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Results are presented of the theory of wings and of wing sections which are of immediate practical value. They are proven and demonstrated by the use of the simple conceptions of kinetic energy and momentum only.
This report contains those results of the theory of wings and of wing sections which are of immediate practical value. They are proved and demonstrated by the use of the simple conceptions of "kinetic energy" and "momentum" only, familiar to every engineer; and not by introducing "isogonal transformations" and "vortices," which latter mathematical methods are not essential to the theory and better are used only in papers intended for mathematicians and special experts.
A research technique to obtain large-scale aerodynamic data in a simulated natural rain environment has been developed. A 10-ft chord NACA 64-210 wing section wing section equipped with leading-edge and trailing-edge high-lift devices was tested as part of a program to determine the effect of highly-concentrated, short-duration rainfall on airplane performance. Preliminary dry aerodynamic data are presented for the high-lift configuration at a velocity of 100 knots and an angle of attack of 18 deg. Also, data are presented on rainfield uniformity and rainfall concentration intensity levels obtained during the calibration of the rain simulation system.
This paper describes a new geometric analysis procedure for wing sections. This procedure is based on the normal mode analysis for continuous functions. A set of special shape functions is introduced to represent the geometry of the wing section. The generators of the NACA 4-digit airfoils were included in this set of shape functions. It is found that the supercritical wing section, Korn airfoil, could be well represented by a set of ten shape functions. Preliminary results showed that the number of parameters to define a wing section could be greatly reduced to about ten. Hence, the present research clearly advances the airfoil design technology by reducing the number of design variables.
This report gives a simple and exact method of calculating the lift distribution on thin wing sections. The most essential feature of the new theory is the introduction of an "ideal angle of attack," this angle being defined as that at which the flow enters the leading edge smoothly or, more precisely, as the angle of attack at which the lift at the leading edge equals zero. The lift distribution at this particular angle is shown to be a characteristic property of the section and has been termed the "basic distribution." it is shown that the lift of a wing section may always be considered to consist of (a) the basic distribution and (b) the additional distribution, where the latter is independent of the mean camber line and thus identical for all thin sections. The specific reason for the poor aerodynamic qualities of thin wing sections is pointed out as being due to the fact that the additional lift in potential flow becomes infinite at the leading edge. It is established that the essential parameter occurring in this analysis is the radius of curvature at the leading edge. It is further established that the actual slope of the lift curve is dependent on this parameter. The theoretical lift distribution is compared with the distribution obtained by direct measurement on a number of the more conventional wing sections. The new theory is of value in calculating the strength of wing sections.
The problem of determining the two dimensional potential flow around wing sections of any shape is examined. The problem is condensed into the compact form of an integral equation capable of yielding numerical solutions by a direct process. An attempt is made to analyze and coordinate the results of earlier studies relating to properties of wing sections. The existing approximate theory of thin wing sections and the Joukowski theory with its numerous generalizations are reduced to special cases of the general theory of arbitrary sections, permitting a clearer perspective of the entire field. The method which permits the determination of the velocity at any point of an arbitrary section and the associated lift and moments is described. The method is also discussed in terms for developing new shapes of preassigned aerodynamical properties.
Two distinct parameterization procedures are developed for investigating the grid sensitivity with respect to design parameters of a wing-section example. The first procedure is based on traditional (physical) relations defining NACA four-digit wing-sections. The second is advocating a novel (geometrical) parameterization using spline functions such as NURBS (Non-Uniform Rational B-Splines) for defining the wing-section geometry. An interactive algebraic grid generation technique, known as Hermite Cubic Interpolation, is employed to generate C-type grids around wing-sections. The grid sensitivity of the domain with respect to design and grid parameters has been obtained by direct differentiation of the grid equations. A hybrid approach is proposed for more geometrically complex configurations. A comparison of the sensitivity coefficients with those obtained using a finite-difference approach has been made to verify the feasibility of the approach. The aerodynamic sensitivity coefficients are obtained using the compressible two-dimensional thin-layer Navier-Stokes equations.
Ackeret began systematic polar measurements on Joukowsky wing sections, which were occasionally conducted in the wind tunnel. Under these conditions a considerable number of wing sections were tested during the last four years and the tests are now more or less concluded.
Thin airfoil theories of an ejector flapped wing section are reviewed. The global matching of the external airfoil flow with the ejector internal flow and the overall ejector flapped wing section aerodynamic performance are examined. Mathematical models of the external and internal flows are presented. The delineation of the suction flow coefficient characteristics are discussed. The idealized lift performance of an ejector flapped wing relative to a jet augmented flapped wing are compared.
In order to find an airfoil for a predetermined pressure distribution, the problem must be posed so that the pressure distribution creates no drag. Another fundamental difficulty is that it is impossible to specify a pressure distribution without first knowing the place where these pressures are to be applied, i.e., the wing-section shape. This difficulty may be avoided by directing the pressure distribution along the contour of the wing section. Then it becomes possible to define the change in wing-section shape which effects a certain modification of the wing-section shape. The limitations underlying the required pressure distribution are discussed and it is found that the sole essential limitation is zero drag. The method is illustrated with an example.
It is stated that the index value 6000, as found in normal tests of wing sections with a 20 cm chord, falls in the same region where the transition of laminar to turbulent flow takes place on thin flat plates. It is to be expected that slightly cambered, thin wing sections will behave similarly. The following test of two such wing sections were made for the purpose of verifying this supposition.
The nocturnal frost formation on a wing section, to explain the hazard associated with frost during takeoff was investigated. A model of nocturnal frost formation on a wing section which predicts when the nocturnal frost will form and also its thickness and density as a function of time was developed. The aerodynamic penalities as related to the nocturnal frost formation properties were analyzed to determine how much the takeoff performance would be degraded by a specific frost layer. With an aircraft takeoff assuming equations representing a steady climbing flight, it is determined that a reduction in the maximum gross weight or a partial frost clearance and a reduction in the takeoff angle of attack is needed to neutralize drag and life penalities which are due to frost. Atmospheric conditions which produce the most hazardous frost buildup are determined.
Circulation Control Wing (CCW) technology is a very effective way of achieving very high lift coefficients needed by aircraft during take-off and landing. This technology can also be used to directly control the flow field over the wing. Compared to a conventional high-lift system, a Circulation Control Wing (CCW) can generate the required values of lift coefficient C(sub L,max) during take-off/landing with fewer or no moving parts and much less complexity. Earlier designs of CCW configurations used airfoils with a large radius rounded trailing edge to maximize the lift benefit. However, these designs also produced very high drag. These high drag levels associated with the blunt, large radius trailing edge can be prohibitive under cruise conditions when Circulation Control is no longer necessary. To overcome this difficulty, an advanced CCW section, i.e., a circulation hinged flap was developed to replace the original rounded trailing edge CC airfoil. This concept developed by Englar is shown. The upper surface of the CCW flap is a large-radius arc surface, but the lower surface of the flap is flat. The flap could be deflected from 0 degrees to 90 degrees. When an aircraft takes-off or lands, the flap is deflected as in a conventional high lift system. Then this large radius on the upper surface produces a large jet turning angle, leading to high lift. When the aircraft is in cruise, the flap is retracted and a conventional sharp trailing edge shape results, greatly reducing the drag. This kind of flap does have some moving elements that increase the weight and complexity over an earlier CCW design. But overall, the hinged flap design still maintains most of the Circulation Control high lift advantages, while greatly reducing the drag in cruising condition associated with the rounded trailing edge CCW design. In the present work, an unsteady three-dimensional Navier-Stokes analysis procedure has been developed and applied to this advanced CCW configuration. The solver can be used in both a 2-D and a 3-D mode, and can thus model airfoils as well as finite wings. The jet slot location, slot height, and the flap angle can all be varied easily and individually in the grid generator and the flow solver. Steady jets, pulsed jets, the leading edge and trailing edge blowing can all be studied with this solver.
This report groups in a uniform manner the aerodynamic properties of commonly used wing sections as determined from tests in various wind tunnels. The data have been collected from reports of a number of laboratories. Where necessary, transformation has been made to the absolute system of coefficients and tunnel wall interference corrections have been applied. Tables and graphs present the data in the various forms useful to the engineer in the selection of a wing section.
The numerical aspect of theoretical work on transonics and supercritical wing sections are compiled. A model of the trailing edge is introduced which eliminates the loss of 15 to 20 percent experienced with heavily aft-loaded models, and it is indicated how drag creep can be reduced at off-design conditions. A rotated finite difference scheme is presented which can handle supersonic as well as subsonic free stream Mach numbers and leads to an effective three-dimensional program for the computation of transonic flow past an oblique wing. In the case of two-dimensional flow, the method is extended to take into account the displacement thickness computed by a semiempirical turbulent boundary layer correction. A series of supercritical wing sections is discussed together with comparisons between experimental and theoretical data. Computer programs and a brief manual for their operation are listed. It is shown that the programs furnish a physically adequate computer simulation of the compressible flows that arise in problems of transonic aerodynamics.
Flight experiments are being conducted as part of a multiphased subsonic transport high-lift research program for correlation with wind-tunnel and computational results. The NASA Langley Transport Systems Research Vehicle (B737-100 aircraft) is used to obtain in-flight flow characteristics at full-scale Reynolds numbers to contribute to the understanding of 3-D high-lift, multi-element flows including attachment-line transition and relaminarization, confluent boundary-layer development, and flow separation characteristics. Flight test results of pressure distributions and skin friction measurements were obtained for a full-chord wing section including the slat, main-wing, and triple-slotted, Fowler flap elements. Test conditions included a range of flap deflections, chord Reynolds numbers (10 to 21 million), and Mach numbers (0.16 to 0.40). Pressure distributions were obtained at 144 chordwise locations of a wing section (53-percent wing span) using thin pressure belts over the slat, main-wing, and flap elements. Flow characteristics observed in the chordwise pressure distributions included leading-edge regions of high subsonic flows, leading-edge attachment-line locations, slat and main-wing cove-flow separation and reattachment, and trailing-edge flap separation. In addition to the pressure distributions, limited skin-friction measurements were made using Preston-tube probes. Preston-tube measurements on the slat upper surface suggested relaminarization of the turbulent flow introduced by the pressure belt on the slat leading-edge surface when the slat attachment line was laminar. Computational analysis of the in-flight pressure measurements using two-dimensional, viscous multielement methods modified with simple-sweep theory showed reasonable agreement. However, overprediction of the pressures on the flap elements suggests a need for better detailed measurements and improved modeling of confluent boundary layers as well as inclusion of three-dimensional viscous effects in the analysis.
The use of a pitot-static probe to determine wing section drag at speeds from Mach 0.5 to approximately 1.0 was evaluated in flight. The probe unit is described and operational problems are discussed. Typical wake profiles and wing section drag coefficients are presented. The data indicate that the pitot-static probe gave reliable results up to speeds of approximately 1.0.
Sensitivity analysis in computational fluid dynamics with emphasis on grids and surface parameterization is described. An interactive algebraic grid-generation technique is employed to generate C-type grids around NACA four-digit wing sections. An analytical procedure is developed for calculating grid sensitivity with respect to design parameters of a wing section. A comparison of the sensitivity with that obtained using a finite difference approach is made. Grid sensitivity with respect to grid parameters, such as grid-stretching coefficients, are also investigated. Using the resultant grid sensitivity, aerodynamic sensitivity is obtained using the compressible two-dimensional thin-layer Navier-Stokes equations.