Hu, Howard H.
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Publication The Dynamics of Two Spherical Particles in a Confined Rotating Flow: Pedalling Motion(2008-03-25) Mukundakrishnan, Karthik; Hu, Howard H.; Ayyaswamy, Portonovo S.We have numerically investigated the interaction dynamics between two rigid spherical particles moving in a fluid-filled cylinder that is rotating at a constant speed. The cylinder rotation is about a horizontal axis. The particle densities are less than that of the fluid. The numerical procedure employed to solve the mathematical formulation is based on a three-dimensional arbitrary Larangian–Eulerian (ALE), moving mesh finite-element technique, described in a frame of reference rotating with the cylinder. Results are obtained in the ranges of particle Reynolds number, 1Publication Direct Simulation of Initial Value Problems for the Motion of Solid Bodies in a Newtonian Fluid Part 1. Sedimentation(1994) Feng, James; Hu, Howard H.; Joseph, Daniel D.This paper reports the result of direct simulations of fluid-particle motions in two dimensions. We solve the initial value problem for the sedimentation of circular and elliptical particles in a vertical channel. The fluid motion is computed from the Navier-Stokes equations for moderate Reynolds numbers in the hundreds. The particles are moved according to the equations of motion of a rigid body under the action of gravity and hydrodynamic forces arising from the motion of the fluid. The solutions are as exact as our finite-element calculations will allow. As the Reynolds number is increased to 600, a circular particle can be said to experience five different regimes of motion: steady motion with and without overshoot and weak, strong and irregular oscillations. An elliptic particle always turn its long axis perpendicular to the fall, and drifts to the centreline of the channel during sedimentation. Steady drift, damped oscillation and periodic oscillation of the particle are observed for different ranges of the Reynolds number. For two particles which interact while settling, a steady staggered structure, a periodic wake-action regime and an active drafting- kissing-tumbling scenario are realized at increasing Reynolds numbers. The nonlinear effects of particle-fluid, particle-wall and interparticle interactions are analysed, and the mechanisms controlling the simulated flows are shown to be lubrication, turning couples on long bodies, steady and unsteady wakes and wake interactions. The results are compared to experimental and theoretical results previously published.Publication An Explicit Finite-Difference Scheme for Simulation of Moving Particles(2006-02-10) Perrin, A.; Hu, Howard HWe present an explicit finite-difference scheme for direct simulation of the motion of solid particles in a fluid. The method is based on a second order MacCormack finite-difference solver for the flow, and Newton’s equations for the particles. The fluid is modeled with fully compressible mass and momentum balances; the technique is intended to be used at moderate particle Reynolds number. Several examples are shown, including a single stationary circular particle in a uniform flow between two moving walls, a particle dropped in a stationary fluid at particle Reynolds number of 20, the drafting, kissing, and tumbling of two particles, and 100 particles falling in a closed box.Publication Direct Simulation of the Sedimentation of Elliptic Particles in Oldroyd-B Fluids(1997) Huang, P. Y.; Hu, Howard H.; Joseph, Daniel D.Cross stream migration and stable orientations of elliptic particles falling in an Oldroyd-B fluid in a channel are studied. We show that the normal component of the extra stress on a rigid body vanishes; lateral forces and torques are determined by the pressure. Inertia turns the longside of the ellipse across the stream and elasticity turns it along the stream; tilted off-center falling is unstable. There are two critical numbers; elasticity and Mach numbers. When the elasticity number is smaller than critical the fluid is essentially Newtonian with broadside-on falling at the centerline of the channel. For larger elasticity numbers the settling turns the longside of the particle along the stream in the channel center for all velocities below a critical one, identified with a critical Mach number of order one. For larger Mach numbers the ellipse flips into broadside-on falling again. The critical numbers are functions of the channel blockage ratio, the particle aspect ratio and the retardation/relaxation time ratio of the fluid. Two ellipses falling nearby, attract, line-up and straighten-out in a long chain of ellipses with longside vertical, all in a row. Stable, off-center tilting is found for ellipses falling in shear thinning fluids and for cylinders with flat ends in which particles tend align their longest diameter with gravity.Publication Stability of a Core-Annular Flow in a Rotating Pipe(1989-10-01) Hu, Howard H.; Joseph, Daniel D.The linear stability of core-annular flow in rotating pipes is analyzed. Attention is focused on the effects of rotating the pipe and the difference in density of the two fluids. Both axisymmetric and nonaxisymmetric disturbances are considered. Major effects of the viscosity ratio, interfacial tension, radius ratio, and Reynolds number are included. It is found that for two fluids of equal density the rotation of the pipe stabilizes the axisymmetric (n= 0) modes of disturbances and destabilizes the nonaxisymmetric modes. Except for small script R sign, where the axisymmetric capillary instability is dominant, the first azimuthal mode of disturbance |n| = 1 is the most unstable. When the heavier fluid is outside centripetal acceleration of the fluid in the rotating pipe is stabilizing; there exists a critical rotating speed above which the flow is stabilized against capillary instability for certain range of small script R sign. When the lighter fluid is outside the flow is always unstable.Publication Direct Numerical Simulation of the Sedimentation of Solid Particles with Thermal Convection(2003-01-01) Gan, Hui; Chang, Jianzhong; Feng, James J.; Hu, Howard H.Dispersed two-phase flows often involve interfacial activities such as chemical reaction and phase change, which couple the fluid dynamics with heat and mass transfer. As a step toward understanding such problems, we numerically simulate the sedimentation of solid bodies in a Newtonian fluid with convection heat transfer. The two-dimensional Navier–Stokes and energy equations are solved at moderate Reynolds numbers by a finite-element method, and the motion of solid particles is tracked using an arbitrary Lagrangian–Eulerian scheme. Results show that thermal convection may fundamentally change the way that particles move and interact. For a single particle settling in a channel, various Grashof-number regimes are identified, where the particle may settle straight down or migrate toward a wall or oscillate laterally. A pair of particles tend to separate if they are colder than the fluid and aggregate if they are hotter. These effects are analysed in terms of the competition between the thermal convection and the external flow relative to the particle. The mechanisms thus revealed have interesting implications for the formation of microstructures in interfacially active two-phase flows.Publication Rheology of a Suspension of Elastic Particles in a Viscous Shear Flow(2011-11-01) Hu, Howard H; Gao, Tong; Ponte-Castañeda, PedroIn this paper we consider a suspension of elastic solid particles in a viscous liquid. The particles are assumed to be neo-Hookean and can undergo finite elastic deformations. A polarization technique, originally developed for analogous problems in linear elasticity, is used to establish a theory for describing the finite-strain, time-dependent response of an ellipsoidal elastic particle in a viscous fluid flow under Stokes flow conditions. A set of coupled, nonlinear, first-order ODEs is obtained for the evolution of the uniform stress fields in the particle, as well as for the shape and orientation of the particle, which can in turn be used to characterize the rheology of a dilute suspension of elastic particles in a shear flow. When applied to a suspension of cylindrical particles with initially circular cross-section, the theory confirms the existence of steady-state solutions, which can be given simple analytical expressions. The two-dimensional, steady-state solutions for the particle shape and orientation, as well as for the effective viscosity and normal stress differences in the suspension, are in excellent agreement with direct numerical simulations of multiple-particle dispersions in a shear flow obtained by using an arbitrary Lagrangian–Eulerian (ALE) finite element method (FEM) solver. The corresponding solutions for the evolution of the microstructure and the rheological properties of suspensions of initially spherical (three-dimensional) particles in a simple shear flow are also obtained, and compared with the results of Roscoe (J. Fluid Mech., vol. 28, 1967, pp. 273–293) in the steady-state regime. Interestingly, the results show that sufficiently soft elastic particles can be used to reduce the effective viscosity of the suspension (relative to that of the pure fluid).Publication Particle Motion in a Liquid Film Rimming the Inside of a Partially Filled Rotating Cylinder(2003-07-24) Joseph, Daniel D.; Wang, J.; Bai, R.; Yang, B. H.; Hu, Howard H.Both lighter- and hydrophobic heavier-than-liquid particles will float on liquid–air surfaces. Capillary forces cause the particles to cluster in typical situations identified here. This kind of clustering causes particles to segregate into islands and bands of high concentrations in thin liquid films rimming the inside of a slowly rotating cylinder partially filled with liquid. A second regime of particle segregation, driven by secondary motions induced by off-centre gas bubbles in a more rapidly rotating cylinder at higher filling levels, is identified. A third regime of segregation of bidisperse suspensions is found in which two layers of heavier-than-liquid particles that stratify when there is no rotation, segregate into alternate bands of particles when there is rotation.Publication Direct Simulation of Initial Value Problems for the Motion of Solid Bodies in a Newtonian Fluid. Part 2. Couette adn Poiseuille Flows.(1994-05-11) Feng, James; Hu, Howard H.; Joseph, Daniel D.This paper reports the results of a two-dimensional finite element simulation of the motion of a circular particle in a Couette and a Poiseuille flow. The size of the particle and the Reynolds number are large enough to include fully nonlinear inertial effects and wall effects. Both neutrally buoyant and non-neutrally buoyant particles are studied, and the results are compared with pertinent experimental data and perturbation theories. A neutrally buoyant particle is shown to migrate to the centreline in a Couette flow, and exhibits the Segré-Silberberg effect in a Poiseuille flow. Non-neutrally buoyant particles have more complicated patterns of migration, depending upon the density difference between the fluid and the particle. The driving forces of the migration have been identified as a wall repulsion due to lubrication, an inertial lift related to shear slip, a lift due to particle rotation and, in the case of Poiseuille flow, a lift caused by the velocity profile curvature. These forces are analysed by examining the distributions of pressure and shear stress on the particle. The stagnation pressure on the particle surface are particularly important in determining the direction of migration.Publication Shape Dynamics and Rheology of Soft Elastic Particles in a Shear Flow(2012-01-31) Gao, Tong; Hu, Howard H; Castañeda, Pedro PonteThe shape dynamics of soft, elastic particles in an unbounded simple shear flow is investigated theoretically under Stokes flow conditions. Three types of motion—- steady-state, trembling, and tumbling—- are predicted, depending on the shear rate, elastic shear modulus, and initial particle shape. The steady-state motion is found to be always stable. In addition, the existence of a trembling regime is documented for the first time in nonvesicle systems, and a complete phase diagram is developed. The rheological properties of dilute suspensions of such soft particles generally exhibit shear-thinning behavior and can even display negative intrinsic viscosity for sufficiently soft particles.