An algorithm for isentropic flow

An efficient algorithm is presented for the solution of the equations of isentropic gas dynamics with a general convex gas law. The scheme is based on solving linearized Riemann problems approximately, and in more than one dimension incorporates operator splitting. In particular, only two function evaluations in each computational cell are required. The scheme is applied to a standard test problem in gas dynamics for a polytropic gas

An efficient flux difference splitting algorithm for unsteady duct flows of a real gas

A numerical scheme is presented for the solution of the Euler equations of compressible flow of a real gas in a single spatial coordinate. This includes flow in a duct of variable cross-section, as well as flow with slab, cylindrical or spherical symmetry, as well as the case of an ideal gas, and can be useful when testing codes for the two-dimensional equations governing compressible flow of a real gas. The resulting scheme requires an average of the flow variables across the interface between cells, and this average is chosen to be the arithmetic mean for computational efficiency, which is in contrast to the usual “square root” averages found in this type of scheme. The scheme is applied with success to five problems with either slab or cylindrical symmetry and for a number of equations of state. The results compare favourably with the results from other schemes.

An efficient numerical method for compressible flows of a real gas using arithmetic averaging

An efficient numerical method is presented for the solution of the Euler equations governing the compressible flow of a real gas. The scheme is based on the approximate solution of a specially constructed set of linearised Riemann problems. An average of the flow variables across the interface between cells is required, and this is chosen to be the arithmetic mean for computational efficiency, which is in contrast to the usual square root averaging. The scheme is applied to a test problem for five different equations of state.

An efficient shock capturing scheme for the pseudo-unsteady equations representing steady inviscid flow

An efficient algorithm is presented for the solution of the steady Euler equations of gas dynamics. The scheme is based on solving linearised Riemann problems approximately and in more than one dimension incorporates operator splitting. The scheme is applied to a standard test problem of flow down a channel containing a circular arc bump for three different mesh sizes.

A non-uniform mesh scheme for compressible flow

A non-uniform mesh scheme is presented for the computation of compressible flows governed by the Euler equations of gas dynamics. The scheme is based on flux-difference splitting and represents an extension of a similar scheme designed for uniform meshes. The numerical results demonstrate that little, if any, spurious oscillation occurs as a result of the non-uniformity of the mesh; and importantly, shock speeds are computed correctly.

An isentropic flow algorithm with body fitted meshes

An efficient algorithm based on flux difference splitting is presented for the solution of the three-dimensional equations of isentropic flow in a generalised coordinate system, and with a general convex gas law. The scheme is based on solving linearised Riemann problems approximately and in more than one dimension incorporates operator splitting. The algorithm requires only one function evaluation of the gas law in each computational cell. The scheme has good shock capturing properties and the advantage of using body-fitted meshes. Numerical results are shown for Mach 3 flow of air past a circular cylinder. Furthermore, the algorithm also applies to shallow water flows by employing the familiar gas dynamics analogy.

Prediction of supercritical flow in open channels

A finite difference scheme based on flux difference splitting is presented for the solution of the one-dimensional shallow water equations in open channels. A linearised problem, analogous to that of Riemann for gas dynamics, is defined and a scheme, based on numerical characteristic decomposition, is presented for obtaining approximate solutions to the linearised problem. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second order scheme which avoids non-physical, spurious oscillations. The scheme is applied to a problem of flow in a river whose geometry induces a region of supercritical flow.

Real gas flows in a duct

A numerical scheme is presented for the solution of the Euler equations of compressible flow of a real gas in a single spatial coordinate. This include flow in a duct of variable cross-section as well as flow with cylindrical or spherical symmetry, and can prove useful when testing codes for the two-dimensional equations governing compressible flow of a real gas. The scheme is applied with success to a problem involving the interaction of converging and diverging cylindrical shocks for four equations of state and to a problem involving the reflection of a converging shock.

Riemann solvers with primitive parameter vectors for two-dimensional compressible flows of a real gas

An analysis of averaging procedures is presented for an approximate Riemann solver for the equations governing the compressible flow of a real gas. This study extends earlier work for the Euler equations with ideal gases.

Gas-phase reactions of NO3 and N2O5 with (Z)-hex-4-en-1-ol, (Z)-hex-3-en-1-ol ('leaf alcohol'), (E)-hex-3-en-1-ol, (Z)-hex-2-en-1-ol and (E)-hex-2-en-1-ol

The night-time atmospheric chemistry of the biogenic volatile organic compounds (Z)-hex-4-en-1-ol, (Z)-hex-3-en-1-ol ('leaf alcohol'), (E)-hex-3-en-1-ol, (Z)-hex-2-en-1-ol and (E)-hex-2-en-1-ol, has been studied at room temperature. Rate coefficients for reactions of the nitrate radical (NO3) with these stress-induced plant emissions were measured using the discharge-flow technique. We employed off-axis continuous-wave cavity-enhanced absorption spectroscopy (CEAS) for the detection of NO3, which enabled us to work in excess of the hexenol compounds over NO3. The rate coefficients determined were (2.93 +/- 0.58) x 10(-13) cm(3) molecule(-1) s(-1), (2.67 +/- 0.42) x 10(-13) cm(3) molecule(-1) s(-1), (4.43 +/- 0.91) x 10(-13) cm(3) molecule(-1) s(-1), (1.56 +/- 0.24) x 10(-13) cm(3) molecule(-1) s(-1), and (1.30 +/- 0.24) x 10(-13) cm(3) molecule(-1) s(-1) for (Z)-hex-4-en-1-ol, (Z)-hex-3en-1-ol, (E)-hex-3-en-1-ol, (Z)-hex-2-en-1-ol and (E)-hex-2-en-1-ol. The rate coefficient for the reaction of NO3 with (Z)-hex-3-en-1-ol agrees with the single published determination of the rate coefficient using a relative method. The other rate coefficients have not been measured before and are compared to estimated values. Relative-rate studies were also performed, but required modification of the standard technique because N2O5 (used as the source of NO3) itself reacts with the hexenols. We used varying excesses of NO2 to determine simultaneously rate coefficients for reactions of NO3 and N2O5 with (E)-hex-3-en-1-ol of (5.2 +/- 1.8) x 10(-13) cm(3) molecule(-1) s(-1) and (3.1 +/- 2.3) x 10(-18) cm(3) molecule(-1) s(-1). Our new determinations suggest atmospheric lifetimes with respect to NO3-initiated oxidation of roughly 1-4 h for the hexenols, comparable with lifetimes estimated for the atmospheric degradation by OH and shorter lifetimes than for attack by O-3. Recent measurements of [N2O5] suggest that the gas-phase reactions of N2O5 with unsaturated alcohols will not be of importance under usual atmospheric conditions, but they certainly can be in laboratory systems when determining rate coefficients.

The use of trajectory cluster analysis to interpret trace gas measurements at Mace Head, Ireland

A first step in interpreting the wide variation in trace gas concentrations measured over time at a given site is to classify the data according to the prevailing weather conditions. In order to classify measurements made during two intensive field campaigns at Mace Head, on the west coast of Ireland, an objective method of assigning data to different weather types has been developed. Air-mass back trajectories calculated using winds from ECMWF analyses, arriving at the site in 1995–1997, were allocated to clusters based on a statistical analysis of the latitude, longitude and pressure of the trajectory at 12 h intervals over 5 days. The robustness of the analysis was assessed by using an ensemble of back trajectories calculated for four points around Mace Head. Separate analyses were made for each of the 3 years, and for four 3-month periods. The use of these clusters in classifying ground-based ozone measurements at Mace Head is described, including the need to exclude data which have been influenced by local perturbations to the regional flow pattern, for example, by sea breezes. Even with a limited data set, based on 2 months of intensive field measurements in 1996 and 1997, there are statistically significant differences in ozone concentrations in air from the different clusters. The limitations of this type of analysis for classification and interpretation of ground-based chemistry measurements are discussed.

Separation of astaxanthin from cells of Phaffia rhodozyma using colloidal gas aphrons (CGA) in a flotation column

The aim of this study is to investigate the separation of astaxanthin from the cells of Phaffia rhodozyma using colloidal gas aphrons (CGA), which are surfactant stabilized microbubbles, in a flotation column. It was reported in previous studies that optimum recoveries are achieved at conditions that favor electrostatic interactions. Therefore, in this study, CGA generated from the cationic surfactant hexadecyl trimethyl ammonium bromide (CTAB) were applied to suspensions of cells pretreated with NaOH. The different operation modes (batch or continuous) and the effect of volumetric ratio of CGA to feed, initial concentration of feed, operating height, and flow rate of CGA on the separation of astaxanthin were investigated. The volumetric ratio was found to have a significant effect on the separation of astaxanthin for both batch and continuous experiments. Additionally, the effect of homogenization of the cells on the purity of the recovered fractions was investigated, showing that the homogenization resulted in increased purity. Moreover, different concentrations of surfactant were used for the generation of CGA for the recovery of astaxanthin on batch mode; it was found that recoveries up to 98% could be achieved using CGA generated from a CTAB solution 0.8 mM, which is below the CTAB critical micellar concentration (CMC). These results offer important information for the scale-up of the separation of astaxanthin from the cells of P. rhodozyma using CGA.

The unsteady flow of a weakly compressible fluid in a thin porous layer II: three-dimensional theory

We consider the problem of determining the pressure and velocity fields for a weakly compressible fluid flowing in a three-dimensional layer, composed of an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting and/or extracting fluid. Numerical solution of this three-dimensional evolution problem may be expensive, particularly in the case that the depth scale of the layer h is small compared to the horizontal length scale l, a situation which occurs frequently in the application to oil and gas reservoir recovery and which leads to significant stiffness in the numerical problem. Under the assumption that $\epsilon\propto h/l\ll 1$, we show that, to leading order in $\epsilon$, the pressure field varies only in the horizontal directions away from the wells (the outer region). We construct asymptotic expansions in $\epsilon$ in both the inner (near the wells) and outer regions and use the asymptotic matching principle to derive expressions for all significant process quantities. The only computations required are for the solution of non-stiff linear, elliptic, two-dimensional boundary-value, and eigenvalue problems. This approach, via the method of matched asymptotic expansions, takes advantage of the small aspect ratio of the layer, $\epsilon$, at precisely the stage where full numerical computations become stiff, and also reveals the detailed structure of the dynamics of the flow, both in the neighbourhood of wells and away from wells.

Continuous-flow processing of gaseous ammonia using a Teflon AF-2400 tube-in-tube reactor: synthesis of thioureas and in-line titrations

A simple tube-in-tube reactor based on the gas-permeable membrane Teflon AF-2400 was used in the continuous flow reaction of gaseous ammonia with isothiocyanates and one isocyanate. A colourimetric in-line titration technique is also reported as a simple method to quantify the amount of ammonia taken up by the solvent in the system.

Field-aligned plasma flow in the quiet, mid-latitude ionosphere deduced from topside soundings

A method for quantifying diffusive flows of O+ ions in the topside ionosphere from satellite soundings is described. A departure from diffusive equilibrium alters the shape of the plasma scale-height profile near the F2-peak where ion-neutral frictional drag is large. The effect enables the evaluation of , the field-aligned flux of O+ ions relative to the neutral oxygen atom gas, using MSIS model values for the neutral thermospheric densities and temperature. Upward flow values are accurate to within about 10%, the largest sources of error being the MSIS prediction for the concentration of oxygen atoms and the plasma temperature gradient deduced from the sounding. Downward flux values are only determined to within 20%. From 60,000 topside soundings, taken at the minimum and rising phase of the solar cycle, a total of 1098 mean scale-height profiles are identified for which no storm sudden commencement had occurred in the previous 12 days and for which Kp was less than 2o, each mean profile being an average of about six soundings. A statistical study ofdeduced from these profiles shows the diurnal cycle of O+ flow in the quiet, topside ionosphere at mid-latitudes and its seasonal variations. The differences betweenand ion flux observations from incoherent scatter radars are considered using the meridional thermospheric winds predicted by a global, three-dimensional model. The mean interhemispheric flow from summer to winter is compared with predictions by a numerical model of the protonospheric coupling of conjugate ionospheres for up to 6 days following a geomagnetic storm. The observed mean (of order 3 × 1016 ions day−1 along a flux tube of area 1 m2 at 1000 km) is larger than predicted for day 6 and the suggested explanation is a decrease in upward flows from the winter, daytime ionosphere between the sixth and twelfth days.