Steady flow with separation past a thin airfoil at high Reynolds numbers

The results of calculating the steady separated flow of a viscous incompressible fluid past a 12% sinusoidal airfoil with and without a splitter plate are presented. The Navier—Stokes equations written in stream-function—vorticity variables are approximated in accordance with a central difference scheme and solved simultaneously by means of the direct method. The results obtained are analyzed from the standpoint of their consistency with the asymptotic theory based on the well-known three-deck scheme. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 155–160, March–April, 1994.     

Parametric study of separation and transition characteristics over an airfoil at low Reynolds numbers

Time-resolved surface pressure measurements are used to experimentally investigate characteristics of separation and transition over a NACA 0018 airfoil for the relatively wide range of chord Reynolds numbers from 50,000 to 250,000 and angles of attack from 0° to 21°. The results provide a comprehensive data set of characteristic parameters for separated shear layer development and reveal important dependencies of these quantities on flow conditions. Mean surface pressure measurements are used to explore the variation in separation bubble position, edge velocity in the separated shear layer, and lift coefficients with angle of attack and Reynolds number. Consistent with previous studies, the separation bubble is found to move upstream and decrease in length as the Reynolds number and angle of attack increase. Above a certain angle of attack, the proximity of the separation bubble to the location of the suction peak results in a reduced lift slope compared to that observed at lower angles. Simultaneous measurements of the time-varying component of surface pressure at various spatial locations on the model are used to estimate the frequency of shear layer instability, maximum root-mean-square (RMS) surface pressure, spatial amplification rates of RMS surface pressure, and convection speeds of the pressure fluctuations in the separation bubble. A power-law correlation between the shear layer instability frequency and Reynolds number is shown to provide an order of magnitude estimate of the central frequency of disturbance amplification for various airfoil geometries at low Reynolds numbers. Maximum RMS surface pressures are found to agree with values measured in separation bubbles over geometries other than airfoils, when normalized by the dynamic pressure based on edge velocity. Spatial amplification rates in the separation bubble increase with both Reynolds number and angle of attack, causing the accompanying decrease in separation bubble length. Values of the convection speed of pressure fluctuations in the separated shear layer are measured to be between 35 and 50% of the edge velocity, consistent with predictions of linear stability theory for separated shear layers.     

The development of a plane laminar flow at low Reynolds numbers

Summary The development of a plane Poiseuille flow at low Reynolds numbers is studied; given any velocity distribution in the section x=0, it is possible to evaluate its evolution along the direction of motion, by means of quite simple calculation. A numerical example is also given.

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Sommario Si esamina l'evoluzione del profilo di velocità in moto piano laminare a bassi numeri di Reynolds. Assegnata una qualsiasi distribuzione di velocità nella sezione x=0, è possibile calcolare come questa si modifichi lungo il percorso. Si fornisce un esempio numerico.

     

Unsteady characteristics of the static stall of an airfoil subjected to freestream turbulence level up to 16%

Fluctuation of the separation point on an airfoil under high turbulence level is investigated using pressure measurements and flow visualisations. The characteristics of the unsteady loads induced by Karman vortex shedding are studied. This is related with a local approach based on the study of the oscillation zone. A method based on the pressure standard deviation is proposed to obtain the length of this zone, which is found to be independent of the turbulence level. This result is in agreement with that obtained by spectral analysis which shows no effect of the turbulence level on the Karman vortex shedding frequency.     

Measurements of turbulent flow in a channel at low Reynolds numbers

Normal and streamwise components of the velocity fields of turbulent flow in a channel at low Reynolds numbers have been measured with laser-Doppler techniques. The experiments duplicate the conditions used in current direct numerical simulations of channel flow, and good, but not exact, agreement is found for single-point moments through fourth order. In order to eliminate LDV velocity bias and to measure velocity spectra, the mean time interval between LDV signals was adjusted to be much smaller than the smallest turbulence time scale. Spectra of the streamwise and normal components of velocity at locations spanning the channel are presented.     

Turbulence modelling of the flow past a pitching NACA0012 airfoil at and Reynolds numbers

This paper provides a study of the NACA0012 dynamic stall at Reynolds numbers 10⁵ and 10⁶ by means of two- and three-dimensional numerical simulations. The turbulence effect on the dynamic stall is studied by statistical modelling. The results are compared with experiments concerning each test case. Standard URANS turbulence modelling have shown a quite dissipative character that attenuates the instabilities and the vortex structures related to the dynamic stall. The URANS approach Organised Eddy Simulation (OES) has shown an improved behaviour at the high Reynolds number range. Emphasis is given to the physical analysis of the three-dimensional dynamic stall structure, for which there exist few numerical results in the literature, as far as the Reynolds number range is concerned. This study has shown that the downstroke phases of the pitching motion are subjected to strong three-dimensional turbulence effects along the span, whereas the flow is practically two-dimensional during the upstroke motion.     

Magnetohydrodynamic flow past a drop at low Reynolds and Hartmann numbers

The flow of an electrically conductive liquid past a solid spherical particle at low Reynolds and Hartmann numbers in longitudinal and transverse magnetic fields was first investigated in [1,2]. The effect of a weak magnetic field on the strength of the resistance of a conductive drop in a dielectric medium was considered in [3]. In the present paper we consider the motion of a conductive liquid drop in an electrically conductive medium and calculate the strength of the resistance in the Stokes approximation for an arbitrary orientation of the uniform magnetic field and in the Oseen approximation for the case in which the direction of the magnetic field coincides with the direction of the oncoming stream. As in the previous studies, we do not consider the possibility of the formation of a double layer on the interface between the phases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 19–25, November–December, 1978.The authors are grateful to G. I. Petrov and the participants in the seminar they conducted for their comments on the work.     

Control of flow separation from a model wing at low Reynolds numbers

The results of an experimental investigation of the structure of the flow separated from the model of a straight wing with point sources of disturbances (bulges) made on its surface are presented. The variations in the three-dimensional flow pattern are analyzed as functions of the bulge shapes and positions. It is found that the flow can be controlled by means of mounting the bulges downstream of the separation line, in the return flow region, since in this case they hinder large-scale vortex formation in the separation zone. The results obtained show that there is an intimate connection between the vortices and the separation zone as a whole. Impeding the vortex structure formation can result in considerable variations in the separation zone structure, up to its complete disappearance.     

Computation of unsteady viscous flow around a locally flexible airfoil at low Reynolds number

A numerical method for fluid–structure interaction is presented for the analysis of unsteady viscous flow over a locally flexible airfoil. The Navier–Stokes equations are solved by ALE–CBS algorithm, coupling with a structural solver with large deformation. Following the validation of the method, a numerical example for the flight of micro-air vehicles at low Reynolds number is chosen for the computation. The coupling effect of flexible structure with different elastic stiffness on aerodynamic performance is demonstrated. A noticeable camber effect is induced by the deflection of the structure as the elastic stiffness of the structure goes smaller. Moreover, when the vibrating frequencies of the structure with smaller elastic stiffness have a close correlation with the shedding frequencies, the positive impact of the vibration of local flexible surface on the lift of the airfoil is highlighted, which results from the formation of the coherent vortices.     

Self-sustained aeroelastic oscillations of a NACA0012 airfoil at low-to-moderate Reynolds numbers

A wind tunnel experimental investigation of self-sustained oscillations of an aeroelastic NACA0012 airfoil occurring in the transitional Re regime is presented. To the authors’ knowledge this is the first time that aeroelastic limit cycle oscillations (LCOs) associated with low Re effects have been systematically studied and reported in the public literature. While the aeroelastic apparatus is capable of two-degree-of-freedom pitch-plunge motion, the present work concerns only the motion of the airfoil when it is constrained to rotate in pure pitch. The structural stiffness is varied as well as the position of the elastic axis; other parameters such as surface roughness, turbulence intensity and initial conditions are also briefly discussed. In conjunction with the pitch measurements, the flow is also recorded using hot-wire anemometry located in the wake at a distance of one chord aft of the trailing edge. It is observed that for a limited range of chord-based Reynolds numbers, 4.5×10⁴Re_c1.3×10⁵, steady state self-sustained oscillations are observed. Below and above that range, these oscillations do not appear. They are characterized by a well-behaved harmonic motion, whose frequency can be related to the aeroelastic natural frequency, low amplitude (θ_max<5.5°) and some sensitivity to flow perturbations and initial conditions. Furthermore, hot-wire measurements for the wing held fixed show that no periodicity in the undisturbed free-stream nor in the wake account for the oscillations. Overall, these observations suggest that laminar separation plays a role in the oscillations, either in the form of trailing edge separation or due to the presence of a laminar separation bubble.     

随机湍流工况低雷诺数风力机翼型优化研究

为改善小型风力机随机湍流工况适应性,以NACA0012翼型为研究对象,采用非嵌入式概率配置点法,获得随机湍流工况下小型风力机叶片翼型运行攻角分布规律;在气动优化中耦合层流分离预测,基于Transition SST模型、拉丁超立方试验设计、Kriging模型和带精英策略非支配排序遗传算法NSGA-II进行高湍流低雷诺数风力机翼型气动优化。结果表明,优化翼型叶片平均风能捕获效率分别提高3.01%和4.76%,标准差分别降低4.76%和14.93%,优化翼型湍流适应性增强。该方法将翼型设计与湍流风况相匹配,为湍流工况低雷诺数翼型及小型风力机设计提供参考。     

Approximate solutions for power-law fluid flow past a particle at low Reynolds numbers

A simple perturbation approximation is proposed for describing flow behaviour of particles immersed in a uniform flow and an extensional flow of power-law fluids. The present solution for particles in a uniform flow field is in good agreement with the numerical solution in the literature. Theoretical predictions indicate that the effect of pseudoplasticity on flow around particles in an extensional flow field is small compared with that for particles in a uniform flow field.From the viewpoint of perturbation techniques, existing analytical solutions based on linearization of the equations of motion for particle in a power-law fluid are re-examined. Mass transfer to a power-law fluid from a particle is also discussed.     

Comparative studies of numerical methods for evaluating aerodynamic characteristics of two-dimensional airfoil at low Reynolds numbers

This study investigates the predictability of the aerodynamic performance of some numerical methods at low Reynolds numbers and their dependency on the geometric shape of airfoil. We conducted three-dimensional large-eddy simulations (3-D LES), two-dimensional laminar simulations (2-D Lam), and Reynolds-averaged Navier–Stokes simulations with Baldwin–Lomax (2-D RANS(BL)) and Spalart–Allmaras (2-D RANS(SA)) turbulence models. Although there is little discrepancy between the 3-D LES, 2-D Lam, and 2-D RANS(SA) results in terms of the lift and drag characteristics, significant differences are observed in the predictability of the separation and reattachment points. The predicted lift, separation, and reattachment points of the 2-D Lam are qualitatively similar to those of the 3-D LES, except for high angles of attack at which a massive separation occurs. The 2-D RANS(SA) shows good predictability of the lift and separation points, but it does not estimate reattachment points accurately. The 2-D RANS(BL) fails to predict the precise separation points, which results in a poor lift predictability. These characteristics appear regardless of the airfoil geometry shapes. The results suggest that a 2-D Lam without any turbulence models can be used to estimate qualitative airfoil aerodynamic characteristics at the low Reynolds numbers.     

The wake of falling disks at low Reynolds numbers

We visualized the wake structure of circular disks falling vertically in quiescent water.The evolution of the wake was shown to be similar to the flow patterns behind a fixed disk.The Reynolds number,Re = Ud/ν,is in the range of 40 200.With the ascension of Reynolds numbers,a regular bifurcation occurred at the first critical Reynolds number Re c 1,leading to a transition from an axisymmetric wake structure to a plane symmetric one;A Hopf bifurcation took place at the second critical Reynolds number Re c 2,as the wake structure became unsteady.Plane symmetry of the wake structure was first lost as periodic vortex shedding appeared,but recovered at higher Reynolds number.The difference between the two critical Reynolds numbers was found to be shape-dependent,as we compared our results for thin discs with those for other falling bodies,such as spheres and cones.This observation could be understood in terms of the instability mechanism of the vortical structure.     

An eigenfunction solution of entry flow in a semi-infinite pipe at low Reynolds numbers

The developing flow in a semi-infinite pipe is solved for by an eigenfunction method. The results are applicable to zero and low Reynolds number flows. The eigenfunction method yields a solution which accurately predicts overshoots in the axial velocity for small axial positions. Results are presented for both uniform and non-uniform inlet conditions. The latter condition has important implications for numerical simulations of the developing flow problem.This research was performed while Mr Benson was a graduate student at Clarkson College, Potsdam, NY, USA.