Numerical analysis on the oscillation of stall cells over a NACA 0012 aerofoil

Abstract

A series of three-dimensional unsteady Reynolds-averaged Navier-Stokes (RANS) simulations are conducted to investigate the formation and oscillation of stall cells over a NACA 0012 aerofoil. The simulations are conducted with various physical and numerical conditions, such as the Reynolds number, angle of attack, chord-to-span ratio and span-wise mesh resolution. Results show a clear relationship between the oscillation of stall cells and the fluctuation of lift (observed between 17 and 19.5 degrees angle of attack at a high chord Reynolds number of one million). This unsteadiness shows some dependency on the span-wise mesh resolution; it is significant with a medium span-wise mesh resolution (corresponding to 10% of the chord) and moderate with finer resolutions (corresponding to 5% and 2.5% of the chord, respectively). In addition, a proper orthogonal decomposition (POD) method is adopted to further analyse the oscillatory characteristics of stall cells. In particular, it is shown that the first few POD modes have clear spatial patterns corresponding to the profile of stall cells and their time coefficients are correlated with the fluctuation of lift, further confirming the correlation between the stall cell oscillations and the lift fluctuation.

Unsteady RANS Simulations of Strong and Weak 3D Stall Cells on a 2D Pitching Aerofoil

“…Especially for the f = 0.1 case, the stall happens after the aerofoil starts pitching down and the C L does not get back to its original linear regime until around 2 • . However, the linear C L curve before and after the dynamic stall is not affected substantially, which agrees with the numerical investigation of [27]. 0.1 case, a strong LEV is first developed and soon grows and takes up the whole aerofoil, whereas the trailing-edge separation bubble is pushed back by the LEV.…”

“…It is worth noticing that most of the experimental studies used a finite wing while some studies observed stall cell formation on very wide aerofoil (AR = 9-12) to eliminate the impact of the tip vortex. Recently, the authors of the present paper have also conducted a numerical study on this issue [27], further extending an earlier numerical study of Manni et al [28]. In these studies, a NACA 0012 aerofoil with an infinitely long span at stall condition was investigated.…”

“…They can be categorized into two different types. For maximum AoA = 19 • , 20 • , and 21 • , the 3D structures resemble the stall cell structures often observed for a static aerofoil, such as those in [27,28]. For these cases, small 3D structures start to develop near the leading edge when the aerofoil is pitching down to around 17 • and then merge into large counter-rotating vortex pairs dominating the whole span.…”

“…The spanwise extent of the computational domain is 2.5c and the number of layers is 25 (i.e., the spanwise resolution is 10% of the chord). This level of spanwise resolution has been shown to be able to capture the unsteadiness of stall cells over a static aerofoil [27]. pitching rate.…”

Link between subsonic stall and transonic buffet on swept and unswept wings: from global stability analysis to nonlinear dynamics

“…Their URANS results showed stall cells with spanwise spacing of 1.4 to 1.8 chord length over a narrow range of angles of attack. Liu & Nishino (2018) studied the unsteady behaviour of stall cells over a NACA0012 at a Reynolds number of and . Previous work by the authors (Plante, Dandois & Laurendeau 2019 b ), based on URANS simulations of an NACA4412 aerofoil at Reynolds , showed the convection of the stall cells in the spanwise direction when the wing is swept.…”