Laminar vortex rings impinging onto porous walls with a constant porosity

Abstract

For the first time, an experiment has been conducted to investigate synthetic jet laminar vortex rings impinging onto porous walls with different geometries by time-resolved particle image velocimetry. The geometry of the porous wall is changed by varying the hole diameter on the wall (from 1.0 mm to 3.0 mm) when surface porosity is kept constant ($\unicode[STIX]{x1D719}=75\,\%$). The finite-time Lyapunov exponent and phase-averaged vorticity field derived from particle image velocimetry data are presented to reveal the evolution of the vortical structures. A mechanism associated with vorticity cancellation is proposed to explain the formation of downstream transmitted vortex rings; and both the vortex ring trajectory and the time-mean flow feature are compared between different cases. It is found that the hole diameter significantly influences the evolution of the flow structures on both the upstream and downstream sides of the porous wall. In particular, for a porous wall with a small hole diameter ($d_{h}^{\ast }=0.067$, 0.10 and 0.133), the transmitted finger-type jets will reorganize into a well-formed transmitted vortex ring in the downstream flow. However, for the case of a large hole diameter of $d_{h}^{\ast }=0.20$, the transmitted vortex ring is not well formed because of insufficient vorticity cancellation. Additionally, the residual vorticity gradually evolves into discrete jet-like structures downstream, which further weaken the intensity of the transmitted vortex ring. Consequently, the transmitted flow structures for the $d_{h}^{\ast }=0.20$ case would lose coherence more easily (or probably even transition to turbulence), resulting in a faster decay of the axial velocity and stronger entrainment of the transmitted jet. For all porous wall cases, the velocity profile of the transmitted jet exhibits self-similar behaviour in the far field ($z/D_{0}\geqslant 6.03$), which agrees well with the velocity distribution of free synthetic jets. With the help of the control-volume approach, the time-mean drag of the porous wall is evaluated experimentally for the first time. It is shown that the porous wall drag increases with the decrease in the hole diameter. Moreover, for a porous wall with a small hole diameter ($d_{h}^{\ast }=0.067$, 0.10 and 0.133), it appears that the porous wall drag mainly derives from the viscous effect. However, as $d_{h}^{\ast }$ increases to 0.20, the form drag associated with the porous wall geometry becomes significant.

The motion of respiratory droplets produced by coughing

“…Figure 7(b) shows the dimensionless time-averaged axial velocity at positions of x = 0.02 m, 0.03 m, 0.04 m, 0.05 m, and 0.06 m. The mean velocity is normalized using the local maximum u max at position x , and the radial position is normalized by the jet half-width b 1/2 , which is defined as the radial distance corresponding to half of u max ( Krishnan and Mohseni, 2010 ; Xu et al. , 2013 ; and Xu et al. , 2018 ).…”

The interactions of rectangular synthetic jets with a laminar cross-flow

“…Note that the horizontal section of the L-shaped cylinder was 100 mm, and that was long enough to avoid the impact of the bent part on the formation of synthetic jets. A detailed introduction to this synthetic jet device could be found in Feng & Wang (2010) and Xu et al (2018). The end of the L-shaped cylinder was flush-mounted in a plate with the jet orifice.…”

“…In addition, the main structures have no obvious change as increases from 1.5 to 3.5 s −1 , and thus a larger of 3.5 s −1 is also used concurrently to characterize the main components in this study. Within the vortex area, the above integrations are calculated for the phase-averaged vorticity satisfying (here denotes the local vorticity peak) to eliminate noise from the PIV data (Feng & Wang 2010; Xu et al 2018). Based on sensitivity analysis, by selecting normalized vorticity levels of 0.05 to 0.2 with 0.05 increment, the circulation of the vortex ring is insensitive to this cut-off level with the difference less than 3 %.…”

“…For a time-dependent flow map that maps fluid particles from their initial position (, t 0 ) to their later position over a finite time T F , the Cauchy–Green strain tensor is expressed as (Haller 2015) and the FTLE can be computed as (Green, Rowley & Haller 2007; Xu et al 2018) where represents the largest singular value of . The LCSs are indicated by ridges in the FTLE field corresponding to the regions of maximum fluid particle separation () or attraction ().…”

Collision of vortex rings upon V-walls

“…Such scenarios will be of special interest, as they entail the direct impact and subsequent interactions between two vortex rings or a vortex ring and solid/non-solid boundaries, as opposed to a discrete vortex-ring entity assumed to be free (or largely free) of external influences. Such scenarios have been studied systematically earlier, including but not limited to those reported by Walker et al (1987), Lim (1989), Lim, Nickels & Chong (1991), Orlandi & Verzicco (1993), Verzicco & Orlandi (1994), Chu, Wang & Chang (1995), Swearingen, Crouch & Handler (1995), Fabris, Liepmann & Marcus (1996), Minota, Nishida & Lee (1997), Naitoh, Banno & Yamada (2001), Arévalo et al (2007), Cheng, Lou & Luo (2010), Couch & Krueger (2011), Mariani et al (2013), New, Shi & Zang (2016) and Xu & Wang (2016) for flat/inclined-walls, Adhikari & Lim (2009), Hrynuk, Van Luipen & Bohl (2012), Naaktgeboren, Krueger & Lage (2012), Cheng, Lou & Lim (2014) and Xu et al (2018) for porous walls, Orlandi (1993), Naitoh, Sun & Yamada (1995), Ren, Zhang & Guan (2015) and New & Zang (2017) for round cylinders, and, more recently, a scenario whereby a vortex ring collides upon a wall with a circular aperture investigated by Hu & Peterson (2018).…”