Airfoil Profile Research Articles

Impact of airfoil profile on the supersonic aerodynamics of delta wings

A nonlinear flow model was employed to predict the flowfield, pressure and force data for delta wings at supersonic speeds. The goal of the study was to investigate the influence the airfoil profiles has on the wing aerodynamics. The analysis covers wing aspect ratios from 0.5-3.0 with leading edge sweep of 0.5-4.0 on diamond, circular arc and NACA modified 4-digit airfoils. Nonlinear aerodynamics are approximated with nonlinear zero-lift wave drag curves, yielding results significantly different from those obtained from linear calculations. The analytical technique, useful in preliminary design studies, indicates in all cases that 90 percent of wave drag is generated at the wing apex and trailing edge.

Transient aerodynamic characteristics of a two-dimensional airfoil during stepwise incidence variation

The present paper discusses the transient aerodynamic characteristics of a two-dimensional low-speed airfoil whose angle of attack is varied impulsively. The study is mainly an experimental one with observations made of the three dynamic loads, the static pressure distribution, and flow on the airfoil surface, following the airfoil motion. The changes in the characteristics and their aerodynamic causes are investigated in terms of the ultimate angle of attack and the rise time. foil other than the two-dimensional motion to be discussed in this paper. For instance, Refs. 7-10 deal with the effects of variations in the flow velocity and in the angle of attack. There are other studies11'12 that have analytically pursued the rela- tionship between dynamic stall and the ambient flowfield. Furthermore, little is known about the effects of Reynolds number, Mach number, airfoil profile, and airfoil motion.13 At this stage of information it is natural that the technology should be based on experimentation. In the present paper, in- stead of a conventional study of an oscillating airfoil, which has been often undertaken, the relations between the transient aerodynamic characteristics of an airfoil with stepwise varied angle of attack and the state of the ambient airflow are ex- perimentally investigated as a basic study leading to applica- tion. Another reason for adopting a stepwise varied input is the desirability of obtaining a simple motion for understand- ing the phenomena in a flow with prominent nonlinearity and hysteresis.

High-lift airfoil design from the hodograph

A practical and general method is described and used to derive particular airfoil sections with the desirable flat roof-top characteristics of some optimum profiles. The method is derived from a solution of the inverse airfoil problem, where the dynamic features required of it by the designer are set in the hodograph plane and the airfoil profile, which will realize those design features obtained by a simple process of numerical integration. AH the physical viability criteria are satisfied ab initio and the particular sections calculated exhibit those desirable features by suitably choosing some transformation constants which are fully defined in the hodograph plane. The pressure recovery at the tail end of the upper surface can be helped to develop naturally without separation taking place by making use, if need be, of the process of natural jet injection into the boundary layer at a welldefined station just ahead of an incipient separation point. Some of these so-derived airfoils are described together with their aerodynamic characteristics. The method can also be used to generate high-performance cascade blading for low-speed (incompressible) work, or airfoils, either isolated or in cascades, for use at compressible (subsonic) flow speeds, with little significant structural complexity added.

A Systematic Computational Design System for Turbine Cascades, Airfoil Geometry, and Blade-to-Blade Analysis

This paper describes a systematic computational design system for two-dimensional turbine cascades. The system includes a sequence of calculations in which airfoil profiles are designed from velocity diagram requirements and specified geometric parameters, followed by an inviscid global streamline curvature analysis, a magnified reanalysis around the leading edge, and a transitional profile boundary layer and wake mixing analysis. A finite area technique and a body-fitted mesh are used for the reanalysis. The boundary layer analysis is performed using the dissipation-integral method of Walz which has been modified in the present application. Several turbine airfoil profile geometry designs are presented. Also two sample cascade design cases and their calculated performance for a range of Mach numbers and incidence angles are given and discussed.

Development of Controlled Diffusion Airfoils for Multistage Compressor Application

A series of Controlled Diffusion Airfoils has been developed for multistage compressor application. These airfoils are designed analytically to be shock-free at transonic Mach numbers and to avoid suction surface boundary layer separation for a range of inlet conditions necessary for stable compressor operation. They have demonstrated, in cascade testing, higher critical Mach numbers, higher incidence range, and higher loading capability than standard series airfoils designed for equivalent aerodynamic requirements. These airfoils have been shown, in single and multistage rig testing, to provide high efficiency, high loading capability, and ease of stage matching, leading to reduced development costs and improved surge margin. The Controlled Diffusion Airfoil profile shapes tend to have thicker leading and trailing edges than their standard series counterparts, which lead to improved compressor durability.

Overall Aerodynamic Performance of an Annular Flat-Plate Airfoil Cascade

THE aerodynamic design of turbomachiner y blading is specified by means of design systems wherein the flow is assumed to be two-dimensional with losses determined from empirical correlations. However, with the continuing requirements for improved efficiency and increased thrust-to-weight ratio, it is evident that new analyses that consider the fundamental three-dimensional flow phenomena existing in blade-row flow passages must be developed, verified by concise data, and subsequently implemented in the design process. Numerical solutions are currently being developed to predict the three-dimensional flow through turbomachine blade rows. To overcome the complexities associated with the flow conditions and the internal geometries, these numerical solutions of necessity involve many computational and physical assumptions. This paper describes experiments performed in a large-scale, subsonic annular cascade facility specifically designed to provide three-dimensional aerodynamic data suitable for code verification. In particular, to minimize the complexities associated with cascade geometry and complex airfoil profiles, the detailed overall threedimensional aerodynamic performance of an extensively instrumented flat-plate airfoil cascade has been experimentally determined over a range of incidence angle values. All of the resulting data are analyzed and correlated with appropriate predictions. Contents

Noise generated by airfoil profiles placed in a uniform laminar flow

The present paper is devoted to the experimental study of the noise generated by an airfoil profile placed in a uniform laminar flow. The far-field acoustic spectrum is shown to be composed of a broadband contribution around frequency fs and a discrete contribution at equidistant frequencies fn, which follow power laws of the forms fs ∼ U1.5 and fn ∼ U0.85. Both contributions can be accounted for by a simple model derived from the original suggestions of Tam (1974) and Fink (1975). It is essentially assumed that the diffraction of the Tollmien-Schlichting instabilities by the trailing edge generates acoustic waves which propagate in the far field and also trigger an aeroacoustic feedback loop, whose length is equal to the distance between the trailing edge and the maximum velocity point of the airfoil.

Transonic swept wings studied by the lifting-line theory

Transonic swept wings are analyzed as a lifting-line problem under a small-disturbance approximation. Basic concepts and principal results of the asymptotic theory are discussed. The study focuses on straight oblique wings and V-shaped swept wings, of which the local centerline curvature can be equated to zero. The three-dimensional (3-D) perturbation of the nonlinear component flow admits a similarity flow structure but requires that all wing sections are generated from a single airfoil profile; the reduced 2-D problems in this case are solved only once for all span stations. Examples of solutions involving high subcritical and slightly supercritical component flows are demonstrated and compared with surface pressure data from 3-D computer codes based on the full-potential equation (FLO 22). Except in the neighborhood of leading edges, where the small-disturbance assumption breaks down, and in the vicinities of wing tips and the symmetry plane, where neither the theory nor the 3-D codes may claim full validity, reasonable agreement is consistently found. The explicit results from the upwash analysis, along with the similarity flow structure, provides a rational approach to the control of 3-D effects in transonic aerodynamic design studies.

An Experimental Study on Noise Reduction of Axial Flow Fans : 1st Report, Effects' of some parameters on blade elements

Study on noise reduction of the axial-flow fans was carried out, varying principal assumed parameters such as the chord length of the blade, the camber of the airfoil, the position of maximum camber, and the surface pressure distribution of the airfoil. A separated flow on the surface of the tow-dimensional airfoil was observed with use of the Schlieren divice, and measurements were made of the strength of turbulence with use of a hot wire probe so as to determine their correlation with fan noise. The airfoil profile was determined by calculation using an optimum pressure distribution. As a result, the relations between the parameters and fan noise reduction have been clarified.

Transonic flows around a carrying airfoil profile

Unsymmetrical gas flows around a carrying airfoil, with velocities close to sonic at infinity, are discussed. In a region situated a certain distance from the profile, an asymptotic solution of the flow problem is constructed. A detailed analysis is made of the dependence of the terms of the asymptotic sequences of the parameters characterizing the transverse and longitudinal dimensions of the body. The law of change in the lifting force as a function of the difference 1 − M∞, which is assumed to be small, is established. The connection between the theoretical results and experimental data is discussed in detail.

Supercritical Airfoil Flowfield Measurements

Detailed measurements in the transonic flow field about a Whitcomb-type supercritical airfoil profile are presented including surface pressure distributions, far wake surveys, spark schlieren photographs, and a series of vector velocity profiles in the boundary layer and in the near wake. A flowfield composite for the transonic drag rise condition is constructed from these data. The boundary-layer measurements are compared with current correlation and computation schemes, and the importance of viscous thickening effects is demonstrated by the results of wave drag rise calculations for the thickened and unthickened profiles.

Optimization of airfoils for maximum lift

The pressure distribution which provides the maximum lift without separation for a monoelement airfoil in an incompressible flow is determined using existing boundary-layer theory and the calculus of variations. The airfoil profiles corresponding to these pressure distributions are determined using second-order airfoil theory. The results indicate maximum lift coefficients as high as 2.8 for Reynolds numbers between five and ten million, and the corresponding drag coefficients are on the order of 0.01. Compressibility has not been considered directly, however the form of the optimum pressure distributions suggests that the critical Mach numbers should be on the order of 0.35.

Fluid Mechanics in the First Half of this Century

THE FIRST DECADE The opening decade of the twentieth century was a period of progress in fluid mechanics. Much was begun that was to continue for many years. Most of the great discoverers in the latter part of the previous century were to be with us still during the decade, and other younger men were to come forward. Let us start by listing some of the happenings. In 1900 and 1901 Benard published descriptions of his experiments on the convective motion of a fluid heated from below. In 1901 Levi-Civita published his first note on the explanation of the resistance of a solid body held in a stream of fluid by postulating the existence of surfaces of discontinuity of velocity, even when the body is of rounded form, without sharp edges. A paper on lifting forces in streams of fluid, by Kutta, appeared in 1902; this contained a solution for the two-dimensional flow of an inviscid fluid past a solid surface in the shape of a circular are, at zero incidence, with circulation round the surface and a finite velocity at the trailing edge. Sir George Gabriel Stokes, who was born in 1819, was chosen as Master of Pembroke College, Cambridge in 1902, and died on February 1, 1903. Chaplygin's 1902 doctoral dissertation on gas jets, with the hodograph transformation of the equations of steady two-dimensional gas flows, and the application to jets, was published in 1904. In 1904 Prandtl read his paper Htiber Fltissigkeitsbewegung bei sehr kleiner Reibung to the Third International Congress of Mathematicians at Heidelberg. In the same year Lord Kelvin published three papers on Waves on water (with one more in each of the years 1905 and 1906). The classical papers of Sommerfeld and Michell on the hydrodynamical theory of lubrication appeared in 1904 and 1905, and Ekman's paper On the influence of the earth's rotation on ocean currents in 1905. Zhukovskii's famous lift theorem, connecting the lift force with the circulation quite generally for the two-dimensional flow of an inviscid fluid, was published in two notes in 1906, one in Russian and one in French. In 1907 and 1908 the works of Orr and Sommerfeld on the stability of fluid motions appeared. Lanchester's book Aerodynamics was published in London in 1907, and a German edition followed in 1909. Near the beginning of 1910 Chaplygin formally enunciated the postulate that out of the infinite number of theoretically possible flows (depending on the magnitude of the circulation) past an airfoil profile with a sharp trailing edge, the flow that is nearest to experiment is the one with a finite velocity at the trailing edge...

On Supersonic Flow Past Thick Airfoils

= = = = = — speed of sound, in units of limiting velocity pressure coefficient airfoil profile undisturbed-flow Mach number pressure gas constant entropy temperature Cartesian coordinates velocity components in x and y directions, in units of limiting velocity velocity, in units of limiting velocity ratio of specific heats flow inclination to undisturbed stream Mach angle behind shock wave at airfoil leading edge shock wave inclination to undisturbed stream coordinate system defined by Eqs. (3) shock-wave profile in (£, rj) plane slope of shock wave in (x, y) plane values of v and 5 at the leading edge ratio of shock-wave curvature to airfoil curvature at leading edge

Aeroelastic Instability at High Mach Number

A brief discussion of the limitations of the piston theory is given. Using Lighthill's approach, the aerodynamic forces on oscillating airfoils are derived in a slightly different form to conform to the NACA practice and the familiar nondimensional flutter coefficients are tabulated for general double and single wedge and parabolic biconvex profiles. Extensive parametric studies are included for preliminary design to aid in estimating the effect on flutter speed and frequency of airfoil thickness and profile, initial angle of attack, modal shape, changes in elastic and inertial properties of the wing, and altitude of flight.