Sound radiation from random quadrupole source distributions in axial flow fans
Inlet turbulence interaction with rotor potential flow as noise source in axial flow fans, developing expression for sound power radiated
Chandrashekhara, N.↗
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Load distributions on slender delta wings having vortex flow
Results obtained through application of potential-flow theory based on a suction flow analogy for incompressible flow are compared to attached-flow theory and to experimental data acquired for sharp-edged delta wings. The error incurred in predicting structural loads on the basis of attached-flow theory is investigated. Force and moment coefficients and load distributions are used in the comparisons. The root bending moment can be estimated by assuming vortex lift concentrated at the wing leading edge. While this may entail some error at large angles of attack (owing to inboard movement of the center of vortex lift), it may furnish an upper bound in evaluating results based on other theories.
Kuhlman, J.↗
Analytical studies of separated vortex flow on highly swept wings
A subsonic potential flow mathematical model of the flow past slender aerodynamic surfaces with sharp edges and separated vortex flow is reported. Comparisons with experimental data are presented for overall forces and pressure distributions for a series of thin, low aspect ratio wings, including both flat and conically cambered ones. A discussion is presented of the limitations of the current theory, and some suggestions are made as to how the theory might be improved. Details of program data input modifications for three-dimensional geometry are described in an appendix.
Kuhlman, J. M.↗
Design and experimental performance of short curved wall diffusers with axial symmetry utilizing slot suction
The feasibility of designing short curved wall axially symmetrical subsonic diffusers utilizing suction through slots in the diffuser walls to prevent flow separation was investigated. A potential flow analysis was made, and a digital computer program was written for determining the diffuser wall contour for prescribed boundary conditions. The flow field included branch flow so that the suction slot geometry could be a part of the diffuser design. One bell shaped diffuser and three annular diffusers with area ratios of either 2.5:1 or 3:1 were designed, fabricated, and tested. Minimum suction requirements of metastable operation ranged from 6.3 percent to 12 percent when operating with inlet air velocities in the 1000 to 250 ft/sec (30 to 76 m/sec) range. For stable operation suction rates from 10 percent to 22 percent were required. In all cases the diffuser effectiveness was above 95 percent based on the conventional definition, and from 81 percent to 94 percent when the suction loss was accounted for. The exit velocity profiles were virtually flat with no more than + or - 9% variation over 95 percent of the exit area when operated with sufficient suction to prevent flow separation.
Yang, T.↗
Advanced surface paneling method for subsonic and supersonic flow
Numerical results illustrating the capabilities of an advanced aerodynamic surface paneling method are presented. The method is applicable to both subsonic and supersonic flow, as represented by linearized potential flow theory. The method is based on linearly varying sources and quadratically varying doublets which are distributed over flat or curved panels. These panels are applied to the true surface geometry of arbitrarily shaped three dimensional aerodynamic configurations.
Erickson, L. L.↗
Aerodynamic shape optimization using control theory
Aerodynamic shape design has long persisted as a difficult scientific challenge due its highly nonlinear flow physics and daunting geometric complexity. However, with the emergence of Computational Fluid Dynamics (CFD) it has become possible to make accurate predictions of flows which are not dominated by viscous effects. It is thus worthwhile to explore the extension of CFD methods for flow analysis to the treatment of aerodynamic shape design. Two new aerodynamic shape design methods are developed which combine existing CFD technology, optimal control theory, and numerical optimization techniques. Flow analysis methods for the potential flow equation and the Euler equations form the basis of the two respective design methods. In each case, optimal control theory is used to derive the adjoint differential equations, the solution of which provides the necessary gradient information to a numerical optimization method much more efficiently then by conventional finite differencing. Each technique uses a quasi-Newton numerical optimization algorithm to drive an aerodynamic objective function toward a minimum. An analytic grid perturbation method is developed to modify body fitted meshes to accommodate shape changes during the design process. Both Hicks-Henne perturbation functions and B-spline control points are explored as suitable design variables. The new methods prove to be computationally efficient and robust, and can be used for practical airfoil design including geometric and aerodynamic constraints. Objective functions are chosen to allow both inverse design to a target pressure distribution and wave drag minimization. Several design cases are presented for each method illustrating its practicality and efficiency. These include non-lifting and lifting airfoils operating at both subsonic and transonic conditions.
Reuther, James↗
Calculation procedures for potential and viscous flow solutions for engine inlets
The method and basic elements of computer solutions for both potential flow and viscous flow calculations for engine inlets are described. The procedure is applicable to subsonic conventional (CTOL), short-haul (STOL), and vertical takeoff (VTOL) aircraft engine nacelles operating in a compressible viscous flow. The calculated results compare well with measured surface pressure distributions for a number of model inlets. The paper discusses the uses of the program in both the design and analysis of engine inlets, with several examples given for VTOL lift fans, acoustic splitters, and for STOL engine nacelles. Several test support applications are also given.
Albers, J. A.↗
Calculation procedures for potential and viscous flow solutions for engine inlets
The method and basic elements of computer solutions for both potential flow and viscous flow calculations for engine inlets are described. The procedure is applicable to subsonic conventional, short-haul, and vertical takeoff aircraft engine nacelles operating in a compressible viscous flow. The calculated results compare well with measured surface-pressure distributions for a number of model inlets. The uses of the program in both the design and analysis of engine inlets are discussed, with several examples given for VTOL lift fans, acoustic splitters, and for STOL engine nacelles. Several test support applications are also given.
Albers, J. A.↗
Amplification, attenuation, and dispersion of sound in inhomogeneous flows
First order effects of gradients in nonuniform potential flows of a compressible gas are included in a dispersion relation for sound waves. Three nondimensional numbers, the ratio of the change in the kinetic energy in one wavelength to the thermal energy of the gas, the ratio of the change in the total energy in one wavelength to the thermal energy, and the ratio of the dillatation frequency (the rate of expansion per unit volume) to the acoustic frequency, play a role in the separation of the effects of flow gradients into isotropic and anisotropic effects. Dispersion and attenuation (or amplification) of sound are found to be proportional to the wavelength for small wavelength, and depend on the direction of wave propagation relative to flow gradients. Modification of ray acoustics for the effects of flow gradients is suggested, and conditions for amplification and attenuation of sound are discussed.
Kentzer, C. P.↗
Amplification, attenuation, and dispersion of sound in inhomogeneous flows
First order effects of gradients in nonuniform potential flows of a compressible gas are included in a dispersion relation for sound waves. Three nondimensional numbers, the ratio of the change in the kinetic energy in one wavelength to the thermal energy of the gas, the ratio of the change in the total energy in one wavelength to the thermal energy, and the ratio of the dilatation frequency (the rate of expansion per unit volume) to the acoustic frequency, play the dominant role permitting the separation of the effects of flow gradients into isotropic and anisotropic effects. Dispersion and attenuation (or amplification) of sound are proportional to the wavelength for small wavelength and depend on the direction of wave propagation relative to flow gradients. Modification of ray acoustics for the effects of flow gradients is suggested and conditions for amplification and attenuation of sound are discussed.
Kentzer, C. P.↗
Discrete-vortex model for the symmetric-vortex flow on cones
A relatively simple but accurate potential flow model was developed for studying the symmetric vortex flow on cones. The model is a modified version of the model first developed by Bryson, in which discrete vortices and straight-line feeding sheets were used to represent the flow field. It differs, however, in the zero-force condition used to position the vortices and determine their circulation strengths. The Bryson model imposed the condition that the net force on the feeding sheets and discrete vortices must be zero. The proposed model satisfies this zero-force condition by having the vortices move as free vortices, at a velocity equal to at the local crossflow velocity at their centers. When the free-vortex assumption is made, a solution is obtained in the form of two nonlinear algebraic equations that relate the vortex center coordinates and vortex strengths to the cone angle and angle of attack. The vortex center locations calculated using the model are in good agreement with experimental values. The cone normal forces as well as center locations are in good agreement with the vortex cloud method of calculating symmetric flow fields.
Gainer, Thomas G.↗
Transonic flow past swept wings
FLO-22 computer program aids in numerical analysis of transonic potential flow past lifting, swept wing. FLO-22 uses relaxation method to solve finite-difference approximation of full-potential equation for transonic flow past configuration consisting of wing or arbitrary planform and dihedral extending from symmetry plane or wall. Comparisons of FLO-22 calculated results with experimental data for both conventional and super-critical transport wings show good agreement.
Caughey, D. A.↗
Unsteady lift forces on highly cambered airfoils moving through a gust
An unsteady airfoil theory in which the flow is linearized about the steady potential flow of the airfoil is presented. The theory is applied to an airfoil entering a gust. After transformation to the W-plane, the problem is formulated in terms of a Poisson's equation. The solutions are expanded in a Fourier-Bessel series. The theory is applied to a circular arc with arbitrary camber. Closed form expressions for the velocity and pressure on the surface of the airfoil are obtained. The unsteady aerodynamic forces are then calculated and shown to contain two terms. One in an explicit closed analytical form represents the contribution of the oncoming vortical disturbance, the other depends on a single quadrature and accounts for the effect of the wake.
Atassi, H.↗
An improved analytical model of the separation region on boattail nozzles at subsonic speeds
A practical engineering calculation was developed to model the viscous effects of a separated, reverse flow region on afterbody pressures and drag. This viscous calculation was iteratively coupled with an inviscid flow calculation by means of an aerodynamic interface. A standard boundary layer displacement thickness was used to modify the afterbody shape where the flow was attached. A discriminating streamline calculation was developed to account for displacement effects of the reverse flow in separated regions with and without a flowing jet. The viscous flow calculation was coupled with a potential flow calculation. The analysis accurately predicted afterbody pressures and drag with variations in Reynolds number, Mach number, and afterbody shape.
Presz, W. M., Jr.↗
A procedure for calculating laminar, transitional and/or turbulent three-dimensional boundary layers including surface curvature effects about arbitrary blunt-nosed bodies
The governing equations for laminar, transitional and/or turbulent, incompressible, three-dimensional boundary layers are solved numerically. The equations are developed in terms of an orthogonal surface coordinate system and include surface curvature effects. The coordinates are generated numerically, while the inviscid flow is obtained from a general potential flow procedure. The only restrictions on body geometry are that it possess a blunt nose and a plane of symmetry. The boundary-layer equations, after being transformed into similarity type variables, are solved using the implicit finite-difference Krause scheme. Various test cases are presented to establish the accuracy of the resulting computer program.
Dwoyer, D. L.↗
An improved analytical model of the separated region on nozzle boattails
A viscous flow calculation is formulated for modelling the effects of separated, reverse flow regions on nozzle afterbody pressures and drags at subsonic Mach numbers. A discriminating streamline approach is used. Effects of skin friction, axial pressure gradient, and nozzle jet entrainment on the separated discriminating streamline shape are included. The viscous flow calculation is coupled to a potential flow calculation. The combined analysis is found to accurately predict both the magnitude of the measured afterbody pressures and drag, and also their variation with Reynolds number, Mach number and afterbody shape.
Presz, W. M., Jr.↗
Transonic flow calculations
The development of relaxation methods to calculate transonic flows is discussed. Rather accurate predictions can be made for a number of flows of interest using the transonic potential flow equation, which may be derived from the Euler equations for inviscid compressible flow by introducing the assumption that the flow is irrotational. Once the choice of a mathematical model has been settled, the numerical procedure for actually computing a solution contains two main elements: the construction of a discrete approximation which converges to the solution of the continuous problem in the limit as the mesh width is reduced to zero, and the solution of the resulting set of nonlinear difference equations by a convergent iterative scheme. The choice of an appropriate coordinate system and its influence on the accuracy of the discrete approximation is discussed. Several applications of the general method are described.
Jameson, A.↗
The computational treatment of supersonic wake flows in INCOREL
Supersonic wake flows are computed in both conical and three-dimensional full potential flows by modeling the wake as a planar cut with a potential discontinuity. Continuity of pressure is satisfied exactly on the wake cut by computing the necessary potential jump at each wake cut grid point. In the conical wake problem, the jump in potential vanishes in the crossflow symmetry plane. Generally, good correlation is achieved for fully three-dimensional wake flows with the planar wake approximation. Matching pressures in the isolated wake flow leads to small variations in the spanwise jump in potential. On the other hand, a small variation in the jump in potential near the wing tip flow can lead to a significant loading in the wake flow if the pressures are not matched.
Siclari, M. J.↗