Book contents
- Frontmatter
- Contents
- Preface
- Preface to the English Edition
- 1 The Theory of Separation from a Smooth Surface
- 2 Flow Separation from Corners of a Body Contour
- 3 Flow in the Vicinity of the Trailing Edge of a Thin Airfoil
- 4 Separation at the Leading Edge of a Thin Airfoil
- 5 The Theory of Unsteady Separation
- 6 The Asymptotic Theory of Flow Past Blunt Bodies
- 7 Numerical Methods for Solving the Equations of Interaction
- References
- Index
6 - The Asymptotic Theory of Flow Past Blunt Bodies
Published online by Cambridge University Press: 07 October 2011
- Frontmatter
- Contents
- Preface
- Preface to the English Edition
- 1 The Theory of Separation from a Smooth Surface
- 2 Flow Separation from Corners of a Body Contour
- 3 Flow in the Vicinity of the Trailing Edge of a Thin Airfoil
- 4 Separation at the Leading Edge of a Thin Airfoil
- 5 The Theory of Unsteady Separation
- 6 The Asymptotic Theory of Flow Past Blunt Bodies
- 7 Numerical Methods for Solving the Equations of Interaction
- References
- Index
Summary
The Background of the Problem
This chapter will be devoted to the analysis of one of the fundamental problems of hydrodynamics: ascertaining the limiting state for the steady flow behind a body of finite size as the Reynolds number Re → ∞ in cases where unseparated flow over the body is impossible, for example, behind a blunt body such as a circular cylinder or a plate placed normal to the oncoming flow. Although in reality such flows already become unsteady at Reynolds numbers of the order of 101–102, and undergo transition to a turbulent state with further increase in Reynolds number, the solution of this problem is of great interest in principle. Moreover, one might anticipate that such a solution would allow the study of fluid flows at moderate Reynolds numbers when a steady flow regime is still maintained but the methods of the theory of slow motion (Re < 1) are no longer applicable.
There are several points of view about possible ways of solving this problem. According to the first of these, already stated by Prandtl (1931) and then developed by Squire (1934) and Imai (1953, 1957b), the limiting flow configuration as Re → ∞ is the classical Kirchhoff (1869) flow with free streamlines and a stagnation zone that extends to infinity and expands asymptotically according to a parabolic law (Figure 6.1). This picture has been severely criticized both because of poor quantitative agreement with experimental results (for measurements of body drag) and also for some fundamental reasons.
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- Asymptotic Theory of Separated Flows , pp. 233 - 265Publisher: Cambridge University PressPrint publication year: 1998