Optimal control of unsteady compressible viscous flows

The control of complex, unsteady flows is a pacing technology for advances in fluid mechanics. Recently, optimal control theory has become popular as a means of predicting best case controls that can guide the design of practical flow control systems. However, most of the prior work in this area has focused on incompressible flow which precludes many of the important physical flow phenomena that must be controlled in practice including the coupling of fluid dynamics, acoustics, and heat transfer. This paper presents the formulation and numerical solution of a class of optimal boundary control problems governed by the unsteady two‐dimensional compressible Navier–Stokes equations. Fundamental issues including the choice of the control space and the associated regularization term in the objective function, as well as issues in the gradient computation via the adjoint equation method are discussed. Numerical results are presented for a model problem consisting of two counter‐rotating viscous vortices above an infinite wall which, due to the self‐induced velocity field, propagate downward and interact with the wall. The wall boundary control is the temporal and spatial distribution of wall‐normal velocity. Optimal controls for objective functions that target kinetic energy, heat transfer, and wall shear stress are presented along with the influence of control regularization for each case. Copyright © 2002 John Wiley & Sons, Ltd.     

Mono-cyclopentadienyl complexes of lanthanum: synthesis and characterization of anilido derivatives

Use of the bulky cyclopentadienyl ligand [η⁵-C₅H₂(SiMe₃)₃-1,2,4]⁻ (Cp?) allows for the isolation of monomeric, mono-ring lanthanide species. As previously reported, (Cp?)K reacts with LaI₃(THF)₄ (THF=tetrahydrofuran) in THF/pyridine to form the mono-ring complex (Cp?)LaI₂(py)₃ (1) (py=pyridine); a minor product of this reaction is the bis-ring species (Cp?)₂LaI(py) (2). The solid state structure of 2 reveals a monomeric compound containing a pseudo-tetrahedral metal center exhibiting no unusual intramolecular contacts. Addition of one equiv of KNHAr (Ar=2,6-ⁱPr₂C₆H₃) to complex 1 in THF generates the mono-anilido compound (Cp?)LaI(NHAr)(THF)₂ (3), which may be converted to the more stable pyridine adduct (Cp?)LaI(NHAr)(py)₂ (4) by the addition of pyridine to 3. An X-ray crystal structure of 3 indicated a trigonal bipyramidal metal center with the anilido group oriented trans to the iodide atom (N1-La1-I1=123.1(3)°). A structural study on the bis-pyridine adduct 4 revealed a similar C_s-symmetric structure with a slightly increased N_anilido-La-I angle of 132.1(2)°. Addition of KNHAr to the di-iodo bipyridine adduct (Cp?)LaI₂(bipy)(py) (5), in which the two iodide atoms are cis-disposed, yields the mono-anilido complex (Cp?)LaI(NHAr)(bipy)(py) (6) (bipy=2,2^′-bipyridine); this compound may also be prepared by the addition of bipy to (Cp?)LaI(NHAr)(py)₂ (4). An X-ray diffraction study shows that the lanthanum center in 6 is octahedrally coordinated by a Cp? ring, an iodide, an anilido group, a pyridine molecule and two nitrogens of a bipy molecule. In this case, the anilido moiety and the iodide ligand are arranged in a cis fashion (N_anilido-La-I=111.2(2)°), resulting in a complex with C₁ symmetry. Both (Cp?)LaI(NHAr)(py)₂ (4) and (Cp?)LaI(NHAr)(bipy)(py) (6) are inactive as catalysts for the hydroamination/cyclization of 2-amino-hex-5-ene.     

New synthetic pathways into dithiazolyl radicals: Preparation and characterisation of 3′-methyl-benzo-1,3,2-dithiazolyl, M’BDTA

A general three-step synthesis to a range of benzo-fused-1,3,2-dithiazolylium salts bearing both electron-withdrawing (CN) and electron-donating (Me) groups is described. This methodology has also been extended to pyridyl derivatives and offers a potential route to a diversity of 1,3,2-dithiazolylium rings and their corresponding 1,3,2-dithiazolyl free radicals. The key steps in the reaction are treatment of a substituted 1,2,-dichlorobenzene with two equivalents of [^tBuS]Na, followed by chlorination to yield the corresponding bis(sulfenyl chloride). Subsequent ring closure with Me₃SiN₃ yields the target 1,3,2-dithiazolylium ring system in good yield. The preparation and crystal structures of 3′-methyl-benzo-1,3,2-dithiazolylium chloride and 3′-methyl-benzo-1,3,2-dithiazolyl are described and the electronic properties of the radical examined through EPR spectroscopy, DFT calculations and variable temperature magnetic susceptibility measurements.