Ph.D Thesis


Ph.D StudentJimmy Philip
SubjectThe Relationship between Streaks and Hairpin Vortices in
Subcritical Wall Bounded Shear Flows
DepartmentDepartment of Aerospace Engineering
Supervisor Full Professors Cohen Jacob
Full Thesis textFull thesis text - English Version


Abstract

The main objective of the research is to study the evolution of the key structures in turbulent flows: streaks and hairpins vortices, using experimental, theoretical and numerical methods. Two canonical flows are considered, plane Poiseuille flow (PPF) and flow in a pipe.

Streaks are generated experimentally in a laminar PPF using injection through a streamwise slot. Flow visualization and velocity measurements (representing mean, instantaneous and phase-locked data) are carried out using hot wire and PIV techniques. The measured streaks grow in accordance with the linear mechanism of transient growth, and the distance of maximum growth (Xmax) is proportional to Reynolds number (Re). New theoretical considerations show that many aspects of the transient growth mechanism can be predicted using just the two least stable modes of laminar PPF. As is observed in experiments, when streaks undergo secondary instability, they become wavy and localized disturbances are formed at the crest of these waves, giving rise to hairpin vortices. The linear stability analysis of the inflectional streak profile correctly predicts the wavelength and the frequency observed in the experiments. However, it under-predicts the growth rate of the hairpin vortices, suggesting a different mechanism for the growth of the hairpins, even though the secondary instability correctly predicts their initiation. Experiments show that the amplitude (in this case the injection velocity of the disturbance, v0) required to produce hairpins varies as Re-3/2. The hairpins once produced continue to sustain in the PPF.

A similar process of streak development (as in PPF) and their secondary instability to produce hairpin vortices are observed experimentally in pipe flow, by artificial injection of continuous disturbances. In pipe flow the scaling is, v0 ~ Re-1 at the generation point. However, the streaks and hairpins decay along the downstream distance (X); a variation in the scaling of v0 Vs Re along X for the initiation of hairpins, confirms this. Measurements of energy in the cross-sectional plane of the pipe, and maps of disturbance velocity at various X-locations show the transient growth and decay of energy. Owing to the increase in the area of the disturbance influence along the X-direction, the energy can transiently increase even when the total disturbance magnitude is decreasing.

Finally, localized hairpin vortices are treated analytically by the temporal evolution of their associated integral characteristic, the fluid impulse. Closed form expressions are derived for the evolution of nonlinear, localized disturbance in an irrotational shear flow, and compared with numerical results.