Direct numerical simulations of forced and unforced separation bubbles on an airfoil at incidence

Abstract

Direct numerical simulations (DNS) of laminar separation bubbles on a NACA-0012 airfoil at Re c = 5 × 10 4 and incidence 5• are presented. Initially volume forcing is introduced in order to promote transition to turbulence. After obtaining sufficient data from this forced case, the explicitly added disturbances are removed and the simulation run further. With no forcing the turbulence is observed to self-sustain, with increased turbulence intensity in the reattachment region. A comparison of the forced and unforced cases shows that the forcing improves the aerodynamic performance whilst requiring little energy input. Classical linear stability analysis is performed upon the time-averaged flow field; however no absolute instability is observed that could explain the presence of self-sustaining turbulence. Finally, a series of simplified DNS are presented that illustrate a three-dimensional absolute instability of the twodimensional vortex shedding that occurs naturally. Three-dimensional perturbations are amplified in the braid region of developing vortices, and subsequently convected upstream by local regions of reverse flow, within which the upstream velocity magnitude greatly exceeds that of the time-average. The perturbations are convected into the braid region of the next developing vortex, where they are amplified further, hence the cycle repeats with increasing amplitude. The fact that this transition process is independent of upstream disturbances has implications for modelling separation bubbles.

Response of a laminar separation bubble to impulsive forcing

“…Furthermore, Theofilis et al (2000) conjectured a self-exciting, globally unstable process in a disturbancefree numerical environment. In practice, convective amplification of disturbances in the separated shear layer leads to the formation of initially two-dimensional vortical structures which manifest as coherent vortex shedding (Jones et al 2008;Hain et al 2009;Serna & Lázaro 2014;Kurelek et al 2016). Once they reach the aft part of the LSB, these spanwise structures undergo three-dimensional breakdown, the underlying mechanism of which is the subject of active investigations.…”

BiGlobal linear stability analysis on low-Re flow past an airfoil at high angle of attack

“…Computing the global spectrum of the flow has successfully led to reduced order models (e.g., the work of Berkooz et al 2 and Schmid 3 ) and control techniques (e.g., the work of Barbagallo et al 4 and Hervé et al 5 ). Linear stability analysis of the separated flow past an airfoil has been performed based on experimental (e.g., the work of Boutilier and Yarusevych 6 ) or direct numerical simulation (DNS) (e.g., the work of Jones et al 7 ) result. The time-averaged flow field is usually used as the base flow which is further assumed to be a locally parallel flow.…”

“…However, the generalization is accompanied by the high computational cost which restricts this method in relatively simple geometries (e.g., the work of Tezuka and Suzuki 13 and Bagheri et al 14 ). For most numerical simulations of flow past an isolated airfoil or other configurations using either the high-fidelity DNS or the large-eddy simulation (LES) approach, the computational domain is normally assumed straight in the spanwise direction and periodic boundary condition is prescribed for all primitive variables (e.g., the work of Jones et al, 7 Kitsios et al, 15 Zhang et al, 16 and Zhang and Samtaney 17,18 ). The variation of the flow along the homogeneous spanwise (z-) direction is significantly weaker than the other two inhomogeneous directions, i.e., ∂φ/∂z ≪ ∂φ/∂ x and ∂φ/∂z ≪ ∂φ/∂ y in which φ is any flow variable.…”

Dynamic pitching effect on a laminar separation bubble

“…Direct numerical simulations (DNS) revealed that the application of volume forcing and low-frequency main flow disturbances to the LSB triggers the K-H instabilities more upstream, reducing bubble size and therefore improving aerodynamic performance (Lou and Hourmouziadis 2000;Wissink and Rodi 2004;Jones et al 2008). Burgmann and Schröder (2008) demonstrated experimentally a decreasing bubble size as well as an upstream shift of the separation, transition and reattachment locations, when increasing Reynolds number (2 × 10 4 -6 × 10 4 ), angle of attack (4 • -8 • ) or free stream turbulence intensity level.…”