Flow Transition Design in Hydraulic Structures

Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Preface
Author
1 Introduction
1.1 Definition
1.2 Necessity
1.3 Classicafition
1.4 Contracting and Expanding Transitions and Their Performance
1.5 Fluming
1.6 Length of Transition
1.7 Shapes of Transition
1.8 Economics of Transition
1.9 Historical Development of Transition
1.9.1 Transition from One Subcritical to Another Subcritical Flow
1.9.2 Transition from Subcritical to Supercritical Flow
1.9.3 Transition from Supercritical to Subcritical Flow
1.9.4 Transition from Supercritical to Supercritical Flow
1.9.5 Closed Conduit Pressure Flow Transition
References
2 Transition Flow Characteristics
2.1 General
2.2 Flow Characteristics in Contracting and Expanding Transitions with Free-Surface Subcritical Flow
2.2.1 Head Losses in Transition
2.2.2 Hydraulic Efficiency of Contracting Transition
2.2.3 Hydraulic Efficiency of Expanding Transition with Eddy-Shaped Boundary
2.2.4 Performance of Transition
2.2.5 Hydraulic Efficiency of Straight Expansion and Flow Regimes
2.2.5.1 Concluding remarks with recommendation
2.2.6 Optimum Length of Transition and Eddy Formation
2.2.7 Stability of Flow in an Expansion
2.2.8 Specific Energy Principles
2.2.8.1 Application of Specific Energy Principles
2.2.9 Fluming of Free Surface Flow
2.2.10 Choking of Subcritical Flow, Afflux, and Flow Profiles
2.2.11 Fluming for Proportionality of Flow
2.3 Characteristics of Flow from a Subcritical to a Supercritical State/Flow over Spillway
2.4 Characteristics of Flow from a Supercritical to a Subcritical Stage/Hydraulic Jump
2.4.1 Hydraulic Jump Characteristics
2.4.1.1 Conjugate/Sequent Depth Relation
2.4.1.2 Types of Jumps
2.4.1.3 Free and Forced Jumps
2.4.1.4 Length of Jump
2.4.1.5 Height of Jump
2.4.1.6 Jump Profile
2.4.1.7 Energy Loss in Jump
2.4.1.8 Efficiency of Jump
2.4.1.9 Relative Loss of Energy
2.4.2 Velocity and Shear Stress Distributions in Hydraulic Jump
2.4.3 Boundary Layer Separation and Flow Regimes in an Expansion
2.5 Supercritical Flow Transition
2.5.1 Flow Characteristics in Supercritical Flow Transition
2.6 Flow Characteristics in Closed Conduit Flow Transitions
2.6.1 Contracting Transition/Confuser
2.6.2 Expanding Transition/Diffuser
2.6.2.1 Head Loss
2.6.2.2 Hydraulic Efficiency of Diffuser (E)
References
3 Different Methods of Hydraulic Design of Flow Transitions
3.1 Introduction
3.2 Design of Contracting Transition in Subcritical Flow
3.2.1 Assuming Linear Variation of Mean Velocity of Flow
3.2.2 Assuming Variation of Mean Velocity as per Jaeger’s Equation
3.2.3 Hinds’s Method of Design
3.3 Design of Expanding Transition in Subcritical Flow
3.3.1 Assuming Linear Variation of Mean Velocity of Flow
3.3.2 Assuming Variation of Mean Velocity as per Jaeger’s Equation
3.3.3 Hinds’s Method of Design of Outlet Transition
3.3.4 Limitations of Conventional Design Method of Expanding Transition
3.4 Design of Transition from Subcritical to Supercritical Flow
3.4.1 Ogee-Type Spillway/Creager’s Profile
3.4.2 Side Channel-Type Spillway
3.4.3 Shaft-Type Spillway
3.4.3.1 Design of Crest Profile
3.4.3.2 Design of Transition Profile
3.4.3.3 Determination of Conduit Size (d) of the Shaft
3.5 Design of Supercritical Flow Transition
3.5.1 Introduction
3.5.2 Mechanism of Shock Waves
3.5.3 Design Criteria of Supercritical Transition
3.5.3.1 Waviness Factor (W[sub(f)])
3.5.3.2 Coriolis Coefficient (α)
3.5.3.3 Lateral Momentum Transfer Coefficient (T[sub(f)])
3.5.3.4 Relative Loss of Energy (∆E/E[sub(1)] )
3.5.4 Design of Supercritical Contracting Transition
3.5.5 Design of Expanding Supercritical Transition
3.5.5.1 Design of Expansion with Rouse Reverse Curve
3.6 Design of Transition in Closed Conduit under Pressure Flow
3.6.1 Design of Contraction
3.6.2 Design of Expansion
References
4 Appurtenances for Economic and Efficient Design of Transition Structures
4.1 Introduction
4.2 Classical Methods of Boundary Layer Flow Control in Subcritical Flow Expansive Transition
4.2.1 Prandtl and Coworkers
4.2.2 Flow Characteristics in Wide-Angle Expansion
4.2.3 Use of Triangular Vanes to Control Boundary Layer Separation
4.3 Performance of Subcritical Expansion with Triangular Vanes
4.3.1 Hydraulic Efcfiiency of Expansion
4.3.2 Velocity Distribution at Exit of Expansion
4.3.3 Standard Deviation of Bed Shear Distribution and Scour
4.3.4 Separation of Flow and Eddies
4.3.5 Experimental Results
4.3.6 Optimum Geometry of Triangular Vanes for Best Performance
4.3.6.1 Optimum Submergence (for Vane Height)
4.3.6.2 Optimum Length (L/T), Spacing (U/B[sub(1)]),and Inclination (θ) of Triangular Vanes
4.3.6.3 Design Curves for Optimum Geometry of Vanes for Best Performance
4.4 Use of Bed Deflector for Control of Separation in Subcritical Expansion
4.5 Control of Separation with Adverse Slope to Floor of Subcritical Expansion
4.5.1 Experimental Results
4.6 Transition from Supercritical to Subcritical Flow with Forced Hydraulic Jump
4.6.1 USBR-Type Stilling Basin
4.6.2 Development of Stilling Basin with Diverging Side Walls
4.6.3 Stabilizing Rollers in Expansion with Adverse Slope to Basin Floor
4.7 Control of Shock Waves in Supercritical Transition
4.7.1 Contracting Transition
4.7.2 Expanding Transition
4.7.3 Control of Shock Waves with Adverse Slope to Floor and Drop at Exit
4.8 Use of Appurtenances for Improving Performance of Closed Conduit Diffuser/Expansion
References
5 Illustrative Designs of Flow Transitions in Hydraulic Structures
5.1 Introduction
5.2 Design of Subcritical Transition for a Concrete Flume Illustrating Hinds’s Method of Design
5.2.1 Inlet Transition
5.2.1.1 Determination of Length
5.2.1.2 Determination of Flow Profile Corrected for Friction Loss
5.2.1.3 Determination of Structural Dimensions and Plan of Transition
5.2.2 Outlet Transition
5.3 Design of Subcritical Transition for an Aqueduct with Warped-Type Hinds’s Inlet Transition and Straight Expansion with Adverse Bed Slope
5.3.1 Inlet Contracting Transition
5.3.1.1 Width of Aqueduct
5.3.1.2 Length of Contracting Transition
5.3.1.3 Computation of Flow Profile
5.3.1.4 Hinds’s Method of Design of Contracting Transition
5.3.2 Design of Expanding Transition with Adverse Bed Slope
5.3.2.1 Length
5.3.2.2 Bed Slope
5.4 Design of Subcritical Contracting Transition Assuming Linear Variation of Mean Velocity and Expanding Transition Provided with Triangular Vanes
5.4.1 Contracting Transition
5.4.1.1 Width (B[sub(0)] ) at the End of Inlet Transition i.e. Width of Flume
5.4.1.2 Flow Depth (y[sub(0)] ), Mean Velocity of Flow (V[sub(0)]), and Froude’s Number of Flow (F[sub(0)])
5.4.1.3 Mean Width of Flow at Different Sections/Plans and Profile of Water Surface
5.4.2 Design of Straight Expanding Transition with Triangular Vanes
5.4.2.1 Determination of Model Scale
5.4.2.2 Determination of Model Flow (Q[sub(m)] ) and Froude’s Number (F[sub(0)])
5.4.2.3 Determination of Vane Dimensions
5.4.3 Design of an Elliptical Guide Bank for a Flumed Bridge as per Lagasse et al. (1995)
5.4.3.1 Waterway
5.4.3.2 Length of Guide Bank
5.5 Design of a Canal Drop Illustrating the Design of (a) Inlet Subcritical Transition by Jaeger Method, (b) Subcritical to Supercritical Transition with Ogee-Type Profile, and (c) Supercritical to Subcritical Transition in a Basin with Diverging Side Walls
5.5.1 Design Data
5.5.2 Computation of Flume Width at Throat (B[sub(0)] ) and Crest Height (∆)
5.5.2.1 Design of Contracting Transition by Jaeger’s Method
5.5.2.2 Design of Ogee-Type Glacis
5.5.2.3 Design of Stilling Basin with Diverging Side Walls and Provided with Adverse Slope to Basin Floor
5.6 Design a Stilling Basin of USBR Type III for an Ogee-Type Spillway
5.6.1 Design Data
5.6.2 Design Steps
5.7 Design of Supercritical Transition
5.7.1 Contracting Transition
5.7.2 Expanding Transition
References
Index