. Inflow conditions with inclination angles between Ψ = 20° and Ψ = 55° and relatively low to moderate wind speeds between V = 16 and V = 26ms^?1 were sufficient to trigger severe edgewise blade vibrations with blade tip amplitudes of several metres. The investigated inflow conditions are considered realistic and might occur when the wind turbine is idling or standing still and the yaw system is unable to align the wind turbine with the incoming wind. Copyright © 2016 John Wiley & Sons, Ltd.     

低雷诺数下不同顶角三棱柱体绕流受力和尾涡脱落机制

为研究三棱柱体绕流特性,采用直接数值模拟方法,对雷诺数为100时顶角为15°~165°的三棱柱的二维绕流问题进行了数值模拟,并与经典的圆柱绕流进行对比分析。结果表明,随着顶角度数的增大,三棱柱体受到的时均阻力不断增大,而升力均方值先增大后减小,在顶角为60°时达到最大值(0.31);随着顶角度数的增大,尾涡强度逐渐增大,泄涡频率先增大后减小,在顶角为60°时,泄涡频率最大;前尾涡脱落产生的中心点与鞍点随新尾涡的产生依次消失,而新的尾涡的中心点与鞍点同时逐渐形成。     

An experimental study on the effects of winglets on the tip vortex interaction in the near wake of a model wind turbine

An experimental study of the near wake up to four rotor diameters behind a model wind turbine rotor with two different wing tip configurations is performed. A straight‐cut wing tip and a downstream‐facing winglet shape are compared on the same two‐bladed rotor operated at its design tip speed ratio. Phase‐averaged measurements of the velocity vector are synchronized with the rotor position, visualizing the downstream location of tip vortex interaction for the two blade tip configurations. The mean streamwise velocity is found not to be strongly affected by the presence of winglet tip extensions, suggesting an insignificant effect of winglets on the time‐averaged inflow conditions of a possible downstream wind turbine. An analysis of the phase‐averaged vorticity, however, reveals a significantly earlier tip vortex interaction and breakup for the wingletted rotor. In contradistinction, the tip vortices formed behind the reference configuration are assessed to be more stable and start merging into larger turbulent structures significantly further downstream. These results indicate that an optimized winglet design can not only contribute to a higher energy extraction in a rotor's tip region but also can positively affect the wake's mean kinetic energy recovery by stimulating a faster tip vortex interaction.     

A spatially advancing turbulent flow and heat transfer in a curved channel

Direct numerical simulation was performed for a spatially advancing turbulent flow and heat transfer in a two‐dimensional curved channel, where one wall was heated to a constant temperature and the other wall was cooled to a different constant temperature. In the simulation, fully developed flow and temperature from the straight‐channel driver was passed through the inlet of the curved‐channel domain. The frictional Reynolds number was assigned 150, and the Prandtl number was given 0.71. Since the flow field was examined in the previous paper, the thermal features are mainly targeted in this paper. The turbulent heat flux showed trends consistent with a growing process of large‐scale vortices. In the curved part, the wall‐normal component of the turbulent heat flux was twice as large as the counterpart in the straight part, suggesting active heat transport of large‐scale vortices. In the inner side of the same section, temperature fluctuation was abnormally large compared with the modest fluctuation of the wall‐normal velocity. This was caused by the combined effect of the large‐scale motion of the vortices and the wide variation of the mean temperature; in such a temperature distribution, large‐scale ejection of the hot fluid near the outer wall, which is transported into the near inner‐wall region, should have a large impact on the thermal boundary layer near the inner wall. Wave number decomposition was conducted for various statistics, which showed that the contribution of the large‐scale vortex to the total turbulent heat flux normal to the wall reached roughly 80% inside the channel 135^° downstream from the curved‐channel inlet. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20275     

An experimental and computational assessment of blockage effects on wind turbine wake development

An experiment was conducted to evaluate the initial wake expansion in scaled wind turbine tests as a means to guide future wake interference studies. Five scaled wind turbine rotors with different diameters were designed for testing in a closed‐loop water channel to evaluate the effects of blockage on the initial wake expansion behind a wind turbine. The initial wake expansion was assessed by using quantitative dye visualization to identify the propagation of tip vortices downstream of the rotor. The thrust coefficient developed by the scaled models was recorded using a six‐component balance and was correlated to the downstream wake expansion. The rotors used in the experiment were operated at a tip speed ratio of 6, a Reynolds number based on the tip speed and tip chord of approximately 23,000 and resulted in blockage values that ranged from 6% to 25%. Dye visualization indicated that the initial wake expansion downstream of a rotor was narrowed and that tip vortex pairing behaviour was modified because of increasing blockage. Blockage effects were significant and resulted in a wake that was more than 50% narrower when blockage was 25% compared with the observed expansion with 10% blockage. A computational simulation was conducted with the Generalized Unsteady Vortex Particle (GENUVP) discrete vortex method code using the rotor in freestream conditions and was compared with the experiments. The magnitude of the wake expansion in the freestream computations was similar to the wake expansion in the experiment when blockage was less than 10%. Copyright © 2013 John Wiley & Sons, Ltd.     

Power‐law flow and heat transfer over an inclined square bluff body: effect of blockage ratio

Flow and heat transfer of non‐Newtonian power‐law fluids over an inclined square cylinder placed inside a channel are studied numerically at low Reynolds numbers. In particular, calculations are carried out for Reynolds number (Re) = 1–40; power‐law index (n) = 0.4–1 and blockage ratio (β) = 12.5–50% at a Prandtl number (Pr) = 50. An increase in blockage ratio results in an increase in the total drag coefficient and decrease in the wake length. The Strouhal number and the root mean square value of the lift coefficient increase with the increasing Reynolds number for the fixed values of blockage ratio and power‐law index. The average Nusselt number increases with power‐law index and/or blockage ratio. The maximum enhancement in heat transfer is approximately 49, 41, and 35% for the values of blockages of 50, 25, and 12.5%, respectively, as compared to the corresponding Newtonian value. The average Nusselt number for the inclined square cylinder (at α = 45^°) is always greater than the average Nusselt number for the regular square cylinder (at α = 0). Finally, simple expressions of drag and Nusselt number have been established for the above range of settings. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res 43(2): 167‐196, 2014; Published online 20 June 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21071     

Performance and wake of a Savonius vertical‐axis wind turbine under different incoming conditions

In this study, the performance, drag, and horizontal midplane wake characteristics of a vertical‐axis Savonius wind turbine are investigated experimentally. The turbine is drag driven and has a helical configuration, with the top rotated 180° relative to the bottom. Both performance and wake measurements were conducted in four different inflow conditions, using Reynolds numbers of Re_D≈1.6×10⁵ and Re_D≈2.7×10⁵ and turbulence intensities of 0.6% and 5.7%. The efficiency of the turbine was found to be highly dependent on the Reynolds number of the incoming flow. In the high Reynolds number flow case, the efficiency was shown to be considerably higher, compared with the lower Reynolds number case. Increasing the incoming turbulence intensity was found to mitigate the Reynolds number effects. The drag of the turbine was shown to be independent of the turbine's rotational speed over the range tested, and it was slightly lower when the inflow turbulence was increased. The wake was captured for the described inflow conditions in both optimal and suboptimal operating conditions by varying the rotational speed of the turbine. The wake was found to be asymmetrical and deflected to the side where the blade moves opposite to the wind. The largest region of high turbulent kinetic energy was on the side where the blade is moving in the same direction as the wind. Based on the findings from the wake measurements, some recommendations on where to place supplementary turbines are made.     

Flow characterization in the near‐wake region of a horizontal axis wind turbine

An experimental study is conducted to investigate the flow dynamics within the near‐wake region of a horizontal axis wind turbine using particle image velocimetry (PIV). Measurements were performed in the horizontal plane in a row of four radially distributed measurement windows (tiles), which are then patched together to obtain larger measurement field. The mean and turbulent components of the flow field were measured at various blade phase angles. The mean velocity and turbulence characteristics show high dependency on the blade phase angle in the near‐wake region closer to the blade tip and become phase independent further downstream at a distance of about one rotor diameter. In the near‐wake region, both the mean and turbulent characteristics show a systemic variation with the phase angle in the blade tip region, where the highest levels of turbulence are observed. The streamlines of the instantaneous velocity field at a given phase allowed to track a tip vortex which showed wandering trend. The tip vortices are mostly formed at r/R > 1, which indicates the wake expansion. Results also show the gradual movement of the vortex region in the axial direction, which can be attributed to the dynamics of the helical tip vortices which after being generated from the tip, rotate with respect to the blade and move in the axial direction because of the axial momentum of the flow. The axial velocity deficit was compared with other laboratory and field measurements. The comparison shows qualitative similarity. Copyright © 2015 John Wiley & Sons, Ltd.     

Numerical investigation of rotational augmentation for S822 wind turbine airfoil

Direct numerical simulations were carried out for an S822 wind turbine blade section at a chord Reynolds number of Re = 100, 000 and an angle of attack of α = 5°. Results for a stationary non‐rotating blade section compare favorably with wind tunnel data by the University of Illinois at Urbana‐Champaign and XFoil predictions. By adding volume forcing terms to the right‐hand side of the Navier–Stokes equations, the Coriolis and centrifugal accelerations resulting from blade rotation are modeled in the blade section simulations. Blade rotation is shown to delay separation especially near the hub, resulting in a lift increase of up to 100% and a drag reduction. The simulations provide insight into a physical mechanism that offers an explanation for the lift increase observed for rotating blade sections when compared with stationary blade sections, which is commonly referred to as rotational augmentation. Rotation is shown to lead to a radial velocity component toward the blade tip in areas where the velocity is substantially different from its free‐stream value, such as near the stagnation point and especially in the separated flow region, and to the appearance of stationary and traveling crossflow vortices. A linear stability theory analysis that compares favorably with the simulation data provides proof that the primary instabilities are of a mixed type, including both a two‐dimensional mode (Tollmien–Schlichting and Kelvin–Helmholtz type) and a stationary and unsteady crossflow mode. The crossflow instabilities accelerate transition, leading to separation delay, lift increase and drag reduction. This effect is very pronounced at 20% blade radius and still present at 80% radius. Because periodicity conditions were applied in the spanwise direction, the present results provide an explanation for rotational augmentation that is not based on the transfer of fluid from the inboard region toward the blade tip (‘centrifugal pumping’). For the low Reynolds number conditions considered here, crossflow instabilities, which destabilize the flow leading to earlier transition and a separation delay, may contribute to rotational augmentation. Copyright © 2012 John Wiley & Sons, Ltd.