Unsteady Transonic Flow Past Airfoils In Rigid Body Motion Classic Reprint

Excerpt from Unsteady Transonic Flow Past Airfoils in Rigid Body Motion We begin our discussion with a brief survey of the behavior of flows past airfoils; when a conventional symmetric airfoil accelerates from subsonic speed to supersonic speed the flow pattern usually develops in the manner shown in Figure 11. As the flight speed of the airfoil reaches the critical speed, the local flow speed equals the local sound speed. Beyond the critical speed, a supersonic region appears on the airfoil which is usually terminated by a nearly normal shock through which the flow speed jumps from super sonic to subsonic. With a further increase in the flight speed, the shock moves aft and the size of the supersonic region and the shock strength both increase. If the pressure jump through the shock is sufficiently large, separation of the boundary layer occurs. This shock induced separation starts when the local Mach number, the ratio of local flow and sound speeds, just upstream of the shock is about to When the boundary layer downstream of the shock separates. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

With the aim of developing a fast and accurate computer code for predicting the aerodynamic forces needed for a flutter analysis we review some basic concepts in computational transonics. The unsteady transonic flow past airfoils in rigid body motion is adequately described by the potential flow equation as long as the boundary layer remains attached. The two dimensional unsteady transonic potential flow equation in quasilinear form with first order radiation boundary conditions is solved by an alternating direction implicit scheme in an airfoil attached sheared parabolic coordinate system. Numerical experiments show that the scheme is very stable and is able to resolve the highly nonlinear transonic effects for flutter analysis within the context of an inviscid theory. (Author).

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 volume complements Transonic aerodynamics (v.81 in the series) which is concerned with steady flow. This is the only book to address the subject of unsteady transonic aerodynamics, a field much different from steady aerodynamics. The most pronounced difference is the complex shock wave motions

The problem of constructing solutions for transonic flow over symmetric airfoils is treated for simplification of the mapping of the incompressible flow is emphasized. In the case of a symmetric Joukowski airfoil without circulation the mapping is relatively simple, but the coefficients in the power series are difficult to evaluate. As a means of simplification an approximate flow is used which differs only slightly from the exact incompressible one when the thickness is small. Flow with circulation is also considered by the same method.