Exact theory of three-dimensional flow separation. Part 1. Steady separation

Abstract

We derive an exact theory of three-dimensional steady separation and reattachment using nonlinear dynamical systems methods. Specifically, we obtain criteria for separation points and separation lines on fixed no-slip boundaries in compressible flows. These criteria imply that there are only four basic separation patterns with welldefined separation surfaces. We also derive a first-order prediction for the separation surface using wall-based quantities; we verify this prediction using flow models obtained from local expansions of the Navier-Stokes equations.

On the birth of stall cells on airfoils

“…The fundamentáis of the reconstruction and classiflcation of separated flow topologies are illustrated in [9,12,17,18]. Far from reaching completion, the application of critical point concepts to the study of flow patterns, and in particular to three-dimensional separated flow, is still an active fleld of research [22]. Topological analysis techniques based on the description of critical points have been employed in order to characterize the flow fleld associated with the stall cells [8,28].…”

Nonlinear Dynamics and Control of Three-Dimensional Separated Flows

“…Fig. 4) of complex separation patterns that are predicted to exist by our 3D steady theory [2,4], but have not yet been identified in practice.…”

Topology-guided Visualization of Constrained Vector Fields

“…Similarly, repelling (1:2) saddles and spiral saddles have their unstable manifold on the boundary, so any boundary curve of it is a reattachment line. The case of spiralling separation (called tornado-type separation in [SGH06]) has not been discussed much in the visualization community.…”

“…Surana et al in their exact theory of flow separation [SGH06] suggest as a criterion "strong hyperbolicity", i.e. large absolute eigenvalues of the saddles in the orthogonal section.…”