Flow Transition Design in Hydraulic Structures

207 Pages·2020·8.116 MB·\207

by  S.K. Mazumder (Author)

Flow Transition
Design in Hydraulic
Structures
Taylor & Francis
Taylor & Francis Group
http://taylorandfrancis.com
Flow Transition
Design in Hydraulic
Structures
S.K. Mazumder
CRC Press
Taylor & Francis Group
52 Vanderbilt Avenue,
New York, NY 10017
© 2020 by Taylor & Francis Group, LLC
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Sudip Mazumder—my younger son
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Contents
Preface ...................................................................................................................xiii
Author .....................................................................................................................xv
1 Introduction .....................................................................................................1
1.1 D efinition................................................................................................1
1.2 N ecessity ................................................................................................1
1.3 C lassification ..........................................................................................2
1.4 Contracting and Expanding Transitions and
Their Performance ..........................................................................4
1.5 F luming ..................................................................................................5
1.6 Length of Transition .............................................................................5
1.7 Shapes of Transition ..............................................................................6
1.8 Economics of Transition .......................................................................9
1.9 Historical Development of Transition ..............................................11
1.9.1 Transition from One Subcritical to Another
Subcritical Flow ......................................................................12
1.9.2 Transition from Subcritical to Supercritical Flow .............16
1.9.3 Transition from Supercritical to Subcritical Flow .............20
1.9.4 Transition from Supercritical to Supercritical Flow ..........21
1.9.5 Closed Conduit Pressure Flow Transition .........................23
References .......................................................................................................24
2 Transition Flow Characteristics .................................................................29
2.1 G eneral..................................................................................................29
2.2 Flow Characteristics in Contracting and Expanding
Transitions with Free-Surface Subcritical Flow ..............................29
2.2.1 Head Losses in Transition ....................................................32
2.2.2 Hydraulic Efficiency of Contracting Transition ................33
2.2.3 Hydraulic Efficiency of Expanding Transition with
Eddy-Shaped Boundary .......................................................36
2.2.4 Performance of Transition ....................................................38
2.2.5 Hydraulic Efficiency of Straight Expansion and
Flow Regimes .........................................................................42
2.2.5.1 Concluding remarks with recommendation ......47
2.2.6 Optimum Length of Transition and Eddy Formation ......47
2.2.7 Stability of Flow in an Expansion ........................................48
2.2.8 Specific Energy Principles ....................................................49
2.2.8.1 Application of Specific Energy Principles ..........52
2.2.9 Fluming of Free Surface Flow ..............................................52
vii
viii Contents
2.2.10 Choking of Subcritical Flow, Afflux, and Flow Profiles ......54
2.2.11 Fluming for Proportionality of Flow ..................................57
2.3 Characteristics of Flow from a Subcritical to a Supercritical
State/Flow over Spillway ...................................................................58
2.4 Characteristics of Flow from a Supercritical to a Subcritical
Stage/Hydraulic Jump ........................................................................60
2.4.1 Hydraulic Jump Characteristics...........................................61
2.4.1.1 Conjugate/Sequent Depth Relation .....................61
2.4.1.2 Types of Jumps........................................................62
2.4.1.3 Free and Forced Jumps ..........................................63
2.4.1.4 Length of Jump .......................................................63
2.4.1.5 Height of Jump ........................................................64
2.4.1.6 J ump Profile.............................................................64
2.4.1.7 Energy Loss in Jump ..............................................65
2.4.1.8 Efficiency of Jump ..................................................65
2.4.1.9 Relative Loss of Energy .........................................65
2.4.2 Velocity and Shear Stress Distributions in
Hydraulic Jump ......................................................................67
2.4.3 Boundary Layer Separation and Flow Regimes in
an Expansion ..........................................................................67
2.5 Supercritical Flow Transition ............................................................67
2.5.1 Flow Characteristics in Supercritical Flow Transition .....68
2.6 Flow Characteristics in Closed Conduit Flow Transitions ...........69
2.6.1 Contracting Transition/Confuser ........................................70
2.6.2 E xpanding Transition/Diffuser ...........................................71
2.6.2.1 H ead Loss ................................................................71
2.6.2.2 Hydraulic Efficiency of Diffuser (E) ....................72
References .......................................................................................................72
3 Different Methods of Hydraulic Design of Flow Transitions ............75
3.1 I ntroduction .........................................................................................75
3.2 Design of Contracting Transition in Subcritical Flow ...................77
3.2.1 Assuming Linear Variation of Mean Velocity of Flow .....78
3.2.2 Assuming Variation of Mean Velocity as per Jaeger’s
Equation ..................................................................................80
3.2.3 Hinds’s Method of Design ....................................................81
3.3 Design of Expanding Transition in Subcritical Flow .....................82
3.3.1 Assuming Linear Variation of Mean Velocity of Flow .....82
3.3.2 Assuming Variation of Mean Velocity as per Jaeger’s
Equation ..................................................................................83
3.3.3 Hinds’s Method of Design of Outlet Transition ................84
3.3.4 Limitations of Conventional Design Method of
Expanding Transition ............................................................85
3.4 Design of Transition from Subcritical to Supercritical Flow ........86
3.4.1 Ogee-Type Spillway/Creager’s Profile ................................86
Contents ix
3∙4∙2 Side Channel-Type Spillway ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙88
3∙4∙3 S haft-Type Spillway ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙91
3∙4∙3∙1 Design of Crest Profile ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙93
3∙4∙3∙2 Design of Transition Profile ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙95
3∙4∙3∙3 Determination of Conduit Size (d) of the Shaft ∙∙∙∙95
3∙5 Design of Supercritical Flow Transition ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙96
3∙5∙1 Introduction ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙96
3∙5∙2 Mechanism of Shock Waves ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙97
3∙5∙3 Design Criteria of Supercritical Transition ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙97
3∙5∙3∙1 Waviness Factor (W)∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙97
f
3∙5∙3∙2 Coriolis Coefficient (α) ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙97
3∙5∙3∙3 Lateral Momentum Transfer Coefficient (T) ∙∙∙∙∙∙98
f
3∙5∙3∙4 Relative Loss of Energy (ΔE/E) ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙98
1
3∙5∙4 Design of Supercritical Contracting Transition ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙98
3∙5∙5 Design of Expanding Supercritical Transition ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙103
3∙5∙5∙1 Design of Expansion with Rouse Reverse
Curve ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙107
3∙6 Design of Transition in Closed Conduit under
Pressure Flow ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙109
3∙6∙1 Design of Contraction ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙109
3∙6∙2 Design of Expansion ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙109
References ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙110
4 Appurtenances for Economic and Efficient Design of Transition
Structures ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙113
4∙1 I ntroduction ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙113
4∙2 Classical Methods of Boundary Layer Flow Control in
Subcritical Flow Expansive Transition ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙116
4∙2∙1 Prandtl and Coworkers ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙116
4∙2∙2 Flow Characteristics in Wide-Angle Expansion∙∙∙∙∙∙∙∙∙∙∙∙∙∙116
4∙2∙3 Use of Triangular Vanes to Control Boundary Layer
Separation ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙117
4∙3 Performance of Subcritical Expansion with
Triangular Vanes ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙117
4∙3∙1 H ydraulic Efficiency of Expansion ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙118
4∙3∙2 Velocity Distribution at Exit of Expansion ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙120
4∙3∙3 Standard Deviation of Bed Shear Distribution and
Scour ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙120
4∙3∙4 Separation of Flow and Eddies ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙121
4∙3∙5 E xperimental Results ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙121
4∙3∙6 Optimum Geometry of Triangular Vanes for Best
Performance ∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙∙122
4∙3∙6∙1 Optimum Submergence (for Vane Height) ∙∙∙∙∙∙∙122
4∙3∙6∙2 Optimum Length (L/T), Spacing (U/B),
1
and Inclination (θ) of Triangular Vanes ∙∙∙∙∙∙∙∙∙∙∙∙123