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At least 127 records · Page 7

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NASA NTRS1984

Lifting surface theory for a helicopter rotor in forward flight

A lifting surface theory was developed for a helicopter rotor in forward flight for compressible and incompressible flow. The method utilizes the concept of the linearized acceleration potential and makes use of the vortex lattice procedure. Calculations demonstrating the application of the method are given in terms of the lift distribution on a single rotor, a two-bladed rotor, and a rotor with swept-forward and swept-back tips. In addition, the lift on a rotor which is vibrating in a pitching mode at 4/rev is given. Compressibility effects and interference effects for a two-bladed rotor are discussed.

Tai, H.↗

NASA NTRS1985

Application of a lifting surface theory for a helicopter in forward flight

A lifting-surface theory has been developed for a helicopter rotor in forward flight for compressible and incompressible flow. The method utilizes the concept of the linearized acceleration potential and makes use of the doublet lattice procedure. Calculations demonstrating the application of the method are given in terms of the lift distribution on a single rotor, a two-bladed rotor, and a rotor with swept-forward and swept-back tips. In addition, the lift on a rotor which is vibrating in a pitching mode at 4/rev is given. Compressibility effects and interference effects for a two-bladed rotor are discussed.

Runyan, Harry L.↗

NASA NTRS1978

Unsteady vortical and entropic distortions of potential flows round arbitrary obstacles

The analysis concerns the alterations produced when small amplitude disturbances, including entropy and vorticity disturbances, are imposed on steady potential flows. For the most general nonacoustic incident distortion field that can be imposed on the uniform upstream flow, it is shown that the perturbation velocity at any point of the resulting unsteady compressible and vortical flow consists of a part that is a known function of the imposed upstream distortion field and the mean flow variables and a potential part that can be found by solving a linear inhomogeneous wave equation with a dipole-type source term whose strength is a known function of the imposed upstream distortion field. The theory is applied to the unsteady flow past a corner, and a closed-form analytical solution is found.

Goldstein, M. E.↗

NASA NTRS1990

Development of a linearized unsteady aerodynamic analysis for cascade gust response predictions

A method for predicting the unsteady aerodynamic response of a cascade of airfoils to entropic, vortical, and acoustic gust excitations is being developed. Here, the unsteady flow is regarded as a small perturbation of a nonuniform isentropic and irrotational steady background flow. A splitting technique is used to decompose the linearized unsteady velocity into rotational and irrotational parts leading to equations for the complex amplitudes of the linearized unsteady entropy, rotational velocity, and velocity potential that are coupled only sequentially. The entropic and rotational velocity fluctuations are described by transport equations for which closed-form solutions in terms of the mean-flow drift and stream functions can be determined. The potential fluctuation is described by an inhomogeneous convected wave equation in which the source term depends on the rotational velocity field, and is determined using finite-difference procedures. The analytical and numerical techniques used to determine the linearized unsteady flow are outlined. Results are presented to indicate the status of the solution procedure and to demonstrate the impact of blade geometry and mean blade loading on the aerodynamic response of cascades to vortical gust excitations. The analysis described herein leads to very efficient predictions of cascade unsteady aerodynamic response phenomena making it useful for turbomachinery aeroelastic and aeroacoustic design applications.

Verdon, Joseph M.↗

NASA NTRS1981

Treatment of conical and nonconical supersonic flows by an implicit marching scheme applied to the full potential equation

An aerodynamic prediction technique based on the full potential equation in conservation form is developed for the treatment of supersonic flows. This technique bridges the gap between simplistic linear theory methods and complex Euler solvers. A novel local density linearization concept and a second order accurate retarded density scheme, both producing the correct artificial viscosity, are introduced in developing an implicit marching scheme for solving the scalar potential. Results for conical flows over delta wings and a wing-body combination and for non-conical flows over bodies of revolution at angles of attack are compared with Euler and nonconservative full potential calculations and experimental data. The present formulation requires an order of magnitude less computer time and significantly less computer memory over Euler codes and exhibits a considerable improvement in computational efficiency and generality over an existing nonconservative full potential code.

Shankar, V.↗

NASA NTRS1983

A three degree-of-freedom, typical section flutter analysis using harmonic transonic air forces

Typical section flutter solutions are obtained using generalized air forces calculated with OPTRAN2, a program based on the transonic small perturbation potential equation, which uses potentials from a nonlinear solution to the steady flow to obtain linear unsteady air forces. Flutter results are calculated with a conventional, linear V-g type solution. Results are presented for a NACA 64A010 airfoil oscillating in plunge and pitch, and with a quarter-chord control surface in the Mach number range of 0.80 to 0.90. The flutter boundary shows a significant 'transonic' bucket, together with changes in flutter mode as, with increasing Mach numbers, a shock appears on the airfoil and then moves aft. Single degree-of-freedom instabilities associated with both the pitch and the control surface motions are identified.

Weatherill, W. H.↗

NASA NTRS1953

A Vector Study of Linearized Supersonic Flow Applications to Nonplanar Problems

A vector study of the partial-differential equation of steady linearized supersonic flow is presented. General expressions which relate the velocity potential in the stream to the conditions on the disturbing surfaces, are derived. In connection with these general expressions the concept of the finite part of an integral is discussed. A discussion of problems dealing with planar bodies is given and the conditions for the solution to be unique are investigated. Problems concerning nonplanar systems are investigated, and methods are derived for the solution of some simple nonplanar bodies. The surface pressure distribution and the damping in roll are found for rolling tails consisting of four, six, and eight rectangular fins for the Mach number range where the region of interference between adjacent fins does not affect the fin tips.

Martin, John C↗

NASA NTRS1959

Formulas Pertinent to the Calculation of Flow-Field Effects at Supersonic Speeds Due to Wing Thickness

Expressions based on linearized supersonic-flow theory are derived for the perturbation velocity potential in space due to wing thickness for rectangular wings with biconvex airfoil sections and for arrow, delta, and quadrilateral wings with wedge-type airfoil sections. The complete range of supersonic speeds is considered subject to a minor aspect-ratio-Mach number restriction for the rectangular plan form and to the condition that the trailing edge is supersonic for the sweptback wings. The formulas presented can be utilized in determining the induced-flow characteristics at any point in the field and are readily adaptable for either numerical computation or analytical determination of any velocity components desired.

Margolis, Kenneth↗

NASA NTRS2003

A Generalized Acoustic Analogy

The purpose of this article is to show that the Navier-Stokes equations can be rewritten as a set of linearized inhomogeneous Euler equations (in convective form) with source terms that are exactly the same as those that would result from externally imposed shear stress and energy flux perturbations. These results are used to develop a mathematical basis for some existing and potential new jet noise models by appropriately choosing the base flow about which the linearization is carried out.

Goldstein, M. E.↗

NASA NTRS2012

Active Combustion Control for Aircraft Gas-Turbine Engines-Experimental Results for an Advanced, Low-Emissions Combustor Prototype

Lean combustion concepts for aircraft engine combustors are prone to combustion instabilities. Mitigation of instabilities is an enabling technology for these low-emissions combustors. NASA Glenn Research Center s prior activity has demonstrated active control to suppress a high-frequency combustion instability in a combustor rig designed to emulate an actual aircraft engine instability experience with a conventional, rich-front-end combustor. The current effort is developing further understanding of the problem specifically as applied to future lean-burning, very low-emissions combustors. A prototype advanced, low-emissions aircraft engine combustor with a combustion instability has been identified and previous work has characterized the dynamic behavior of that combustor prototype. The combustor exhibits thermoacoustic instabilities that are related to increasing fuel flow and that potentially prevent full-power operation. A simplified, non-linear oscillator model and a more physics-based sectored 1-D dynamic model have been developed to capture the combustor prototype s instability behavior. Utilizing these models, the NASA Adaptive Sliding Phasor Average Control (ASPAC) instability control method has been updated for the low-emissions combustor prototype. Active combustion instability suppression using the ASPAC control method has been demonstrated experimentally with this combustor prototype in a NASA combustion test cell operating at engine pressures, temperatures, and flows. A high-frequency fuel valve was utilized to perturb the combustor fuel flow. Successful instability suppression was shown using a dynamic pressure sensor in the combustor for controller feedback. Instability control was also shown with a pressure feedback sensor in the lower temperature region upstream of the combustor. It was also demonstrated that the controller can prevent the instability from occurring while combustor operation was transitioning from a stable, low-power condition to a normally unstable high-power condition, thus enabling the high-power condition.

DeLaat, John C.↗

NASA NTRS1932

Calculation of potential flow past airship bodies in yaw

An outline of Von Karman's method of computing the potential flow of airships in yaw by means of partially constant dipolar superposition on the axis of the body is followed by several considerations for beginning and end of the superposition. Then this method is improved by postulating a continuous, in part linearly variable dipolar superposition on the axis. The second main part of the report brings the calculation of the potential flow by means of sources and sinks, arranged on the surface of the airship body. The integral equation which must satisfy this surface superposition is posed, and the core reduced to functions developed from whole elliptical normal integrals. The functions are shown diagrammatically. The integration is resolvable by iteration. The consequence of the method is good. The formulas for computing the velocity on the surface and of the potential for any point conclude the report.

Lotz, I↗

NASA NTRS1947

Calculation of the Pressure Distribution on Bodies of Revolution in the Subsonic Flow of a Gas: Axially Symmetrical Flow - Part 1

The present report concerns a method of computing the velocity and pressure distributions on bodies of revolution in axially symmetrical flow in the subsonic range. The differential equation for the velocity potential Phi of a compressible fluid motion is linearized tn the conventional manner, and then put in the form Delta(Phi) = 0 by affine transformation. The quantity Phi represents the velocity potential of a fictitious incompressible flow, for which a constant superposition of sources by sections is secured by a method patterned after von Karman which must comply with the boundary condition delta(phi)/delta(n) = 0 at the originally specified contour. This requirement yields for the "pseudo-stream function" psi a differential equation which must be fulfilled for as many points on the contour as source lengths are assumed. In this manner, the problem of defining the still unknown source intensities is reduced to the solution of an inhomogeneous equation system. The pressure distribution is then determined with the aid of Bernoulli's equation and adiabatic equation of state. Lastly, the pressure distributions in compressible and incompressible medium are compared on a model problem.

Bilharz, Herbert↗

NASA NTRS2009

Characterization of the Effect of Wing Surface Instrumentation on UAV Airfoil Performance

Recently proposed flight research at NASA Dryden Flight Research Center (DFRC) has prompted study into the aerodynamic effects of modifications made to the surfaces of laminar airfoils. The research is focused on the high-aspect ratio, laminar-flow type wings commonly found on UAVs and other aircraft with a high endurance requirement. A broad range of instrumentation possibilities, such as structural, pressure, and temperature sensing devices may require the alteration of the airfoil outer mold line as part of the installation process. This study attempts to characterize the effect of installing this additiona1 instrumentation on key airfoil performance factors, such as transition location, lift and drag curves, and stall point. In particular, the general case of an airfoil that is channeled in the spanwise direction is considered, and the impact on key performance characteristics is assessed. Particular attention is focused on exploring the limits of channel depth and low-Reynolds number on performance and stall characteristics. To quantify the effect of increased skin friction due to premature transition caused by protruding or recessed instrumentation, two simplified, conservative scenarios are used to consider two potential sources of diaturbance: A) that leading edge alterations would cause linearly expanding areas (triangles) of turbulent flow on both surfaces of the wing upstream of the natural transition point, and B) that a channel or bump on the upper surface would trip turbulent flow across the whole upper surface upstream of the natural transition point. A potentially more important consideration than the skin friction drag increment is the change in overall airfoil performance due to the installation of instrumentation along most of the wingspan. To quantify this effect, 2D CFD simulations of the flow over a representative mid-span airfoil section were conducted in order to assess the change in lift and drag curves for the airfoil in the presence of disturbed flow due to the installed instrumentation. A discussion as to the impact on high-altitude and low-speed operation of this and similar aircraft is provided.

Ratnayake, Nalin A.↗

NASA NTRS1989

Development and application of a program to calculate transonic flow around an oscillating three-dimensional wing using finite difference procedures

A finite difference method for solving the unsteady transonic flow about harmonically oscillating wings is investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The differential equation for the unsteady potential is linear with spatially varying coefficients and with the time variable eliminated by assuming harmonic motion. Difference equations are derived for harmonic transonic flow to include a coordinate transformation for swept and tapered planforms. A pilot program is developed for three-dimensional planar lifting surface configurations (including thickness) for the CRAY-XMP at Boeing Commercial Airplanes and for the CYBER VPS-32 at the NASA Langley Research Center. An investigation is made of the effect of the location of the outer boundaries on accuracy for very small reduced frequencies. Finally, the pilot program is applied to the flutter analysis of a rectangular wing.

Weatherill, Warren H.↗

NASA NTRS1954

Lift and moment coefficients expanded to the seventh power of frequency for oscillating rectangular wings in supersonic flow and applied to a specific flutter problem

Linearized theory for compressible unsteady flow is used to derive the velocity potential and lift and moment coefficients in the form of oscillating rectangular wing moving at a constant supersonic speed. Closed expressions for the velocity potential and lift and moment coefficients associated with pitching and translation are given to seventh power of the frequency. These expressions extend the range of usefulness of NACA report 1028 in which similar expressions were derived to the third power of the frequency of oscillation. For example, at a Mach number of 10/9 the expansion of the potential to the third power is an accurate representation of the potential for values of the reduced frequency only up to about 0.08; whereas the expansion of the potential to the seventh power is an accurate representation for values of the reduced frequency up to about 0.2. The section and total lift and moment coefficients are discussed with the aid of several figures. In addition, flutter speeds obtained in the Mach number range from 10/9 to 10/6 for a rectangular wing of aspect ratio 4.53 by using section coefficients derived on the basis of three-dimensional flow are compared with flutter speeds for this wing obtained by using coefficients derived on the basis of two-dimensional flow.

Nelson, Herbert C↗

NASA NTRS2012

Computational Optimization of a Natural Laminar Flow Experimental Wing Glove

Computational optimization of a natural laminar flow experimental wing glove that is mounted on a business jet is presented and discussed. The process of designing a laminar flow wing glove starts with creating a two-dimensional optimized airfoil and then lofting it into a three-dimensional wing glove section. The airfoil design process does not consider the three dimensional flow effects such as cross flow due wing sweep as well as engine and body interference. Therefore, once an initial glove geometry is created from the airfoil, the three dimensional wing glove has to be optimized to ensure that the desired extent of laminar flow is maintained over the entire glove. TRANAIR, a non-linear full potential solver with a coupled boundary layer code was used as the main tool in the design and optimization process of the three-dimensional glove shape. The optimization process uses the Class-Shape-Transformation method to perturb the geometry with geometric constraints that allow for a 2-in clearance from the main wing. The three-dimensional glove shape was optimized with the objective of having a spanwise uniform pressure distribution that matches the optimized two-dimensional pressure distribution as closely as possible. Results show that with the appropriate inputs, the optimizer is able to match the two dimensional pressure distributions practically across the entire span of the wing glove. This allows for the experiment to have a much higher probability of having a large extent of natural laminar flow in flight.

Hartshom, Fletcher↗

NASA NTRS1991

Unified Aeroacoustics Analysis for High Speed Turboprop Aerodynamics and Noise: Development of Theory for Blade Loading, Wakes, and Noise - Volume 1

A unified theory for the aerodynamics and noise of advanced turboprops are presented. Aerodynamic topics include calculation of performance, blade load distribution, and non-uniform wake flow fields. Blade loading can be steady or unsteady due to fixed distortion, counter-rotating wakes, or blade vibration. The aerodynamic theory is based on the pressure potential method and is therefore basically linear. However, nonlinear effects associated with finite axial induction and blade vortex flow are included via approximate methods. Acoustic topics include radiation of noise caused by blade thickness, steady loading (including vortex lift), and unsteady loading. Shielding of the fuselage by its boundary layer and the wing are treated in separate analyses that are compatible but not integrated with the aeroacoustic theory for rotating blades.

Hanson, D. B.↗

NASA NTRS1980

Implicit computations of unsteady transonic flow governed by the full-potential equation in conservation form

An alternating-direction implicit algorithm is presented for solving the conservative, full-potential equation for unsteady, transonic flow. A new development is the time-linearization of the density function. This linearization reduces the solution process from one of solving a system of two equations at each mesh point to one of solving a single equation. Two sample cases are computed. First, a one-dimensional traveling shock wave is computed and compared with the analytic solution. Second, a two-dimensional case is computed of a flow field that results from a thickening and subsequently thinning airfoil. The resulting flow field, which includes a traveling shock wave, is compared to the flow field obtained from the low-frequency, small-disturbance, transonic equation.

Goorjian, P. M.↗