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NASA NTRS1976

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.↗

NASA NTRS1977

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.↗

NASA NTRS1979

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.↗

NASA NTRS1980

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.↗

NASA NTRS1980

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.↗

NASA NTRS1980

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.↗

NASA NTRS1981

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.↗

NASA NTRS1982

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.↗

NASA NTRS1983

An analytical and experimental comparison of the flow field of an advanced swept turboprop

An argon ion laser velocimeter with four beams was used to measure the detailed flow-field of an advanced eight blade propeller with 45% of tip sweep in an 8x6 foot supersonic wind tunnel. Data were obtained at a free stream Mach number of 0.8, the design advance ratio of 3.06 and a power coefficient of 1.8. Data are presented for inlet flow, exit flow, flow within the blades and flow slightly outside the blade tips. The data are compared to a lifting line theory. In general, the results of the comparison are considered favorable.

Neumann, H. E.↗

NASA NTRS1983

Energetics and optimum motion of oscillating lifting surfaces

Low-frequency, unsteady, lifting-line theory is used to characterize the energetics and optimum motion of an unswept rigid wing oscillating harmonically in an inviscid, incompressible flow. The energetics calculations account for the leading edge suction force, the power absorbed in the wing oscillations, and the energy loss rate produced by vortex shedding. Optimization is achieved by minimizing the average energy loss rate in relation to a given thrust, and a unique solution is found in the three dimensional case for low, reduced frequencies. The two-dimensional solution is nonunique, a condition which is examined in terms of the normal modes of the energy loss rate matrix. An invisible mode with a hydrodynamic efficiency of 100 pct is obtained in the two-dimensional case, causing the nonuniqueness of the solution by yielding no fixed positive thrust through perfect unsteady feathering.

Ahmadi, A. R.↗

NASA NTRS1984

A computational method for helicopter vortex wakes

A method for calculating the wake geometry and blade loads for a hovering helicopter rotor is presented. The approach incorporates a simplified free wake model of the rotor in a finite difference calculation of the flow field. A variation of the 'cloud-in-cell' technique, modified to eliminate self-induced velocity errors for curved vortex filaments, is used. Simple lifting line theory is used to calculate the blade loads. Calculations showing the effect of vortex core size and the number of vortex filaments representing the wake are presented. For large numbers of vortices, it is seen that the wake geometry fails to converge. However, only a few vortices are needed to adequately represent the wake. Comparisons with experimental results are also presented.

Roberts, T. W.↗

NASA NTRS1985

An asymptotic theory for the interference of large aspect ratio swept wings and multiple propeller slipstreams

This paper presents an asymptotic method for the analysis of the interference of multiple tractor propeller slipstream with large aspect ratio swept wings. It is assumed that the height of the slipstream is of the order of the wing chord and its spanwise extent is of the order of the wing span. Three different flow regions are identified by employing different stretching transformations. Asymptotic expansions are made in each of the three regions, using the chord to span ratio as the small expansion parameter. The details of the nonuniform flow in the slipstream enter into the wing sectional analysis. In the outer limit, the wing shrinks to a swept lifting line, and the slipstream reduces to a thin sheet of jet carrying the momentum gain from the propeller. The curvature of this jet sheet results in a pressure difference which is represented by a vortex sheet. The governing equations are solved by discretization. Several examples are considered for which experimental data are available. Comparison of the present results with the experimental data as well as other numerical solutions showed generally good agreement.

Prabhu, R. K.↗

NASA NTRS1986

Formal optimization of hovering performance using free wake lifting surface theory

Free wake techniques for performance prediction and optimization of hovering rotor are discussed. The influence functions due to vortex ring, vortex cylinder, and source or vortex sheets are presented. The vortex core sizes of rotor wake vortices are calculated and their importance is discussed. Lifting body theory for finite thickness body is developed for pressure calculation, and hence performance prediction of hovering rotors. Numerical optimization technique based on free wake lifting line theory is presented and discussed. It is demonstrated that formal optimization can be used with the implicit and nonlinear objective or cost function such as the performance of hovering rotors as used in this report.

Chung, S. Y.↗

NASA NTRS1986

Energetics and optimum motion of oscillating lifting surfaces of finite span

In certain modes of animal propulsion in nature, such as bird flight and fish swimming, the efficiency compared to man-made vehicles is very high. In such cases, wing and tail motions are typically associated with relatively high Reynolds numbers, where viscous effects are confined to a thin boundary layer at the surface and a thin trailing wake. The propulsive forces, which are generated primarily by the inertial forces, can be calculated from potential-flow theory using linearized unsteady-wing theory (for small-amplitude oscillations). In the present study, a recently developed linearized, low-frequency, unsteady lifting-line theory is employed to calculate the (sectional and total) energetic quantities and optimum motion of an oscillating wing of finite span.

Ahmadi, A. R.↗

NASA NTRS1986

Recent developments in rotary-wing aerodynamic theory

Current progress in the computational analysis of rotary-wing flowfields is surveyed, and some typical results are presented in graphs. Topics examined include potential theory, rotating coordinate systems, lifting-surface theory (moving singularity, fixed wing, and rotary wing), panel methods (surface singularity representations, integral equations, and compressible flows), transonic theory (the small-disturbance equation), wake analysis (hovering rotor-wake models and transonic blade-vortex interaction), limitations on computational aerodynamics, and viscous-flow methods (dynamic-stall theories and lifting-line theory). It is suggested that the present algorithms and advanced computers make it possible to begin working toward the ultimate goal of turbulent Navier-Stokes calculations for an entire rotorcraft.

Johnson, W.↗

NASA NTRS1986

Integrated aerodynamic/structural design of a sailplane wing

Using lifting-line theory and beam analysis, the geometry (planiform and twist) and composite material structural sizes (skin thickness, spar cap, and web thickness) were designed for a sailplane wing, subject to both structural and aerodynamic constraints. For all elements, the integrated design (simultaneously designing the aerodynamics and the structure) was superior in terms of performance and weight to the sequential design (where the aerodynamic geometry is designed to maximize the performance, following which a structural/aeroelastic design minimizes the weight). Integrated designs produced less rigid, higher aspect ratio wings with favorable aerodynamic/structural interactions.

Grossman, B.↗

NASA NTRS1988

An unsteady helicopter rotor: Fuselage interaction analysis

A computational method was developed to treat unsteady aerodynamic interactions between a helicopter rotor, wake, and fuselage and between the main and tail rotors. An existing lifting line prescribed wake rotor analysis and a source panel fuselage analysis were coupled and modified to predict unsteady fuselage surface pressures and airloads. A prescribed displacement technique is used to position the rotor wake about the fuselage. Either a rigid blade or an aeroelastic blade analysis may be used to establish rotor operating conditions. Sensitivity studies were performed to determine the influence of the wake fuselage geometry on the computation. Results are presented that describe the induced velocities, pressures, and airloads on the fuselage and on the rotor. The ability to treat arbitrary geometries is demonstrated using a simulated helicopter fuselage. The computational results are compared with fuselage surface pressure measurements at several locations. No experimental data was available to validate the primary product of the analysis: the vibratory airloads on the entire fuselage. A main rotor-tail rotor interaction analysis is also described, along with some hover and forward flight.

Lorber, Peter F.↗

NASA NTRS1987

A free-wake rotor analysis including ground effect

The objective of this work is to develop a computer program which analytically estimates the wake geometry, vorticity, and velocity distribution over a rotor and in the neighboring airflow for a variety of conditions in and out of ground effect. The resulting wake is used to provide an assessment of the blade loading distribution for various hover and low speed flight conditions. The computer program is based on a lifting line free wake model and provides stable solutions for a variety of steady state conditions, including ground effect and forward flight. The wake program was validated by comparing the computed wake geometry and experimental test data for two different rotors.

Saberi, H. A.↗