A LOCAL MESH REFINEMENT ALGORITHM APPLIED TO TURBULENT FLOW

This paper presents a local mesh refinement procedure based on a discretization over internal interfaces where the averaging is performed on the coarse side. It is implemented in a multigrid environment but can optionally be used without it. The discretization for the convective terms in the velocity and the temperature equation is the QUICK scheme, while the HYBRID-UPWIND scheme is used in the turbulence equations. The turbulence model used is a two-layer k–ϵ model. We have applied this formulation on a backward-facing step at Re=800 and on a three-dimensional turbulent ventilated enclosure, where we have resolved a geometrically complex inlet consisting of 84 nozzles. In both cases the concept of local mesh refinements was found to be an efficient and accurate solution strategy. © 1997 by John Wiley & Sons, Ltd.     

Gas transport properties of soluble poly(phenylene sulfone imide)s

Gas transport of helium, hydrogen, carbon dioxide, oxygen, argon, nitrogen, and methane in three soluble poly(phenylene sulfone imide)s based on 2,2-bis(3,4-decarboxyphenyl) hexafluoropropane dianhydride (6FDA) has been investigated. The effects of increasing length of well-defined oligo(phenylene sulfone) units on the gas permeabilities and diffusivities were determined and correlated with chain packing of the polymers. Activation energies of diffusion and permeation were calculated from temperature-dependent time-lag measurements. The influences of the central group in the diamine moiety of 6FDA-based polyimides on physical and gas transport properties are discussed. The incorporation of a long oligo(phenylene sulfone) segment in the polymer backbone decreases gas permeability and permselectivity simultaneously. The decreases in permeability coefficients can be mainly related to decreases in diffusion coefficients. Changing the central group of diamine moiety from  S to  SO₂ leads to a 45–50% decrease in CO₂ and O₂ permeabilities without appreciable increase in the selectivities. This is considered to be due to the formation of charge transfer complexes. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1855–1868, 1997     

An implicit mixed finite-volume–finite-element method for solving 3D turbulent compressible flows

The development of new aeronautic projects require accurate and efficient simulations of compressible flows in complex geometries. It is well known that most flows of interest are at least locally turbulent and that the modelling of this turbulence is critical for the reliability of the computations. A turbulence closure model which is both cheap and reasonably accurate is an essential part of a compressible code. An implicit algorithm to solve the 2D and 3D compressible Navier–Stokes equations on unstructured triangular/tetrahedral grids has been extended to turbulent flows. This numerical scheme is based on second-order finite element–finite volume discretization: the diffusive and source terms of the Navier–Stokes equations are computed using a finite element method, while the other terms are computed with a finite volume method. Finite volume cells are built around each node by means of the medians. The convective fluxes are evaluated with the approximate Riemann solver of Roe coupled with the van Albada limiter. The standard k–ϵ model has been introduced to take into account turbulence. Implicit integration schemes with efficient numerical methods (CGS, GMRES and various preconditioning techniques) have also been implemented. Our interest is to present the whole method and to demonstrate its limitations on some well-known test cases in three-dimensional geometries. © 1997 John Wiley & Sons, Ltd.     

Effect of available volumes on radial distribution functions

The traditional method of analyzing solution structuring properties of solutes using atom–atom radial distribution functions (rdfs) can give rise to misleading interpretations when the volume occupied by the solute is ignored. It is shown by using the examples of O(4) in α- and β-D-allose that a more reliable interpretation of rdfs can be obtained by normalising the rdf using the available volume, rather than the traditional volume of a spherical shell. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 363–367, 1998     

Rheological properties and the interface in polycarbonate/impact modifier blends: Effect of modifier shell molecular weight

Core-shell impact modifiers are used to enhance the impact strength of thermoplastics such as polycarbonate. The shell of the modifier is designed specifically to interact with the matrix polymer because interfacial adhesion between the modifier and matrix is important in improving the impact strength. Several methods have been proposed to study the interactions at the modifier/matrix interface. One measure of this interaction is the strength of lap joints. The degree of interactions at the interface can be characterized as the thickness of the interfacial region where the chains of the two polymers mix. Yet another aspect is related to the effect of interfacial interactions on the dynamic mechanical properties of the blend. Previous studies have shown that the viscoelastic properties of these blends deviate from the emulsion models that have been proposed for such blends. The deviation of the measured viscoelastic behavior of these blends compared to that predicted by the models has been attributed to the formation of network structure of particles in the blend. The formation of the network structure is a consequence of larger effective volumes of the particles due to interactions at the interface with the matrix. This study provides a means of using rheological properties and the emulsion models to estimate the extent of interaction at the modifier/matrix interface. In blends used in this study it can be shown that the interactions between the modifier and matrix extend far beyond the boundary between the two and the estimated effective volume fraction of modifier is much larger than the actual modifier content in the blend. The effective volume fraction is frequency dependent and decreases with increasing frequency. The data suggest that beyond certain frequencies the modifier no longer interacts with the matrix and the system has properties similar to the matrix with holes. The data are presented which indicate that, within the range studied, lower modifier shell molecular weight results in a higher level of interaction with polycarbonate. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1095–1105, 1998     

Carbon dioxide–poly(vinylidene fluoride) interactions at high pressure

The article reports on the behaviour of poly(vinylidene fluoride) in carbon dioxide at 42°C and 80°C and in a pressure range of 0.1–30 MPa. Experimental techniques for the measurement of gas mass uptake and polymer dilatation are described and the corresponding data are reported as mass sorption and dilatation isotherms, respectively. The mass uptake experiment was also used to follow the evolution of the coefficient of diffusion of carbon dioxide into the polymer as a function of pressure or concentration. An analysis for the calculation of the partial molar volume of carbon dioxide as a function of pressure is also given, which shows that the ‘apparent’ partial molar volume of the carbon dioxide decreases with pressure to very low values, at high pressure. The computed values are significantly less than those for either the liquid or the solid phases of pure carbon dioxide, and also lower than some data previously reported for silicone elastomers. A consideration of the origins of this apparent anomaly is given in the conclusions. © 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2435–2447, 1998     

A finite volume method for fluid flow in polar cylindrical grids

In the numerical simulation of fluid flows using a polar cylindrical grid, grid lines meet at a single point on the axis of the polar cylindrical grid system; this makes the grids around the axis degenerate from being general quadrilaterals into triangles. Therefore, a special treatment must be performed when the axis has to be included in the computational domain in order to solve a non-axisymmetrical fluid flow problem. In this paper a new numerical method has been developed to deal with the difficulty of the axis when the control volume technique is used with a non-staggered grid arrangement. Two illustrative examples of the proposed method are presented for simulating the fluid flows on the axis and all the numerical results obtained for the two examples are shown to be in good agreement with the available analytical solutions. © 1998 John Wiley & Sons, Ltd.     

A bore-capturing finite volume method for open-channel flows

A high-resolution finite volume hydrodynamic solver is presented for open-channel flows based on the 2D shallow water equations. This Godunov-type upwind scheme uses an efficient Harten–Lax–van Leer (HLL) approximate Riemann solver capable of capturing bore waves and simulating supercritical flows. Second-order accuracy is achieved by means of MUSCL reconstruction in conjunction with a Hancock two-stage scheme for the time integration. By using a finite volume approach, the computational grid can be irregular which allows for easy boundary fitting. The method can be applied directly to model 1D flows in an open channel with a rectangular cross-section without the need to modify the scheme. Such a modification is normally required for solving the 1D St Venant equations to take account of the variation of channel width. The numerical scheme and results of three test problems are presented in this paper. © 1998 John Wiley & Sons, Ltd.     

Domain decomposition for the incompressible Navier–Stokes equations: solving subdomain problems accurately and inaccurately

For the solution of practical flow problems in arbitrarily shaped domains, simple Schwarz domain decomposition methods with minimal overlap are quite efficient, provided Krylov subspace methods, e.g. the GMRES method, are used to accelerate convergence. With an accurate subdomain solution, the amount of time spent solving these problems may be quite large. To reduce computing time, an inaccurate solution of subdomain problems is considered, which requires a GCR-based acceleration technique. Much emphasis is put on the multiplicative domain decomposition algorithm since we also want an algorithm which is fast on a single processor. Nevertheless, the prospects for parallel implementation are also investigated. © 1998 John Wiley & Sons, Ltd.