PIV measurements of the K-type transition in natural convection boundary layers

Abstract

The K-type transition of a natural convection boundary layer of Ra = 9.8 × 109 is studied by PIV (Particle Image Velocimetry) measurements. To excite the transition, Tollmien-Schlitchting (TS) and oblique waves of the same frequency are introduced into the upstream boundary layer in the form of velocity perturbations. It is found that resonant interactions between the characteristic frequency of the natural convection boundary layer and the superimposed TS and oblique waves are present, which trigger the K-type transition of the boundary layer. The typical aligned Λ-shaped flow structures characterising the K-type transition present in the transition of Blasius boundary layers are also observed in the present natural convection boundary layers. They occur when the primary instability grows to a certain extent. The appearance of the spanwise mode characterised by the aligned Λ-shaped flow structures is found to be an ‘abrupt’ process, although the development of the three-dimensionality in the natural convection boundary layer is found to be a ‘gradual’ process. A peak in the typical profile of the Root-Mean-Square (RMS) of the amplitude of streamwise velocity is also noted around the transition point, beyond which distinct three-dimensional Λ-shaped flow structures are observed. The transition point has been determined consistently using different approaches. A Bicoherence analysis suggests that the interaction between the external excitation frequency and the characteristic frequency of the boundary layer is responsible for the production of new harmonic frequencies and resonance groups. The PIV measurements have been extended to a range of perturbation frequencies for the boundary layer, and the dependence of the K-type transition on the perturbation frequency is discussed.