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Program is revised of NASA/Lockheed program to numerically analyze complex viscous flow about slotted airfoils. Airfoil to be analyzed can contain as many as 10 components with negative or positive overlap. Program is written in FORTRAN IV and Assembled for batch execution on CYBER 175 only.
PROFILE program solves diverse and inverse airfoil-flow problems. It combines conformational mapping method for design of airfoils with prescribed velocity-distribution characteristics, panel method for potential-flow analysis, and boundary-layer method. PROFILE is written in FORTRAN IV for implementation on CDC 6000-series computer.
Force and surface pressure distributions were measured for the 21% LS(1)-0421 modified airfoil fitted with 20% aileron, 25% slotted flap and 10% slot lip spoiler. All tests were conducted at a Reynolds number of 2.2 x 10 to the 6th power and a Mach number of 0.13. The lift, drag, pitching moments, control surface normal force and hinge moments, and surface pressure distributions are included in the results. Incremental performance of flap and aileron are discussed and compared to the GA(W)-2 airfoil. Spoiler control which shows a slight reversal tendency at high alpha, is examined.
Low speed wind tunnel tests were conducted to evaluate the effects on performance of modifying a 23 percent thick low speed airfoil. The airfoil contour was altered to reduce the upper-surface adverse pressure gradient and hence reduce boundary layer separation. The chord Reynolds number varied from about 2,000,000 to 9,000,000.
Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. The steady velocity potential is obtained first from the well-known nonlinear equation for steady transonic flow. The unsteady velocity potential is then obtained from a linear differential equation in complex form with spatially varying coefficients. Since sinusoidal motion is assumed, the unsteady equation is independent of time. An out-of-core direct solution procedure was developed and applied to two-dimensional sections. Results are presented for a section of vanishing thickness in subsonic flow and an NACA 64A006 airfoil in supersonic flow. Good correlation is obtained in the first case at values of Mach number and reduced frequency of direct interest in flutter analyses. Reasonable results are obtained in the second case. Comparisons of two-dimensional finite difference solutions with exact analytic solutions indicate that the accuracy of the difference solution is dependent on the boundary conditions used on the outer boundaries. Homogeneous boundary conditions on the mesh edges that yield complex eigenvalues give the most accurate finite difference solutions. The plane outgoing wave boundary conditions meet these requirements.
An airfoil section for use on helicopter rotor blades was defined and analyzed by means of potential flow/boundary layer interaction and viscous transonic flow methods to meet as closely as possible a set of advanced airfoil design objectives. The design efforts showed that the first priority objectives, including selected low speed pitching moment, maximum lift and drag divergence requirements can be met, though marginally. The maximum lift requirement at M = 0.5 and most of the profile drag objectives cannot be met without some compromise of at least one of the higher order priorities.
The implementation of the approximate factorization algorithm and its ability to efficiently and accurately describe transonic flow about an NACA 64A010 airfoil section is examined. The approximate factorization algorithm is developed from the nondimensional, conservative, vectorized Navier-Stokes equations expressed in curvilinear coordinates. Equations of state and transport coefficient relations appropriate to atmospheric air are appended to close the system of partial differential equations. An algebraic turbulence model is also incorporated into the equation set. This algorithm was verified by investigating the flow about an NACA 64A010 airfoil at 0, 2, and 3.5 deg angle of attack for free-stream conditions of 2,000,000 Reynolds number and 0.8 Mach number. Overall results were in good qualitative agreement with wind tunnel data sets. However, while nondimensional times of six were attained, numerical difficulties prevented any case from reaching a true steady state.
The multi-component airfoil program (Langley-MCARF) for attached flow is modified to accept the free vortex sheet separation-flow model program (Analytical Methods, Inc.-CLMAX). The viscous effects are incorporated into the calculation by representing the boundary layer displacement thickness with an appropriate source distribution. The separation flow model incorporated into MCARF was applied to single component airfoils. Calculated pressure distributions for angles of attack up to the stall are in close agreement with experimental measurements. Even at higher angles of attack beyond the stall, correct trends of separation, decrease in lift coefficients, and increase in pitching moment coefficients are predicted.
The time-domain equations of motion of elastic airfoil sections forced by control surface motions and gusts were developed for the case of incompressible flow. Extensive use was made of special functions related to the inverse transform of Theodorsen's function. Approximations for the special cases of zero stream velocity, small time, large and time are given. A numerical solution technique for the solution of the general case is given. Examples of the exact transient response of an airfoil are presented.
A flow visualization technique, referred to as the smoke-wire, was used for visualization of the transition of the free shear layer associated with the laminar separation bubble of a NACA 66 sub 3-018 airfoil section at low Reynolds number (50,000-130,000). The smoke-wire technique allows the introduction of fine smoke streaklines into the flow field through the electrical resistive heating of a very fine wire which has been coated with oil and which is located upstream from the leading edge of the airfoil section. Streakline data were collected using both high speed still and motion picture photography.
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).
The major aspects of a code for the design of shockless airfoils in two-dimensional transonic flow are reviewed. The code is based on a method of analytic continuation into the domain of two complex characteristic variables, which makes it possible to associate a shockless airfoil with a given pressure distribution. This procedure is compared with another more direct method based on a two-dimensional analysis code that has had wide acceptance by the aircraft industry.
A static aeroelastic analysis is presented of the divergence of untapered wings with conventional and supercritical airfoil sections at sweep angles of zero and -15 deg. One bending and one torsion mode were employed for a uniform rectangular cantilevered beam with the elastic axis at midchord, and calculations were based on a two-dimensional differential equations formulation in the structural coordinate system and in simple strip theory. A minimum divergence speed in the transonic range is obtained which is associated with the rearward shift of the aerodynamic center, and a 17% difference in minimum divergence dynamic pressure is found between a supercritical and a conventional wing. It is noted that although the strip method employed allows the assessment of the sensitivity of airfoil shapes to divergence, three-dimensional transonic aerodynamic methods should be used to predict wing divergence characteristics.
Implicit finite-difference scheme efficiently computes unsteady potential flow about airfoils. Formulation uses density and velocity potential as dependent variables. Conservation form is retained to assure that shock wave location and speed are computed correctly. Scheme fills need for method to calculate efficiently unsteady potential flow about airfoils and to predict flutter and other unsteady aeroelastic phenomena in transonic flow regimes.
Three new options were incorporated into an existing computer program for the design and analysis of low speed airfoils. These options permit the analysis of airfoils having variable chord (variable geometry), a boundary layer displacement iteration, and the analysis of the effect of single roughness elements. All three options are described in detail and are included in the FORTRAN IV computer program.
The procedure solves the Navier-Stokes equations by the consistently split linearized block implicit method of Briley and McDonald in a body fitted coordinate system. The procedure is described and results are presented for flow about an airfoil whose incidence changes from 6 degrees to 19 degrees at a Reynolds number of one million and Mach number of 0.2. In addition, the unsteady flow about an airfoil held at a constant 19 degree incidence is examined and compared to data.
The operation of the TAIR (Transonic AIRfoil) computer code, which uses a fast, fully implicit algorithm to solve the conservative full-potential equation for transonic flow fields about arbitrary airfoils, is described on two levels of sophistication: simplified operation and detailed operation. The program organization and theory are elaborated to simplify modification of TAIR for new applications. Examples with input and output are given for a wide range of cases, including incompressible, subcritical compressible, and transonic calculations.
The evolution of unsteady boundary layers on oscillating airfoils is investigated by solving the governing equations by the Characteristic Box scheme. The difficulties associated with computing the first profile on a given time line, and the velocity profiles with partial flow reversal are solved. A sample calculation is performed for an external velocity distribution typical of those found near the leading edge of thin airfoils. The viability of the calculation procedure is demonstrated.