Separated-Flow Transition: Part 3 — Primary Modes and Vortex Dynamics

Abstract

This paper clearly identifies the possible modes of transition in the separated boundary layers and their specific characteristics. This study distinguishes between the short and long bubbles primarily based on the separated flow structure. A hypothetical description of the vortex structure and evolution for each separated-flow transition mode is provided. The present approach in analyzing separated-flow transition is based on the assumption that the transition to turbulence in separated boundary layers is a result of the superposition of the effects of two different types of instability. The first type of instability is the Kelvin-Helmholtz (KH) instability. It occurs and develops in the shear layer at a specific location downstream of the separation point. The concentration of spanwise vorticity grows in time and remains in place through the vortex sheet roll-up mechanism. The roll-up vortex interacts with the wall and induces periodic ejection of near-wall fluid into the separated shear layer. The ejection process takes place at a location identifiable by the maximum displacement of shear layer, xMD. The second type of instability is the (convective) Tollmien-Schlichting (TS) instability. It originates in the boundary layer prior to the separation point and continues to evolve in the separated shear layer. The mechanism for the TS instability also leads to roll-ups, but it involves viscous tuning of the instability waves. Thus, the separated-flow transition is the result of spatially developing, often competing instabilities. The ejection induces the onset of transition for laminar short and long bubble modes of transition and controls the mid-transition point of transitional separation mode. The ejection may be accompanied by vortex shedding. Shedding occurs in the laminar separation - short bubble mode and occasionally in the transitional separation mode; however, it is not present in the laminar separation - long bubble mode of transition.

A Prediction Model for Separated-Flow Transition

“…The analysis of the low free-stream turbulence intensity (Tu = 0.3 to 0.6 %) data of Hatman (1997) and partially presented in Hatman and Wang (1998 a, b, c) led to the observation that the location of maximum bubble elevation (xMD) is the key parameter for correlating the separated-flow transition. Using this parameter, specific regions were delineated for each mode of the separated-flow transition.…”

“…A detailed description of each primary mode is given below. The vortex dynamics associated with the three primary modes is presented in Hatman and Wang (1998 c).…”

“…The onset of transition takes place prior to boundary layer separation and the early transition is similar to the natural transition in attached boundary layers. The late transition is affected by the addition of KH instability and nearwall fluid ejection (see Hatman and Wang, 1998 c). The transitional separation bubble can be accompanied by vortex shedding.…”

“…Recent studies (Malkiel andMayle, 1995, Hazarika andHirsch, 1995) have provided basic information about how transition originates and develops in separated boundary layers. It is commonly accepted that the detached laminar shear layer is inherently unstable and promotes the growth of disturbances, leading to an earlier laminar-to-turbulent transition.…”

Transition in separation bubbles: physical mechanisms and passive control techniques

“…and Wang(1999) proposed a set of empirical transition models based a series of experiments aimed at examining the nature of separated-flow transition at low freestream turbulence levels(H atm an and Wang, 1998a;H atm an and Wang, 19986;H atm an and Wang, 1998c). Their model for transition onset in a separated shear layer is:…”