Correction of wandering smoothing effects on static measurements of a wing-tip vortex

Abstract

Wandering is a typical feature of wing-tip vortices and it consists in random fluctuations of the vortex core. Consequently, vortices measured by static measuring techniques appear to be more diffuse than in reality, so that a correction method is needed. In the present paper statistical simulations of the wandering of a Lamb-Oseen vortex are first performed by representing the vortex core locations through bi-variate normal probability density functions. It is found that wandering amplitudes smaller than 60% of the core radius are well predicted by using the ratio between the RMS value of the mean cross-velocity and its slope measured at the mean vortex center. Furthermore, the principal axes of wandering can be accurately evaluated from the opposite of the cross-correlation coefficient between the spanwise and the normal velocities measured at the mean vortex center. The correction of the wandering smoothing effects is then carried out through four different algorithms that perform the deconvolution of the mean velocity field with the probability density function that represents the wandering. The corrections performed are very accurate for the simulations with wandering amplitudes smaller than 60% of the core radius, whereas errors become larger with increasing wandering amplitudes. Subsequently, the whole procedure to evaluate wandering and to correct the mean velocity field is applied to static measurements, carried out with a fast-response five-hole pressure probe, of a tip vortex generated from a NACA 0012 half-wing model. It is found that the wandering is predominantly in the upward-outboard to downward-inboard direction. Furthermore, the wandering amplitude grows with increasing streamwise distance from the wing, whereas it decreases with increasing angle of attack and free-stream velocity.

Obstacle-induced spiral vortex breakdown

“…Consequently, the measured velocity, U p , on an infinitesimal ellipse (x p ; y p ), may be seen as the weighted average of the real velocity, U, associated with the vortex axis displacement, (x v ; y v ) which is modeled by a bivariate probability density function, D w , as proposed by Devenport et al (1996) and confirmed by Heyes and Hubbard (2003) and Iungo et al (2009):…”

“…In order to deconvolve the underlying velocity field U from our measurements U m according to Eq. 9, two deconvolution methods proposed by Iungo et al (2009) and Devenport et al (1996) may be found in the literature. Iungo's method, which is inspired from blind deconvolution techniques used in astrophysics and medical imaging, requires well-resolved 2D flow fields at each z-location.…”

Aperiodicity in the near field of full-scale rotor blade tip vortices

“…Vortex wandering in the near field is caused by external perturbation including background turbulence (Heyes et al 2003;Iungo et al 2009). With increasing wake age, the vortex susceptibility to outer excitation increases.…”

Tracer particle momentum effects in vortex flows

“…However, single-point scans of vortex flows (such as the hot-wire and multi-hole pressure probe data of Beninati & Marshall (2005), Birch et al (2004), Birch & Lee (2005), Chow et al (1997) and Dacles-Mariani et al (1995), to list but a few) will tend to underpredict vortex strength owing to the smoothing effect of vortex 'meandering', or the random, low-frequency modulation in the trajectory of the vortex centre. While a number of schemes have been proposed to correct single-point scans of vortex wakes for the effect of meandering (such as those of Devenport et al (1996), Bailey & Tavoularis (2008) and Iungo et al (2009)), it has also been shown that, with meandering amplitudes which are large but within the range of those observed experimentally, the reconstruction of the vortex velocity field from point measurements becomes impossible (Birch 2012).…”