Quarter-chord Axis Research Articles

Assessment of Turbulence Models for Unsteady Separated Flows Past an Oscillating NACA 0015 Airfoil in Deep Stall

This paper provides 2D Computational Fluid Dynamics (CFD) investigations, using OpenFOAM package, of the unsteady separated fully turbulent flows past a NACA 0015 airfoil undergoing sinusoidal pitching motion about its quarter-chord axis in deep stall regime at a reduced frequency of 0.1, a free stream Mach number of 0.278, and at a Reynolds number, based on the airfoil chord length, , of . First, eighteen 2D steady-state computations coupled with the SST model were carried out at various angles of attack to investigate the static stall. Then, the 2D Unsteady Reynolds-Averaged Navier-Stokes (URANS) simulations of the flow around the oscillating airfoil about its quarter-chord axis were carried out. Three eddy viscosity turbulence models, namely the Spalart-Allmaras, Launder-Sharma , and SST were considered for turbulence closure. The results are compared with the experimental data where the boundary layer has been tripped at the airfoil’s leading-edge. The findings suggest that the SST performs best among the other two models to predict the unsteady aerodynamic forces and the main flow features characteristic of the deep stall regime. The influence of moving the pitching axis downstream at mid chord was also investigated using URANS simulations coupled with the SST model. It was found that this induces higher peaks in the nose-down pitching moment and delays the stall onset. However, the qualitative behavior of the unsteady flow in post-stall remains unchanged. The details of the flow development associated with dynamic stall were discussed

Study of wake characteristics behind an oscillating NACA 0012 airfoil in deep dynamic stall regime

PurposeThis study aims to investigate the wake behind an oscillating airfoil at a various angle of incidence and Reynolds number in a deep dynamic stall condition.Design/methodology/approachNACA 0012 airfoil is allowed to undergo harmonic pitching motion about the quarter chord axis at Reynolds numbers of 0.5 * 105, 1.17 * 105, 1.7 * 105 and 2.12 * 105, and the reduced frequency of 0.1. The experiments are conducted at a set of mean and amplitude angle of attack that covered the angle of incidence from −5° to 25°. The wake rake is placed at a distance of one chord from the trailing edge of the airfoil.FindingsThe hysteresis of the flow during the upstroke and the downstroke motion are captured. The huge growth in the velocity defect and the wake thickness beyond the angle of attack of 15° explicate the appearance of the strong unsteady effects on the wake. The results also show that at the reduced frequency of 0.1, the wake structure is of drag producing type due to the momentum deficit.Originality/valueStreamwise velocity profile and the turbulent intensity profiles are presented to show the effects of Reynolds number and angle of incidence on the wake behind the oscillating airfoil at the reduced frequency of 0.1, and in the intermediate range of Reynolds number is the novelty of the study.

INFLUENCE OF SURFACE ROUGHNESS ON THE DYNAMIC STALL OF A ROTARY WING SECTION IN SUBSONIC FLOW

Wear involves the losses of some material from the surface and leads to the surface roughness. In the present work, the influence of surface roughness on the dynamic stall of a rotary wing section in subsonic flow has been investigated with different degree of surface roughness. The airfoil surface roughness was estimated using arithmetic mean roughness value (ISO-4287/1). For this purpose an indicial response method for unsteady, two dimensional flow is used to calculating the unsteady lift and pitching moment of NACA 0012 airfoil undergoing a pitching oscillation in the deep dynamic stall regime. Using the ANSYS-5.8 software as a source for the preliminary static data that required by the indicial method. The investigation is done through a number of test cases with different mean angles of attack, amplitude and reduced frequencies for airfoil oscillating around its quarter chord axis. The results include the time dependent behaviour and hysteresis loops of the lift and pitching moment for the airfoil with different degree of surface roughness. For rough airfoil an aerodynamic characteristic showed a reduction in the lift coefficient, separation point moved forward to the leading edge, the boundary layer reattachment take place at smaller angle of attack, the stall angle decrease and the pitching moment coefficient decrease as compared with smoother airfoil. So the periodic test must be done and re-coating the rotary wing if the surface roughness increased.

Inflatable Leading Edge-Based Dynamic Stall Control considering Fluid-Structure Interaction

The inflatable leading edge (ILE) is explored as a dynamic stall control concept. A fluid-structure interaction (FSI) numerical method for the elastic membrane structure is constructed based on unsteady Reynolds-averaged Navier-Stokes (URANS) and a mass-spring-damper (MSD) structural dynamic model. Radial basis function- (RBF-) based mesh deformation algorithm and Laplacian and optimization-based mesh smoothing algorithm are adopted in flowfield simulations to achieve the pitching oscillation of the airfoil and to ensure the mesh quality. An airfoil is considered at a freestream Mach number of 0.3 and chord-based Reynolds number of 3.92×106. The airfoil is pitched about its quarter-chord axis at a sinusoidal motion. The numerical results indicate that the ILE can change the radius of curvature of the airfoil leading edge, which could reduce the streamwise adverse pressure gradient and suppress the formation of dynamic stall vortex (DSV). Although the maximum lift coefficient of the airfoil is slightly reduced during the control process, the maximum drag and pitching moment coefficients of the airfoil are greatly reduced by up to 66% and 75.2%, respectively. The relative position of the ILE has a significant influence on its control effect. The control laws of inflation and deflation also affect the control ability of the ILE.

A combined airfoil with secondary feather inspired by the golden eagle and its influences on the aerodynamics

Bird flight is a remarkable adaption that has allowed thousands of species to colonize all terrestrial habitats. A golden eagle has impressive flying abilities, such as hovering, perching, preying and attacking. To reveal the flying abilities, avian geometry of a golden eagle was extracted based on noncontact surface measurements using a ROMBER three-dimensional laser scanner. Distributions of a camber line, thickness and a secondary feather line of the extracted point cloud were fitted using convenient analytical expressions. A traditional airfoil was established with the camber line and thickness, then a combined airfoil was constructed by combining the traditional airfoil with a secondary feather. Oscillations of an airfoil as well as rapid pitch up were simplified as a sine wave around the quarter chord axis. Thereafter, both steady and unsteady aerodynamic performances of the airfoil are computed, the influences of the secondary feather on the steady and unsteady aerodynamics were further studied.

Unsteady Flow Physics of Airfoil Dynamic Stall

A series of wind-tunnel experiments was conducted on a dynamically pitching NACA 0012 airfoil in order to understand the unsteady flow physics associated with dynamic stall at a transitional Reynolds number of . The airfoil was pitched about the quarter-chord axis following a linear ramp maneuver at . A series of high-frequency unsteady surface pressure measurements were acquired in order to investigate the time-dependent behavior of the flow in the immediate vicinity of the airfoil. These surface pressure measurements actively displayed the evolution of the airfoil boundary layer, leading-edge laminar separation bubble, and dynamic stall vortex. A detailed time-frequency analysis of surface pressure measurements was performed in order to identify the dominant frequencies associated with the unsteady laminar separation bubble. This analysis was also used to study the evolution of the length scales associated with flow structures near the airfoil leading edge, which emerged before the formation of the dynamic stall vortex. Finally, time-resolved particle image velocimetry measurements were acquired to study the evolution of the off-body flowfield during the development of dynamic stall.

Cross-correlation analysis of synchronized PIV and microphone measurements of an oscillating airfoil

The present study focuses on the correlation between the flow structures evolving during the dynamic stall processes of a two-dimensional NACA64-618 airfoil, which performs a sinusoidal movement about its quarter chord axis, and their aeroacoustic response in the far field. Experiments are conducted in an anechoic wind tunnel at a Reynolds number of $$8 \times 10^{5}$$ based on the chord length and include simultaneous velocity field measurements in the vicinity of the airfoil and microphone measurements in the acoustic far field. A causality correlation method based on phase locked snapshots of the velocity field allows for the identification of specific structures at different phases of the dynamic stall life cycle that contribute to the sound generation process. The sound emission during the stall development and flow reattachment phases is attributed to coherent structures evolving downstream of the trailing edge. When the flow is fully stalled, the region that contributes to the sound emission increases. The position of the sound emitting coherent structures also fluctuates stronger between oscillation cycles during full stall.

Analysis of Dynamic Stall on a Pitching Airfoil Using High-Fidelity Large-Eddy Simulations

The onset of unsteady separation and dynamic stall vortex formation over a constant-rate pitching airfoil is analyzed by means of high-fidelity large-eddy simulations. The flowfields are computed by employing a previously developed and extensively validated high-fidelity implicit large-eddy simulation approach based on high-order compact schemes. A NACA 0012 airfoil section is considered at a freestream Mach number of and chord-based Reynolds numbers of . The wing is pitched about its quarter-chord axis at a nominally constant nondimensional rate of from a small initial incidence to an angle of attack beyond the onset of dynamic stall. The unsteady boundary-layer behavior that precedes the dynamic stall vortex formation is described in detail. It is found that the process is characterized by the presence of a laminar separation bubble that contracts with increasing angle of attack as leading-edge suction builds up. Beyond a critical incidence, the laminar separation bubble breaks down and rapid suction collapse ensues. Abrupt turbulent separation follows, allowing the turbulent boundary-layer vorticity to coalesce into a coherent dynamic stall vortex. The remaining turbulent boundary-layer vorticity rolls up into a shear-layer vortex that imparts a much weaker signature on the surface pressure. Maximum surface pressure fluctuations of very high frequency are observed near the leading edge just before laminar separation bubble bursting. The fluctuation level drops significantly as the shear layer moves away from the airfoil surface.

Influence of Rotation on Dynamic Stall

A computational investigation of the effect of rotation on two-dimensional (2D) deep dynamic stall has been undertaken, showing that the effect of rotation is to reduce the severity of the pitching moment peak and cause earlier reattachment of the flow. A generic single blade rotor geometry was investigated, which had a pitching oscillation around the quarter-chord axis while in hover, causing angle-driven dynamic stall. The results at the midpoint of the blade have the same Mach number (0.31), Reynolds number (1.15 × 106), and pitching motion (α = 13° ± 7°) as a dynamic stall test case for which significant experimental wind tunnel data and 2D computations exist. The rotating blade is compared with 2D computations and computations using the same blade without rotation at Mach 0.31 and with the same pitching motion. All test cases involve geometries propagating into undisturbed flow with no downwash. The three-dimensional (3D) grid computed without rotation had lower lift at the reference section than for a 2D computation with the same geometric angle of attack time history, and the lift overshoot classically observed for Spalart–Allmaras turbulence models during 2D dynamic stall was significantly reduced in the 3D case. Rotation reduced the strength of the dynamic stall vortex, which reduced the accompanying pitching moment peak by 25%.

Measurements of velocity Field in the wake of an oscillating wind turbine blade

AbstractA series of tests were carried out to study the unsteady wake behaviour behind an aerofoil which is a section of a wind-turbine blade. The model is oscillated in pitch about its quarter chord axis at various reduced frequencies, amplitudes, and mean angles-of-attack. Instantaneous and mean velocity profiles were obtained using total and static pressure at 35 vertically aligned points behind the aerofoil via two similar rakes. The rakes were located at a distance of 1·5 chord length behind the model. An estimation of the real time and average variations of the linear momentum deficit during the oscillation cycle is obtained and has been compared with the corresponding static data. The results show that oscillation amplitude and reduced frequency have pronounced effects on the wake characteristics.

Two-Dimensional Aerodynamic Models of Insect Flight for Robotic Flapping Wing Mechanisms of Maximum Efficiency

In the “modified quasi-steady” approach, two-dimensional (2D) aerodynamic models of flapping wing motions are analyzed with focus on different types of wing rotation and different positions of rotation axis to explain the force peak at the end of each half stroke. In this model, an additional velocity of the mid chord position due to rotation is superimposed on the translational relative velocity of air with respect to the wing. This modification produces augmented forces around the end of each stroke. For each case of the flapping wing motions with various combination of controlled translational and rotational velocities of the wing along inclined stroke planes with thin figure-of-eight trajectory, discussions focus on lift-drag evolution during one stroke cycle and efficiency of types of wing rotation. This “modified quasi-steady” approach provides a systematic analysis of various parameters and their effects on efficiency of flapping wing mechanism. Flapping mechanism with delayed rotation around quarter-chord axis is an efficient one and can be made simple by a passive rotation mechanism so that it can be useful for robotic application.

Vortex-shedding characteristics in the wake of an oscillating airfoil at low Reynolds number

An experimental investigation was carried out to study the unsteady characteristics of vortex shedding in the near wake of an oscillating airfoil. The airfoil was given a harmonic pitching motion about the quarter-chord axis at four reduced frequencies: 0.1, 0.2, 0.3, and 0.4. The mean incidence and the oscillating amplitude were 0° and 3°, respectively. The velocity in the wake was measured by hot-wire anemometry. Smoke-wire visualization was also carried out to look into the link between the boundary layer flow and the shedding frequency variation. To analyze the frequency characteristics of the vortex shedding, we composed a short-time spectrum by the autoregressive (AR) method and a moving window. It was found that the shedding frequency in the wake of oscillating airfoil was much different from that for the case of steady airfoil at a given angle of attack, implying that the state of the boundary layer dictated the vortex-shedding characteristics. The vortex-shedding frequency was found to vary with the phase angle of oscillation, not with the angle of attack, for a given reduced frequency. The range of variation of the shedding frequency was diminished as the reduced frequency of oscillation increased.

Two-dimensional structure of the wake behind a pitching airfoil with higher non-dimensional pitching rate

Two-dimensional flow patterns have been visualized by two kinds of dyes and a VTR camera in a water tunnel at Re = 4.0 ×10³ in order to study how flow patterns of vortex changed behind a pitching airfoil with various pitching rates and pitching amplitudes. The tested airfoil was NACA0010. The experiment was performed under the conditions such as the pitching motions with sinusoidal or triangular wave around its mid- or quarter-chord axis. The non-dimensional pitching rates were k = 1.97, 2.81 and 4.22. The pitching amplitudes were changed as A = ±2·, ±6· and ±12·, however the mean angle of attack was fixed at α_m = 0·. As a result, the followings were clarified. The flow pattern of thrust producing vortex street was observed in the wake behind the pitching airfoil with a higher non-dimensional pitching rate. Similar flow patterns of the vortex were observed in spite of the differences in the location of pitching motion axis, in the pitching motion wave profile and in the pitching amplitude. Moreover, the pitching motion around the quarter-chord axis with triangular wave could realize the thrust producing vortex street more easily.

Effects of Initial Acceleration on the Flow Field Development Around Rapidly Pitching Airfoils

Computational results are presented to show how the acceleration period at the start of nominally constant pitch rate trajectories affects the dynamic stall process. Large amplitude motions of an NACA 0012 airfoil pitching about the quarter-chord axis were studied using constant (ON/OFF) acceleration profiles with nondimensional acceleration periods ranging between 0.039 to 0.6, and large pitch rates (0.1 ≤ Ω* ≡ α˙ c/2U∞≤0.4). The initial acceleration is observed to affect the integrated loads, surface pressure distribution, and the evolution of reversed flow regions just above the surface of the airfoil only during the acceleration period and for a relatively short time δτ ≤ 0.25 afterwards; τ≡ tU∞/c. After that time, all of these quantities only depend on the instantaneous angle of attack for a given pitch rate. These results are consistent with and explain previous experimental flow visualization observations. The onset of leading edge separation at high and low pitch rates is shown to be characterized by different processes. At low pitch rates leading edge separation occurs after the reversed flow front originating at the trailing edge has reached the leading edge. At higher pitch rates leading edge separation and the upstream progression of the (trailing edge) reversed flow front develop independently.

Application of Transonic Codes to Flutter Analysis of Conventional and Supercritical Airfoils

Transonic flutter analyses are performed for two conventional airfoils, NACA 64A006 and NACA 64A010, and three supercritical airfoils, MBB A-3, CAST 7, and the NASA TF-8A wing section at 65.3% semispan. Two degrees of freedom, plunging and pitching about the quarter-chord axis, are considered. The aerodynamic data are obtained by using the two transonic aerodynamics codes LTRAN2 (indicial and time integration methods) and STRANS2/UTRANS2 (harmonic analysis method). The unsteady aerodynamic data are computed within the low reduced frequency range. For all airfoils, the effect of Mach number on flutter speed is studied for several values of four different aeroelastic parameters. For the MBB A-3 supercritical airfoil, the effect of angle of attack on flutter speed is studied. For the cases of a flat plate and a NACA 64A006 airfoil, time response results are obtained by LTRAN2. Applicability and limitations of the two transonic codes are evaluated. Results for the transonic flutter characteristics of these airfoils are discussed and some comparisons are made. ah b,c

Constrained and Unconstrained Flow about a Pitching Foil

HIS paper presents a numerical method of evaluating the unsteady flows around lifting profiles in motion in a twodimensional perfect fluid. A particular study is made of quasisteady flow about a rigid foil of RAE 104 profile in pitching oscillation about the quarter-chord axis with a zero incidence mean. The effects of flow constraint from equidistant parallel walls is presented, together with corresponding results. Contents In an early analysis of two-dimension al unsteady motion,! a potential flow theory for small-amplitude pitching oscillations of thin aerofoils made the assumption that the wake vortices moved downstream in a single plane at the velocity of the undisturbed fluid. A later analytical method included the effects of aerofoil thickness and a possible oscillation of the rear stagnation point.2 A numerical method for unsteady two-dimensional flow of a perfect fluid around moving bodies of arbitrary cross section3'4 was developed from a steady flow method5'6 in which the lifting profile was represented by a distribution of source and vortex elements. In the following numerical model, a moving profile with a defined trailing edge is represented by n uniform straight source segments of strength ajf j=l...n, arranged segmentally around the profile. In general, a circulation TC occurs about the profile which is represented by a distribution of m vortices of strength yjf j=\,...,m, located within the profile. The flow is considered for successive instants at times / = 0, t = eAt, e = l,2,3..., during the motion, and the following conditions are imposed at each instant: 1) The normal flow velocity component at the center / of each line source segment is equal to the corresponding velocity component of the segment. 2) The flow velocity component at the trailing edge in the direction normal to the bisector of the trailing-edge angle equals the velocity component of the trailing edge in that direction. Hence no discontinuity is permitted between the upper and lower surface tangential velocities at the trailing edge, and the Kutta condition is satisfied at each instant. In unsteady flow, a change in the profile circulation TC is associated with net transport of vorticity from the profile boundary layers into the wake. This is represented in the model by the detachment of a discrete vortex element of constant strength TWJ from the trailing edge during each time interval between successive instants. Hence the Kutta condition essentially is relaxed during each time interval. After detachment, the vortex elements convect downstream to represent the wake and form an integral part of the flow calculation. The total circulation r on a closed path taken around the foil and wake is constant and equal to the circulation at the commencement of the motion. Hence,

Theoretical Pressure Distributions for a Thin Airfoil Oscillating in Incompressible Flow

Formulas are derived for the theoretical pressures acting on a thin airfoil and aileron combination oscillating with harmonic motion of small amplitude in incompressible flow. Calculations of pressure distribution are made at several representative values of the frequency parameter 1/k for airfoil translation, for airfoil rotation about the quarter-chord, and for hinged-surface flapping motions. The tabulated data thus obtained are plotted. INTRODUCTION T FORCES AND MOMENTS for the harmonically oscillating airfoil have previously been •derived by Theodorsen without the pressure formulas having been explicitly stated. A number of German pape r s 2 6 have been written covering various phases of the subject. Of these, Dietze has developed pressure formulas (for translation, pitch about the leading edge, and control surface flapping) which, when referred to the quarter-chord axis, can be shown to be in agreement with those developed in this paper. In these German investigations, as in Theodorsen's, the primary objective was to obtain the lifts and moments; therefore, computations were not made to show typical pressure distributions. • In a recent investigation to determine the magnitude and phase of aileron hinge moments due to an aileron oscillating harmonically in a transonic airstream, pressure-measuring units were installed in the wing and aileron upper and lower surfaces to measure the oscillating pressures. The pressure pickups were designed specifically for the conditions existent in that test and were, therefore, not satisfactory for measuring the oscillating pressures a t the lower dynamic pressures of normal flight speeds. Formulas were derived and computations for theoretical oscillating pressures were made for the range of parameters expected in tha t test in order t ha t comparisons with the experimental pressures could be made. The derivations and the tables of computed pressures for the incompressible flow are presented below in anticipation of the development of . pressure-measuring techniques to check the theoretical flutter coefficients in the usual velocity range.