Stojanovic, I., & Braun, S. (2022, September 15). Viscous layer dynamics of the Euler-Prandtl stage in marginal separation [Conference Presentation]. 14th European Fluid Mechanics Conference (Athens), Athens, Greece.
In the present work we consider the incipient stages of the transition from laminar to turbulent flow caused by a localized separation of a boundary layer. From a high Reynolds number asymptotic viewpoint the early development of this so-called bypass transition can be described in four characteristic stages, see Figure 1, of which we focus on the last one. Starting from the classical boundary lay...
In the present work we consider the incipient stages of the transition from laminar to turbulent flow caused by a localized separation of a boundary layer. From a high Reynolds number asymptotic viewpoint the early development of this so-called bypass transition can be described in four characteristic stages, see Figure 1, of which we focus on the last one. Starting from the classical boundary layer theory, the laminar flow is forced to separate locally due to an imposed adverse pressure gradient (i). Taking into account the interaction between the displacement of the viscous layer and the induced pressure from the inviscid outer region allows the characterization of reverse flow regions (ii). The resulting evolution of the marginal separation stage typically develops a finite-time singularity. This breakdown is resolved by yet another triple-deck (TD) interaction with smaller length and time scales (iii). The computation of the TD stage indicates the formation of a spike at the rear of the separation bubble. However, the TD stage fails to cover the subsequent vortex wind-up process, which is governed by the Euler-Prandtl (EP) stage (iv). This stage is represented by two non-interacting regions, i.e. the inviscid Euler region (investigated by Kuzdas2) and the viscous Prandtl layer, which is of key interest in our study. This layer is introduced to satisfy the no-slip condition. The pressure gradient is imposed from the Euler region and the initial condition follows from the blow-up structure of the TD stage.
Such high Reynolds number flows can be observed for example at the leading edge suction side of a slender airfoil at a small angle of attack. The method of matched asymptotic expansions is used to analyze the Navier-Stokes equations. The resulting equations are solved by means of a spectral collocation method based on Chebyshev polynomials in wall-normal and streamwise direction. A backward Euler finite-difference scheme is applied for the time discretization.
The work is supported by the Austrian Science Fund FWF (grant no. P31873-N32).
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Project title:
Bypass Transition aus asymptotischer Sicht: P31873-N32 (Fonds zur Förderung der wissenschaftlichen Forschung (FWF))
