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At least 595 records · Page 33

Numerical solution of the Navier-Stokes equations for arbitrary two-dimensional airfoils

A method for numerical solution of the Navier-Stokes equations for the flow about arbitrary airfoils or other bodies is presented. This method utilizes a numerically generated curvilinear coordinate system having a coordinate line coincident with the body contour. Streamlines, velocity profiles, and pressure and force coefficients for several airfoils and an arbitrary rock are given. Potential flow solutions are also presented. The procedure capable of treating multiple-element airfoils, and potential flow results are presented.

Thames, F. C.↗

Application of multivariable search techniques to the optimization of airfoils in a low speed nonlinear inviscid flow field

Multivariable search techniques are applied to a particular class of airfoil optimization problems. These are the maximization of lift and the minimization of disturbance pressure magnitude in an inviscid nonlinear flow field. A variety of multivariable search techniques contained in an existing nonlinear optimization code, AESOP, are applied to this design problem. These techniques include elementary single parameter perturbation methods, organized search such as steepest-descent, quadratic, and Davidon methods, randomized procedures, and a generalized search acceleration technique. Airfoil design variables are seven in number and define perturbations to the profile of an existing NACA airfoil. The relative efficiency of the techniques are compared. It is shown that elementary one parameter at a time and random techniques compare favorably with organized searches in the class of problems considered. It is also shown that significant reductions in disturbance pressure magnitude can be made while retaining reasonable lift coefficient values at low free stream Mach numbers.

Hague, D. S.↗

Airfoil shape for flight at subsonic speeds

An airfoil is examined that has an upper surface shaped to control flow accelerations and pressure distribution over the upper surface and to prevent separation of the boundary layer due to shock wave formulation at high subsonic speeds well above the critical Mach number. A highly cambered trailing edge section improves overall airfoil lifting efficiency. Diagrams illustrating supersonic flow and shock waves over the airfoil are shown.

Whitcomb, R. T.↗

Acoustic radiation and surface pressure characteristics of an airfoil due to incident turbulence

A theoretical and experimental investigation of the noise and unsteady surface pressure characteristics of an isolated airfoil in a uniform mean velocity, homogeneous, nearly-isotropic turbulence field was conducted. Wind tunnel experiments were performed with a 23 cm chord, two dimensional NACA 0012 airfoil over a free stream Mach number range of 0.1 to 0.5. Far-field noise spectra and directivity were measured in an anechoic chamber that surrounded the tunnel open jet test section. Spanwise and chordwise distribution of unsteady airfoil surface pressure spectra and surface pressure cross-spectra were obtained. Incident turbulence intensities, length scales, spectra, and spanwise cross-spectra, required in the calculation of far-field noise and surface pressure characteristics were also measured.

Paterson, R. W.↗

Vortex noise from nonrotating cylinders and airfoils

An experimental study of vortex-shedding noise was conducted in an acoustic research tunnel over a Reynolds-number range applicable to full-scale helicopter tail-rotor blades. Two-dimensional tapered-chord nonrotating models were tested to simulate the effect of spanwise frequency variation on the vortex-shedding mechanism. Both a tapered circular cylinder and tapered airfoils were investigated. The results were compared with data for constant-diameter cylinder and constant-chord airfoil models also tested during this study. Far-field noise, surface pressure fluctuations, and spanwise correlation lengths were measured for each configuration. Vortex-shedding noise for tapered cylinders and airfoils was found to contain many narrowband-random peaks which occurred within a range of frequencies corresponding to a predictable Strouhal number referenced to the maximum and minimum chord. The noise was observed to depend on surface roughness and Reynolds number.

Schlinker, R. H.↗

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

A uniformly valid second-order theory is developed for calculating the unsteady incompressible flow that occurs when an airfoil is subjected to a convected sinusoidal gust. Explicit formulas 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.

Goldstein, M. E.↗

Transonic flow about airfoils

Program analyzes airfoils that permit transonic flow for subsonic free-stream mach numbers. Transonic refers to aircraft speeds less than speed of sound, but close enough so that top of wing, where airflow is fastest, mach number becomes greater than 1. Program should aid design phase of new airfoil and in analysis of existing airfoils.

Bauer, F.↗

Experimental and theoretical low-speed aerodynamic characteristics of a Wortmann airfoil as manufactured on a fiberglass sailplane

A low turbulence pressure tunnel evaluation is reported for low speed aerodynamic characteristics of the FX 66-17AII-182 airfoil as manufactured on a fiberglass sailplane. The results were compared with data for design coordinates obtained from another low turbulence wind tunnel and with theoretical calculations generated by a viscous flow airfoil computer program. The investigation was performed over a Reynolds number range, based on airfoil chord, of approximately 0.5 x 1 million to 6 million and a Mach number range of about 0.05 to 0.35. Comparison with data from another wind tunnel for the design coordinates showed slightly higher drag for the manufactured section.

Somers, D. M.↗

Computation of viscous transonic flow about a lifting airfoil

The viscous transonic flow about a stationary body in free air was numerically investigated. The geometry chosen was a symmetric NACA 64A010 airfoil at a freestream Mach number of 0.8, a Reynolds number of 4 million based on chord, and angles of attack of 0 and 2 degrees. These conditions were such that, at 2 degrees incidence unsteady periodic motion was calculated along the aft portion of the airfoil and in its wake. Although no unsteady measurements were made for the NACA 64A010 airfoil at these flow conditions, interpolated steady measurements of lift, drag, and surface static pressures compared favorably with corresponding computed time-averaged lift, drag, and surface static pressures.

Walitt, L.↗

Design of high lift airfoils with a Stratford distribution by the Eppler method

Airfoils having a Stratford pressure distribution, which has zero skin friction in the pressure recovery area, were investigated in an effort to develop high lift airfoils. The Eppler program, an inverse conformal mapping technique where the x and y coordinates of the airfoil are developed from a given velocity distribution, was used.

Thomson, W. G.↗

Low-speed aerodynamic characteristics of a 13.1-percent-thick, high-lift airfoil

Low speed sectional characteristics of a high lift airfoil are studied and a comparison is made of those characteristics with the predictions of the theoretical methods used in the airfoil's design. The 13.1 percent-thick, UI-1720 airfoil was found to achieve the predicted maximum lift coefficient of nearly 2.0. No upper-surface, flow separation was found below the stall angle of attack of 16 degrees; it appeared that stall was due to an abrupt leading edge flow separation.

Sivier, K. R.↗

A numerical study of the unsteady leading edge separation bubble on an oscillating airfoil

A preliminary study of the unsteady viscous flow in the region of an airfoil leading edge was performed, in which the interaction between the viscous and inviscid flow fields is neglected. The solution method uses the finite difference form of the governing equations throughout the separated flow field and incorporates a transition model based on the integral turbulence kinetic energy equation. The validity of the numerical procedure is verified by making comparisons with analytical solutions to several test problems, including unsteady flow over a plate oscillating in its own plane. The method was then applied to the problem of unsteady viscous flow over a NACA 0012 airfoil oscillating sinusoidally in pitch. The flow field characteristics were in qualitative agreement with experimental results. The bubble moved forward on the airfoil and decreased in size as incidence was increased. Viscous flow in the leading edge region was found to be quasi-steady, while bubble height varied inversely with Reynolds number.

Kreskovsky, J. P.↗

Studies of flow separation and stalling on one- and two-element airfoils at low speeds

Research has been conducted on the nature of airfoil behavior at pre- and post-separated angles of attack. Detailed wind tunnel studies have been made of boundary layer and wake fields for the GA(W)-1 airfoil, and the airfoil with a 0.3 chord Fowler flap. Experimental data are compared with theoretical predictions from a multi-element viscous flow computer program. Theoretical predictions are reasonably accurate for unseparated flows, but have serious errors when separation is present. Some recent techniques for modeling post-separated flow behavior are discussed in light of the present experiments.

Seetharam, H. C.↗

Computation of viscous transonic flow about a lifting airfoil

The Reynolds averaged Navier-Stokes equations are solved numerically for the viscous transonic flow about a stationary NACA 64A010 airfoil in free air. This paper presents descriptions of the numerical method, turbulence models employed, and boundary conditions appropriate to simulation of free-air flight. Computed results are presented for the airfoil at a free-stream Mach number of 0.8, angles of attack of 0 and 2 deg, and a Reynolds number based on a chord of 4 x 10 to the 6th. For the lifting case, unsteady periodic motion was calculated along the aft portion of the airfoil and in its wake. Recent experimental results obtained by Johnson indicate periodicity aft of the shock closely approximates the computed frequency, but the amplitude of the disturbances was significantly less than the calculated amplitude.

Walitt, L.↗

An experimental evaluation of the application of the Kirchhoff formulation for sound radiation from an oscillating airfoil

The Kirchhoff integral formulation is evaluated for its effectiveness in quantitatively predicting the sound radiated from an oscillating airfoil whose chord length is comparable with the acoustic wavelength. A rigid airfoil section was oscillated at samll amplitude in a medium at rest to produce the sound field. Simultaneous amplitude and phase measurements were made of surface pressure and surface velocity distributions and the acoustic free field. Measured surface pressure and motion are used in applying the theory, and airfoil thickness and contour are taken into account. The result was that the theory overpredicted the sound pressure level by 2 to 5, depending on direction. Differences are also noted in the sound field phase behavior.

Brooks, T. F.↗

Two-dimensional wind tunnel test of an oscillating rotor airfoil, volume 1

A two dimensional wind tunnel test was conducted to obtain the quasisteady and unsteady characteristics of an advanced airfoil designed for helicopter rotor applications. Differential pressures were measured at 17 locations along the chord of the airfoil model. The airfoil motions were sinusoidal forced-pitch oscillations about the quarter chord at amplitudes varying from 2.5 to 10.0 degrees and at frequencies from 23 Hz to 90 Hz. The quasisteady tests were conducted at Mach numbers from 0.2 to 0.9, and the oscillatory tests between M = 0.2 and M = 0.7. At quasisteady conditions a limited number of drag measurements were made with a wake-traversing probe.

Dadone, L. U.↗

Water-tunnel experiments on an oscillating airfoil at RE equals 21,000

Flow visualization experiments were performed in a water tunnel on a modified NACA 0012 airfoil undergoing large amplitude harmonic oscillations in pitch. Hydrogen bubbles were used to: (1) create a conveniently striated and well preserved set of inviscid flow markers; and (2) to expose the succession of events occurring within the viscous domain during the onset of dynamic stall. Unsteady effects were shown to have an important influence on the progression of flow reversal along the airfoil surface prior to stall. A region of reversed flow underlying a free shear layer was found to momentarily exist over the entire upper surface without any appreciable disturbance of the viscous-inviscid boundary. A flow protuberance was observed to develop near the leading edge, while minor vortices evolve from an expanding instability of the free shear layer over the rear portion of the airfoil. The complete breakdown of this shear layer culminates in the successive formation of two dominant vortices.

Mcalister, K. W.↗

Onset of condensation effects with a NACA 0012-64 airfoil tested in the Langley 0.3-meter cryogenic tunnel

A 0.137m airfoil was tested in a 0.3m transonic cryogenic tunnel at free stream Mach numbers of 0.75, 0.85, and 0.95 over a total pressure range from 1.2 to 5.0 atmospheres. The onset of condensation effects were found to correlate more with the amount of supercooling in the free stream than it did with the supercooling in the region of maximum local Mach number over the airfoil. Effects in the pressure distribution over the airfoil were generally seen to appear over its entire length at nearly the same total temperature. Both observations suggest the possibility of heterogeneous nucleation occurring in the free stream. The potential operational benefits of the supercooling realized are presented in terms of increased Reynolds number capability at a given tunnel total pressure, reduced drive fan power if Reynolds number is held constant, and reduced liquid nitrogen consumption if Reynolds number is again constant. Depending on total pressure and free stream Mach number, these three benefits are found to respectively vary from 7 to 19%, 11 to 25%, and 9 to 20%.

Hall, R. M.↗