Abstract
Modulating the boundary layer velocity profile is a very promising strategy for achieving transition delay and reducing the friction of the plate. By perturbing the flow with counter-rotating vortices that undergo transient, non-modal growth, streamwise-aligned streaks are formed inside the boundary layer, which have been proved (theoretical and experimentally) to be very robust flow structures. In this paper, we employ efficient numerical methods to perform a parametric stability investigation of the three-dimensional incompressible flat-plate boundary layer with finite-amplitude streaks. For this purpose, the Boundary Region Equations (BREs) are applied to solve the nonlinear downstream evolution of finite amplitude streaks. Regarding the stability analysis, the linear three-dimensional plane-marching Parabolized Stability Equations (PSEs) concept constitutes the best candidate for this task. Therefore, a thorough parametric study is presented, analyzing the instability characteristics with respect to critical conditions of the modified incompressible zero-pressure-gradient flat-plate boundary layer, by means of finite-amplitude linearly optimal and suboptimal disturbances or streaks. The parameter space is extended from low- to high- amplitude streaks, accurately documenting the transition delay for low-amplitude streaks and the amplitude threshold for streak shear layer instability or bypass transition, which drastically displaces the transition front upstream.
Highlights
For a validation of the formulation employed in this paper, the reader is referred to the work in [25], where a three-dimensional vortex flow is simulated and compared with results provided by Direct Numerical Simulation
The configuration contemplated here is a spanwise periodic array of steady streaks developed inside the boundary layer of a flat plate at zero angle of incidence, see Figure 1
This work proposes a parametric investigation of the flat plate Blasius boundary layer disturbed through streamwise streaks, encountered as perturbations induced through passive or active flow control techniques
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. In the investigation presented in [19], streaks are generated on a flat plate by finite suction through a spanwise-oriented array of discrete holes In this case, robust and steady highintensity streaks of high- and low-speed regions were induced to create a spanwise mean velocity gradients for laminar flow control. We use efficient numerical techniques to investigate the stability characteristics of streaky boundary-layer flows across the large parameter space of spanwise wavelengths, initial amplitudes, and streak inflow disturbance shape To achieve this goal, we will apply the Boundary Region Equations (BREs) to obtain the numerical streaky base flow.
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