A mixed algorithm for the calculation of rapidly varying fluid flows: The impulsively started circular cylinder

A mixed discrete Fourier transform-Finite difference algorithm is developed and used for the calculation of rapidly changing viscous fluid flows past a circular cylinder. The numerical approach has been designed to overcome certain difficulties arising for high Reynolds number simulations. The foremost advantage of the technique lies in its fast calculations of the convolution sums portraying the convective terms of the governing equations. Third-order spatial discretizations and fourth-order time marching are implemented. New schemes are proposed for the boundary conditions at the solid wall and at large distances. The techniques are tested on a case study with other schemes (summarized by Roache¹) in order to obtain an optimal choice. Definite indications on the stability and accuracy of boundary condition schemes are achieved. Support for the statement of dominant importance of boundary conditions is also given. A comparison of computational results with experimental data is presented for the case study of the flow past an impulsively started cylinder at Reynolds number 20. The time development of the symmetrical zone of recirculation, which is formed at an early stage of the flow, has been studied for 300 ≤ Re ≤ 9500 by means of the proposed algorithm. Computational results, comparisons with experimental data² and discussion of upper limits of validity of the procedure will be presented in a companion paper.     

A Convenient Procedure for he Synthesis o 2,3,4,6-Tetra-O-benzyl-D-gluconolactam and D-Nojirilactam

Swern oxidation of 2,3,4,5-tetra-O-benzyl-D -glucose ( 1 ) followed by ammonolysis gave the crystalline amide 3 which was oxidized (DMSO/pyridine · SO₃) to yield the oxo-amide 4 and the hydroxy-lactams 5 and 6 . Cyclization of 4 to the very slowly equilibrating 5 and 6 was completed by treatment with AcOH in CHCl₃. The configuration of the hydroxy-lactams was assigned on the basis of NOEs. Reduction (Et₃SiH/BF₃ · Et₂O) of the hydroxy-lactams either individually or as a mixture led to 2,3,4,6-tetra-O-benzyl-_D-gluconolactam ( 7 ). The procedure, based upon modifications of a patent, does not require chromatography; the overall yield of 7 from 1 is 43%. Hydrogenolysis of 7 gave _D-nojirilactam ( 8 ); benzylation led to the known pentabenzyl-_D-nojirilactam ( 9 ) and to the unsaturated lactam 10 .     

Synthesis,reactivity and X-ray structure of the complex [(depe)2Fe(S2CPEt3)](BPh4)2 (depe = 1,2-bis(diethylphosphino)ethane)

The reaction of the zwitterion Et₃PCS₂, with iron (II) tetrafluoroborate in the presence of 1,2-bis(diethylphosphino) ethane (depe) and NaBPh₄ gave the unusual complex [(depe)₂Fe(S₂CPEt₃)] (BPh₄)₂ (I), whose structure has been determined by X-ray analysis. A dithioformatoiron(II) complex was made by treating I with NaBH₄.     

Binding energy of a hydrogen impurity in an f.c.c. lattice

Hydrogen impurities in f.c.c. lattices, Pd metal for example, can occupy two interstitial sites, with tetrahedral or octahedral symmetries. Using the Husimi cactus to represent the f.c.c. lattice and two clusters to describe the two different interstices, we calculate the densities of states and the occupation numbers at the impurity site and on its nearest neighbours. The binding energies are calculated and plotted against the hopping integral between the hydrogen and its neighbours (t_a). We found that the octahedral site is the stable one for values of t_a from 0 to 1.5 eV.     

Photooxidation of 1,3-butadiene containing systems: Rate constant determination for the reaction of acrolein with ⋅OH radicals

The photooxidation of the 1,3-butadiene–NO–air system at 298 ± 2 K was investigated in an environmental chamber under simulated atmospheric conditions. The irradiation gave rise to the formation of acrolein in a 55% yield, based on 1,3-butadiene initial concentration for all the experimental runs. The rate of formation of acrolein was the same as that of 1,3-butadiene consumption, indicating that acrolein is the major product of the 1,3-butadiene oxidation in air. The dependence of acrolein concentration on irradiation time showed thata secondary process, identified as an oxidation of acrolein by ^?OH radicals, was occurring during the photochemical runs. The rate constant of this secondary process was determined by measuring the relative rates of disappearance of acrolein and n-butane during the irradiation of acrolein-n-butane-NO-air mixtures. The so obtained relative rate constant value was placed on an absolute basis using a reported rate constant for the n-butane + ^?OH reaction; a value of (1.6 ± 0.2) × 10¹⁰ M^?1 sec^?1 was obtained.     

A one pot, metathesis-hydrogenation sequence for the selective formation of carbon-carbon bonds

A combination of homogeneous hydrogenation and metathesis reactions allows highly efficient, stepwise chemo- and stereoselective formation of three separate 2,7-diaminosuberic acid derivatives in a single pot without isolation of intermediates.