等速上仰翼型动态失速现象研究

翼型大迎角绕流的静态失速将造成升力突降和气动性能急剧恶化，但利用非定常运动所产生 的动态失速效应，可以大大地延缓气流分离和失速现象的发生. 采用Rogers发 展的双时间步Roe格式，求解拟压缩性修正不可压N-S方程. 数值模拟了低雷诺数 ($Re=4.8 \times 10^{4}$)条件下NACA0015翼型作等速上仰($\alpha =0^{\circ} \sim 60^{\circ}$)的动态失速过程，同Walker的试验结果比 较，验证了计算结果的正确性. 研究了该过程中主涡、二次涡和三次涡的发展，升 力系数随攻角变化，以及不同上仰速度对动态失速效应所造成的影响.     

Effect of uncertainty on the bifurcation behavior of pitching airfoil stall flutter

In this paper the effect of system parametric uncertainty on the stall flutter bifurcation behavior of a pitching airfoil is studied. The aerodynamic moment on the two-dimensional rigid airfoil with nonlinear torsional stiffness is computed using the ONERA dynamic stall model. The pitch natural frequency, a cubic structural nonlinearity parameter, and the structural equilibrium angle are assumed to be uncertain. The effect on the amplitude of the response, the bifurcation of the probability distribution, and the flutter boundary is considered. It is demonstrated that the system parametric uncertainty results already in 5% probability of pitching stall flutter at a 12.5% earlier position than the point where a deterministic analysis would predict unstable behavior. Probabilistic collocation is found to be more efficient than the Galerkin polynomial chaos method and Monte Carlo simulation for modeling uncertainty in the post-bifurcation domain.     

Investigation of the unsteady flow velocity field above an airfoil pitching under deep dynamic stall conditions

The unsteady flow field above a NACA 0012 airfoil pitching under deep dynamic stall conditions has been investigated in a low-speed wind tunnel by means of particle image velocimetry. The measurements of the instantaneous flow velocity field show the characteristic features of the dynamic stall process: formation and development of an organized vortex structure for increasing incidences and the subsequent separation. Vorticity and divergence estimated from the measured data give a good insight into the complex flow behaviour during the downstroke motion. Furthermore, small-scale structures could be observed in the separated flow field and even within the dynamic stall vortex.The authors would like to thank Dr. Schäfer (ISL) for his support in organizing the cooperative measurements, Mr. Seyb (DLR) for his help during the recording of PIV images, Dr. Bretthauer (DLR) and Mr. Vollmers (DLR) for his assistance during the phase of evaluation and post processing of the PIV recordings and Dr. Geißler (DLR) for helpful discussions on the dynamic stall problem.     

Calculation of dynamic stall on an oscillating airfoil

A mathematical model of an unsteady separated flow around an oscillating airfoil is considered. This model is based on a viscid-inviscid approach. The points of separation and the intensity of vorticity displaced into the external flow are determined using boundary-layer equations in an integral form. Dynamic stall on an oscillating airfoil is studied. The mechanism and nature of antidamping are discovered. Novosibirsk State Technical University, Novosibirsk 630092. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 81–85, May–June, 2000.     

Simulation of dynamic stall for a NACA 0012 airfoil using a vortex method

The unsteady, incompressible, viscous laminar flow over a NACA 0012 airfoil is simulated, and the effects of several parameters investigated. A vortex method is used to solve the two-dimensional Navier–Stokes equations in the vorticity/stream-function form. By applying an operator-splitting method, the “convection” and “diffusion” equations are solved sequentially at each time step. The convection equation is solved using the vortex-in-cell method, and the diffusion equation using a second-order ADI finite difference scheme. The airfoil profile is obtained by mapping a circle in the computational domain into the physical domain through a Joukowski transformation. The effects of several parameters are investigated, such as the reduced frequency, mean angle of attack, location of pitch axis, and the Reynolds number. It is observed that the reduced frequency has the most influence on the flow field.     

An investigation on the lift force of a wing pitching in dynamic stall for a comfort control vessel

On the basis of a comfort control system for ocean vessels, the control forces and moments in the form of lift forces from active wings are of important interest. In an ocean vessel comfort control system, active wings or fins are commonly used and constantly adjust their angles of attack to produce optimal sea-keeping conditions. The unsteady nature of the flow field around a wing, and the behaviour of the generated lift force must be understood in order to optimize the comfort control system. This paper presents experimental data on the flow past a pitching wing, paying particular attention to the lagging effects between the fluid dynamic lift force and the motion of the wing at large angles of attack as a function of peak angle of attack and reduced frequency of oscillation. The range of motion investigated has been chosen according to the applicability of a comfort control wing surface. Numerical data is also included to aid explanation on some of the witnessed phenomena.     

Investigation of three-dimensional dynamic stall on an airfoil using fast-response pressure-sensitive paint

Dynamic stall on a pitching OA209 airfoil in a wind tunnel is investigated at Mach 0.3 and 0.5 using high-speed pressure-sensitive paint (PSP) and pressure measurements. At Mach 0.3, the dynamic stall vortex was observed to propagate faster at the airfoil midline than at the wind-tunnel wall, resulting in a “bowed” vortex shape. At Mach 0.5, shock-induced stall was observed, with initial separation under the shock foot and subsequent expansion of the separated region upstream, downstream and along the breadth of the airfoil. No dynamic stall vortex could be observed at Mach 0.5. The investigation of flow control by blowing showed the potential advantages of PSP over pressure transducers for a complex three-dimensional flow.     

Computational study of a pitching bio-inspired corrugated airfoil

The phenomenon of insect flight has been of scientific interest for many years and is more recently inspiring modern engineering devices such as Micro Aerial Vehicles (MAVs). Insect flight is characterized by unsteady fluid dynamics at low Reynolds numbers. The importance of viscous effects to the successful flapping flight of insects has been identified and with the current state of computing and Computational Fluid Dynamics (CFD) these effects can now be studied in detail. The present work attempts to simplify this complex phenomenon by considering symmetric oscillating rotational motion of a wing (pitching). What is of interest in this study is how the shape of a corrugated idealized insect wing affects the performance and flow characteristics around the pitching wing. Two dimensional CFD on an oscillating wing has been performed and reported. Measurements were taken to ensure the accuracy of the computational solution and the results validated against experimental PIV results. A range of frequencies and rotational amplitudes have been investigated. Lift and drag coefficients have been analyzed for all cases to quantify the effects of unsteady flow features on the performance of the oscillating wing. It was found that the wing shape used in this study resulted in the viscous features formed on the top of the wing exhibiting high sensitivity to the oscillating conditions and these influenced the performance of the wing. The flow features formed on the bottom of the wing remained similar throughout the cases tested. In the pitching regime this wing profile did not perform as well as published results for smooth airfoils in terms of thrust and propulsion efficiency. However this may be due to reduced frequency effects becoming important at our high pitching amplitude which need to be investigated further. There may be other oscillatory regimes that more accurately represent flapping flight in which the corrugated foil outperforms a smooth counterpart but these are yet to be investigated. Further research in this area may help answer the question as to how evolutionarily significant other benefits of a corrugated wing, such as being light and strong, are compared to its aerodynamic properties, the present results seem to favor the former.     

Numerical investigations into the asymmetric effects on the aerodynamic response of a pitching airfoil

The effects of asymmetric sinusoidal motion on pitching airfoil aerodynamics were studied by numerical simulations for 2-D flow around a NACA0012 airfoil at Re=1.35×10⁵. Various unsteady parameters (amplitude of oscillation, d; reduced frequency, k) were applied to investigate the effect of asymmetry parameter S on the instantaneous force coefficients and flow patterns. The results reveal that S has a noticeable effect on the aerodynamic performance, as it affects the instantaneous force coefficient, maximum lift and drag coefficient, hysteresis loops and the flow structures.     

Influence of heat transfer on the aerodynamic performance of a plunging and pitching NACA0012 airfoil at low Reynolds numbers

The unsteady low Reynolds number aerodynamics phenomena around flapping wings are addressed in several investigations. Elsewhere, airfoils at higher Mach numbers and Reynolds numbers have been treated quite comprehensively in the literature. It is duly noted that the influence of heat transfer phenomena on the aerodynamic performance of flapping wings configurations is not well studied. The objective of the present study is to investigate the effect of heat transfer upon the aerodynamic performance of a pitching and plunging NACA0012 airfoil in the low Reynolds number flow regime with particular emphasis upon the airfoil's lift and drag coefficients. The compressible Navier–Stokes equations are solved using a finite volume method. To consider the variation of fluid properties with temperature, the values of dynamic viscosity and thermal diffusivity are evaluated with Sutherland's formula and the Eucken model, respectively. Instantaneous and mean lift and drag coefficients are calculated for several temperature differences between the airfoil surface and freestream within the range 0–100 K. Simulations are performed for a prescribed airfoil motion schedule and flow parameters. It is learnt that the aerodynamic performance in terms of the lift C_L and drag C_D behavior is strongly dependent upon the heat transfer rate from the airfoil to the flow field. In the plunging case, the mean value of C_D tends to increase, whereas the amplitude of C_L tends to decrease with increasing temperature difference. In the pitching case, on the other hand, the mean value and the amplitude of both C_D and C_L decrease. A spectral analysis of C_D and C_L in the pitching case shows that the amplitudes of both C_D and C_L decrease with increasing surface temperature, whereas the harmonic frequencies are not affected.     

Dynamic mode decomposition based analysis of flow over a sinusoidally pitching airfoil

Dynamic mode decomposition (DMD) has proven to be a valuable tool for the analysis of complex flow-fields but the application of this technique to flows with moving boundaries is not straightforward. This is due to the difficulty in accounting in the DMD formulation, for a body of non-zero thickness moving through the field of interest. This work presents a method for decomposing the flow on or near a moving boundary by a change of reference frame, followed by a correction to the computed modes that is determined by the frequency spectrum of the motion. The correction serves to recover the modes of the underlying flow dynamics, while removing the effect of change in reference frame. This method is applied to flow over sinusoidally pitching airfoils, and the DMD analysis is used to derive useful insights regarding flow-induced pitch oscillations of these airfoils.     

Bifurcations in the transonic flow past a symmetric airfoil

Transonic flow past an airfoil with a small curvature in its midchord region is numerically investigated. The branching of the stationary solutions of the Euler equations is established and attributed to flow instability at certain angles of attack and freestream Mach numbers. The dependence of the lift coefficient on these parameters is studied.     

An experimental study of the effects of pitch-pivot-point location on the propulsion performance of a pitching airfoil

An experimental investigation was conducted to characterize the evolution of the unsteady vortex structures in the wake of a pitching airfoil with the pitch-pivot-point moving from 0.16C to 0.52C (C is the chord length of the airfoil). The experimental study was conducted in a low-speed wind tunnel with a symmetric NACA0012 airfoil model in pitching motion under different pitching kinematics (i.e., reduced frequency k=3.8–13.2). A high-resolution particle image velocimetry (PIV) system was used to conduct detailed flow field measurements to quantify the characteristics of the wake flow and the resultant propulsion performance of the pitching airfoil. Besides conducting “free-run” PIV measurements to determine the ensemble-averaged velocity distributions in the wake flow, “phase-locked” PIV measurements were also performed to elucidate further details about the behavior of the unsteady vortex structures. Both the vorticity–moment theorem and the integral momentum theorem were used to evaluate the effects of the pitch-pivot-point location on the propulsion performance of the pitching airfoil. It was found that the pitch-pivot-point would affect the evolution of the unsteady wake vortices and resultant propulsion performance of the pitching airfoil greatly. Moving the pitch-pivot-point of the pitching airfoil can be considered as adding a plunging motion to the original pitching motion. With the pitch-pivot-point moving forward (or backward), the added plunging motion would make the airfoil trailing edge moving in the same (or opposite) direction as of the original pitching motion, which resulted in the generated wake vortices and resultant thrust enhanced (or weakened) by the added plunging motion.     

Numerical simulation of thin airfoil stall by using a modified DES approach

The detached‐Eddy simulation (DES) method was applied to calculate pre‐ and post‐stall aerodynamic characteristics of airfoil stall. A discrepancy between numerical and experimental data was observed near the stall regime for the airfoil NACA64_A‐ 006 which is a thin airfoil stall type. The reason of this discrepancy and one possible way for improvement of the numerical model are discussed here. It is shown that the use of the Baldwin–Lomax model in the RANS region improves the DES results in this case. If the relevant factors (grid density, time step, turbulence model, etc.) are appropriately taken into account, the DES approach could reliably predict stall aerodynamical characteristics. Copyright © 2006 John Wiley & Sons, Ltd.     

An investigation into the effects of unsteady parameters on the aerodynamics of a low Reynolds number pitching airfoil

The growing applications of low Reynolds number (LRN) operating vehicles impose the need for accurate LRN flow solutions. These applications usually involve complex unsteady phenomena, which depend on the kinematics of the vehicle such as pitching, plunging, and flapping of a wing. The objective of the present study is to address the issues related to LRN aerodynamics of a harmonically pitching NACA0012 airfoil. To this end, the influence of unsteady parameters, namely, amplitude of oscillation, d, reduced frequency, k, and Reynolds number, Re, on the aerodynamic performance of the model is investigated. Computational fluid dynamics (CFD) is utilized to solve Navier–Stokes (N–S) equations discretized based on the Finite Volume Method (FVM). The resulting instantaneous lift coefficients are compared with analytical data from Theodorsen’s method. The simulation results reveal that d, k, and Re are of great importance in the aerodynamic performance of the system, as they affect the maximum lift coefficients, hysteresis loops, strength, and number of the generated vortices within the harmonic motion, and the extent of the so-called figure-of-eight phenomenon region. Thus, achieving the optimum lift coefficients demands a careful selection of these parameters.     

Wake structure and aerodynamic characteristics of an auto-propelled pitching airfoil

In the present study, we investigate the wake configuration as well as the flow aerodynamic and propulsive characteristics of a system equipped with a nature-inspired propulsion system. The study focuses on the effect of a set of pitching frequency and amplitude values on the flow behavior for a symmetric foil performing pitching sinusoidal rolling oscillations. The viscous, non-stationary flow around the pitching foil is simulated using ANSYS FLUENT 13. The foil movement is reproduced using the dynamic mesh technique and an in-house developed UDF (User Define Function). Our results show the influence of the pitching frequency and the amplitude on the wake. We provide the mechanisms relating the system behavior to the applied forces. The frequency varies from 1 to 400 Hz and the considered amplitudes are 18%, 24%, 30%, 37%, 53%, 82% and 114% of the foil chord.     

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.