Characteristics of Flow Past a Symmetric Airfoil at Low Reynolds Number: A Nonlinear Perspective

2012 ◽  
Author(s):  
M. Saif Ullah Khalid ◽  
Imran Akhtar
Keyword(s):  
Reynolds Number ◽  
Period Doubling ◽  
Nonlinear Behavior ◽  
Phase Portraits ◽  
Aerodynamic Forces ◽  
Flow Past ◽  
Time Histories ◽  
Lift And Drag ◽  
Naca 0012 ◽  
Even Harmonics

Flow separation in airfoils have been extensively studied to analyze the underlying physics of the phenomenon. The phenomenon being nonlinear requires tools to reveal various features involving stall, bifurcation, and transition to chaos. In this study, we perform numerical simulations of the flow past a symmetric airfoil (NACA-0012) at 1,000 Reynolds number to compute the aerodynamic forces at different angles of attack (α). The time histories and spectral analysis reveal important features of nonlinear behavior in the flow around the airfoil. We find that the steady state temporal solutions for aerodynamic forces; lift and drag, contain both odd and even harmonics which indicate the presence of quadratic as well as cubic nonlinearity in the system. These results also help to understand nonlinear behavior of the system as a function of α. Considering the angle of attack for airfoil as a control parameter, we observe that to achieve the static stall, flow becomes chaotic adopting a route through period-doubling and quasi-periodic regimes. Using phase portraits and Poincare maps between the states of the system, period-doubling is observed in this nonlinear system at α = 22° leading to chaos at α = 27°.

A new method of solving Oseen’s equations and its application to the flow past an inclined elliptic cylinder

1954 ◽  
Vol 224 (1157) ◽  
pp. 141-160 ◽  
Keyword(s):  
Reynolds Number ◽  
Elliptic Cylinder ◽  
Cylindrical Body ◽  
Thickness Ratio ◽  
Successive Approximations ◽  
Angle Of Incidence ◽  
Mathieu Functions ◽  
Flow Past ◽  
Transcendental Functions ◽  
Lift And Drag

In this paper is developed a general method of solving Oseen’s linearized equations for a two-dimensional steady flow of a viscous fluid past an arbitrary cylindrical body. The method is based on the fact that the velocity in the neighbourhood of the cylinder can be generally expressed in terms of a pair of analytic functions, the determination of which from the appropriate boundary condition can be effected by successive approximations in powers of the Reynolds number, R . The method enables one to obtain the velocity distribution near the cylinder and the lift and drag acting on it in the form of power series in R , without recourse to manipulation of higher transcendental functions such as Bessel and Mathieu functions for circular and elliptic cylinders, respectively. As an example of the application of the method, the uniform flow past an elliptic cylinder at an arbitrary angle of incidence is considered. Analytical expressions for the lift and drag coefficients are obtained, which are correct to the order of R , the lowest order terms being O ( R -1 ) and numerical calculations are carried out for the thickness ratio t = 0, 0.1, 0.5, 1 and the Reynolds number R = 0.1, 1. It is found that drag increases slightly with increase of either thickness ratio or angle of incidence, and that lift decreases with increase of thickness ratio while, as a function of the angle of incidence, it has a maximum at about 45°.

scholarly journals An Experimental Analysis on the Effects of Stagger on the Aerodynamic Forces of Tandem Wings

AVIA ◽  
2021 ◽  
Vol 2 (2) ◽  
Author(s):  
Y Parlindungan ◽  
S Tobing
Keyword(s):  
Experimental Analysis ◽  
Numerical Study ◽  
Lift Coefficient ◽  
Angle Of Attack ◽  
Aerodynamic Performance ◽  
Open Loop ◽  
Aerodynamic Forces ◽  
Subsonic Wind Tunnel ◽  
Lift And Drag ◽  
Naca 0012

This study is inspired by the flapping motion of natural flyers: insects. Many insects have two pairs of wings referred as tandem wings. Literature review indicates that the effects of tandem wing are influenced by parameters such as stagger (the stream-wise distance between the aerodynamic center of the front and the rear airfoil), angle-of-attack and flow velocity. As a first stage, this study focuses on the effects of stagger (St) on the aerodynamic performance of tandem wings. A recent numerical study of stagger on tandem airfoils in turbulent flow (Re = 6000000) concluded that a larger stagger resulted in a decrease in lift force, and an increase in drag force. However, for laminar flow (Re = 2000), increasing the stagger was not found to be detrimental for aerodynamic performance. Another work also revealed that the maximum lift coefficient for a tandem configuration decreased with increasing stagger. The focus of this study is to perform an experimental analysis of tandem two-dimensional (2D) NACA 0012 airfoils. The two airfoils are set at the same angle-of-attack of 0° to 15° with 5° interval and three variations of stagger: 1c, 1.5c and 2c. The experiments are conducted using an open-loop-subsonic wind tunnel at a Reynolds number of 170000. The effects of St on the aerodynamic forces (lift and drag) are analyzed

Effect of Tube Spacing on the Vortex Shedding Characteristics of Laminar Flow Past an Inline Tube Array

2008 ◽  
Author(s):  
C. Liang ◽  
X. Luo ◽  
G. Papadakis
Keyword(s):  
Reynolds Number ◽  
Vortex Shedding ◽  
Unstructured Grid ◽  
Flow Patterns ◽  
Instantaneous Flow ◽  
Flow Past ◽  
Recirculation Zones ◽  
Shedding Frequency ◽  
Drag And Lift ◽  
Lift And Drag

The effect of tube spacing on the vortex shedding characteristics and fluctuating forces in an inline tube array is examined. The array consists of 6 cylinders in tandem, the examined Reynolds number is 100 and the flow is laminar. The numerical methodology and the code employed to solve the equations in an unstructured grid are validated against available results from the literature for the flow past two cylinders in tandem. Computations are then performed for the 6 row inline bank for 8 pitch-to-diameter ratios s ranging from 2.1 to 4. The instantaneous flow patterns are visualised for different spacings and the lift and drag coefficients for all cylinders are recorded and analysed. At the smallest spacing examined (s = 2.1) there are five stagnant and symmetric recirculation zones and weak vortex shedding activity occurs behind the last cylinder only. As s increases, the symmetry of the recirculation zones breaks leading to vortex shedding. This process progressively moves upstream, so that for s = 4 there is clear shedding for every row. The shedding frequency behind each cylinder is the same and increases with tube spacing. A spacing region between 3d and 3.6d is identified, within which rms drag and lift coefficients attain maximum values. This behaviour is explained with the aid of instantaneous flow patterns.

scholarly journals Very Large-Eddy Simulations of the Flow Past an Oscillating Cylinder at a Subcritical Reynolds Number

2020 ◽  
Vol 10 (5) ◽  
pp. 1870
Author(s):  
Zhongying Xiong ◽  
Xiaomin Liu
Keyword(s):  
Reynolds Number ◽  
Vortex Shedding ◽  
Lift Coefficient ◽  
Vortex Pair ◽  
Excitation Amplitude ◽  
Oscillating Cylinder ◽  
Flow Past ◽  
Large Eddy ◽  
Lift And Drag ◽  
Strong Vortex

This work focuses on flow past a circular cylinder at a subcritical Reynolds number. Although this classical study has been a concern for many years, it is still a challenging task due to the complexity of flow characteristics. In this paper, a high-efficiency very large-eddy simulation method is adopted and verified in order to handle the oscillating boundary. A series of numerical simulations are conducted to investigate the transient flow around the oscillating cylinder. The results show that the vortex shedding mode varies with an increase in the excitation amplitude and the excitation frequency. Vortex shedding is a lasting process under the condition of a low excitation amplitude that leads to irregular fluctuations of the lift and drag coefficients. For a vortex shedding mode that exhibits a strong vortex pair and a weak vortex pair or a weak single vortex, the temporal evolution of the lift coefficient of the oscillating cylinder shows irregular ”jumping” at a specific time per cycle corresponding to the shedding of the strong vortex pair. The vortex shedding mode and the frequency and time of the vortex shedding co-determine the temporal evolutions of the lift and drag coefficient.

Numerical Study of Aerodynamic Forces of Two Airfoils in Tandem Configuration at Low Reynolds Number

2021 ◽  
Author(s):  
N. Hosseini ◽  
M. Tadjfar ◽  
A. Abba
Keyword(s):  
Reynolds Number ◽  
Numerical Study ◽  
Low Reynolds Number ◽  
Aerodynamic Forces ◽  
Tandem Configuration ◽  
Pitching Airfoil ◽  
Reduced Frequency ◽  
Low Reynolds ◽  
Lift And Drag ◽  
Two Parameters

Abstract For a tandem airfoil configuration, an airfoil is placed in the wake of an upstream airfoil. This interaction affects the aerodynamic forces of the airfoils, especially the downstream one. In the present study a tandem configuration consists of an upstream pitching airfoil and a downstream stationary airfoil is investigated. This study aims to investigate the role of reduced frequency and pitch amplitude of the upstream airfoil’s motion on lift and drag coefficients of two airfoils. These two parameters play an important role in the formation of vortices. The investigation is done for Selig-Donovan 7003 (SD7003) airfoils at low Reynolds number of 30,000 using a computational fluid dynamics. Incompressible URANS equations were employed for solving the flow field. It was found that for a fixed reduced frequency of 0.5 thrust is produced on the hindfoil for a part of cycle for different pitch amplitudes from light to deep stall while for a fixed pitch amplitude at different reduced frequencies high level of thrust or drag can be produced. The reason is related to the type and intensity of vortex-blade interaction.

scholarly journals Effect of Reynolds Number on Aerodynamics of Airfoil with Gurney Flap

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Shubham Jain ◽  
Nekkanti Sitaram ◽  
Sriram Krishnaswamy
Keyword(s):  
Reynolds Number ◽  
Lift Coefficient ◽  
Angle Of Attack ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Critical Range ◽  
Gurney Flap ◽  
Stall Angle ◽  
Lift And Drag ◽  
Naca 0012

Steady state, two-dimensional computational investigations performed on NACA 0012 airfoil to analyze the effect of variation in Reynolds number on the aerodynamics of the airfoil without and with a Gurney flap of height of 3% chord are presented in this paper. RANS based one-equation Spalart-Allmaras model is used for the computations. Both lift and drag coefficients increase with Gurney flap compared to those without Gurney flap at all Reynolds numbers at all angles of attack. The zero lift angle of attack seems to become more negative as Reynolds number increases due to effective increase of the airfoil camber. However the stall angle of attack decreased by 2° for the airfoil with Gurney flap. Lift coefficient decreases rapidly and drag coefficient increases rapidly when Reynolds number is decreased below critical range. This occurs due to change in flow pattern near Gurney flap at low Reynolds numbers.

Loads on a Harmonically Oscillating Cylinder

2007 ◽  
Author(s):  
Osama A. Marzouk ◽  
Ali H. Nayfeh
Keyword(s):  
Reynolds Number ◽  
Spectral Analysis ◽  
Abrupt Change ◽  
Phase Portraits ◽  
Near Wake ◽  
Harmonic Motion ◽  
Synchronization Region ◽  
Second Mode ◽  
Shedding Frequency ◽  
Lift And Drag

A harmonic motion of a cylinder acts as a forcing source to the near wake. Depending on the amplitude and frequency of this motion, the lift exerted on the cylinder may be synchronized or not synchronized with the frequency of the motion. Here, we numerically investigate the behavior of the wake, particularly the induced forces on the cylinder, at a low Reynolds number when the forcing frequency is varied from half to twice the shedding frequency of the wake. Within the synchronization region, an abrupt change in the wake, reflected in a discontinuity in the lift, leads to two different flow modes. In the first mode, increasing the motion frequency causes the lift to increase; whereas in the second mode, this relation is reversed. We analyzed the behavior outside the synchronization region, where the lift is not synchronized with the motion. Poincare´ sections, phase portraits, and spectral analysis were used to characterize different behaviors (e.g., period-n, quasi-periodic, and chaos) of the lift and drag. Also, we performed nonstationary analysis in which the cylinder frequency was varied with different rates and observed typical nonstationary responses in which the jumps were eliminated.

Large Eddy Simulation of the Flow Past Pitching NACA0012 Airfoil at 1E5 Reynolds Number

2014 ◽  
Author(s):  
Venkata Ravishankar Kasibhotla ◽  
Danesh Tafti
Keyword(s):  
Reynolds Number ◽  
Flow Field ◽  
Three Dimensional ◽  
Dynamic Stall ◽  
Eddy Simulation ◽  
Naca0012 Airfoil ◽  
Flow Past ◽  
Reduced Frequency ◽  
Large Eddy ◽  
Naca 0012

The paper is concerned with the prediction and analysis of dynamic stall of flow past pitching NACA-0012 airfoil at 105 Reynolds number based on the chord length of the airfoil and at reduced frequency of 0.188 in a three dimensional flow field. The turbulence in the flow field is resolved using large eddy simulations with dynamic Smagorinsky model at the sub grid scale. The lift hysteresis plots indicate closer match to experimental results, although discrepancies exist during the downstroke. The development of dynamic stall vortex, vortex shedding and reattachment as predicted by the present study are discussed in detail. This study has shown that the downstroke phase of the pitching motion is strongly three dimensional and is highly complex, whereas the flow is practically two dimensional during the upstroke.

scholarly journals Heteroclinic Bifurcation Behaviors of a Duffing Oscillator with Delayed Feedback

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Shao-Fang Wen ◽  
Ju-Feng Chen ◽  
Shu-Qi Guo
Keyword(s):  
Necessary Conditions ◽  
Duffing Oscillator ◽  
Period Doubling ◽  
Melnikov Method ◽  
Threshold Value ◽  
Phase Portraits ◽  
Heteroclinic Bifurcation ◽  
Velocity Feedback ◽  
Time Histories ◽  
New Phenomena

The heteroclinic bifurcation and chaos of a Duffing oscillator with forcing excitation under both delayed displacement feedback and delayed velocity feedback are studied by Melnikov method. The Melnikov function is analytically established to detect the necessary conditions for generating chaos. Through the analysis of the analytical necessary conditions, we find that the influences of the delayed displacement feedback and delayed velocity feedback are separable. Then the influences of the displacement and velocity feedback parameters on heteroclinic bifurcation and threshold value of chaotic motion are investigated individually. In order to verify the correctness of the analytical conditions, the Duffing oscillator is also investigated by numerical iterative method. The bifurcation curves and the largest Lyapunov exponents are provided and compared. From the analysis of the numerical simulation results, it could be found that two types of period-doubling bifurcations occur in the Duffing oscillator, so that there are two paths leading to the chaos in this oscillator. The typical dynamical responses, including time histories, phase portraits, and Poincare maps, are all carried out to verify the conclusions. The results reveal some new phenomena, which is useful to design or control this kind of system.

scholarly journals A Parametric Study of Trailing Edge Flap Implementation on Three Different Airfoils Through an Artificial Neuronal Network

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 828
Author(s):  
Igor Rodriguez-Eguia ◽  
Iñigo Errasti ◽  
Unai Fernandez-Gamiz ◽  
Jesús María Blanco ◽  
Ekaitz Zulueta ◽  
...  
Keyword(s):  
Aerodynamic Coefficients ◽  
Trailing Edge ◽  
High Lift ◽  
Trailing Edge Flaps ◽  
Artificial Neural Network Ann ◽  
Lift And Drag ◽  
Artificial Neuronal Network ◽  
Naca 0012 ◽  
Drag Ratio ◽  
Lift To Drag Ratio

Trailing edge flaps (TEFs) are high-lift devices that generate changes in the lift and drag coefficients of an airfoil. A large number of 2D simulations are performed in this study, in order to measure these changes in aerodynamic coefficients and to analyze them for a given Reynolds number. Three different airfoils, namely NACA 0012, NACA 64(3)-618, and S810, are studied in relation to three combinations of the following parameters: angle of attack, flap angle (deflection), and flaplength. Results are in concordance with the aerodynamic results expected when studying a TEF on an airfoil, showing the effect exerted by the three parameters on both aerodynamic coefficients lift and drag. Depending on whether the airfoil flap is deployed on either the pressure zone or the suction zone, the lift-to-drag ratio, CL/CD, will increase or decrease, respectively. Besides, the use of a larger flap length will increase the higher values and decrease the lower values of the CL/CD ratio. In addition, an artificial neural network (ANN) based prediction model for aerodynamic forces was built through the results obtained from the research.

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