Three Dimensional Boundary Layers

Chapter 1

Abstract

considered.

1. Introduction

3

flow structures, applications

Vladimir Shalaev

3D Boundary Layer Theory

Some new analytical results in 3D boundary layer theory are reviewed and discussed. It includes the perturbation theory for 3D flows, analyses of 3D boundary layer equation singularities and corresponding real flow structures, investigations of 3D boundary layer distinctive features for hypersonic flows for flat blunted bodies including the heat transfer and the laminar-turbulent transition and influences of these phenomena on flows, and the new approach to the analysis of the symmetric flow instability over thin bodies and studies of the control possibility with the electrical discharge using new model of this phenomenon interaction with the 3D boundary layer. Some new analytical solutions of boundary layer and Navier-Stokes equations are presented. Applications of these results to analyze viscous flow characteristics of real objects such as aircraft wings, fuselages, and other bodies are

Keywords: 3D boundary layer, asymptotic perturbation theory, singularities,

Despite the intensive development of computer technologies and numerical methods for the Navier-Stokes and Reynolds equations, problems of the threedimensional boundary layer are of significant interest in the fluid dynamics. So far these problems have been little studied as a result of objective difficulties related with the large dimensionality and complexity of equations. Therefore, analytic results in this field can play an important role in the depth understanding of fluid dynamics phenomena and their study. In this part, some modern results in the

The small perturbation theory for inviscid flows is well developed and widely applied to estimate aerodynamic characteristics of real flight apparatus. Also it has been attempted to develop such theory for the boundary layer [1]. However, the zero approximation ("flat plate" approximation, zero cross-flow approximation) only given a rational contribution and were used in calculations. Equations for perturbations were complex. They required a numerical solution that was not much simpler than the full equation system. Father investigations of three-dimensional effects in the boundary layer theory became possible only after developments of computers with the enough power, numerical methods, and turbulence models [2]. Another approach was developed on the base of the rational perturbation theory

including the first-order approximation [3–10] for some class of flows, such as flows over aircraft wings and fuselages at small angle of attack, which have high importance as for the theory and the practice. In this case, zero-order approximation functions do not depend on the cross coordinate. Equations of the first-order

three-dimensional boundary layer theory are discussed.
