Sinusoidal Gust Research Articles

An oscillating rig for the generation of sinusoidal flows

An oscillating rig consisting of two 'two-dimensional' aerofoils enclosed between two vertical wind tunnel walls is capable of generating upwash and/or streamwise sinusoidal gusts. This design has certain advantages over some previous unsteady flow wind tunnels. The upwash velocity predicted from potential flow for aerofoil pitching oscillations is in reasonable agreement with that obtained from the experiment.

Unsteady response of rectangular wings in spanwise uniform shear flow

In engineering applications, it is important to estimate aerodynamic forces on wings in nonuniform flow. Wakes produced by objects ahead of wings frequently affect the performance of airplanes, turbomachines, etc. In this paper, a theory of wings oscillating in shear flow is presented. The whole flowfield is assumed to be inviscid and incompressible, and, furthermore, the shear flow velocity is assumed to vary linearly along the wing span. For this problem, lifting surface theory is applied. An integral equation, which is similar to that for potential flow, is derived under the assumption of small perturbations, arid then solved numerically by the mode function method. Generalized forces, Q^, which can be easily related to unsteady lift forces and moments, are obtained; moreover, response functions of wings to sinusoidal heaving oscillations and a sinusoidal gust are calculated for three different amounts of shear flow. The results are compared for several frequencies and show that the effect of shear is not large except in the limiting case. However, the generalized forces and gust response functions are affected by .the shear to some extent, even when the degree of shear is moderate. The effect increases as the frequency becomes larger.

Forces on Staggered Airfoil Cascades in Unsteady In-Phase Motion

We consider incompressible potential flow through a cascade of staggered thin airfoils in general, unsteady, in-phase motion. With the assumptions of the Kutta condition and linearized wakes, exact analytical expressions are derived for pressure distribution, lift, and moment, using conformal mapping applied to the velocity field. The results are then specialized to harmonic motion, and applied to plunging, pitching, and sinusoidal gusts. All the results are expressed in closed-form as quadratures, and reduce to the well-known relations for thin airfoil theory, as the solidity decreases to zero. They agree with the unstaggered results of Kemp and Ohashi when the stagger angle is zero. Typical numerical results are given in the figures. They should serve as a measure of the accuracy of numerical or approximate solutions, as well as representing in a simple way the effects of stagger and solidity on unsteady cascade aerodynamics.

Aerodynamic coefficients in generalized unsteady thin airfoil theory

Two cases are considered: (1) rigid body motion of an airfoil-flap combination consisting of vertical translation of given amplitude, rotation of given amplitude about a specified axis, and rotation of given amplitude of the control surface alone about its hinge; the upwash for this problem is defined mathematically; and (2) sinusoidal gust of given amplitude and wave number, for which the upwash is defined mathematically. Simple universal formulas are presented for the most important aerodynamic coefficients in unsteady thin airfoil theory. The lift and moment induced by a generalized gust are evaluated explicitly in terms of the gust wavelength. Similarly, in the control surface problem, the lift, moment, and hinge moments are given as explicit algebraic functions of hinge location. These results can be used together with any of the standard numerical inversion routines for the elementary loads (pitch and heave).

Unsteady Flow through Airfoil Cascades : 2nd Report, Sinusoidal Gusts which Have Different Phase Angles between Adjacent Airfoils

Unsteady Flow through Airfoil Cascades : 2nd Report, Sinusoidal Gusts which Have Different Phase Angles between Adjacent Airfoils

Unsteady Flows Through Cascades : Sinusoidal gusts having different phase for each blade

An analytical method is given for the determination of the lift fluctuation on flat plate airfoils in cascade due to transverse and chordwise gusts. The acceleration potential method is used in combination with conformal mapping method. In order to take account of the phase difference of the gusts between adjacent blades, a new mapping function is introduced. The blades are mapped to several unit circles on which the acceleration potential is given to satisfy the boundary conditions. Unsteady lift forces are given for three different stagger angles, five different pitches of the cascades and three different phase differences. The phase difference has the effect to make the lift forces greater than that for the case of the same phase, and this tendency is remarkable when the reduced frequency of the gust is small.

Forces on Unstaggered Airfoil Cascades in Unsteady In-Phase Motion

Incompressible flow through an unstaggered cascade in general, unsteady, in-phase motion is considered. By methods of thin-airfoil theory, using the assumptions of wakes trailing back at the through-flow velocity, and the Kutta condition, exact analytical expressions are derived for loading, lift and moment. As application, harmonic motion is considered for plunging, pitching, and sinusoidal gusts. Numerical values of lift and moment for these three cases are given graphically (tables are available from the authors). The results show strong analogies with isolated unsteady thin-airfoil theory. They should prove useful as simple examples of unsteady effects in cascades, and as check cases for other approximate or purely numerical analyses.

Approximate unsteady thin-airfoil theory for subsonic flow

An analytical solution of the Possio integral equation is obtained for low reduced-frequency to, correct to or- der wM/(l-M2). The resulting loading, lift, and moment differ from that derived from GASP theory by Osborne, in agreement with recent work of Amiet, who has shown GASP theory to be inapplicable to two- dimensional flow with shed vorticity. The solution is applied to a generalized gust, a power law upwash, plunging motion, pitching motion, and a sinusoidal gust. Comparisons with numerical solutions are given for lift in the latter three cases. They show that one of the forms of the solution, the Osborne lift times a phase correction, is remarkably accurate up to coM/(l —M2) = ir/4. This approximation should prove convenient and useful in applications. HE nonsteady load distribution on two-dimension al thin airfoils oscillating in subsonic flow is governed by the Possio integral equation, which has no known exact analytical solution. There have been many numerical approaches to its solution over the years, and also a number of approximate analytical approaches. For a given airfoil motion, the forces depend on two parameters, the stream Mach number M and the reduced frequency of oscillation co. The task of any ap- proximate analytical solution is to give a satisfactory ap- proximation in as large a region of the M, co plane (M< 1) as possible. Some years ago, Miles1 briefly discussed the com- pressibility correction to the incompressible problem (which has an exact solution). He transformed the governing dif- ferential equation and boundary conditions by a combined Galilean and Lorentz transformation, expanded to first order in coM//3 2, where /32 = 1 — M2, and derived a compressibilit y correction rule. In another paper, Miles2 derived a quasisteady theory by expanding the Possio integral equation to first order in co. Recently, Amiet and Sears3 applied the method of matched asymptotic expansions to small- perturbation subsonic flows, and, again, obtained Miles' correction rule1 in the course of their work, which has been called GASP (Glauert-Amiet-Sears-Prandtl) theory. Osborne4 applied this correction rule to obtain analytical formulas for the lift and moment of oscillating, thin two- dimensional airfoils flying in a generalized gust, a sinusoidal gust, and in plunging motion, although his results were in finite form only for the sinusoidal gust. Kemp5 showed that the results for the generalized gust and the plunging motion also could be put in finite form, and added the other in- teresting case of pitching motion. (He also showed, sub- sequently6, that the lift and moment for any integer power law upwash distribution could be derived by purely algebraic

A complete second-order theory for the unsteady flow about an airfoil due to a periodic gust

In this paper we develop a uniformly valid, second-order theory for calculating the unsteady incompressible flow that occurs when an airfoil is subjected to a convected sinusoidal gust. Explicit formulae for the airfoil response functions (i.e. fluctuating lift) are given. The theory accounts for the effect of the distortion of the gust by the steady-state potential flow around the airfoil, and this effect is found to have an important influence on the response functions. A number of results relevant to the general theory of the scattering of vorticity waves by solid objects are also presented.

The Unsteady Forces on Flat‐Plate‐Airfoils in Cascade Moving through Sinusoidal Gusts

AbstractThis paper presents an analysis for the determination of the lift fluctuation on flat‐plate‐airfoils in cascade due to transverse and chordwise gusts. The acceleration potential method is used in combination with conformal mapping method. This method gives an utterly simple analysis even for cascades, without the complicated integral equations enevitable for the determination, of vortex distribution in velocity‐field analysis. The computational results show that the pitch and the stagger angle of the cascade have much influence upon the magnitude of the fluctuating lift, but not so much upon phase angle.

Unsteady Flow Through Airfoil Cascades : 1st Report, Unsteady Lift on Airfoils in Cascade Moving Through Transverse and Chordwise Sinusoidal Gusts

Unsteady Flow Through Airfoil Cascades : 1st Report, Unsteady Lift on Airfoils in Cascade Moving Through Transverse and Chordwise Sinusoidal Gusts

Prediction of Unsteady Airloads for Oblique Blade-Gust Interaction in Compressible Flow

The techniques of Galilean-Lorentz transformation and matched asymptotic expansions are used to simplify the procedure of calculating the lift and pressure distribution induced on an infinite-span thin wing interacting with an oblique sinusoidal gust in subsonic flow. This technique requires that the product of the flow Mach number and the reduced frequency be small. Under this condition, the inner region of the transformed space behaves as an incompressible flow, so that existing incompressible flow theories can be used as a basis to construct closed-form solutions for the airload induced on the wing. This approach is an extension of the GASP approximation developed by Amiet and Sears (1970). Results are obtained for both the magnitude and the phase of the unsteady lift due to interaction with gust. These results are compared with available numerical results. Some discrepancies are noted and discussed.

Stability analysis and design for aircraft gust alleviation control

This paper is concerned with the stability analysis and the development of an on-line two-level gust alleviation control system for a high-speed aircraft operating in an unknown environment. As is well known, such an aircraft experiences dynamic instability in its lateral motion when subjected to the longitudinal and lateral gusts. This is due to the phenomenon of lateral-longitudinal aerodynamic cross-coupling. In the first part of this paper the instability behaviour, in the presence of a longitudinal gust, of two typical high-speed aircraft is analyzed. From theoretical and simulation studies it is shown that for a sinusoidal gust, and for a given configuration, the instability region is a function of both the amplitude and frequency of the gust disturbance. In the second part of the paper, an on-line gust alleviation control system is synthesized for such an aircraft operating over a wide range of unknown environmental conditions. This control system employs a two-level control structure. The controller, however, does not require an explicit knowledge of the aircraft parameters or the environment. Typical simulation results are presented which verify the theoretical predictions.

Elastic Launch Vehicle Response to Sinusoidal Gusts

Covers advancements in spacecraft and tactical and strategic missile systems, including subsystem design and application, mission design and analysis, materials and structures, developments in space sciences, space processing and manufacturing, space operations, and applications of space technologies to other fields.

Vortex induced helicopter blade loads and noise

The fluctuating lift on a helicopter rotor blade passing close to a tip vortex shed from a preceding blade may generate an intense cyclic banging noise, called blade slap, which is one of the most offensive of all helicopter noises. Such blade/vortex interactions are modeled by a finite aspect ratio wing flying at uniform speed over a carpet of equally spaced, infinitely long, line vortices. By using linearized lifting surface theory the harmonic blade loads are expressed as a Fourier series with coefficients involving the same “sinusoidal gust transfer function” that figures prominently in the analysis of aircraft response to atmospheric turbulence. An established theory ( Lowson and Ollerhead, 1969 ) can be used to calculate the radiated noise harmonics in terms of the Fourier coefficients. Consideration of the noise propagated to the far field of a blade-fixed reference frame indicates that blade slap noise is only weakly influenced by aspect ratio. For a blade passing over the vortices at fixed height, acoustic power generation is proportional to the inverse third power of the height and is efficient only if the vortex spacing is about five times the height.

Unsteady thin-airfoil theory for subsonic flow.

An approximate theory has been developed for the unsteady motion of a two-dimensional thin airfoil in subsonic flow. The basic theory is restricted by the condition that (s//?2)2 <^ 1, where e is i/(2n) times the product of the Mach number M and the conventional reduced frequency CM, and ft2 = 1 —M 2. Closed-form expressions are presented for the forces on, the circulation about, and the strength of the vortex wake emanating from a two-dimensional thin airfoil that is subjected to the general class of oscillating upwash distribution whose A dependence may be expanded in a cosine series. Expressions are also set down for three particularly important examples of this upwash distribution, namely the Kemp-type upwash, the convected sinusoidal gust, and the flutter case. Some preliminary comparisons of the present method with the few existing theories for the sinusoidal-gust case reveals good agreement up to at least M = 0.6 and for relatively large values of e.

翼の突風応答に関する研究

In this report, the gust responses of a threedimensional elastic wing are investigated theoretically and experimentally, where the two kinds of gust, sinusoidal gust and random gust, are treated. It is assumed here that the deformation of an elastic wing is generated by bending moment and torsional moment which act on a wing independently.First, for the responses to the sinusoidal gust, the modes of deformation are calculated applying the modes of natural oscillation of a cantilever beam. The results of calculation agree well with the experimental values.Next, the frequency transfer functions of deformations by bending moment and torsional moment are obtained for the random gust responses. In this case, the phase difference of the gust along the wing span is taken into consideration. The calculated results agree well with the experimental results.

Lift and Pressure Fluctuations of a Cambered Airfoil Under Periodic Gusts and Applications in Turbomachinery

Previous authors have considered the unsteady lift of a flat-plate (zero-cambered) airfoil travelling through sinusoidal gusts. The present paper extends the analysis to cambered airfoils with angle of attack moving through both longitudinal and transverse gusts. Closed-form analytical solutions are obtained. The results are used to calculate the unsteady lift on a blade moving through periodic wakes in an axial-flow turbomachine. Knowledge gained by this analysis clearly indicates design trends to obtain minimum lift fluctuations. Since the interference effects of neighboring blades are ignored in this analysis, the conclusions on turbomachinery are strictly valid only for cascades with low solidity.

Flow in the wake of a cascade of oscillating airfoils.

A study has been made of the amplitude and phase of the vertical osciUations in the wake behind 1) a cascade of airfoils oscillating in phase and 2) a cascade of airfoils at zero incidence with oscillating flaps. It was found that in both cases the amplitude of the flow oscillations in the wake remained approximately constant downstream for the values of frequency parameter and airfoil spacing considered. From the results of some preliminary experimental work it appears that sinusoidal gusts could be reproduced in an open jet wind tunnel fitted with either system, but the second type of airfoil-flap arrangement is preferable in practice. The difficulties resulting from flow separation and early stalling which arise with the first system do not appear until much higher angular amplitudes are used when only the flaps are oscillated.

翼の突風応答に関する研究

In this report, the gust responses of a three dimensional wing are investigated theoretically and experimentally i.e. the responses to the sinusoidal gust and the random gust are obtained theoretically and the both are compared with the experimental results respectively.The responses to the sinusoidal gust are calculated by the method of lifting-line theory and the response functions are obtained for the wing of various aspect ratio. These results are compared to the experimental values which were obtained by the wind tunnel experiments for the wing of aspect ratio of 3.16. As the results, it is found that the both agree well with each other.For the responses to the random gust, the power spectral density functions and the frequency transfer functions of the lift force of a wing are calculated with the method of lifting-line theory. In this case, it is considered that the gust varies along the wing span i.e. the reduced frequency along the wing span, k2, is introduced. Therefore, the frequency transfer functions have two variables and these results are compared with the experimental values and the both agree well with each other.