Effects of Reynolds number and thickness on an undulatory self-propelled foil

Abstract

The effects of the Reynolds number (Re) and thickness on an undulatory self-propelled foil were numerically investigated using the immersed boundary method. Re varied from 50 to 2 × 105, which encompasses the viscous, intermediate, and inertial regimes using a NACA 0012 airfoil. An investigation of the thickness was performed on NACA airfoils with maximum thicknesses of 0.04 ∼ 0.24 at two Re values (5 × 104 and 500). The results indicated that the foil can achieve a higher forward velocity, perform less work, and exhibit a higher propulsive efficiency with increasing Re. However, the effect of Re is asymptotic beyond 5 × 104. Four types of vortex structures exist, and the transition from one regime to another is closely related to hydrodynamic changes. In the thickness study, thinner foils outperformed thicker foils in terms of the forward velocity and input power at both Re values. However, the efficiency related to the conversion of input power into kinetic energy for NACA 0004 was the lowest. An optimum thickness exists that depends on Re. At higher Re, the vortical structure differs for each thickness with the deflection angle, whereas at low Re, the location of the separation point strongly influences the hydrodynamics.

Self-directed propulsion of an unconstrained flapping swimmer at low Reynolds number: hydrodynamic behaviour and scaling laws

“…A similar observation can be found in the previous work (Zhang et al. 2018). In addition, there is a threshold value of above which the propulsive direction is reversed.…”

Computational Model Construction and Analysis of the Hydrodynamics of a Rhinoptera Javanica

“…Thus it leads to the increment of resistance and pushes the optimal St to higher values. In the previous study [6], the authors showed that St of fish will inevitably increase when swimming at a low speed. When the Reynolds number is greater than a certain range, the optimal St will fall into the range of 0.2 − 0.4.…”

Propulsion of a foil undergoing a flapping undulatory motion from the impulse theory in the linear potential limit

“…Note also the excellent agreement between the theoretical results forC T and the numerical results obtained by Le et al (2010) for any value of ψ, particularly in figure 3(a) where the non-dimensional flexure amplitude δ m is smaller. Next we consider the numerical results of Zhang et al (2018) and of Dong & Lu (2007), who analysed two different undulatory motions, i.e. with b = 0 in the present notation.…”

“…Examples of three of these motions are plotted in figure 4, with the corresponding values of the parameters in the present model given in table 1. Also included are the values of the parameters corresponding to the selected numerical results of Zhang et al (2018) and Dong & Lu (2007), which are compared below with the present theoretical results, together with other references and some additional information about the numerical simulations. Figure 5 compares the lift coefficient from the numerical results of Zhang et al (2018) for several NACA profiles with the present theoretical results.…”

“…Also included are the values of the parameters corresponding to the selected numerical results of Zhang et al (2018) and Dong & Lu (2007), which are compared below with the present theoretical results, together with other references and some additional information about the numerical simulations. Figure 5 compares the lift coefficient from the numerical results of Zhang et al (2018) for several NACA profiles with the present theoretical results. The numerical results for the different foil thicknesses are all quite close to each other, and with a good agreement with the present zero-thickness theoretical results, with a slightly better agreement for the NACA0016 profile, but for no particular reason.…”