Mixed mode transition to turbulence in boundary layers

Bose, Rikhi
Major Professor
Paul Durbin
Committee Member
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Aerospace Engineering
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Aerospace Engineering

Boundary layer transition has been investigated by means of direct numerical simulation. The incompressible Navier Stokes equations have been solved for flow over a smooth flat plate. General consensus is that laminar to turbulent transition is via orderly or bypass route. The motivation of the present simulations is to specifically study the transition mechanisms when precursor of orderly

transition, the Tollmien-Schlichting waves and the precursor of bypass transition, the Klebanoff streaks, both take part in triggering transition, when neither by itself is sufficient. \textit{Mixed mode} transition has been studied in both Blasius and adverse pressure gradient boundary layers. The Klebanoff streaks are instigated inside the boundary layer by invoking free-stream turbulence at inlet. Time-periodic TS wave eigenfunction has been superimposed to the inlet velocity profile. In adverse pressure gradient,

the TS waves are spontaneously excited.

In both zero and adverse pressure gradients, three transition routes are obtained depending on perturbation magnitudes of the TS wave and intensity of free-stream turbulence. When intensity of free-stream turbulence is low, transition is via distortion of TS waves. $\Lambda$ vortices form and their breakdown triggers transition. When intensity of free-stream turbulence is high, classical bypass transition is recovered. When the strength of both the TS wave and free-stream disturbances are low, transition is via apparent interaction of the TS waves and Klebanoff streaks. Helical structures form and break down to trigger transition. The critical layer of the helical instability is close to the wall. Previous studies demonstrate that the outer mode breakdown is most dominant in Blasius boundary layer.

The inner mode has been found to be dominant in adverse pressure gradient boundary layers.

Present simulations provide a clearer picture. The inner modes could also be dominant in zero pressure gradient boundary layers, provided, instability waves are present and the intensity of free-stream turbulence is about $1\%$. The outer modes are consequence of high amplitude Klebanoff streaks instigated by high intensity free-stream turbulence. Stronger Klebanoff streaks stabilize the base profile and consequently the instability waves. Therefore, inner breakdown is suppressed.

Simulations in adverse pressure gradient demonstrate that the spontaneously excited instability waves are highly receptive to the inlet disturbance spectra. The growth rate of the instability waves are much higher due to inflectional base profile so that these could potentially couple with the Klebanoff streaks. The instability waves could be identified inside the boundary layer even at high levels of free-stream forcing. The instability waves were found to participate in transition process in all the cases simulated.

This indicates that in adverse pressure gradient boundary layers, mixed mode transition is almost always relevant.