Book contents
- Frontmatter
- Contents
- Preface
- Notation
- Abbreviations
- 1 Brief review of basic hydrodynamic theory
- 2 Properties of distributions of singularities
- 3 Kinematic boundary conditions
- 4 Steady flows about thin, symmetrical sections in two dimensions
- 5 Pressure distributions and lift on flat and cambered sections at small angles of attack
- 6 Design of hydrofoil sections
- 7 Real fluid effects and comparisons of theoretically and experimentally determined characteristics
- 8 Cavitation
- 9 Actuator disc theory
- 10 Wing theory
- 11 Lifting-line representation of propellers
- 12 Propeller design via computer and practical considerations
- 13 Hull-wake characteristics
- 14 Pressure fields generated by blade loading and thickness in uniform flows; comparisons with measurements
- 15 Pressure fields generated by blade loadings in hull wakes
- 16 Vibratory forces on simple surfaces
- 17 Unsteady forces on two-dimensional sections and hydrofoils of finite span in gusts
- 18 Lifting-surface theory
- 19 Correlations of theories with measurements
- 20 Outline of theory of intermittently cavitating propellers
- 21 Forces on simple bodies generated by intermittent cavitation
- 22 Pressures on hulls of arbitrary shape generated by blade loading, thickness and intermittent cavitation
- 23 Propulsor configurations for increased efficiency
- Appendices
- Mathematical compendium
- References
- Authors cited
- Sources of figures
- Index
17 - Unsteady forces on two-dimensional sections and hydrofoils of finite span in gusts
Published online by Cambridge University Press: 07 May 2010
- Frontmatter
- Contents
- Preface
- Notation
- Abbreviations
- 1 Brief review of basic hydrodynamic theory
- 2 Properties of distributions of singularities
- 3 Kinematic boundary conditions
- 4 Steady flows about thin, symmetrical sections in two dimensions
- 5 Pressure distributions and lift on flat and cambered sections at small angles of attack
- 6 Design of hydrofoil sections
- 7 Real fluid effects and comparisons of theoretically and experimentally determined characteristics
- 8 Cavitation
- 9 Actuator disc theory
- 10 Wing theory
- 11 Lifting-line representation of propellers
- 12 Propeller design via computer and practical considerations
- 13 Hull-wake characteristics
- 14 Pressure fields generated by blade loading and thickness in uniform flows; comparisons with measurements
- 15 Pressure fields generated by blade loadings in hull wakes
- 16 Vibratory forces on simple surfaces
- 17 Unsteady forces on two-dimensional sections and hydrofoils of finite span in gusts
- 18 Lifting-surface theory
- 19 Correlations of theories with measurements
- 20 Outline of theory of intermittently cavitating propellers
- 21 Forces on simple bodies generated by intermittent cavitation
- 22 Pressures on hulls of arbitrary shape generated by blade loading, thickness and intermittent cavitation
- 23 Propulsor configurations for increased efficiency
- Appendices
- Mathematical compendium
- References
- Authors cited
- Sources of figures
- Index
Summary
As a preparation for determining unsteady forces on propellers in ship wakes, we first consider two-dimensional sections beset by travelling gusts. Our development of the unsteady force on such sections differs from that given in the seminal work of von Kármán & Sears (1938) by adopting a procedure which is easily extended to wings and propellers. Their formula for unsteady sectional lift is recovered, being that of lift at an effective angle of attack which varies with the parameter k = ωc/2U, the “reduced” frequency. Turning to hydrofoils of finite span, we derive results for low aspect ratio in steady flow. For wings in gusts there is no analytical inversion of the integral equation which involves a highly singular kernel function. Graphical results are given from numerical solutions for a range of aspect ratios which reveal diminishing unsteady effects with decreasing aspect ratio.
Corresponding reduced frequencies for propeller blades in terms of expanded- blade-area ratio are shown to be high relative to aerodynamic experience. This indicates that two-dimensional, unsteady section theory cannot be applied to wide-bladed (low-aspect-ratio) propellers.
TWO–DIMENSIONAL SECTIONS
The blades of a propeller orbit through the spatially non-uniform flow of the hull wake and consequently experience cyclic variations in the flow normal to their sections. For blades of small chord-to-radius, this is analogous to the case of a two-dimensional section moving at constant speed through a stationary, cyclic variation in cross flow distributed as a standing wave along the course of the moving section.
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- Hydrodynamics of Ship Propellers , pp. 315 - 333Publisher: Cambridge University PressPrint publication year: 1993