Projective Limit Random Probabilities on Polish Spaces

A pivotal problem in Bayesian nonparametrics is the construction of prior distributions on the space M(V) of probability measures on a given domain V. In principle, such distributions on the infinite-dimensional space M(V) can be constructed from their finite-dimensional marginals---the most prominent example being the construction of the Dirichlet process from finite-dimensional Dirichlet distributions. This approach is both intuitive and applicable to the construction of arbitrary distributions on M(V), but also hamstrung by a number of technical difficulties. We show how these difficulties can be resolved if the domain V is a Polish topological space, and give a representation theorem directly applicable to the construction of any probability distribution on M(V) whose first moment measure is well-defined. The proof draws on a projective limit theorem of Bochner, and on properties of set functions on Polish spaces to establish countable additivity of the resulting random probabilities.

Unsteady transition in an axial-flow turbine. Part 2. Cascade measurements and modeling

Part 1 of this paper reanalyzed previously published measurements from the rotor of a low-speed, single-stage, axial-flow turbine, which highlighted the unsteady nature of the suction surface transition process. Part 2 investigates the significance of the wake jet and the unsteady frequency parameter. Supporting experiments carried out in a linear cascade with varying inlet turbulence are described, together with a simple unsteady transition model explaining the features of seen in the turbine.

Unsteady transition in an axial-flow turbine. Part 1. Measurements on the turbine rotor

Previously published measurements in a low-speed, single-stage, axial-flow turbine have been reanalyzed in the light of more recent understanding. The measurements include time-resolved hot-wire traverses and surface hot film gage measurements at the midspan of the rotor suction surface with three different rotor-stator spacings. This paper investigates the suction surface boundary layer transition process, using surface-distance time plots and boundary layer cross sections to demonstrate the unsteady and two-dimensional nature of the process.

Intermittency transport modeling of separated flow transition

An intermittency transport model is proposed for modeling separated-flow transition. The model is based on earlier work on prediction of attached flow bypass transition and is applied for the first time to model transition in a separation bubble at various degrees of free-stream turbulence. The model has been developed so that it takes into account the entrainment of the surrounding fluid. Experimental investigations suggest that it is this phenomena which ultimately determines the extent of the separation bubble. Transition onset is determined via a boundary layer correlation based on momentum thickness at the point of separation. The intermittent flow characteristic of the transition process is modeled via an intermittency transport equation. This accounts for both normal and streamwise variation of intermittency and hence models the entrainment of surrounding flow in a more accurate manner than alternative prescribed intermittency models. The model has been validated against the well established T3L semicircular leading edge flat plate test case for three different degrees of free-stream turbulence characteristic of turbomachinery blade applications.

The transition mechanism of highly-loaded LP turbine blades

A detailed experimental investigation was conducted into the interaction of a converted wake and a separation bubble on the rear suction surface of a highly loaded low-pressure (LP) turbine blade. Boundary layer measurements, made with 2D LDA, revealed a new transition mechanism resulting from this interaction. Prior to the arrival of the wake, the boundary layer profiles in the separation region are inflexional. The perturbation of the separated shear layer caused by the converting wake causes an inviscid Kelvin-Helmholtz rollup of the shear layer. This results in the breakdown of the laminar shear layer and a rapid wake-induced transition in the separated shear layer.