Correspondence flows for wings in linearized potential fields at subsonic and supersonic speeds
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FLUTTER ANALYSIS OF FLAT RECTANGULAR PANELS BASED ON THREE-DIMENSIONAL SUPERSONIC POTENTIAL FLOW
Analysis of flutter of flat rectangular panels at low supersonic mach numbers using air forces from exact linearized potential-flow theory
FLUTTER↗
A finite element method for potential aerodynamics around complex configurations
A general formulation for steady and oscillatory, subsonic and supersonic, potential linearized aerodynamic flow around complex configurations is presented. A linear integral equation relating the unknown potential on the surface of the body to the known downwash is used. The formulation is applied to the analysis of the flow field around wings and wing-body combinations. The surface is divided into small quadrilateral elements which are approximated with a hyperboloidal surface. The potential is assumed to be constant within each element. This yields a set of linear algebraic equations. The coefficients are evaluated analytically. Numerical results for steady and oscillatory, subsonic and supersonic flows indicate that the method, intrinsically general and flexible, is also fast, accurate and in excellent agreement with existing results.
Chen, L.-T.↗
A theoretical basis for extending surface-paneling methods to transonic flow
The surface integral terms in Green's third identity are often used to solve the Prandtl-Glauert (linear potential-flow) equation with panel methods. This can be done, as in the PAN AIR code, for either subsonic or supersonic flow about complete aircraft. The extension to transonic flow is suggested by the volume integral terms of Green's third identity. The mathematical basis for this extension, without the use of body-fitted grids, is presented. Supercritical transonic results computed from a two-dimensional transonic PAN AIR research code demonstrate the method.
Erickson, L. L.↗
Steady, subsonic, lifting surface theory for wings with swept, partial span, trailing edge control surfaces
A method for computing the lifting pressure distribution on a wing with partial span, swept control surfaces is presented. This method is valid within the framework of linearized, steady, potential flow theory and consists of using conventional lifting surface theory in conjuction with a flap pressure mode. The cause of a numerical instability that can occur during the quadrature of the flap pressure mode is discussed, and an efficient technique to eliminate the instability is derived. This technique is valid for both the flap pressure mode and regular pressure modes and could be used to improve existing lifting surface methods. Examples of the use of the flap pressure mode and comparisons among this method, other theoretical methods, and experiments are given. Discrepancies with experiment are indicated and candidate causes are presented. It is concluded that the method can lead to an efficient and accurate solution of the mathematical problem when a partial span, trailing edge flap is involved.
Medan, R. T.↗
Unsteady Subsonic Loadings Due to Control-Surface Motion
RHOIV computer program predicts unsteady lifting-surface loadings caused by motions of leading edge and trailing-edge control surfaces having sealed gaps at hinge lines and side edges. Analysis is based on linear, subsonic, potential-flow theory using kernel function method. Linear combinations of pressure distributions are used that are continuous except at planform edges and hinge lines. Loading solution is obtained by downwash collocation for deflection or motion of main wing and control surfaces.
Rowe, W. S.↗
Development of a linear unsteady aerodynamic analysis for finite-deflection subsonic cascades
A linear unsteady potential flow analysis, which accounts for the effects of blade geometry and steady turning, is being developed to predict the aerodynamic response to blade vibrations in the fan, compressor or turbine stages of modern jet engines. In previous work numerical solutions were restricted to cascades of sharp-edged blades aligned with the mean flow. Under the present effort the solution procedure has been extended to treat blades with rounded or blunt edges. As part of this effort an analytical model-problem study has been conducted to clarify the behavior of first-order perturbation solutions in the vicinity of airfoil edges. Further, a numerical approximation using concepts from singular perturbation theory has been developed to resolve the unsteady boundary value problem for cascades of blunt leading-edged blades. Numerical results for NACA 0012 cascades, including detailed results in the vicinity of a blade leading edge, are presented and evaluated.
Verdon, J. M.↗
Experimental Test Of Aerodynamic Computer Program
Linear potential-flow theory applied to advanced airplane design. Report discusses use of PANAIR computer program to predict airflow about advanced fighter aircraft. Predictions compared with measurements about scale model of aircraft in wind tunnel at mach numbers of 0.6, 0.9, and 1.2 and at angles-of-attack from 0 to 10 degree.
Madson, M. D.↗
The effect of steady aerodynamic loading on the flutter stability of turbomachinery blading
An aeroelastic analysis is presented which accounts for the effect of steady aerodynamic loading on the aeroelastic stability of a cascade of compressor blades. The aeroelastic model is a two degree of freedom model having bending and torsional displacements. A linearized unsteady potential flow theory is used to determine the unsteady aerodynamic response coefficients for the aeroelastic analysis. The steady aerodynamic loading was caused by the addition of airfoil thickness and camber and steady flow incidence. The importance of steady loading on the airfoil unsteady pressure distribution is demonstrated. Additionally, the effect of steady loading on the tuned flutter behavior and flutter boundaries indicates that neglecting either airfoil thickness, camber or incidence could result in nonconservative estimates of flutter behavior.
Smith, Todd E.↗
The effect of steady aerodynamic loading on the flutter stability of turbomachinery blading
An aeroelastic analysis is presented which accounts for the effect of steady aerodynamic loading on the aeroelastic stability of a cascade of compressor blades. The aeroelastic model is a two degree of freedom model having bending and torsional displacements. A linearized unsteady potential flow theory is used to determine the unsteady aerodynamic response coefficients for the aeroelastic analysis. The steady aerodynamic loading was caused by the addition of airfoil thickness and camber and steady flow incidence. The importance of steady loading on the airfoil unsteady pressure distribution is demonstrated. Additionally, the effect of steady loading on the tuned flutter behavior and flutter boundaries indicates that neglecting either airfoil thickness, camber or incidence could result in nonconservative estimates of flutter behavior.
Smith, Todd E.↗
Time-domain Green's Function Method for three-dimensional nonlinear subsonic flows
The Green's Function Method for linearized 3D unsteady potential flow (embedded in the computer code SOUSSA P) is extended to include the time-domain analysis as well as the nonlinear term retained in the transonic small disturbance equation. The differential-delay equations in time, as obtained by applying the Green's Function Method (in a generalized sense) and the finite-element technique to the transonic equation, are solved directly in the time domain. Comparisons are made with both linearized frequency-domain calculations and existing nonlinear results.
Tseng, K.↗
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.↗
High-order numerical solutions using cubic splines
The cubic spline collocation procedure for the numerical solution of partial differential equations was reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy for a nonuniform mesh and overall fourth-order accuracy for a uniform mesh. Application of the technique was made to the Burger's equation, to the flow around a linear corner, to the potential flow over a circular cylinder, and to boundary layer problems. The results confirmed the higher-order accuracy of the spline method and suggest that accurate solutions for more practical flow problems can be obtained with relatively coarse nonuniform meshes.
Rubin, S. G.↗
Calculations on the forces and moments for an oscillating wing-aileron combination in two-dimensional potential flow at sonic speed
The linearized theory for compressible unsteady flow is used, as suggested in recent contributions to the subject, to obtain the velocity potential and the lift and moment for a thin harmonically oscillating, two-dimensional wing-aileron combination moving at sonic speed. The velocity potential is derived by considering the sonic case as the limit of the linearized supersonic theory. From the velocity potential explicit expressions for the lift and moment are developed for vertical translation and pitching of the wing and rotation of the aileron. The sonic results are compared and found to be consistent with previously obtained subsonic and supersonic results. Several figures are presented showing the variation of lift and moment with reduced frequency and Mach number and the influence of Mach number on some cases of bending-torsion flutter.
Nelson, Herbert C↗
A generalized-capacity-matrix technique for computing aerodynamic flows
A numerical generalized-capacity-matrix technique is developed for application to aerodynamic flow computations. This technique allows the very fast direct (noniterative) numerical elliptic solvers to be used in problems with arbitrary internal boundaries and with a wide class of boundary conditions, including numerical application of the Kutta condition on an airfoil without iteration. Accuracy, speed, and usefulness of the technique are demonstrated with linear problems for potential flows over airfoil shapes. The method's main advantages, however, can be exploited within iterative procedures for a variety of complex flow problems governed by systems of equations not necessarily elliptic or linear.
Martin, E. D.↗
Theoretical and computational dynamics of a compressible flow
An introduction to the theoretical and computational fluid dynamics of a compressible fluid is presented. The general topics addressed include: thermodynamics and physical properties of compressible fluids; 1D flow of an inviscid compressible fluid; shock waves; fundamental equations of the dynamics of a compressible inviscid non-heat-conducting and radiating fluid, method of small perturbations, linearized theory; 2D subsonic steady potential flow; hodograph and rheograph methods, exact solutions of 2D insentropic steady flow equations, 2D steady transonic and hypersonic flows, method of characteristics, linearized theory of 3D potential flow, nonlinear theory of 3D compressibe flow, anisentropic (rotational) flow of inviscid compressible fluid, electromagnetogasdynamics, multiphase flows, flows of a compressible fluid with transport phenomena.
Pai, Shih-I↗
On the use of parametric differentiation to predict weak shock waves
The method of parametric differentiation is shown to be an effective means to transform both the time-linearized and the fully nonlinear transonic small disturbance potential flow equations to a linear system of equations. The globally linearized equations are then solved in phase space by finite difference methods and integral equation methods. The predicted birth, growth, and motion of weak shock waves in two-dimensional transonic flows are compared with existing theory and experiment.
Harris, W. L.↗
Numerical solution of nonlinear partial differential equations of mixed type
A review is presented of some recently developed numerical methods for the solution of nonlinear equations of mixed type. The methods considered use finite difference approximations to the differential equation. Central difference formulas are employed in the subsonic zone and upwind difference formulas are used in the supersonic zone. The relaxation method for the small disturbance equation is discussed and a description is given of difference schemes for the potential flow equation in quasi-linear form. Attention is also given to difference schemes for the potential flow equation in conservation form, the analysis of relaxation schemes by the time dependent analogy, the accelerated iterative method, and three-dimensional calculations.
Jameson, A.↗