平板大攻角绕流升力和阻力系数的计算

二维平板或二维对称薄翼型大攻角绕流升力和阻力系数与攻角之间存在的函数关系一般用数据表格的形式给出。本文根据垂直平板绕流阻力实验数据和对称薄翼型全攻角绕流实验数据,分析得到了平板大攻角绕流总压力及其升力分量和阻力分量系数的近似计算公式。结果表明：平板总压力系数约等于攻角正弦值的2倍;总压力的阻力分量系数约等于攻角正弦值平方的2倍;升力分量系数约为攻角2倍的正弦值。计算结果与两组试验数据具有较好的一致性。     

Low Reynolds number airfoil aerodynamic loads determination via line integral of velocity obtained with particle image velocimetry

The small magnitude lift forces generated by both a NACA 0012 airfoil and a thin flat plate at Re?=?29,000 and 54,000 were determined through the line integral of velocity, obtained with particle image velocimetry, via the application of the Kutta–Joukowsky theorem. Surface pressure measurements of the NACA0012 airfoil were also obtained to validate the lift coefficient C _l. The bound circulation was found to be insensitive to the size and aspect ratio of the rectangular integration loop for pre-stall angles. The present C _l data were also found to agree very well with the surface pressure-determined lift coefficient for pre-stall conditions. A large variation in C _l with the loop size and aspect ratio for post-stall conditions was, however, observed. Nevertheless, the present flat-plate C _l data were also found to collectively agree with the published force-balance measurements at small angles of attack, despite the large disparity exhibited among the various published data at high angles. Finally, the ensemble-averaged wake velocity profiles were also used to compute the drag coefficient and, subsequently, the lift-to-drag ratio.     

棱柱绕流流动的数值模拟

利用数值方法对长宽比为1／3, 1和3的棱柱绕流在雷诺数为100的非稳态流动特性进行了分析和研究。采用有限体积法对棱柱绕流的二维流动N-S方程进行离散求解,分析和研究了非稳态的棱柱绕流流场,升力系数,阻力系数和涡动特性,数值模拟的结果与相关文献的数据比较吻合。通过上述研究能够为了解棱柱绕流的非稳态流动特性提供有力的帮助。而对棱柱三维流动的模拟分析和对雷诺数的变化对棱柱流动特性的影响进行研究,将为掌握棱柱绕流的工程特性打下基础。     

带控制片方柱绕流的非定常数值模拟

对高雷诺数下带控制片的方体(在方柱之前放置一小尺度的柱形薄片)非定常绕流进行了数值模拟。数值模拟方法采用RNG重整化群紊流模型，SIMPLE算法，在非定常计算中引入双重时间步方法，将方体和控制片区域作为求解域的一部分作整体求解。结果表明，控制片与方柱之间距离的不同，使得控制片所形成的涡被抑止或产生卡门涡街，从而对柱体侧面边界层的分离发生影响，产生三种典型的流态，柱体时均阻力系数相对于无控制片的情况迅速减小，当控制片偏离柱体轴心时，柱体升力系数迅速增大，偏心至柱体外壁面附近达到极大值。阻力系数达到最小值后将产生跳跃式的增大，而升力系数在达到最大值后也将产生跳跃式的减小。     

Reduction of the Induced Drag of a Supersonic Wing

The oblique wing effect, i.e., a reduction in the wave drag for given lift, cannot be realized for a delta wing with supersonic leading edges owing to the lift reduction in the wing mid-section. To preserve the effect, the disturbances generated by the delta wing vertex must be eliminated by adding a body (wedge) to the wing by replacing the streamsurfaces behind the shock with rigid surfaces. Moreover, using wing tip deflection, and thereby reducing the wave drag to zero, makes it possible to obtain a lift- drag ratio close to that of the limiting, infinitely long flat plate.     

Drag characteristics of a turbulent boundary layer over a flat plate with transverse square grooves

 The effect of transverse square grooves on the drag characteristics of a flat plate has been investigated using direct drag measurements in a tow tank. Two flat plates with 2.5 and 5 mm transverse square grooves, with groove spacing (s) to groove width (w) ratio, s/w=10, 20 and 40, were tested at plate length Reynolds numbers in the range 2–10×10⁶. There is an increase in drag over the “smooth” plate for all s/w configurations. Received: 31 December 1997/Accepted: 4 April 1998     

GROUND EFFECT OF FLOW AROUND AN ELLIPTIC CYLINDER IN A TURBULENT BOUNDARY LAYER

The flow characteristics around an elliptic cylinder with an axis ratio of AR=2 located near a flat plate were investigated experimentally. The elliptic cylinder was embedded in a turbulent boundary layer whose thickness is larger than the cylinder height. For comparison, the same experiment was carried out for a circular cylinder having the same vertical height. The Reynolds number based on the height of the cylinder cross-section was 14000. The pressure distributions on the cylinder surface and on the flat plate were measured for various gap distances between the cylinder and the plate. The wake velocity profiles behind the cylinder were measured using hot-wire anemometry. In the near-wake region, the vortices are shed regularly only when the gap ratio is greater than the critical value of G/B=0·4. The critical gap ratio is larger than that of a circular cylinder. The variation of surface pressure distributions on the elliptic cylinder with respect to the gap ratio is much smaller than that on the circular cylinder. This trend is more evident on the upper surface than the lower one. The surface pressures on the flat plate recover faster than those for the case of the circular cylinder at downstream locations. As the gap ratio increases, the drag coefficient of the cylinder itself increases, but the lift coefficient decreases. For all gap ratios tested in this study, the drag coefficient of the elliptic cylinder is about half that of the circular cylinder. The ground effect of the cylinder at small gap ratio constrains the flow passing through the gap, and restricts the vortex shedding from the cylinder, especially in the lower side of the cylinder wake. This constraint effect is more severe for the elliptic cylinder, compared to the circular cylinder. The wake region behind the elliptic cylinder is relatively small and the velocity profiles tend to approach rapidly to those of a flat plate boundary layer     

An experimental study of a bio-inspired corrugated airfoil for micro air vehicle applications

An experimental study was conducted to investigate the aerodynamic characteristics of a bio-inspired corrugated airfoil compared with a smooth-surfaced airfoil and a flat plate at the chord Reynolds number of Re _C  = 58,000–125,000 to explore the potential applications of such bio-inspired corrugated airfoils for micro air vehicle designs. In addition to measuring the aerodynamic lift and drag forces acting on the tested airfoils, a digital particle image velocimetry system was used to conduct detailed flowfield measurements to quantify the transient behavior of vortex and turbulent flow structures around the airfoils. The measurement result revealed clearly that the corrugated airfoil has better performance over the smooth-surfaced airfoil and the flat plate in providing higher lift and preventing large-scale flow separation and airfoil stall at low Reynolds numbers (Re _C  < 100,000). While aerodynamic performance of the smooth-surfaced airfoil and the flat plate would vary considerably with the changing of the chord Reynolds numbers, the aerodynamic performance of the corrugated airfoil was found to be almost insensitive to the Reynolds numbers. The detailed flow field measurements were correlated with the aerodynamic force measurement data to elucidate underlying physics to improve our understanding about how and why the corrugation feature found in dragonfly wings holds aerodynamic advantages for low Reynolds number flight applications.     

Flow field analysis of a turbulent boundary layer over a riblet surface

The near-wall flow structures of a turbulent boundary layer over a riblet surface with semi-circular grooves were investigated experimentally for the cases of drag decreasing (s ⁺=25.2) and drag increasing (s ⁺=40.6). One thousand instantaneous velocity fields over riblets were measured using the velocity field measurement technique and compared with those above a smooth flat plate. The field of view was 6.75 × 6.75 mm² in physical dimension, containing two grooves. Those instantaneous velocity fields were ensemble averaged to get turbulent statistics including turbulent intensities and turbulent kinetic energy. To see the global flow structure qualitatively, flow visualization was also carried out using the synchronized smoke-wire technique under the same experimental conditions. For the case of drag decreasing (s ⁺=25.2), most of the streamwise vortices stay above the riblets, interacting with the riblet tips frequently. The riblet tips impede the spanwise movement of the streamwise vortices and induce secondary vortices. The normalized rms velocity fluctuations and turbulent kinetic energy are small near the riblet surface, compared with those over a smooth flat plate. Inside the riblet valleys, these are sufficiently small that the increased wetted surface area of the riblets can be compensated. In addition, in the outer region (y ⁺ > 30), these values are almost equal to or slightly smaller than those for the smooth plate. For the case of drag increasing (s ⁺=40.6), however, most of the streamwise vortices stay inside the riblet valleys and contact directly with the riblet surface. The high-speed down-wash flow penetrating into the riblet valley interacts actively with the wetted riblet surface and increases the skin friction. The rms velocity fluctuations and turbulent kinetic energy have larger values compared with those over a smooth flat plate. Received: 24 March 1999/Accepted: 10 March 2000     

The flexibility effect of a plate according to various angles of attack in a free-stream

This paper presents a computational fluid–structure interaction analysis for a flexible plate in a free-stream to investigate the effects of flexibility and angle of attack on force generation. A Lattice Boltzmann Method with an immersed boundary technique using a direct forcing scheme model of the fluid is coupled to a finite element model with rectangular bending elements. We investigated the effects of various angles of attack of a flexible plate fixed at one of the end edges in a free-stream at a Reynolds number of 5000, which represents the wing flapping condition of insects and small birds in nature. The lift of the flexible plate is maintained at the large angle of attack, whereas the rigid plate shows the largest lift at angles of attack around 30–40° and then drastic reductions in the lift at the large angle of attack. If we consider the efficiency as the lift divided by the drag, the flexible plate shows better efficiency at angles of attack greater than 30° compared to the rigid plate. The better performance of the flexible plate at large angles of attack comes from the deformation of the plate, which produces an interaction between the trailing edge vortex and the short edge vortex. The horseshoe-shaped vortex produced by a large vortex interaction at the trailing edge side has an important role in increasing the lift, and the small projection area due to the deformation reduces the drag. Furthermore, we investigate the role of flexibility on the lift and the drag force of the rectangular plate in a free-stream as the Reynolds number increases. Whenever a large vortex interaction at the trailing edge side is shown, the efficiency of the rectangular plate is improved. Especially, the flexible plate shows better efficiency as the Reynolds number increases regardless of the angle of attack.     

临近空间高超声速气动布局研究

临近空间飞行器存在多种不同的布局形式,而针对不同气动布局概念之间的系统研究则相对缺乏．采用数值模拟方法,对临近空间飞行器三类典型气动布局概念--扁平升力体、翼身融合体和翼身组合体开展系统的计算与分析,通过对比不同布局的升阻特性、静稳定特性、舵效特性等,获得不同布局概念气动性能优劣的初步评估．结果表明：扁平升力体的升力和阻力比较大,升阻比最低,容积率则最大,侧向稳定性最好;翼身组合体的升力和阻力比较小,升阻比最高,容积率比较低,侧向静稳定性较差;翼身融合体布局的特性介于翼身组合体和扁平升力体布局之间．     

Aerodynamic characteristics of low-aspect-ratio prismatic bodies near a screen

Data are presented on the drag and lift coefficients of prismatic bodies with an aspect ratio of =0.15–1.0 near a screen. The bodies were placed in the low velocity stream so that the planes of the square bases of the bodies were parallel to the screen plane. Body orientation in the scream corresponded to the minimum projected frontal area. The experiments were conducted in the Reynolds number range from 2·10⁵ to 9·10⁵ (the characteristic linear dimension is the side of the base). It is shown that approach of the prismatic models to the screen, simulating the ground, leads to some change of the drag coefficient and the appearance of a significant lift force tending to separate the model from the screen.     

绕栅中水翼空化流动的数值和实验研究

采用数值计算和实验研究的方法研究了绕水翼和栅中水翼的非定常空化流动. 实验采用高速录像技术分别观察了绕水翼和栅中水翼云状空化形态随时间的变化, 测量了升阻力, 并对测量数据进行了频率分析. 计算时空化模型选用了能比较准确描述旋涡空化非定常特性的Kubota模型, 湍流模型采用能准确捕捉流场非定常特性的FBM模型. 计算模型的可靠性用实验结果进行验证. 结果表明, 计算与实验的结果基本一致, 相比绕单个水翼的空化流动, 绕栅中水翼的空穴厚度比较薄, 翼型近壁处的逆压梯度较小, 反向射流的速度较小, 且水汽混合区速度梯度较小, 空穴的脱落周期变长, 平均升阻力系数较小      

Numerical study of the natural convective cooling of a vertical plate

We study numerically in this paper the natural convective cooling of a vertical plate. The full transient heat conduction equation for the plate, coupled with the natural convection boundary layer equations are solved numerically for a wide range of the parametric space. Assuming a large Rayleigh number for the natural convection flow, the balance equations are reduced to a system of three differential equations with three parameters: the Prandtl number of the fluid, Pr, a non-dimensional plate thermal conductivity α and the aspect ratio of the plate ?. The nondimensional cooling time depends mainly on α/?², obtaining a minimum of this time for values of 1?α??².     

Turbulent wall pressure fluctuation measurements on a towed model at high Reynolds numbers

Turbulent wall pressure fluctuation measurements were made in water on a towed model of length 129.8 (m) and diameter 3.8 (cm) for steady speeds from 6.2 (m/s) to 15.5 (m/s). The drag on the model was measured with a strut mounted load cell which provided estimates of the momentum thickness and friction velocity. Momentum thickness Reynolds numbers Re _θ varied from 4.8 × 10⁵ to 1.1 × 10⁶. The ratio of momentum thickness to viscous length scale is significantly greater than for flat plate cases at comparable Re _θ. The effectiveness of inner and outer velocity and length scales for collapsing the pressure spectra are discussed. The wavenumber–frequency spectra show a convective ridge at higher frequencies similar to flat plate boundary layers. At low frequencies, energy broad in wavenumber extends outside the convective ridge and acoustic cone, with no characteristic wave speed. Wall pressure cross-spectral levels scaled with similarity variables are shown to increase with increasing tow speed, and to follow decay constants consistent with flat plate cases. The convection velocities also display features similar to flat plate cases.     

Effects of a trapped vortex cell on a thick wing airfoil

The effects of a trapped vortex cell (TVC) on the aerodynamic performance of a NACA0024 wing model were investigated experimentally at Re = 10⁶ and 6.67×10⁵6.67\times 10^{5}. The static pressure distributions around the model and the wake velocity profiles were measured to obtain lift and drag coefficients, for both the clean airfoil and the controlled configurations. Suction was applied in the cavity region to stabilize the trapped vortex. For comparison, a classical boundary layer suction configuration was also tested. The drag coefficient curve of the TVC-controlled airfoil showed sharp discontinuities and bifurcative behavior, generating two drag modes. A strong influence of the angle of attack, the suction rate and the Reynolds number on the drag coefficient was observed. With respect to the clean airfoil, the control led to a drag reduction only if the suction was high enough. Compared to the classical boundary layer suction configuration, the drag reduction was higher for the same amount of suction only in a specific range of incidence, i.e., α = −2° to α = 6° and only for the higher Reynolds number. For all the other conditions, the classical boundary layer suction configuration gave better drag performances. Moderate increments of lift were observed for the TVC-controlled airfoil at low incidence, while a 20% lift enhancement was observed in the stall region with respect to the baseline. However, the same lift increments were also observed for the classical boundary layer suction configuration. Pressure fluctuation measurements in the cavity region suggested a very complex interaction of several flow features. The two drag modes were characterized by typical unsteady phenomena observed in rectangular cavity flows, namely the shear layer mode and the wake mode.     

Aerodynamic Performance of a Gliding Swallowtail Butterfly Wing Model

In the present study, we perform a wind-tunnel experiment to investigate the aerodynamic performance of a gliding swallowtail-butterfly wing model having a low aspect ratio. The drag, lift and pitching moment are directly measured using a 6-axis force/torque sensor. The lift coefficient increases rapidly at attack angles less than 10° and then slowly at larger attack angles. The lift coefficient does not fall off rapidly even at quite high angles of attack, showing the characteristics of low-aspect-ratio wings. On the other hand, the drag coefficient increases more rapidly at higher angles of attack due to the increase in the effective area responsible for the drag. The maximum lift-to-drag ratio of the present modeled swallowtail butterfly wing is larger than those of wings of fruitfly and bumblebee, and even comparable to those of wings of birds such as the petrel and starling. From the measurement of pitching moment, we show that the modeled swallowtail butterfly wing has a longitudinal static stability. Flow visualization shows that the flow separated from the leading edge reattaches on the wing surface at α < 15°, forming a small separation bubble, and full separation occurs at α ≥ 15°. On the other hand, strong wing-tip vortices are observed in the wake at α ≥ 5° and they are an important source of the lift as well as the main reason for broad stall. Finally, in the absence of long hind-wing tails, the lift and longitudinal static stability are reduced, indicating that the hind-wing tails play an important role in enhancing the aerodynamic performance.     

Fluid flow and heat transfer around circular cylinder – flat and curved plates combinations

Experimental studies were carried out to investigate the fluid flow and heat transfer around a heated circular cylinder which was placed at various distances of a wall boundary with different geometries (flat or curved plate) with subcritical Reynolds number ranging from 3.5×10³ to 10⁴. The effects of plate geometry (aspect ratio: W|H=1.0,1.5 and 2.0, and rim angle, φ=0°,60°,90°, and 120°) and gap ratio, (G|D=0.0,0.86,2.0,7.0,10.0) on the fluid flow and heat transfer characteristics (static pressure around cylinder surface, wake width, base pressure, pressure drag coefficients, velocity distribution, and both local and mean Nusselt numbers) were presented. Also flow visualization was carried out to illustrate the flow patterns around the cylinder at various gap ratios (G|D). It was found that the heat transfer and fluid flow characteristics are dependent on the plate geometry at all tested gap ratios, except for G|D=7.0 and 10.0, they are independent of the plate geometry.     

The effect of a splitter plate on the flow around a finite prism

The effect of a wake-mounted splitter plate on the flow around a surface-mounted finite-height square prism was investigated experimentally in a low-speed wind tunnel. Measurements of the mean drag force and vortex shedding frequency were made at Re=7.4×10⁴ for square prisms of aspect ratios AR=9, 7, 5 and 3. Measurements of the mean wake velocity field were made with a seven-hole pressure probe at Re=3.7×10⁴ for square prisms of AR=9 and 5. The relative thickness of the boundary layer on the ground plane was δ/D=1.5–1.6 (where D is the side length of the prism). The splitter plates were mounted vertically from the ground plane on the wake centreline, with a negligible gap between the leading edge of the plate and rear of the prism. The splitter plate heights were always the same as the heights of prisms, while the splitter plate lengths ranged from L/D=1 to 7. Compared to previously published results for an “infinite” square prism, a splitter plate is less effective at drag reduction, but more effective at vortex shedding suppression, when used with a finite-height square prism. Significant reduction in drag was realized only for short prisms (of AR≤5) when long splitter plates (of L/D≥5) were used. In contrast, a splitter plate of length L/D=3 was sufficient to suppress vortex shedding for all aspect ratios tested. Compared to previous results for finite-height circular cylinders, finite-height square prisms typically need longer splitter plates for vortex shedding suppression. The effect of the splitter plate on the mean wake was to narrow the wake width close to the ground plane, stretch and weaken the streamwise vortex structures, and increase the lateral entrainment of ambient fluid towards the wake centreline. The splitter plate has little effect on the mean downwash. Long splitter plates resulted in the formation of additional streamwise vortex structures in the upper part of the wake.     

Optimal airfoil shapes for low Reynolds number flows

Flow over NACA 0012 airfoil is studied at α = 4^° and 12^° for Re?500. It is seen that the flow is very sensitive to Re. A continuous adjoint based method is formulated and implemented for the design of airfoils at low Reynolds numbers. The airfoil shape is parametrized with a non‐uniform rational B‐splines (NURBS). Optimization studies are carried out using different objective functions namely: (1) minimize drag, (2) maximize lift, (3) maximize lift to drag ratio, (4) minimize drag and maximize lift and (5) minimize drag at constant lift. The effect of Reynolds number and definition of the objective function on the optimization process is investigated. Very interesting shapes are discovered at low Re. It is found that, for the range of Re studied, none of the objective functions considered show a clear preference with respect to the maximum lift that can be achieved. The five objective functions result in fairly diverse geometries. With the addition of an inverse constraint on the volume of the airfoil the range of optimal shapes, produced by different objective functions, is smaller. The non‐monotonic behavior of the objective functions with respect to the design variables is demonstrated. The effect of the number of design parameters on the optimal shapes is studied. As expected, richer design space leads to geometries with better aerodynamic properties. This study demonstrates the need to consider several objective functions to achieve an optimal design when an algorithm that seeks local optima is used. Copyright © 2008 John Wiley & Sons, Ltd.