1. Introduction and Background: An Overview

Abstract

Previous chapter Next chapter Frontiers in Applied Mathematics Transonic Aerodynamics: Problems in Asymptotic Theory1. Introduction and Background: An OverviewL. Pamela Cook and Gilberto SchleinigerL. Pamela Cook and Gilberto Schleinigerpp.1 - 7Chapter DOI:https://doi.org/10.1137/1.9781611970975.ch1PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutExcerpt Transonic aerodynamics involves flows about surfaces for which the flow speed q is close to the speed of sound a (the Mach number of the flow M=q/a≈1 ). These flows are dominated by nonlinear effects and have, in steady flow, both subsonic and supersonic regions within the flow. The flow is thus governed by a system of equations that, in steady flow, is of mixed type. The equations are nonlinear and they must ultimately be solved numerically. However, asymptotic analysis has greatly simplified and enriched both the theory and the computations of these flows. Asymptotic analysis reduces the number of parameters involved, can simplify the geometry, and clarifies near and far field conditions. It is the asymptotic theory of transonic aerodynamics which forms the basis for this monograph; this monograph does not focus on computational aspects of transonic aerodynamics. Much progress has been made during the last 20 years on computation of flows in the transonic regime, and surveys as well as research articles can be found elsewhere. Present day commercial aircraft (e.g., the 747) cruise in the transonic range. For an airplane flying in a uniform stream, as the Mach number M∞ =U/ a∞ far upstream approaches one, the drag rises precipitously. Thus there is a great interest in analyzing the transonic range of flight, its stability properties, and especially the question of designing reduced drag (shockless or weak shock) wings. One of the useful advances in transonic aerodynamics, valid for small disturbances (e.g., flow past thin airfoils or slender bodies) and in fact used throughout this monograph, is transonic small disturbance theory (TSD). This is a limiting formulation (valid as M∞ →1 and the thickness ratio δ → 0). It is useful in that it strips extraneous terms from the governing equations so that the simplest canonical description results. In this monograph both inviscid and viscous transonic flows as well as steady and time-dependent flows are discussed. A few comments on two-dimensional (2D) steady inviscid flows are given below to orient the reader. For further background and more general flows see [1], [2] and the appropriate chapters in this monograph. Previous chapter Next chapter RelatedDetails Published:1993ISBN:978-0-89871-310-7eISBN:978-1-61197-097-5 https://doi.org/10.1137/1.9781611970975Book Series Name:Frontiers in Applied MathematicsBook Code:FR12Book Pages:x + 88Key words:transonic aerodynamics, asymptotic theory, wind-tunnel flows, conservation, dispersion