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Formulas are given for the propelling or drag force experience in a uniform air stream by an airfoil or an airfoil-aileron combination, oscillating in any of three degrees of freedom; vertical flapping, torsional oscillations about a fixed axis parallel to the span, and angular oscillations of the aileron about a hinge.
The interference of the wind-tunnel boundaries on the downwash behind an airfoil has been experimentally investigated and the results have been compared with the available theoretical results for open-throat wind tunnels. As in previous studies, the simplified theoretical treatment that assumes the test section to be an infinite free jet has been shown to be satisfactory at the lifting line. The experimental results, however, show that this assumption may lead to erroneous conclusions regarding the corrections to be applied to the downwash in the region behind the airfoil where the tail surfaces are normally located. The results of a theory based on the more accurate concept of the open-jet wind tunnel as a finite length of free jet provided with a closed exit passage are in good qualitative agreement with the experimental results.
The results of previous reports dealing with airfoil section characteristics and span load distribution data are coordinated into a method for determining the air forces and their distribution on airplane wings. Formulas are given from which the resultant force distribution may be combined to find the wing aerodynamic center and pitching moment. The force distribution may also be resolved to determine the distribution of chord and beam components. The forces are resolved in such a manner that it is unnecessary to take the induced drag into account. An illustration of the method is given for a monoplane and a biplane for the conditions of steady flight and a sharp-edge gust. The force determination is completed by outlining a procedure for finding the distribution of load along the chord of airfoil sections.
For the purpose of studying the transition from laminar to turbulent flow, boundary-layer measurements were made in the NACA full-scale wind tunnel on three symmetrical airfoils of NACA 0009, 0012, and 0018 sections. The effects of variations in lift coefficient, Reynolds number, and airfoil thickness on transition were investigated. Air speed in the boundary layer was measured by total-head tubes and by hot wires; a comparison of transition as indicated by the two techniques was obtained. The results indicate no unique value of Reynolds number for the transition, whether the Reynolds number is based upon the distance along the chord or upon the thickness of the boundary layer at the transition point. In general, the transition is not abrupt and occurs in a region that varies in length as a function of the test conditions.
Extensive experimental measurements have been made of the downwash angles and the wake characteristics behind airfoils with and without flaps and the data have been analyzed and correlated with the theory. A detailed study was made of the errors involved in applying lifting-line theory, such as the effects of a finite wing chord, the rolling-up of the trailing vortex sheet, and the wake. The downwash angles, as computed from the theoretical span load distribution by means of the Biot-Savart equation, were found to be in satisfactory agreement with the experimental results. The rolling-up of the trailing vortex sheet may be neglected, but the vertical displacement of the vortex sheet requires consideration. By the use of a theoretical treatment indicated by Prandtl, it has been possible to generalize the available experimental results so the predictions can be made of the important wake parameters in terms of the distance behind the airfoil trailing edge and the profile-drag coefficient. The method of application of the theory to design and the satisfactory agreement between predicted and experimental results when applied to an airplane are demonstrated.
The NACA has conducted an investigation to determine the performance that can be obtained from a multistage axial-flow compressor based on airfoil research. A theory was developed; an eight-stage axial-flow compressor was designed, constructed, and tested. The performance of the compressor was determined for speeds from 5000 to 14,000 r.p.m with varying air flow at each speed. Most of the tests were made with air at room temperature. The performance was determined in accordance with the Committee's recommended procedure for testing superchargers. The expected performance was obtained, showing that a multistage compressor of high efficiency can be designed by the application of airfoil theory.
By use of the methods of thin airfoil theory, which include effects of compressibility, relations are developed which permit the rapid determination of the pressure distribution over an unstaggered cascade of airfoils of a given profile, and the determination of the profile shape necessary to yield a given pressure distribution for small chord/gap ratios. For incompressible flow the results of the theory are compared with available examples obtained by the more exact method of conformal transformation. Although the theory is developed for small chord/gap ratios, these comparisons show that it may be extended to chord/gap ratios of order unity, at least for low-speed flows. Choking cascades, a phenomenon of particular importance in compressor design, is considered.
Report presents the results of an investigation conducted in the Langley 19-foot pressure tunnel to determine the maximum lift and stalling characteristics of two thin wings equipped with several types of flaps. Split, single slotted, and double slotted flaps were tested on one wing which had NACA 65-210 airfoil sections and split and double slotted flaps were tested on the other, which had NACA 64-210 airfoil sections. Both wings were zero sweep, an aspect ratio of 9, and a taper ratio of 0.4.
A low-turbulence wind-tunnel investigation was made of an NACA 64a010 airfoil having a porous surface to determine the reduction in section total-drag coefficient that might be obtained at large Reynolds numbers by the use of suction to produce continuous inflow through the surface of the airfoil (area suction). In addition to the experimental investigation, a related theoretical analysis was made to provide a basis of comparison for the test results.
The two-dimensional, incompressible potential flow past a lattice of airfoils of arbitrary shape is investigated theoretically. The problem is treated by usual methods of conformal mapping in several stages, one stage corresponding to the mapping of the framework of the arbitrary line lattice and another significant stage corresponding to the Theodorsen method for the mapping of the arbitrary single wing profile into a circle. A particular feature in the theoretical treatment is the special handling of the regions at an infinite distance in front of and behind the lattice. Expressions are given for evaluation of the velocity and pressure distribution at the airfoil boundary. An illustrative numerical example is included.
The basic ideas of a new method for treating the problem of the airfoil are presented, and a review is given of the problems thus far computed for incompressible and supersonic flows. Test results are reported for the airfoil of circular plan form and the results are shown to agree well with the theory. As a supplement, a theory based on the older methods is presented for the rectangular of small aspect ratio.
A theory is developed for the airfoil of finite span at supersonic speed analogous to the Prandtl airfoil theory of 1918-1919 for incompressible flow. In addition to the profile and induced drags, account must be taken at supersonic flow of still another drag, namely, the wave drag, which is independent of the wing aspect ratio. Both wave and induced drags are proportional to the square of the lift and depend on the Mach number, that is, the ratio of flight to sound speed. In general, in the case of supersonic flow, the drag-lift ratio is considerably less favorable than is the case for incompressible flow. Among others the following examples are considered: 1) lifting line with constant lift distribution (horseshoe vortex); 2) computation of wave and induced drag and the twist of a trapezoidal wing of constant lift density; 3) computation of the lift distribution and drag of an untwisted rectangular wing.
This report discusses progress made on NASA Cooperative Agreement NCC2-545, 'An Experimental Study of a Turbulent Boundary Layer in the Trailing-Edge Region of a Circulation-Control Airfoil,' during the period 1 Oct. 1992 - 30 Jun. 1993. The study, being conducted by Jeff Brown of the Eloret Institute, in conjunction with the Experimental Fluid Dynamics Branch at NASA Ames (Dennis Johnson, technical monitor), features 2-component laser Doppler velocimeter (LDV) measurements in the trailing edge and wake regions of a generic circulation-control airfoil model. The final experimental phase of the study will be carried out in the Ames High Reynolds Number Channel II (HRC2) transonic blow-down facility. During the 9-month period covered by this report, important data were acquired using the near-wall laser Doppler velocimeter (LDV) whose development has been described in previous reports. These data point strongly to the viability of this new technique for measuring the full Reynolds Stress Tensor in 3D flows.
The VR-7 airfoil was experimentally studied with and without a leading-edge slat at fixed angles of attack from 0 deg to 30 deg at Re = 200,000 and for unsteady pitching motions described by alpha equals alpha(sub m) + 10 deg(sin(wt)). The models were two dimensional, and the test was performed in a water tunnel at Ames Research Center. The unsteady conditions ranged over Re equals 100,000 to 250,000, k equals 0.001 to 0.2, and alpha(sub m) = 10 deg to 20 deg. Unsteady lift, drag, and pitching-moment measurements were obtained along with fluorescent-dye flow visualizations. The addition of the slat was found to delay the static-drag and static-moment stall by about 5 degrees and to eliminate completely the development of a dynamic-stall vortex during unsteady motions that reached angles as high as 25 degrees. In all of the unsteady cases studied, the slat caused a significant reduction in the force and moment hysteresis amplitudes. The reduced frequency was found to have the greatest effect on the results, whereas the Reynolds number had little effect on the behavior of either the basic or the slatted airfoil. The slat caused a slight drag penalty at low angles of attack, but generally increased the lift/drag ratio when averaged over the full cycle of oscillation.
A study of Navier-Stokes calculations of flows about multielement airfoils using a chimera grid approach is presented. The chimera approach utilizes structured, overlapped grids which allow great flexibility of grid arrangement and simplifies grid generation. Calculations are made for two-, three-, and four-element airfoils, and modeling of the effect of gap distance between elements is demonstrated for a two element case. Solutions are obtained using the thin-layer form of the Reynolds averaged Navier-Stokes equations with turbulence closure provided by the Baldwin-Lomax algebraic model or the Baldwin-Barth one equation model. The Baldwin-Barth turbulence model is shown to provide better agreement with experimental data and to dramatically improve convergence rates for some cases. Recently developed, improved farfield boundary conditions are incorporated into the solver for greater efficiency. Computed results show good comparison with experimental data which include aerodynamic forces, surface pressures, and boundary layer velocity profiles.
The flow field over an airfoil contains several distinct flow characteristics, e.g. laminar, transitional, turbulent boundary layer flow, flow separation, unstable free shear layers, and a wake. This diversity of flow regimes taxes the presently available Reynolds averaged turbulence models. Such models are generally tuned to predict a particular flow regime, and adjustments are necessary for the prediction of a different flow regime. Similar difficulties are likely to emerge when the large eddy simulation technique is applied with the widely used Smagorinsky model. This model has not been successful in correctly representing different turbulent flow fields with a single universal constant and has an incorrect near-wall behavior. Germano et al. (1991) and Ghosal, Lund & Moin have developed a new subgrid-scale model, the dynamic model, which is very promising in alleviating many of the persistent inadequacies of the Smagorinsky model: the model coefficient is computed dynamically as the calculation progresses rather than input a priori. The model has been remarkably successful in prediction of several turbulent and transitional flows. We plan to simulate turbulent flow over a '2D' airfoil using the large eddy simulation technique. Our primary objective is to assess the performance of the newly developed dynamic subgrid-scale model for computation of complex flows about aircraft components and to compare the results with those obtained using the Reynolds average approach and experiments. The present computation represents the first application of large eddy simulation to a flow of aeronautical interest and a key demonstration of the capabilities of the large eddy simulation technique.
Wind tunnel tests have been conducted on a NASA GA(W)-2 airfoil section at Reynolds number of 2.2 x 10(exp 6) and Mach number of 0.13. Detailed measurements of flow fields associated with turbulent boundary layers have been obtained at angles of attack of 10.3, 14.4, and 18.3 deg. Pre- and post-separated velocity and pressure survey results over the airfoil and in the associated wake are presented. Extensive force, pressure, tuft survey, hot-film survey, local skin friction, and boundary layer data are also included. Pressure distributions and separation point locations show good agreement with theory for the two lower angles of attack. Boundary layer displacement thickness, momentum thickness, and shape factor agree well with theory up to the point of separation. There is considerable disparity between extent of flow reversal in the wake as measured by pressure and hot-film probes. The difference is attributed to the intermittent nature of the flow reversal.
Wind tunnel tests have been conducted on an NACA 2412 airfoil section at Reynolds number of 2.2 x 10(exp 6) and Mach number of 0.13. Detailed measurements of flow fields associated with turbulent boundary layers have been obtained at angles of attack of 12.4 degrees, 14.4 degrees, and 16.4 degrees. Pre- and post-separated velocity and pressure survey results over the airfoil and in the associated wake are presented. Extensive force, pressure, tuft survey, hot-film survey, local skin friction, and boundary layer data are also included. Pressure distributions and separation point locations show good agreement with theory for the two layer angles of attack. Boundary layer displacement thickness, momentum thickness, and shape factor agree well with theory up to the point of separation. There is considerable disparity between extent of flow reversal in the wake as measured by pressure and hot-film probes. The difference is attributed to the intermittent nature of the flow reversal.