Luoding Zhu

An efficient immersed boundary-lattice Boltzmann method for the hydrodynamic interaction of elastic filaments

We have introduced a modified penalty approach into the flow-structure interaction solver that combines an immersed boundary method (IBM) and a multi-block lattice Boltzmann method (LBM) to model an incompressible flow and elastic boundaries with finite mass. The effect of the solid structure is handled by the IBM in which the stress exerted by the structure on the fluid is spread onto the collocated grid points near the boundary. The fluid motion is obtained by solving the discrete lattice Boltzmann equation. The inertial force of the thin solid structure is incorporated by connecting this structure through virtual springs to a ghost structure with the equivalent mass. This treatment ameliorates the numerical instability issue encountered in this type of problems. Thanks to the superior efficiency of the IBM and LBM, the overall method is extremely fast for a class of flow-structure interaction problems where details of flow patterns need to be resolved. Numerical examples, including those involving multiple solid bodies, are presented to verify the method and illustrate its efficiency. As an application of the present method, an elastic filament flapping in the Kármán gait and the entrainment regions near a cylinder is studied to model fish swimming in these regions. Significant drag reduction is found for the filament, and the result is consistent with the metabolic cost measured experimentally for the live fish.

Interaction of two tandem deformable bodies in a viscous incompressible flow

Previous laboratory measurements on drag of tandem rigid bodies moving in viscous incompressible fluids found that a following body experienced less drag than a leading one. Very recently a laboratory experiment (Ristroph & Zhang, Phys. Rev. Lett ., vol. 101, 2008) with deformable bodies (rubble threads) revealed just the opposite – the leading body had less drag than the following one. The Reynolds numbers in the experiment were around 10 4 . To find out how this qualitatively different phenomenon may depend on the Reynolds number, a series of numerical simulations are designed and performed on the interaction of a pair of tandem flexible flags separated by a dimensionless vertical distance (0 ≤ D ≤ 5.5) in a flowing viscous incompressible fluid at lower Reynolds numbers (40 ≤ Re ≤ 220) using the immersed boundary (IB) method. The dimensionless bending rigidity b and dimensionless flag mass density used in our work are as follows: 8.6 × 10 −5 ≤ b ≤ 1.8 × 10 −3 , 0.8 ≤ ≤ 1.0. We obtain an interesting result within these ranges of dimensionless parameters: when Re is large enough so that the flapping of the two flags is self-sustained, the leading flag has less drag than the following one; when Re is small enough so that the flags maintain two nearly static line segments aligned with the mainstream flow, the following flag has less drag than the leading one. The transitional range of Re separating the two differing phenomena depends on the value of b . With Re in this range, both the flapping and static states are observed depending on the separation distance D . When D is small enough, the flags are in the static state and the following flag has less drag; when D is large enough the flags are in the constant flapping state and the leading flag has less drag. The critical value of D depends on b .

Coupling modes of three filaments in side-by-side arrangement

A viscous flow past three filaments in side-by-side arrangement is studied by a numerical simulation and is accompanied by a previously established linear stability analysis. Other than the coupling modes reported previously, which include the in-phase mode, symmetrical mode, and out-of-phase mode, three additional modes are identified in the nonlinear regime by systematically varying the separation distance between the filaments. These modes are the half-frequency mode, irrational-frequency mode, and erratic flapping state. The dynamic characteristics of each mode at the saturated state is described, including the flapping amplitude, frequency, drag force, and mechanical energy of the filaments. Four typical vortex structures are observed in the wake of the filaments and are described as the coalesced vortices, symmetrical vortices, erratic vortices, and independent vortex streets. The vortex structures are closely related to the coupling modes and the dynamic characteristics of the filaments. As the Rey...

Locomotion of a flapping flexible plate

The locomotion of a flapping flexible plate in a viscous incompressible stationary fluid is numerically studied by an immersed boundary-lattice Boltzmann method for the fluid and a finite element method for the plate. When the leading-edge of the flexible plate is forced to heave sinusoidally, the entire plate starts to move freely as a result of the fluid-structure interaction. Mechanisms underlying the dynamics of the plate are elucidated. Three distinct states of the plate motion are identified and can be described as forward, backward, and irregular. Which state to occur depends mainly on the heaving amplitude and the bending rigidity of the plate. In the forward motion regime, analysis of the dynamic behaviors of the flapping flexible plate indicates that a suitable degree of flexibility can improve the propulsive performance. Moreover, there exist two kinds of vortex streets in the downstream of the plate which are normal and deflected wake. Further the forward motion is compared with the flapping-b...

Simulation of a pulsatile non-Newtonian flow past a stenosed 2D artery with atherosclerosis

Atherosclerotic plaque can cause severe stenosis in the artery lumen. Blood flow through a substantially narrowed artery may have different flow characteristics and produce different forces acting on the plaque surface and artery wall. The disturbed flow and force fields in the lumen may have serious implications on vascular endothelial cells, smooth muscle cells, and circulating blood cells. In this work a simplified model is used to simulate a pulsatile non-Newtonian blood flow past a stenosed artery caused by atherosclerotic plaques of different severity. The focus is on a systematic parameter study of the effects of plaque size/geometry, flow Reynolds number, shear-rate dependent viscosity and flow pulsatility on the fluid wall shear stress and its gradient, fluid wall normal stress, and flow shear rate. The computational results obtained from this idealized model may shed light on the flow and force characteristics of more realistic blood flow through an atherosclerotic vessel.

Scaling laws for drag of a compliant body in an incompressible viscous flow

Motivated by an important discovery on the drag scaling law (the 4/3 power law) of a flexible fibre in a flowing soap film by Alben et al. (Nature vol. 420, 2002, p. 479) at high Reynolds numbers (2000 < Re < 40000), we investigate drag scaling laws at moderate Re for a compliant fibre tethered at the midpoint and submerged in an incompressible viscous flow using the immersed boundary (IB) method. Our work shows that the scaling of drag with respect to oncoming flow speed varies with Re, and the exponents of the power laws decrease monotonically from approximately 2 towards 4/3 as Re increases from 10 to 800.

Viscous flow past a flexible fibre tethered at its centre point: vortex shedding

Motivated by a laboratory experiment reported in Alben, Shelley & Zhang (Nature, vol. 420, 2002, p. 479), we performed simulations of an elastic fibre anchored at its centre point and immersed in a flowing viscous incompressible fluid by the immersed boundary (IB) method. We focus on the influence of some dimensionless parameters on vortex shedding from the fibre for Re in the range [30, 800]. Three sets of simulations were designed to investigate the influence of Reynolds number Re, dimensionless fibre flexure modulus K b , and dimensionless fibre length L on vortex shedding. According to the simulation results, Re, K b , and L each has a significant influence on the structure of shed vortices. However, Re has little influence on the vortex shedding frequency. With the increase of dimensionless bending modulus, the dimensionless vortex shedding frequency (f vs ) and the critical Reynolds number (Re c ) decrease approximately as power-law functions. Both f vs and Re c increase approximately linearly as dimensionless fibre length increases.

Viscous flow past a collapsible channel as a model for self-excited oscillation of blood vessels

Motivated by collapse of blood vessels for both healthy and diseased situations under various circumstances in human body, we have performed computational studies on an incompressible viscous fluid past a rigid channel with part of its upper wall being replaced by a deformable beam. The Navier-Stokes equations governing the fluid flow are solved by a multi-block lattice Boltzmann method and the structural equation governing the elastic beam motion by a finite difference method. The mutual coupling of the fluid and solid is realized by the momentum exchange scheme. The present study focuses on the influences of the dimensionless parameters controlling the fluid-structure system on the collapse and self-excited oscillation of the beam and fluid dynamics downstream. The major conclusions obtained in this study are described as follows. The self-excited oscillation can be intrigued by application of an external pressure on the elastic portion of the channel and the part of the beam having the largest deformation tends to occur always towards the end portion of the deformable wall. The blood pressure and wall shear stress undergo significant variations near the portion of the greatest oscillation. The stretching motion has the most contribution to the total potential elastic energy of the oscillating beam.

Simulation of an inhomogeneous elastic filament falling in a flowing viscous fluid

We simulated the freely falling motion of an inhomogeneous flexible filament immersed in an incompressible viscous fluid under the action of gravity by the immersed boundary method. Our simulations show that the falling motion of an inhomogeneous filament is stable with respect to disturbances of small magnitude irrespective of the mass and bending modulus distributions. However, sufficiently large disturbances may bring the filament motion into a significantly different state: the filament deforms, rotates, and drifts towards one of the side boundaries while falling in the flowing fluid under the action of gravity. In addition our results indicate unstable filament motion depends more strongly on the bending modulus than the mass density. Our simulations also show the existence of two similar states for a homogeneous filament. The motions of inhomogeneous and homogeneous filaments are compared, and both quantitative and qualitative differences in the unstable motions are found. This is a starting point t...

A deformable plate interacting with a non-Newtonian fluid in three dimensions

We consider a deformable plate interacting with a non-Newtonian fluid flow in three dimensions as a simple model problem for fluid-structure-interaction phenomena in life sciences (e.g., red blood cell interacting with blood flow). A power-law function is used for the constitutive equation of the non-Newtonian fluid. The lattice Boltzmann equation (the D3Q19 model) is used for modeling the fluid flow. The immersed boundary (IB) method is used for modeling the flexible plate and handling the fluid-plate interaction. The plate drag and its scaling are studied; the influences of three dimensionless parameters (power-law exponent, bending modulus, and generalized Reynolds number) are investigated.