Xueming Shao

A direct-forcing fictitious domain method for particulate flows

A direct-forcing fictitious domain (DF/FD) method for the simulation of particulate flows is reported. The new method is a non-Lagrange-multiplier version of our previous DLM/FD code and is obtained by employing a discrete @d-function in the form of bi(tri-) function to transfer explicitly quantities between the Eulerian and Lagrangian nodes, as in the immersed boundary method. Due to the use of the collocation-point approach for the rigidity constraint and the integration over the particle domain, the Lagrangian nodes are retracted a little from the particle boundary. Our method in case of a prescribed velocity on the boundary is verified via the comparison to the benchmark results on the flow over a fixed cylinder in a wide channel and to our spectral-element results for a channel with the width of four cylinder diameters. We then verify our new method for the case of the particulate flows through various typical flow situations, including the sedimentation of a circular particle in a vertical channel, the sedimentation of a sphere in a vertical pipe, the inertial migration of a sphere in a circular Poiseuille flow, the behavior of a neutrally-buoyant sphere in Couette flow, and the rotation of a prolate spheroid in Couette flow. The accuracy and robustness of the new method are fully demonstrated, in particular for the case of relatively low Reynolds numbers and the neutrally-buoyant case.

A fictitious domain method for particulate flows with heat transfer

The distributed-Lagrange-multiplier/fictitious-domain (DLM/FD) method of Glowinski et al. [R. Glowinski, T.-W. Pan, T.I. Hesla, D.D. Joseph, A distributed Lagrange multiplier/fictitious domain method for particulate flows, Int. J. Multiphase Flow 25 (1999) 755-794] is extended to deal with heat transfer in particulate flows in two dimensions. The Boussinesq approximation is employed for the coupling between the flow and temperature fields. The fluid-flow equations are solved with the finite-difference projection method on a half-staggered grid. In our operator splitting scheme. the Lagrange multipliers at the previous time level are kept in the fluid equations, and the new Lagrange multipliers for the rigid-body motion constraint and the Dirichlet temperature boundary condition are determined from the reduced saddle-point problem, whereas a very simple scheme based on the fully explicit computation of the Lagrange multiplier is proposed for the problem in which the solid heat conduction inside the particle boundary is also considered. Our code for the case of fixed temperature on the immersed boundary is verified by comparing favorably our results on the natural convection driven by a hot cylinder eccentrically placed in a square box and on the sedimentation of a cold circular particle in a vertical channel to the data in the literature. The code for the case of freely varying temperature on the boundaries of freely moving particles is applied to analyze the motion of a catalyst particle in a box and in particular the heat conductivities of nanofluids and sheared non-colloidal suspensions, respectively. Our preliminary computational results support the argument that the micro-heat-convection in the fluids is primarily responsible for the unusually high heat conductivity of nanofluids. It is shown that the Peclet number plays a negative role in the diffusion-related heat conductivity of a sheared non-colloidal suspension, whereas the Reynolds number does the opposite.

Inertial migration of spherical particles in circular Poiseuille flow at moderately high Reynolds numbers

The inertial migration of spherical particles in a circular Poiseuille flow is numerically investigated for the tube Reynolds number up to 2200. The periodic boundary condition is imposed in the streamwise direction. The equilibrium positions, the migration velocity, and the angular velocity of a single particle in a tube cell are examined at different Reynolds numbers, particle-tube size ratios, and tube lengths. Inner equilibrium positions are observed as the Reynolds number exceeds a critical value, in qualitatively agreement with the previous experimental observations [J.-P. Matas, J. F. Morris, and E. Guazzelli, J. Fluid Mech. 515, 171 (2004)]. Our results indicate that the hydrodynamic interactions between the particles in different periodic cells have significant effects on the migration of the particles at the tube length being even as large as 6.7 particle diameters and they tend to stabilize the particles at the outer Segre–Silberberg equilibrium positions and to suppress the emergence of the in...

Hydrodynamic studies on two traveling wavy foils in tandem arrangement

In this study, the hydrodynamic interactions between two tandem foils undergoing fishlike swimming motion are investigated numerically by solving the Navier–Stokes equations with the immersed-boundary method. The two foils represent two tandem propellers attached on a concept ship. The thrusts and efficiencies at three typical Strouhal numbers, i.e., St=0.4, 0.6, and 0.8, are investigated. The results show that a fish situated directly behind another one does not always undergo a lower thrust. Whether it experiences a thrust enhancement or reduction depends on the Strouhal number. At a relatively low Strouhal number (e.g., St=0.4), the usual wake drag-reduction effect predominates over the drag-enhancement effect caused by the reverse von Karman vortices, resulting in a thrust enhancement. The opposite happens at a relatively high Strouhal number (e.g., St=0.8). The downstream fish can benefit from the upstream one by slalom between the vortices rather than through them. For the upstream fish, the thrusts...

Numerical studies of the effects of large neutrally buoyant particles on the flow instability and transition to turbulence in pipe flow

The effects of large neutrally buoyant particles on the flow instability and turbulence transition in pipe flow are investigated with the fictitious domain method. The periodic boundary condition is introduced in the streamwise direction. The work comprises two parts. In the first part, the pressure gradient is kept constant, and the purpose is to study the particle-induced flow instability. In our previous study [X. Shao, Z. Yu, and B. Sun, Phys. Fluids 20, 103307 (2008)10.1063/1.3005427], it was observed that a particle of a/R = 0.1 (a and R being the radii of the particle and the tube, respectively) induced the flow structure characterized by two pairs of weak and stable streamwise vortices at the Reynolds number of 1000. In the present study, our results show that the flow structure loses stability at the Reynolds number of 1500. However, it is interesting that the system eventually reaches a stable state: the particle spirals forward along the tube wall, accompanied by a stable flow structure for the...

Hydrodynamic performance of a fishlike undulating foil in the wake of a cylinder

The hydrodynamic performances of a fishlike undulating foil in the wake of a D-section cylinder are numerically investigated by using a modified immersed boundary method. The results regarding the effects of various controlling parameters, including the distance between the foil and the D-cylinder, the frequency and the phase angle of foil’s undulation, and the phase angle of heaving motion on the thrust and the input power, are reported. It is observed that the foil without undulation in the vortex street can gain a thrust, as a result of the fact that the passing vortices produce reverse flows with respect to the mainstream in vicinity of the foil surface. When an undulating foil is placed at different distances behind the D-section cylinder, different wake structures form behind the cylinder. The wake area can be divided into three domains: suction domain, thrust enhancing domain, and weak influence domain. The undulation of the foil can inhibit the roll-up instability of the shear layers and vortex shedding from the cylinder and consequently significantly enlarge the suction domain, compared to the foil-free case or the stationary foil case. The thrust on the foil first increases and then decreases, as the distance between the foil and the cylinder increases. The undulation plays a negative role in the foil propulsion when the foil is located near the cylinder (largely in the suction domain) and a positive role when the distance between the foil and the cylinder is beyond a critical value. The mean thrusts do not vary significantly with the undulation phase angle when the heaving motion is not considered and the undulation amplitude studied is relatively small, instead, they are significantly affected by the phase angle of the heaving motion. The foil bypassing the vortices undergoes both minimum thrust and input power, whereas the one passing through vortices experiences a larger thrust. The phase angle difference between the heave and the undulation is important.

Hydrodynamics in a diamond-shaped fish school

Abstract In this paper, the computational fluid dynamics was applied to fish-like swimming, and the propulsion mechanism of this motion was focused. Although previous researchers have suggested that a diamond shape of fish school is helpful for drag reduction and efficiency enhancement, and individuals can benefit from such a school, experimental data or numerical studies on the hydrodynamics of interactions among members in the fish school are lacking. An improved immersed boundary method was employed for the simulations, and a basic element of three fishes was picked out from the diamond-shaped fish school. The conclusion is drawn that a fish situated laterally midway between two fish of the preceding column can benefit from the reversed Karman vortex street shedding from the upstream fish; and therefore the propulsion efficiency is increased, and the power consumed is reduced. Such a result accords well with the previous hypothesis.

Inertial effects of the semi-passive flapping foil on its energy extraction efficiency

The inertia plays a significant role in the response of a system undergoing flow-induced vibrations, which has been extensively investigated by previous researchers. However, the inertial effects of an energy harvester employing the mechanism of flow-induced vibrations have attracted little attention. This paper concentrates on a semi-passive energy extraction system considering its inertial effects. The incompressible Navier-Stokes equations are solved using a finite-volume based numerical solver with a moving grid technique. A partitioned method is used to couple the fluid and structure motions with the sub-iteration technique and an Aitken relaxation, which guarantees a strong fluid-structure coupling. In addition, a fictitious mass is added to resolve the numerical instability aroused by low density ratios. First, at a fixed mass ratio of r = 1, we identify an optimal set of parameters, at which a maximum efficiency of η = 34% is achieved. Further studies with r ranging from 0.125 to 100 are performed...

Hydrodynamics of a flapping foil in the wake of a D-section cylinder

The water environment of swimming fish in nature is always complex which includes various vortices and fluctuations. In order to study the interaction between the fish and its surrounding complex flow, the physical model with a D-section cylinder placed at the front of a flapping foil is employed. The D-section cylinder is used to produce vortices to contact with the foil as well as the vortices shed from the foil. According to the experimental work of Gopalkrishnan et al., there are three interaction modes between vortices shed from the cylinder and the flapping foil, which are expanding wake, destructive interaction and constructive interaction. Here in this article, three of those typical cases are picked up to reproduce the vortices interaction modes with the modified immersed boundary methods and their hydrodynamic performances are studied further. Results show that, for expanding wake mode and destructive interaction mode, the incoming vortices contact with the foil strongly, inducing relative low pressure domains at the leading-edge of the foil and enlarging the thrust of foils. For constructive mode, the foil slalom between the shed vortices from the D-section cylinder do not contact with them obviously and the foil’s thrust is only enlarged a little.

NUMERICAL STUDIES ON THE PROPULSION AND WAKE STRUCTURES OF FINITE-SPAN FLAPPING WINGS WITH DIFFERENT ASPECT RATIOS

An immersed-boundary method is used to investigate the flapping wings with different aspect ratios ranging from 1 to 5. The numerical results on wake structures and the performance of the propulsion are given. Unlike the case of the two-dimensional flapping foil, the wing-tip vortices appear for the flow past a three-dimensional flapping wing, which makes the wake vortex structures much different. The results show that the leading edge vortex merges into the trailing edge vortex, connects with the wing tip vortices and then sheds from the wing. A vortex ring forms in the wake, and exhibits different patterns for different foil aspect ratios. Analysis of hydrodynamic performances shows that both thrust coefficient and efficiency of the flapping wing increase with increasing aspect ratio.