Control of separated flows by time periodic Lorentz forces

Electromagnetic, i.e. Lorentz forces, may be used to influence the flow of electrically conducting fluids. The present paper investigates the application of time periodic Lorentz forces to the control of the suction side flow on a NACA 0015 hydrofoil. Experimental results, consisting of flow visualizations and force measurements, characterizing the control effect in the low Reynolds number range of 10⁴Re10⁵, are presented. A comparison of the forcing effect with stationary Lorentz forces on one hand and conventional oscillatory blowing on the other hand is given as well.     

翼型绕流的电磁力控制

将表面包覆电磁激活板的翼型,按一定的攻角,置于流动的弱电介质溶液中,电磁激活板可产生作用于流体的切向电磁力(Lorentz力),从而改变流体边界层的结构. 在转动水槽中,对翼型绕流及电磁力控制下的绕流形态进行了实验研究. 结果表明,未加电磁力时,前缘涡的脱落点是不确定的,与流场具体条件有关,而后缘涡仅在尖角处脱落. 前缘涡与后缘涡相互影响,并周期性的脱体,在尾部形成涡街. 施加电磁力后,当力的方向与流动方向相同时,可以在一定程度上抑制分离,消除涡街,其效果与减小攻角类似. 加反向电磁力时,则相当于加大攻角,在翼型体的背风面形成涡街.      

电磁力控制翼型绕流分离的增升减阻效率研究

电磁力可有效对流体流动进行控制,增升减阻,抑制流动分离,制约其推广应用的瓶颈为控制效率问题.为提高其控制效率,基于翼型绕流的电磁力控制,对电磁力增升减阻的控制效率问题进行数值研究. 根据能量守恒定律,推导电磁力控制能耗的比,基于升力和阻力计算节省能量. 定义电磁力的控制效率为能量节省与电磁力控制所需能耗的比值,研究不同工况下电磁力增升减阻的控制效率. 发现在控制开始阶段,电磁力能量主要消耗在增加边界层流体的动能上,电磁力控制效率非常低,但电磁力控制效率会随着电磁力工作时间的增长而增加;电磁力控制效率随着来流速度的增加呈指数下降;通过增加电磁力激活板的输入能量可增强电磁力的控制效果,但无法明显增加其控制效率.      

An improvement to the Kunz preconditioner and numerical investigation of hydrofoil interactions in tandem

ABSTRACT

Numerical simulations of the tandem-system flow are widely conducted because of the complex interactions of the configuration. The cavitation phenomenon is an important factor that affects the hydrofoil in tandem. In this paper, we developed a new parameter for the Kunz preconditioner based on the local cavitation volume fraction. To assess this parameter, a type of Fourier footprint analysis and numerical test of the hydrofoil are adopted. The preconditioning method is also conducted in hydrofoil turbulent cavitation flows with RANS turbulence models, to prove that this method has good stability and convergence. Based on this, a tandem Clark-Y hydrofoil configuration is investigated. The results show that the distance of components has a strong influence on the cavitation and lift coefficient of the tandem hydrofoils. Therefore, the purpose of this study is to provide guidance on the design of marine vehicles that have tandem configurations.     

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 modelling of confined flow past a cylinder of square cross-section at various orientations

Results are presented for the unsteady, two-dimensional flow and heat transfer due to a square obstruction of diameter d located asymmetrically between the parallel sliding walls of a channel with length-to-height ratio W/H = 6·44. Analysis is based on the numerical solution of spatially and temporally second-order accurate finite difference approximations of the transport equations expressed in curvilinear co-ordinates. Laminar, constant property flow is assumed for obstruction configurations in which the blockage ratio is d/H = 0·192, the nearest-wall distances are g/d = 0·2, 0·5 and 1, the orientation angles are α=0°, 10° and 20° and the Reynolds numbers are Re=100, 500, and 1000. Preparatory testing of the numerical procedure was performed for a variety of documented flows to verify its physiconumerical accuracy and obtain estimates of the residual grid-dependent uncertainties in the variables calculated. Heat transfer, drag and lift coefficients and Strouhal numbers for the present flow were finally calculated to within 4%–7% of their grid-dependent values using non-uniformly spaced grids consisting of (x=99, y=55) nodes. Above a critical value of the Reynolds number, which depends on the geometrical parameters, the flow is characterized by alternate vortex shedding from the obstruction top and bottom surfaces. Streamline, vorticity and particle streakline plots provide qualitative impressions of the unsteady vortical flow. Especially noteworthy are the extremes in the lift coefficient which ranges from large positive values for an obstruction with g/d=0·2 and α=10° to negative values for one with g/d=0·5 and α=0°. Both the drag and lift coefficients as well as the Strouhal number exhibit non-monotonic variations with respect to the parameters explored. Asymmetries in the obstruction location and orientation account for relatively large vortex-induced periodic variations in heat transfer, especially along the wall nearest the obstruction. Notable differences are also predicted for the heat transfer coefficients of the individual obstruction surfaces as a function of the orientation angle.     

Experimental investigation of a hydrofoil designed via hydrostructural optimization

In the last decade, there has been an increased interest in the use of multidisciplinary optimization techniques for the design of aerospace, maritime, and wind engineering systems. However, validation of numerically optimized results using experimental measurements has been scarce. In this paper, numerical predictions are compared with experimental measurements of the hydrodynamic forces, deformations, and cavitation performance for a baseline NACA 0009 hydrofoil and an optimized hydrofoil. Both hydrofoils are made of solid aluminum, and are cantilevered at the root. One of the hydrofoils is optimized using a high-fidelity hydrostructural solver combined with a gradient-based optimizer, as detailed by Garg et al. (2017). The numerical predictions agree well with experimental measurements for both the baseline NACA 0009 and the optimized hydrofoils. For the optimized hydrofoil, the mean differences between the predicted and measured values for mean lift, drag coefficient, and moment coefficients, are 2.9%, 5.1%, and 3.0%, respectively. For the non-dimensional tip bending deflection, the mean difference is 3.4%. Although the optimized hydrofoil is significantly thicker to withstand higher loads than the baseline, it yields an overall measured increase in the lift-to-drag ratio of 29% for lift coefficients ranging from $-0.15$ to 0.75 and exhibits significantly delayed cavitation inception compared to the baseline. The improvement in hydroelastic and cavitation performance is attributed to the changes in the distribution of camber, twist, thickness, and the leading edge radius of the optimized hydrofoil. The results validate the analysis and optimization of the high-fidelity hydrostructural design optimization approach, and opens up new possibilities for the design of high-performance hydrofoils, marine propellers, and turbines.     

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.     

PIV measurements of the asymmetric wake of a two dimensional heaving hydrofoil

Particle image velocimetry is used to examine the flow behind a two-dimensional heaving hydrofoil of NACA 0012 cross section, operating with heave amplitude to chord ratio of 0.215 at Strouhal numbers between 0.174 and 0.781 and a Reynolds number of 2,700. The measurements show that for Strouhal numbers larger than 0.434, the wake becomes deflected such that the average velocity profile is asymmetric about the mean heave position of the hydrofoil. The deflection angle of the wake, which is related to the average lift and drag on the hydrofoil, is found to lie between 13° and 18°. An examination of the swirl strength of the vortices generated by the hydrofoil motion reveal that the strongest vortices, which are created at the higher Strouhal numbers, dissipate most rapidly. This research article was submitted for the special issue on Animal locomotion: The hydrodynamics of swimming (Vol. 43, No. 5).     

A method to carry out shape optimization with a large number of design variables

A new method for shape optimization with relatively large number of design variables is proposed. It is well known that gradient‐based methods converge to a local optimum. As a result, utilization of a richer design space does not necessarily lead to a better design. This is demonstrated via the design of an airfoil for maximum lift for Re = 1000 and α = 4° flow. The airfoil is represented by fourth‐order non‐uniform rational B‐splines, and the control points are used as design variables. Starting with a NACA0012 airfoil, it is found that the optimal airfoil obtained with 13 control points has far superior aerodynamic performance than the ones obtained with 39 and 61 control points. For effective utilization of a richer design space, it is proposed that the number of design variables be increased gradually. The method is demonstrated by designing high lift airfoils for Re = 1000 and 1 × 10⁴. The objective function is the maximization of the time‐averaged lift coefficient for α = 4°. The optimization cycle with 27 control points is initiated with the optimal airfoil obtained with 13 control points. The process is continued with gradual increase in the number of design variables. Beyond a certain number of control points, the optimization leads to a spontaneous appearance of corrugations on the upper surface of the airfoil. The corrugations are responsible for the generation of small vortices that add to the suction on the upper surface of the airfoil and lead to enhanced lift. A stabilized finite element method is used to solve the unsteady flow and adjoint equations. Copyright © 2012 John Wiley & Sons, Ltd.     

Reynolds-number-effects in flow around a rectangular cylinder with aspect ratio 1:5

The paper reports on experiments carried out over a wide range of Reynolds numbers in a high pressure wind tunnel. The model was a sharp-edged rectangular cylinder with aspect ratio height/width 1:5 (width/span ratio 1:10.8), which was investigated in both basic orientations, lengthwise (4×10³<Re<4×10⁵) and perpendicular to the flow (2.7×10⁴<Re<6.4×10⁵). The Reynolds number is based on the height of the model normal to the flow. Steady and unsteady forces were measured with a piezoelectric balance. Thus along with steady (i.e. time averaged values) including the base pressure coefficient, also power spectra and probability density functions were measured yielding for example Strouhal numbers, higher statistical moments, etc. A response diagram for the vortex resonance phenomenon was taken for the natural bending motion of the slender model. If lift coefficient for constant angle of attack is plotted against Reynolds number, a significant Reynolds number effect is seen. For α=4°, the curve shows an inflection point and the lift varies between 0.3 and 0.6. For α=6° and 2° there are similar variations shifted to lower and higher values of Re, respectively. Probably the shapes of separation bubbles that depend on the Reynolds number are responsible for these effects. No Reynolds number effects were observed when the long side was normal to the flow, an orientation where reattachment at the side walls is not possible. Comparing both basic cases (α=0° and 90°), the interpretation of the probability distributions of lift force leads to the conclusion that the possibility of reattachment (α=0°) seems to enhance the degree of order in the vortex shedding process.     

An experimental study of fluctuating lift on a square-section cylinder oscillating transversely in a uniform stream

Experiments on a square-section cylinder fixed and forced to oscillate transversely in a uniform stream were conducted in a water tank. The Reynolds number of the experiments is in the range of 3·10³ to 10⁴, the amplitude to side length ratioA/D is up to 0.7 and the range of reduced velocity is 4.5<V _r <12. This study aims at investigating the lock-in phenomenon, the fluctuating lift and the phase shift between fluctuating lift and displacement of the oscillating cylinder. The problems on the aeroelastic instability relating to present experimental results have been discussed. The flow visualization clearly shows that there are drastic changes of vortex-shedding from cylinder at the resonance point and the upper end of the lock-in range. The results of the flow visualization give better understanding of the physical mechanism of the phase shift. Project supported by National Natural Science Foundation of China     

Numerical simulation of the flow around a porous covering square cylinder in a channel via lattice Boltzmann method

In this paper, a detailed investigation on the flow past a porous covering cylinder is presented through the lattice Boltzmann method. The Brinkman‐Forchheimer‐extended Darcy model is adopted for the entire flow field with the solid, fluid, and porous medium. The effects of several parameters, such as porous layer thickness, Darcy number, porosity, and Reynolds number on flow field are discussed. Compared with the case of a solid cylinder, the present work shows that the porous layer may play an important role on the flow, the lift and drag force exerted on the cylinder. The numerical results indicate that the maximal drag coefficient C_d and maximal amplitude of lift coefficient C_l exist at certain Darcy number which is in the range of 10^?6–10^?2. Copyright © 2010 John Wiley & Sons, Ltd.     

翼型空化绕流数值研究

空化是发生在流体机械上的复杂过程，理论研究遇到很大困难。本文引入合适的空化数值模型，将空腔界面近似为自由面，用界面构造精度较高的流体体积方法求解空腔位置，通过直接求解原始变量的NavuerStokes方程，数值模拟了无界域中空化在翼型上发生、发展和脱落的周期过程；并分析了空化产生对翼型表面的压力分布、翼型收到的阻力和升力的影响。结果表明，空化出现在翼型上表面；由于空化的产生，翼型表面压力分布不稳定，导致升力、阻力和流场压力出现波动，这是实际中产生噪声和损失的主要原因。     

Computation of two‐dimensional flows past ram‐air parachutes

Computational results for flow past a two‐dimensional model of a ram‐air parachute with leading edge cut are presented. Both laminar (Re=10⁴) and turbulent (Re=10⁶) flows are computed. A well‐proven stabilized finite element method (FEM), which has been applied to various flow problems earlier, is utilized to solve the incompressible Navier–Stokes equations in the primitive variables formulation. The Baldwin–Lomax model is employed for turbulence closure. Turbulent flow computations past a Clarck‐Y airfoil without a leading edge cut, for α=7.5°, result in an attached flow. The leading edge cut causes the flow to become unsteady and leads to a significant loss in lift and an increase in drag. The flow inside the parafoil cell remains almost stagnant, resulting in a high value of pressure, which is responsible for giving the parafoil its shape. The value of the lift‐to‐drag ratio obtained with the present computations is in good agreement with those reported in the literature. The effect of the size and location of the leading edge cut is studied. It is found that the flow on the upper surface of the parafoil is fairly insensitive to the configuration of the cut. However, the flow quality on the lower surface improves as the leading edge cut becomes smaller. The lift‐to‐drag ratio for various configurations of the leading edge cut varies between 3.4 and 5.8. It is observed that even though the time histories of the aerodynamic coefficients from the laminar and turbulent flow computations are quite different, their time‐averaged values are quite similar. Copyright © 2001 John Wiley & Sons, Ltd.     

Fluid forces on a square cylinder in oscillating flows with non‐zero‐mean velocities

The unsteady forces on a square cylinder in sinusoidally oscillating flows with non‐zero‐mean velocities are investigated numerically by using a weakly compressible‐flow method with three‐dimensional large eddy simulations. The major parameters in the analysis are Keulegan–Carpenter number (KC) and the ratio between the amplitude and the mean velocities of the approaching flow (A_R). By varying the values of KC and A_R the resulting drag and lift of the cylinders are analyzed systematically at two selected approaching‐flow attack angles (0 and 22.5^°). In the case of the non‐zero attack angle, results show that both the drag and lift histories can be adequately described by Morison equations. However, Morison equations fail to correctly describing the lift history as the attack angle is zero. In addition, when the ratio of A_R/KC is near the Strouhal number of the bluff‐body flow, the resulting drag is promoted due to the occurrence of resonance. Based on the results of systematic analyses, finally, the mean and inertia force coefficients at the two selected attack angles are presented as functions of KC and A_R based on the Morison relationships. Copyright © 2008 John Wiley & Sons, Ltd.     

摆动方式对水翼输入功率的影响

利用投影浸入边界法,研究了不同主动摆动方式对水翼输入功率的影响。计算模型采用二维NACA0012翼型,雷诺数Re=800。最大摆角θ0=75°,摆动频率f的变化范围为0.1Hz~0.2Hz,非正弦摆动参数β的变化范围为1~3。首先,研究摆动频率f和非正弦摆动参数β对平均输入功率的影响,研究发现,平均输入功率随着f和β值的增加而增加,但当f0.16 Hz,β2.5时,平均输入功率急剧增加。其次,在摆动频率f=0.16 Hz时,研究不同非正弦摆动参数β下力矩系数、输入功率系数以及升阻力系数随时间的变化规律,研究发现,随着β值的增加,峰值输入功率也逐渐增加,而且β值影响峰值输入功率出现的位置。最后,研究不同β值下,变化的尾流发展对输入功率的影响,认为水翼上下表面产生的后缘涡与升阻力有关系,水翼上表面的负涡对水翼摆动产生阻力,而下表面的负涡对水翼摆动产生升力,从而对水翼摆动的输入功率产生影响。     

Fluid-structure interaction simulation of three-dimensional flexible hydrofoil in water tunnel

The closely coupled approach combined with the finite volume method (FVM) solver and the finite element method (FEM) solver is used to investigate the fluid-structure interaction (FSI) of a three-dimensional cantilevered hydrofoil in the water tunnel. The FVM solver and the coupled approach are verified and validated by comparing the numerical predictions with the experimental measurements, and good agreement is obtained concerning both the lift on the foil and the tip displacement. In the noncavitating flow, the result indicates that the growth of the initial incidence angle and the Reynolds number improves the deformation of the foil, and the lift on the foil is increased by the twist deformation. The normalized twist angle and displacement along the span of the hydrofoil for different incidence angles and Reynolds numbers are almost uniform. For the cavitation flow, it is shown that the small amplitude vibration of the foil has limited influence on the developing process of the partial cavity, and the quasi two-dimensional cavity shedding does not change the deformation mode of the hydrofoil. However, the frequency spectrum of the lift on the foil contains the frequency which is associated with the first bend frequency of the hydrofoil.     

The ultra-low Reynolds number airfoil wake

Lift force and the near wake of an NACA 0012 airfoil were measured over the angle (α) of attack of 0°–90° and the chord Reynolds number (Re _c ), 5.3 × 10³–5.1 × 10⁴, with a view to understand thoroughly the near wake of the airfoil at low- to ultra-low Re _c . While the lift force is measured using a load cell, the detailed flow structure is captured using laser-Doppler anemometry, particle image velocimetry, and laser-induced fluorescence flow visualization. It has been found that the stall of an airfoil, characterized by a drop in the lift force, occurs at Re _c  ≥ 1.05 × 10⁴ but is absent at Re _c  = 5.3 × 10³. The observation is connected to the presence of the separation bubble at high Re _c but absence of the bubble at ultra-low Re _c , as evidenced in our wake measurements. The near-wake characteristics are examined and discussed in detail, including the vortex formation length, wake width, spanwise vorticity, wake bubble size, wavelength of K–H vortices, Strouhal numbers, and their dependence on α and Re _c .     

Aerodynamics of intermittent bounds in flying birds

Flap-bounding is a common flight style in small birds in which flapping phases alternate with flexed-wing bounds. Body lift is predicted to be essential to making this flight style an aerodynamically attractive flight strategy. To elucidate the contributions of the body and tail to lift and drag during the flexed-wing bound phase, we used particle image velocimetry (PIV) and measured properties of the wake of zebra finch (Taeniopygia guttata, N = 5), flying at 6–10 m s⁻¹ in a variable speed wind tunnel as well as flow around taxidermically prepared specimens (N = 4) mounted on a sting instrumented with force transducers. For the specimens, we varied air velocity from 2 to 12 m s⁻¹ and body angle from −15° to 50°. The wake of bounding birds and mounted specimens consisted of a pair of counter-rotating vortices shed into the wake from the tail, with induced downwash in the sagittal plane and upwash in parasagittal planes lateral to the bird. This wake structure was present even when the tail was entirely removed. We observed good agreement between force measures derived from PIV and force transducers over the range of body angles typically used by zebra finch during forward flight. Body lift:drag (L:D) ratios averaged 1.4 in live birds and varied between 1 and 1.5 in specimens at body angles from 10° to 30°. Peak (L:D) ratio was the same in live birds and specimens (1.5) and was exhibited in specimens at body angles of 15° or 20°, consistent with the lower end of body angles utilized during bounds. Increasing flight velocity in live birds caused a decrease in C _L and C _D from maximum values of 1.19 and 0.95 during flight at 6 m s⁻¹ to minimum values of 0.70 and 0.54 during flight at 10 m s⁻¹. Consistent with delta-wing theory as applied to birds with a graduated-tail shape, trimming the tail to 0 and 50% of normal length reduced L:D ratios and extending tail length to 150% of normal increased L:D ratio. As downward induced velocity is present in the sagittal plane during upstroke of flapping flight, we hypothesize that body lift is produced during flapping phases. Future efforts to model the mechanics of intermittent flight should take into account that flap-bounding birds may support up to 20% of their weight even with their wings fully flexed.