Singularities at rims in three-dimensional fluid flow

Asymptotic solutions are presented for Stokes flow near circular rims in three-dimensional geometries. Using nonstandard toroidal coordinates, asymptotic analytical expressions are derived for different corner angles. In comparison to the two-dimensional case, an extra critical corner angle value is derived, below which the swirling behaviour of a particle is absent. Illustrations of the motion of a particle near a rim in a three-dimensional fluid flow are given for different corner angles

A subgrid model for large-eddy simulation of particle-laden channel flow

DNS and LES of particle-laden turbulent channel flow, in which the particles experience a drag force, are performed. Simulations at three di®erent Stokes numbers andfor two different subgrid models are carried out. In this flow turbophoresis leads to anaccumulation of particles near the walls. It is shown that the turbophoresis and particle dispersion in LES are reduced, if the filtered fluid velocity is used in the particle equation of motion. This is a combined effect of the disregard of the subgrid scales in the fluid velocity and of the inadequacy of the subgrid model in the fluid equations. To alleviate this problem an inverse filtering model is proposed and incorporated into the particle equations. The model is shown to enhance turbophoresis and particle dispersion in actual LES. For the dynamic eddy-viscosity model this results in a good agreement with the DNS-predictions

Mass transport in a partially covered fluid-filled cavity

A method of computing the concentration field of dissolved material inside an etch-hole is presented. Using a number of assumptions, approximate convection-diffusion equations are formulated, and analytical descriptions for the concentration in different parts of the domain are obtained. By coupling these descriptions the concentration field can be computed. The assumptions and the results are validated by comparison with solutions based on a finite-volume method. Results of the boundary-layer method are given for two characteristic etch-hole geometries. The described boundary-layer method is efficient in terms of computational time and memory, because it does not require the construction of a computational grid in the interior of the domain. This advantage will be exploited in a future paper where the method will be used to simulate wet-chemical etching

Comparison of dns of compressible and incompressible turbulent droplet-laden heated channel flow with phase transition

In this paper a turbulent channel flow with dispersed droplets is examined. The dispersed phase is allowed to have phase transition, which leads to heat and mass transfer between the phases, and correspondingly modulates turbulent flow properties. As a point of reference we examine the flow of water droplets in air, containing also the vapor of water. The key element of this study concerns the treatment of the carrier phase as either a compressible or an incompressible fluid. We compare simulation results obtained with a pseudo-spectral discretization for the incompressible flow to those obtained with a finite volume approach for the compressible flow. The compressible formulation is not tailored for low Mach flow and we need to resort to a Mach number that is artificially high for simulation feasibility. We discuss differences in fluid flow, heat- and mass transfer and dispersed droplet properties. The main conclusion is that both formulations give a good general correspondence. Flow properties such as velocity fields agree very closely, while heat transfer as characterized by the Nusselt number differs by around 25%. Droplet sizes are shown to be slightly larger, particularly in the center of the channel, in case the compressible formulation is chosen. A low-Mach compressible formulation is required for a fully quantitative comparison

Thermodynamics and hydrodynamics of ³He-⁴He mixtures

The specific heat of liquid 3He–4He mixtures is usually written in terms of the sum of the specific heat of a 3He-quasiparticle gas and the specific heat of the pure 4He component. The thermodynamics based on this starting point is derived. Relations of important quantities and their low- and high-temperature limits are given. These are used to derive expressions for the velocity of second sound. This latter quantity is a very important source of information for the Fermi gas properties. Finally, the Fermi gas parameters are summarized in the chapter. The experimental aspects of the 3He–4He hydrodynamics are treated. The appearance of mutual friction that has long been neglected in this field is discussed, together with the properties of the critical velocities. The phenomenological equations of motion are given. The occurrence of mutual friction is a strong indication that 4He vortices play an important role in 3He–4He hydrodynamics. From the equation of motion of quantized 4He vortices, the observed cubic velocity dependence of the 4He chemical potential difference is explained on purely dimensional grounds. A differential equation is given from which the temperature profile in a cylindrical tube in which 3He flows through superfluid 4He can be calculated

A boundary element method for compound non-Newtonian drops

A boundary integral method for the simulation of the deformation of axisymmetric compound non-Newtonian drops suspended in a Newtonian fluid which is subjected to an axisymmetric flow eld is developed. The boundary integral formulation for Stokes flow is used and the non-Newtonian stress is treated as a source term. The latter yields an extra integral over the domain of the non-Newtonian material in the boundary integral formulation. By transforming the integral representation for the velocity to cylindrical coordinates we can reduce the dimension of the computational problem. Apart from a numerical validation of the method we present simulation results for a drop consisting of an Oldroyd-B fluid and a viscoelastic material. Moreover, we extend the method to compound drops, which are composed of a viscous inner core encapsulated by a viscoelastic material. The simulation results for these drops are consistent with theoretical results from the literature. Moreover, it is shown that the method can be used to identify the dominant breakup mechanism of compound drops and its relation to the specic non-Newtonian character of the drops