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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.
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.
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.
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.
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.
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.
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.
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.
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%.
An analytical study was conducted to predict the aerodynamic characteristics of two helicopter rotor airfoils. Documentation of the predictive process covers the development of empirical factors used in conjunction with computer programs for airfoil analysis. Tables of lift, drag, and pitching-moment coefficient for each airfoil were prepared for two dimensional, steady flow conditions at Mach numbers from 0.3 to 0.9 and Reynolds numbers of 7,700,000 to 23,000,000, respectively.
Theoretical predictions of several versions of the multielement airfoil computer program are evaluated. The computed results are compared with experimental high lift data of general aviation airfoils with a single trailing edge flap, and of airfoils with a leading edge flap and double slotted trailing edge flaps. Theoretical and experimental data include lift, pitching moment, profile drag and surface pressure distributions, boundary layer integral parameters, skin friction coefficients, and velocity profiles.
A compressible Navier-Stokes solution procedure is applied to the flow about an isolated airfoil. Two major problem areas were investigated. The first area is that of developing a coordinate system and an initial step in this direction has been taken. An airfoil coordinate system obtained from specification of discrete data points developed and the heat conduction equation has been solved in this system. Efforts required to allow the Navier-Stokes equations to be solved in this system are discussed. The second problem area is that of obtaining flow field solutions. Solutions for the flow about a circular cylinder and an isolated airfoil are presented. In the former case, the prediction is shown to be in good agreement with data.
The behavior of unsteady aerodynamic loadings on airfoils oscillating in transonic flow has been investigated numerically with particular attention given to supercritical airfoil sections. A previously developed finite difference method, which is based on the full potential equation and which uses a quasi-conservative scheme for proper capture of a shock wave motion, was employed for the present study. The unsteady aerodynamic pressure and load distributions on several different airfoil sections are presented with particular emphasis on the effects of free-stream Mach number, reduced frequency, and mean angle of attack. These parameters are demonstrated to have a significant effect on the behavior of the unsteady aerodynamic loadings. Comparisons of the present calculations with the exact inviscid solution and with the experimental results are also presented.
The numerical calculation of unsteady two dimensional airloads which act upon thin airfoils in subsonic ventilated wind tunnels was studied. Neglecting certain quadrature errors, Bland's collocation method is rigorously proved to converge to the mathematically exact solution of Bland's integral equation, and a three way equivalence was established between collocation, Galerkin's method and least squares whenever the collocation points are chosen to be the nodes of the quadrature rule used for Galerkin's method. A computer program displayed convergence with respect to the number of pressure basis functions employed, and agreement with known special cases was demonstrated. Results are obtained for the combined effects of wind tunnel wall ventilation and wind tunnel depth to airfoil chord ratio, and for acoustic resonance between the airfoil and wind tunnel walls. A boundary condition is proposed for permeable walls through which mass flow rate is proportional to pressure jump.
Techniques for calculating high Reynolds number flow around an airfoil undergoing dynamic stall are reviewed. Emphasis is placed on predicting the values of lift, drag, and pitching moments. Methods discussed include: the discrete potential vortex method; thin boundary layer method; strong interaction between inviscid and viscous flows; and solutions to the Navier-Stokes equations. Empirical methods for estimating unsteady airloads on oscillating airfoils are also described. These methods correlate force and moment data from wind tunnel tests to indicate the effects of various parameters, such as airfoil shape, Mach number, amplitude and frequency of sinosoidal oscillations, mean angle, and type of motion.
The viscous/potential flow past single-element and multielement airfoils is studied theoretically and experimentally. A computerized analysis, based on iteratively coupled potential-flow and boundary-layer analysis, is used to predict the flow field of the airfoil. The method yields detailed characteristics of conventional laminar and turbulent boundary layers, turbulent wakes, and confluent boundary layers. The viscous flows are analyzed with a method that uses finite-difference solutions of the boundary-layer equations. Reynolds stress in the boundary layers and wakes is simulated with eddy viscosity models for the various flow zones. The viscous calculations are carried into the wake of the airfoil where the drag is found from the defect in the wake momentum.
TRANDES program provides aircraft engineer with accurate and efficient tool for analysis of steady, irrotational, transonic flow over specified two dimensional airfoil in free air. Program is used to design airfoils having prescribed pressure distribution, including effects of weak viscous interaction. TRANDES yield accurate solutions efficiently for biconvex, conventional, and aftcambered airfoils.
The measurement capabilities of laser velocimetry and holographic interferometry in transonic airfoil testing were demonstrated. Presented are representative results obtained with these two nonintrusive techniques on a 15.24 cm chord airfoil section. These results include the density field about the airfoil, flow angles in the inviscid flow and viscous flow properties including the turbulent Reynolds stresses. The accuracies of the density fields obtained by interferometry were verified from comparisons with surface pressure and laser velocimeter measurements.