On K\"ahler conformal compactifications of U(n)U(n)-invariant ALE spaces

We prove that a certain class of ALE spaces always has a Kahler conformal compactification, and moreover provide explicit formulas for the conformal factor and the Kahler potential of said compactification. We then apply this to give a new and simple construction of the canonical Bochner-K\"ahler metric on certain weighted projective spaces, and also to explicitly construct a family Kahler edge-cone metrics on $\mathbb{CP}^2$, with singular set $\mathbb{CP}^1$, having cone angles $2\pi\beta$ for all $\beta>0$. We conclude by discussing how these results can be used to obtain certain well-known Einstein metrics.Comment: 14 page

A Summary of Computations of Ingestion at the University of Bath

Rim seals in gas turbines are used to reduce the potentiallydamaging ingestion of hot gas into the rotor-stator wheel-space of aturbine stage. Sealing air, bled from the compressor, is also used toreduce or prevent ingestion, but this can be at the expense of stageefficiency.This paper summarises recent research into the computation ofthe fluid dynamics and heat transfer of ingestion carried out at theUniversity of Bath. 3D Unsteady Reynolds-averaged Navier-Stokes (URANS) simulations have been carried out, and muchmore economical simplified steady state computational modelshave also been tested. The results of the computations are comparedwith experimental measurements (also made at the University) ofpressure, tracer gas concentration based sealing effectiveness, swirland heat transfer for different generic and also engine-representative rim seals. The computations allow insight intothe flow physics of ingestion and factors affecting the most efficientuse of sealing air, as well as providing information to support thedevelopment of the theoretical models of ingestion that are usefulto engine designers. The experimental test facility permits measurementand ranking of sealing effectiveness for a range of differentrim seal configurations