Study of the aerodynamics of in-plane motion

2001 ◽  
Vol 215 (2) ◽  
pp. 89-104
Author(s):  
S T Shaw ◽  
N Qin
Keyword(s):  
Mach Number ◽  
Stokes Equations ◽  
Lift Coefficient ◽  
Transfer Operator ◽  
Unsteady Aerodynamics ◽  
Equation Model ◽  
Step Change ◽  
Phase Lag ◽  
Reduced Frequency ◽  
Advance Ratio

A computational analysis is performed of the unsteady aerodynamics associated with the blade sections of helicopter rotors in forward flight. The unsteady flow is studied through solutions of the two- dimensional Reynolds averaged Navier-Stokes equations together with a strongly coupled two-equation model of turbulence. Two motions are studied. The first motion is that of an aerofoil subjected to harmonic in-plane oscillations. The influence of advance ratio and reduced frequency is investigated. It is shown that, in the absence of shock waves, the flow is periodic with a reduced frequency equal to that of the forcing motion. However, the flow development lags behind the forcing motion. Furthermore, for constant reduced frequency the phase lag is independent of advance ratio. In addition to harmonic motion, the aerodynamic response to a step change in Mach number is investigated. Using an assumed form of the response of lift coefficient to a step change in Mach number, a lift transfer operator for step changes in Mach number is obtained in the Laplace domain. An analytical expression for the response to harmonic Mach number oscillations is then obtained from the transfer operator. The resulting formulation for the aerodynamic response confirms that the lag between the forcing motion and the aerodynamic response is independent of advance ratio.

The Low Reduced Frequency Limit of Vibrating Airfoils: Part II — Numerical Experiments

2015 ◽  
Author(s):  
Almudena Vega ◽  
Roque Corral
Keyword(s):  
Stokes Equations ◽  
Unsteady Aerodynamics ◽  
Mean Value ◽  
Navier Stokes ◽  
Influence Coefficient ◽  
Navier Stokes Equations ◽  
Unsteady Pressure ◽  
Reduced Frequency ◽  
Influence Coefficients ◽  
Frequency Regime

This paper studies the unsteady aerodynamics of vibrating airfoils in the low reduced frequency regime with special emphasis in its impact on the scaling of the work per cycle curves using an asymptotic approach (Part I) and numerical simulations. A perturbation analysis of the linearized Navier-Stokes equations at low reduced frequency is presented and some conclusions are drawn (Part I of the corresponding paper). The first important result is that the loading of the airfoil plays an essential role in the trends of the phase and modulus of the unsteady pressure field caused by the vibration of the airfoil. For lightly loaded airfoils the unsteady pressure and the influence coefficients scale linearly with the reduced frequency whereas the phase departs from π/2 and changes linearly with the reduced frequency. As a consequence the work-per-cycle is proportional to the reduced frequency for any inter-blade phase angle and it is independent of its sign. For highly loaded airfoils the unsteady pressure modulus is fairly constant exhibiting only a small correction with the reduced frequency, while the phase departs from zero varies linearly with it. In this case only the mean value of the work-per-cycle scales linearly with the reduced frequency. This behavior is independent of the geometry of the airfoil and in first approximation of the mode-shape. For symmetric cascades the work-per-cycle scales linearly with the reduced frequency irrespectively of whether the airfoil is loaded or not. Simulations using a frequency domain linearized Navier-Stokes solver have been carried out on a low-pressure turbine airfoil section, the NACA0012 and NACA65 profiles and a flat plate operating at different flow conditions to show the generality and correctness of the analytical conclusions. Both the traveling-wave and influence coefficient formulations of the problem are used in combination to increase the understanding and explore the nature of the unsteady pressure perturbations.

The Low Reduced Frequency Limit of Vibrating Airfoils—Part I: Theoretical Analysis

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
Roque Corral ◽  
Almudena Vega
Keyword(s):  
Stokes Equations ◽  
Order Approximation ◽  
Unsteady Aerodynamics ◽  
Mean Value ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Unsteady Pressure ◽  
Reduced Frequency ◽  
Influence Coefficients ◽  
Frequency Regime

This paper studies the unsteady aerodynamics of vibrating airfoils in the low reduced frequency regime with special emphasis on its impact on the scaling of the work-per-cycle curves, using an asymptotic approach. A perturbation analysis of the linearized Navier–Stokes equations for real modes at low reduced frequency is presented and some conclusions are drawn. The first important result is that the loading of the airfoil plays an essential role in the trends of the phase and modulus of the unsteady pressure caused by the vibration of the airfoil. For lightly loaded airfoils, the unsteady pressure and the influence coefficients (ICs) scale linearly with the reduced frequency whereas the phase departs from π/2 and changes linearly with the reduced frequency. As a consequence, the work-per-cycle scales linearly with the reduced frequency for any interblade phase angle (IBPA), and it is independent of its sign. For highly loaded airfoils, the unsteady pressure modulus is fairly constant exhibiting only a small correction with the reduced frequency, while the phase departs from zero and varies linearly with it. In this case, only the mean value of the work-per-cycle scales linearly with the reduced frequency. This behavior is independent of the geometry of the airfoil and the mode shape in first-order approximation in the reduced frequency. For symmetric cascades, the work-per-cycle scales linearly with the reduced frequency irrespective of whether the airfoil is loaded or not. These conclusions have been numerically confirmed in Part II of the paper.

An Experimental Determination of the Unsteady Aerodynamics in a Controlled Oscillating Cascade

1977 ◽  
Vol 99 (1) ◽  
pp. 88-96 ◽  
Author(s):  
S. Fleeter ◽  
A. S. Novick ◽  
R. E. Riffel ◽  
J. E. Caruthers
Keyword(s):  
Phase Angle ◽  
Unsteady Aerodynamics ◽  
Time Dependent ◽  
Phase Lag ◽  
Reduced Frequency ◽  
On Line ◽  
Torsional Frequency ◽  
Airfoil Cascade ◽  
Interblade Phase Angle

A unique supersonic inlet flow field unsteady cascade experiment is described wherein the time-dependent pressure distribution within an harmonically oscillating airfoil cascade is quantitatively determined. The torsional frequency of oscillation and the inter-blade phase angle are precisely controlled by means of on-line digital computers. The dynamic data obtained include the chordwise distribution of the unsteady pressure magnitude and its phase lag as referenced to the airfoil motion. Parameters varied include the cascade inlet Mach number, the interblade phase angle, and the reduced frequency. The time-dependent data are correlated with state-of-the-art analytical predictions.

The Low Reduced Frequency Limit of Vibrating Airfoils: Part I — Theoretical Analysis

2015 ◽  
Author(s):  
Roque Corral ◽  
Almudena Vega
Keyword(s):  
Stokes Equations ◽  
Unsteady Aerodynamics ◽  
Mean Value ◽  
Navier Stokes ◽  
Influence Coefficient ◽  
Navier Stokes Equations ◽  
Unsteady Pressure ◽  
Reduced Frequency ◽  
Influence Coefficients ◽  
Frequency Regime

This paper studies the unsteady aerodynamics of vibrating airfoils in the low reduced frequency regime with special emphasis in its impact on the scaling of the work per cycle curves using an asymptotic approach (Part I) and numerical simulations (Part II). A perturbation analysis of the linearized Navier-Stokes equations for real modes at low reduced frequency is presented and some conclusions are drawn. The first important result is that the loading of the airfoil plays an essential role in the trends of the phase and modulus of the unsteady pressure caused by the vibration of the airfoil. For lightly loaded airfoils the unsteady pressure and the influence coefficients scale linearly with the reduced frequency whereas the phase departs from π/2 and changes linearly with the reduced frequency. As a consequence the work-per-cycle scales linearly with the reduced frequency for any inter-blade phase angle and it is independent of its sign. For highly loaded airfoils the unsteady pressure modulus is fairly constant exhibiting only a small correction with the reduced frequency, while the phase departs from zero and varies linearly with it. In this case only the mean value of the work-per-cycle scales linearly with the reduced frequency. This behavior is independent of the geometry of the airfoil and the modeshape in first approximation. For symmetric cascades the work-per-cycle scales linearly with the reduced frequency irrespectively of whether the airfoil is loaded or not. Simulations using a frequency domain linearized Navier-Stokes solver have been carried out on a low-pressure turbine airfoil section, the NACA0012 and NACA65 profiles and a flat plate to show the generality and correctness of the analytical conclusions (Part II of the corresponding paper). Both, the traveling-wave and influence coefficient formulations of the problem are used in combination to increase the understanding and explore the nature of the unsteady pressure perturbations.

The Low Reduced Frequency Limit of Vibrating Airfoils: Part IIIA — Theoretical Quantification and Influence of Unsteady Loading

2016 ◽  
Author(s):  
Roque Corral ◽  
Almudena Vega
Keyword(s):  
Vibration Mode ◽  
Stokes Equations ◽  
Unsteady Aerodynamics ◽  
Operating Conditions ◽  
Navier Stokes ◽  
Airfoil Surface ◽  
Navier Stokes Equations ◽  
Reduced Frequency ◽  
Frequency Regime ◽  
Unsteady Loading

This paper studies the unsteady aerodynamics of vibrating airfoils in the low reduced frequency regime with special emphasis on its impact on the work per cycle curves. In Part I of the corresponding paper, a perturbation analysis of the linearized Navier-Stokes equations for real modes at low reduced frequency was presented and some conclusions were drawn. It was discovered that a new parameter, the unsteady loading, plays an essential role in the trends of the phase and modulus of the unsteady pressure caused by the oscillation of the airfoil. In this third (a) part, the theory is extended in order to quantify the new parameter. It is shown that this parameter depends solely on the steady flowfield on the airfoil surface and the vibration mode-shape. As a consequence, the effect of changing the design operating conditions or the vibration mode onto the work-per-cycle curves (and therefore in the stability) can be easily predicted and, what is more important, quantified without conducting additional flutter analysis. The relevance of the parameter has been numerically confirmed in the Part IIIb of the paper.

Numerical investigation of the unsteady aerodynamics of NACA 0012 with suction surface protrusion

2019 ◽  
Vol 92 (2) ◽  
pp. 186-200
Author(s):  
Aslesha Bodavula ◽  
Rajesh Yadav ◽  
Ugur Guven
Keyword(s):  
Vortex Shedding ◽  
Stokes Equations ◽  
Lift Coefficient ◽  
Unsteady Aerodynamics ◽  
Leading Edge ◽  
Navier Stokes ◽  
Suction Surface ◽  
Content Type ◽  
Energy Harvesters ◽  
Naca 0012

Purpose The purpose of this paper is to investigate the effect of surface protrusions on the flow unsteadiness of NACA 0012 at a Reynolds number of 100,000. Design/methodology/approach Effect of protrusions is investigated through numerical simulation of two-dimensional Navier–Stokes equations using a finite volume solver. Turbulent stresses are resolved through the transition Shear stress transport (four-equation) turbulence model. Findings The small protrusion located at 0.05c and 0.1c significantly improve the lift coefficient by up to 36% in the post-stall regime. It also alleviates the leading edge stall. The larger protrusions increase the drag significantly along with significant degradation of lift characteristics in the pre-stall regime as well. The smaller protrusions also increase the frequency of the vortex shedding. Originality/value The effect of macroscopic protrusions or deposits in rarely investigated. The delay in stall shown by smaller protrusions can be beneficial to micro aerial vehicles. The smaller protrusions increase the frequency of the vortex shedding, and hence, can be used as a tool to enhance energy production for energy harvesters based on vortex-induced vibrations and oscillating wing philosophy.

Numerical Simulation of Unsteady Aerodynamic Loads over an Aerofoil in Transonic Flow

2013 ◽  
Vol 644 ◽  
pp. 275-278 ◽  
Author(s):  
Yu Qian ◽  
Jun Li Yang ◽  
Xiao Jun Xiang ◽  
Ming Qiang Chen
Keyword(s):  
Mach Number ◽  
Euler Equations ◽  
Unsteady Aerodynamics ◽  
Angle Of Incidence ◽  
Periodic Motions ◽  
Aerodynamic Loads ◽  
Unsteady Aerodynamic ◽  
Reduced Frequency ◽  
Sinusoidal Motion ◽  
Naca 0012

The unsteady aerodynamic loads are the basic of the aeroelasitc. This paper focuses on the computation of the unsteady aerodynamic loads for forced periodic motions under high subsonic Mach numbers. The flow is modeled using the Euler equations and an unsteady time-domain solver is used for the computation of aerodynamic loads for forced periodic motions. The Euler equations are discretized on curvilinear multi-block body conforming girds using a cell-centred finite volume method. The implicit dual-time method proposed by Jameson is used for time-accurate calculations. Rigid body motions were treated by moving the mesh rigidly in response to the applied sinusoidal motion. For NACA 0012 airfoil, a validation of the unsteady aerodynamics loads is first considered. Furthermore, a study for understanding the influence of motion parameters, the Mach number, mean angle of incidence, reduced frequency, amplitude, was also conducted. A reverse of the trend of hysteretic loops can be observed with the increasing of the Mach number. Nonlinear hysteretic loops are turned up when increasing the amplitude and the reduced frequency during the applied pitch sinusoidal motion.

scholarly journals Physics of Vibrating Airfoils at Low Reduced Frequency

2013 ◽  
Author(s):  
Almudena Vega ◽  
Roque Corral
Keyword(s):  
Mach Number ◽  
Acoustic Waves ◽  
Unsteady Aerodynamics ◽  
Low Pressure ◽  
Travelling Wave ◽  
Navier Stokes ◽  
Influence Coefficient ◽  
Reduced Frequency ◽  
Influence Coefficients ◽  
Key Aspects

The unsteady aerodynamics of low pressure turbine vibrating airfoils in flap mode is studied in detail using a frequency domain linearized Navier-Stokes solver. Both the travelling-wave and influence coefficient formulations of the problem are used to highlight key aspects of the physics and understand different trends such as the effect of reduced frequency and Mach number. The study is focused in the low-reduced frequency regime which is of paramount relevance for the design of aeronautical low-pressure turbines and compressors. It is concluded that the effect of the Mach number on the unsteady pressure phase can be neglected in first approximation and that the unsteadiness of the vibrating and adjacent airfoils is driven by vortex shedding mechanisms. Finally a simple model to estimate the work-per-cycle as a function of the reduced frequency and Mach Number is provided. The edge-wise and torsion modes are presented in less detail but it is shown that acoustic waves are essential to explain its behaviour. The non-dimensional work-per-cycle of the edge-wise mode shows a large dependence with the Mach number while in the torsion mode a large number of airfoils is needed to reconstruct the work-per-cycle departing from the influence coefficients.

Aeroelastic Analysis of Membrane Microair Vehicles—Part II: Computational Study of a Plunging Membrane Airfoil

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Peter J. Attar ◽  
Raymond E. Gordnier ◽  
Jordan W. Johnston ◽  
William A. Romberg ◽  
Ramkumar N. Parthasarathy
Keyword(s):  
Strouhal Number ◽  
Stokes Equations ◽  
Computational Study ◽  
Lift Coefficient ◽  
Angle Of Attack ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Reduced Frequency ◽  
Lift And Drag ◽  
Intermediate Value

In the second paper of the two part study of membrane microair vehicles, computations are performed for a plunging membrane airfoil. The computational model uses a sixth-order finite difference solution of the Navier–Stokes equations coupled to a finite element solution of a set of nonlinear string equations. The effect, on the structural and fluid response, of plunging Strouhal number, reduced frequency, and static angle of attack is examined. Qualitatively, the flow field is found to be very complex with interactions of vortices shed from various locations along the chord of the airfoil. At a low angle of attack and a low Strouhal number, increasing reduced frequency results in a decrease and an increase in the mean sectional lift and drag coefficients, respectively. Also, at a low angle of attack, increasing the Strouhal number has minimal effect at high and low values of reduced frequencies, but a significant effect is found at an intermediate value of reduced frequency. When the effect of angle of attack is studied for fixed values of Strouhal number and reduced frequency, it is found that the act of plunging gives improved mean sectional lift when compared with the case of a fixed flexible airfoil. The improvement does not increase monotonically with the angle of attack but instead is maximum at an intermediate value. Finally, increasing the value of the membrane prestrain, which stiffens the airfoil, results in a reduced value of the sectional lift coefficient for a given Strouhal number, reduced frequency, and angle of attack.

Simulation of Unsteady Flow Around a Cylinder

2015 ◽  
Vol 3 (2) ◽  
pp. 28-49
Author(s):  
Ridha Alwan Ahmed
Keyword(s):  
Stokes Equations ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Mean Value ◽  
Navier Stokes ◽  
Cylinder Surface ◽  
Navier Stokes Equations ◽  
Flow Around A Cylinder ◽  
Numerical Grid ◽  
Good Agreement

       In this paper, the phenomena of vortex shedding from the circular cylinder surface has been studied at several Reynolds Numbers (40≤Re≤ 300).The 2D, unsteady, incompressible, Laminar flow, continuity and Navier Stokes equations have been solved numerically by using CFD Package FLUENT. In this package PISO algorithm is used in the pressure-velocity coupling.        The numerical grid is generated by using Gambit program. The velocity and pressure fields are obtained upstream and downstream of the cylinder at each time and it is also calculated the mean value of drag coefficient and value of lift coefficient .The results showed that the flow is strongly unsteady and unsymmetrical at Re>60. The results have been compared with the available experiments and a good agreement has been found between them

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