Sharp interface immersed boundary method for simulating three-dimensional swimming fish

Abstract

A second order finite-difference numerical method is used to solve the Navier-Stokes equations of incompressible flow, in which the solid body with complex geometry is immersed into the fluid domain with orthogonal Cartesian meshes. To account for influences of the solid body, interactive forces are applied as boundary conditions at Cartesian grid nodes located in the exterior but in the immediate vicinity of the solid body. Fluid flow velocities in these nodes are reconstructed to track and control the deformation of the solid body, in which the local direction normal to the body surface is employed using the level-set function. The capabilities of this method are demonstrated by the application to fish swimming, and the computed behaviors of swimming fish agree well with experimental ones. The results elucidate that the ability of swimming fish to produce more thrust and high efficiency is closely related to the Reynolds number. The single reverse Kármán street tends to appear when both the Strouhal number and tail-beating frequency are small, otherwise the doublerow reverse Kármán street appears. The algorithm can capture the geometry of a deformable solid body accurately, and performs well in simulating interactions between fluid flow and the deforming and moving body. ARTICLE HISTORY

Numerical Investigation of Dimensionless Parameters in Carangiform Fish Swimming Hydrodynamics

“…Some authors have employed inviscid methodologies to estimate the thrust and the power generated by swimming fish in high Reynolds numbers, such as the elongated body theory (EBT) proposed by Lighthill’s model [ 12 , 25 , 44 , 45 , 46 ]. However, some works have argued that the thrust is overestimated [ 15 , 47 ].…”

“…This challenge becomes even more complex when trying to compute propulsive efficiency using the thrust generated by an undulating body, as it introduces the complication of distinguishing between thrust and drag forces within such a dynamic system [8,15]. Some authors have employed inviscid methodologies to estimate the thrust and the power generated by swimming fish in high Reynolds numbers, such as the elongated body theory (EBT) proposed by Lighthill's model [12,25,[44][45][46]. However, some works have argued that the thrust is overestimated [15,47].…”

Structural design and mechanism verification of multi-tailed collaborative robotic fish

“…Many research results on bionic underwater robot with multi tails have emerged in recent years. Cui et al [9] proposed a sharp interface immersion boundary method to simulate 3D swimming, which can accurately capture the geometry of deformation and interaction between moving bodies. Lucas et al [10] revealed that the airfoil like precursor of scads can generate negative pressure to reduce the forward resistance of fish and improve the propulsion efficiency.…”