Temporal adaptive Euler/Navier-Stokes algorithm involving unstructured dynamic meshes
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Kleb, W. L.↗
Engineering topics
Williams, M. H.
Publications and source records attributed to Williams, M. H..
A panel method for counter rotating propfans
A time domain source-doublet surface paneling method is developed for analyzing the unsteady loads on counter rotating propellers in incompressible irrotational flow. A scheme for treating the blade-wake interaction problem is described. Sample results for single rotation propellers are given, with comparisons to alternate theories and experiment. Finally, some preliminary results for quasi-steady and fully unsteady loads on counter rotating systems are presented.
Williams, M. H.↗
Nonisentropic unsteady three dimensional small disturbance potential theory
Modifications that allow for more accurate modeling of flow fields when strong shocks are present were made into three dimensional transonic small disturbance (TSD) potential theory. The Engquist-Osher type-dependent differencing was incorporated into the solution algorithm. The modified theory was implemented in the XTRAN3S computer code. Steady flows over a rectangular wing with a constant NACA 0012 airfoil section and an aspect ratio of 12 were calculated for freestream Mach numbers (M) of 0.82, 0.84, and 0.86. The obtained results are compared using the modified and unmodified TSD theories and the results from a three dimensional Euler code are presented. Nonunique solutions in three dimensions are shown to appear for the rectangular wing as aspect ratio increases. Steady and unsteady results are shown for the RAE tailplane model at M = 0.90. Calculations using unmodified theory, modified theory and experimental data are compared.
Gibbons, M. D.↗
Three dimensional unsteady aerodynamics and aeroelastic response of advanced turboprops
A method for the prediction of steady and unsteady aerodynamic loads and aeroelastic response of advanced turboprops is presented. The aerodynamic analysis uses three dimensional unsteady linearized compressible flow theory to compute the blade pressure distribution. The aeroelastic analysis is based on a normal mode representation of the structure. The method is applicable to both conventional and advanced turbo-prop configurations, provided that blade stall and transonic shock waves are not important factors. Aerodynamic results are presented which validate the model in various limits by comparisons to alternative theories and experimental data. Finally, results of a stability analysis of an advanced turboprop are given, with comparisons to measurements made at NASA Lewis Research Center.
Williams, M. H.↗
Nonisentropic unsteady three dimensional small disturbance potential theory
Nonisentropic modifications to the three-dimensional transonic small disturbance (TSD) theory, which allows for more accurate modeling of transonic flow fields, are described. The modified flux equation and entropy corrections are presented; the Engquist-Osher differencing (1980) is added to the solution algorithm in order to eliminate the velocity overshoots upstream of shocks. The modified theory is tested in the XTRAN3S finite difference computer code. Steady flows over a rectangular NACA 0012 wing with an aspect ratio of 12 are calculated and compared to Euler equation solutions; good correlation is observed between the data and the modified TSD theory provides more accurate data, particularly for the lift curve slope. The nonisentropic theory is evaluated on an RAE tailplane model for steady and unsteady flows and the modified theory results agree well with the experimental data.
Gibbons, M. D.↗
Flow instabilities in transonic small-disturbance theory
The dynamics of unsteady transonic small disturbance flows about two-dimensional airfoils is examined, with emphasis on the behavior in the region where the steady state flow is nonunique. It is shown that nonuniqueness results from an extremely long time scale instability which occurs in a finite Mach number and angle of attack range. The similarity scaling rules for the instability are presented and the possibility of similar behvior in the Euler equations is discussed.
Williams, M. H.↗
Flow instabilities in transonic small disturbance theory
The dynamics of unsteady transonic small disturbance flows about two-dimensional airfoils is examined, with emphasis on the behavior in the region where the steady state flow is nonunique. It is shown that nonuniqueness results from an extremely long time scale instability which occurs in a finite Mach number and angle of attack range. The similarity scaling rules for the instability are presented and the possibility of similar behavior in the Euler equations is discussed.
Williams, M. H.↗
Non-isentropic unsteady transonic small disturbance theory
Modifications to transonic small disturbance theory (TSD) which more accurately model the Euler equations and seem to remove the problem of nonunique potential flow solutions are presented. The modifications are implemented in the two-dimensional computer code XTRAN2L, and steady and unsteady flow calculations made for the NACA 0012, NLR 7301, and NACA 64A010A airfoils. Comparisons are made with unmodified and modified TSD, Euler, and full potential theories and with experimental data. The modified theory requires only minor coding changes in existing algorithms for calculating small disturbance flows, and results in relatively small increases in computational cost.
Fuglsang, D. F.↗
The effect of a normal shock on the aeroelastic stability of a panel
The effect of a standing shock wave on the static and dynamic aeroelastic stability of a flexible panel is investigated using a linear structural and aerodynamic theoretical model. It is found that the shock is generally stabilizing. The lowest critical dynamic pressures are associated with shock positions downstream from the panel, where the panel is uninfluenced by the shock.
Williams, M. H.↗
Linear/nonlinear behavior in unsteady transonic aerodynamics
(Previously cited in issue 12, p. 1923, Accession no. A81-29496)
Dowell, E. H.↗
Solution of the unsteady subsonic thin airfoil problem
The problem of a thin airfoil subject to simple harmonic disturbances in a uniform subsonic free stream is solved by extension of a technique developed earlier for a stationary strip vibrating in a uniform fluid. Explicit expressions are given for the lift and moment, acoustic directivity pattern, and total acoustic power for arbitrary upwash and, in particular, for the 'elementary disturbances': plunge, pitch and a stationary transverse gust. Numerical results for a simple skewed gust are presented and compared to the high-frequency asymptotic theory of Martinez and Widnall.
Williams, M. H.↗
Diffraction by a finite strip
A new approach is presented to diffraction problems involving plane strip barriers or slit apertures. These are problems that display the effects of multiple interacting edges. The approach taken here provides exact, compact solutions. The theory is introduced through a series of examples that are, in fact, the 'standard' problems of the subject, diffraction of a plane oblique wave by a slit, for example. In each case, the solutions are found to depend explicitly on a single 'special' function and its Fourier transform. These fundamental functions are described, with the emphasis placed on practical computational methods. The example problems are all couched in the language of acoustics.
Williams, M. H.↗
An assessment of theoretical models for viscous and transonic flow
Topics discussed include shear flow models, simplified models for treating separation, classical linear theory, a local linearization theory, a transonic linear theory, a transonic nonlinear theory, the experiment of Davis, and the experiment of Tijdeman. It is concluded that shear flow models, which have proven very accurate in taking into account boundary layer effects for panel flutter, are likely to be less so for lifting surface flutter. For many applications in transonic flow, transonic linear theory will be adequate.
Dowell, E. H.↗
Linear/nonlinear behavior in unsteady transonic aerodynamics
The accurate calculation of the aerodynamic forces in unsteady transonic flow requires the solution of the nonlinear flow equations. The aeroelastician, on the other hand, seeks to treat his problems (flutter, for example) by means of linear equations whenever possible. He may do this, even when the underlying flow is nonlinear, if the perturbation forces are linear over some (perhaps small) range of unsteady amplitude of motion. This paper assesses the range of parameters over which linear behavior occurs. In particular calculations are made for an NACA 64A006 airfoil oscillating in pitch over a range of amplitudes, frequencies, and Mach numbers. The primary aerodynamic method used is the well known LTRAN2 code of Ballhaus and Goorjian that provides a finite-difference solution to the low frequency, small disturbance, two-dimensional potential flow equation. Comparisons are made with linear subsonic theory, local linearization, and, for steady flow, with the full potential equation code of Bauer, Garabedian, and Korn.
Dowell, E. H.↗
Aerodynamic coefficients in generalized unsteady thin airfoil theory
Two cases are considered: (1) rigid body motion of an airfoil-flap combination consisting of vertical translation of given amplitude, rotation of given amplitude about a specified axis, and rotation of given amplitude of the control surface alone about its hinge; the upwash for this problem is defined mathematically; and (2) sinusoidal gust of given amplitude and wave number, for which the upwash is defined mathematically. Simple universal formulas are presented for the most important aerodynamic coefficients in unsteady thin airfoil theory. The lift and moment induced by a generalized gust are evaluated explicitly in terms of the gust wavelength. Similarly, in the control surface problem, the lift, moment, and hinge moments are given as explicit algebraic functions of hinge location. These results can be used together with any of the standard numerical inversion routines for the elementary loads (pitch and heave).
Williams, M. H.↗
The inversion of singular integral equations by expansion in Jacobi polynomials
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Williams, M. H.↗
Linearization of unsteady transonic flows containing shocks
The problem of determining unsteady airloads on a thin, three-dimensional, planar wing oscillating with infinitesimal amplitude in a transonic flow is considered. The flow is assumed to be governed by the transonic small disturbance equation. The unsteady disturbance is taken to be a small perturbation superposed on a given steady mean flowfield. The equations governing the unsteady field, allowing for induced oscillations of any embedded shocks, are obtained. The linearization is shown to fail, locally, at the intersection of a shock with the wing surface, although the failure has little influence on the sectional characteristics of the wing.
Williams, M. H.↗
Unsteady thin airfoil theory for transonic flows with embedded shocks
Classical unsteady thin airfoil theory fails for low frequencies at the subsonic freestream Mach number, because of the formation of a shock wave that shields the forward region of the airfoil from aft generated disturbances. In the present paper, the classical thin airfoil theory is modified to account for the presence and induced motion of such shocks. The modification consists of taking the steady local Mach number to be a simple step discontinuity, normal to the undisturbed flow, separating two uniform regions. Predicted regions are shown to correlate well both with the experiment and finite difference calculations.
Williams, M. H.↗