Sean McKee

A finite difference technique for simulating unsteady viscoelastic free surface flows

This work is concerned with the development of a numerical method capable of simulating viscoelastic free surface flow of an Oldroyd-B fluid. The basic equations governing the flow of an Oldroyd-B fluid are considered. A novel formulation is developed for the computation of the non-Newtonian extra-stress components on rigid boundaries. The full free surface stress conditions are employed. The resulting governing equations are solved by a finite difference method on a staggered grid, influenced by the ideas of the marker-and-cell (MAC) method. Numerical results demonstrating the capabilities of this new technique are presented for a number of problems involving unsteady free surface flows.

Curing simulation of thermoset composites

Abstract This paper deals with the modelling and simulation of resin flow, heat transfer and the curing of multilayer thermoset composite laminates during processing in an autoclave. Darcys Law and Stokes’ slow-flow equations are used for the flow model and, for approximately isothermal flows, a similarity solution is developed. This permits the decoupling of the velocity and thermal fields. A two-dimensional convection–diffusion heat equation with an internal heat generation term is then solved numerically, together with the equation for the rate of cure, using a finite difference scheme on a moving grid. The simulations are performed with varying composite thicknesses, and a comparison of numerical results with known experimental data confirms the approximate validity of the model.

Derivation of a pdf kinetic equation for the transport of particles in turbulent flows

A transport equation for the particle phase space density (probability density function (pdf) kinetic equation) is derived for the motion of a dilute suspension of particles in a turbulent flow. The underlying particle equation of motion is based upon a Langevin equation but with a non-white noise driving force derived from an Eulerian aerodynamic force field whose statistics are assumed known. Specifically both the particle position and velocity are considered to be functionals of the driving force and an application of a more general form of the Furutsu-Novikov theorem leads to closed expressions for the phase space diffusion current (i.e. the net force due to the turbulence acting on the particles per unit volume of phase space). In the case of a Gaussian random driving force the closed expressions reduce to a simple Boussinesq form in gradients of the pdf with respect to particle velocity and position. As a practical application solutions of the equation are compared with results obtained from particle tracking in a developing simple shear generated by large eddy simulation.

Modelling drug-eluting stents

In this study, we consider a family of mathematical models to describe the elution of drug from polymer-coated stents into the arterial wall. Our models include the polymer layer, the media, the adventitia, a possible topcoat polymer layer and atherosclerotic plaque. We investigate the relative importance of transmural convection, diffusion and drug-dependent parameters in drug delivery and deposition. Furthermore, we investigate how the release rate from the stent can be altered and examine the resulting effect on cellular drug concentrations.

A numerical technique for solving unsteady non-Newtonian free surface flows

Abstract A numerical method has been developed for solving two-dimensional generalized Newtonian fluid flow with multiple free surfaces. It is an extension of the GENSMAC code which solves the time-dependent Navier-Stokes equations for the primitive variables of velocity and pressure in an arbitrary domain. Like GENSMAC, it is a finite-difference technique, based on staggered grids, using (virtual) marker particles as a means of flow visualization. The code has been employed to solve three time-dependent problems: extrudate die swell, viscous jet buckling, and injection moulding in complex cavities. Both Newtonian and non-Newtonian results are displayed.

Collocation methods for second-kind Volterra integral equations with weakly singular kernels

In this paper it is shown that the use of uniform meshes leads to optimal convergence rates provided that the analytic solutions of a particular class of Volterra integral equations (VIEs) are smooth. If the exact solutions are not smooth, however, suitable transformations can be made so that the new VIEs possess smooth solutions. Spline collocation methods with uniform meshes applied to these new VIEs are then shown to be able to yield optimal (global) convergence rates. The general theory is applied to a typical case, i.e. the integral kernels consisting of the singular term ( t − s ) −½.

Numerical simulation of viscous flow : Buckling of planar jets

The phenomenon of viscous fluid buckling has a long and distinguished history, dating back to Taylor (1968). This paper is concerned with demonstrating that a numerical method, GENSMAC, is capable of simulating this physical instability. A table of the parameter values (e.g. the Reynolds number, the Froude number, inlet width, inlet velocity and aspect ratio) is provided giving details of when buckling occurs and when it does not. This allows the deduction of a possible buckling condition in terms of the Reynolds number and the ratio of height of the jet to the inlet width, modifying a previous hypothesis. Visualization of jet buckling is provided. This work has been motivated by the need of industry to understand jet filling of containers; jet buckling can lead to air entrapment and this is undesirable. Copyright

An experimental and numerical investigation of container filling with viscous liquids

This work is concerned with a study of container filling, with particular reference to the food industry. A computer code was developed and an experimental rig was built, the main purpose being to validate the software. The computational fluid dynamic (CFD) code, called GENSMAC, was specifically designed for relatively slow viscous flow and was capable of capturing multiple free surfaces. This paper focuses on the design of the experimental rig and how it functions. The visual output of the code is then compared with high-speed photographic shots of glucose syrup being jetted into a tub for a selected number of flow regimes

Curing simulation by autoclave resin infusion

This paper deals with the modelling and simulation of resin flow, heat transfer and the curing of a multilayer thermoset composite by the resin film infusion process. For approximately isothermal flows, the model is based on Darcys Law and Stokes equations where a similarity solution is obtained and subsequently used in a two-dimensional convection-diffusion heat equation coupled with a rate of cure equation. A finite difference scheme is applied to the energy equation on a moving grid and simulations for varying laminate thicknesses and number of plies are performed.

Exact analytic solutions to turbulent particle flow equations

A technique for solving a certain class of partial differential equations is used to obtain exact solutions for particle dispersion in an unbounded Gaussian random flow field in which the mean flow is a simple shear and the turbulence is homogeneous and stationary. Results are compared with those of a simple random walk simulation and those obtained from tracking particles in a simple developing shear generated by LES.