Shaolin Mao

On the drag force of a viscous sphere with interfacial slip at small but finite Reynolds numbers

We investigate the hydrodynamic drag force on a viscous sphere in a fluid of different viscosities at small but finite Reynolds numbers when interfacial slip is present at the surface of the sphere. The sphere is small enough for it to retain its spherical shape, as is the case with most small droplets. By using a singular perturbation method, the exterior flow field of the droplet is decomposed into an inner region, where the viscous effects dominate, and an outer region, where the inertia is important. The interior flow of the viscous sphere is also solved analytically. By applying appropriate boundary conditions to the surface of the viscous sphere and matching the conditions between the inner and outer flow fields, stream functions up to the order of Re2 log Re for both the exterior and the interior flow are obtained. Thus, an analytical expression for the drag force coefficient of the viscous droplet is derived. This general expression yields, as special cases, several other expressions that are applicable to spheres that translate rectilinearly under more restrictive conditions. One of the practical conclusions from this study is that the presence of interfacial slip can significantly reduce the drag force on a droplet.

A Three-Dimensional Resolved Discrete Particle Method for Studying Particle-Wall Collision in a Viscous Fluid

Particle collisions with the walls are very important in understanding the fluid-particle behavior near the walls and determining the boundary conditions of the particulate phases in two-fluid models. In this paper, we examine the velocity characteristics of several types of particles near solid walls by applying a resolved discrete particle method (RDPM), which also uses the immersed boundary approach to model the solid particles. We assume that the particles are spherical with an initial velocity that is prescribed. The particles are allowed to traverse part of the viscous fluid until they collide with the solid wall. The collision force on the particle is modeled by a soft-sphere collision scheme with a linear spring-dashpot system. The hydrodynamic force on the particle is solved directly from the RDPM. By following the trajectories of several particles, we investigate the effect of the collision model parameters to the dynamics of particle close to the wall. We report here the rebound velocity of the particle, the coefficient of restitution, and the particle slip velocity at the wall as functions of the collision parameters. DOI: 10.1115/1.4002432 Interparticle and wall collisions are very important in particlefluid flows. The dynamic behavior of such flows is decided by these collisions, especially when the flow is dense and the particles move at high velocity. Particulate flow modeling, as an effective and robust tool to study many issues associated with particular flows segregation, agglomeration, and clustering, requires the ability of accurately resolving interparticle and wall collisions. The correct handling of these collisions is an essential element for the discrete particle method DPM, which will not work without an accurate knowledge of the collisions 1. Generally, a grid used in a DPM simulation is not fine enough to resolve the lubrication force that develops between the particles or between a particle and a solid boundary. Therefore, an artificial mechanism is necessary to be introduced in the numerical simulation to account for the collision force during collision processes. Without such a mechanism in the model, it is likely that the particles will penetrate significantly into each other’s computational boundary, thus, terminating the computation or rendering the results meaningless. There are a few collision schemes that have been developed and applied in the numerical simulation of particulate flows: Ladd 2,3 suggested using lubrication force to repel two particles when

Condensation Analysis of Exhaust Gas Recirculation System for Heavy-Duty Trucks

The exhaust gas recirculation (EGR) system has been widely used in the automotive and heavy-duty trucks to reduce NOx ,S Ox, and other controlled emissions. A liquid-cooled or air-cooled heat exchanger is the main constituent of the EGR system. The heat exchanger decreases the temperature of the exhaust gases mixture that flows through the EGR channels and the lower temperatures reduce the content of the controlled gas emissions. Condensation of water vapor is an undesirable by-product of the EGR systems because, in combination with the emission gases, it forms the corrosive sulfuric and nitric acids. The U.S. EPA has suggested that engine makers should turn off their EGR systems periodically to avoid the formation of the corrosive sulfuric and nitric acids. In order to accurately predict the corrosion process, a condensation model has been developed to investigate the rates of formation and diffusion of nitric acid and sulfuric acid to the cold tube surface. A three-dimensional computational fluid dynamics (CFD) simulation has been conducted for a typical EGR cooler during normal operating conditions of Tier 4 heavy-duty trucks. A lumped, 1D heat and mass transfer model has also been developed to study the most important physical aspects of the condensation process. The CFD and the analytical results of the rate of condensation and local fluid properties are an important and inexpensive complement to more expensive experimental measurements and testing. Such models may be used to improve the design and to optimize the operating conditions of the EGR systems and may become valuable tools in the design and manufacturing of the next generation of EGR systems for diesel engines. The model developed is general and the techniques and numerical results of this study may be extended to engine reliability, corrosion reduction, and damage prevention of other industrial engines. [DOI: 10.1115/1.4004745]