An asymptotic theory of turbulent separation
1989; Elsevier BV; Volume: 17; Issue: 1 Linguagem: Inglês
10.1016/0045-7930(89)90014-5
ISSN1879-0747
Autores Tópico(s)Aerodynamics and Fluid Dynamics Research
ResumoThe problem addressed in this paper is the turbulent counterpart of the classical Goldstein analysis of laminar separation points. In the present paper we present a new asymptotic theory of turbulent boundary layers and we use it to determine the singular behavior of solutions of the boundary layer equations at the point of zero skin friction in a prescribed pressure distribution. In the first part of the paper we describe a new asymptotic theory of turbulent boundary layers which is based on formal expansions in terms of two parameters: Reynolds number Re → ∞ and α → 0, where α is a turbulence model constant appearing in the zero equation turbulence model employed in the present study. In order to establish the accuracy of the theory, solutions obtained with the new theory for equilibrium turbulent flow are compared with "exact" solutions of Mellor and Gibson. In the second part of the paper the local behavior of solutions of the turbulent boundary layer equations with a zero equation turbulent model is established using the new asymptotic theory. It is demonstrated that the solution of the turbulent boundary layer equations are singular at separation points if the pressure distribution is prescribed just as in the laminar case. However, the nature of the singularity is different in laminar and turbulent flow. We show that the approach to zero skin friction is linear in turbulent flow as compared to the square root behavior of the laminar "Goldstein" singularity.
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