| dc.description.abstract | A characteristic of high-velocity open channel flows is the phenomenon of self-aeration, in which atmospheric air is entrained into and mixed with the flow, creating the appearance of white water. This phenomenon is frequently observed in flows down steep chutes and spillways. Studies of this complex process have remained mostly empirical. However, it has been recognized that systematic knowledge of air entrainment is essential for the design of hydraulic structures involving high-velocity open channel flows.
To obtain a better and more rational understanding of the phenomenon, detailed investigations were undertaken at the Indian Institute of Science, Bangalore. The results of these investigations are briefly summarized below.
Scope and Structure of the Study
The foremost aspect of the investigations relates to the definitions of basic terms and instrumentation. The studies are presented sequentially as the phenomenon occurs in flows down steep chutes or spillways. They include:
Characteristics of mean velocity distribution before air entrainment
Inception of air entrainment
Entrainment and distribution of air in the flow
The thesis consists of seven chapters:
Chapter 1: Introduction
Provides an introduction to the subject
Includes a brief literature survey
Describes the need and scope of the problem
Chapter 2: Definitions and Instrumentation
Defines terms such as air-water velocity and air-water density
Presents equations correlating these terms with mean air concentration
Details a new electrical probe developed for measuring air concentration
Principle: Measures the difference between the electrical conductivity of an air-water mixture and that of water alone
Describes a simple mechanical calibration method involving:
Sampling air-water mixture
Separating air and water
Measuring their volumes separately
Modifies Halbronn’s method for measuring air-water velocity for further investigations
Chapter 3: Velocity Distribution Before Air Entrainment
Studies the distribution of mean velocity in boundary layer flow and turbulent flow
Presents:
A generalized expression for mean velocity near the wall based on eddy viscosity
A series expansion for the defect layer profile
An expression for shear stress distribution in turbulent flow using a polynomial assumption
Validates theoretical expressions with experimental results, showing good agreement
Chapter 4: Inception Characteristics
Examines the nature of flow at the inception zone using stroboscopic light
Formulates a criterion for inception of air entrainment called the Inception Number, based on energy concepts of surface eddies
Calculates its critical value from model and prototype data
Proposes a graphical method to locate the inception zone on free-overfall spillways for various discharges
Develops a theoretical equation for instability inception based on Kelvin-Helmholtz instability
Studies Vedernikov’s criterion for free surface instability
Chapter 5: Entrainment Characteristics
Defines and correlates terms such as Entrainment Constant and Concentration Constant
Formulates momentum and energy equations for aerated flow in prismatic channels
Derives:
Approximate relation between mean air concentration, Froude number, and headloss
Empirical relationships between local non-aerated Froude number, headloss, and mean water concentration
Considers effects of Manning’s n and channel shape
Defines bulkage depth factor and correlates it with mean air concentration
Suggests a method to predict aerated flow characteristics from non-aerated flow data
Chapter 6: Distribution Characteristics
Divides self-aerated flow into:
Wall turbulent zone
Free turbulent zone
Develops theoretical equations for air concentration and velocity in the free turbulent zone, validated with experimental results
Studies velocity distribution in the wall turbulent zone using the velocity defect law
Examines concentration distribution by dividing the zone into inner and outer regions based on eddy viscosity
Correlates extrapolated concentration curves with experimental data
Solves a transport equation for inner region concentration distribution, showing good agreement
Develops a criterion based on:
Ratio of rising velocity of air bubbles to shear velocity
Concentration gradient at the outer edge of the inner region
Explains different states of flow with respect to air concentration distribution | |
