Finite element analysis in combustion phenomena

This paper is concerned with the exposition of finite element applications to combustion problems. The subject of computational fluid dynamics, including combustion calculations, has long been dominated by finite differences. Recently, however, the finite element method has emerged as a potential candidate for computational modelling in fluid mechanics. It is well known that reactive fluids with combustion present additional complications because of disparity in reaction rates commonly referred to as ‘stiff’. The present paper reviews basic questions arising from combustion problems in applications of finite element techniques to the solution of problems associated with chemical kinetics, diffusion, waves, convection, etc. Finally, an example of a hydrogen-oxygen reaction is presented for practical applications. Extension to the finite element modelling of turbulence, sprays, boundary layers, shock waves, etc. in combustion must await significant developments of numerical strategies associated with a more complete understanding of physical phenomena and chemical kinetics.     

A review of some finite element methods to solve the stationary Navier-Stokes equations

In this paper the integrated solution approach, the penalty function approach and the solenoidal approach for the finite element solution of the stationary Navier-Stokes equations are compared. It is shown that both the penalty function approach and the solenoidal approach compare favourably to the integrated solution method. For fine meshes the solenoidal approach appears to be the cheapest method.     

Numerical calculation of equivalent moment of inertia for a fluid in a cylindrical container with partitions

A 3-D numerical code was developed to solve the irrotational flow of an ideal fluid inside a moving cylindrical container with partitions. The problem is formulated in terms of two Poisson equations, the velocity equation and the pressure equation. These are expressed in terms of finite differences and solved by a procedure of line over relaxation. From the fluid pressure we computed the resultant moment on the container which was then expressed in terms of the equivalent moment of inertia. The code was checked against analytical results of Moiseyev and we found an agreement of 2–5 per cent even for a sparse mesh. We then demonstrated the capability of the code by computing the equivalent moment of inertia for various configurations with full and partial partitions.     

Solution of three-dimensional natural convection about a vertical square rod in a cylindrical enclosure

The problem of three-dimensional laminar natural convection in a vertical enclosure with an inner square rod is treated by a numerical method in boundary-fitted co-ordinates. The inner and outer cylinders are heated and cooled, respectively, to maintain different constant surface temperatures. The horizontal enclosure surfaces are maintained at adiabatic conditions. The Prandtl number is that of air, 0·703, and the Rayleigh numbers span the conduction, transition and boundary layer regimes of flow. The radius ratio is 1, and the aspect ratio (cylinder length divided by maximum annular gap) is 1. The results of the study provide data useful in the design and performance assessment of nuclear reactor spent fuel shipping casks.     

Fluctuations for a ∇φ interface model with repulsion from a wall

We consider a interface model on a one-dimensional lattice with repulsion from a hard wall. We suppose that the repulsion is of the form c^––1, where c,>0 and denotes the height of the interface from the wall. We prove convergence of the equilibrium fluctuations around the hydrodynamic limit to the solution of a SPDE with singular drift. If c0 the system becomes the Funaki-Olla interface model with reflection at the wall, whose equilibrium fluctuations converge to the solution of a SPDE with reflection. We give a new proof of this result using the characterization of such solution as the diffusion generated by an infinite dimensional Dirichlet Form, obtained in a previous paper. Our method is based on a study of integration by parts formulae w.r.t. the equilibrium measure of the interface model and allows to avoid the proof of the so called Boltzmann-Gibbs principle. We also obtain convergence of finite dimensional distributions of non-equilibrium fluctuations around the stationary hydrodynamic limit 0.This work has been supported by a Marie Curie Fellowship of the European Community programme IHP under contract number HPMF-CT-2002-01568.Mathematics Subject Classification (2000):Primary 60K35, 60H15. Secondary 82B24, 82B41     

First-principles calculations of thermodynamic properties of TiB2 at high pressure

The equations of state (EOS) and other thermodynamic properties of TiB₂ are investigated using ab initio plane-wave pseudopotential density functional theory method. The obtained results are in good agreement with the experimental measured data and other theoretical calculated ones. Through the quasi-harmonic Debye model, in which the phononic effects are considered, the dependences of relative volume V/V₀ on pressure P, cell volume V on temperature T, and Debye temperature Θ and specific heat C_V on pressure P are successfully obtained.     

Regularity of solutions of certain parabolic system with nonstandard growth condition

By the use of Moser iteration and Campanato space estimate, theL ^∞ andC ^α regularity estimate of the gradient of solutions of nonlinear parabolic system with nonstandard growth conditions are obtained under the natural structure constraints. This work was supported by NNSF of China under Grant 39570223 and Grant 19675005     

Continuous TLC as a pilot technique for optimization of gradient HPLC. 1. Theoretical considerations for stepwise gradient TLC with binary mobile phase

Equations describing gradient elution in TLC, with a mobile phase of a constant composition in each step, have been derived. These equations are useful for calculating retention volumes from isocratic TLC data. Equations originally derived for gradient HPLC were adapted for TLC. The validity of the equations has been experimentally verified. The satisfactory agreement between experiment and theory for binary mobile phase composed of methyl ethyl ketone and n-heptane suggests that TLC can be used as a pilot technique for gradient HPLC.