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Dissertation

Unsteady lifting surface theory applied to a propeller and helicopter rotor

01 Jan 1973-
TL;DR: In this paper, the authors developed a theory for determining the aerodynamic forces for unsteady, compressible subsonic flow on a propeller and helicopter rotor using the doublet-lattice method.
Abstract: This thesis is concerned with the development of a theory for determining the aerodynamic forces for unsteady, compressible subsonic flow on a propeller and helicopter rotor. The acceleration potential method was used in developing the basic equations and the method has been programmed for the propeller on a computer and some results are given. The integral equations was solved by the doublet-lattice method, which consists of placing "load" lines at certain locations on the chord and satisfying the down-vash condition at other selected positions. The examples presented include the spanvise and chordwise loading on a rotating propeller for incompressible flow, an example of compressible flow calculations and finally, a calculation illustrating the loss of aerodynamic damping of a propeller blade due to the passage of the blade over its own wake.
Citations
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Book
01 Aug 1967
TL;DR: Aerodynamics of V/STOL flight as discussed by the authors, Aerodynamic of V and STOL flight, aircraft propulsion, propulsion, and propulsion, V2V flight, and V2StOL flight.
Abstract: Aerodynamics of V/STOL flight , Aerodynamics of V/STOL flight , مرکز فناوری اطلاعات و اطلاع رسانی کشاورزی

220 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that prop-fans satisfy well-known criteria for use of linearized theory at transonic speeds by virtue of small aspect ratio and small thickness ratio.
Abstract: Acceleration potential techniques from three-dimensional thin wing theory have been generalized for propeller and prop-fan analysis. Helicoidal reference surfaces take the place of the planar surface in wing theories; otherwise the theories are equivalent. The acoustic branch of the theory, including nonlinear source terms, extends and unifies frequency domain noise theories dating back to Gutin. For aerodynamic applications, it is shown that prop-fans satisfy well-known criteria for use of linearized theory at transonic speeds by virtue of small aspect ratio and small thickness ratio. The results are in the form of integral equations for downwash as functions of thickness and steady or unsteady loading distributions. For the case of no rotation, the kernel functions reduce to well-known kernels of wing theory. The analysis, within the restrictions of linearization , treats rigorously any planform and any flight condition including the combination of subsonic roots and supersonic tips typical of prop-fans. The effects of thickness, camber, angle of attack, sweep, offset, blade interference, and tip relief are all treated without approximation.

117 citations

Journal ArticleDOI
TL;DR: In this paper, a nonlinear aerodynamic model of airfoils is proposed to predict a subsonic helical tip Mach number with the blade element/vortex theory.
Abstract: The blade element method is an indispensible engineering design tool. It executes rapidly on a personal computer and is capable of accurate propeller performance predictions. An extensive literature survey reveals that for conventional high-aspect ratio propeller blades lifting surface and computational fluid dynamics approaches add a large degree of complexity without providing significantly improved performance prediction capabilities as compared to the blade element/vortex theory. The accuracy of the blade element method is, however, highly dependent on the fidelity of the airfoil aerodynamic model. The primary focus of this paper is on presenting a nonlinear aerodynamic model of airfoils that can be used in combination with the blade element method for enhanced propeller performance prediction over a wide range of advance ratios. The proposed nonlinear airfoil model includes effects of angles of attack up to 90 degrees and compressibility corrections. Results of this method are validated against experimental measurements. Excellent agreement between experiment and prediction is shown for subsonic helical tip Mach numbers.

5 citations

Proceedings ArticleDOI
16 Jun 2014
TL;DR: A non-linear aerodynamic model of airfoils to be used in combination with a blade element code for the purpose of propeller performance prediction, which adds to the versatility, efficiency, and accuracy of the blade element method.
Abstract: The blade element method is an indispensible engineering design tool. It executes rapidly on a personal computer and is capable of accurate propeller performance predictions. An extensive literature survey serves to show that for conventional high-aspect ratio propeller blades lifting surface and computational fluid dynamics approaches add a large degree of complexity without providing significantly improved performance prediction capabilities as compared to the blade element/vortex theory. The accuracy of the blade element method is, however, highly dependent on the accuracy of the airfoil aerodynamic model. The primary focus of this paper is thus to present a non-linear aerodynamic model of airfoils to be used in combination with a blade element code for the purpose of propeller performance prediction. This non-linear airfoil model includes the behavior of the lift and drag coefficients up to 90 degrees angle of attack as well as corrections for compressible flow phenomena. Propeller performance predictions using the proposed airfoil model are compared against experimental data. Very good agreement between experiment and prediction validates the model, though it is limited to subsonic helical tip Mach numbers. The non-linear aerodynamic model presented in this paper adds to the versatility, efficiency, and accuracy of the blade element method.

3 citations

Journal ArticleDOI
TL;DR: In this paper, the chordwise velocity and the derivative d$/dt of the velocity potential at the leading edge of a thin rotor blade in subsonic flow were re-examined to assess unsteady and compressibility effects on the induced drag using a leading-edge suction model.
Abstract: Estimating induced drag for a helicopter in forward flight is a three-dimensional, unsteady aerodynamic problem complicated by fluid compressibility and wake geometry. Based on an acceleration potential approach, the chordwise velocity and the derivative d$/dt of the velocity potential at the leading edge of a thin rotor blade in subsonic flow were re-examined in this paper to assess unsteady and compressibility effects on the induced drag using a leading-edge suction model. The chordwise velocity was shown to have a singular and a continuous component. The d$/dt was shown to be continuous and hence does not contribute to induced drag. The induced drag calculated from the leading-edge suction model and the more traditional model to be referred to as the induced angle model were compared to quantify the differences in the two approaches. The results show that variations can be significant. While these variations cannot substantiate the validity of either approach, it is clear that the leading edge suction model is simpler to apply with fewer assumptions. b A A d

3 citations

References
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Book
01 Jan 1937

11,054 citations

Journal ArticleDOI
TL;DR: In this paper, a theory for estimating the sound radiated from a fluid flow, with rigid boundaries, which as a result of instability contains regular fluctuations or turbulence is initiated, based on the equations of motion of a gas.
Abstract: A theory is initiated, based on the equations of motion of a gas, for the purpose of estimating the sound radiated from a fluid flow, with rigid boundaries, which as a result of instability contains regular fluctuations or turbulence. The sound field is that which would be produced by a static distribution of acoustic quadrupoles whose instantaneous strength per unit volume is ρv i v j + p ij - a 2 0 ρ δ ij , where ρ is the density, v i the velocity vector, p ij the compressive stress tensor, and a 0 the velocity of sound outside the flow. This quadrupole strength density may be approximated in many cases as ρ 0 v i v j . The radiation field is deduced by means of retarded potential solutions. In it, the intensity depends crucially on the frequency as well as on the strength of the quadrupoles, and as a result increases in proportion to a high power, near the eighth, of a typical velocity U in the flow. Physically, the mechanism of conversion of energy from kinetic to acoustic is based on fluctuations in the flow of momentum across fixed surfaces, and it is explained in § 2 how this accounts both for the relative inefficiency of the process and for the increase of efficiency with U . It is shown in § 7 how the efficiency is also increased, particularly for the sound emitted forwards, in the case of fluctuations convected at a not negligible Mach number.

4,697 citations

Journal ArticleDOI
TL;DR: In this article, a linearized formulation of the surface is obtained by idealizing the surface as a set of lifting elements which are short line segments of accelerationpotential doub? lets, and the normal velocity induced by an element of unit strength is given by an integral of the subsonic kernel function.
Abstract: Approximate solutions from the linearized formulation are obtained by idealizing the surface as a set of lifting elements which are short line segments of acceleration-potential doub? lets. The normal velocity induced by an element of unit strength is given by an integral of the subsonic kernel function. The load on each element is determined, by, satisfying normal velocity boundary conditions at a set of points oil the surface. It is seen a posteriori

893 citations

Journal ArticleDOI
TL;DR: In this article, an approximate solution for the irrotational motion of a screw surface in an inviscid fluid was given by Prandtl, which is the main object of this work to find the exact solution.
Abstract: The vortex-theory of screw propellers develops along similar lines to aerofoil theory. There is circulation of flow round each blade; this circulation vanishes at the tip and the root. The blade may be replaced by a bound vortex system, which, for the sake of simplicity, may be taken, as a first approximation, to be a bound vortex line. The strength of the vortex at any point is equal to Γ, the circulation round the corresponding blade section. From every point of this bound vortex spring free, trailing vortices, whose strength per unit length is —∂Γ/∂ r , where r is distance from the axis of the screw. When the interference flow of this vortex system is small compared with the velocity of the blades, the trailing vortices are approximately helices, and together build a helical or screw surface. Part of the work supplied by the motor is lost in producing the trailing vortex system. When the distribution of Γ along the blade is such that, for a given thrust, the energy so lost per unit time is a minimum, then the flow far behind the screw is the same as if the screw surface formed by the trailing vortices was rigid, and moved backwards in the direction of its axis with a constant velocity, the flow being that of classical hydro dynamics in an inviscid fluid, continuous, irrotational, and without circulation. The circulation round any blade section is then equal to the discontinuity in the velocity potential at the corresponding point of the screw surface. Further, for symmetrical screws, the interference flow at the blade is half that at the corresponding point of the screw surface far behind the propeller. An approximate solution for the irrotational motion of a screw surface in an inviscid fluid was given by Prandtl. The accuracy of the approximation increases with the number of blades and with the ratio of the tip speed to the velocity of advance, but for given values of these numbers we have no means of estimating the error, since the exact solution of the problem has not yet been found. It is the main object of this work to find the exact solution.

518 citations