Investigation of boundary layer development in a multistage LP turbine

This paper describes an investigation of the behavior of suction surface boundary layers in a modern multistage Low Pressure turbine. An array of eighteen surface-mounted hot-film anemometers was mounted on a stator blade of the third stage of a 4-stage machine. Data were obtained at Reynolds numbers between 0.9 × 105 and 1.8 × 105 and 1.8 × 105. At the majority of the test conditions, wakes from upstream rotors periodically initiated transition at about 40% surface length. In between these events, laminar separation occurred at about 75% surface length. It is inferred that the effect of the wakes on the performance of the bladerow is limited and that steady flow design methods should provide an adequate assessment of LP turbine performance during design.

Investigation of boundary layer development in a multistage LP turbine

This paper describes an investigation of the behavior of suction surface boundary layers in a modern multistage Low-Pressure turbine. An array of 18 surface-mounted hot-film anemometers was mounted on a stator blade of the third stage of a four-stage machine. Data were obtained at Reynolds numbers between 0.9 × 105 and 1.8 × 105. At the majority of the test conditions, wakes from upstream rotors periodically initiated transition at about 40 percent surface length. In between these events, laminar separation occurred at about 75 percent surface length. Because the wake-affected part of the flow appeared to be only intermittently turbulent, laminar separation also occurred at about 75 percent surface length while this flow was instantaneously laminar. At all but the lowest Reynolds numbers, the time-mean boundary layer appeared to have re-attached by the trailing edge even though it was not fully turbulent. It is inferred that the effect of the wakes on the performance of the blade row is limited and that steady flow design methods should provide an adequate assessment of LP turbine performance during design.

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.

Uniform stability of a particle approximation of the optimal filter derivative

Sequential Monte Carlo methods, also known as particle methods, are a widely used set of computational tools for inference in non-linear non-Gaussian state-space models. In many applications it may be necessary to compute the sensitivity, or derivative, of the optimal filter with respect to the static parameters of the state-space model; for instance, in order to obtain maximum likelihood model parameters of interest, or to compute the optimal controller in an optimal control problem. In Poyiadjis et al. [2011] an original particle algorithm to compute the filter derivative was proposed and it was shown using numerical examples that the particle estimate was numerically stable in the sense that it did not deteriorate over time. In this paper we substantiate this claim with a detailed theoretical study. Lp bounds and a central limit theorem for this particle approximation of the filter derivative are presented. It is further shown that under mixing conditions these Lp bounds and the asymptotic variance characterized by the central limit theorem are uniformly bounded with respect to the time index. We demon- strate the performance predicted by theory with several numerical examples. We also use the particle approximation of the filter derivative to perform online maximum likelihood parameter estimation for a stochastic volatility model.