Mean and fluctuating pressure in boat-tail separated flows at transonic speeds

Experiments were carried out investigating the features of mean and unsteady surface pressure fluctuations in boat-tail separated flows relevant to launch vehicle configurations at transonic speeds. The tests were performed on a generic axisymmetric body in the Mach-number range of 0.7-1.2, and the important geometrical parameters, namely, the boat-tail angle and diameter ratio, were varied systematically. The measurements made included primarily the mean and unsteady surface-pressure fluctuations on nine different model configurations. Flow-visualization studies employing a surface oil flow, and schlieren techniques were carried out to infer features like boundary-layer separation, reattachment, and shock waves in the flow. The features of mean and fluctuating surface pressures are discussed in detail including aspects of similarity. It has been observed that, on a generic configuration employed in the present study, the maximum levels of surface-pressure fluctuations in the reattachment zone are appreciably lower than those found on launch vehicle configurations having a bulbous or hammerhead nose shape. A simple correlation is suggested for the maximum value of rms pressure fluctuations in the reattachment zone at different freestream Mach numbers.

Organometallic chemistry of chiral diphosphazane ligands: Synthesis and structural characterisation

The diphosphazane ligands of the type, (C20H12O2)PN(R)P(E)Y2 (R = CHMe2 or (S)-*CHMePh; E = lone pair or S; Y2 = O2C20H12 or Y = OC6H5 or OC6H4Me-4 or OC6H4OMe-4 or OC6H4But-4 or C6H5) bearing axially chiral 1,1'-binaphthyl-2,2′-dioxy moiety have been synthesised. The structure and absolute configuration of a diastereomeric palladium complex, [PdCl2{ηsu2}-((O2C20H12)PN((S)-*CHMePh)PPh2] has been determined by X-ray crystallography. The reactions of [CpRu(PPh3)2Cl] with various symmetrical and unsymmetrical diphosphazanes of the type, X2PN(R)PYY′ (R = CHMe2 or (S)-*CHMePh; X = C6H5 or X2 = O2C20H12; Y=Y′= C6H5 or Y = C6H5, Y′ = OC6H4Me-4 or OC6H3Me2-3,5 or N2C3HMe2-3,5) yield several diastereomeric neutral or cationic half-sandwich ruthenium complexes which contain a stereogenic metal center. In one case, the absolute configuration of a trichiral ruthenium complex, viz. [Cp*Ruη2-Ph2PN((S)-*CHMePh)*PPh (N2C3HMe2-3,5)Cl] is established by X-ray diffraction. The reactions of Ru3(CO)12 with the diphosphazanes (C20H12O2)PN(R)PY2 (R = CHMe2orMe; Y2=O2C20H12or Y= OC6H5 or OC6H4Me-4 or OC6H4OMe-4 or OC6H4But-4 or C6H5) yield the triruthenium clusters [Ru3(CO)10{η-(O2C20H12)PN(R)PY2}], in which the diphosphazane ligand bridges two metal centres. Palladium allyl chemistry of some of these chiral ligands has been investigated. The structures of isomeric η3-allyl palladium complexes, [Pd(η3-l,3-R′2-C3H3){η2-(rac)-(02C20H12)PN(CHMe2)PY2}](PF6) (R′ = Me or Ph; Y = C6H5 or OC6H5) have been elucidated by high field two-dimensional NMR spectroscopic and X-ray crystallographic studies.

Organometallic chemistry of diphosphazanes. Part 15. Half-sandwich cyclopentadienyl ruthenium complexes of achiral and chiral diphosphazanes

Reaction of [CpRu(PPh3)(2)Cl] (1) {Cp = eta(5)-(C5H5)} with X2PN(CHMe2) PYY' {X = Y = Y' = Ph (L-1); X = Y = Ph, Y' = OC6H4Me-4 (L-4); X = Y = Ph, Y' = OC6H3Me2- 3,5 (L-5); X = Y = Ph, Y' = N2C3HMe2 (L-6)} yields the cationic chelate complexes, [CpRu(eta(2)-(X2PN(CHMe2) PYY')) PPh3] Cl. On the other hand, the reaction of 1 with X2PN(CHMe2)PYY' {X = Ph, YY' = O2C6H4(L-3)} gives the complex, [CpRu(eta(1)-L-2)(2)PPh3] Cl. Both types of complexes are formed with X2PN(CHMe2) PYY' {X = Ph, YY' = O2C6H4 (L-3)}. The reaction of 1 with (R),(S)-(H12C20O2) PN(CHMe2) PPh2 (L-7) yields both cationic and neutral complexes, [CpRu{eta(2)-(L-7)} PPh3] Cl and [CpRu{eta(1)-(L-7)}(2)PPh3] Cl and [CpRu{eta(2)-(L-7)}Cl]. The reactions of optically pure diphosphazane, Ph2PN(*CHMePh) PPhY (Y = Ph (L-8); Y = N2C3HMe2-3,5 (L-9)) with 1 give the neutral and cationic ruthenium complexes, [CpRu{eta(2)-(Ph2PN(R) PPhY)} Cl] and [CpRu{eta(2)-(Ph2PN(R)PPhY)} PPh3] Cl. "Chiral-at-metal" ruthenium complexes of diphosphazanes have been synthesized with high diastereoselectivity. The absolute configuration of a novel ruthenium complex, (SCSPRRu)-[(eta(5)-C5H5) Ru*{eta(2)-(Ph2PN(*CHMePh)P*Ph( N2C3HMe2-3,5))} Cl] possessing three chiral centers, is established by X-ray crystallography. The reactions of [CpRu{eta(2)-(L-8)} Cl] with mono or diphosphanes in the presence of NH4PF6 yield the cationic complexes, [CpRu{eta(2)-(L-8)}{eta(1)-(P)}] PF6 {P = P(OMe)(3), PPh3, Ph2P(CH2)(n)PPh2 (n = 1 or 2)}.

A differential-geometric analysis of singularities of point trajectories of serial and parallel manipulators

In this paper, we present a differential-geometric approach to analyze the singularities of task space point trajectories of two and three-degree-of-freedom serial and parallel manipulators. At non-singular configurations, the first-order, local properties are characterized by metric coefficients, and, geometrically, by the shape and size of a velocity ellipse or an ellipsoid. At singular configurations, the determinant of the matrix of metric coefficients is zero and the velocity ellipsoid degenerates to an ellipse, a line or a point, and the area or the volume of the velocity ellipse or ellipsoid becomes zero. The degeneracies of the velocity ellipsoid or ellipse gives a simple geometric picture of the possible task space velocities at a singular configuration. To study the second-order properties at a singularity, we use the derivatives of the metric coefficients and the rate of change of area or volume. The derivatives are shown to be related to the possible task space accelerations at a singular configuration. In the case of parallel manipulators, singularities may lead to either loss or gain of one or more degrees-of-freedom. For loss of one or more degrees-of-freedom, ther possible velocities and accelerations are again obtained from a modified metric and derivatives of the metric coefficients. In the case of a gain of one or more degrees-of-freedom, the possible task space velocities can be pictured as growth to lines, ellipses, and ellipsoids. The theoretical results are illustrated with the help of a general spatial 2R manipulator and a three-degree-of-freedom RPSSPR-SPR parallel manipulator.