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At least 91 records · Page 5

Modified Matrix Method for Calculating Steady-State Span Loading on Flexible Wings in Subsonic Flight

A method is presented for shortening the computations required to determine the steady-state span loading on flexible wings in subsonic flight. The method makes use of tables of downwash factors to find the necessary aerodynamic-influence coefficients for the application of lifting-line theory. Explicit matrix equations of equilibrium are converted into a matrix power series with a finite number of terms by utilizing certain characteristic properties of matrices. The number of terms in the series is determined by a trial-and-error process dependent upon the required accuracy of the solution. Spanwise distributions of angle of attack, airload, shear, bending moment, and pitching moment are readily obtained as functions of qm(sub R) where q denotes the dynamic pressure and mR denotes the lift-curve slope of a rigid wing. This method is intended primarily to make it practical to solve steady-state aeroelastic problems on the ordinary manually operated desk calculators, but the method is also readily adaptable to automatic computing equipment.

Gainer, Patrick A.↗

Improvements to the Blade Element Momentum Formulation of OpenFAST for Skewed Inflows

In this work, we modify the blade element momentum algorithm of OpenFAST to improve its predictions under large skewed inflow conditions. We use the well-known Glauert's skew correction and introduce continuous extension of the model for high-thrust conditions. We present the rationale behind Glauert's empirical model and discuss the different conventions possible for the axial induction factor. We verify the model against the higher-fidelity lifting-line vortex method and blade-resolved computational fluid dynamics, and we observe that the new implementation enhances the accuracy and reliability of OpenFAST's aerodynamic modeling capabilities in conditions involving large skew angles. For the parametric studies run using the different codes, we find that the power changes with the skew angle as cos 1.7 (θ skew ) and the thrust as cos 0.65 (θ skew ). An analysis of the azimuthal variation of the induced velocities in the rotor plane reveals that current redistribution models used in blade element momentum codes may need to be refined.

17 WIND ENERGY↗

Progress in the validation of rotor aerodynamic codes using field data

Within the framework of the fourth phase of the International Energy Agency (IEA) Wind Task 29, a large comparison exercise between measurements and aeroelastic simulations has been carried out featuring three simulation cases in axial, sheared and yawed inflow conditions. Results were obtained from more than 19 simulation tools originating from 12 institutes, ranging in fidelity from blade element momentum (BEM) to computational fluid dynamics (CFDs) and compared to state-of-the-art field measurements from the 2 MW DanAero turbine. More than 15 different variable types ranging from lifting-line variables to blade surface pressures, loads and velocities have been compared for the different conditions, resulting in over 250 comparison plots. The result is a unique insight into the current status and accuracy of rotor aerodynamic modeling. For axial flow conditions, a good agreement was found between the various code types, where a dedicated grid sensitivity study was necessary for the CFD simulations. However, compared to wind tunnel experiments on rotors featuring controlled conditions, it remains a challenge to achieve good agreement of absolute levels between simulations and measurements in the field. For sheared inflow conditions, uncertainties due to rotational and unsteady effects on airfoil data result in the CFD predictions standing out above the codes that need input of sectional airfoil data. However, it was demonstrated that using CFD-synthesized airfoil data is an effective means to bypass this shortcoming. For yawed flow conditions, it was observed that modeling of the skewed wake effect is still problematic for BEM codes where CFD and free vortex wake codes inherently model the underlying physics correctly. The next step is a comparison in turbulent inflow conditions, which is featured in IEA Wind Task 47. Doing this analysis in cooperation under the auspices of the IEA Wind Technology Collaboration Program (TCP) has led to many mutual benefits for the participants. The large size of the consortium brought ample manpower for the analysis where the learning process by combining several complementary experiences and modeling techniques gave valuable insights that could not be found when the analysis is carried out individually.

17 WIND ENERGY↗

Analysis of high-aspect-ratio jet-flap wings of arbitrary geometry

An analytical technique to compute the performance of an arbitrary jet-flapped wing is developed. The solution technique is based on the method of Maskell and Spence in which the well-known lifting-line approach is coupled with an auxiliary equation providing the extra function needed in jet-flap theory. The present method is generalized to handle straight, uncambered wings of arbitrary planform, twist, and blowing (including unsymmetrical cases). An analytical procedure is developed for continuous variations in the above geometric data with special functions to exactly treat discontinuities in any of the geometric and blowing data. A rational theory for the effect of finite wing thickness is introduced as well as simplified concepts of effective aspect ratio for rapid estimation of performance.

Lissaman, P. B. S.↗

Analysis of high aspect ratio jet flap wings of arbitrary geometry.

Paper presents a design technique for rapidly computing lift, induced drag, and spanwise loading of unswept jet flap wings of arbitrary thickness, chord, twist, blowing, and jet angle, including discontinuities. Linear theory is used, extending Spence's method for elliptically loaded jet flap wings. Curves for uniformly blown rectangular wings are presented for direct performance estimation. Arbitrary planforms require a simple computer program. Method of reducing wing to equivalent stretched, twisted, unblown planform for hand calculation is also given. Results correlate with limited existing data, and show lifting line theory is reasonable down to aspect ratios of 5.

Lissaman, P. B. S.↗

System design of a rudder coordination system

The application of the parameter optimization computer program to the design of a rudder coordination system for the F-8 airplane is summarized. The flight condition was Mach 0.56 at 20,000 feet altitude. The system configuration selected consisted of signal paths that fed yaw rate and aileron signals to the rudder. The two signal paths were summed and then modified by a high pass filter to eliminate any steady state bias signal. The input axis of the yaw gyro was perpendicular to the aircraft zero lift line and the trim angle of attack was 7.75 degrees. The parameter optimization was used to design the complete system first, and then a root locus analysis of the individual component effects was made. The results are presented.

Whitaker, H. P.↗

Effects of asymmetry on the dynamic stability of aircraft

The oblique wing concept for transonic aircraft was proposed to reduce drag. The dynamic stability of the aircraft was investigated by analytically determining the stability derivatives at angles of skew ranging from 0 and 45 deg and using these stability derivatives in a linear analysis of the coupled aircraft behavior. The stability derivatives were obtained using a lifting line aerodynamic theory and found to give reasonable agreement with derivatives developed in a previous study for the same aircraft. In the dynamic analysis, no instability or large changes occurred in the root locations for skew angles varying from 0 to 45 deg with the exception of roll convergence. The damping in roll, however, decreased by an order of magnitude. Rolling was a prominent feature of all the oscillatory mode shapes at high skew angles.

Fantino, R. E.↗

Preservation of wing leading edge suction at the plane of symmetry as a factor in wing-fuselage design

Most fuselage geometries cover a portion of the wing leading edge near the plane of symmetry, and it seems reasonable to expect that a large fraction of the leading edge suction which would be developed by the covered wing at high angles of attack is not developed on the fuselage. This is one of the reasons that the Oswald span efficiency factor for the wing body combination fails to approach the value predicted by lifting line theory for the isolated wing. Some traditional and recent literature on wing-body interference is discussed and high Reynolds number data on wing-body-nacelle drag are reviewed. An exposed central leading edge geometry has been developed for a sailplane configuration. Low Reynolds number tests have not validated the design concept.

Larrabee, E. E.↗

Determination of optimum planforms for control surfaces

A theoretical analysis is made to determine the optimum chord distribution, location, and extent of control surfaces, with the ratio of hinge moment to effectiveness as the criterion. Expressions for the effectiveness - for ailerons, the rolling moment, and for tail surfaces, the change of lift on the tail due to deflection of the surface-were derived from lifting line theory. Solutions found for a range of airfoil planforms indicate that, regardless of the characteristics of the tail surface, the chord of the rudder or the elevator should be very nearly constant over its span. The optimum ailerons are also of a characteristics shape, varying little with the planform of the wing.

Jones, R. T.↗

Historical evolution of vortex-lattice methods

A review of the beginning and some orientation of the vortex-lattice method were given. The historical course of this method was followed in conjunction with its field of computational fluid dynamics, spanning the period from L.F. Richardson's paper in 1910 to 1975. The following landmarks were pointed out: numerical analysis of partial differential equations, lifting-line theory, finite-difference method, 1/4-3/4 rule, block relaxation technique, application of electronic computers, and advanced panel methods.

Deyoung, J.↗

The effects of trailing vorticity on the flow through highly loaded cascades

This paper presents a procedure whereby three-dimensional inviscid flow through a highly loaded turbomachinery cascade of lifting lines can be treated by methods corresponding to classical aerodynamic theory. In contrast to earlier linearized (thin airfoil) three-dimensional theory, the present study allows analysis of the flow corresponding to the large turning and/or large pressure ratios induced by practical rotors or stators. For the sake of simplicity, the present paper is limited to incompressible flow through a highly loaded rectilinear cascade and to the design problem; i.e., given blade loading. Formulas are derived for both the mean and the three-dimensional components of the flow; in particular, the velocities at the blades induced by the trailing vorticity associated with nonuniform blade circulation are determined.

Mccune, J. E.↗

Simplified unsteady aerodynamic concepts, with application to parameter estimation

A simplified aerodynamic force model based on the physical principle of Prandtl's lifting line theory and trailing vortex concept has been developed to account for unsteadiness in the aircraft dynamics. The wake is assumed to be compressed to a single shed vortex element of appropriate strength moving downstream at a speed sufficient to approximate the Wagner function. Results are presented illustrating the ability of the simplified theory to duplicate exact solutions in unsteady aerodynamics. Further, consideration is given to the utility of the model in a parameter identification application.

Wells, W. R.↗

Maximum likelihood identification of aircraft parameters with unsteady aerodynamic modelling

A simplified aerodynamic force model based on the physical principle of Prandtl's lifting line theory and trailing vortex concept has been developed to account for unsteady aerodynamic effects in aircraft dynamics. Longitudinal equations of motion have been modified to include these effects. The presence of convolution integrals in the modified equations of motion led to a frequency domain analysis utilizing Fourier transforms. This reduces the integro-differential equations to relatively simple algebraic equations, thereby reducing computation time significantly. A parameter extraction program based on the maximum likelihood estimation technique is developed in the frequency domain. The extraction algorithm contains a new scheme for obtaining sensitivity functions by using numerical differentiation. The paper concludes with examples using computer generated and real flight data

Keskar, D. A.↗

Summary of advanced methods for predicting high speed propeller performance

Three advanced analyses for predicting aircraft propeller performance at high subsonic speeds are described. Two of these analyses use a lifting line representation for the propeller blades and vortex filaments for the blade wakes but differ in the details of the solution. The third analysis is a finite difference solution of the unsteady, three dimensional Euler equations for the flow between adjacent blades. Analysis results are compared to data for a high speed propeller having eight swept blades integrally designed with the spinner and nacelle.

Bober, L. A.↗

The effects of leading edge modifications on the post-stall characteristics of wings

An investigation of the effects of leading edge modifications on the post-stall characteristics of two rectangular planform wings in a series of low speed wind tunnel tests is presented. Abrupt discontinuities in the leading edge shape of the wings were produced by placing a nose glove over a portion of the span or by deflecting sections of a segmented leading edge flap. Six component balance data, oil flow visualization photographs, and pressure distribution measurements were obtained, and tests made to study the development of flow separation at stall on small scale planform wing models. Results of oil flow visualization tests at and beyond stall showed the formation of counter-rotating swirl patterns on the upper surface of the '2-D' and '3-D' wings, and results of a numerical lifting line technique applied to wings with leading edge modifications are included.

Winkelmann, A. E.↗

Summary of advanced methods for predicting high speed propeller performance

Three advanced analyses for predicting aircraft propeller performance at high subsonic speeds are described. Two of these analyses use a lifting line representation for the propeller blades and vortex filaments for the blade wakes but differ in the details of the solution. The third analysis is a finite difference solution of the unsteady, three-dimensional Euler equations for the flow between adjacent blades. Analysis results are compared to data for a high speed propeller having 8 swept blades integrally designed with the spinner and nacelle. These analyses provide tools for the propeller designer ranging from a short running program for initial design studies to a very long running program for checking final configurations.

Bober, L. J.↗

The UTRC wind energy conversion system performance analysis for horizontal axis wind turbines (WECSPER)

The theory for the UTRC Energy Conversion System Performance Analysis (WECSPER) for the prediction of horizontal axis wind turbine performance is presented. Major features of the analysis are the ability to: (1) treat the wind turbine blades as lifting lines with a prescribed wake model; (2) solve for the wake-induced inflow and blade circulation using real nonlinear airfoil data; and (3) iterate internally to obtain a compatible wake transport velocity and blade loading solution. This analysis also provides an approximate treatment of wake distortions due to tower shadow or wind shear profiles. Finally, selected results of internal UTRC application of the analysis to existing wind turbines and correlation with limited test data are described.

Egolf, T. A.↗

A prescribed wake rotor inflow and flow field prediction analysis, user's manual and technical approach

A user's manual is provided which includes the technical approach for the Prescribed Wake Rotor Inflow and Flow Field Prediction Analysis. The analysis is used to provide the rotor wake induced velocities at the rotor blades for use in blade airloads and response analyses and to provide induced velocities at arbitrary field points such as at a tail surface. This analysis calculates the distribution of rotor wake induced velocities based on a prescribed wake model. Section operating conditions are prescribed from blade motion and controls determined by a separate blade response analysis. The analysis represents each blade by a segmented lifting line, and the rotor wake by discrete segmented trailing vortex filaments. Blade loading and circulation distributions are calculated based on blade element strip theory including the local induced velocity predicted by the numerical integration of the Biot-Savart Law applied to the vortex wake model.

Egolf, T. A.↗