MBCNS2 Example Book

MBCNS2 is a small collection of programs for the simulation of transient two-dimensional (or axisymmetric) flows. It is part of the larger collection of compressible flow simulation codes found at http://www.mech.uq.edu.au/cfcfd/. This manual is a collection of example simulations: scripts, results and commentary. It may be convenient for new users of the code to identify an example close to the situation that they wish to model and then adapt the scripts for that example.

A wavelet-based adaptive technique for adsorption problems involving steep gradients

A general, fast wavelet-based adaptive collocation method is formulated for heat and mass transfer problems involving a steep moving profile of the dependent variable. The technique of grid adaptation is based on sparse point representation (SPR). The method is applied and tested for the case of a gas–solid non-catalytic reaction in a porous solid at high Thiele modulus. Accurate and convergent steep profiles are obtained for Thiele modulus as large as 100 for the case of slab and found to match the analytical solution.

High frequency (1000 Hz) tympanometry in normal neonates

The characteristics of high frequency (1000 Hz) acoustic admittance results obtained from normal neonates were described in this study. Participants were 170 healthy neonates (96 boys and 74 girls) aged between 1 and 6 days (mean = 3.26 days, SD = 0.92). Transient evoked otoacoustic emissions (TEOAEs), and 226 Hz and 1000 Hz probe tone tympanograms were obtained from the participants using a Madsen Capella OAE/middle ear analyser. The results showed that of the 170 neonates, 34 were not successfully tested in both ears, 14 failed the TEOAE screen in one or both ears, and 122 (70 boys, 52 girls) passed the TEOAE screen in both ears and also maintained an acceptable probe seal during tympanometry. The 1000 Hz tympanometric data for the 122 neonates (244 ears) showed a single-peaked tympanogram in 225 ears (92.2 %), a flat-sloping tympanogram in 14 ears (5.7 %), a double-peaked tympanogram in 3 ears (1.2 %) and other unusual shapes in 2 ears (0.8 %). There was a significant ear effect, with right ears showing significantly higher mean peak compensated static admittance and tympanometric width, but lower mean acoustic admittance at +200 daPa and gradient than left ears. No significant gender effects or its interaction with ear were found. The normative tympanometric data derived from this cohort may serve as a guide for detecting middle ear dysfunction in neonates.

Dissolution of a solid sphere in an unbounded, stagnant liquid

An exact analytical solution is obtained for the transient dissolution of solid spheres in a diffusion-controlled environment. This result provides a useful reference point for drug testing in humans. The dimensionless solution is expressed in terms of a single parameter, which accounts for solubility, bulk flow, and stagnant fluid composition. A simple, explicit and exact expression was found to predict time-to-complete dissolution (TCD). An approximate solution was also found which tracks the exact case for low solubility conditions.

Effect of ionic strength and clay mineralogy on Na-Ca exchange and the SAR-ESP relationship

The relationship between sodium adsorption ratio (SAR) and exchangeable sodium percentage (ESP) for all soils has traditionally been assumed to be similar to that developed by the United States Salinity Laboratory (USSL) in 1954. However, under certain conditions, this relationship has been shown not to be constant, but to vary with both ionic strength and clay mineralogy. We conducted a detailed experiment to determine the effect of ionic strength on the Na+-Ca2+ exchange of four clay minerals (kaolinite, illite, pyrophyllite, and montmorillonite), with results related to the diffuse double-layer (DDL) model. Clays in which external exchange sites dominated (kaolinite and pyrophyllite) tended to show an overall preference for Na+, with the magnitude of this preference increasing with decreasing ESP. For these external surfaces, increases in ionic strength were found to increase preference for Na+. Although illite (2:1 non-expanding mineral) was expected to be dominated by external surfaces, this clay displayed an overall preference for Ca2+, possibly indicating the opening of quasicrystals and the formation of internal exchange surfaces. For the expanding 2:1 clay, montmorillonite, Na+-Ca2+ exchange varied due to the formation of quasicrystals (and internal exchange surfaces) from individual clay platelets. At small ionic strength and large ESP, the clay platelets dispersed and were dominated by external exchange surfaces (displaying preference for Na+). However, as ionic strength increased and ESP decreased, quasicrystals (and internal exchange surfaces) formed, and preference for Ca2+ increased. Therefore, the relationship between SAR and ESP is not constant and should be determined directly for the soil of interest.