Initial and Boundary Conditions for the Lattice Boltzmann Method

A new approach of implementing initial and boundary conditions for the lattice Boltzmann method is presented. The new approach is based on an extended collision operator that uses the gradients of the fluid velocity. The numerical performance of the lattice Boltzmann method is tested on several problems with exact solutions and is also compared to an explicit finite difference projection method. The discretization error of the lattice Boltzmann method decreases quadratically with finer resolution both in space and in time. The roundoff error of the lattice Boltzmann method creates problems unless double precision arithmetic is used.Comment: 42 pages in Postscript, with additional 27 Postscript figures Physical Review E, Submitted December 92, Revised June 9

Drape optimization in woven composites manufacture.

This paper addresses the optimisation of forming in manufacturing of composites. A simplified finite element model of draping is developed and implemented. The model incorporates the non-linear shear response of textiles and wrinkling due to buckling of tows. The model is validated against experimental results and it is concluded that it reproduces successfully the most important features of the process. The simple character of the model results in low computational times that allow its use within an optimisation procedure. A genetic algorithm is used to solve the optimisation problem of minimising the wrinkling in the formed component by selecting a suitable holding force distribution. The effect of regularisation is investigated and the L-curve is used to select a regularisation parameter value. Optimised designs resulting from the inversion procedure have significantly lower wrinkling than uniform holding force profiles, while regularisation allows force gradients to be kept relatively low so that suggested process designs are feasible

Analytical solutions of the lattice Boltzmann BGK model

Analytical solutions of the two dimensional triangular and square lattice Boltzmann BGK models have been obtained for the plain Poiseuille flow and the plain Couette flow. The analytical solutions are written in terms of the characteristic velocity of the flow, the single relaxation time $\tau$ and the lattice spacing. The analytic solutions are the exact representation of these two flows without any approximation.Comment: 10 pages, no postscript figure provide

Feynman's ratchet and pawl: an exactly solvable model

We introduce a simple, discrete model of Feynman's ratchet and pawl, operating between two heat reservoirs. We solve exactly for the steady-state directed motion and heat flows produced, first in the absence and then in the presence of an external load. We show that the model can act both as a heat engine and as a refrigerator. We finally investigate the behavior of the system near equilibrium, and use our model to confirm general predictions based on linear response theory.Comment: 19 pages + 10 figures; somewhat tighter presentatio

Lattice-Boltzmann and finite-difference simulations for the permeability for three-dimensional porous media

Numerical micropermeametry is performed on three dimensional porous samples having a linear size of approximately 3 mm and a resolution of 7.5 $\mu$m. One of the samples is a microtomographic image of Fontainebleau sandstone. Two of the samples are stochastic reconstructions with the same porosity, specific surface area, and two-point correlation function as the Fontainebleau sample. The fourth sample is a physical model which mimics the processes of sedimentation, compaction and diagenesis of Fontainebleau sandstone. The permeabilities of these samples are determined by numerically solving at low Reynolds numbers the appropriate Stokes equations in the pore spaces of the samples. The physical diagenesis model appears to reproduce the permeability of the real sandstone sample quite accurately, while the permeabilities of the stochastic reconstructions deviate from the latter by at least an order of magnitude. This finding confirms earlier qualitative predictions based on local porosity theory. Two numerical algorithms were used in these simulations. One is based on the lattice-Boltzmann method, and the other on conventional finite-difference techniques. The accuracy of these two methods is discussed and compared, also with experiment.Comment: to appear in: Phys.Rev.E (2002), 32 pages, Latex, 1 Figur

Strain development in curing epoxy resin and glass fibre/epoxy composites monitored by fibre Bragg grating sensors in birefringent optical fibre

Fibre Bragg gratings (FBGs) fabricated in linearly birefringent fibres were embedded in glass fibre/epoxy composites and in the corresponding unreinforced resin to monitor the effective transverse strain development during the cure process. The optical fibres containing the FBG sensors were aligned either normal or parallel to the reinforcement fibres in unidirectional glass fibre/epoxy prepregs. The chemical cure kinetics of the epoxy resin system used were studied using differential scanning calorimetry, in order to investigate the correlation between the strain monitoring results and the evolution of the curing reaction. A non-parametric cure kinetics model was developed and validated for this purpose. The effective transverse strain measured by the FBGs demonstrated high sensitivity to the degree of cure as a result of the densification of the resin caused by the curing reaction. The effective compressive transverse strain developed during the reaction, and thus the corresponding sensitivity to chemical changes, was higher in the case of the sensing fibre aligned normal to the reinforcement fibres than in the case of the sensor fibre parallel to the reinforcement fibres. Small but measurable sensitivity to cure induced changes was observed in the case of the unreinforced resin

Manufacture of a rotor blade pitch horn using binder yarn fabrics

The use of binder yarn fabrics in rotor blade applications is investigated in this work. A preforming procedure is incorporated in manufacturing, resulting in higher degree of automation and a reduction of process steps. The performance of the process is evaluated with respect to cost savings compared to prepregging technologies