Transition scenario and transition control of the flow over a semi-infinite square leading-edge plate

Abstract

In recent investigations of the flow over a square leading-edge flat plate, elliptic instability and transient growth of perturbations are proposed to explain the turbulent transition mechanism of the separating and reattaching flow reported in early experimental visualizations. An original transition scenario as well as a transition control method is presented by a detailed numerical study in this paper. The transient growth of perturbations in the separation bubble induces the primary instability that causes the 2D unsteady flow consisting of Kelvin-Helmholtz (KH) vortices. The pairing instability of the KH vortices induces the subharmonic secondary instability, and then resonance transition occurs. The streamwise Lorentz force as the control input is applied in the recirculation region where the separation bubble generates. The maximum energy amplification magnitude of perturbations takes a linear attenuation with the interaction number; thus, the primary instability is reduced under control. The interaction number represents the strength of the streamwise Lorentz force relative to the inertial force of the fluid. The reduced primary instability is not strong enough to induce the secondary instability, so the flow is globally stable under control. Three-dimensional direct numerical simulation confirms the results of the linear stability analysis. Although the growth rate of the convectively unstable secondary instability is limited by the flow field scale, the feedback loop of the energy transfer promotes the resonance transition. However, as the separation bubble scale is reduced and the feedback loop is broken by the streamwise Lorentz force, the three-dimensional transition is suppressed and a skin-friction drag reduction is achieved.

An almost subharmonic instability in the flow past rectangular cylinders

“…At lower A, we argue that this instability is not observed because the dynamics of the base flow is quite different (Chiarini et al 2022b), and much less time is available for the recirculation regions to interact with each other. An identical mechanism was later proposed by Huang et al (2017) to explain the onset of three-dimensionality in the flow over a blunt flat plate; see also Abdalla & Yang (2004). However, the flow past a rectangular cylinder is quite different from that past a blunt flat plate.…”

“…The same triggering mechanism is responsible for the transition to three-dimensionality in the flow over a blunt flat plate. In this case, however, the 3-D instability of the Kelvin-Helmholtz vortices shed from the LE is exactly subharmonic (Chaurasia & Thompson 2011;Huang et al 2017), since the base flow does not satisfy the spatio-temporal symmetry.…”

“…Choi & Yang (2014) studied the secondary instability of the flow past rectangular cylinders ranging from a flat plate normal to the flow (A → 0) to the square cylinder (A = 1): the decrease of A was found to stabilise modes A, B and QP, while two other (synchronous and quasi-periodic) modes, called A2 and QP2, become unstable (see also Thompson et al 2006). Chaurasia & Thompson (2011) and Huang et al (2017) studied the flow past a semi-indefinite plate of finite thickness, i.e. A → ∞.…”

Structure of turbulence in the flow around a rectangular cylinder

“…They observed that the separated shear layer rolls up to form hairpin-like structures whose arrangement depends on the Reynolds number. A similar scenario is described by Chaurasia & Thompson (2011) and Huang et al (2017), who studied the three-dimensional instability of the flow over a long, sharp rectangular plate. They found that vortices shed from the LE are elliptically unstable to three-dimensional perturbations, and originate hairpin-like structures.…”

The Hydrodynamic Noise Suppression of a Scaled Submarine Model by Leading-Edge Serrations

“…His research mainly focused on flow separation suppression, and did not focus on noise reduction. In addition, the primary instability of a squared leading-edge flat plate is reduced under a transition control method [25]. Therefore, to obtain better hydrodynamic noise suppression using leading-edge serrations, we must investigate the effect of flow control and noise reduction together.…”