Evolution of wake structures behind oscillating hydrofoils with combined heaving and pitching motion

Abstract

The wake of an oscillating teardrop hydrofoil with combined heaving and pitching motion was studied numerically at Reynolds number of 8000 and Strouhal numbers of $St=0.21{-}0.94$ . The lower Strouhal number exhibited high efficiency propulsion with small thrust generation. However, larger thrust generation at high $St$ required more power, which lowered the propulsive efficiency. Quantitative assessment of vortex evolution, along with qualitative investigation of the formation and interaction of primary structures, revealed the association with elliptic instability characteristics for both co-rotating and counter-rotating vortex structures in both wakes. With respect to advection of the leading-edge vortex, the pressure distribution further depicted evidence of spanwise instability with distinct temporal evolution along the suction and pressure surfaces of the oscillating foil. Three-dimensional assessment of wake structures located downstream of the trailing edge depicted the existence of dislocations associated with primary vortex ‘rollers’. At low $St$ , these were limited to fine spanwise corrugations (valleys and bulges) on weaker leading edge rollers, which enlarged as the rollers advected downstream. In contrast, at high $St$ , the wake exhibited conjoint hairpin-horseshoe vortex structures that led to stronger deformations on the coupled vortex rollers. The statistical characteristics of secondary structures resembled the long wavelength mode and mode A identified previously for purely pitching and heaving foils, respectively. They also mimicked mode B for stationary cylinders. Novel wake models are introduced based on a complete vivid three-dimensional depiction of coherent wake structures.

Characterization of bifurcated dual vortex streets in the wake of an oscillating foil

“…Although this characteristic of 2P D pairs resembled some similarities with the Mode-1 configuration described previously by Cleaver et al (2011), the 2P wake observed here exhibited no merger between similar-sign leading and trailing edge vortices. Further, the findings noted here were also in definite contrast to the observations made for typical vortex dipoles that are formed only on account of trailing edge structures (Cleaver et al 2012;Calderon et al 2014;He & Gursul 2016;Verma & Hemmati 2021b).…”

“…However, two vortex streets constituting fully developed 2P D pairs diverge away from the wake centreline with φ approaching 180 • (see figure 8e). Structures forming such fully developed dipole-like configurations possess similar strengths of circulation and size, which was also reported by Cleaver et al (2012), Calderon et al (2014), He & Gursul (2016) and Verma & Hemmati (2021b). Experimental studies of Cleaver et al (2012) and Calderon et al (2014) discussed the formation of dipoles and couples behind oscillating foils in purely heaving motion and further explained their prominent association and coincidence with deflected wake modes (i.e.…”

“…Extensive efforts for verification and validation of the numerical solver with respect to domain size, spatial and temporal grid, OGA solver and boundary conditions can be found in Hemmati et al. (2019) and Verma & Hemmati (2020, 2021 b ).…”

“…Besides extensive experimental investigations (Van Buren et al 2019), recent two-dimensional numerical studies by Lagopoulos et al (2019) and Zheng et al (2019) discussed the wake and performance metrics for a foil performing coupled two degrees of freedom oscillations, for a fixed phase angle 90 • (or 270 • in the reference frame of Van Buren et al 2019). Verma & Hemmati (2021b) also described evolution of the primary wake structures of an oscillating foil in coupled heaving and pitching motion. However, this investigation was limited to φ = 270 • and 330 • , which corresponded to kinematic regimes for high propulsive efficiencies and production of greater thrust, respectively (Van Buren et al 2019).…”

“…2019). Verma & Hemmati (2021 b ) also described evolution of the primary wake structures of an oscillating foil in coupled heaving and pitching motion. However, this investigation was limited to and , which corresponded to kinematic regimes for high propulsive efficiencies and production of greater thrust, respectively (Van Buren et al.…”