A NUMERICAL SOLUTION OF THE FLOW AROUND A SPHERE IN A CIRCULAR CYLINDER

A numerical solution of the Navier-Stokes equations is presented for Poiseuille flow around an axially placed, fixed sphere in a circular cylinder. Streamlines and isovorticity lines are calculated from the governing equations for the strearnfunction and the vorticity. Isobars are calculated from a Poisson equation, derived from the Navier-Stokes equations. The pressure and vorticity distribution on the surface of the sphere, the additional pressure drop and the drag coefficients are presented. Solutions are obtained for Reynolds numbers up to 150 (based on cylinder diameter and mean velocity). The wall effects are examined by comparison with results of previous investigations for an unbounded flow around a sphere.     

The content and composition of sterols and sterol esters in low erucic acid rapeseed (Brassica napus)

The low temperature crystallization technique for the enrichment of “minor” components, such as sterols and sterol esters, from vegetable oils was applied to low erucic acid rapeseed oils. The recovery of free sterols and sterol esters was estimated by use of¹⁴C-cholesterol and¹⁴C-cholesterol oleate. 80% of the free sterols and 45% of the sterol esters were recovered in the liquid fraction, while in two studies total recoveries were 95% and 99%, respectively. This technique showed some selectivity toward the sterol bound fatty acids when compared to direct preparative thin layer chromatography (TLC) of the crude oil. Gas liquid chromatography (GLC) analysis of the free and esterified sterols as TMS-derivatives showed very little selectivity in the enrichment procedure. The fatty acid patterns of the sterol esters demonstrated, however, a preference in the liquid fraction for those sterol esters which have a high linoleic and linolenic acid content. The content of free sterols was 0.3–0.4% and that of sterol esters 0.7–1.2% of the rapeseed oils in both winter and summer types of low erucic acid rapeseed (Brassica napus) when the lipid classes were isolated by direct preparative TLC of the oils. The free sterols in the seven cultivars or breeding lines analyzed were composed of 44–55% sitosterol, 27–36% campesterol, 17–21% brassicasterol, and a trace of cholesterol. The esterified sterols were 47–57% sitosterol, 36–44% campesterol, 6–9% brassicasterol, and traces of cholesterol and Δ5-avenasterol. The fatty acid patterns of these esters were characterized by ca. 30% oleic acid and ca. 50% linoleic acid, whereas these acids constitute 60% and 20%, respectively, of the total fatty acids in the oil. Little or no variation in sterol and sterol ester patterns with locality within Sweden was observed for the one cultivar of summer rapeseed investigated by the low temperature crystallization technique.     

Adsorption on activated carbon in countercurrent flow: An experimental study

The work describes adsorption experiments from aqueous solutions on activated carbon using a counter-current adsorber. Phenol and paranitrophenol were used for single component adsorption and molasses colour for multicomponent adsorption experiments. Isotherms were determined using simple equilibrium experiments. Three different techniques were used for determination of the kinetics. These were finite bath, infinite bath and fixed bed experiments. A mathematical model for countercurrent adsorption was tested. The model includes the effect of film diffusion and pore diffusion as well as surface diffusion, and can handle systems with a nonlinear isotherms. Kinetic data in the form of an average diffusivity in the carbon determined from the finite bath experiments and isotherm data did not predict the operation of the countercurrent column well. Data from the fixed bed experiments predicted countercurrent column operation much better. This is deemed to be due to inhomogeneities in the carbon used, resulting in a fairly quick initial uptake of the main part of the solute and a slower uptake of a minor amount.     

Hydrodynamics and steel tube wastage in a fluidized bed at elevated temperature

Hydrodynamic measurements were made in a bubbling fluidized bed operated at 550°C at three different excess gas velocities (0.15, 0.40 and ). The bed has a cross-sectional area of with an immersed tube bank consisting of 59 horizontal stainless steel tubes (AISI 304L), 21 of which are exchangeable, thus allowing erosion studies. Capacitance probe analysis was used to determine the mean bubble rise velocity, the mean bubble frequency, the mean pierced bubble length, the mean bubble volume fraction and the mean visible bubble flow rate. Tube wastage was calculated from roundness profiles obtained by stylus profilometry.A redistribution of the bubble flow towards the center of the bed occurs when the excess gas velocity is increased. Measurements along a target tube, situated next to the capacitance probe, usually show greater material wastage at the central part of the tube, since the mean bubble rise velocity and the mean visible bubble flow rate are higher there. It is suggested that the greater material degradation is also an effect of the through-flow of a particle-transporting gas stream in the bubbles. With increasing height above the distributor plate the circumferential wastage profiles for the lowest excess gas velocity show a gradual change from an erosion pattern with one maximum (Type B behavior) to a pattern with two maxima (Type A behavior). Power spectral density distributions of the fluctuating pressure signals show that this is a result of the formation of larger bubbles, when the fluidization regime is changed in the upper part of the bed. At the highest excess gas velocity the bubble flow becomes more constrained due to a more rapid coalescence of the bubbles and the tubes show Type A wastage profiles throughout the bed.     

The Inhibitive Effect of Traces of SO2 on the Oxidation of Iron

The oxidation of Fe was investigated at 500–700°C in the presence of O₂ with 0–1000 ppm SO₂. The exposures were carried out in a thermobalance and lasted for 24 h. The oxidized samples were investigated by grazing-angle XRD, SEM/EDX, GDOES and XPS. The rate of oxidation of pure iron is slowed down by traces of O₂ in O₂ below 600°C while SO₂ has no effect on oxidation rate at higher temperatures. Exposure to SO₂<600°C resulted in the formation of small amounts of sulfate at the gas/oxide interface. In addition, sulfur, probably sulfide, accumulated at the metal/oxide interface. The influence of SO₂ on oxidation rate is attributed to surface sulfate. The sulfur distribution in the scale is rationalized in terms of the thermodynamic stability of compounds in the Fe–O–S system. Exposure to SO₂ caused the formation of hematite whiskers.     

The influence of thermal annealing on residual stresses and mechanical properties of arc-evaporated TiCxN1−x (x=0, 0.15 and 0.45) thin films

We report the stress relaxation behavior of arc-evaporated TiC_xN_1−x thin films during isothermal annealing between 350 and 900°C. Films with x=0, 0.15, and 0.45, each having an initial compressive intrinsic stress σ_int=−5.4 GPa, were deposited by varying the substrate bias V_s and the gas composition. Annealing above the deposition temperature leads to a steep decrease in the magnitude of σ_int to a saturation stress value, which is a function of the annealing temperature. The corresponding apparent activation energies for stress relaxation are E_a=2.4, 2.9, and 3.1 eV, for x=0, 0.15, and 0.45, respectively. TiC_0.45N_0.55 films with a lower initial stress σ_int=−3 GPa, obtained using a high substrate bias, show a higher activation energy E_a=4.2 eV. In all the films, stress relaxation is accompanied by a decrease in defect density indicated by the decreased width of X-ray diffraction peaks and decreased strain contrast in transmission electron micrographs. Correlation of these results with film hardness and microstructure measurements indicates that the stress relaxation is a result of point-defect annihilation taking place both during short-lived metal-ion surface collision cascades during deposition, and during post-deposition annealing by thermally activated processes. The difference in E_a for the films of the same composition deposited at different V_s suggests the existence of different types of point-defect configurations and recombination mechanisms.     

Computing Minimum Area Homologies

Calculating and categorizing the similarity of curves is a fundamental problem which has generated much recent interest. However, to date there are no implementations of these algorithms for curves on surfaces with provable guarantees on the quality of the measure. In this paper, we present a similarity measure for any two cycles that are homologous, where we calculate the minimum area of any homology (or connected bounding chain) between the two cycles. The minimum area homology exists for broader classes of cycles than previous measures which are based on homotopy. It is also much easier to compute than previously defined measures, yielding an efficient implementation that is based on linear algebra tools. We demonstrate our algorithm on a range of inputs, showing examples which highlight the feasibility of this similarity measure.     

Distributed non-cooperative robust MPC based on reduced-order models

In this paper, a non-cooperative distributed MPC algorithm based on reduced order model is proposed to stabilize large-scale systems. The large-scale system consists of a group of interconnected subsystems. Each subsystem can be partitioned into two parts: measurable part, whose states can be directly measured by sensors, and the unmeasurable part. In the online computation phase, only the measurable dynamics of the corresponding subsystem and neighbour-to-neighbour communication are necessary for the local controller design. Satisfaction of the state constraints and the practical stability are guaranteed while the complexity of the optimization problem is reduced. Numerical examples are given to show the effectiveness of this algorithm.     

Combining the triangle method with thermal inertia to estimate regional evapotranspiration — Applied to MSG-SEVIRI data in the Senegal River basin

Spatially distributed estimates of evaporative fraction and actual evapotranspiration are pursued using a simple remote sensing technique based on a remotely sensed vegetation index (NDVI) and diurnal changes in land surface temperature. The technique, known as the triangle method, is improved by utilizing the high temporal resolution of the geostationary MSG-SEVIRI sensor. With 15 min acquisition intervals, the MSG-SEVIRI data allow for a precise estimation of the morning rise in land surface temperature which is a strong proxy for total daytime sensible heat fluxes. Combining the diurnal change in surface temperature, dT_s with an interpretation of the triangular shaped dT_s − NDVI space allows for a direct estimation of evaporative fraction. The mean daytime energy available for evapotranspiration (R_n − G) is estimated using several remote sensors and limited ancillary data. Finally regional estimates of actual evapotranspiration are made by combining evaporative fraction and available energy estimates. The estimated evaporative fraction (EF) and actual evapotranspiration (ET) for the Senegal River basin have been validated against field observations for the rainy season 2005. The validation results showed low biases and RMSE and R² of 0.13 [−] and 0.63 for EF and RMSE of 41.45 W m^− 2 and R² of 0.66 for ET.