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Published in:
Introduction and Literature Review Read chapter Read first chapter

2021 | OriginalPaper | Chapter

3. Uncertain Power from a Hydro-Kinetic Turbine in Steady Flow

Author : Monika Johanna Kreitmair

Published in: The Effect of Uncertainty on Tidal Stream Energy Resource Estimates

Publisher: Springer International Publishing

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Abstract

This chapter examines the influence of uncertainty in bed friction on hydro-kinetic power extracted from steady flow through a strait represented by a one-dimensional open channel in the stream-wise direction. The flow is driven by a constant head difference between the channel ends. First, an analytic closed-form solution for the power in terms of bed roughness coefficient \(C_d\) from a steady one-dimensional model is derived. Next, three methods for the propagation of uncertainty from bed friction to power estimates are compared.

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previous chapter Derivation of the Shallow Water Equations
next chapter Uncertainty in Background Friction
Footnotes
1
An \( m \times m\) system of partial differential equations of the form of a conservation law \(\partial _t \mathbf {q} + \partial _x \mathbf {f} = \mathbf {s}\) may be classified by considering the quasi-linear form \(\partial _t \mathbf {q} + \mathbf {A} \partial _x \mathbf {q} = \mathbf {s}\). Here \(\mathbf {A}\) is the Jacobian matrix \(\mathbf {A} = \partial _{\mathbf {q}} \mathbf {f}\), with eigenvalues \(\lambda _i\), \(i=1, 2, \ldots , m\). A \(2 \times 2\) system with two distinct and real eigenvalues is strictly hyperbolic and has two linearly independent eigenvectors defining the characteristics of the system (see [16]).
 
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Metadata
Title
Uncertain Power from a Hydro-Kinetic Turbine in Steady Flow
Author
Monika Johanna Kreitmair
Copyright Year
2021
Book
The Effect of Uncertainty on Tidal Stream Energy Resource Estimates

Print ISBN: 978-3-030-57657-8

Electronic ISBN: 978-3-030-57658-5

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-57658-5_3