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Analytic Solutions for Flows Through Cascades

  • Book
  • © 2020

Overview

Authors:
  1. Peter Jonathan Baddoo

    1. Department of Mathematics, Massachusetts Institute of Technology, Boston, USA

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  • Nominated as an outstanding Ph.D. thesis by the ?University of Cambridge, Cambridge, United Kingdom
  • Exceptionally clear presentation with beautiful figures
  • Eludicates the fundamental mechanicsms of complicated physical phenomena with sophisticated mathematical analysis
  • Utilises methods from the breadth of applied mathematics, particularly complex analysis

Part of the book series: Springer Theses (Springer Theses)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xvi
    Download chapter PDF

  2. Introduction

    • Peter Jonathan Baddoo
    Pages 1-20

  3. Potential Flow Through Cascades of Thin, Impermeable Aerofoils

    • Peter Jonathan Baddoo
    Pages 21-55

  4. Scattering by Cascades of Aerofoils with Realistic Geometry

    • Peter Jonathan Baddoo
    Pages 57-138

  5. Potential Flow Through Cascades of Thin, Porous Aerofoils

    • Peter Jonathan Baddoo
    Pages 139-163

  6. Scattering by Cascades of Aerofoils with Complex Boundary Conditions

    • Peter Jonathan Baddoo
    Pages 165-212

  7. Potential Flow Through Cascades with Multiple Aerofoils per Period

    • Peter Jonathan Baddoo
    Pages 213-239

  8. The Quasi-Periodic Compact Green’s Function

    • Peter Jonathan Baddoo
    Pages 241-251

  9. Conclusion

    • Peter Jonathan Baddoo
    Pages 253-256

  10. Back Matter

    Pages 257-258
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, Massachusetts Institute of Technology, Boston, USA

    Peter Jonathan Baddoo

About the author

Dr Peter J. Baddoo is an Instructor of Applied Mathematics at MIT. Previously he was an EPSRC Doctoral Prize Fellow at Imperial College London. He recieved a PhD in Applied Mathematics from the University of Cambridge and an MMath from the University of Oxford. His research interests lie in the applications of complex analysis and data-driven techniques to tackle physical problems, such as those arising in fluid dynamics. He is the recipient of several prizes, including "Best Paper" awards from the AIAA and ICA, as well as an Early Career Fellowship from the London Mathematical Society.

Bibliographic Information

  • Book Title: Analytic Solutions for Flows Through Cascades

  • Authors: Peter Jonathan Baddoo

  • Series Title: Springer Theses

  • DOI: https://doi.org/10.1007/978-3-030-55781-2

  • Publisher: Springer Cham

  • eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

  • Hardcover ISBN: 978-3-030-55780-5Published: 01 September 2020

  • Softcover ISBN: 978-3-030-55783-6Published: 01 September 2021

  • eBook ISBN: 978-3-030-55781-2Published: 31 August 2020

  • Series ISSN: 2190-5053

  • Series E-ISSN: 2190-5061

  • Edition Number: 1

  • Number of Pages: XVI, 258

  • Number of Illustrations: 14 b/w illustrations, 61 illustrations in colour

  • Topics: Mathematical Methods in Physics, Engineering Fluid Dynamics, Engineering Acoustics

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