Analytic Solutions For Flows Through Cascades

This thesis is concerned with flows through cascades, i.e. periodic arrays of obstacles. Such geometries are relevant to a range of physical scenarios, chiefly the aerodynamics and aeroacoustics of turbomachinery flows. Despite the fact that turbomachinery is of paramount importance to a number of industries, many of the underlying mechanisms in cascade flows remain opaque. In order to clarify the function of different physical parameters, the author considers six separate problems. For example, he explores the significance of realistic blade geometries in predicting turbomachinery performance, and the possibility that porous blades can achieve noise reductions. In order to solve these challenging problems, the author deploys and indeed develops techniques from across the spectrum of complex analysis: the Wiener–Hopf method, Riemann–Hilbert problems, and the Schottky–Klein prime function all feature prominently. These sophisticated tools are then used to elucidate the underlying mathematical and physical structures present in cascade flows. The ensuing solutions greatly extend previous works and offer new avenues for future research. The results are not of simply academic value but are also useful for aircraft designers seeking to balance aeroacoustic and aerodynamic effects.

The first International Symposium on Unsteady Aerodynamics and Aero elasticity of Turbomachines was held in Paris in 1976, and was followed by symposia at Lausanne in 1980, Cambridge in 1984, Aachen in 1987, Bei jing in 1989, and Notre Dame in 1991. The proceedings published following these symposia have become recognized both as basic reference texts in the subject area and as useful guides to progress in the field. It is hoped that this volume, which represents the proceedings of the Sixth International Symposium on Unsteady Aerodynamics of Turbomachines, will continue that tradition. Interest in the unsteady aerodynamics, aeroacoustics, and aeroelasticity of turbomachines has been growing rapidly since the Paris symposium. This expanded interest is reflected by a significant increase in the numbers of contributed papers and symposium participants. The timeliness of the topics has always been an essential objective of these symposia. Another important objective is to promote an international exchange between scien tists and engineers from universities, government agencies, and industry on the fascinating phenomena of unsteady turbomachine flows and how they affect the aeroelastic stability of the blading system and cause the radiation of unwanted noise. This exchange acts as a catalyst for the development of new analytical and numerical models along with carefully designed ex periments to help understand the behavior of such systems and to develop predictive tools for engineering applications.

A selection of annotated references to unclassified reports and journal articles that were introduced into the NASA scientific and technical information system and announced in Scientific and technical aerospace reports (STAR) and International aerospace abstracts (IAA).