A PRESSURE-BASED EULER SCHEME FOR TRANSONIC INTERNAL AND EXTERNAL FLOW SIMULATION

SUMMARY

The development of a pressure-based Euler scheme, based on a collocated grid arrangement and solving for Cartesian mass flux components is described. An implicit numerical dissipation model, which includes second and fourth difference terms expressed in pressure, is demonstrated. A smoothing function, which includes a two-level filter, is used to adjust the second order-dissipation. The successful calculations for the inviscid transonic aerodynamic flow around airfoil NACA0012 are presented. The transonic quasi-one-dimensional flow calculation in a converging-diverging nozzle is chosen as an example of an internal flow simulation.     

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.     

Local spin II

Equations are discussed for computing, from ah initio wavefunctions, average values of quantities like S_A. S_B which appear in the Heisenberg model Hamiltonian of magnetism. These equations are based on projection operators onto local regions of space. They result in local spin operators S_A which obey the definition of angular momentum operators and commute with each other. These averages are evaluated for UHF and CI wavefunctions for a few examples of closed and open shell molecules. The calculations are compared with the assumptions made in the Noodleman method for evaluating the parameters in the Heisenberg Hamiltonian and with various definitions of bond order.     

Ab initio Compton maps of small molecules

A closed form expression for the evaluation of directional Compton profiles (DCP) from the position space one-electron reduced density matrix expanded in Cartesian Gaussian basis functions is presented. The Compton map, i.e. a two-dimensional contour plot of the DCP function J(q) in a selected plane, is introduce as a convenient method for describing the DCP Examples of theoretical Compton maps are given for the hydrogen molecule ion (both ground and excited states), water, ammonia, ethylene and ¹A₁ methylene molecules in their ground states. Compton maps generated with Hartree-Fock, configuration interaction and density functional theory methods are compared.     

Travelling waves in a reaction-diffusion system modelling fungal mycelia

We discuss travelling-wave solutions of a system of coupledreaction—diffusion equations used by the authors to describethe macroscopic behaviour of fungal mycelia. Such systems havebeen used in a multitude of applications; and, in particular,Merkin and Needham (1990, Proc. R. Soc. Lond. A 430, 315–45)have studied a certain formulation as a model for generic isothermalchemical reactions. We show that an alternative analysis providesmore complete results in ascertaining the conditions under whichtravelling-wave solutions exist and that it allows a wider rangeof parameter values to be considered; this is essential to theapplication considered in the present case. Numerical investigationsof travelling-wave solutions and the related initial-value problemare included to motivate and extend the analysis.     

Analytical models of rotary clectromagnetic stirring

Electromagnetic stirring (EMS) is widely used in the steel industryas a means of improving the as-cast structure of a continuously-castbillet. Proponents of the technique have claimed that EMS notonly promotes homogeneous grain growth, but also reduces shrinkageporosity and improves surface quality. EMS is less commonlyused for grain refining in other metallurgical industries, butfrequently appears in welding, vacuum arc refining, and single-crystalpulling. In this paper, we shall consider rotary magnetic stirring.We shall show that, for many geometries, the magnitude and distributionof the induced flow may be predicted without recourse to numericalsimulations. Moreover, we shall show that the same magneticbody force can lead to entirely different velocity fields, dependingon the shape of the liquid pool.     

Shock Tube Measurements of Ignition Delay Times for the Butanol Isomers Using the Constrained‐Reaction‐Volume Strategy

Ignition delay times of sec‐, iso‐, and tert‐butanol were measured behind reflected shock waves using both conventional operation and a new constrained‐reaction‐volume (CRV) strategy. This CRV filling method constrains the volume of reactive gases, thereby producing near‐constant‐pressure test conditions for reflected shock measurements. The initial reflected shock conditions cover temperatures ranging from 828 to 1095 K, pressures near 20 atm and an equivalence ratio of 1.0 in air mixtures. Additional data were also collected at 30 atm and at φ = 0.5 for iso‐butanol/O₂/N₂ mixtures. At 20 atm and φ = 1.0, the ignition delay time increases for the isomers in the following order: n‐butanol, iso‐butanol and sec‐butanol, and tert‐butanol. Modeling of all collected data using the Vasu and Sarathy (Energy Fuel 2013, 27, 7072–7080) mechanism showed overall good agreement with the experimental data.     

Biography

The mononegative, dinegative and monopositive ions of biphenylene have been formed in solution. The electronic spectra of the negative ions (in tetrahydrofurane and dimethoxyethane solution) have been measured in the range 10 000–44 000 cm^-1, and that of the positive ion (in H₂SO₄ solution) in the range 10 000–35 000 cm^-1. The presence of paramagnetic ions in the solutions of the singly-charged species has been confirmed by measurement of electron spin resonance absorption. The long wavelength electronic spectra of the monopositive and mononegative ions are closely similar, which confirms the essentially ‘aromatic’ character of the biphenylene structure. Assignments are proposed for the principal bands in the spectra of the ions and the neutral molecule. Explicit calculation of the energies of the excited states by an approximate self-consistent field molecular orbital method yields results in reasonably good overall agreement with the experimental energy spectra. There is evidence from relative intensities of some of the bands that the ‘pairing’ of bonding and antibonding sets of molecular orbitals which is characteristic of benzenoid alternant hydrocarbons is partially removed in biphenylene. This may result from a difference of electronegativity of the carbon atoms in the 4-membered ring from that of the remaining carbon atoms.     

Local and global behaviour of steady-state solutions of the Sel'kov model

In this paper we discuss steady-state solutions of the systemof reaction-diffusion equations known as the Sel'kov model.This model has been the subject of much discussion; in particular,analytical and numerical results have been discussed by Lopez-Gomezet al. (1992, IMA J. Num. Anal. 12, 405–28). We show thata simple analysis of the bifurcation function associated withthe system can explain many of the numerical observations, suchas the formation and development of loops of nontrivial solutions,in a simpler and more complete manner than the analysis of Lopez-Gomezet al. This allows for a clearer understanding of the qualitativebehaviour of the set of nontrivial solutions and hence of thebifurcation diagram.