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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Arrangement of vortex lattices

A new method is developed for solving the lifting-surface equation for thin wings. The solution requires the downwash equation to be in the form of Cauchy integrals which can be interpreted as a vortex lattice with the positions of the vortices and control points dictated by the finite sum used to approximate the integrals involved. Lan's continuous loading method is employed for the chordwise integral since it properly accounts for the leading-edge singularity, Cauchy singularity, and Kutta condition. Unlike Lan, the spanwise loading is also continuous and the Cauchy singularity in the spanwise integral is also properly accounted for by using the midpoint trapezoidal rule and the theory of Chebyshev polynomials. This technique yields the exact classical solution to Prandtl's lifting-line equation.The solution to the lifting-surface equation for rectangular wings was found to compare well with other continuous loading methods, but with much smaller computational times, and to converge faster than other vortex lattice methods.

Dejarnette, F. R.↗
NASA NTRS1988

Calculation of the distributed loads on the blades of individual multiblade propellers in axial flow using linear and nonlinear lifting surface theories

In recent years much attention has been given to the development of methods and programs for the calculation of the aerodynamic characteristics of multiblade, saber-shaped air propellers. Most existing methods are based on the theory of lifting lines. Elsewhere, the theory of a lifting surface is used to calculate screw and lifting propellers. In this work, methods of discrete eddies are described for the calculation of the aerodynamic characteristics of propellers using the linear and nonlinear theories of lifting surfaces.

Pesetskaya, N. N.↗
NASA NTRS1947

Experimental and Calculated Characteristics of Several NACA 44-series Wings with Aspect Ratios of 8, 10, and 12 and Taper Ratios of 2.5 and 3.5

The aerodynamic characteristics of seven unswept tapered wings were determined by calculation from two-dimensional data and by wind-tunnel tests in order to demonstrate the accuracy of the calculations and to show some of the effects of aspect ratio, taper ratio, and root thickness-chord ratio. The characteristics were calculated by the usual application of the lifting-line theory which assumes linear section lift curves and also by an application of the theory which allows the use of nonlinear lift curves. A correction to the lift for the effect of chord was made by using the Jones edge-velocity factor. The wings had aspect ratios of 8, 10, and 12, taper ratios of 2.5 and 3.5, and NACA 44-series airfoils.

WINGS, TAPERED - CHARACTERISTICS↗
NASA NTRS1954

Method for calculating the rolling and yawing moments due to rolling for unswept wings with or without flaps or ailerons by use of nonlinear section lift data

The methods of NACA reports 865 and 1090 have been applied to the calculation of the rolling-moment and yawing-moment coefficients due to rolling for unswept wings with or without flaps or ailerons. The methods are based on lifting-line theory and allow the use of nonlinear section lift data. The method presented in this report permits calculations to be made somewhat beyond maximum lift for wings having no twist or continuous twist and employing airfoil sections which do not display large discontinuities in the lift curves. Calculations can be made up to maximum lift for wings with discontinuous twist such as that produced by partial-span flaps or ailerons, or both. Two calculated examples are presented in simplified computing forms in order to illustrate the procedures involve.

Martina, Albert P↗
NASA NTRS1980

Advanced propeller aerodynamic analysis

The analytical approaches as well as the capabilities of three advanced analyses for predicting propeller aerodynamic performance are presented. It is shown that two of these analyses use a lifting line representation for the propeller blades, and the third uses a lifting surface representation.

Bober, L. J.↗
NASA NTRS1977

Propeller Study. Part 2: the Design of Propellers for Minimum Noise

The design of propellers which are efficient and yet produce minimum noise requires accurate determinations of both the flow over the propeller. Topics discussed in relating aerodynamic propeller design and propeller acoustics include the necessary approximations and assumptions involved, the coordinate systems and their transformations, the geometry of the propeller blade, and the problem formulations including the induced velocity, required in the determination of mean lines of blade sections, and the optimization of propeller noise. The numerical formulation for the lifting-line model are given. Some applications and numerical results are included.

Ormsbee, A. I.↗
NASA NTRS1978

A uniqueness proof for a transonic flow problem

The uniqueness of the first-order lifting-line correction to the two-dimensional transonic small disturbance potential for the flow past a lifting, three-dimensional, large-aspect-ratio wing is proved. The correction is the solution of a linear equation of mixed type in the plane slit along the positive x-axis. The boundary data consist of Neumann data, continuity restrictions, the Kutta condition, and the form of the asymptotic behavior at infinity. The zeroth-order flow is assumed to be shock-free, and hence the correction is shock-free.

Cook, L. P.↗
NASA NTRS1992

Development of an analytical method to predict helicopter main rotor performance in icing conditions

Historically, certification of a helicopter for flight into known icing conditions was a problem. This is because of the current emphasis on flight testing for verification of system performance. Flight testing in icing conditions is difficult because, in addition to being dangerous and expensive, many times conditions which are sought after cannot be readily found in nature. The problem is compounded for helicopters because of their small range in comparison to many fixed wing aircraft. Thus, helicopters are forced to wait for conditions to occur in a certain region rather than seeking them out. These and other drawbacks to flight testing prompted extreme interest in developing validated alternatives to flight testing. One such alternative is theoretical prediction. It is desirable to have the ability to predict how a helicopter will perform when subjected to icing conditions. Herein, calculations are restricted to the main rotor, and are illustrated. The computational tool used to obtain performance is the lifting line analysis of B65. B65 incorporates experimental data into data banks in order to determine the section lift, drag, and moment characteristics of various airfoils at different Mach numbers and angles of attack. The local flow angle is calculated at user specified radial locations. This flow angle, along with the local Mach number is then cross referenced with the airfoil tables to obtain the local section characteristics. The local characteristics are then integrated together to obtain the entire rotor attributes. Once the clean performance is known, characterization of the type and shape of ice which accretes on the rotor blades is obtained using the analysis of LEWICE. The Interactive Boundary Layer (IBL) method then calculates the 2-D characteristics of the iced airfoil for input into the airfoil data bank of B65. Calculations are restricted to natural ice shedding and it is assumed that no de-icing takes place. Once the new lift, drag, and moment characteristics are known for the entire blade radius, this information is fed into B65, where the iced performance is then calculated.

Britton, Randall K.↗
NASA NTRS1974

Lifting surface theory of axial compressor blade rows. I - Subsonic compressor. II - Transonic compressor

A linearized three-dimensional lifting surface theory is considered, taking into account relations to axisymmetric 'through-flow' or actuator disk theories, general results for flow within the blade row, relations to two-dimensional cascade theory, and finite blade and wake effects. Numerical results are presented, giving attention to the problem of wakeless flow and of wake flow. Expressions for wake functions are given in an appendix. The lifting line velocity potential employed by Namba (1972) is used as a starting point in the discussion of the lifting surface theory. A study of subsonic conditions is supplemented by an investigation of a transonic compresso, taking into account the general three-dimensional solution, induced velocities, and the acoustic pressure field.

Okurounmu, O.↗
NASA NTRS1979

A study of the blown flap/jet flap analogy

A study of the blown flap/jet flap analogy has been undertaken. Analytical predictions were made using both improved lifting line and optimized vortex lattice models for the jet flap. Results were compared with experimental data for three propulsive lift systems; the jet augmented flap, the externally blown flap, and the upper surface blown flap. Force increments due to changes in geometry and jet parameters were well approximated in most cases, although the absolute values of the aerodynamic forces were usually underestimated. The relatively simple jet-flap models gave performance predictions of accuracy comparable to more complex analyses.

Hough, G. R.↗
NASA NTRS1999

Predicted Aerodynamic Characteristics of a NACA 0015 Airfoil Having a 25% Integral-Type Trailing Edge Flap

Using the two-dimensional ARC2D Navier-Stokes flow solver analyses were conducted to predict the sectional aerodynamic characteristics of the flapped NACA-0015 airfoil section. To facilitate the analyses and the generation of the computational grids, the airfoil with the deflected trailing edge flap was treated as a single element airfoil with no allowance for a gap between the flap's leading edge and the base of the forward portion of the airfoil. Generation of the O-type computational grids was accomplished using the HYGRID hyperbolic grid generation program. Results were obtained for a wide range of Mach numbers, angles of attack and flap deflections. The predicted sectional lift, drag and pitching moment values for the airfoil were then cast in tabular format (C81) to be used in lifting-line helicopter rotor aerodynamic performance calculations. Similar were also generated for the flap. Mathematical expressions providing the variation of the sectional lift and pitching moment coefficients for the airfoil and for the flap as a function of flap chord length and flap deflection angle were derived within the context of thin airfoil theory. The airfoil's sectional drag coefficient were derived using the ARC2D drag predictions for equivalent two dimensional flow conditions.

Hassan, Ahmed↗
NASA NTRS1960

Experimental and Theoretical Study of a Rectangular Wing in a Vortical Wake at Low Speed

A systematic study has been made, experimentally and theoretically, of the effects of a vortical wake on the aerodynamic characteristics of a rectangular wing at subsonic speed. The vortex generator and wing were mounted on a reflection plane to avoid body-wing interference. Vortex position, relative to the wing, was varied both in the spanwise direction and normal to the wing. Angle of attack of the wing was varied from -40 to +60. Both chordwise and spanwise pressure distributions were obtained with the wing in uniform and vortical flow fields. Stream surveys were made to determine the flow characteristics in the vortical wake. The vortex-induced lift was calculated by several theoretical methods including strip theory, reverse-flow theory, and reverse-flow theory including a finite vortex core. In addition, the Prandtl lifting-line theory and the Weissinger theory were used to calculate the spanwise distribution of vortex-induced loads. With reverse-flow theory, predictions of the interference lift were generally good, and with Weissinger's theory the agreement between the theoretical spanwise variation of induced load and the experimental variation was good. Results of the stream survey show that the vortex generated by a lifting surface of rectangular plan form tends to trail back streamwise from the tip and does not approach the theoretical location, or centroid of circulation, given by theory. This discrepancy introduced errors in the prediction of vortex interference, especially when the vortex core passed immediately outboard of the wing tip. The wake produced by the vortex generator in these tests was not fully rolled up into a circular vortex, and so lacked symmetry in the vertical direction of the transverse plane. It was found that the direction of circulation affected the induced loads on the wing either when the wing was at angle of attack or when the vortex was some distance away from the plane of the wing.

Smith, Willard G.↗
NASA NTRS1981

Factors Influencing the Predicted Performance of Advanced Propeller Designs

The assumptions on which conventional propeller aerodynamic performance analyses are based can be seriously violated when advanced high speed propellers are analyzed. Studies were performed using a lifting line representation for the propeller to determine the sensitivity of predicted propeller performance to various assumptions in the analysis. Items studied include the method of determining blade section lift and the effects of blade section drag, camber and blade sweep. The effects of nonuniform flow into the propeller and compressibility were also studied. Comparisons of analytical and experimental results are presented to demonstrate the overall validity of the results.

Bober, L. J.↗
NASA NTRS1981

Factors influencing the predicted performance of advanced propeller designs

The assumptions on which conventional propeller aerodynamic performance analyses are based can be seriously violated when advanced high speed propellers are analyzed. Studies have been performed using a lifting line representation for the propeller to determine the sensitivity of predicted propeller performance to various assumptions in the analysis. Items which have been studied include the method of determining blade section lift and the effects of blade section drag, camber and blade sweep. The effects of nonuniform flow into the propeller and compressibility have also been studied. Comparisons of analytical and experimental results are presented to demonstrate the overall validity of the results.

Bober, L. J.↗
NASA NTRS1953

Method for calculating the rolling and yawing moments due to rolling for unswept wings with or without flaps or ailerons by use of nonlinear section lift data

The methods of NACA Reports 865 and 1090 have been applied to the calculation of the rolling- and yawing-moment coefficients due to rolling for unswept wings with or without flaps or ailerons. The methods allow the use of nonlinear section lift data together with lifting-line theory. Two calculated examples are presented in simplified computing forms in order to illustrate the procedures involved.

CONTROLS - COMPLETE WINGS↗
NASA NTRS1952

Method for calculating lift distributions for unswept wings with flaps or ailerons by use of nonlinear section lift data

A method is presented which allows the use of nonlinear section lift data in the calculation of the spanwise lift distribution of unswept wings with flaps or ailerons. This method is based upon lifting line theory and is an extension to the method described in NACA rep. 865. The mathematical treatment of the discontinuity in absolute angle of attack at the end of the flap or aileron involves the use of a correction factor which accounts for the inability of a limited trigonometric series to represent adequately the spanwise lift distribution. A treatment of the apparent discontinuity in maximum section lift coefficient is also described. Simplified computing forms containing detailed examples are given for both symmetrical and asymmetrical lift distributions. A few comparisons of calculated characteristics with those obtained experimentally are also presented.

Sivells, James C↗
NASA NTRS1991

Aerodynamic parameter studies and sensitivity analysis for rotor blades in axial flight

The analytical capability is offered for aerodynamic parametric studies and sensitivity analyses of rotary wings in axial flight by using a 3-D undistorted wake model in curved lifting line theory. The governing equations are solved by both the Multhopp Interpolation technique and the Vortex Lattice method. The singularity from the bound vortices is eliminated through the Hadamard's finite part concept. Good numerical agreement between both analytical methods and finite differences methods are found. Parametric studies were made to assess the effects of several shape variables on aerodynamic loads. It is found, e.g., that a rotor blade with out-of-plane and inplane curvature can theoretically increase lift in the inboard and outboard regions respectively without introducing an additional induced drag.

Chiu, Y. Danny↗
NASA NTRS1991

Aerodynamic parametric studies and sensitivity analysis for rotor blades in axial flight

The analytical capability is offered for aerodynamic parametric studies and sensitivity analyses of rotary wings in axial flight by using a 3D undistorted wake model in curved lifting line theory. The governing equations are solved by both the Multhopp Interpolation technique and the Vortex Lattice method. The singularity from the bound vortices is eliminated through the Hadamard's finite part concept. Good numerical agreement between both analytical methods and finite differences methods are found. Parametric studies were made to assess the effects of several shape variables on aerodynamic loads. It is found, e.g., that a rotor blade with out-of-plane and inplane curvature can theoretically increase lift in the inboard and outboard regions respectively without introducing an additional induced drag.

Chiu, Y. D.↗