Chracteristics of self-aerated flows

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