Computational Methods For Unsteady Transonic Flows

This report provides a direct comparison of the calculations for the flow field about an oscillating airfoil in a transonic freestream predicted by two computational methods; namely, harmonic analysis and time integration. Details of the two methods are summarized and results for NACA64A010 airfoil oscillating in pitch are considered. Comparisons of the unsteady pressure distribution and resultant lift are presented for several values of free-stream Mach number, angle of attack, and reduced frequency of oscillation. (Author).

A bibliography of recent developments in unsteady transonic flow is presented. Papers have been divided into survey, experimental, and theoretical classifications, selected publications have been reviewed, and a more comprehensive set of publications has been listed and summarized in tabular form. Primary emphasis has been placed on numerical solution of unsteady transonic flow problems. Relevant steady methods have been included. (Author)

In developing this book, we decided to emphasize applications and to provide methods for solving problems. As a result, we limited the mathematical devel opments and we tried as far as possible to get insight into the behavior of numerical methods by considering simple mathematical models. The text contains three sections. The first is intended to give the fundamen tals of most types of numerical approaches employed to solve fluid-mechanics problems. The topics of finite differences, finite elements, and spectral meth ods are included, as well as a number of special techniques. The second section is devoted to the solution of incompressible flows by the various numerical approaches. We have included solutions of laminar and turbulent-flow prob lems using finite difference, finite element, and spectral methods. The third section of the book is concerned with compressible flows. We divided this last section into inviscid and viscous flows and attempted to outline the methods for each area and give examples.

This classic monograph on unsteady transonic flow — the flow of air encountered at speeds at or near the speed of sound — is of continuing interest to students and professionals in aerodynamics, fluid dynamics, and other areas of applied mathematics. After a brief Introduction, Swedish physicist Mårten T. Landahl presents a chapter in which the two-dimensional solution is derived, succeeded by a discussion of its relation to the subsonic and supersonic solutions. Three chapters on low aspect ratio configurations follow, covering triangular wings and similar planforms with curved leading edges, rectangular wings, and cropped delta wings, and low aspect ratio wing-body combinations. The treatment concludes with a consideration of the experimental determination of air forces on oscillating wings at transonic speeds.

This thesis explores linear and non-linear computational methods for solving unsteady flow. The eventual goal is to apply these methods to two-dimensional and three-dimensional flutter predictions. In this study the quasi-one-dimensional nozzle is used as a framework for understanding these methods and their limitations. Subsonic and transonic cases are explored as the back-pressure is forced to oscillate with known amplitude and frequency. A steady harmonic approach is used to solve this unsteady problem for which perturbations are said to be small in comparison to the mean flow. The use of a linearized Euler equations (LEE) scheme is good at capturing the flow characteristics but is limited by accuracy to relatively small amplitude perturbations. The introduction of time-averaged second-order terms in the Non-Linear Harmonic (NLH) method means that a better approximation of the mean-valued solution, upon which the linearization is based, can be made. The nonlinear time-accurate Euler solutions are used for comparison and to establish the regimes of unsteadiness for which these schemes fails. The usefulness of the LEE and NLH methods lie in the gains in computational efficiency over the full equations.

This report describes a study performed to evaluate a 3D, full potential, computational method developed at the Lockheed-Georgia. This computational method was used to compute both steady and unsteady compressible flows about an F-5 fighter wing model. Comparisons are made between computed steady and unsteady aerodynamic data and available experimental data for the F-5 planform. Correlations are presented for steady, unsteady and quasi-steady surface pressure distributions and integrated loads coefficients. Originator-assigned keywords include: Computational fluid dynamics, Unsteady aerodynamics, and Transonic flow.