Stator well flows in axial compressors

This paper reports a study of the flow conditions in spaces often found beneath the stationary blades of modern compressors – stator wells. The design of the stator wells in a modern high-pressure turbofan can be a limiting factor. This study shows good comparison with existing experimental data upon the pressures and velocities in related geometries. The deleterious effects upon machine performance of the flows between the stator well and the mainstream are considered. The purpose of this paper is to show that these effects, especially seal leakage, can be reduced by the incorporation of fins on the rotating component of the downstream well. This works by increasing the tangential velocity in this region, so reducing the pressure there and thus the inter-well leakage for a given radial clearance in the intermediate labyrinth seal and hence the outflow into the mainstream from the upstream well.     

Discharge coefficients for flow through holes normal to a rotating shaft

A possible design for a more compact gas turbine engine uses contra-rotating high pressure (HP) and intermediate pressure (IP) turbine discs. Cooling air for the IP turbine stages is taken from the compressor and transferred to the turbine stage via holes in the drive shaft. The aim of this work was to investigate the discharge coefficient characteristics of the holes in this rotating shaft, and, in particular, to ascertain whether the sense of rotation of the shaft with respect to the discs affected these significantly. This paper reports mostly on experimental measurements of the discharge coefficients. Some CFD modelling of this flow was carried out and this has helped to explain the experimental work. The experimental results show the effects on the discharge coefficient of rotational speed, flow rate, and co- and contra-rotations of the shaft relative to the discs. The measured values of the discharge coefficient are compared with established experimental data for non-rotating holes in the presence of a cross-flow. For stationary shaft and discs, co-rotation of the shaft and discs and differential rotation with the disc speed less than the shaft (in the same rotational direction), the discharge coefficients are in reasonable agreement with these data. For differential rotation (including contra-rotation) with the disc speed greater than the shaft, there is a significant decrease in discharge coefficient.     

Finite aperiodic semigroups with commuting idempotents and generalizations

It is proved that any pseudovariety of finite semigroups generated by inverse semigroups, the subgroups of which lie in some proper pseudovariety of groups, does not contain all aperiodic semigroups with commuting idempotents. In contrast we show that every finite semigroup with commuting idempotents divides a semigroup of partial bijections that shares the same subgroups. Finally, we answer in the negative a question of Almeida as to whether a result of Stiffler characterizing the semidirect product of the pseudovarieties ofR-trivial semigroups and groups applies to any proper pseudovariety of groups.     

Polysiloxane-Modified Mesoporous Materials

We report the preparation of polysiloxane-modified mesoporous silica gels derived from the acid catalysed hydrolysis of tetraethoxysilane (TEOS) and oligomeric silanol terminated polydimethylsiloxane (PDMS) in the presence of the non-ionic surfactant, octaethylene glycol monohexadecyl ether. The gels were characterised using thermal gravimetric analysis (TGA), infra-red (IR) spectroscopy, X-ray diffraction (XRD) and ²⁹Si solid state cross-polarisation (CP) magic-angle spinning (MAS) nuclear magnetic resonance (NMR) spectroscopy. TGA and IR spectroscopy showed the loss of surfactant after calcination and a decrease in the Si–OH band at 950 cm^–1 indicated further condensation had occurred. This was confirmed by the increase in Q⁴ at –110 ppm, in ²⁹Si MAS NMR spectroscopy, which also showed that calcination had led to the redistribution of PDMS forming a T species. XRD data showed ordering within the structure, with an initial d-spacing of 45 Å, decreasing to 35 Å after calcination.     

A Variational Approximation Scheme for¶Three-Dimensional Elastodynamics¶with Polyconvex Energy

We construct a variational approximation scheme for the equations of three-dimensional elastodynamics with polyconvex stored energy. The scheme is motivated by some recently discovered geometric identities (Qin [18]) for the null Lagrangians (the determinant and cofactor matrix), and by an associated embedding of the equations of elastodynamics into an enlarged system which is endowed with a convex entropy. The scheme decreases the energy, and its solvability is reduced to the solution of a constrained convex minimization problem. We prove that the approximating process admits regular weak solutions, which in the limit produce a measure-valued solution for polyconvex elastodynamics that satisfies the classical weak form of the geometric identities. This latter property is related to the weak continuity properties of minors of Jacobian matrices, here exploited in a time-dependent setting. Accepted November 18, 2000?Published online April 23, 2001