University of Alberta
Experimental and Numerical Study of Plunging Flow in Vertical Dropshafts
By
Aqeel Jalil
A thesis submitted to the Faculty of Graduate Studies and Research in partial of fulfillment of the requirements for the degree of
Doctor of Philosophy in Water Resources Engineering
Department of Civil and Environmental Engineering Edmonton, Alberta
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We raise to degrees (of wisdom) whom we please: but over all endued with knowledge is one, the All-Knowing (Chapter 14: verse 76) Abstract
Dropshafts are part of the collection system for conveying stormwater or wastewater from surface to lower level in cities that have noticeable differences in topography or to carry the flow from the surface sewer system to an underground storage or intercepting tunnel. The hydraulics of plunge flow and air-water flow in dropshafts is still poorly understood due to the complexity of flow in dropshaft. The amount of air entrained and transported along the dropshaft, and the energy dissipation due to free falling water are major concerns for urban system drainage designers.
This thesis presents an experimental study on the hydraulic performance of plunge flow dropshafts. The main purpose of this study is to understand the hydraulic performance in terms of the nature of the flow, air entrainment and energy dissipation in dropshafts of different configurations. This involves the study of the effect of inlet entrance shape, dropshaft height, outlet to vertical shaft diameter ratio, tailwater depth at outlet pipe, providing sump in plunge pool, junction connection type between vertical shaft and outlet pipe, and outlet pipe direction. The experimental results were generalized including the criteria for the transition between flow regimes in a vertical shaft, energy dissipation, and air entrainment as well as the water depth in the plunge pool and in inlet and outflow pipes. The generalized results anticipated providing a basis for improving the current guidelines for optimizing the plunge flow design and construction.
The experimental study also investigated the effect of air vent size on the air entrainment. The results of air entrainment revealed that the air vent is limiting the air supply entering the dropshaft for small vent size (air supply limit), so the airflow depends on air vent configuration. For larger vent size, the air supply becomes unlimited, and the air entertainment is controlled by the water flow (air entrainment limit).
The thesis examined the capability of using computational fluid dynamics(CFD) simulations for the flow in plunge dropshafts. The numerical simulations were based on the two-phase flow (inhomogeneous) Euler-Euler approach (both air and water treated as continuous flow) with traditional K — e turbulence model. The momentum transfer through the air/water interface was used based on the free surface momentum transfer model. The computed flow parameters from the numerical simulations for air and water were validated and evaluated by comparisons with the experimental measurements. The CFD simulations were used also to study the scale effect on the hydraulic modeling in the plunge flow dropshaft by testing different scale models.
The study confirmed the suitability of using the CFD for modeling plunge flow in vertical dropshafts. Acknowledgements
To begin with, I am truly grateful to Almighty God for everything; all the blessings
I have are due to him alone. This thesis is dedicated to my children Yasmeen, Tamara, and Jaffer who were all born during my research.
I would like to express my gratitude to my supervisors Dr. Peter Steffler and Dr.
Nallamuthu Rajaratnam for their invaluable guidance and advice. Their encouragement and enthusiasm during my research helped me overcome many obstacles. It was a privilege to work under their supervision. Special thanks also go to
Mr. Perry Fedun for his proactive technical support during the installation of the experimental setup.
I also wish to express sincere thanks to the water resources engineering professors who offered very useful insight for my thesis. I also deeply appreciate the financial support that was given from the University of Alberta and the City of Edmonton and
Natural Sciences and Engineering Research Council of Canada (NSERC). Special appreciation goes to former colleagues Hesham Fouli, Yasser Shammaa, Stephen
Edwini-Bonsu, Iran Lima Neto, Adriana Camino, and others too numerous to mention. It was my pleasure to work with all of them and share knowledge and experience.
Finally, I owe a special thanks to my wife for her support, understanding, and patience. I would like to thank all of my sisters for their love and encouragement. In loving memory of my parents who always believed in me and gave me confidence. Table of Contents
Chapter 1
General Introduction 1
1.1 Dropshaft Components 2
1.2 Dropshafts Types 4
1.2.1 Vortex flow type 5
1.2.2 Plunge flow type 7
1.3 Value of the Study 8
1.4 Objectives of the Study 9
1.5 Thesis Organization 10
References 13
Chapter 2
A Preliminary Study of Plunging Flow in Vertical Dropshafts
2.1 Introduction 15
2.2 Experimental Setup 17
2.3 Experimental Results 18
2.3.1 Flow patterns of plunge flow dropshaft 18
2.3.2 Air entrainment 20
2.3.3 Energy dissipation 22
2.4 Summary and Conclusions 23
References 30
Chapter 3
Comparison between Elbow and Straight Inlet Entrance for Plunge-Flow
Dropshafts
3.1 Introduction 32 3.2 Experimental Apparatus 34
3.3 Flow Description 36
3.4 Hydraulic Properties 38
3.4.1 Inlet water depth 38
3.4.2 Plunge pool water depth 39
3.4.3 Water depth in outlet pipe 40
3.4.4 Average outlet velocity 40
3.5 Energy Dissipation 41
3.6 Air Entrainment 42
3.6 Summary and Conclusions 43
References 56
Chapter 4
The Effect of Plunge Pool Configuration on the Performance of Dropshafts
4.1 Introduction 57
4.2 Experimental setup 59
4.3 Experimental Flow Conditions 60
4.3.1 Inlet flow depth 60
4.3.2 Outlet pipe flow condition 61
Baffle series 61
Sump series 62
Junction series 63
4.3.3 Hydraulic jump in outlet pipe 63
4.4 Energy Dissipation 65
4.5 Air Entrainment 67
4.6 Summary and Conclusions 68 References 79
Chapter 5
The Effect of the Size of Air Vents and Outflow Direction on the Performance of
Plunge-Flow Dropshafts
5.1 Introduction 81
5.2 Experimental Setup 83
5.3 Flow Characteristics 85
5.3.1 Specific energy in inlet pipe 85
5.3.2 Flow description in vertical shaft 87
5.3.3 Flow in outlet pipe 89
5.4 Energy Dissipation 90
5.5 Air Entrainment 91
5.6 Estimation of the Pressure Drop in Vertical Shaft 94
5.7 Summary and Conclusions 95
References 112
Chapter 6
CFD Modeling of Plunge-Flow in Vertical Dropshafts
6.1 Introduction 113
6.2 Governing Equations 115
6.2.1 Continuity Equation 116
6.2.2 Momentum Equation 116
6.2.3 Interphase momentum transfer models 117
6.2.4 Turbulence model 118
6.3 Computational Model Parameters 119
6.3.1 Flow geometry 119 6.3.2 Boundary conditions 120
6.3.3 Grid size analysis 121
6.4 Results and Discussion 122
6.4.1 Comparison between momentum transfer models 122
6.4.2 Water depth in inlet pipe of simulation results 124
6.4.3 Flow pattern simulations in plunge flow dropshaft 124
6.4.3 The effect of air vent size on airflow rate 125
6.4.5 Maximum pressure at the bottom of the vertical shaft 126
6.4.6 Air entrainment 127
6.4.7 Energy dissipation 128
6.5 Scale Effects on Hydraulic Modeling of Air Entrainment 129
6.6 Summary and Conclusions 131
References 146
Chapter 7
Conclusions 148
Appendix A
Oblique Impingement of Circular Water Jets on Plane Boundaries
A.l Introduction 153
A.2 Experimental Arrangement and Experiments 155
A.3 Experimental Results and Analysis 157
A.3.1 Water depth profiles 157
A.3.2 Velocity profiles 159
A.3.3 Bed shear stress 160
A.4 Conclusions 160
References 173 Appendix B
CFD Modelling of Oblique Water Circular Jet Impingement on a Flat Surface
B.l Introduction 175
B.2 Homogeneous model 177
B.3 Computational geometry 178
B.4 Boundary Conditions 180
B.5 Gird Generation and Mesh Refinement 181
B.6 Numerical Simulation Results and Quality Assurance 182
B.6.1 Simulation error 182
B.6.2 Water depth and velocity profiles 184
B.6.3 Pressure field 188
B.6.4 Shear stress 190
B.7 Summary and Conclusions 192
References 214 List of Tables
Table 5.1 The range of the velocity measurements and percentage error 98
Table A. 1 Details of the experiments 162 List of Figures
Figure 1.1 Typical dropshaft components (Adapted from Williamson 2001) 4
Figure 1.2 Types of vortex inlets 6
Figure 1.3 Types of plunge flow inlets (Adapted from Williamson 2001) 8
Figure 2.1 View of experimental arrangement (a) dropshaft (b) energy dissipator.. .24
Figure 2.2 Possible flow patterns in plunge dropshaft pool: (a) regime (I), (b) regime
(II), and (c) regime (III) 25
Figure 2.3 Experimental results of the transition between flow regimes (a) The
relative discharges with dimensionless dropshaft height (b) Dimensionless water
pool depth with dimensionless dropshaft height 26
Figure 2.4 The relation between relative airflow and relative discharge for different
dropshaft height, and air opening diameter 27
Figure 2.5 The Relation between relative airflow with dimensionless water discharge
for different dropshaft height for air inlet diameter 31.75mm 27
Figure 2.6 Dimensionless residual head as a function of dimensionless flow rate Q+
28
Figure 2.7 Rate of relative energy dissipation as a function of dimensionless flow rate
a 28
Figure 2.8 Rate of relative energy dissipation as a function of dimensionless
dropshaft height 29
Figure 3.1 Definition sketch of the experimental setup 46
Figure 3.2 Flow visualization for drop height 2.2m (a) straight inlet and flat vertical
shaft bottom with 152.4mm outlet pipe diameter (b) elbow inlet and semicircular
vertical shaft bottom with 296mm outlet pipe diameter 47 Figure 3.3 Change of normalized drop distance to vertical shaft diameter with relative
discharge for elbow and straight inlet dropshaft 48
Figure 3.4 Change of the normalized inlet depth to inlet pipe diameter with relative
discharge for elbow and straight inlet entrance 49
Figure 3.5(a, b) Change of dimensionless pool water depth in dropshaft for straight
and elbow inlet entrance with relative discharge for (a) 296mm outlet pipe
diameter (b) 152.4 mm outlet pipe diameter 50
2 Figure 3.6 Change of dimensionless parameter (hp/D0Ut) (Dout/Ds) with relative
discharge for straight and elbow inlet entrance 51
Figure 3.7 The normalized outlet water depth with outlet diameter as a function of
relative discharge for elbow and straight inlet entrance 52
Figure 3.8 Outlet water velocity as a function of relative discharge (Q*) for elbow and
straight inlet entrance 53
Figure 3.9 Relative energy dissipation (r\) related to the relative discharge (Q*) for
elbow and straight inlet entrance 54
Figure 3.10 Variation of the relative air discharge ((3) with the relative water
discharge (Q*) for elbow and straight inlet entrance 55
Figure 4.1 Definition sketch of the experimental setup 70
Figure 4.2 Visualization of 152.4mm outlet pipe diameter with (a) flat vertical shaft
bottom without sump and (b) flat vertical shaft bottom with 0.3m sump
depth 71
Figure 4.3 Visualization of the junctions on the vertical shaft bottom (a) semicircular
junction, (b) elbow junction, and (c) flat bottom junction 71
Figure 4.4 Change of the normalized inlet depth to inlet pipe diameter with relative
discharge for elbow and straight inlet entrance 72 Figure 4.5 Change of normalize outlet water depth to the outlet diameter with relative
discharge (Q*) for (a) baffle series, (b) sump series, and (c) junction series 73
Figure 4.6 Change of average outlet velocity with relative discharge (Q*) for (a)
baffle series, (b) sump series, and (c) junction series 74
Figure 4.7 Flow visualization of: (a) submerged hydraulic jump at the entrance of
outlet pipe, and (b) free hydraulic jump at outlet pipe 75
Figure 4.8 Schematic diagram of relationships between normalize location of the
hydraulic jump measured form outlet entrance free hydraulic jump to the outlet
pipe diameter with relative discharge 76
Figure 4.9 Relative energy dissipation (n) related to the relative discharge (Q*) for (a)
baffle series, (b) sump series, and (c) junction series 77
Figure 4.10 Variation of the relative air discharge (P) with the relative water
discharge (Q*) for (a) baffle series, (b) sump series, and (c) junction series 78
Figure 5.1 Definition sketch of experimental setup 99
Figure 5.2 Visulization of experimental configuration (a) 90° (b) 180° outflow
direction 100
Figure 5.3 Change of the normalized water depth in the inlet pipe to the pipe diameter
with relative discharge for (a) 90° (b) 180° outflow direction 101
Figure 5.4 Comparison between measured and calculated normalized specific energy
to the inlet pipe diameter with relative discharge 102
Figure 5.5 change of normalized of the front and behind drop distance (measured
from inlet pipe invert) of the falling water to the shaft diameter with relative
discharge 102
Figure 5.6 Visualization of flow parttrens at the bottom of vertical shaft for (a) 90°
(b) 180° outflow direction 103 Figure 5.7(a, b) The normalized outlet water depth with pipe diameter as a function
of relative discharge for (a) 90°(b) 180° outflow direction 104
Figure 5.8(a, b) Water velocity at outlet pipe as a function of relative discharge for
(a) 90° (b) 180° outflow direction 105
Figure 5.9(a, b) Change of relative energy dissipation with relative discharge for (a)
90° (b) 180° outflow direction 106
Figure 5.10 The relation between the airflow normalized to the water flow with
relative discharge for different air vent sizes placed on the top of vertical shaft
for (a) 90° (b) 180° outflow direction 107
Figure 5.11 The relation between the airflow normalized to the water flow with
relative discharge for different air vent sizes placed on the top of feeding tank for
(a) 90° (b) 180° outflow direction 108
Figure 5.12 The relation between total airflow normalized to water flow with relative
discharge for combination of two air vents placed on the top of vertical shaft and
feeding tank for (a) 90° (b) 180° outflow direction 109
Figure 5.13 Comparison between 90° and 180° outflow direction for the normalized
airflow to water flow with relative discharge for different air vent sizes placed on
the top of vertical shaft and combination of two air vents placed on the top of
vertical shaft and feeding tank 110
Figure 5.14 The relation between the estimated pressure drop (in Pascal) inside the
vertical shaft with the relative discharge for different size of air vents placed on
the top of vertical shaft for (a) 50.8mm ,(b) 152.4mm, and (c) 296mm (fully
open) Ill
Figure 6.1 The geometry of the flow domain for plunge flow dropshaft 134 Figure 6.2 Comparison of numerical simulations of water surface profile at symmetry
plane (Q,= 0.274, D0/Ds= 0.107, L/Ds = 3.38) for (a) free surface model (Cd =
0.01), and (b) mixture model (Cd = 0.01, dap = 2.5mm) 135
Figure 6.3 Comparison of numerical simulations of water surface profile at symmetry
plane for free surface model (Q, = 0.274, D0/Ds= 0.107, L/Ds =3.38) for drag
coefficient: (a) Cd =0.01; (b) Cd =0.1; (c) Cd =0.44; (d) Cd =l;(e)Cd =5; and
(f) Cd =10 136
Figure 6.4(a, b) the relation between (a) average air velocity (m/sec) at top of air
vent, and (b) average water velocity (m/sec) at outlet pipe with Cd/dap for
mixture model (Q, = 0.274, D0/Ds = 0.107, L/Ds = 3.38) 137
Figure 6.5 Comparison of simulated water depth at entrance normalized with inlet
pipe diameter with the average experimental measurement for different relative
discharges 138
Figure 6.6 Comparisons between experimental and simulated flow patterns in plunge
flow dropshaft: (a) regime (I); (b) regime (II); (c) regime (III) 139
Figure 6.7 Comparison of simulated velocity field (shown in the left column) in
plunge dropshaft pool with experimental observations (shown in right column):
(a) regime (I); (b) regime (II); (c) regime (III) 140
Figure 6.8 Comparison between simulated and experimental results of relative air
w m entrainment (Qa/Qw) i ratio of air vent to vertical shaft diameter (D0/Ds ).
141
Figure 6.9 Relationship between the normalized maximum pressure with total head at
inlet (Pmax/y H) at the bottom of the vertical shaft with relative discharge (Q„)
for different dropshaft heights 141 Figure 6.10 Comparison between simulated and experimental normalized maximum
air entrainment (Qa/Qw) with relative discharge (Q.) for different dropshaft
heights 142
Figure 6.11 Comparison between simulated and experimental normalized energy
dissipation with relative discharge (Q») for different dropshaft heights 142
Figure 6.12(a, b) Comparison of normalized water depth at Q»=0.146 and
Q»=0.733 for different scale models for (a) water depth inlet pipe at section of
0.4Lr from vertical shaft center (b) water depth at outlet pipe at section of
0.3Lr from the center of vertical shaft 143
Figure 6.13(a, b) Comparison of normalized velocity profile in vertical shaft at
intersection of symmetry plane with cross section at height of 0.6Lr from the
bottom of the vertical shaft for different scale models (a) Q„=0.146 and (b)
Q.=0.733 144
Figure 6.14 Change of maximum velocity in vertical shaft at intersection of
symmetry plane and cross section at height of 0.6Lr from the bottom of the
vertical shaft with scale ratio for (a) Q„=0.146 and (b) Q»=0.733 145
Figure 6.15 Variation of the simulated relative air discharge at air vent with the
relative water discharge (Q„) for different scale models 145
Figure A.1 (a) Normal and (b) Oblique impingement of a circular water jet on a flat
plate, (c) Plan view of obliquely impinging jet 163
Figure A.2 Experimental arrangement 164
Figure A.3 Flow in the impingement region of water jets (a, b) 50.8 mm jet at #=15°
and 30° and (c, d) 101.6 mm jet at 9=15° & 30° 164 Figure A.4 Variation of jet thickness in the centerplane for (a) d=50.8 mm (b)
d=101.6 mm and (c) d=152.4 mm, for several values of 9. 165
Figure A.5 Typical thickness profiles of the deflected jet in the transverse direction
ford=101.6mmfor(a) 0=15° (b) 0=30° and (c) 0=45° 166
Figure A.6 Variation of the normalized thickness in the deflected jet with x/d with
three different thickness scales of (a) diameter of jet d (b) thickness of the jet tx
at x/d = 1 and (c) thickness of the jet t5 at x/d = 5 167
Figure A.7 Variation with x/d of the normalized jet thickness scales (a) tx/d (b)
t5/d and (c) average values of tt/d and t5/d 168
Figure A.8 (a) Normalized thickness profile in the deflected jet in the transverse
direction and (b) variation of the length scale L for the transverse thickness
profiles in terms of jet diameter d 169
Figure A.9 Dimensionless velocity profiles in the centerplane of the deflected jet for
(a) d=101.6 mm, 0=15° and U0 =4.93 m/s (b) d=101.6 mm, 0=30° and U0
=4.93 m/s (c) d=152.4 mm, 0=15° and U0 =5.46 m/s (d) d=152.4 mm, 0=30°
and U0 =5.46 m/s (e) d=152.4 mm, 0=45° and U0 =4.93 m/s 170
Figure A.10 Variation of the (a) boundary layer thickness in the deflected jet with the
distance x from the impingement point (b) normalized maximum velocity um in
terms of U'0 with x/d 171
Figure A.11 Variation of the (a) bed shear stress on the centerline with longitudinal
distance and (b) centerline normalized bed shear stress with x/d 172
Figure B.l Jet impingement layout of CFD 195
Figure B.2 Estimation of iteration error of pressure coefficient at the stagnation point
for the initial mesh for impingement angles 15° and 90° (constant jet height
series, Uo= 7.5 m/sec) 196 Figure B.3 Change of the pressure coefficient at the stagnation point for different
impingement angles with the number of nodes (constant jet height series, Uo= 7.5
m/sec) 196
Figure B.4 (a-f) Change of streamline patterns at the symmetry plane for different
impingement jet angles (constant jet height series, U0=5.5 m/sec) 197
Figure B.5 Change of normalized stagnation point displacement from the center of
impingement with the impingement angle of the jet 197
Figure B.6 Change of normalized water depth profiles with x/d in the symmetry plane
for different impingement angles (constant impingement length series, Uo= 7.5
m/sec) 198
Figure B.7 Comparison between experimental and numerical simulations for the
normalized water surface profile with x/d (9=15°, h=150mm, U0=5.46 m/sec
(exp.3115); 9=30°, h=185mm, U0=5.26 m/sec (exp.3230); 9=45°, h=222mm, U0
=4.93 m/sec (exp.3345)) 199
Figure B.8 Change of ratio of the backflow to the total inflow at the impingement
point section with the impingement angle of the jet for the constant impingement
length series and the constant jet height series 199
Figure B.9 (a-f) Change of velocity contours (10% normalized velocity interval) at
the symmetry plane for different impingement angles (constant impingement
length series U0=7.5 m/sec) 200
Figure B.10 (a-f) Change of velocity profile of the deflected jet at different locations
long the symmetry plane for different impingement angles (constant
impingement length series, U0=7.5 m/sec) 201 Figure B.ll Change of the normalized boundary layer thickness in the deflected jet
with x/d at different impingement angles (constant impingement length series,
U0=7.5m/sec) 202
Figure B.12 Change of the normalized maximum velocity Um in terms of U'0 with x/d
at different impingement angles (constant impingement length series, U0=7.5
m/sec) 202
Figure B.13 (a-f) Comparison between experimental and numerical simulation
velocity profiles along the centerline of the deflected jet (0=15°, h = 150mm,
U0=5.46 m/sec, d= 152.4 mm (exp. 3115)) 203
Figure B.14 (a-f) Pressure distribution contours (10% normalize pressure intervals)
for different impingement angles for the constant impingement length series and
the constant jet height series, (U0=7.5 m/sec) 204
Figure B.15 (a-b) Change of the pressure distribution contours (10% normalized
pressure intervals) for the impingement angle 15°, and for different jet flow
velocities (constant impingement length series) 205
Figure B.16 (a-b) Normalized pressure distribution at the surface on the symmetry
plane for different impingement angles and for different jet flow velocities
(constant impingement length series) 206
Figure B.17 Change of the normalized stagnation pressure for different impingement
angles and for different jet flow velocities (constant impingement length series
and the constant jet height series) 207
Figure B.18 (a-f) Shear stress distribution contours (10% normalized shear stress
intervals) for different impingement angles (constant impingement length series
(U0=7.5 m/sec)) 208 Figure B.19 (a-f) Shear stress distribution contours (10% normalized shear stress
intervals) for different impingement angles (constant jet height series (U0 =7.5
m/sec)) 209
Figure B.20 (a-b) Shear stress distribution contours (10% normalized shear stress
intervals) at impingement angle 15°, and for different jet flow velocities
(constant impingement length series) 210
Figure B.21 (a-b) Normalized shear stress distribution on the surface at the symmetry
plane, and for different impingement angles (constant impingement length
series) 211
Figure B.22 Change of the dimensionless maximum shear stress with the
impingement angle, and for different jet velocities (constant impingement length
series, and the constant jet height series) 212
Figure B.23 Change of the normalized maximum shear stress with impingement
angles, and for different jet flow velocities (constant impingement length series
and the constant jet height series) 212
Figure B.24 Comparison between experimental and numerical simulation results for
the shear stress along the centerline of the deflected jet (9=30°, h=185 mm, U0
=5.26 m/sec (exp.3230), and 9=45° h= 222 mm, U0 =4.93 m/sec (exp.3345)).
213 Notations
A = Water flow cross section area;
Aout= Outlet pipe cross section area;
As= Vertical shaft pipe cross section area;
Avs = Cross section area of the air vent pipe;
Aap= Interfacial area density between the air phase and water phase;
B= Thickness of falling water jet;
Cd= Drag coefficient between the air phase and water phase;
D = Pipe diameter; d = Hydraulic depth of water flow, which defined as A/T ;
D0 = Diameter of air vent pipe; dc = Water depth at the critical section in inlet pipe;
Din = Inflow pipe diameter; din = Water depth in the inlet pipe;
= d0ut Water depth in the outlet pipe; da(j= Interfacial length scale between the air phase and water phase;
Ds = Vertical shaft pipe diameter ;
Dvb = Air vent pipe diameter that placed on feeding tank ;
Dvs = Air vent pipe diameter that placed on vertical shaft; e = Baffle height;
Ec = Specific energy at critical section;
E0 = Specific energy ;
/ = Pipe Froude number, which defined as / = V/J(gDin); f = Friction factor; Fa = Buoyancy force, which defined as Fa = —{pa — pp) g;
F0 = Approach Froude number, which defined as F0 = v/VCgd); g = Acceleration due to gravity;
#!= Inlet total head calculated at critical depth section or inlet pipe; hp = Water depth at the plunge pool;
Hres = Residual total head in outlet pipe; k= Turbulence kinetic energy per unit volume; ke = Loss coefficient due to entrance from atmosphere to air vent pipe; kSE = Loss coefficient due to sudden expansion from air vent to vertical shaft;
L = Vertical distance from invert of inlet pipe to the bottom of the outflow pipe;
Lr= Model scale ratio;
I = Length of the air vent pipe;
Mp,a = Interfacial momentum exchange between the air phase and water phase; n = Manning's Roughness coefficient; p = Air pressure inside the vertical shaft; Pressure of respective phase pa = Atmospheric pressure;
Qa = Airflow rate or discharge entrained in the dropshaft;
Qw = Volumetric flow rate or discharge of water through the inlet pipe;
Q, = Relative discharge, which is defined as Q, = QwHiQ^tn )>
Q+ = Dimensionless water discharge, which defined as Q+ = QwH(gDfn L); r = Volume fraction of the respective phase;
S = Sump depth;
T = Top width of water flow;
U = Mean velocity vector of the respective phase;
V = Average velocity as pipe full flow; v = Average velocity of water flow;
Va = Average air velocity in the vent pipe;
Xf = The location of impact of the falling water jet on vertical shaft or the location of
spreading water flow meeting from behind measured from invert of inlet pipe; yx = Supercritical sequent water depth; y2 = Supercritical sequent water depth; yt = Tailwater depth; y+= The dimensionless distance measured from the wall;
Z = The perpendicular distance measured from the vertical shaft wall; a = Refer to the liquid phase (water) in numerical simulations;
P = Air entrainment or air concentration (P), which defined asQa/Qw; Refer to the
gaseous phase (air) in numerical simulations;
H = Viscosity of phase;
S = Air vents pipe thickness; pa = Mass density of air;
Pap~ Mixture mass density of air and water; y= Specific weight of water;
77 = Relative energy dissipation, which defined as (H1 — //res)/#i; fi = Viscosity of the fluid; e= Kinetic energy dissipation rate;
arcos f«Wi» = ^ ~ Win/D)) ~ 2(1 - 2(dtn/D)) V(din/D)(l - (dln/D)) Appendix A d = Diameter of jet at nozzle or end of pipe; h = Vertical distance or height of center of jet above plate;
H = Impingement distance, along the jet, to the plate;
L = Transverse distance where t =0.5tm; r = Radial distance from impingement point; r2 = Correlation coefficient; t = Thickness of deflected jet; tm= Thickness of deflected jet in the centerplane; u = Velocity in the x -direction at any point in the deflected jet; um= Maximum velocity;
U0= Velocity of jet at nozzle or end of pipe producing the jet; x = Longitudinal distance from the impingement point along the plate; y = Vertical distance above the plate; z = Transverse distance on the plate, from the centerplane;
8= Boundary layer thickness;
9= Angle of the impinging jet from the horizontal plate; p = Mass density of fluid (water);
= Azimuthal angle from the centerline on the plate; v = Kinematic viscosity of fluid (water = lxlO"6 m2/s);
T0 = Bed shear Stress on the plate; Appendix B
Cd= Drag coefficient between the air phase and water phase;
x Cf = Dimensionless shear stress(skin friction) defined as Cf = , 2;
p s Cp = Pressure coefficient defined as Cp = 2 ; d = Diameter of jet at nozzle or end of pipe; g = Acceleration due to gravity;
H = Impingement distance, along the jet, to the plate; h = Vertical distance or height of center of jet above plate; k = Turbulence kinetic energy per unit volume;
P = Static pressure of perspective phase; pM = the mixture pressure where pM = pa = Pp\
Ps = pressure at the stagnation point (maximum pressure); r = Volume fraction of the respective phase;
Re = Reynolds number;
U = Mean velocity of respective direction and phase;
Um = Maximum velocity;
UM = Mixture flow mean velocity calculated by UM = — (ra paUa + rB paUB); PM H H r
U'0 = Velocity of the jet at the source adjusted for the fall through the jet height (h).
U0= Mean velocity of jet at nozzle or end of pipe producing the jet; x = Longitudinal distance from the impingement point along the plate; xs = the displaced distance between the impingement point and stagnation point y = Vertical distance above the plate; a = Refer to the liquid phase (water) in numerical simulations;
3 = Refer to the gaseous phase (air) in numerical simulations; 8- Boundary layer thickness;
£ = Kinetic energy dissipation rate; fi = Viscosity of phase;
\iM = Phases mixture viscosity which calculated by: \iM = ra fia + r@ \i$
0 = Angle of the impinging jet from the horizontal plate; p = Mass density of respective phase; pM = Mixture mass density calculated by pM = ra pa + rp p^; x= Shear stress on the surface; xmax = Maximum shear stress on the surface; x= Shear stress on the surface;
Tmax = Maximum shear stress on the surface; Chapter 1 General Introduction
Dropshafts are part of the collection system for conveying storm water or wastewater from the surface sewer to a deeper sewer, underground storage, or intercepting tunnels. Dropshafts are commonly used in water supply systems to convey water from a higher elevation to a lower elevation. The collection system containing dropshafts makes the hydraulic design complex in spite of the fact that the idea is simple: direct flow from the upper level sewers towards the vertical shaft where it falls by gravity to the lower sewer level.
The main objectives of dropshaft design are to minimize the energy of the falling flow, and reduce the amount of air entrained, which is transported into the collection system. Dropshaft structure design should achieve these objectives in a reliable and efficient manner under a wide range of flow conditions. The consequences of poor performance may result in serious damage to the structure. An inadequate design may also result in destructive pressure surges (surcharged flow), exacerbate corrosion, increase odorous gases, restrict the flow capacity, and contribute to flooding in upstream areas that are frequently encountered today in the existing sewer systems.
Zhou et al. (2002) reported severe infrastructure damage due to a surge flow event in
Edmonton, and Guo and Song (1991) reported manhole cover blowouts and geysers at two dropshafts in Minnesota.
The sewer dropshaft creates turbulent flow, which releases volatile organic compounds (VOCs), and other odorous gases. The airborne release of VOCs from the sewer distributed throughout the urban areas may be of concern with respect to
1 widespread public exposure and inhalation risks (Koziel and Corsi 1998). These emissions are the cause of public odour complaints coming from the areas surrounding sewer dropshafts as well as causing extensive damage to concrete and metal pipes in the sewer system. The main problems of dropshafts in the water supply systems are the amount of energy dissipated and air entrainment that reduces the pipe discharge capacity.
1.1 Dropshafts Components
The major components of the dropshaft used for wastewater and storm water are: the inlet structure, the vertical shaft, and the outlet structure, which consist of a combination of energy dissipater, deaeration chamber, and vent pipe. Figure 1.1 shows the essential components of the dropshafts. The following is a brief description of these components.
Diversion chamber, is used to direct the flow from the surface sewer to the inlet structure. The diversion chamber may include a flow control structure such as stop logs or sluice gate.
Inlet structure: is located at the top of the vertical shaft, which receives flow from diversion chamber. An approach channel is often provided between the diversion chamber and inlet structure when necessary to steady the flow for smooth entry into inlet structure. The design of the inlet structure affects the amount of air entrained through the dropshaft. Inlets may be designed to allow the flow to plunge down the vertical shaft, or are designed to generate the vortex action.
Dropshafts: is the vertical shaft with a constant diameter that conveys flow from the inlet structure to the underground storage, or intercepting tunnel.
2 Deaeration chamber: is located at the base of the dropshaft to change the direction of falling flow that exits in the vertical shaft to the horizontal connecting tunnel (Adit).
The function of the deaeration chamber is to prevent entrained air from being transported into the intercepting tunnel. The deaeration chambers provide air space for entertained air to come out of the mixture to recirculate in the dropshaft or be released within the dropshaft site. The need for and the design of deareation chambers depends on a number of factors that affect the air entrainment including the inlet type, need for energy dissipation devices, and operating condition in the intercepting tunnel.
Vent pipe. A pipe that is connected between deaeration chamber and inlet structure to allow released air to recirculate within the dropshaft structure, or to permit the air to be released into the atmosphere, or to connect with odour control facilities. The vent pipe may be incorporated into the dropshaft directly by utilizing a vertical wall to separate the paths carrying water and air.
Adit: A connection tunnel that connects the downstream deaeration chamber with the main tunnel. Some hydraulics issues must be carefully considered because the location of connections will influence main tunnel ventilation i.e. the angle of entry, physical shape of the connection, and the location of the vertical connection to the main tunnel (i.e. at crown or invert).
Appurtenant structures: Separate structures may be included i.e. flow control devices, monitoring equipment, and odour control facilities.
3 Deaeration Chamber
Main Tunnel
Figure 1.1 Typical dropshaft components (Adapted from Williamson 2001).
1.2 Dropshafts Types
There are numerous variations in the design of drop structures currently in use.
Drop structures used for wastewater and storm water can classified in two general types according to the inlet configuration that is attached to the vertical shaft, which are mainly classified as Vortex flow types or Plunge flow types.
4 1.2.1 Vortex flow type
Vortex flow is generated by a special design of the inlet structure to make the circulating water cling to and flow along the sides of the vertical shaft of the dropshaft. Vortex-generating inlets have been developed to minimize air entrainment and potential odorous, and to dissipate energy from the falling flow. In general, vortex inlets are considered undesirable, as they involve a loss of performance, cause vibrations, and transport air bubbles (Khatsuria 2005). However, some vortex dropshafts have performed efficiently without any undesirable effects.
Several inlet configurations are used to produce vortex flow and these can be classified into five broad categories as shown in Fig. 1.2
(a) Circular: the dropshaft is concentric with a vortex inlet that has a horizontal floor.
Circular inlets have rarely used because it requires large depth to discharge
requisite flow (Anderson 1961) (Fig. 1.2 (a)).
(b) Scroll: The side of vortex inlet curls towards the dropshaft and it has a horizontal
floor. Jain and Kennedy (1983) presented the details of the hydraulic design of
scroll inlet (Fig. 1.2(b)).
(c) Spiral (vortex): the approach channel initiates the vortex flow into the dropshaft
by winding downwards. The spiral inlets have been used in mountain areas where
the approach flow can be frequently supercritical flow (Hager 1990, Jain and
Ettema 1991) (Fig. 1.2(c)).
(d) Tangential: the flow from the approach channel enters the inlet through a
constricted section with sloping floor into the vertical shaft. Tangential inlets are
the simplest and most compact of the vortex flow inlets. Jain (1984) have
conducted systematic studies on the hydraulic characteristics of tangential inlets
(Fig. 1.2(d)).
5 (e) Helical: the approach flow that is introduced into helicoidal channel at an
inclination while the flow goes down the vertical shaft by the helicoidal ramp
(Kennedy et al. 1988) (Fig. 1.2 (e)).
(a) Circular (b) Scroll (c) Spiral
5 (d) Tangential (e) Helical
Figure 1.2 Types of vortex inlets.
Detailed reviews on various configurations of vortex flow dropshaft were provided by Jain and Ettema (1987), and Vischer and Hager (1995). Some improvements to vortex flow dropshafts have been made by modifying the inlet or vertical shaft configuration. Quick (1990) introduced what is called vertical slot vortex dropshaft.
Jain (1987) studied the lower portion of the vertical shaft that is smaller than that of
6 the upper portion where the upper and lower portions are connected by a short transition. Toda et al. (1996) studied vortex-flow dropshafts with a contraction in the lower part of the vertical conduit. Jain et al. (1990) improved the constant pitch and full ramp dropshaft, and designed a helicoidal-ramp along only the lower part of the dropshaft which is referred to a truncated helicoidal ramp dropshafts.
1.2.2 Plunge flow type
In the plunge flow dropshaft, the flow enters the dropshaft radially and is dropped directly down the vertical shaft. The common inlet structures used in plunge flow dropshafts are the straight drop inlet, the bellmouth, and elbow inlet (Fig. 1.3). The geometry of plunge flow dropshafts could be square, rectangular, circular or a combination between them. The flow also could enter from one side of the vertical shaft without a smooth transition, hit the vertical conduit and fall along the vertical conduit (Chanson 2004). Rajaratnam et al. (1997) studied the plunge flow in a vertical dropshaft with an elbow-type connected to the vertical shaft. Plunge flow dropshafts can also be affected by vertical conduit modifications when a series of vertical dropshafts are used which is called dropshaft cascades (Chanson 2002), or by adding steps in the vertical conduit, which is called stepped- flow dropshaft (Yoshoka et al.
1984). The plunge flow dropshaft may include plunge pool or impact cups at the base of the vertical shaft to dissipate energy.
7 2E 7 \ \y
Straight Drop Inlet Bellmouth Inlet Elbow Inlet
Figure 1.3 Types of plunge flow inlets.
1.3 Value of the Study
The main purpose of this research is to enhance our knowledge of the hydraulics of plunge flow dropshafts. The results of the experimental and numerical modeling of plunge flow dropshaft are of crucial importance for the design and construction of collection systems. Until now, the general practice has been to neglect the energy dissipation of the falling water in the vertical dropshaft (Rajaratnam and Mainali
1995). The predictions of the depth and velocity of the flow in the downstream outlet conduit for different dropshaft heights are important to calculate the energy dissipation in the dropshaft. Dropshaft structures are one of the greatest contributions to the airflow in sewer systems. Airflow in the sewer system is perhaps one of the most complex hydraulic flow phenomena.
The studies on the airflow in plunge flow dropshafts are very limited and the results of this study can be generalized for practical use. The generalized results of
8 this study with the existing airflow models in the sewer pipe will provide a scientific knowledge of airflow movement in sewer systems. An understanding of, and an ability to accurately estimate the induction and deduction of air flow in manholes of municipal sewers is important for identifying the locations of emissions of volatile organic compounds (VOCs) in sewer networks. The city of Edmonton is keenly interested in identifying possible "hot spots", i.e. locations where VOC emissions can lead to significant public complaints and possibly health risks.
1.4 Objectives of the Study
The present research focuses on the hydraulics of plunge-flow dropshafts. The main objectives of the study are intended to improve the existing knowledge by:
(1) Understanding the flow patterns of plunge-flow dropshafts with elbow-type and straight-type inlets for different flow rates, and vertical shaft heights.
(2) Studying the airflow and the parameters that have influenced the air entrainment in the dropshaft i.e. dropshaft height, inlet junction type, water flow rate, inlet and outlet water depth, outlet connection with vertical shaft, and plunge pool depth. The results of the study are presented in inlet parameters for practical use.
(3) Comparing the energy dissipation of different configurations of dropshaft setup to provide at least a preliminary estimation, which can be used for the design and construction of plunge-flow dropshafts.
(4) Exploring the potential of a general-purpose computational fluid dynamics (CFD) code for computing detailed characteristics of the air-water (two-phase) flow in dropshafts. The experimental results were used to validate, at least partially, the modelled air-water flow in dropshafts.
9 1.5 Thesis Organization
The research reported in the thesis was written based on a paper format. The introductions of the Chapters are almost the same due to the limitations of available research, and studies on plunge flow dropshafts; therefore, there is little change between the introductions of the Chapters. The research started in Chapter 2 with preliminary experiments was conducted to understand the performance of plunge- flow dropshafts with an elbow inlet entrance in terms of nature of the flow, air entrainment, and energy dissipation in the dropshaft. Seven series of experiments for different dropshaft heights were performed to observe the flow pattern of falling water in the vertical shaft. The trajectory of falling water was traced, and the point where falling water hit the vertical shaft was measured. The flow patterns of falling water are divided into three regimes. The transition between these regimes is related to the dimensionless dropshaft height. The airflow rate entering the dropshaft was estimated by measuring the pressure in a short pipe, which is connected to the vertical shaft top cover.
In Chapter 3, a series of experiments were conducted to compare the difference between an elbow and straight inlet entrance, dropshaft height, and the effect of outlet pipe diameter on the hydraulic performance and air entrainment of plunge flow dropshafts. Detailed flow measurements involved the filling ratio in inlet pipe, the flow condition in outlet pipe, and the depth in forming pool at the bottom of the vertical shaft. The airflow inside the vertical shaft was measured using a hot wire anemometer. The flow patterns in the vertical shaft were analyzed and compared to the preliminary experiments.
Chapter 4 focuses on the effect of plunge pool on the hydraulic performance of dropshafts. Several configurations were tested in order to dissipate or absorb the 10 energy of the falling flow. The experiments involved studying the effect of providing sump on the base of vertical shaft or tailwater depth at outlet pipe by restricting the outflow with baffle on the dropshaft hydraulic performance. The study was extended to investigate the effect of junction type on the bottom of the vertical shaft. The junctions tested were the original semi circular junction that have been used in previous experiments, the elbow junction, and the straight junction with flat bottom.
Detailed flow measurements were presented on the variation of water depth in the inlet and outlet as well as the air entrained in the vertical shaft for all configurations.
Chapter 5 investigates the effect of the size of air vent on the air entrainment of the plunge flow dropshafts. The experimental work was extended to investigate the effect of the outflow direction on the hydraulic performance of dropshaft. The calculated specific energy in the inlet pipe for an 180° outflow direction was compared to theoretical expressions for computing specific energy at the control section for free water fall in horizontal pipe.
Chapter 6 examined the capability of the commercial CFD software (Ansys CFX
11.0) to predict the flow pattern and velocity field of air and water in dropshaft. The numerical simulation is solved based on the two fluid Euler-Euler approach for two- phase flow (both air and water treated as continuous fluid), and three-dimensional flow model. The momentum transfer through air/water interface used in this modeling was based on the free surface momentum transfer model. The standard k — e turbulence model for air water mixture was adapted for the turbulence modeling. The numerical simulation results of water and air was compared with the experimental data. The CFD study was extended to examine the scale effect of the hydraulic modeling in the plunge flow dropshaft by testing different scale models. The numerical simulation results showed there is no scale effect on the plunge flow 11 dropshafts in terms of air entrainment or water flow for the scale models that were tested.
A general conclusion of this study is provided in Chapter 7 along with some discussion and recommendations for further study.
Another concern is the force due to the impact of the falling water on the vertical shaft. Evaluating the impact force is hard to measure experimentally in the dropshafts, and difficult to predict analytically due to the complexity of the falling flow phenomena. The falling water in the dropshaft can be simplified as a circular water jet impinging on the surface. Appendix A presented the experimental results of the oblique impingement of a circular water jet on a plane boundary, and the CFD simulation results were presented in Appendix B. The results of the experimental and numerical simulations for the water depth and velocity profiles, pressure field, and shear stress were plotted with a focus on the centerline plane along the jet pipe.
12 References
Anderson, S.H., (1961). "Model Studies of Storm-Sewer Drop Shafts. (Technical
Paper No. 35, Series B). Prepared for the Department of Public Works, City of
Saint Paul. Minneapolis: St. Anthony Falls Hydraulics Laboratory, University of
Minnesota.
Chanson, H. (2002). "An Experimental Study of Roman Dropshaft Hydraulics."
Journal of Hydraulic Research, IAHR, 40(1): 3-12.
Chanson, H. (2004). "Hydraulics of Rectangular Dropshafts." Journal of Irrigation
and Drainage Engineering, ASCE, 130(6): 523-529.
Guo, Q., and Song, C.S. (1991). "Dropshaft hydrodynamics under transient
conditions." Journal of Hydraulic Engineering, ASCE, 117(8): 1042-1055.
Hager, W.H. (1990). "Vortex Drop Inlet for Supercritical Approaching Flow." Journal
of Hydraulic Engineering, ASCE, 116(8):1048-1054.
Jain, S.C., (1984). "Tangential Vortex-Inlet." Journal of Hydraulic Engineering,
ASCE, 110(12): 1693-1699.
Jain, S.C., and Ettema, R., (1987). "Vortex-Flow intakes." Energy Dissipater, IAHR,
Hydraulics Structures Design Manual, No.l, Rotterdam: Balkema, Chapter 7:125-
137.
Jain, S.C., and Kennedy, J.F., (1983). "Vortex-flow drop structures for the Milwaukee
Metropolitan sewerage district inline storage system." Iowa Institute of Hydraulic
Research (IIHR), Report No. 264.
Jain, S.C., Paez, D., and Kennedy (1990). "Air Entrainment in Helicoidal-ramp drop
structure" Fifth International Conference on Urban Storm Drainage, 963-968.
Kennedy, J.F., Jain, S.C., Quinones, R.R., (1988). "Helicoidal-ramp dropshaft."
Journal of Hydraulic Engineering, ASCE, 114(3)315-114. 13 Khatsuria R.M. (2005). "Hydraulic of Spillways and Energy Dissipators" Marcel
Dekker, New York, 649 pages.
Koziel, J.A., and Corsi, R.L. (1998). "VOC emissions from municipal sewers:
hotspots." Proceedings of the 91st annual meeting and exhibition of Air and Waste
Management Association, San Diego, California.
Toda, K. and Inoue, K. (1999). "Hydraulic Design of Intake Structure of Deeply
Located Underground Tunnel Systems." Water Science and Technology,
39(9):137-144.
Quick, M.C. (1990). "Analysis of Spiral Vortex and Vertical Slot Vortex Dropshafts."
Journal of Hydraulic Engineering, ASCE, 116(3): 309-325.
Rajaratnam, N., and Mainali, A. (1995). "Hydraulic Design of Dropshafts for the City
of Edmonton Drainage System." report prepared for city of Edmonton, University
of Alberta, Edmonton, Alberta.
Rajaratnam, N., Mainali, A., and Hsung, C.Y. (1997). "Observations on Flow in
Vertical Dropshafts." Journal of Hydraulic Engineering, ASCE, 123(5):486-491.
Vischer, D.L., and Hager, W.H., (1995). "Vortex Drops" Energy Dissipaters: IAHR
Hydraulic Structure Design Manual, No.9, Rotterdam: Balkema, 167-181.
Williamson, S., (2001) "Drop structure design for wastewater and stormwater
collection Systems." Parsons Brinckerhoff, New York, 2001.
Yoshioka T. Mastuda S., and Nagai T. (1984). "Flexible Energy Dissipator for High
Head Conditions.", Double Core Unit Model, 3rd International Conference on
Urban Storm Drainage: 157-166.
Zhou, F., Hicks, F. E., and Steffler, P. M. (2002). "Transient flow in a rapidly filling
horizontal pipe containing trapped air." Journal of Hydraulic Engineering, ASCE,
128(6):625-634. 14 Chapter 2
A Preliminary Study of Plunging Flow in Vertical Dropshafts1
2.1 Introduction
The combination of dropshafts with the collection system makes the hydraulic system complex. Most research investigations on dropshafts are limited to experimental studies in hydraulic laboratories. Developing mathematical models to evaluate this complex flow related to air entrainment and hydraulic transient is difficult. Using computational fluid dynamics (CFD) for numerical simulations for dropshaft modeling is still in the early stages due to the complex configuration of the dropshaft, detailed experimental observations of velocity, and pressure distribution fields of air and water in the plunge-flow dropshafts, which are not available to validate. The main objectives of dropshaft design are to know the effect of the falling flow on energy dissipation, and the amount of air that is entrained by the falling flow and transported to the downstream part of the collection system.
The major components of the dropshaft are the inlet structure, the vertical shaft, and the outlet structure that consists of a combination of energy dissipator, and air separation chamber. The inlet structure provides a smooth transition from horizontal flow at the upper level to the vertical shaft. The nature of the flow in the dropshaft is dictated by its inlet configuration, which is mainly classified as a vortex flow inlet or plunge flow inlet. The vortex flow is generated by a special inlet design to make the water vortex cling to and flow around the vertical conduit of the dropshaft. Several inlet configurations are used to produce a vortex flow i.e. the circular inlet, the scroll
1 Part of this chapter has been published as a paper in the proceedings of the 17th Canadian Hydrotechnical Conference, Hydrotechnical Engineering, Cornerstone of a Sustainable Society, Edmonton, Alberta August 17-19, 2005, Urban Hydraulics section, 957-964. 15 inlet, the spiral inlet (Hager 1990), the tangential inlet (Jain 1984), and the vertical slot vortex (Quick 1990). The hydraulic performance of vortex dropshafts has been studied by many researchers, and a detailed review on various configurations of vortex flow dropshaft is provided by Jain and Ettema (1987), and Vischer and Hager
(1995).
The vortex flow can also be generated by vertical shaft configurations. Helicoidal ramp dropshafts (Kennedy et al. 1988), vortex-flow dropshafts with the lower portion of the vertical conduit smaller than the upper portion where the upper and the lower portion are connected by a short transition (Jain 1987), and vortex-flow dropshafts with contractions in the lower part of the vertical conduit (Toda et al. 1996) are examples of vertical conduit configuration.
In plunge flow dropshafts, the flow enters the dropshaft radially and is dropped directly down the vertical shaft. The common inlets used in plunge flow drop structure are the straight drop inlet, and the bellmouth and elbow inlet type, which is used in this study. The geometry of plunge flow dropshafts can be square, rectangular, circular, or a combination between them. The flow can also enter from one side of the vertical shaft, hit the vertical conduit, and fall along the vertical conduit (Chanson
2002), or plunge flow dropshaft with an elbow-type inlet (Rajaratnam 1997). Plunge flow can be affected by vertical conduit configurations when a series of vertical dropshafts are used which are called dropshaft cascades (Chanson 2002), or by adding steps in the vertical conduit which are called stepped-flow dropshafts (Yoshoka et al.
1984).
The vortex drop structures have proved to be superior to plunge flow in terms of energy dissipation and air entrainment (Jain and Kennedy 1984), but the plunge flow dropshafts are still commonly used in modern sewers and storm water sewers
16 (Chanson 2002). The advantages of plunge flow drop structure are: the simple design, easy construction of inlet structure, proven performance as energy dissipators in very high dropshaft, and less cost compared to vortex inlet structure.
The hydraulic of plunge flow and air-water flow in dropshafts have not been systematically documented (Rajaratnam et al. 1997). In this study, experiments were conducted to understand the performance of plunge-flow dropshaft with an elbow- type inlet in terms of nature of flow, air demand, and energy dissipation in the dropshaft.
2.2 Experimental Setup
Seven series of experiments were performed to observe the behaviour of plunge flow in a vertical dropshaft. The plunge flow was created by the flow from the inlet pipe located near the top of the vertical shaft. The diameter of the horizontal inlet pipe was 0.152m, and the flow to this pipe was provided from an elevated tank at the top of the building. The elevated constant head tank was supplied with water by a pump installed at the main laboratory sump. The inlet was joined to the vertical shaft by an elbow with an invert radius equal to the diameter of the inlet pipe. The discharge end of the elbow was fixed to the vertical side of a Plexiglas vertical shaft with a diameter of 0.296m. The height of the inlet pipe was adjusted to 4.35, 2.95, 2.55, 1.95, 1.45,
1.05m by shortening the vertical shaft from the lower side as measured from the invert of the outlet pipe. The lower part of the vertical shaft was joined to a horizontal pipe (0.5m length) of the same diameter and material. The downstream end of this horizontal pipe was connected to a plastic pipe 1.9 m in length of the same diameter that was connected to a lab manhole. Both pipes represent the outlet of the dropshaft.
This arrangement is shown in Fig. 2.1(a). 17 The flow rate was measured by means of a magnetic flow meter, which was installed at the beginning of the inlet pipe. To dissipate the high water head at the inlet pipe that came from the elevated tank, an energy dissipator was installed inside the inlet pipe to prevent the high impact of water with the vertical shaft (see Fig. 2.1(b)).
The air demand in the dropshaft was measured using the same procedure that was used in Rajaratnam et al. (1997) by measuring the pressure in a short pipe 20cm long
(air vent) fitted to the cover of the vertical shaft. Two different pipe diameters for the air vent were used to measure the pressure: 31.75mm for the first 5 series and 50.8mm for the last 2 series. By measuring the pressure difference between the atmosphere and inside the air vent pipe using water manometer, it was possible to calculate the airflow into the dropshaft that was caused by water flow in the dropshaft. The flow depths in the outlet pipe were measured by a point gauge located about 1 m from the vertical shaft. In each series, several experiments were performed starting with a small discharge. The discharge was gradually increased until the inlet pipe was running full.
2.3 Experimental Results
2.3.1 Flow patterns of plunge flow dropshaft
Several flow patterns were observed as a function of the relative discharge Qt, which is defined as Qt = QwH{gDfn), where Qw =volumetric flow rate or discharge of water through the inlet pipe and dropshaft, Din =inlet pipe diameter (m), and g — acceleration due to gravity (m/sec2).
At low flow rates, and short dropshaft heights, the water falls as a free falling jet in the vertical shaft. The falling jet after falling through a certain height becomes circular and retains its circular shape until hitting the bottom of the vertical shaft (regime I).
The hydraulic of this regime are similar to the hydraulics of vertical drop structures. 18 When the flow hit the bottom, it divided in two directions: the forward flow along the outlet pipe, and the reverse flow, which re-circulates at the bottom of the vertical shaft forming the plunge pool. The water depth in the plunge pool in this regime was small and increased as the impact angle of the falling jet decreased. In this regime, the maximum pressure occurred at bottom of outlet due to direct impact of the water jet.
For flow rates greater than a certain value of regime (I), the shape of this falling jet acquired a horseshoe shape, with open ends located on the inner side. The falling jet hit the other side of the vertical shaft (regime II), and water clung to the vertical shaft and flowed down along the shaft. At the impingement area, a central ridge was formed on the wall of the shaft along with a spreading flow, and as the discharge increased, the thickness of the central ridge and width of spreading flow increased until it covered the vertical shaft diameter (regime III). Rajaratnam et al. (1997) made similar observations. The spreading flow of the falling jet around the shaft produced a water curtain across the entrance to the outlet pipe at the bottom of the shaft that prevented the water from flowing freely to the outlet pipe. The spreading flow down the shaft entered the pool at the bottom of the shaft as a part of a turbulent cylindrical wall jet with its length changing from approximately 0.1 Ds to 0.9 Ds where Ds = vertical shaft pipe diameter (m). In this regime, considerable air entrainment and energy dissipation took place in the plunge pool. The flow in the outlet pipe came mainly from the sides of the entrance of the outlet pipe which mixed and flowed as a super-critical open channel stream, accompanied with swirling wings above the free surface. This flow was found to be very turbulent and very aerated.
At a larger discharge, the water jet retained the horseshoe shape. The falling jet collided with the other side of the vertical shaft dividing into a splash jet directed upwards and a downward main directed jet. The downward main jet spreads and 19 covers the whole diameter of the vertical shaft in a short distance along the shaft
(regime III), and was spiralling down the walls of the vertical shaft. As the discharge increases, the point of impingement moves up; the downward velocity of spreading flow becomes stronger and the pool water depth at the bottom of the shaft increases.
The pattern of flow in this regime is similar to regime II except that the spreading flow enters the plunge pool as a thin cylindrical wall jet with a radius approximately equal that of the vertical shaft. The flow at the pool and the flow leaving the vertical shaft were found to be very turbulent, unsteady, and very aerated so the color of the water changed to white. The flow patterns of these regimes are shown in Fig. 2.2.
The experimental results of the transition between the flow regimes are shown in
Fig. 2.3. Figure 2.3(a) shows the change of the relative discharge Qt for the transition of flow regimes in terms of the dimensionless dropshaft height L/Ds in which L is the dropshaft height measured from the invert of the inlet pipe to the bottom of the outflow pipe. While Fig. 2.3(b) shows the change in the normalized water depth in the plunge pool hp/Ds where hp is water depth at plunge pool in terms of the dimensionless dropshaft height L/Ds. It is clear from Figure 2.3(a, b) that the threshold of relative water discharges Qt, and normalized water pool depth hp/Ds for the transition between regimes (I and II), and regimes (II and III) decreased with increasing the normalized dropshaft height L/Ds .
2.3.2 Air entrainment
As the water falls down the vertical shaft, air is entrained or mixed with the water flow. The amount of air entrained and transported along the dropshaft in the plunge pool depended on several mechanisms. The first mechanism took place on the impingement area of the falling jet with the bottom of the outlet pipe (regime I), 20 which is similar to the air entrainment at drops (Rajaratnam and Kwan 1996), or on the opposite side of the vertical shaft (regime II and III).
The second mechanism occurred at the falling water jet surface inside the vertical shaft. Some air was dragged along by the cylindrical wall jet surface. Surface disturbances can arise from a number of sources including instabilities, turbulent eddies reaching the free surface, as well as longitudinal vorticity (Ervine 1999). This mechanism may not be important unless the vertical shaft is high (Rajaratnam et al.
1997).The third mechanism occurred at the impingement of the spreading flow
(cylindrical wall jet) with the plunge pool: free surface instabilities developed, and air bubble entrainment might be observed (Chanson 1997). This process is called plunging jet entrainment. The air that is entrained by these mechanisms may rise to the pool surface and be released back to the shaft or carried into the downstream of outlet pipes. The results of air measurement for the seven series of experiments as well as the average data of Rajaratnam et al. (1997) experiments are shown in Figures
2.4 and 2.5. Figure 2.4 shows the variation of the relative airflow rate with Q, where Qa is the volumetric flow rate or discharge of air through the vertical shaft. The results revealed that the air entrainment increases with increasing the air vent diameter
( D0) when comparing the result of series 1 to 5 with series 6 and 7. The air entrained also increased with increasing the height of the vertical shaft. Figure 2.5 shows the relation between the dimensionless flow rate Q+, which is defined as Q+ =
Qw/J{gDfn L), with a relative airflow rate for series 1 to 5. The results in Fig. 2.5 confirmed that the air entrained in the dropshaft increased with increasing the dropshaft height, in particular for L/Ds > 6.59 .
21 2.3.3 Energy dissipation
Dropshafts can be classified as an energy dissipator because of the high drop between the inlet and outlet pipes. In regime I, most energy dissipation occurred when the free falling jet hit the bottom of the vertical shaft, similar to the dissipation that happens in a drop structure but on a smaller scale. In this regime, the impact and scouring forces are the greatest due to the directly falling of the jet on the vertical shaft bottom. In regimes II and III, the energy dissipation occurred when the falling jets impinged the other side of the shaft wall, frictional resistance of the spreading flow due to the roughness of the walls of the vertical shaft, the mixing of spreading flow down the shaft when water entered the plunge pool, and the change of flow direction from vertical to horizontal flow at the outlet pipe. Forming the pool and entrained air can act as a "buffer" that minimizes the impact of the falling flow at the base of the vertical shaft.
The energy dissipation calculation was done by assuming that the inlet and outlet pipes operated as a free surface flow. The total energy in the inlet pipe was calculated by using the end depth ratio method given by Dey (2001) by calculating the critical depth near the end of the inlet pipe for any given discharge. The total energy of the outlet pipe was calculated by measuring the water depth using a point gauge. The relative energy dissipation was calculated by dividing the difference in total energy between the inlet and outlet pipes to the total energy of inlet pipe.
The residual energy Hres/H1 data are presented in Fig. 2.6 as a function of the dimensionless flow rate Q+where the residual head in the outlet pipe is Hres and Hx is the inlet head calculated at the critical depth section. The relative energy loss for the dropshaft can be quantified by r\ = (//j — Hres)/Hx is plotted with a dimensionless flow rate Q+ in Fig. 2.7. Figures 2.6 and 2.7 revealed that the energy dissipation in the 22 plunge flow dropshaft for a specific dropshaft height decreased with increasing the water discharge, and for a specific water discharge, it increased with the L/Ds ratio.
The average energy dissipation for each data series as a function of L/Ds ratio is plotted in Fig. 2.8. In general, the results revealed the energy dissipation increased with increasing the dropshaft height.
Comparing these results with the energy dissipation in the vortex dropshaft by
Vischer and Hager (1995) who estimated that 85% of the energy was dissipated for
L/Ds =50 and Manning's n of 0.12. Jain and Kennedy (1984) predicted a 90% energy loss in the dropshaft of L/Ds =100 with a friction factor of 0.03. The present results have shown that the plunge flow drop with the elbow inlet is also quite effective for energy dissipation.
2.4 Summary and Conclusions
An experimental study on the performance of plunge flow dropshafts was conducted for different dropshaft heights. The flow pattern of plunge flow in the dropshaft was divided into three regimes depending on the inflow relative discharge, and dimensionless dropshaft height. The results revealed that the air entrainment for a specific dropshaft height increases with increasing the water discharge, and for a specific discharge, increases with increasing the dropshaft height. The energy dissipation in the plunge flow dropshaft also increased with increasing the dropshaft height, and for a specific dropshaft height decreases with increasing the water discharge.
23 Fig.(a) n
Dropshaft \-4 1^1
m--A
Figure 2.1 View of experimental arrangement (a) dropshaft (b) energy dissipator.
24 Fig. (a) Fig. (b) Fig. (c)
W \\ O: ,-i^ ^-^
Figure 2.2 Possible flow patterns in plunge dropshaft pool: (a) regime (I), (b) regime
(II), and (c) regime (III).
25 1.0 • Transition between -egime I & II 0.9 (a)- • • Transition between regime II & III 0.8 • 0.7 • • • 0.6 II a 0.5 0.4 D 0.3 D
0.2 D 0.1 • A 0.0 0 2 4 6 8 10 12 14 16
L/Ds
1.2 i i i IV\\ • Transition between regime I & II 1.1 I") • 1.0 • • Transition between reeime II & III • 0.9 • I I 0.8 0.7 oI/I 0.6 • 0.5 • p D 0.4 |l 0.3 D 0.2 0.1 0.0 8 10 12 14 16 L/Ds
Figure 2.3 Experimental results of the transition between flow regimes (a) The relative discharges with dimensionless dropshaft height (b) Dimensionless water pool depth with dimensionless dropshaft height.
26 2.5 • Series 1, L/Ds=14.7 , Do=31.75mm o • Series 2, L/Ds=9.96, 2.0 • < > Do=31.75mm A Series 3, L/Ds=6.59 , o o o <> Do=31.75mm 1.5 A Series 4, L/Ds=4.90 , % » . <> Do=31.75mm > O Series 5, lVDs=3.55 , 5 !1 _ II 1.0 • 4 Do=31.75mm • . • Series 6, iyDs=4.90, °* 1 | Do=50.80mm * I 1 i ;J O Series 7, L/Ds=8.61, 0.5 "Kl T Do=50.80mm X Raj data, L/Ds=6.63 , 0.0 Do=31.75mm 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Q.
Figure 2.4 The relation between relative airflow and relative discharge for different dropshaft height, and air opening diameter.
1.6 D Series 1, L/Ds=14.7 , 1.4 * Do=31.75mm • Series 2, L/Ds=9.96, 1.2 p Do=31.75mm 1.0 •* • A Series 3, L/Ds=6.59 , A D • • u<8k Do=31.75mm It. n D " 0.8 n D A & A 5 D DA^ 2 * " * A Series 4, L/Ds=4.90, 0.6 Do=31.75mm >!g> ^^O^A * A % <§> O Series 5, L/Ds=3.55 , 0.4 Do=31.75mm x Raj data, L/Ds=6.63, 0.2 Do=31.75mm 0.0 0.00 0.10 0.20 0.30 0.40
Figure 2.5 The Relation between relative airflow with dimensionless water discharge for different dropshaft height for air inlet diameter 31.75mm.
27 0.25
O ° ° 0.20 o ° 0 A A o A A AAA 0.15 ° x * A C a Series 1 , L/Ds=14.7 o AA A "g 0.10 • Series 2 , L/Ds=9.96 O . A . " • - if" • • A Series 3 , L/Ds=6.56
n n • n A Series 4 , L/Ds=4.90 0.05 n D ;°°° o Series 5 , L/Ds=3.55 0.00 0.00 0.10 0.20 0.30 0.40 0.50
Figure 2.6 Dimensionless residual head as a function of dimensionless flow rateQ+.
100
D Series 1, L/Ds=14.7 95 A ° n D n i-i - " u o rj • Series i., L/L>s=9.9b P 10 A Series 3, L/Ds=6.63 O A A • • • • • • 90 4, L/US=4.9U O A A Series _j O A A o Series 5, L/Ds=3.55 ft A bb x 0) o £ AAA c A 111 0 A A A 0) o > 80 ° O 4-> ° o o n Ol QC 75
70 0.00 0.10 0.20 0.30 0.40 0.50
Figure 2.7 Rate of relative energy dissipation as a function of dimensionless flow rate
Q+.
28 "-9
VI 01 1/1 yu " O _J 00 " go I- oftflu - V
7PI JO V RI ac fin - 8 10 12 14 16
L/Ds
Figure 2.8 Rate of average relative energy dissipation as a function of dimensionless dropshaft height.
29 References
Dey, S. (2001). "EDR in Circular Channels." Journal of Irrigation and Drainage
Engineering, ASCE, 127(2), 110-112.
Ervine, D.A. (1998). "Air Entrainment in Hydraulic Structure: a Review." Proc. Instn
Civ.Engrs Wat., Marit. & Energy, 130, Sept., 142-153.
Hager, W.H. (1995). "Vortex Drop Inlet for Supercritical Approaching Flow." Journal
of Hydraulic Engineering, ASCE, 116(8): 1048-1054.
Jain, S.C. (1984). "Tangential Vortex-Inlet." Journal of Hydraulic Engineering,
ASCE, 110(12): 1693-1699.
Jain, S.C. (1987). "Free Surface Swirling Flow in a Vertical Dropshaft." Journal of
Hydraulic, ASCE, 113(10): 1277-1289.
Jain, S.C, and Ettema, R. (1987). "Vortex Drops" Energy Dissipater: IAHR
Hydraulics Structures Design Manual, No.l, Chapter 7:125-137.
Jain, S.C. and Kennedy, J.F. (1984). "Vortex-flow drop." Proceedings- International
Symposium on Urban Hydrology, Hydraulics, and Sediment Control, University
of Kentucky, 115-120.
Kennedy, J.F., Jain, S.C, and Quinones, R.R. (1988). "Helicolidal-Ramp Dropshaft."
Journal of Hydraulic Engineering, ASCE, 114(3): 315-325.
Quick, M.C (1990). "Analysis of Spiral Vortex and Vertical Slot Vortex Dropshafts."
Journal of Hydraulic Engineering, ASCE, 116(3): 309-325.
Rajaratnam, N., Mainali, A., and Hsung, CY. (1997). "Observations on Flow in
Vertical Dropshafts." Journal of Hydraulic Engineering, ASCE, 123(5): 486-491.
Rajaratnam, N., and Kwan, A.Y.P. (1996). "Air Entrainment at Drops." Journal of
Hydraulic Research, IAHR, 34(5): 579-587.
30 Toda, K., and Inoue, K. (1999). "Hydraulic Design of Intake Structure of Deeply
Located Underground Tunnel Systems." Water Science and Technology, 39(9),
137-144.
Vischer, D.L., and Hager, W.H. (1995). "Vortex Drops" Energy Dissipaters: IAHR
Hydraulic Structure Design Manual, No.9:167-181.
Yoshioka, T., Mastuda, S., and Nagai, T. (1984). "Flexible Energy Dissipator for
High Head Conditions, Double Core Unit Model.", Third International
Conference on Urban Storm Drainage, 157-166.
31 Chapter 3
Comparison between Elbow and Straight Inlet Entrance
for Plunge-Flow Dropshafts
3.1 Introduction
Dropshafts of various types are used in hydraulic structures to transfer water from a higher to lower level. The dropshafts are typically used in reservoir intakes, water distribution, hydroelectric power, and urban sewer systems. The dropshaft designs need to be developed, and customized to suit the application purpose. In the urban sewer systems, the dropshafts are mainly used in steep urban catchment basins. A suitable dropshaft or series of dropshafts along the sewer pipes are needed to reduce the hydraulic slope, and consequently the flow velocity. The design criteria of sewer systems that the maximum velocity allowed in the sewer pipe should not exceed 3 m/sec (Metcalf & Eddy 1981). The high velocity in the sewer system reduces the life span of the sewer pipe due to abrasion of the sewer walls. The high velocity (high
Froude number) may also lead to a hydraulic jump in the sewer pipe by abrupt cross sectional changes, junctions with other sewers, or bends that cause the flow to choke.
The current knowledge on dropshafts available from the dropshaft literature is scarce and not systematically documented (Rajaratnam 1997). Moreover, the complexity of the falling water phenomena is due to the presence of air in the dropshaft that mixes with the water flow. The forces due to the impact of the falling water flow in the vertical shaft are difficult to predict analytically. Accordingly, most studies on dropshafts proposed using an experimental approach. Although there are many kinds of drop shafts currently used in urban sewer systems, dropshafts can be
32 classified in two general types according to the inlet characteristics at the top of the
vertical shaft: the vortex type and the plunge type. Vortex type dropshafts cause the
flow to spiral down and cling to the walls of the vertical shaft. In the plunge type, the
flow is directed to plunge down the vertical shaft and may occupy the full cross
section of the vertical pipe. Various designs for plunge dropshafts have been used in
urban sewer systems, which mainly depend on the inlet configuration, straight drop
inlet, elbow drop inlet, and bellmouth drop or radial flow inlet. Christodoulou (1991)
investigated the supercritical approach flow in small straight circular dropshaft
manholes. He concluded that both head loss and water level in dropshaft manholes
depend mainly on a dimensionless drop parameter in the form of an inverse Froude
number, which is expressed in terms of the dropshaft height and the flow velocity.
Christodoulou also found the water level in manholes depends on whether the outflow
is parallel or normal to the inflow. Rajaratnam et al. (1997) performed experiments on
a circular dropshaft with an elbow inlet type. Rajaratnam et al. stated that it is
necessary to provide a curved inlet at the top of the dropshaft to increase its carrying
capacity. They concluded that the energy loss in plunge dropshafts is significant and
the air entrainment expressed as Qa/Qw decreases from 1.4 to 0.5 as the relative
discharge increases from 0.1 to about one. Chanson (2004) studied the hydraulics of
vertical rectangular plunge dropshafts with a straight inlet. The study focused on the
effect of the dropshaft pool, outflow direction, and drop shaft height. Chanson
concluded that the pool depth and shaft height have little effect on the rate of energy
dissipation while it increases for a right angled outflow relative to the inflow direction. Giovanni et al. (2007) studied the effect of the approach flow Froude number, dropshaft height, dimension of the inlet and the outlet, and the shape of the manhole or vertical shaft bottom on the performance of the dropshaft manhole. The
33 study concluded that the dimensionless factor including the product of approach flow
pipe filling times the approach Froude number represented an effective parameter to
adequately describe both energy loss and pool water depth.
In this study, an extensive series of experiments were completed to compare the
difference between an elbow and straight inlet entrance for plunge flow dropshafts for
two different L/Ds (where L is dropshaft height and Ds is vertical shaft diameter)
ratios. Two different outlet diameters were used in this study to investigate the effect
of the ratio of the outlet to the vertical shaft cross section area. Detailed flow
measurements involved the approach flow condition of the inlet pipe i.e. the filling
ratio of the inlet pipe as well as the flow condition in the outlet pipe. The flow pattern
in the vertical shaft was analyzed depending on the incoming relative discharge. The
energy dissipation was calculated and the air entrainment was measured. It was hoped
that this study might then give accurate and reliable predications of the hydraulics
characteristics and air entrainment for the dropshaft designers.
3.2 Experimental Apparatus
The experimental apparatus was designed to perform a generalized experimental
analysis on the plunge dropshaft. As shown in the definition sketch (Fig. 3.2) of the
experimental setup and hydraulic parameter, the water was pumped from the main
laboratory sump to an elevated rectangular tank (0.6m width X 1.14m long X 0.9m height) by a 0.152m pipe connected at the bottom of the tank. A magnetic flow meter was installed on the pipe to measure the water flow(Qw)- The connection of the pipe was covered with two layers of plastic mesh fixed firmly with weights in order to calm the pumped water. The water flow entered the dropshaft from a horizontal pipe that was connected to the side of the elevated tank, which represented the inlet pipe. 34 The diameter of the 3.25m long Plexiglass horizontal inlet pipe (Din) was 0.152m.
The inlet pipe can be joined with the Plexiglass vertical shaft with a diameter (Ds) of
0.296m by an elbow with an invert radius equal to the diameter of the inlet pipe or with a straight junction. Two different configurations at the lower part of the vertical shaft were used. The semi circular bottom with a radius equal to the radius of the outlet pipe was used with the outlet diameter (Dout) of 0.296m and 4m in length.
The second configuration was the flat bottom that was used with an outlet diameter
(Dout) of 0.152m and 4m in length. The height of the inlet pipe (L) was adjusted from 3.2 to 2.2 by shortening the vertical shaft from the bottom. The discharge end of the outlet pipe returned the flow to the main laboratory sump.
The water depth in the inlet pipe (din) was measured by using point gauge and piezometers of reading accuracies of 0.5mm located at a distance of 1.6 m from the vertical shaft. The water depth in the outlet pipe (dout) was measured with piezometers located at 3m downstream from the vertical shaft. One of the main purposes of the design of the experimental apparatus was to measure the airflow so that the top of the elevated tank was sealed to ensure that no air entered with the water flow from the inlet pipe. The top of the vertical shaft was kept fully open to allow the air to flow down the shaft for the 0.296m outlet diameter series. For the 0.152m outlet diameter, an air supply pipe with the same outlet diameter and 0.3m in length was placed on top of the vertical shaft. A hotwire anemometer of ±0.1 m/sec accuracy of full-scale range was used to measure the air velocity at the top of the vertical shaft.
The air discharge (Qa) was calculated by integrating the velocity profile along the centerline of the vertical shaft. The arrangement is shown in Fig 3.2.
35 3.3 Flow Description
Following the analysis of the preliminary experiments, the flow patterns are
classified in three regimes. Regime (I): the inlet jet falls directly on the bottom of the
vertical shaft; regime (II), the falling jet hits the side of the vertical shaft and flows
down the shaft; regime (III) where the falling jet impinges on the side of the vertical
shaft, and the spreading water covers the entire vertical shaft diameter.
In these experiments, regime (I) was shown only in very small discharges below the flow measurements range. The observation was different due to using different configurations to dissipate the energy of the pumped flow. Accordingly, the flow in this setup produced mainly regimes (II) and (III). Regime (II) applies to the falling jet
impinging on the opposite wall and forming a central ridge on the wall of the vertical shaft with a spreading flow down the shaft due to gravity. The spreading flow developed a vertical water curtain covering the outlet pipe that prevented the water from flowing freely to the outlet pipe. The falling spreading flow hit the bottom of the vertical shaft, and separated the flow in two horizontal directions: the forward direction along the outlet pipe, and the backward flow that recirculates, and forms the water plunge pool. The flow in the outlet pipe mainly came from the sides of the entrance of the outlet pipe that mixed and flowed as a supercritical free surface flow.
As the water discharge increased, the impinging of the falling jet with the vertical shaft formed a small roller at the top of the impact region (splash jet).
As the discharge increases, the falling jet spreads and covers the whole diameter of the vertical shaft for a short distance (regime III) and spirals down the wall of the vertical shaft. The location of the impingement point moves up. The downward velocity that enters the water pool at the bottom of the vertical shaft is stronger and
36 the water pool depth (hp) in the shaft increases. The flow leaving the vertical shaft
pool was found to be very turbulent, unsteady, and very aerated.
The flow pattern describing the dropshaft flow mainly depends on the jet impact
location on the vertical shaft. The jet impact location depends on (1) the falling jet
size or the filling ratio, (2) the approach flow Froude number of the inlet pipe, and (3)
the type of connection between the inlet and the vertical shaft. The jet impact location
also depends (4) on the ratio of the inlet to the vertical shaft diameters, and to (5) the
ratio of the dropshaft height to vertical shaft diameter.
Let us define the distance(Xf), which represents the location of the impact jet on
the vertical shaft measured from the invert of the inlet pipe before the elbow. Figure
3.3 shows the change of normalized drop distance to the vertical shaft diameter with
relative discharge^,) which is defined asQ, = Qw/>l(jjDfny. where Qw =
volumetric flow rate or discharge of water through the inlet pipe and dropshaft,
2 Din inlet pipe diameter (m), and g = acceleration due to gravity (m/sec ) for the
elbow and straight inlet entrance. In general, the location of the impact jet (Xf)
increased with increasing the curvature of the connection between the inlet pipe and
vertical shaft. The results regarding the location of the impact jet Xf for the straight
and elbow inlet entrances show that the elbow entrance is lower rather than straight,
about 1.5 Ds for a small discharge, and is reduced to 1 Ds at larger flows. These
experiments confirmed that it is good idea to use an elbow entrance if we are
interested in lowering the location of the impingement point of the falling jet. Figure
3.3 revealed that the location of the impact of the jet decreased with increasing the water discharge. The location of the impact jet also decreased with increasing the approaching Froude number for the same filling ratio. The experimental observation of the transition between regimes (II) 37 and (III) in terms of the relative discharge ((?,) for the existing setup occurred approximately at Q„ = 0.36 for the dropshaft height (L) 3.2m and Q, = 0.41 for the dropshaft height (L) 2.2m.
3.4 Hydraulic Properties
3.4.1 Inlet water depth
The normalized inlet depth or filling ratio of the inlet pipe(d£n/Din) as a function of the relative discharge (Q„) are provided in Fig. 3.4. As shown in Fig. 3.4 the flow in the inlet pipe began with a partly filled water flow and changed to a fully pressurized pipe flow as the water flow rate increased.
The water depth in the inlet pipe is almost identical for the straight and elbow entrances with the vertical shaft because the location of the measurement point (1.2m from the vertical shaft) is away from the change in water profile in the inlet pipe. The change in water profile is mainly caused by acceleration in the water flow due to falling water in the vertical shaft.
The transition from a partly filled to a pressurized pipe flow is complex and involves a mixture of air and water in general (Hager 1999). Hager (1999) confirmed that the transition depends significantly on the so-called pipe Froude number / =
VHidDin) where V is mean flow velocity assuming the pipe is full. The free surface occurs at / < 0.544 (Q, = 0 .43) and the pipe is fully pressurized at / >
1.15 (Q, = 0.90). In these experiments, the transition between the free surface and pressurized pipe flow and approximately occurred at Qt = 0.85 as seen in Fig. 3.4.
The transition from the free surface to the cavity flow was more influenced by the detailed supply geometry, slope of the inlet pipe, and the surface roughness of the pipe. The transition from the free surface to the cavity flow is observed to be at 38 Qt = 0.50 (f = 0.64) within the upper range of the average value of / = 0.544 that
is reported by Hager (1999).
3.4.2 Plunge pool water depth
The depth in the plunge pool was measured with measuring tape. The accuracy of the measurement decreases with increasing the discharge since the flow fluctuates and becomes very turbulent and very aerated in the plunge pool with increasing water discharge. The average measurements recorded that the fluctuation in the pool water depth was approximately 2% for a low flow rate and increased to approximately 20% for a large flow rate. The water depth in the pool was normalized to the outlet diameter (Dout) of 0.296m and 0.152m that was used in the experimental setup. The dimensionless water depth (hp/D0Ut) as a function of the relative discharge ((?*)for the two different outlet diameters is given in Fig. 3.5(a, b). The entrance end of the outlet pipe is usually submerged where (hp/D0Ut > 1).
As seen in Fig. 3.5(a), for a large outlet diameter, the water depth in the plunge pool increased with increasing the water flow rate. The type of inlet entrance also affected the water depth in the pool. The pool water depth for the elbow entrance was found to be higher than the straight entrance particularly for a small flow rate. The pool water depth increased with decreasing the vertical shaft pipe diameter or outlet pipe diameter. It is interesting to note that after the transition between regime II and regime III for a straight inlet with a small outlet diameter, there is a sudden jump in the plunge pool water depth as shown in Fig. 3.5(b). As seen in Fig. 3.5(a, b), the increasing water depth in the plunge pool is found to be proportional to the ratio of the cross section area of the outlet pipe to the vertical shaft pipe (Aout/As) or (Dout/
2 2 Ds) . The effect of the ratio(Dout/Ds) which is equal to one for a large outlet pipe 39 since the diameter of the vertical shaft and outlet pipe is the same, whereas the ratio is
equal to 0.265 for the small outlet pipe is multiplied by the normalized water
depth (hp/D0Ut) and plotted as a function of the relative discharge ((?,) as seen Fig.
3.6. The dropshaft height seemed to have little effect on the pool water depth. The
other parameters such as the outlet pipe direction and tail water depth that have an
effect on the water depth in the plunge pool will be investigated in the following
Chapters.
3.4.3 Water depth in outlet pipe
The measured water depth in the small and large outlet pipes was normalized with the outlet pipe diameter and presented as a function of the relative discharge (Q„) as
shown in Fig. 3.7. Figure 3.7 revealed that the dropshaft height, type of inlet entrance, and outlet pipe diameters have an effect on the outlet water depth. In general, the water depth in the outlet pipe decreased with increasing the dropshaft height. As expected, the water depth increased with decreasing the outlet pipe diameter. It is interesting to note that the water depth in the outlet pipe reached the maximum value at the transition between regimes II and III, and began to decrease a little with increasing discharge, and then started to increase again as shown in Fig. 3.7. Figure
3.7 showed that the elbow entrance dropshaft has a higher water depth in the outlet pipe than in the straight entrance especially at large water flow rates.
3.4.4 Average outlet velocity
The average outlet velocity is calculated by dividing the water discharge by the cross section area of the water depth at the outlet. The results revealed that the average velocity for the large and small outlet pipes have the same range as seen in 40 Fig. 3.8. In these experiments for a small discharge (regime II), the dropshaft height had little effect on the average outlet velocity, whereas the straight inlet entrance had a higher outlet velocity than the elbow entrance. As the water discharge increased
(Regime III), the difference in the average velocity in the outlet pipe also increased between the elbow and straight dropshaft as seen in Fig. 3.8. At a large flow rate, the effect of the dropshaft height became dominant, and the average velocity in the outlet increased with increasing the dropshaft height.
3.5 Energy Dissipation
One of the primary objectives of the dropshaft design is to minimize the effect of the falling flow by dissipating the energy. The energy dissipation was caused by the impingement of the falling water with the wall of the vertical shaft and by friction loss of the spreading flow due to the roughness of the shaft walls. The additional energy loss was due to the mixing of the spreading flow down the shaft when it entered the plunge pool, and changed the flow direction from vertical to horizontal. Even if no planning was made to form a plunge pool, a pool will form to provide the necessary pressure to turn the direction of the flow from the vertical spreading flow to an almost horizontal flow at the outlet pipe. Forming the pool will also reduce the impact of the falling jet, or spreading flow on the bottom of the vertical shaft.
The energy dissipation was obtained by measuring the water depths in the inlet and outlet pipes, and calculating the energy head at the measuring sections. Assuming that
Hi is the inlet energy head and Hres is the residual head at the outlet pipe. The relative energy dissipation (rj) is represented by the ratio of the difference in head between the inlet and outlet pipes to inlet head. The energy dissipation is decreased by increasing
41 the water flow rate as seen in Fig. 3.9 i.e. for a small discharge (regime II), energy
dissipation is very high and reaches values close to 95% which means almost all of
the kinetic energy is dissipated in the dropshaft. The effect of the type of inlet
entrance is very small in regime II, and for a large flow rate (regime III) which
becomes dominant as seen in Fig. 3.9. In general, it can be concluded that the elbow
entrance dissipates more energy than the straight inlet. The energy dissipation
increases with increasing the dropshaft height and the outlet diameter for the same discharge. The results for the elbow entrance is within the range of the energy loss data that was reported by Rajaratnam et al. (1997) in spite of the inlet feeding configuration which was different.
3.6 Air Entrainment
The airflow in dropshafts is caused by the free surface falling water, which drags the air, and during the strikes of the falling water jets with the wall and at the bottom of the vertical shaft, the air is entrained. The entrained air depends on the flow condition of the incoming water, the bubble behaviour in the plunge pool, and the geometry ratio between the inlet and outlet to the vertical shaft. As mentioned before, the flow pattern in the vertical shaft is regimes II and III, and there is no direct contact between the outlet and vertical shaft airspace. The air entrainment in the dropshaft is mainly due to the transported air bubbles from the bottom of the vertical shaft (plunge pool) rising up to the water surface and being released at the outlet pipe.
The maximum air entrainment in the vertical shaft (Qa) is normalized to the water
an discharge(Qw) as /? = (?a/Qw d plotted as a function of the relative discharge Q, as seen in Fig. 3.10(a, b). It is clear from Fig. 3.10(a, b) that (3 decreases when Q* increases or when L/Ds decreases. The effect of L/Ds seems to be smaller for a higher 42 discharge since the models with a limited drop height are predominated by the falling jet impinging into the water pool (Rajaratnam et al. 1997). Figure 3.10 revealed that the air entrainment is a function of the geometry ratio between the outlet to vertical shaft pipe diameter(D0Ut/Ds). The air entrainment increased by increasing(D0Ut/Ds).
As seen in Fig. 3.10, the ratio(Dout/Ds = 1) entrained more air than the ratio(Dout/
Ds = 0.515) due to the deaeration space which increased by increasing the outlet diameter. The results also revealed that the elbow inlet entrained more air than the straight inlet, which was expected since the inlet elbow curvature increased the falling jet velocity. Ervine (1998) suggested that the jet velocity at the impingement point with a pool dropshaft controls the air entrainment in the plunge pool.
3.7 Summary and Conclusions
An experimental study comparing the performance of the elbow and straight inlet entrances for the plunge flow dropshaft was conducted using a drop height of 3.2m and 2.2m. The effect of the ratio of the outlet to vertical shaft diameter was also studied by using a different outlet diameter. The water depth in the inlet and outlet pipes was measured as well as the depth in the forming pool at the bottom of the vertical shaft. The maximum airflow that was demanded by the falling water was measured using a hotwire anemometer.
The flow pattern in the vertical shaft was observed and compared to the preliminary experiments. The results revealed that the elbow inlet dropshaft lowered the impinging point of the falling jet with the vertical shaft between 1.5 Ds for a small discharge to 1 Ds for a higher discharge than the straight inlet. The results showed that the pool water depth for the elbow entrance was higher than the straight entrance in particular for a small flow rate. The submergence of the pool water depth depended 43 on the outlet diameter and was associated with a higher flow rate (regime III). For a
specific discharge, the water depth in the plunge pool was found to be proportional to
the square ratio of the outlet pipe diameter to the vertical shaft pipe diameter(Dout/
2 Ds) . The water depth in the outlet pipe was normalized with the outlet pipe diameter
and found to reach the maximum value at the transition between regimes II and III.
The elbow entrance dropshaft was shown to have a higher water depth in the outlet than the straight entrance at a larger water flow rate. Accordingly, the straight inlet
entrance had a higher outlet velocity than the elbow inlet entrance. The dropshaft
height was found to have small effect on the outlet average velocity for a small flow
rate (regime II), whereas the effect of the dropshaft height became dominant, and the average velocity in the outlet was increased by increasing the dropshaft height at a
large flow rate.
The energy dissipation for the plunge dropshaft was significant. The elbow entrance was found to dissipate more energy than the straight inlet. The energy dissipation was found to increase with increasing the dropshaft height, and with
increasing the outlet diameter for the same discharge. The results also revealed that the elbow inlet entrained more air than the straight inlet. The airflow required by the falling water in terms of the water discharge was found to increase with increasing(Z)out/Ds), and decreased with increasing the water discharge.
The advantages of providing an elbow entrance to the inflow pipe at the top of the vertical shaft can be summarized as: (1) Lowering the impingement point which minimizes the potential for blockage, (2) Higher pool depth that acts like a "cushion" minimizing the impact of the falling flow at the bottom of the vertical shaft, and (3)
44 Dissipate more energy which minimizes wear and tear in the outlet pipes. The disadvantage is that the elbow entrance entrains more air than the straight inlet.
45 Feeding Tank
Inlet pipe (Di„ =152,4 mm) JE ^ Vertical shaft (D,=296 mm) Damping mesh Elbow or straight / entrance 1 L =3 2m -2.2m
K Feeding pipe
Outlet pipe (D„m= 296 or 152.4 mm) 3 hp I •^r /> Plunge pool
Figure 3.1 Definition sketch of the experimental setup
46 Fig.(a) [:' dj, n Fig.(b)
r
"SiHvA.: r -'.^
Sssj
';'( aT3 (r
&± Figure 3.2 Flow visualization for 2.2m drop height (a) straight inlet and flat vertical shaft bottom with 0.152m outlet pipe diameter (b) elbow inlet and semicircular vertical shaft bottom with 0.296m outlet pipe diameter.
47 • elbow entrance (L= 3.2m , Dout=296mm) O elbow entrance (L= 3.2m , Dout=152.4mm) • elbow entrance (L= 2.2m , Dout=296mm) O elbow entrance (L= 2.2m , Dout=152.4mm) t .*_•_ • straight entrance (L= 3.2m , Dout=296mm) o % h • D straight entrance (L= 3.0m , Dout=152.4mm) • • • straight entrance (L= 2.2m , Dout=296mm) o° A straight entrance (L= 2.2m , Dout=152.4mm) 6 • J 3L * & ft oo oo j£_*. ^H-D^-^J- <* fe 6* chA
0.2 0.4 0.6 0.8 Q.
Figure 3.3 Change of normalized drop distance to vertical shaft diameter with relative discharge for elbow and straight inlet dropshaft.
48 y
• elbow entrance (L= 3.2m , Dout=296mm) O elbow entrance (L= 3.2m , Dout=152.4mm) * • elbow entrance (L= 2.2m , Dout=296mm) O elbow entrance (L= 2.2m , Dout=152.4mm) • straight entrance (L= 3.2m , Dout=296mm) D straight entrance (L= 3.0m , Dout=152.4mm) • straight entrance (L= 2.2m , Dout=296mm) A straight entrance (L= 2.2m , Dout=152.4mm)
0.2 0.4 0.6 0.8 Q. Figure 3.4 Change of the normalized inlet depth to inlet pipe diameter with relative discharge for elbow and straight inlet entrance.
49 1.2 Fig.(a) • elbow entrance (L= 3.2m , Dout=296mm) • • elbow entrance (L= 2.2m , Dout=296mm) • • • straight entrance (L= 3.2m , Dout=296mm) • straight entrance (L= 2.2m , Dout=296mm) • * 0.8 * • • • • • • • • o • + • ?0.6 • ! " * 0.4 # -: \' • • • 5 A
0.2
0.2 0.4 0.6 0.8 Q.
3.5 Fig.(b) | a O elbow entrance (L= 3.2m , Dout =152.4mm) o 3 A O elbow entrance (L= 2.2m , Dout=152.4mm) • D straight entrance (L= 3.0m , Dout=152.4mm) °o A 2.5 LA " A straight entra ice (i= i.im, uoiit=i5Z.4mm j ^
o a _°-1.5 o 0 a o a m 0.5 o H1 ^fi
0.2 0.4 0.6 0.8
Figure 3.5(a, b) Change of dimensionless pool water depth in dropshaft for straight and elbow inlet entrance with relative discharge for (a) 296mm outlet pipe diameter
(b) 152.4 mm outlet pipe diameter.
50 • elbow entrance (L= 3 .2m, Dout=296mm) O elbow entrance (L= 3 .2m, Dout=152.4mm) • elbow entrance (L= 2 2m, Dout=296mm) O elbow entrance (L= 2 .2m, Dout=152.4mm) • straight entrance (L= 3.2m, Dout=296mm) D straight entrance (L= 3.0m, Dout=152.4mm) • straight entrance (L= 2.2m, Dout=296mm) o 2.2m, Dout=152.4mm) A straight entrance (L= • 3L A* • • • *" £
•.•: i o o • o • i o O B IB h
0.2 0.4 0.6 0.8
Figure 3.6 Change of dimensionless parameter (hp/Dout) (Dout/Ds) with relative discharge for straight and elbow inlet entrance.
51 • elbow entrance (L= o O 3.2m, Dout=296mm) o O o o o O elbow entrance (L= o A o o o 3.2m, Dout=152.4mm) « A ° <-> o A • elbow entrance (L= 2.2m, Dout=296mm) o A A A A A o O elbow entrance (L= 4B ° DD D • 2.2m, Dout=152.4mm) D ° D D D •S • straight entrance(L= 3.2m,Dout=296mm) A • • • o w • • • Dstraight entrance (L= ft • • • • 3.0m, Dout= 152.4mm) • # • •: A * ^ i A straight entrance (l_= • • • i 1 « ' 2.2m, Dout=296mm) 1 f A straight entrance (L= 2.2m,Dout=152.4mm)
0.2 0.4 0.6 0.8 Q.
Figure 3.7 The normalized outlet water depth with outlet diameter as a function of relative discharge for elbow and straight inlet entrance.
52 D D • elbow entrance (L= n 3.2m, Dout=296mm) A A n O elbow entrance (L= 3.2m, Dout=152.4mm) A • elbow entrance (L= D 4 A 2.2m, Dout=296mm) D O • A * O elbow entrance (L= D • 2.2m, Dout=152.4mm) • straight entrance(L= D A • • o • 3.2m,Dout=296mm) % • * 4 B A • Dstraight entrance (L= . * A ' A^A • 3.0m, Dout=152.4mm) * A straight entrance (L= • ft #•*• till 2.2m, Dout=296mm) 5 ** A straight entrance (L= 2.2m, Dout=152.4mm)
0.2 0.4 0.6 0.8 Q. Figure 3.8 Outlet water velocities as a function of relative discharge for elbow and straight inlet entrance.
53 • elbow entrance (L= 3.2m,Dout=296mm) •*#• t*M- m O elbow entrance (L= 5f • 3.2m,Dout=152.4mm) • 8 . • elbow entrance (L= £1 % . 2.2m, Dout=296mm) A A o o * • o O elbow entrance (L= a 2.2m, Dout=152.4mm) • • straight entrance (L= • 3.2m,Dout=296mm) £) A A D straight entrance (L= 3.0m,Dout=152.4mm) & A straight entrance (L= (A 2.2m, Dout=296mm)
A straight entrance (L= 2.2m, Dout= 152.4mm)
0.2 0.4 0.6 0.8
Q. Figure 3.9 Relative energy dissipation (r\) related to the relative discharge (Q„) for elbow and straight inlet entrance.
54 • elbow entrance (L= 3.2m, Dout=296mm) • O elbow entrance (L= 3.2m, Dout= 152.4mm) • • elbow entrance (L= m 2.2m, Dout=296mm) • • O elbow entrance (L= 2.2m, Dout=152.4mm) • • • straight entrance (L= 3.2m,Dout=296mm) • • straight entrance (L= • • - • 3.0m, Dout= 152.4mm) o A o A straight entrance (L= 2.2m,Dout=296mm) R Q A 1 J J * A straight entrance (L= A A A ^i i A A 2.2m, Dout= 152.4mm) f s 8 ft 0.2 0.4 0.6 0.8
Q. Figure 3.10 Variation of the relative air discharge (/?) with the relative water discharge ((?,) for elbow and straight inlet entrance.
55 References
Chanson, H. (2004). "Hydraulics of Rectangular dropshafts." Journal of Irrigation and
Drainage Engineering, ASCE, 130(6): 523-529.
Christodoulou, G.C. (1991). "Drop Manholes in Supercritical pipelines." Journal of
Irrigation and Drainage Engineering, ASCE, 117(1): 37-47.
Ervine, D.A. (1998). "Air Entrainment in Hydraulic Structure: a Review." Proc. Instn
Civ.Engrs Wat., Marit. & Energy, 130, Sept. ,142-153.
Giovanni, D.M., Rudy, G., Francesco, G., Hager, W.H. (2007). "Circular Drop
Manholes Preliminary Experimental Results." 32nd Congress of International
Association of Hydraulic Engineering and Research (IHAR), July 1-6, Venice -
Italy.
Hager, W.H. (1999). "Cavity Outflow from a Nearly Horizontal Pipe." International
Journal of Multiphase Flow, 25: 349-364.
Hager, W.H. (1995). "Vortex Drop Inlet for Supercritical Approaching Flow."
Journal of Hydraulic Engineering, ASCE, 116(8): 1048-1054.
Metcalf & Eddy, Inc. (1981). Wastewater Engineering: Collection and Pumping of
Wastewater, McGraw-Hill series in water resources and environmental
engineering , New York, 432 pages
Rajaratnam, N., Mainali, A., and Hsung, C.Y. (1997). "Observations on Flow in
Vertical Dropshafts." Journal of Environmental Engineering, ASCE, 123(5):486-
491.
56 Chapter 4
The Effect of Plunge Pool Configuration on the Performance of
Dropshafts
4.1 Introduction
The function of a dropshaft is to transport water safely at a large vertical distance, which requires careful design for energy dissipation and for air entrainment. As the height of the vertical shaft increases, the impact and potential for structural damage at the bottom and the wall of the vertical shaft increases where impact and scouring forces are greatest. Although dropshafts are commonly used in sewers, storm-water systems, downstream of culverts, and large spillway shafts (Rajaratnam et al. 1997;
Chanson 1998, 2002, 2004, Visher and Hager 1998, Toda and Inoue 1999), dropshafts are not systematically documented (Rajaratnam et. al.1997). In general, there is little information on the hydraulic performances of plunge dropshafts. There is a continuing need to design dropshafts which provide features that combine effective energy dissipation associated with the elevation drop e.g. removing any air that mixes or entrains with water as it descends and minimizes the hydraulic head loss when the tunnels are surcharged which increases the stability of the system.
Modeling studies have also explored the effect of impact, scouring, and erosion.
Various modifications were employed in an effort to determine the most effective and economical means to dissipate the energy so that the velocities in the dropshaft outlets do not exceed the design values (Anderson and Dahlin 1975). The impact of the flow on the dropshaft floor depends on the height of the drop. Even for relatively shallow drops, provisions for plunge pools should be made to reduce the magnitude of the
57 impact. The plunge pool may be created by forming a sump at the base of the vertical shaft or by restricting the flow with a weir or similar devices in the outlet of the drop structure to back up the flow, which is used to reduce the effect of the impact. Sump and plunge pools should be self-draining and minimize the accumulation of debris.
Plunge pools are often difficult to maintain and accumulated debris may fill the pool volume. Plunge pool sumps may add significant size to the dropshaft structure and increase the depth of excavation. A pool is typically formed behind a baffle wall with a slotted opening that allows the pool to drain. Contrary to design assumptions, the downstream condition that may impose a supercritical flow should be avoided as it would lead to the formation of a hydraulic jump and possible transition of the flow from free surface to pressurized pipe. Another alternative procedure can be employed to increase the energy dissipation such as impact caps (casserole, deflector baffle).
Jain and Kennedy (1983) argued that the more recent dropshaft designs have a tendency not to include these devices since they are relatively expensive and inconvenient to construct. They favour using wear resistance material.
One of the early designs for plunge flow dropshaft structures has been developed at the University of Minnesota's St. Anthony Falls Hydraulic Research Laboratory
(Anderson and Dahlin 1975) which is one of the major considerations in all dropshaft structure designs for the Tunnel and Reservoir Plan (TARP) in Chicago. These types of structures may include an energy-absorbing device (i.e. sump, impact cap) at the base of the vertical shaft.
Air entrainment is another concern in vertical dropshafts. A proper deaeration is needed to prevent the reduction in the pipe discharge capacity. Some work on air entrainment in plunge dropshafts has been published (Anderson 1961; Whillock and
Thorn (1973); Rajaratnam et al. 1997); however, further studies are needed for a
58 complete representation of air entrainment in dropshafts. Some publications studied
the hydraulics of air-water properties in the plunge pool (Chanson 2002, 2004), and
the air entrainment by the plunging jet falling down within a dropshaft (Ervin (1982);
Ciaravino et al. (2005) Gualtieri and Pulci Doria (2006).
In these experiments, some configurations were tested to dissipate or absorb
energy from the falling flow. The experimental study focuses on the effect of the
plunge pool that formed by providing a sump on the base of the vertical shaft, and by
restricting the flow at the outlet pipe with baffle on the performance of the dropshaft.
The study extended to investigate the effect of the junction type at the bottom of the
vertical shaft. Detailed flow measurements were obtained on the variation of water
depth in the inlet and outlet pipes as well as the air entrained into the vertical shaft for
all configurations. It was anticipated that the results would provide new insight into the hydraulics of plunge flow dropshafts.
4.2 Experimental Setup
The experiments were performed in a dropshaft that was built at the hydraulic
laboratory at the University of Alberta. The same facility was previously used in
Chapter 3. Water was supplied to the dropshaft inlet by an elevated tank, and water discharge was measured using a magnetic flow meter installed at the pump feeding pipe. The diameter of the inlet pipe (Din) was 0.152m, and two different outlet diameters(D0Ut) were used (0.296m and 0.152m). The length of the straight inlet and outlet pipes were 3.2m and 4.0m respectively. Both pipes were horizontal. The dropshaft height in the invert (L) was between 3.0-3.2m, and the vertical shaft diameter (Ds) was 0.296m. The outlet flow was drained into the hydraulic laboratory
59 sump through a same diameter elbow. Thus, a free surface flow at the outlet without a backwater effect can be assumed for the downstream pipe.
In the first configuration (baffle series), the plunge pool was made by backing up the flow with a baffle installed at the end of the outlet pipe. Four different baffle heights (e) were used in order to have initial tailwater depths of 46, 57, 76, and
97mm. This configuration was used with the elbow inlet entrance with a 0.296m outlet diameter, whereas the second and third configurations were used with the straight inlet entrance dropshaft. The sketch of the setup can be seen in Fig. 4.1. In the second configuration (sump series), a circular sump with an approximate depth of
(S=0.3m) equal to the diameter of the vertical shaft was installed below the outlet pipe invert. Two different outlet diameters were used (0.296m and 0.152m respectively).
A photo of this configuration is provided in Fig. 4.2. In the third configuration
(junction series), three different connections between the vertical shaft and outlet pipes that have the same diameter were tested. The junctions tested were the original semi circular junction, the elbow junction, and the straight junction with a flat bottom
(see Fig. 4.3).
4.3 Experimental Flow Conditions
4.3.1 Inlet flow depth
The depth of the flow in the inlet pipe was measured for all experiments at one location at 1.2m from the edge of the vertical shaft. The height of the water surface was measured with a point gauge, and by measuring the pressure head with a piezometer located at the bottom of the pipe. When the inlet pipe was full, the pressure was measured by taking the average of the pressure head of the top, and at the bottom. The water depth in the inlet pipe (din) for all configurations was 60 normalized with an inlet pipe diameter, and plotted as a function of the relative discharge ((?») as shown in Fig. 4.4.
The inlet measuring station was located at an adequate distance from the tangential inlet so that the curvature in the water surface close to the inlet entrance with vertical shaft did not affect the flow depth at the station. The curve corresponding to the upstream measurement could be used to determine the depth of the flow in the inlet pipe for any given discharge.
4.3.2 Outlet pipe flow condition
The depth of the flow in the outlet pipe (dout) was measured for all experiments at one location at 0.7m from the end of the outlet pipe. The height of the water surface was measured by measuring the pressure head with a piezometer located at the bottom of the pipe. The average velocity at the measuring section was calculated by dividing the water discharge by the cross section area of the water flow. The flow in the outlet pipes was always found to be partly full for all configurations used in these experiments.
Baffle series
The normalized outlet depth (d0Ut/D0Ut) with the relative discharge for the baffles series is provided in Fig. 4.5(a). It is clear that the depth of the flow in the outlet pipe at the measuring station is increased with increasing the baffle height (e) except for cases where the hydraulic jump in the outlet pipe passed the measurement station. The flow condition changed from a supercritical flow to a subcritical flow due to the existence of tailwater depth in the outlet pipe. The change of average water velocity for the different baffles height is provided in Fig. 4.6(a). It was concluded that adding 61 the baffle would increase the tailwater depth, which will decrease the average velocity at the outlet due to the increase in the water cross section area. The high velocity is shown in Fig. 4.6(a) for the small baffle series was for the supercritical flow of the hydraulic jump that occurred and passed the measuring station. A detailed explanation will be presented in this Chapter.
Sump series
For the sump series, it is interesting to note that the water depth in the outlet pipe increased with increasing the discharge until it reached the maximum value during the transition between regimes II and III. When the discharge further increased, the water depth began to decrease a little, and then started to increase again as shown in Fig.
4.5(b).
As compared to no sump experiments, the presence of the sump in the dropshaft as seen in Fig. 4.5(b) will decrease the water depth in the outlet. This result was expected since the water impact with a solid body dissipates more energy than the impact with a water body. The average velocity in the outlet is provided in Fig. 4.6(b). The flow condition in the outlet pipe was found to be supercritical, and the average velocity increased with increasing the discharge as seen in Fig. 4.6(b). It in is interesting to note that the average velocity for the small and large outlet pipes that had been used have close values until it reaches the maximum depth. For a large discharge, the small pipe has a higher velocity value in order to force the discharge in the small cross section area. As seen in Fig. 4.6(b), the average velocity is higher for the plunge pool with sump experiments than for no sump experiments.
62 Junction series
The normalized outlet water depths for the three different junctions that were used on the base of the dropshaft are provided in Fig. 4.5(c). Figure 4.5(c) reveals that the straight junction with a flat pool base, for a relative discharge of Q, < 0.5 has a larger water depth in the outlet than the semi circular pool base, or elbow junctions whereas, for a relative discharge of Qt > 0.5, the flat base and the elbow base junctions have the same outlet water depth.
The average velocity of the elbow base junction for a relative discharge Qt <
0.5 is higher than the others for a relative discharge of Q* < 0.5, and for Qt > 0.5, the semi circular base has an average velocity value higher than the other junctions as seen in Fig. 4.6(c).
4.3.3 Hydraulic jump in outlet pipe
Based on the observations of the baffle series experiments, the hydraulic jump or supercritical swell will form in the presence of tailwater depth (yt) (backwater). For a small tailwater depth (yt /Dout = 0.15) and for a small discharge, it was found that the hydraulic jump started as a submerged hydraulic jump near the outlet entrance due to the tailwater depth (yt) which is larger than the subcritical sequent depth (y2). The subcritical sequent depths of these jumps can be approximately predicted with an integral momentum equation if the supercritical sequent depth (yj and relative discharge (Q«) are known (Stahl and Hager 1999). As the water discharge increased, the sequent depths of the hydraulic jump y1 and y2 increased. When yt is equal toy2, the hydraulic jump will form near the entrance of the outlet pipe at a relative discharge of Qt = 0.16. With a further increase in discharge, the hydraulic jump began to move toward the outlet end. It was noted that the hydraulic jump passed the 63 outlet water depth measuring station at a relative discharge of Q» = 0.37 where the supercritical flow water depth was noticed. The visualization of the hydraulic jump can be seen in Fig. 4.7.
Similar observations were noted for the tailwater depth yt /Dout = 0.19 except where the hydraulic jump formed at the outlet entrance where the relative discharge was Q, — 0.37, and the jump passed the measuring location atQ, = 0.53. For the higher tailwater depth, the jump occurred at a relative discharge of Qt = 0.27 for a normalized tailwater depth of yt /Dout = 0.26. Whereas, the hydraulic jump occurred at Q* = 0.42 for yt /Dout = 0.33. The hydraulic jump did not pass the outlet water depth measuring location for yt /Dout = 0.26 and yt /Dout = 0.33. A sketch of the relationship between the normalized hydraulic jump locations with the outlet pipe diameter measured from the outlet entrance with a relative discharge is provided in Fig. 4.8.
Let us consider the inflow from the inlet pipe by calculating the approach Froude number, which defined as F0 = v/J(gd), in which v is the average velocity of water flow (m/sec), g = acceleration due to gravity (m/sec2), and d is the hydraulic depth of water flow (m) which defined as A/T where A is the water flow cross section area (m2), and T is the top width of water flow in inlet pipe(m). The range of the approach Froude number (F0) in outlet pipe was 1.3 to 3.5 in these experiments, and the hydraulic jump was classified as a weak jump. It was observed that the hydraulic jump had lateral wings on the side with rather weak circulation regions near the water surface (see Fig. 4.8). Similar observations for these particular hydraulic jumps were reported (Rajaratnam and Mainali (1995), and Stahl and Hager (1999)).
64 4.4 Energy Dissipation
As previously mentioned, the energy dissipation for the transferred flow from a higher level to a lower level is a major concern that needs to be estimated in the design of a dropshaft structure. The energy dissipation in these experiments was evaluated by measuring the water depth in two sections. The first section was at the approaching flow at the inlet pipe, which has an approximate elevation of L =
3m to 3.2m. The second section was located at the outlet pipe at a distance of 0.7m from the pipe end. The dissipated energy between sections one and two mainly involved the wall friction, water impact at the base of the pool, air-water mixture in the plunge pool, and in some cases, the hydraulic jump in the outlet pipe that occurred between the measuring sections.
Following the same procedure that was used in previous Chapters by assuming Hx is the inlet energy head and Hres is the residual head at the outlet pipe, the efficiency of the energy dissipation can be quantified by n. The relative energy dissipation for the baffle series is shown in Fig. 4.9(a). Figure 4.9(a) revealed that for Qt < 0.1, the no tailwater depth case dissipated more energy than the cases with tailwater depth. It was concluded that for a low flow rate the impact of the flow as a source of dissipated energy decreased with increasing the tailwater water depth. The increase in water depth in the plunge pool from the tailwater behaves like a "cushion" which absorbs the impact of the falling water. As a result, for a low discharge ( Qt < 0.1), the energy dissipation decreased with increasing the tailwater depth. The tailwater depth had no effect on the energy dissipation that occurred due to the impingement of water flow on the vertical shaft, and on the wall friction of the spreading flow. As the water discharge increased, the flow pattern became more complicated. The energy dissipation included mixing in the plunge pool, and the hydraulic jump that might 65 occur at the outlet pipe. The behaviour of the flow in the plunge pool is very similar to a submerged jet that produces intense turbulence, and dissipates more energy with increasing the plunge pool depth as seen in Fig. 4.9(a).
The energy dissipation for the sump series experiment is provided in Fig. 4.9(b).
As shown in Fig. 4.9(b), providing a sump with a depth equal to the diameter of the vertical shaft has very small effect on the energy dissipation. Rajaratnam and Mainali
(1995) made a similar conclusion for a similar setup, which noted that the dynamic pressure of the impact on the pool base for a dropshaft with a sump depth equal to the diameter of the vertical shaft would be roughly equal to the values for no sump case.
Anderson (1961) also mentioned that the force of the jet easily penetrated the deep sump or water cushion. He indicated that the water cushion above was not an effective means of energy dissipation unless the surrounding pool was large in comparison to the shaft diameter, and the point of the outflow was located at a distance from the jet impingement area.
The effect of the sump is shown only for a small outlet pipe (Dout = 0.152m ), and for a large discharge (Q, > 0.6) as shown in Fig. 4.9(b). The reason is that the water depth in the plunge pool (/ip) above the outlet pipe invert becomes about 1.5 to
2 times the diameter of the vertical shaft.
The effect of the type of junction at the base of the vertical shaft with the outlet pipe can be seen in Fig. 4.9(c). The elbow junction seems to dissipate less energy for a small discharge, and the flat bed junction is the best in terms of energy dissipation.
The difference in energy dissipation between the junctions was found to be insignificant as seen in Fig. 4.9(c).
66 4.5 Air Entrainment
The rate of air entering the vertical shaft was measured for all configurations. The effect of tailwater flow on air entrainment or air concentration (P), which is defined as the ratio of the air discharge (Qa) to water discharge (Qw) is shown Fig. 4.10(a). In general, the air entrainment decreased with increasing the relative discharge as seen
Fig. 4.10(a). In addition, the air entrainment decreased with increasing the tailwater depth especially for a higher discharge. This result was expected since most of the air entrained is likely to be carried to the outlet pipe that depends on the water velocity leaving the vertical shaft. As previously mentioned, the increase in the tailwater depth will decrease the average velocity at the outlet due to the increase in the cross section area and, as a result will decrease the air entrainment.
Figure 4.10(b) revealed that providing a sump with a depth equal to the diameter of the vertical shaft has little effect on air entrainment in the dropshaft. The air entrainment is also a function of the geometry ratio between the outlet to vertical shaft pipe diameter (Dout/Ds) as shown in Fig. 4.10(b). The air entrainment for Dout =
0.296m is larger than for Dout = 0.152m due to the difference in the deaeration space, which is increased by increasing the top width of the water surface in the outlet pipe. A similar conclusion was made in Chapter 3.
The air entrainment for different junction series is provided in Fig. 4.10(c).The semi circular bottom entrains more air (approximately 33 %) than a flat or elbow bottom type for a higher discharge of Q, > 0.5 as seen in Fig. 4.10(c). The difference is due to the change in average water velocity leaving the vertical shaft between the junctions.
67 4.6 Summary and Conclusions
Three different configuration series of plunge dropshafts were investigated systematically to study the effect of tailwater depth, sump, and type of junction at the bottom of the vertical shaft. The study mainly focused on energy dissipation and air entrainment. The water depths were measured at the inlet and outlet pipes. The maximum airflow demanded by the falling water was measured using a hotwire anemometer.
Experimental observation showed that the presence of tailwater depth would create a hydraulic jump in the outlet pipe that would change the flow from a supercritical to subcritical flow. The location of the hydraulic jump in the outlet pipe depended on the water discharge and tailwater depth. The results revealed that the no tailwater depth case dissipated more energy than the cases with tailwater depth. The air entrainment was found to decrease with increasing the tailwater depth especially for a higher discharge.
Installing a sump at the bottom of the vertical shaft was found to decrease the water depth in the outlet pipe. This difference in water depth between no sump and sump cases depended on the discharge, and the geometry ratio between the outlet to vertical shaft pipe diameter (,D0Ut/Ds). The energy dissipation for no sump cases is higher than for dropshafts provided with sump. The air entrainment is also a function of the geometry ratio between the outlet to vertical shaft pipe diameter (Dout/Ds) which decreased with decreasing the geometry ratio. The results show that when the outlet and vertical shaft diameter is equal, providing sump with a depth equal to the vertical shaft diameter it has no effect on the energy dissipation, and has very little effect on air entrainment in the dropshaft.
68 The type of junction at the base of the vertical shaft with the outlet pipe has little effect on the water depth in the outlet pipe. The difference in energy dissipation between the junctions was found.to.be insignificant (approximately 1%)., whereas, the semi circular bottom junction entrains more air around (33 %) than a flat or elbow bottom type junction for a higher discharge of Q* > 0.5.
It can be concluded that using a tailwater at the outlet pipe will create a hydraulic jump that dissipates more energy, and will change the flow type from supercritical to subcritical flow to control allowable maximum flow velocity that is dictated by wear consideration.
There is no benefit of adding a sump to the vertical shaft unless the magnitude of water impact on the bottom of the dropshaft needs to be reduced. The sump should be self-draining and minimize the accumulation of debris.
69 I -Air Inlet
Inlet pipe (Din =152.4 mmh *\
Vertical shaft (Ds=296 mm)...
Elbow or straight entrance Semi-circular junction Elbow ' junction K' T Flat Bottom junction
Outlet pipe (POUi= 296 or 152.4 mm)
j Sump J |S=0.3m'' Baffle (e = 46, 57, 76; Plunge pool or 97 mm height)
Figure 4.1 Definition sketch of the experimental setup
70 • Fig.(a)
Figure 4.2 Visualization of 152.4mm outlet pipe diameter with (a) flat vertical shaft
bottom without sump and (b) flat vertical shaft bottom with 0.3m sump depth.
Figure 4.3 Visualization of the junctions on the vertical shaft bottom (a) semicircular junction, (b) elbow junction, and (c) flat bottom junction.
71 x Baffle series e/Dout=0
D Baffle series e/Dout=0.15
D Baffle series e/Dout=0.19 $ ? * Baffle series e/Dout=0.26 T^ x Baffle series e/Dout=0.33 III O Sump series S/Dout=0 -f (Dout=296mm) • Sump series S/Dout=l (Dout=296mm) O Sump series S/Dout=0 1 (Dout=152.4mm) • Sump series S/Dout=2 -1* (Dout=152.4mm) A semicircular junction
A elbow junction
A flat bottom junction
0.2 1.4 0.6 0.1 Q.
Figure 4.4 Change of the normalized inlet depth to inlet pipe diameter with relative discharge for elbow and straight inlet entrance.
72 0.7 X x Baffle series X 0.6 e/Dout=0 - Fig.(a) - X 33 X * X * D Baffle series 0.5 u< X X X •H X * m e/Dout=0.15 * * w to, X * ED Baffle series • a e 0 • e/Dout=0.19 • • * Baffle series V X X 0.2 X e/Dout=0.26 X X X X D D 0 X X a x Baffle series 0.1 X * e/Dout=0.33 0 0.2 0.4 0.6 0.8 Q.
0.50 O Sump series — Fig.(b) 0.45 0 S/Dout=0 0.40 o o • (Dout=296mm) ^ o o o • 0.35 o o o • Sump series o • • • • • S/Dout=l 0.30 J> • • (Dout=296mm) I 0.25 $ Q o Sump series
0.25
Fig-(c) A A A • A A A 0.20 A A semicircular 4A A 4* junction I 0.15 • A elbow 1**A A * junction A • flat bottom tj° 0.10 * A * 'A junction
0.05
0.00 0.4 0.8 0.2 Q. 0.6
Figure 4.5 Change of normalized outlet water depth to the outlet diameter with relative discharge (Q*) for (a) baffle series, (b) sump series, and (c) junction series.
73 3.0
2.5 x Baffle series • X e/Dout=0 Fig.(a) • X 8 2.0 • X D Baffle series • X e/Dout=0.15 :i.5 V X E3 Baffle series X X X e/Dout=0.19 X X s Baffle series !,o X t»| e/Dout=0.26 X f * f £ X Baffle series 10.5 * * 1 1 1 £ I £ £ e/Dout=0.33 0.0 09 1 0.2 0.4 Ct0.f 6 0.8
— 4.0 - o Sump series — Fig.(b) 01 • • S/Dout=0 «/Ul ) 1 " > C C . o o (Dout=296mm) + • Sump series • o S/Dout=l >cit y n c • o (Dout=296mm) o O vel ( § 8 O Sump series 3 i . + • • o 0 S/Dout=0 tle t n c _^» !L^ 3 J..-I (Dout=152.4mm) o %-t^t s °^ • Sump series ;: r$ ° S/Dout=2 n •; - oJ (Dout=152.4mm) 0.0 - 0.2 0.4 0.6 0.8 Q. 3.0
2.5 A A Fig-(c) A A 01 A VI 2.0 A semicircular E. A junction A >• 1.5 A 4. A A elbow A . A A A * i £ * junction S A f A A i t 1.0 A * A flat bottom I £ i junction O 0.5
0.0 0.2 0.4 0.6 0.8 Q.
Figure 4.6 Change of average outlet velocity with relative discharge (Q*) for (a) baffle series, (b) sump series, and (c) junction series.
74 Figure 4.7 Flow visualization of: (a) submerged hydraulic jump at the entrance of outlet pipe, and (b) free hydraulic jump at outlet pipe.
75 .• 1 / I / / / • / -** / y' / _?-" _ / *~ • ..-••• .-" .- ^
yt/Dout-0.15 outle t .... yt/Dout=0.19 meas uring yt/Dout=0.2( statio n yt/Dout=0.3-!
6 8 10 12 14 VDout
Figure 4.8 Schematic diagram of relationship between the normalized locations of the free hydraulic jump measured form outlet entrance to the outlet pipe diameter with relative discharge.
76 CT* Tl P Energy dissipation (r|) % Energy dissipation (TJ) % |-b OQ Energy dissipation (T|) % C cta> ^1 ^J oo oo ID U3 O •vl 00 00 ID O >J ^J 00 oo
T3 erg y 3 ro ro ser i xo XQ CD tn D. • >#> m p Ifl 3 ^3 D. T3 O 5* o o • P o 1 • o » a s® O t—.. 3 B » <> «0 D SjSS 3c J O H • • -^1 c^ m o •-t 3 O o o P S- 01 in CD en ni "1 • < •0 xm ra^ . nVI «-*o • 3" CD o •> X X- •I O o O ft 00 bo CO 00 c • > X *} f
OQ •—* in in o A U3 A lO o r+l/i r+t/w> r+vr* v>> r+r-f inm i-fi-t min O W ro NJ m en m Ol ro^ u> -i w iifBHiBHroiin"(t> M(t) II )
0.2 0.4 0.6 0.8
o O Sump series Fip (bu) • rig. l / S/Dout=0 (Dout=296mm) • Sump series S/Dout=l 0 (Dout=296mm) o Sump series o S/Dout=0 • (Dout=152.4mm) • Sump series S/Dout=2 • • • • • :t» t 1 a * (Dout=152.4mm) 0.2 0.4 0.6 0.8 Q.
A A Fig.(c) A semicircular A junction
ft A elbow junction A A. Aflat bottom A A junction A ^ A *n & i & 4
0.2 0.4 0.6 0.8 Q. Figure 4.10 Variation of the relative air discharge (P) with the relative water discharge
(Q*) for (a) baffle series, (b) sump series, and (c) junction series.
78 Reference
Anderson, S.H. (1961). "Model Studies of Storm-Sewer Drop Shafts." St. Anthony
Falls Hydraulic Laboratory, University of Minnesota, Minneapolis Minnesota,
Technical Paper 35 Series B.
Anderson, A.G. and Dahlin, W.Q. (1975). "Model Studies of Dropshaft for the
Tunnel and Reservoir." St. Anthony Falls Hydraulic Laboratory, University of
Minnesota, Minneapolis, Minnesota, Project report 154.
Chanson, H. (1998). "The Hydraulics of Roman Aqueducts, Steep Chutes, Cascades
and Dropshaft." University of Queensland, Australia, Research report no. CE156.
Chanson, H. (2002). "An Experimental Study of Roman Dropshaft Hydraulics.",
Journal of Hydraulic Research IHAR, 40(1), 3-12
Chanson, H. (2004). "Hydraulics of Rectangular Dropshafts." Journal of Irrigation
and Drainage Engineering, ASCE, 130(6):523-529.
Chanson, H., Aoki, S., and Hoque, A. (2002). "Similitude of Air Entrainment at
Vertical Circular Plunging Jets." ASME Fluid Engineering Division Summer
Meeting Montreal
Ciaravino, L., Gualtieri, P., and Pulci Doria, G. (2005). "Complementary
Experimental Methods for Measurements of Air Entrainment in Vertical
Dropshafts." Computational Methods and Experimental Measurements XII, WIT
Transaction on Modelling and Simulation, WIT Press, 41:817-827.
Ervine, D.A. (1998). "Air Entrainment in Hydraulic Structure: a Review." Proc. Instn
Civ.Engrs Wat., Marit. & Energy, 130, Sept. 142-153.
Gualtieri, P., and Pulci Doria, G. (2006). "Air Entrainment in Vertical Dropshafts
with an Orifice." Vorticity and Turbulence Effects in Fluid Structure Interactions:
79 An Application to Hydraulic Structure Design, WIT Press, Southampton, UK,
157-187.
Jain, S. C. and Kennedy, J. F. (1983). "Vortex-Flow Drop Structures for the
Milwaukee Metropolitan Sewerage District Inline Storage System." Iowa Institute
of Hydraulic, University of Iowa, Iowa City, Iowa, IIHR Report 264.
Rajaratnam, N., and Mainali, A. (1995) "Hydraulic Design of Dropshafts for the City
of Edmonton Drainage System." report prepared for city of Edmonton, University
of Alberta, Edmonton, Alberta.
Rajaratnam, N., Mainali, A., and Hsung, C.Y. 1997. "Observations on Flow in
Vertical Dropshafts." Journal of Hydraulic Engineering, ASCE, 123(5):486-491.
Stahl, H., and Hager, W.H. (1999). "Hydraulic Jump in Circular Pipe." Canadian
Journal of Civil Engineering, 26(3):368-373.
Vischer, D., and Hager, W.H. (1998). "Dam Hydraulics" John Wiley, Chichester, UK,
316 pages.
Whillock, A.F., and Thorn, M.F.C. (1973). "Air Entrainment in Dropshafts."
Construction Industry Research and Information Association, Technical note 48.
80 Chapter 5
The Effect of the Size of Air Vents and Outflow Direction on the
Performance of Plunge-Flow Dropshafts
5.1 Introduction
The phenomenon of air entrainment in dropshafts plays an important element in hydraulic structure design. The falling water inside the vertical shaft creates sub- atmospheric pressure in the shaft. The airflow is due to the pressure difference between the atmospheric pressure at the entrance of the ventilation pipe and the sub- atmospheric pressure inside the vertical shaft. The magnitude of the sub-atmospheric pressure inside the vertical shaft depends on the entrainment rate between air and water, and the air vent resistance. High-pressure difference can be achieved if the air ventilation is sealed or there is no air supply. Depending on the magnitude of the sub- atmospheric pressure, this could cause several problems in the dropshaft including a rise in water level in the plunge pool at the bottom of the vertical shaft. At a certain value of sub-atmospheric pressure, it is possible the water pressure that rises in the plunge pool could puncture the water curtain that is formed by the falling jet with a cylindrical wall jet along the wall of the vertical shaft. When this occurs, the water level in the plunge pool falls rapidly, and the rapid rise and fall of the water level in plunge pool gives rise to unsteadiness in the system that might cause vibrations and produce noise with the flow. Furthermore, if the sub-atmospheric pressure in the dropshaft falls to very low values, it might cause cavitations at spots of high flow velocity including the flow entrance to the vertical shaft, and at locations along the wall where the falling water impinges (Rajaratnam and Mainali 1995).
81 If adequate air is supplied, most of the air may be carried to the outlet of the dropshaft unless some air circulation in the dropshaft ventilation is provided for the air to be released back into the dropshaft. Furthermore, if the outlet pipe of the dropshaft operates as running full, the air may accumulate into pressurized air pockets that occupy the upper part of the outlet pipe, which will reduce the carrying capacity of the pipe. This air might be highly pressurized, and violently blow through the dropshaft or at any manhole along the system causing serious structural damage to the sewer system. The air released at the vertical shaft vicinity often causes the most concern (odours) since these emissions are a source for volatile organic compounds
(VOCs) which depends upon the vertical dropshaft height, wastewater strength, and flow characteristics (Zytner et.al (1997).
So far, the most efficient and economical solution for dropshaft ventilation is to minimize the quantity of air that is entrained with the flow by providing a deareation chamber. This allows the entrained air at the vertical shaft and plunge pool to be released from the flow, which reduces the potential of air high pressure to be created at the dropshaft outlet or main tunnel. This air returns via another small shaft located at the deaeration chamber after the vertical shaft that feeds the air demand of the dropshaft.
The quantity of air entrainment cannot be solved with traditional fluid mechanics equations. Studies using small and large-scale dropshaft models have been used to establish the relationship between design parameters, which has an impact on the entrained air so that the performance in the prototype can be more accurately predicted. Most dropshaft models that have been tested in relation to the air entrainment suggest that a poor correlation exists between the model and prototype results (Hydraulic Modeling ASCE 2000).
82 This Chapter investigates the effect of air vent size on the air entrainment of plunge flow dropshafts. Although laboratory models cannot accurately predict the air entrainment for the prototypes, these models cannot duplicate the complexities that exist in actual air entraining in vertical dropshafts. It was anticipated that this investigation would provide an approximate estimation of air entrainment that helps to determine the appropriate design and proper location for vertical dropshaft ventilation.
The experimental work extended to investigate the effect of outflow direction on the hydraulic performance and air entrainment. The hydraulic performance involved flow condition in inlet pipe, outlet pipe, and flow pattern in vertical shaft, which plotted as a function of the incoming relative discharge. The calculated specific energy in the inlet pipe for 180° outflow direction was compared to the theoretical expressions of Hager (1999) and Dey (2001) for computations of critical energy at critical control sections of free fall in horizontal or mildly sloping circular pipes to predict the critical specific energy.
5.2 Experimental Setup
The experimental setup as shown in Fig. 5.1 is similar to the one previously used in Chapters 3 and 4. Water was pumped to an elevated rectangular tank (0.6m width
X 1.14m long X 0.9m height) by a 0.152m diameter feeding pipe connected at the bottom of the tank. A magnetic flow meter was installed on the pump-feeding pipe to measure the water flow(Qw). The water entered the vertical shaft by a 0.152m horizontal pipe 3.2m in length that connected the side of the elevated tank and the vertical shaft, which is referred to as the inlet pipe. The vertical shaft and outlet diameter both have the same diameter of 0.296m. The height of the vertical shaft is 83 3.2m while the length of the outlet pipe is 4m. Two different outflow directions were used in this setup; the traditional 180° and 90° as shown in Fig. 5.2(a, b). The outlet discharge returned the flow to the hydraulic lab sump.
The experimental setup provided two ventilation entrances (systems). The first one
(shaft ventilation) which is an air vent set on the top of the vertical shaft that allows air to enter from the top of vertical shaft. The second one (inlet ventilation) which is an air vent set on the top of the sealed elevated tank to allow air to enter together with water in the inlet pipe when the flow is partly full. The third set of experiments was the combination of shaft and inlet ventilations that is referred to as 2-way ventilation.
Three different sizes of air vent pipe diameter were used for shaft ventilation (Dvs)
50.8mm, 152.4mm, and 296mm (fully open), while two different sizes of air vent were used for inlet ventilation (Dvb) 50.8 and 152.4mm in diameter. The airflow velocity on the air vent was measured by hotwire anemometer (the error is ± 1% of the full-scale reading with O.lm/sec reading resolution) placed on the top of air vent.
The air discharge (Qa) was calculated by multiplying the average air velocity by the air vent cross section area.
The water depth in the inlet pipe was measured by using point gauge and piezometers connected at the bottom and the top of the pipe located at a distance of about 1.2m from the edge of the vertical shaft. The water depth in outlet pipe was measured by using piezometers connected at the bottom located 3 m downstream from the vertical shaft.
84 5.3 Flow Characteristics
5.3.1 Specific energy in inlet pipe
The specific energy E0 at inlet pipe with reference to the bottom of inlet pipe as
datum is defined as:
E0 = din + ^ (5.1)
where din is water depth in inlet pipe and v is the average velocity that can be
calculated by dividing the water discharge by the water flow cross section area.
The measured water depth for all experiments was normalized to inlet pipe
diameter and plotted as a function of the relative discharge (Q„) as seen in Fig. 5.3(a,
b). As expected from Fig. 5.3(a, b), there was no effect of the outflow direction on
flow depth in inlet pipe.
The average specific energy of inlet water depth for the experiments of 180°
outflow pipe direction was compared with the theoretical calculations of Dey (2001).
For a circular channel, the Froude number of the water flow at the upstream section
(Dey 2001) can be expressed as:
0 25 Fo = n.314 Q. K^X^frW"))] - (5.2) kdin/D)
and the specific energy can be given as:
D \ D ) 16 V(«W0)(1-(«WD)) '
in which F0=Froude number of the approach flow, which is v/V(gd), d = hydraulic
depth (T/A), and T =top width of the flow at water depth of din , A flow area of a
circular pipe which is expressed as:
2 A = 0.25D foln/D) (5.4)
in which
85 kdinlD) = *rcos(l - 2{din/D)) - 2(1 - 2(din/D)) J(din/D)(l - (din/D)) (5.5)
The concept of free falling water in circular channels is adapted to estimate the discharge using a known end depth. When the inlet pipe is either horizontal or mildly sloping, the flow becomes critical (din = dc) at the control section, where dc is the water depth at the critical section. Thus, the Froude number at the control section is unity (F0 = 1). The generalized equation of the relative discharge is derived from
Equation 5.2 and the normalized specific energy from Equation 5.3 will be:
0 = ^
D \D) 16V((Jc/D)(l-(dc/D)) *• " '
Equation (5.6) is solved by trial and error by assuming(dc/£>), calculating Qt, and then comparing the calculated Qt with the measured Q„. The iterations were repeated until the difference between the calculated and measured values of Qt became very small for a specific value of (dc/D). The normalized specific energy at critical depth
Ec is calculated by using Equation 5.7.
Hager (1999) simplified the Froude number from the approximation of the cross sectional area of a circular section to be:
F0 = -j2z= (5.8)
The Froude number for the circular section is therefore proportional to the water discharge Qw, the square root of the water depth, and to the fourth root of the pipe diameter D. Setting F0=\ in Equation 5.8 enables explicit determination for the critical depth dc by this expression:
dc = (5.9)
86 According to Equation 5.9, dc depends only on the fourth root of the pipe diameter. Hager argued that the difference between the exact values of dc with that calculated from Equation 5.9 is less than 4% for the range 0.2< dc/D <0.91. The normalized specific energy at critical depth Ec is given by the following expression:
Ec 3/5 D = -3[Q*] (5.10) for the range 0.1< <2»<0.75 the difference from their exact values is less than 4%.
The calculated critical specific energy of Dey (2001) and Hager (1999) was compared to the measured specific energy by assuming the measured location is very close to the critical depth section and the energy loss between the two locations is very small.
Figure 5.4 shows that this assumption was acceptable since the difference between the measured and calculated specific energy is very small. As seen in Fig. 5.4, Dey's
Equation for calculating specific energy is closer to the experimental data than
Hager's Equation that mainly related to Hager's approximations. It can be concluded that theoretical expressions of specific energy can be used with confidence to estimate the specific energy of partly full water flow in inlet pipe for any given discharge.
5.3.2 Flow description in vertical shaft
The flow pattern was classified similar to the preliminary experiments. In these experiments, regime (II) and (III) were observed. For regime (II), the falling jet impinges on the opposite vertical shaft wall and forms a central ridge with a spreading flow down the shaft due to gravity. As the discharge increases, the falling jet spreads along the vertical shaft diameter, and meets from behind and spirals down the wall of the vertical shaft (regime (III)). The orientation of the outlet pipe with the inlet pipe did not have any effect on flow patterns in the vertical shaft.
87 Let us define the location of the impact of the falling jet on the opposite vertical
shaft, and the location of the spreading flow when it completely covered the vertical
shaft diameter along vertical shaft. These locations were measured from the invert of
the inlet pipe as the front and behind drop distance (Xf). Figure 5.5 shows the drop
distance(Xf), which is normalized with vertical shaft diameter and plotted as a
function of relative discharge(Q»). As seen in Fig. 5.5, the transition between regimes
(II) and (III) in terms of the relative discharge (Q») for these experiments occurred
approximately at Q»=0.32. It is clear that the drop distance (Xf) is decreasing with
increasing the water discharge i.e. it changed from 5.1DS at Q»=0.05 to 1.2DS at
Q„=0.95 for the impact jet on the vertical shaft and changed from 7.5DS at Q*=0.32
to 2.1DS at Q*=0.95 for the location where flow covered completely the vertical shaft
diameter.
The downward spreading flow hit the bottom of the vertical shaft, which was
separated in two horizontal directions: the forward flow along the outlet pipe and the
backward flow that circulated and formed the water plunge pool. The falling
spreading flow along the vertical shaft developed a vertical water curtain, which
covered the outlet pipe entrance that prevented the water from flowing freely to the
outlet pipe. The flow in outlet pipe comes mainly from the sides of outlet entrance.
The orientation of outlet pipe with inlet pipe has great effect on the flow leaving the vertical shaft. For the 90° orientation, the maximum thickness of the falling jet is 90° away from the centerline of outlet entrance, which decreases along the vertical shaft diameter in both directions. Accordingly, the thickness of water curtain is different for both sides at the outlet entrance so the flow leaving the vertical shaft from a smaller thickness side is more than the higher thickness side that makes the flow spiral along the outlet pipe wall as seen in Fig. 5.6 (a). 88 For 180° outflow direction, the maximum thickness of the falling jets is located at the middle of the outlet entrance and decreases in both directions around the vertical shaft diameter. In this case, the flow leaving the vertical shaft from the sides of outlet entrance is equal, and flows as supercritical along the outlet pipe as seen in Fig. 5.6(b)
5.3.3 Flow in outlet pipe
The water depth in the outlet pipe was measured for all experiments, normalized with the outlet pipe diameter, and plotted as a function of the relative discharge (Q„) as shown in Fig. 5.7(a, b). Figure 5.7(a, b) showed that the water depth in the outlet pipe for 90° outflow direction is higher than for 180° outflow direction; in particular for Q,< 0.5. The difference in results was related to the water curtain thickness. For a
90° outflow direction, the water flow was easier to penetrate the side of the water curtain at the entrance of the outlet pipe than at 180° flow direction where the maximum thickness occurred at the center of the outlet entrance. As a result, the water depth in outlet for 90° outflow direction was higher than 180° outflow direction.
When the discharge increased to regime (III) where the falling jet covered the whole diameter of the vertical shaft, the difference of water curtain thickness between
90° and 180° became small so the water depth in outlet pipe was approximately the same as seen in Fig. 5.7(a, b).
The average outlet velocity is calculated by dividing the water discharge by the water flow cross section area at the water depth measuring station. As seen in Fig.
5.8(a), the water velocity in 180° outflow directions is higher than for 90° outflow directions. As the water discharge increased (regime III), the average velocity for 90° and 180° outflow directions had the same range as seen in Fig. 5.8(b).
89 5.4 Energy Dissipation
The energy dissipation in the dropshafts was caused by the impingement of the falling water with the vertical shaft, and was due to friction losses of the downward spreading flow with the vertical shaft wall. There are also friction losses due to the impact of the downward spreading flow with the bottom of the vertical shaft, mixing in plunge pool, and changing the direction of the flow from vertical to horizontal in outlet pipe.
The energy dissipation was obtained by measuring the water depth in inlet and outlet pipes, and calculating the energy in the inflow and outflow streams. Assuming that Hx is the inlet energy head and Hres is the residual head at outlet pipe, the efficiency of energy dissipation can be quantified by rj = (//j — Hres)/Hx. The relative energy dissipation (77) is presented in Fig. 5.9(a, b) for the 90° and 180° outflow direction experiments. As seen in Fig. 5.9(a, b), the energy dissipation ranges between 90-98% for the flow range used in these experiments. The energy dissipation is very high so dropshafts are usually classified as energy dissipators because of the high drop between inlet and outlet pipes. From Fig. 5.9(a, b), it is clear that the energy dissipation decreases with increasing the water discharge. The effect of outlet pipe orientation with inlet pipe seems to have a very small effect when comparing
Fig. 5.9(a) for 90° outflow direction with Fig. 5.9(b) for 180° outflow direction. The difference in energy dissipation found to be insignificant (less than 1%) between the different outflow directions. A similar conclusion was made in Chapter 4 when the effect of the junction type at the base of the vertical shaft with outlet pipe was investigated. Similar experiments of Chanson (2004) on rectangular dropshafts concluded that the 90° outflow direction has a greater energy dissipation (10 to 20%) than the 180° outflow direction. The high difference in energy dissipation in the 90 Chanson experiment was mainly due to the difference in flow patterns for the similar flow rate in the vertical shaft.
5.5 Air Entrainment
The main objective of this experimental work was the study of air entrainment in vertical shafts at different configurations in order to gain a better understanding of the mechanisms of air entrainment in dropshafts, and the quantitative relation between airflow and water flow. The air entrainment in dropshafts is a result of the entrainment that forces air through the water surface, and water body, and is transported by the water flow. As mentioned before, the falling water flowing freely down the vertical shaft will create sub-atmospheric pressure inside the vertical shaft.
In order to maintain moderate pressure in the vertical shaft, air is often allowed to enter the system, and when it accumulates, it is released from the sewer system. The supply of air may be unlimited i.e. air supply from the atmosphere with a fully open vertical shaft or limited from an air vent, which may or may not be connected to the atmosphere by an air pipe. In this case, the air entrainment depends on the air vent size, air duct resistance, water flow, and air pressure inside the vertical shaft.
The airflow (Qa) entering the dropshaft is normalized to the water discharge
an (Qw) as p = (Qa/Qw) d plotted as a function of the relative discharge^,) . Figures
5.10(a, b), 5.11 (a, b), and 5.12(a, b) show the variation of p with (Q») for different sizes of air vent placed at the top of the vertical shaft, at the top of the feeding tank for the air entering through the inlet pipe, and at the top of the vertical shaft and the feeding tank together for 90° and 180° outflow directions. The quantity of airflow going through the dropshaft depends on the vent resistance, which consists of losses due to the entrance of air from the atmosphere to the vent, friction loss with the vent 91 wall, and sudden expansion from the vent to the shaft. The resistance depends mainly on vent geometry, and air velocity at the vent. The airflow resistance increases with decreasing the pipe diameter for a particular airflow rate and is increased with increasing the air velocity for a particular vent diameter.
The process of air entrainment when controlled by vent configurations is called the air supply limit (Wood 1991), whereas air entrainment is controlled by the water flow is called the air entrainment limit. The air entrainment limit depends on fluid properties i.e. viscosity and surface tension, approach water flow Froude number, surface disturbances and the turbulent fluctuations of water flow that enhances air entrainment (inception limit), and the transport capacity of the flow that is governed by the downstream flow conditions (transport limit). When the air entrainment limit in the dropshaft is higher than the air supply limit, the air vent will control airflow that comes inside the dropshaft. In this case, high negative pressure inside the vertical shaft is expected. If the air supply limit is higher than the air entrainment limit, the air vent will not have any control on airflow coming into the dropshaft, and the pressure inside the shaft will be close to atmospheric pressure.
It is clear from Figures 5.10 to 5.12 that the air entering the shaft is increased with increasing the diameter of the air vent from 50.8mm to 152.4mm where the air vent controls the air entrainment limit. The unusual results for a fully open vertical shaft of
296mm diameter that entrains less air than 152.4mm vent diameter as seen in Fig.
5.10(a, b) is mainly due to hotwire error measurements. According to the manufacturer's manual of hotwire anemometer HHF42 that was used for measuring air velocity, the accuracy is ± 1% of the full scale. The hot wire velocity range is 0.2-
20 m/s with a reading resolution of 0.1 m/s. The range of the velocity measurements and the estimated percentage error are given in Table 5.1. The accuracy of velocity 92 measurements for a fully open vertical shaft is around ± (18% to 50%), and for
152.4mm air vent diameter is around ± (3.6% to 20%). The hotwire readings for low air velocity (i.e. 1 m/sec) have a small accuracy ± 20% of actual air velocity reading.
The difference in airflow measurements between 296mm (fully open) and 152.4mm air vent diameter is around 20%, which is within the hotwire measurement errors. It would be expected that the air entrainment for air vent diameter of 296mm would be higher than that for a 152.4mm air vent if there is an air supply limit control or at least will be the same if the air vent size does not have any control on the airflow. From
Figures (5.10 to 5.12), a general conclusion can be made that the air vent has no control on the airflow when diameter of air vent (DVs) is greater than half of vertical shaft diameter (DVs > 0-5 Ds), or the air vent cross section area (AVs) is more than quarter of vertical shaft area (AVs > 0.25 As).
The comparison of the air entrainment for 90° and 180° outflow directions is provided in Fig. 5.13 for 152.4mm shaft ventilation, and 2-way 152.4mm air vents placed at the vertical shaft and feeding tank experiments. It is clear from Fig. 5.13 that the air entrainment for 90° outflow direction is higher than for a 180° direction during regime (II) flow in vertical shaft, and the air entrainment is almost the same after the transition between regimes (II) and (III) (Q* = 0.32). The difference in air entrainment between outflow directions in the regime (II) flow pattern in vertical shaft is mainly due to the difference in the contact area between the outlet and vertical shaft airspace. As mentioned before, the maximum thickness is located in the middle of outlet entrance and decreases in both directions around the shaft diameter for 180° outflow direction while for 90° outflow direction, the maximum thickness is 90° away from the centerline of outlet entrance, which decreases along the vertical shaft
93 diameter in both directions. Accordingly, for certain small flows in regime (II), the contact area in airspace between the vertical shaft and outlet pipe for 90° is higher than that of 180° outflow direction. For this reason, it is expected 90° outflow direction entrains more air than 180° outflow direction.
5.6 Estimation of the Pressure Drop in Vertical Shaft
For the vertical shaft ventilation series, it was possible to estimate the sub- atmospheric pressure inside the vertical shaft. The airflow was provided by measuring the air velocity in the vent pipe, which was placed on the top of the dropshaft. If the atmospheric pressure is pa and the air pressure inside the vertical shaft is p and the length of the air vent I pipe, A Bernoulli -type Equation can be written between points outside and inside the shaft as:
Pa ke Pad KsE P Al) 2 2gDvs 2 ~ V where Va is air velocity in the ventilation pipe of diameter of Dvs , f is the friction factor , ke is the entrance loss coefficient, kSE is the loss due to sudden expansion from air vent to vertical shaft, and pa is the mass density of air. Equation 5.11 can be further arranged as:
Ap -ke-ke SE + -P- (5.12) PaVi/2 " DVS where Ap = pa — P
According to the diagram of resistance to flow at the entrance into tubes and conduits
(Idelchik 1994), the entrance coefficient (ke) depends on the ratio of pipe thickness
(8) to the pipe diameter(D), and the distance from wall to which it is mounted (b) to the pipe diameter(Z)). ke is taken as 0.5 , 0.52, and 0.59 for ventilation pipe diameter of 0.051m, 0.152m, and 0.296m respectively. 94 The sudden expansion losses occurred due to the shearing action between the incoming high velocity in vent pipe and the surrounding air in vertical shaft. As a result, much of the kinetic energy was dissipated by the eddy currents and turbulence.
The loss of sudden expansion coefficient can be expressed as:
«*-(l-*?)' <513> in which Avs is the ventilation pipe cross-section area and As is the vertical shaft cross-section area. The calculated kSE was 0.94, 0.54, and 0 for ventilation pipe diameter of 0.051m, 0.152m, and 0.296m respectively. The last term in Equation 5.12 represents the losses due to friction inside the ventilation pipe wall and the friction factor that was obtained by using Colebrook formula (White 2006).
The results of the pressure drop inside the vertical shaft for shaft ventilation series as provided in Fig. 5.14(a, b, and c). As seen in Fig. 5.14(a, b, and c) the pressure drop is increased with decreasing the air vent diameter. As mentioned before, the pressure difference will be maximum if the air vent is closed and decreases to zero for unlimited air supply. The characteristics of the air vent associated with the pressure drop can be used to control the air supply rate entering the dropshaft.
5.7 Summary and Conclusions
An experimental study on the vertical dropshaft was conducted to study the effect of outflow direction on the hydraulic performance, and the effect of the size of the air vent on air entrainment in the vertical shaft. The calculated specific energy in the inlet pipe was compared to the simplified theoretical expressions of specific energy at critical sections of free fall in horizontal or mildly sloping circular pipes. The comparison of results in specific energy between experiments and theoretical
95 expressions showed that the difference is small, and that the theoretical expressions can be useful in estimating the specific energy in the inlet pipe for any given discharge.
The flow patterns in the vertical shaft and the location of the impact of the falling jet on the opposite vertical shaft were observed. It found that outflow direction does not have any effect on the flow pattern in the vertical shaft. On the other hand, the water depth in the outlet pipe for 90° outflow direction was higher than 180° outflow direction, in particular for Q»< 0.5.
Significant energy losses were observed in the vertical dropshaft flow.
Experimental results showed energy losses of about 90 to 98% for the flow range used in the experiments. The energy loss decreased with increasing water discharge. The outflow direction had a very small effect on the energy losses.
The results of air entrainment revealed that the air vent is limiting the air supply entering the dropshaft if the air vent cross section area is less than a quarter of vertical shaft area (AVs < 0.25 As),or the diameter of air vent is less than half of vertical shaft diameter (Dvs < 0.5 Ds). When the air entrainment is controlled by the vent configuration, the airflow depends on the characteristics of the air vent and the corresponding pressure difference in the vertical shaft. By increasing the vent size, the air supply becomes unlimited, and the pressure difference is decreased close to zero and the air entertainment is controlled by the water flow (air entrainment limit).
The air entrainment in this case depends on fluid properties, approach flow Froude number, turbulent intensity, and the transport capacity of the flow.
The comparison of the air entrainment for 90° and 180° outflow directions revealed that the air entrainment for 90° outflow direction is higher than that of 180°
96 for low flow rate (regime II) and it is almost the same for a high flow rate (regime
III) Table 5.1 The range of the velocity measurements and precentage error
Air Vent Dia. Velociy Range Error Range (mm) (m/sec) %
50.4 3-20 3-1 152.4 1-5.5 20-3.6 296 0.4- 1.1 50-18
98 Inlet Ventilation Shaft Ventilation i i Air Vent (DVb=50.8mm or 152.4mm) i >~or 296mm)
Feeding Tank
Inlet pipe (D™ =152.4 mm) 33; N \ Vertical shaft (D.=296 mm) Damping mesh Elbow entrance
L =3.2m
K Feeding pipe Outlet pipe (Dou,= 296 mm) r
/ Plunge pool
Figure 5.1 Definition sketch of experimental setup.
99 Fig. (b)^, •^^t^f^i
I'
Figure 5.2 Visaulization of experimental configuration (a) 90° (b) 180° outflow direction.
100 1.2
Fig- (a) - 0.8 G 0.6 •Q-% ® O Dvs=50.8mm (90deg.) O 2 way opening Dvs=Dvb=50.8 mm (90deg.) 0.4 & D Dvs=152.4mm (90deg.) ® D 2 way opening Dvs=Dvb=152.4mm (90deg.) 0.2 A Dvs=296mm (90deg.) 0.2 0.4 0.6 0.8 1.2 1.2 hg. (b) O 0.8 0 o B 0 D 0.6 9 r, \ H 8 O 2 way opening Dvs=Dvb=50.8 mm (180deg.) 8 0.4 - •Dvs=152.4mm(180deg.) D 2 way opening Dvs=Dvb=152.4mm (180deg.) 0.2 A Dvs=296mm (180deg.) A 2 way opening Dvs=296mm, Dvb=152.4mm (180deg.) 0.2 0.4 0.6 0.8 1.2 Figure 5.3 Change of the normalized water depth in the inlet pipe to the pipe diameter with relative discharge for (a) 90°(b) 180° outflow direction. 101 2 1.8 1.6 • ^^ 1.4 1.2 • 1 < 0.8 • measured 0.6 « caleulated ( de y; 0.4 • calculated ( Haeer) 0.2 0 0.2 0.4 0.6 0.8 Figure 5.4 Comparison between measured and calculated normalized specific energy to the inlet pipe diameter with relative discharge. 8 • 7 • • A front drop distance 6 • behind drop distance • 5 A • • • • • • £3 • A A A A A • 2 "• A A A 1 0 0 0.2 0.4 QJ)t 0.6 0.8 Figure 5.5 change of normalized of the front and behind drop distance (measured from inlet pipe invert) of the falling water to the shaft diameter with relative discharge. 102 £ 'kr^'w' Pg- (b) _^ I \MII Figure 5.6 Visualization of flow parttrens at the bottom of vertical shaft for (a) 90°(b) 180° outflow direction. 103 0.35 0.3 Fie. (a) 6 6° © 0.25 § a £ * a a 1 0.2 EL O m 9 O Dvs=50.8mm (90deg.) •o° 0.15 O 2 way opening Dvs=Dvb=50.8 mm (90deg.) 0 D Dvs=152.4mm (90deg.) 0.1 D 2 way opening Dvs=Dvb=152 .4mm (90deg.) 0.05 A Dvs=296mm (90deg.) 0.2 0.4 0.6 0.8 1.2 0.3 • 0.25 • A Fig. (b) T~r s* 8 0.2 • * 1 s 0.15 o * 3vs=50.8mm (180deg.) o;. way opening Dvs=Dvb=50.8 mm (180deg.) 8 0.1 B» • Dvs=152.4mm (180deg.) D 2 way opening Dvs=Dvb=152.4mm (180deg.) 0.05 AC)vs=296m m (180 Jeg.) 0.2 0.4 0.6 0.8 1.2 Q. Figure 5.7 (a, b) The normalized outlet water depth with pipe diameter as a function of relative discharge for (a) 90°(b) 180° outflow direction. 104 Fig. (a) 2.5 O Dvs=50.8mm (90deg.) u © 2 way opening Dvs=Dvb=50.8 mm O 2 way opening Dvs=Dvb=152.4mm | 15 (90deg.) « 1 3 o & S ®> 0.5 0.2 0.4 0.6 0.8 1.2 2.5 Fig. (b) _^ 2 15 £u _o s |T 0) • Dvs=50.8mm (180deg.) > 8 ** 1 O 2 way opening Dvs=Dvb=50.8 mm (180deg.) 4-> 0 s 3 o • Dvs=152.4mm (180deg.) o $ D 2 way opening Dvs=Dvb=152.4mm (180deg.) 0.5 • Dvs=296mm (180deg.) 0.2 0.4 0.6 0.8 1.2 Q. Figure 5.8 (a, b) Water velocity at outlet pipe as a function of relative discharge for (a) 90°(b) 180° outflow direction. 105 100 99 Fip (a) 98 a 05 97 10 (SJ O P w IB C 96 o re 95 O Dvs=50.8mm (90deg.) Q. S5I | 94 Q A 0 2 way opening Dvs=Dvb=50.8 mm (90deg.) d ft 93 ET O Dvs=152.4mm (90deg.) fl) C 92. § LU D 2 way opening Dvs=Dvb=152 .4mm 91 - (90deg.) % A Dvs=296mm (90deg.) 0 o 90 g 89 0.2 0.4 0.6 0.8 1.2 100 • Dvs=50.8mm 180deg.) 99 ricr ih\ > i&-\0) O 2 way opening Dvs=Dvb=50.8 mm (180deg.) 98 ff • Dvs=152.4mm (180deg.) ~ w • D 2 way opening Dvs=Dvb=152.4mm (180deg.) — 97 8s 96 l A Dvs=296mm (180deg.) 8 95 1 i 1 i 94 •o 2 • 60 93 V c 92 * A B • 91 Au 90 0.2 0.4 0.6 0.8 1.2 Q* Figure 5.9 (a, b) Change of relative energy dissipation with relative discharge for (a) 90°(b) 180° outflow direction. 106 35 30 Fio l-\\ rig-iaj • O Dvs=50.8mm (90 deg.) 25 A D Dvs=152.4mm (90 deg.) 20 • i A Dvs=296mm (90 deg.) A • C?*15 A 3 10 * a A D O A 0 * °A B B o o o o o o O 0 O O o o o o 0.2 0.4 0.6 0.8 1.2 14 12 • Fig-(b) • Dvs=50.8mm 10 (180 deg.) A • Dvs=152.4mm (J (180 deg.) A Dvs=296mm (180 deg.) • • • • • B A A *::: AAA i~~r 9 • • • • • • • • • • • • • • 0.2 0.4 0.6 0.8 1.2 Figure 5.10 The relation between the airflow normalized to the water flow with relative discharge for different air vent sizes placed on the top of vertical shaft for (a) 90°(b) 180° outflow direction. 107 o Pic l-,\ •l&-\al • Dvb=50.8mm O (90 deg.) O Dvb=152.4mm o (90 deg.) d O D D D • o • D 6> n_ _— 0.1 0.2 0.3 0.4 0.5 3.5 • 3 Fio lh\ • rlg-lDJ • • Dvb=50.8mm 2.5 • (180 deg.) • • Dvb=152.4mm 2 • (180 d(2g- J 5 1.5 • • • • • • • • 1 • " 0.5 • • • 0 0.1 0.2 0.3 0.4 0.5 0.6 Q. Figure 5.11 The relation between the airflow normalized to the water flow with relative discharge for different air vent sizes placed on the top of feeding tank for (a) 90°(b) 180° outflow direction. 108 , . OTota l 2 way opening ( uvs=uvD=bl>.8mm) iyu aeg.) ° F g(a) • T otal 2 way opening ( Dvs=Dvb=152.4mm) (90 deg.) a D o D a D U D ° o a D ° ° o 0 o o o o o o 0.2 0.4 0.6 0.8 Q. • r^ i F g-(b) • Total 2 way opening ( Dvs=Dvb=152.4mm) (180 dec) • • • • • • • • • • • • ™ • • • • • • • • • • • • • • • 0.2 1.4 _ 0.6 0.8 Figure 5.12 The relation between total airflow normalized to water flow with relative discharge for combination of two air vents placed on the top of vertical shaft and feeding tank for (a) 90°(b) 180° outflow direction. 109 35 30 • D Dvs=152.4mm (90 deg.) 25 • Total 2 way opening (Dvs=Dvb=152.4mm) (90 deg.) • 0 Dvs=152.4mm (180 deg.) c/20 D • Total 2 way opening (Dvs=Dvb=152.4mm) (180 deg.) 5 15 D O • D 10 • • Bp • !!• > • | T~ O 1 ^ ~W f • 0.2 0.4 0.6 0.8 1.2 Q. Figure 5.13 Comparison between 90° and 180° outflow direction for the normalized airflow to water flow with relative discharge for different air vent sizes placed on the top of vertical shaft and combination of two air vents placed on the top of vertical shaft and feeding tank. 110 600 Fig.(a) 500 O Dvs=50.8 mm (90 aeg.j o o 400 • Dvs=50.8 mm (180 deg.) o • "ji[ 300 o • • • a • 0 < 200 • o • 100 o ° ° -+-M-JL t • 8° 0.2 0.4 0.6 0.8 1.2 30 D D Fig.(b) 25 D • Dvs =152.4mm (!3 0 deg.) 20 • • Dvs =152.4mm ( L80deg.) a. • a. 15 < • • D 10 3 a F 5 • ° n B • • • • 0.2 0.4 0.6 0.8 1.2 0.9 0.8 Fig.(c) a a 0.7 • Dvs=296mm (90 deg.) 0.6 • Dvs=296mm (18 0 deg.) • 1o 0.5 • • 0.4 a. • < 0.3 a 0.2 P, D D D 0.1 ° • " D P a • • 0 • • «J• - •" 0.2 0.4 0.6 0.8 1.2 Figure 5.14 The relation between the estimated pressure drop (in Pascal) inside the vertical shaft with the relative discharge for different size of air vents placed on the top of vertical shaft for (a) 50.8mm ,(t>) 152.4mm, and (c) 296mm (fully open). Ill Reference ASCE Manuals and Reports on Engineering Practice No.97 (2000). "Hydraulic Modeling: Concept and Practice." Sponsored by the Environmental and Water Resources, Institute of the American Society of Civil Engineers, ASCE, 390 pages. Chanson, H. (2004). "Understanding Air-Water Transfer in Rectangular Dropshafts." Journal of Environmental Engineering and Science, NRC Research Press, 3(5):319-330. Dey, S. (2001). "EDR in Circular Channels." Journal of Irrigation and Drainage Engineering, ASCE, 127(2): 110-112. Hager, W.H. (1999). "Wastewater Hydraulic: Theory and Practice." Springer, 628 pages Idelchik, I.E. (1994). Handbook of Hydraulic Resistance, 3rd Edition, Research Institute for Gas Purification, Moscow, Russia, 790 pages. Rajaratnam, N., and Mainali, A. (1995) "Hydraulic Design of Dropshafts for the City of Edmonton Drainage System." report prepared for City of Edmonton, University of Alberta, Edmonton, Alberta. Zytner, R.G., Madani-Isfahani, A., and Corsi, R.L. (1997). "Oxygen Uptake and VOC Emissions at Enclosed Sewer Drop Structure." Journal Environmental Research, 69(3):286-494. White, F.M. (2006). "Fluid Mechanics." Sixth Edition, McGraw-Hill ,896 pages. Wood, I.R. (1991). "Air entrainment in free-surface flows." IAHR Hydraulic Structures Design Manual No.4, Balkema, Rotterdam, The Netherlands, 142 pages. 112 Chapter 6 CFD Modeling of Plunge-Flow in Vertical Dropshafts2 6.1 Introduction Dropshaft as a component in the collection system is to convey water or wastewater from an upper level to a lower level. The flow in a dropshaft is complex although the concept is simple: direct the flow from the upper sewers towards a vertical shaft where it falls by gravity towards the lower sewer. Air is dragged along with the water and must be handled carefully to prevent capacity and odour problems. Detailed experimental measurements of water velocity, air velocity, and pressure distribution along the dropshaft are not available and are difficult to obtain. Using Computational Fluid Dynamics (CFD) to model plunging flow dropshafts may help to understand the flow field and pressure distribution along the vertical dropshaft. However, this is not a trivial computational challenge. Modeling efforts in two-phase flows have been attempted with various levels of sophistication. Previous work has been mainly restricted to the use of volume of fluid (VOF) methods for two and three-dimensional problems in free surface motion and bubble growth. However, for stratified flows some investigators have attempted to use separated flow models. Some investigators, including Akai et al. (1981) and Issa (1988), obtained steady flow solutions in rectangular channels with the interface treated as a free surface type boundary condition. Shoham and Taitel (1984) presented one of the early CFD models of turbulent stratified pipe flow. The gas region was treated as a bulk flow, and the liquid region 2 Part of this chapter has been published as a paper in the proceedings of the 17th Canadian Hydrotechnical Conference, Hydrotechnical Engineering, Cornerstone of a Sustainable Society , Edmonton, Alberta August 17-19 , 2005,Urban Hydraulics section, 937-944. 113 flow field was calculated using a finite difference solution of two dimensional axial Momentum Equations with the turbulent viscosity calculated from Zero Equation models. Solutions for turbulent liquid flows were obtained in horizontal and slightly inclined pipes of 25.4mm diameter. Issa (1988) also obtained solutions for a stratified gas-liquid pipe flow with a smooth interface. The flow field in both phases was calculated using the standard k - s turbulence model with wall functions. The result showed reasonable agreement with the predictions from the mechanistic model of Taitel and Dukler (1976); however, they were confined to a relatively small pipe of 25.4mm. Newton and Behnia (2000) extended the work of Issa for a larger 50mm diameter pipe. They solved the two-dimensional axial Momentum Equation in each phase, and the turbulent viscosity was obtained with a low Reynolds number k - s model. They applied the standard wall damping function for a single phase to the two-phase flow. Emphasis was placed on predicting the pressure gradient and liquid hold up. They also presented some computed wall shear and interfacial stress distributions. Gao et al. (2003) simulated stratified oil water flow in a horizontal pipe numerically by using a single Momentum Equation and Volume Of Fluid model (VOF) to compute turbulent smooth two-phase flow. The RNG k - E model combined with a near wall low Re turbulence model was applied to each phase, and a continuum surface approximation was used for the calculation of surface tension. The predictions of velocity field, pressure drop, and liquid hold up were compared with experimental data. In this study, an evaluation of the ability of CFD to predict the plunging flow in the vertical shaft was made where free surface flow is involved. The emphasis of this work is to examine the capability of the commercial CFD package CFX-11 to predict 114 the flow pattern and velocity field in dropshafts for the two-phase flow (air and water). This package was selected because of the free surface and multiphase flow capabilities as well as the flexible and automatic meshing system. The results of the computational models were validated and evaluated by comparing the results with experimental data in terms of the flow pattern in vertical shaft and energy dissipation. The results and discussion include a comparison between the momentum transfer models, the ability of CFD to simulate air entrainment, maximum possible pressure at the base of the dropshaft, and the effect of air vent size on air entrainment. The study was extended to discuss the scale effect of the hydraulic modeling in plunge flow dropshafts on the numerical simulation results. 6.2 Governing Equations The flow in plunge type dropshafts involves two-phase (air and water) free surface flow with interpenetration between phases. This kind of flow can be simulated by the Eulerian-Eulerian approach for a multiphase flow (inhomogeneous model). In this model, each phase is supposed to behave as a continuous medium occupying the entire domain where the amount of each phase present is given by the volume fraction. Thus, the equations governing two-phase flow are the conservation laws of mass, and momentum for each individual phase in addition to a set of auxiliary relations. Moreover, for turbulent flows, additional Equations to compute the turbulent viscosity or Reynolds stresses are needed. The number of these Equations depends on the turbulence model used. 115 6.2.1 Continuity Equation The Continuity Equation for each phase is solved in order to determine the individual volume fractions. Let us refer to the liquid phase (water) as a and to the gaseous phase (air) as (3. By averaging over a small control volume, the Continuity Equations for water and air can be written as: i(.raPa) + V-(raPaUa) = 0 (6.1) i{rpPp) + ^-(rpPpUp) = 0 (6.2) where p ,U and r represent respectively the density, velocity, and volume fraction of the respective phase. The summation of the volume fraction over the phases is constant and equal to one. ra + rp = 1 (6.3) 6.2.2 Momentum Equation The momentum conservation equation without mass transfer between phases for phase a (i.e.) can be presented as: T jt (ra pa Ua) + V- (rB paUa®Ua) = V • [ra na (v Ua + (V Ua) )] -raVp + ra nag + MPia (6.4) where \ta represents the viscosity of phase a, p is the pressure, Mpa is the interfacial momentum exchange between the air phase and water phase, and g is the gravitational acceleration. The term p in the model includes the buoyancy force as well as the static pressure force. The buoyancy force is calculated by Fa = — (pa -p )g. In the presence of any flow disturbance, it is assumed that the bulk pressure of all phases has instantaneous 116 equalization. Therefore, the pressure of the mixture at all points is the same for both phases (Ansys 2003). Pa=Pp = P (6-5) 6.2.3 Interphase momentum transfer models The interphase momentum represents the effect of the presence of one phase on the other phase. The interphase momentum transfer is the sum of all interfacial forces, and the momentum exchange from an air phase to a water phase is equal and opposite of that from water to air (MPA = - Map). The interface drag force is the most important force to be modeled for two continuous phases like a stratified or free surface flow. The total drag exerted by phase (3 on phase a per unit volume is defined in terms of a non-dimensional drag coefficient CD between phases: Dap = CDAapPap\Up-Ua\(Up - Ua) (6.6) Pap = rapa + rp pp (6.7) in which Aap is the interfacial area density per unit volume, pap is the mixture density. In the mixture momentum transfer, both phases a and P are treated symmetrically. The interfacial area density is calculated from: A*=% (6.8, where dap is the interfacial length scale that must be specified. An interfacial length scale that is going to be used to mimic the surface contact area for modeling drag force is similar to the disperse / continuous two phase flow. In this case, the interfacial length scale is more likely to be in a "bubble diameter" sort of order. The interface area density (surface delta function) Aap between phases in a free surface model is 117 determined by the gradient of volume fraction. For a two-phase flow, the following equation is used for interfacial area density: Aafi = iVrJ (6.9) This model was adapted for the numerical simulation since this relation implied that the volume integral of Aap is equal to the real free surface area (Egorov 2004). 6.2.4 Turbulence model The effect of turbulence on interfacial mass and momentum transfer is a difficult modeling task and is an active area of research. Similar to single-fluid flow, researchers have used several models to describe turbulence. These models depend on the flow type and vary in complexity from simple algebraic models, two equations model, and the state-of-the-art Reynolds-stress models, which all are adapted in CFX- 11. The homogenous turbulence models are preferred for two-phase flow modeling. In homogenous turbulence, bulk turbulence equations are solved which are the same as single-phase equations but with phase properties and phase velocities being replaced with mixture properties and mixture velocities. This option is recommended for free surface flow, stratified flow, and other situations where the phases tend to separate out (Cokljat et.al 2000). In this model, Reynolds stresses in Reynolds- averaged Navier- Stokes Equations are modeled by the product of an isotropic eddy viscosity and the local rate of strain. The eddy viscosity is obtained from the product of local turbulence length and velocity scales. The turbulence velocity scale is represented by k '2 where k is the turbulence kinetic energy per unit volume and the turbulence length scale is determined from the turbulence kinetic energy dissipation rate (e) per unit volume. Both k and e are derived from transport equations which are closed by using a number of semi empirical procedures in which standard constants 118 are employed (Rodi 1984).The turbulence models require estimates for k and e at the inlet and opening boundary condition. In these numerical simulations, the k and e estimates for turbulence at the inlet and opening were provided in terms of turbulent intensity (3.7 %), and length scale (0.3 * D) estimates where D is the pipe diameter (Ansys 2003). The turbulence intensity of 3.7% was a good estimate in the absence of experimental data for a circular inlet since the nominal turbulence intensities range from l%to5%. 6.3 Computational Model Parameters 6.3.1 Flow geometry The model geometry and boundaries are shown in Fig. 6.1. The dropshaft consists of three parts. The inlet pipe has a diameter of 0.152m, and lm in length from the centerline of the vertical shaft pipe. The vertical shaft and the outlet pipes are 0.296m in diameter, and the outlet pipe is lm in length measured from the centerline of the vertical shaft. The length of the vertical shaft varied from lm to 4m. The dropshaft boundaries include the inlet entrance where the water enters the dropshaft and is labeled as an inlet. Similar to the experimental setup, the inlet pipe was connected to the vertical shaft by an elbow with a radius equal to the diameter of the inlet pipe. The top of the vertical shaft that is labelled as an opening allows the air to enter or leave the dropshaft. In some simulations, an air vent pipe with different size is placed at the top of vertical shaft so in this case the top of air vent represent an opening. Similar to the experimental setup, the air was not permitted to enter from the inlet pipe so we could now easily estimate the net air discharge due to the water flow from the opening. The discharge end of the outlet pipe is labelled as an outlet. The flow was found to be symmetrical along the vertical central of the dropshaft geometry 119 so only half of the dropshaft was modeled to save computational time and memory. The vertical central plane is labelled symmetry. The remaining dropshaft boundaries are labelled as a wall. 6.3.2 Boundary conditions Appropriate boundary conditions need to be specified at all external boundaries of the flow geometry as well as a good initial flow condition. Unfortunately, due to difficulties in measuring the water and air velocity profiles in the experimental studies, the measured average quantities are used as an input for the numerical simulation. For the inlet, a mass flow rate boundary condition for water was used and the inlet pipe was assumed to be running full. The numerical model was able to predict whether the flow is full or partly full after a short distance in the inlet pipe. At the outlet, a static pressure boundary condition was used since downstream outlet in experiments was free overfall. The reference pressure is set to be atmospheric so the relative static (gauge) pressure at the outlet boundary is given as zero. In this case, it is not necessary to specify the water depth in the outlet. An opening type boundary condition was used at the top of the vertical shaft to allow the air to cross the boundary condition in both directions. An atmospheric pressure with a direction normal to the boundary condition was used (the relative pressure was set to zero). A scalable wall-function for near wall modeling was used for all pipe and shaft boundaries. At the plane of symmetry, symmetry boundary condition was used so the normal velocity is zero and the gradient of other variables in the transverse coordinate direction are also taken to be zero. 120 6.3.3 Grid size analysis The simulation domain was discretized into a small control volume using a mesh generated by CFX-mesh. The CFX-11 mesh generator created a structured mesh near the wall region and unstructured mesh inside the domain, which formed grids of tetrahedral and prisms shapes. Grid convergence requires that at a certain grid size, the numerical result will not change significantly as the grid size decreases. A mesh sensitivity test was conducted to determine the mesh density and the convergence criteria to be used for the simulation. Convergence is often hard to achieve to a residual guideline with these simulations. The flow does not reach a steady state but exhibits an oscillation in pool height with discrete eddies generated by the cylindrical falling downward jet. Failure to converge residuals is often manifested in a very small isolated area of the flow in a separation or re-attachment point where some unstable flow situations exist that occur in the plunge pool (Ansys 2006). This small area of unstable flow that causes lack of tight convergence of the maximum residuals does not affect the overall prediction so the solution is still valid (Ansys 2006). Normally, residuals are approximately a factor of 10 smaller than the maximum residual, but for this situation, the residuals become lower than the maximum residuals by a factor of 100 or more. Based on the iteration accuracy and computational effort of the flow, a decision was made that the normalized maximum residual target was less than 10-5 for the hydrodynamic equations, and 10~3 for the volume fraction equations. The imbalances of the air and water mass in the flow domain were taken to be less than 2% in order to consider the solution converged. Three different meshes for the lm dropshaft height were created by changing the minimum and maximum edge lengths, and taking the maximum body spacing similar 121 to the maximum edge length: meshl 0.2cm:2.0cm (30338 nodes), mesh2 0.15cm:1.5cm (64490 nodes), and mesh3 0.1cm: 1.0cm (188080 nodes) respectively. In the near wall regions, boundary layer development requires a fine mesh to capture the high velocity gradient and the shear effects. The total thickness of the boundary layer mesh for all cases was 1cm. The dimension (normal to the wall) of the elements adjacent to the surface was set so that the y+ restriction was met where y+the dimensionless distance is measured from the wall. The value of y+ for the first node from the wall was kept y+ < 200 for the automatic wall treatment that was used in the numerical simulation. Moving away from the wall, five layers were placed with the expansion factor set to 1.2. The sensitivity of the numerical results was checked by comparing the air mass flow rate at opening since water flow parameters were less sensitive. The difference in air mass flow rate was around 50% between mesh 1 and mesh 2, and was less than 10% between mesh 2 and mesh 3. Considering the qualitative nature of this study and the accuracy of the experimental results, the mesh2 discretization intensity was deemed adequate. Typically, using this mesh, run times on a 2.6 GHz Xeon processor with 3 Gigabytes of RAM were about 1 to 2 days. Multiphase computations appear to take at least one order of magnitude longer than single-phase computations. 6.4 Results and Discussion 6.4.1 Comparison between momentum transfer models Sensitivity analysis was conducted to examine the effect of drag coefficient Cd and interfacial length scale dap for momentum transfer models on the numerical simulation results. For the mixture model, the result of combining Equation 6.8 with Equation 6.7 makes the drag force a function of Cd/dap, and for a free surface model, 122 the drag force is only a function of Cd. It is interesting to report that both models give the same simulation results if ratio ofCd/dap for mixture model has the same value as Cd for the free surface model. Figure 6.2 shows the comparison between water surface profiles at the symmetry plane for free surface and mixture models. The drag coefficient plays the major rule for momentum transfer between water and air phases as seen in Fig. 6.3. Figure 6.3 shows that the increase of Q will increase the dispersing rate of the water phase so the momentum transfer between air and water will increase. The airflow in dropshafts is mainly due to the momentum transfer between air and water so that the airflow will increase with increasing drag coefficient Cd in free surface model or the ratio of Cd/dap in mixture model. Figure 6.4(a) shows the change of air velocity at top of air vent for different Cd/dap values for mixture model. It is obvious that the air velocity is very sensitive to the value of Cd/dap . Figure 6.4(b) shows the change of water velocity calculated at end of outlet pipe with a different value of Cd/dap. In general, the change in the drag coefficient has little effect on water flow when compared to the airflow. As seen in Fig. 6.4(b), reducing the drag coefficient from default value of (Q=0.44, dap=lmm) will increase the water velocity at the falling jet, and that makes the impingement point higher in vertical shaft. As a result, the friction losses of water with pipe wall will increase, and outlet water velocity will decrease. Increasing the drag coefficient will increase the water dispersing, and increase the momentum transfer that will reduce the water velocity. In this study, the default value in CFX-11 of Q=0.44 was used for numerical simulations when the results were compared with experimental data. 123 6.4.2 Water depth in inlet pipe of simulation results Following the experiments, the inlet pipe was assumed to be running full by setting the volume fraction for water to unity to prevent the air from entering the dropshaft from the inlet pipe. The numerical model was able to predict accurately whether the flow in the inlet pipe was full or partly full depending on water mass flow rate. The results of the average water depth in inlet pipe at a section of about 0.1m from inlet entrance for the numerical simulations was plotted as a function of relative discharge (QJ, and was compared with the average experimental data for all experiments that were presented in previous Chapters for dropshaft with an elbow entrance. Figure 6.5 confirmed that the CFX numerical simulation predicated the flow condition and water depth in the inlet pipe to a reasonable degree. 6.4.3 Flow pattern simulations in plunge flow dropshaft The numerical results obtained by employing CFX-11 were compared with the experimental observations. Three different regimes were observed in the experiments. At low flow rates, the free falling jet hit the bottom of the vertical shaft. This was called regime I, which is similar to free fall water drop. When the water hit the bottom, it divided in two directions: the forward flow along the outlet pipe and the reverse flow, which re-circulated in the bottom of the vertical shaft forming the plunge pool. The water depth in the plunge pool in this regime was found to be small. The simulated and observed results of the free falling jet in the vertical shaft are shown in Figure 6.6(a), and Figure 6.7(a). In this regime, there is high air entrainment in the numerical simulation due to the high dispersal of the water in the shaft. This dispersal of water can be reduced by reducing the grid size to capture the thickness of the falling water sheet. 124 As the water flow rate increases, the falling water jet hits the opposite side of the vertical shaft (regime II). The water then clings to the vertical shaft and flows down while spreading around the shaft (Fig. 6.6(b)). The width of the flow spreading down the shaft depends on the water flow rate, and the vertical shaft diameter (Ds). It varied from approximately 0.1 Ds to 0.9DS of the vertical shaft. In this regime, considerable air entrainment and energy dissipation takes place in the plunge pool as shown in Fig 6.7(b). At a larger discharge, the falling water jet collides on the opposite side of the vertical shaft and divides into a splash jet directed upwards, and the main jet directed downwards (regime III). The downward jet spreads and covers the whole diameter of the vertical shaft for a short distance along the shaft as shown in Fig. 6.6(c). The thickness of the downward jet decreases along the shaft and around the shaft diameter. The location of the point of impingement moves up as the discharge increases. The flow at the pool and the flow leaving the vertical shaft were found to be turbulent, unsteady, and very aerated (Fig. 6.7(c)). 6.4.4 The effect of air vent size on airflow rate The falling water in the vertical shaft dragged the air inside the shaft while the interaction and mixing between air and water, and in the plunge pool caused air entrainment. In experimental as well as in numerical simulations, the diameter of the air vent pipe was found to control the airflow inside the dropshaft. In the numerical simulation, different sizes of air vent diameters were tested to examine the effect of the air vent size on the airflow inside the dropshaft. Figure 6.8 shows the variation of relative airflow rate of Qa/Qw with the ratio of the air vent pipe diameter to the vertical shaft diameter D0/Ds for the relative water discharge Q»=l, and drop shaft 125 height L/Ds = 6.67. The results of the numerical simulations were compared with the experimental data reported in Chapter 2 as shown in Fig. 6.8. The comparison between the simulated and experimental results was fair considering the difference in the results were less than 5%. 6.4.5 Maximum pressure at the bottom of the vertical shaft In dropshaft design, it is important to estimate the maximum possible pressure that occurs at the bottom of the vertical shaft. The maximum pressure was located at the bottom of the plunge pool at the center of the connection of the vertical shaft with the outlet pipe due to the maximum jet thickness and velocity, which occurred along the center of the cylindrical falling jet. Based on the dimensional analysis, the main parameters are the maximum dynamic pressure recorded on the dropshaft floor versus total head of incoming falling jet that was calculated at entrance of inlet pipe. The effect of plunge pool depth that formed at the bottom of the vertical shaft seemed to be small, and little energy was dissipated in the plunge pool before impacting the floor. Puertas and Dolz (2005) reported that the pool depth effect could be neglected if the B/hp < 0.6 where B is the falling jet thickness and hp is pool depth. It is obvious that the thickness of the falling jet in the plunge dropshafts is much smaller than the plunge pool depth. Figure 6.9 shows the change of normalized maximum pressure on dropshaft floor with relative discharge for different dropshaft heights. As seen in Fig. 6.9, the normalized maximum pressure represents a percentage of total head for incoming flow that converts to the stagnation pressure. As previously mentioned, for the same discharge the loss in energy head is increased with increasing dropshaft height due to the increase of the friction area of the flow in vertical shaft. The numerical results 126 showed that for a certain dropshaft height, the maximum pressure also increases with increasing the flow rate due to the increase in falling water velocity. 6.4.6 Air entrainment One of main objectives of the numerical simulations was to examine the capability of numerical modeling to predict the amount of entrained air in the vertical shaft. The air entrainment at the water surface is based on the premise that turbulent eddies raise small water elements above a free surface that may trap air and carry it back into the body of water. The volume of air entrained per unit time should be proportional to the interfacial area density and the height of disturbances above the mean surface level. The air entrainment also occurred when the falling water jet entered the plunge pool; the turbulent model in the numerical simulation generated a sufficient level of turbulence, which allowed the turbulence to mix the air into the bulk of the water so the air entrainment process took place. As previously explained, air entrainment is dependent on the air vent size. A fully open vertical shaft at the top in the numerical simulation was used similar to the experimental setup that was used in Chapter 3 to avoid air restriction by the air vent. The comparison of air entrainment between experimental and numerical simulations for different flow rates, and different dropshaft heights is shown in Fig. 6.10. Results show that the numerical simulation has a reasonable prediction for Q, > 0.4. On the other hand, for Q, < 0.4 there is a difference between the results due to the experimental data, which are reported to have an average accuracy of ± 20%. The numerical simulations for low flow rates show high dispersal of the falling jet that increases the error by increasing the interfacial area density and may require using a 127 mesh refinement for the advection of volume fractions for the volume fraction equations. 6.4.7 Energy dissipation Energy dissipation is an important design consideration for all drop structures to ensure the downstream flow in the collection system goes back to normal condition to protect the wall pipes from erosion. The result of the numerical simulation has been examined to see how it effectively simulates the energy dissipation of the falling flow through the impact and friction with wall pipes, turbulence and mixing of air and water in plunge pool, and changing the flow direction. In the numerical simulation, the initial energy was obtained by calculating the total pressure for the average mass flow of water phase at the entrance of the inlet pipe. The total pressure (in Pascal) in a two phase-flow simulation is defined as: Ptot = v + i:a^Paui (6.10) The total energy at the inlet pipe (H^) (in Pascal) is obtained by adding the elevation of dropshaft height measured from the pipe invert multiplied by specific weight of water (y). The total energy at discharge end of the outlet pipe (//res) (in Pascal) is the same as the total pressure since the invert of outlet pipe was used as a datum. Similar to experimental data, the efficiency of energy dissipation can be quantified by 77 = (Ht — Hres)/H1. The comparison of relative energy dissipation (77) between the numerical simulation and experimental data of Chapter 3 of elbow inlet series are presented in Fig. 6.11. The energy dissipation in the numerical simulation predicted fairly in comparison with the experimental data. The numerical simulation confirmed that the energy dissipation would decrease with increasing the water discharge and with decreasing dropshaft height. 128 6.5 Scale Effects on Hydraulic Modeling of Air Entrainment The theory of hydraulic modeling is based on geometric, kinematic and dynamic similarities between model and prototype. The most important parameters in the dynamic similarity for hydraulic structures are the viscous, surface tension and gravity forces. In hydraulic structures models, water and/or air are commonly used as flowing fluid so it is impossible to keep Froude, Reynolds and Weber numbers in the model, and that will cause the scale effects unless a full-scale model is used. Froude number modeling normally is selected where entrainment of air babbles in free surface flow and gravity effects are predominant. It was recognized in most model studies that air entrainment is not scaled correctly using Froude number in hydraulic structures modeling. The effect of the model scale on air entrainment was that of significantly reducing the air entrainment ratio for small-scale models (Ervine and Elsawy 1975, Jain and Kennedy 1984, Stephenson and Metcalf 1991). The scale effects on air entrainment are mainly because the air entrainment is a part of turbulence phenomena, which is influenced by both inertial and viscous forces as represented by Reynolds number as well as the consideration of air-water mixtures, and the possibility of surface tension being aggravated. In this study, numerical models were scaled to examine scale effects in the numerical modeling. The basic numerical model geometry was of 0.15m pipe diameter, and lm in length for inlet and outlet pipes, and 0.3m diameter, and lm in height for vertical shaft. The inlet and outlet pipe have straight junctions with the vertical shaft pipe. The basic numerical model is represented by the scale ratio Lr = 1. The basic numerical model was scaled up in geometry to Lr = 3 and Lr = 6 , and then scaled down to Lr = 0.5. Similar to previous simulations, only half of the dropshaft was modeled, and mesh2 grid size that was used for meshing, and scaled 129 with the geometry to save computational time due to machine memory limitation. If the basic numerical model in dropshaft represents a typical storm water of full-scale dropshaft of 1.2m, the scale ratio will be approximately four. The incoming flow was scaled according to Freudian model. The sensitivity of the numerical results in scaling was checked by comparing the water depth at the intersection of the symmetry plane with cross section plane at a distance of 0.4Lr from the centerline of the vertical shaft for inlet pipe, and at a distance of 0.3Lr for outlet pipe for two different relative water flow rates Q„=0.146 and Q»=0.733. As seen in Fig. 6.12(a, b), the normalized water depth in inlet and outlet pipes for all scaled models is the same. The velocity profile at intersection of the symmetry plane with cross section plane at a height of 0.6Lr from the bottom of the vertical shaft was compared for the same two relative water discharges to examine the effect of growth of boundary layer on scale models. The results showed that there is very little difference in normalized velocity profiles as seen in Fig. 6.13(a, b) since no slip boundary condition was used for all pipe walls. The scale of roughness would be a problem in the scaling of physical models. The maximum velocity occurred at a distance of Z/Ds = 0.053 where Z is the perpendicular distance measured from the vertical shaft wall. The maximum velocity of velocity profiles was plotted as a function of the scale ratio for the relative water discharge Q»=0.146 and Q»=0.733 as seen in Fig. 6.14. The simulated maximum velocity was also compared with the calculated maximum velocity based on Freudian model from the basic numerical model Lr — 1. The comparison in maximum velocity showed that the numerical models predicted the maximum velocity for scaled models very well, and Froude scaling was adequate for scale sizes that were used. 130 The scale effects of the air entrainment are not shown in the numerical simulation results, and the normalized air entrainment of scaled numerical models coincides as seen in Fig. 6.15. This conclusion was expected since all hydraulic parameters for the scaled models are the same. In addition, the numerical scale models are within the criteria that were suggested by some investigators to avoid the scale effects on air entrainment for the shaft or siphon spillway. For example, some investigators have established a minimum velocity of 0.8 to 1.1 m/sec in the model at the location of air entrainment (Casteleyn et al. 1977, Khatsuria 2005). Others suggest that Reynolds number of the incoming flow in the model to be at least 5xl05 or greater to reduce the scale effects while studying phenomena originated by turbulence (Khatsuria 2005). It recognized that surface tension scale effects took place for Lr < 0.05 to 0.1 (Wood 1991, Chanson 1997, 2004). 6.6 Summary and Conclusions The objective of this study was to examine the capability of using the commercial (CFD) package CFX-11 for simulating a two-phase flow in the plunge flow dropshaft. Using CFD may provide a better understanding of air and water flow fields as well as pressure distribution fields, and provide useful insights into the highly complex flow in vertical dropshafts. The water and airflow were successfully modeled using the Eulerian-Eulerian approach for the two-phase flow. The governing equations were formulated using Reynolds averaging for mass and momentum. The standard k - s turbulence model for air-water mixture was adapted for the turbulence modeling. Two different momentum transfer models were tested, the mixture model and free surface model. The results showed that both models give the same results if the ratio of Cd/dap in the mixture model and Cd in the free surface model has the same value. 131 The free surface momentum transfer model was selected with a default value of the drag coefficient between phases (0.44), and adapted for the numerical simulation. Further investigations are recommended to evaluate the drag coefficient for a wider range of water discharges. The numerical simulations of water flow patterns in plunge flow dropshaft compared favourably with the experimental observations. The numerical simulations were able to predict the three different regimes that were observed in the physical experiments, and the water depth and flow condition in the inlet pipe whether it was full or partly full. The energy dissipation in the numerical simulations was found to match fairly with experimental results. The maximum possible pressure that occurred on the bottom of the vertical shaft was estimated from the numerical simulations results. The results of maximum pressure were presented in non-dimensional parameters to estimate the percentage of incoming flow total head that converts to the stagnation pressure. The other main objective of the numerical simulations was to examine the capability of numerical modeling to predict the amount of entrained air in the vertical shaft. The numerical simulation was able to predict the air entrainment in the dropshaft within a reasonable accuracy; in particular for Q* > 0.4. Nevertheless, for Q, < 0.4 the numerical results exhibited some differences in comparison with the experimental data due to the high dispersal of the falling jet for low flow rate that increases the error by increasing the interfacial area density. A very fine mesh was needed to obtain accurate results for low flow rate which is not possible with the computer that was used. The numerical simulations were also used to examine the effect of the air vent size on the air entrainment in the plunge flow dropshaft, and the results were compared with the experimental data. 132 The study was extended to investigate the scale effect of the hydraulic modeling in plunge flow dropshafts on the numerical simulation results. The original scale model was scaled up in size to three and six times and scaled down to half size. The study concluded that there is no scale effect on the flow in plunge dropshafts in terms of air entrainment or water flow since the flow in the numerical scale models is within the criteria that are reported to avoid the scale effects on the hydraulic modeling. In summary, the study confirmed that CFD is a promising tool for the analysis and design of drop structures for wastewater and stormwater collection systems. 133 Figure 6.1 The geometry of the flow domain for plunge flow dropshaft. 134 (a) Free surface model (b) Mixture model Cd =0.01 Cd =0.25, da/?=2.5mm Figure 6.2 Comparison of numerical simulations of water surface profile at symmetry plane (Q,= 0.274, D0/Ds= 0.107, L/Ds = 3.38) for (a) free surface model (Q = 0.01), and (b) mixture model (Q = 0.01, dap = 2.5mm). 135 1.00 n 0.75 (b) Cd=0.1 (a) Cd=0.01 0.50 -0.25 0.00 1.00 IP 0.75 050 0.25 0.00 Water volume fraction Figure 6.3 Comparison of numerical simulations of water surface profile at symmetry plane for free surface model ((?» = 0.274, D0/Ds= 0.107, L/Ds =3.38) for drag coefficient: (a) Cd =0.01; (b) Q =0.1; (c) Cd =0.44; (d) Cd =1; (e) Cd =5; and (f) Cd =10. 136 18 ?16 (0 Fig. (a) + .= 12 | 10 o <• 8 13 ^* * 6 u • o * + S 4 > 5 2 Cd/«od/d p 1.8 - « • < • •• h i > ^1.2 Fi g-(b) o 13 0.8 fo.6 o ® 0.4 So.2 (0 5 „ \j J. 4. J -r j w Cd/dap Figure 6.4(a, b) the relation between (a) average air velocity (m/sec) at top of air vent, and (b) average water velocity (m/sec) at outlet pipe with Cd/dap for mixture model (Qt = 0.274, D0/Ds = 0.107, L/Ds = 3.38). 137 1.2 I • CFX rt Art <*> Art 1 OExr.> . V W V v •v 0.8 %«* 0.6 A o c >«" O Q" ^ 0.4 <>• 0.2 0.2 0.4 0.6 0.8 Q. Figure 6.5 Comparison of simulated water depth at entrance normalized with inlet pipe diameter with the average experimental measurement for different relative discharges. 138 (a) M 3'J ary m i«y-oc Figure 6.6 Comparisons between experimental and simulated flow patterns in plunge flow dropshaft: (a) regime (I); (b) regime (II);(c) regime (III). 139 (a) .'li; (b) ••^ •:.9 (c) «£ Figure 6.7 Comparison of simulated velocity field (shown in the left column) in plunge dropshaft pool with experimental observations (shown in right column): (a) regime (I); (b) regime (II); (c) regime (III). 140 4 -— ACFX - 3.5 k. • A Exp. 3 • 2.5 2 d 1.5 A 1 A 0.5 0 0.2 0.4 0.6 0.8 1.2 D0/Ds Figure 6.8 Comparison between simulated and experimental results of relative air entrainment (Qa/Qw) vvith ratio of air vent to vertical shaft diameter (D0/Ds ). 0.8 • L/Ds=3.38 0.7 • • • L/Ds=6.75 • 0.6 AL/Ds=10.13 • ^0.5 • "^0.4 .*. • • E °- 0.3 • • • • • A • • 0.2 • • • 0.1 0 0 0.2 0.4 0.6 0.8 1 Q. Figure 6.9 Relationship between the normalized maximum pressure with total head at inlet (Pma.x/yH) at the bottom of the vertical shaft with relative discharge ((?») for different dropshaft heights. 141 45 40 35 • CFX (UDs=3.38) 30 • CFX (L/Ds=6.76) 25 a ACFX(L/Ds=10.14) 20 a" OExp. (L/Ds=7.43) 15 A AExp. (L/Ds=10.81) O 10 » 5". p** *!**«* 6 >«> & ••& 0 0.2 0.4 0.6 0.8 1 Q. Figure 6.10 Comparison between simulated and experimental normalized maximum air entrainment (Qa/Qw) with relative discharge ( 100 <*<&£*C OQ5*Q fi> A $>£>£ 6 •& 90 • • • 80 • • • c 70 o "•5 60 5 • CFX (L/Ds=3.38) £ ° • CFX(L/Ds=6.76) (A Q 40 ACFX(L/Ds=10.14) O) 30 o OExp. (L/Ds=7.43) c 20 Ul AExp. (L/Ds=10.81) 10 0.2 0.4 0.6 0.8 1.2 Q. Figure 6.11 Comparison between simulated and experimental normalized energy dissipation with relative discharge (Qm) for different dropshaft heights. 142 1 0.9 Fig. (a) - 0.8 1 0.7 c 0.6 • Lr=0.5 9; 0.5 • Lr=1 ' 0.4 ALr=3 0.3 t • Lr=6 0.2 0.1 0 0.2 0.4 0.6 0.8 Q. 0.7 06 +- Fig. (b) 0.5 J 0.4 • Lr=0.5 S 0.3 • Lr=l 0.2 ALr=3 • Lr=6 0.1 0 4 0.2 0.4 0.6 0.8 Q. Figure 6.12(a, b) Comparison of normalized water depth at Q„=0.146 and (J,=0.733 for different scale models for (a) water depth inlet pipe at section of 0.4Lr from vertical shaft center (b) water depth at outlet pipe at section of 0.3Lr from the center of vertical shaft. 143 1 Fig. (a) _^ Lr=0.5 * Lr=1 Lr=3 Lr=6 0.1 0.2 0.3 0.4 0.5 Z/Ds 0.1 0.2 0.3 0.4 Z/De Figure 6.13(a, b) Comparison of normalized velocity profile in vertical shaft at intersection of symmetry plane with cross section at height of 0.6Lr from the bottom of the vertical shaft for different scale models (a) Q»=0.146 and (b) Q»=0.733. 144 9 8 7 ^6 SI* -^-simulated (Q*=0.146) I4 -A-calculated (Q*=0.146) —•—simulated (Q*=0.733) - —$—calculated (Q* =0.733) 1 1 3 4 Lr Figure 6.14 Change of maximum velocity in vertical shaft at intersection of symmetry plane and cross section at height of 0.6Lr from the bottom of the vertical shaft with scale ratio for (a) &=0.146 and (b) Q,=0.733. A 1 —n c A \ —•—Lr=1 -*-Lr=3 \ 5 ** " \ -»-Lr=6 \ r* q - \ O J \ k_ \ 1 - v- \^ 0 - -* 1 • 11 0.2 0.4 0.6 0.8 1.2 Q. Figure 6.15 Variation of the simulated relative air discharge at air vent with the relative water discharge (Qt) for different scale models. 145 References ANSYS CFX (2006), CFX-11 Solver Theory, and Solver Modeling Guide, Software Manuals. Akai, M., Inoue A., Aoki, S., (1981) "The Prediction of Stratified Two-phase Flow with a Two-Equation Model of Turbulence." International Journal of Multiphase Flow 7: 21-39. Casteleyn, J. A, Kolkman P.A. (1977) "Air Entrainment in Siphons: Results of Test in Two Scale Models and Attempt at Extrapolation" Proceedings of IAHR 17th Congress, Baden-Baden, BDR, Aug. 1977. Chanson, H. (1997) "Air Bubble Entrainment in Free Surface Turbulent Shear Flows." Academic Press, London, UK, 401 pages. Chanson, H. (2004) "Environmental Hydraulics of Open Channel Flows", Elsevier Butterworth-Heinemann, Oxford, UK, 483 pages. Cokljat, D., Ivanov, V.A., Srasola, F.J., and Vasquez, S.A. (2000), "Multiphase K- Epsilon Models for Unstructured Meshes." ASME 2000 Fluids Engineering Division Summer Meeting, June 11-15, Boston Massachusetts, USA. Egorov,Y. (2004) "Validation of CFD codes with PTS- relevant test cases." ECORA, EVOL-ECORA-D07, [http://domino.grs.de/ecora%5Cecora.nsf/pages/Public] Ervine, D.A. , and Elsawy, E.M. (1975 ) "Some Scale Effects on modeling Air- Regulated Siphon Spillways." Proceedings of the Symposium on Design & Operation of Siphons and Siphon Spillways, BHRA Fluid Eng., London, UK, Paper B2, B2-9-18. Geo, H., Gu, H., Guo L. (2003) "Numerical Study of Stratified Oil-water Phase Turbulent Flow in Horizontal Tube." International Journal of Heat and Mass Transfer 46: 749-754. 146 Issa , R.I. (1988) "Prediction of Turbulent Stratified, Two Phase Flow in Inclined Pipes and Channels." International Journal of Multiphase Flow 14: 141-154. Jain, S.C., and Kennedy, J.F. (1984) "Vortex-Flow Drop Structures." Symposium on the Scale Effects in Modeling Hydraulic Structures, Esslingen, Germany ,Sept. 3- 6, Paper 6.7, 6.7-1-4 Jalil, A. and Rajaratnam N. (2005). An Experimental Study of Plunging Flow in Vertical Dropshaft." Proceeding of 17th Canadian Hydrotechnical Conference, Edmonton, Alberta, Canada, August 17-19. Newton, C.H. and Behnia, M. (2000) "Numerical Calculation of Turbulent Stratified Gas-liquid Pipe Flows." International Journal of Multiphase Flow 26: 327-337. Rodi, W. (1980) "Turbulence Models and Their Application in Hydraulics: A state of the Art Review." International Association for Hydraulic Research IAHR, the Netherlands, 104 Pages. Stephenson, D. and Metcalf J. R. (1991) "Model Studies of Air Entrainment in the Muela Drop Shaft." Proc. Instn Civ. Engrs, Part 2, (91), Sept., 417-434. Taitel,Y. and Dukler A.E., (1976) "A Model for Predicting Flow Regime Transitions in Horizontal and Near Horizontal Gas-liquid Flow." American Institute for Chemical Engineers AIChE, Journal 22:47-55 Wood, I.R. (1991) "Air Entrainment in Free-Surface Flows." IAHR Hydraulic Structures Design Manual No.4, Hydraulic Design Considerations, Balkema Publ., Rotterdam, The Netherlands, 149 pages. 147 Chapter 7 Conclusions This thesis presents an investigation of the hydraulic performance of plunge flow in vertical dropshafts by using experimental and computational approaches. The hydraulics of plunge flow is still poorly understood due to the complexity of the flow in dropshafts so little research is currently available on plunge flow dropshafts. In this study, experiments were conducted to understand the performance of plunge flow dropshafts in terms of the nature of the flow, air entrainment, and energy dissipation in the dropshaft for different configurations. The study started with preliminary experiments on plunge flow dropshafts with an elbow-type inlet for different dropshaft heights. The flow patterns of the plunge flow were identified and divided into three regimes depending on relative discharge and dimensionless dropshaft height. Regime (I) happens at a low flow rate and at a certain height when the free falling jet hits the bottom of vertical shaft. The hydraulic of this regime is similar to the hydraulics of vertical drop structures. With increasing water discharge, the location of the impingement point moves up and hits the vertical shaft wall (regime II). Regime (II) applies to the falling jet impinging on the opposite wall that forms a central ridge on the wall of the vertical shaft with a flow spreading down the shaft due to gravity. The spreading flow with its length changing approximately from 0.1DS to 0.9DS developed a vertical water curtain covering the outlet pipe entrance that prevented the water from flowing freely to the outlet pipe. The flow in the outlet pipe mainly came from the sides of the entrance of the outlet pipe that mixed and flowed as a supercritical free surface flow. With a further increase in water 148 discharge, the falling jet spreads and covers the whole diameter of the vertical shaft for a short distance (regime III), and spirals down the wall of the vertical shaft. The transition between flow regimes and water depth in plunge pool, which forms in the bottom of the vertical shaft was found to depend on the incoming flow rate, and dropshaft height. The results also revealed that the air entrainment for a specific dropshaft height increases with increasing the water discharge, and for a specific water discharge increases with increasing the dropshaft height. The energy dissipation in the plunge flow dropshaft also increased with increasing the dropshaft height, and for a specific dropshaft height decreases with increasing the water discharge. New experiments have been done with a modified setup to improve the quality of the results such as: (1) Substituting the energy dissipator that is installed at the inlet pipe in preliminary experiments with an elevated rectangular tank to dissipate the energy of pumped water (2) Using a hotwire anemometer to measure the air velocity instead of measuring the pressure in air vent pipe which is very hard to read with a big air vent (3) Replacing the cast iron inlet pipe and PVC plastic outlet pipe with a transparent Plexiglas pipe which helps to observe the condition of inflow and outflow in the dropshaft. The effect of the shape of inlet entrance on dropshaft hydraulic performance was investigated for elbow and straight inlet entrances. The results revealed that the elbow inlet entrance lowered the impinging point of the falling jet with vertical shaft between 1.5DS to 1DS. The water depth in the plunge pool for an elbow entrance was found to be higher than the straight entrance especially for small flow rates. The elbow inlet entrance was also found to dissipate more energy and entrain more air than the straight entrance. 149 The effect of the ratio of the outlet to vertical shaft diameter on dropshaft hydraulics performance was also investigated by changing the outlet pipe diameter. The water depth in plunge pool was found to be proportional to the square ratio of 2 outlet pipe diameter to the vertical shaft diameter (0Out/Ds) - The energy dissipation increased with increasing outlet pipe diameter while the air entrainment was found to decrease with increasing outlet pipe diameter. Experimental observations showed that the presence of tailwater depth would create hydraulic jump in outlet pipe that changes the outflow from supercritical to subcritical flow. The location of the hydraulic jump on outlet pipe depends on the water discharge and the depth of tailwater. The results revealed that for a low discharge(Q» < 0 .1), the energy dissipation decreased with increasing tailwater depth and for (Q* > 0.1) the presence of tailwater depth will increase the energy dissipation due to extra energy being dissipated from the hydraulic jump that is formed in outlet pipe. The air entrainment was found to decrease with increasing tailwater depth especially for a higher flow rate. Adding a sump with a depth equal to the diameter of the vertical shaft to the dropshaft was also investigated. The results revealed that providing sump will decrease the water depth in outlet but it has very little effect on the energy dissipation and air entrainment in comparison with no sump experiments. Three different types of junction at the base of the vertical shaft with outlet pipe were tested in some experiments: the original semi circular, elbow, and straight with a flat bottom. The study showed that the junction type has little effect on the water depth in outlet pipe and the difference in energy dissipation between junctions was around 1%. The semi circular bottom entrains more air (about 33%) than the other junction for a higher flow rate (Q, > 0 .5). 150 The experiments also involved studying the effect of outflow direction on the hydraulic performance and air entrainment. The outflow direction had very small effect on the energy dissipation but the water depth in outlet pipe for 90° outflow direction was higher than that of 180° in particular for higher flow rate (Q, > 0 .5). The air entrainment of 90° outflow direction is higher than the 180° outflow direction for the flow within regime II and it is almost the same for a higher flow rate (regime III). Finally, the experimental study investigated the effect of air vent size on the air entrainment of plunge flow dropshafts. The results revealed the air entrainment in the dropshaft is controlled by the air vent configuration if the air vent cross section area is less than a quarter of vertical shaft area (Avs < 0.25 As) ,or the diameter of air vent is less than half of vertical shaft diameter (Dvs < 0.5 Ds). In this case, the airflow entering the dropshaft depends on the characteristics of the air vent and the corresponding pressure difference in the vertical shaft. Increasing the vent size made the air supply become unlimited, and the pressure difference decreased approximately to zero and the air entertainment in this case was controlled by the water flow (air entrainment limit). For the air entrainment limit, the airflow depends on fluid properties, approach flow Froude number, turbulent intensity, and the transport capacity of the flow. A three dimensional computational fluid dynamics (CFD) code, Ansys CFX 11.0, was used to examine the flow patterns of air and water for different water flow rates, and dropshaft heights. The numerical simulations were based on an inhomogeneous two-phase flow model (Euler-Euler approach for two-phase flow) with traditional K — e turbulence model. The momentum transfer through the air water interface used in the simulation was based on the free surface momentum transfer model. The 151 numerical simulation results were validated by the preliminary experimental measurements. It was found that the inhomogeneous model accurately predicted the bulk variables of the flow including the flow pattern in the vertical shaft, water depth in the plunge pool, the energy dissipation coefficients, and the airflow rate. The numerical simulation results confirm that CFD could be used as a tool to design better and more efficient drop structures for wastewater or storm water collection systems. The overall knowledge provided in this study is applicable for plunge dropshaft design practice. The results of this study were presented in non-dimensional form to provide a preliminary estimation that can be used for the design and construction of plunge-flow dropshafts. The parameters investigated in this study are believed to have direct impact on the main issues such as odour control, ventilation, and hydraulic operation of dropshafts. Even though the experimental study involved most parameters that have an effect on the flow in plunge type dropshafts, there are many other parameters that are still needed for further study. For example, the effect of model scaling on the hydraulic performance, flow regimes in vertical shaft, and air entrainments. Effort should also be made through experiments to understand the effect of outlet air pressure, installing air recirculation shafts, and de-aeration chamber on air entrainment. 152 Appendix A Oblique Impingement of Circular Water Jets on Plane Boundaries3 A.l Introduction The impingement of plane and circular water or air jets on solid and erodible surfaces finds application in a number of engineering problems. Jets issuing from hydraulic outlet works like weirs, culverts, vertical-takeoff aircrafts, various spraying devices, and the cavitating water jet drill are some examples. The perpendicular of plane and circular submerged jets (air jets in air or water jets in water) on plane surfaces have been studied more extensively (Bradshaw and Love, 1959; Poreh and Cermak, 1959; Porch et al., 1967; Gauntner et al., 1970; Beltaos and Rajaratnam, 1974, 1977; Rajaratnam, 1976). Note: These papers provide a list of other related investigations) than the impingement of water jets in air. Impinging circular water jets have applications to flow from culverts and some dams. Considering a circular water jet in air, impinging vertically on a horizontal plane surface as shown in Fig. A. 1(a), the deflected axisymmetric jet spreads radially and its thickness (or depth) t at any radial distance r is readily obtained from the Continuity Equation ?j-U0 = 2nrtU0 (A.l) wherein d is the diameter of the nozzle from which the jet is issuing with a velocity of U0 which is assumed to be constant in the deflected jet. Thus, the thickness t varies inversely with the radius r. If now the jet is made to impinge obliquely on the plane surface at an angle of 8 with the horizontal plate as shown in Figures. A. l(b, c), 3 The content of this chapter has been published in the Journal of Hydraulic Research (JHR). Jalil, A., and Rajaratnam N., Journal of Hydraulic Research. Vol. (44), No.(6), 2006, pp807-814. 153 which show the flow pattern in the plane of symmetry as well as a plan view. Because of the radially asymmetric spreading of the jet on the plate, unlike the case of the obliquely impinging plane jet, it does not appear to be possible to predict theoretically the distribution of the jet thickness, which will be a function of the radial distance r from the impingement point and the azimuthal angle^. The oblique impingement of circular (submerged) air jets has been studied experimentally by Yakovlevsky and Krasheninnicov (1966); Naib (1974); Beltaos (1976); Foss (1979); Borges and Viegas (1981) and Araujo et al. (1981). For an air jet placed on the plate with the angle of the jet equal to 15°, 30° and 45°, Naib investigated the spreading of the deflected jet and the velocity field for x/d up to about 35 where d is the diameter of the jet and x is the longitudinal distance from the jet along the plate. Naib found the velocity distribution in the deflected jet was similar and wall jet- like and that the lateral spreading rate was about five to seven times that in the perpendicular direction. Naib also found that for the 9 up to about 30°, there was hardly any backward flow in the deflected jet whereas for 6= 45°, there was some backward flow. Beltaos (1976) studied oblique impingement of circular jets with H/d in the range of about 15-50, with 0= 20°, 30°, 45° and 60°, where H is the axial distance of the nozzle from the plate. Beltaos (1976) measured the pressure field on the plate as well as the boundary shear stress (with a Preston tube) and mean velocity distribution in the deflected jet, in the plane of symmetry, which appeared to be wall jet-like. Araujo et al. (1981) measured mean velocity profiles, including some turbulent stresses, for 9 = 0°, 10°, 15° and 20°. Foss (1979) made some velocity measurements with a hotwire, for an impinging circular jet with 0=45°. 154 We have not found any publications on the oblique impingement of circular water jets on plane boundaries but it would appear that in the impingement region, the water jets in air might share some common characteristics with submerged jets. This paper considers the oblique impingement of water jets and presents the results of an experimental study with water jets of diameter d equal to 50.8, 101.6 and 152.4 mm with jet velocity U0 in the range of 3.1-9.85 m/s, with the jet outlet placed at a vertical impingement distance h from the plate varying from 45 to 255 mm. A.2 Experimental Arrangement and Experiments The experimental arrangement is shown in Fig. A.2. Water was pumped from the laboratory sump to an overhead pipeline and the jets emerged from the end of this pipe, which had a straight length of about 3 m. These jets impinged on a horizontal smooth plate placed on supports inside a rectangular flume, 1.22m wide, 0.65m deep and 18m long, at a height of about 300 mm above the bed. This rectangular aluminum plate was 6mm thick, 1.04m wide and 2.10m long and had grid lines painted on it at intervals of 20mm. For producing the smallest jet of diameter of 50.8 mm, a nozzle insert was pushed inside the pipe whereas the larger jets with diameters of 101.6mm and 152.4mm were discharged from the end of the pipe itself. If h is the vertical distance of the center of the end of this pipe above the plate, h was in the range of 45 to 255mm. The thickness of the deflected jet was measured with a point gauge with 0.1mm accuracy. Velocity measurements were made with a Prandtl tube with an external diameter of 3mm. The angle of jet nozzle 0 with the horizontal plate was varied from 15° to 75° (see Table A.l). The mean velocity U0 of the jets was obtained by dividing the flow rate by the area of cross-section of either the nozzle or pipe, 155 which produced the jet. The jet velocity was varied from 3.1 to 9.85m/s with the Reynolds number of the jet varying approximately from 380,000 to 700,000. In the first series with the smallest jet, experiments were performed with 0= 15°, 30°, 45°, 60° and 75°, for three values of U0= 8.87, 8.87, and 9.85 m/s. In this series of experiments, the thickness of the deflected jet was measured in the centerplane in the forward flow region only. In the second series with the 101.6mm jet, U0 was varied from 3.1 to 4.93 m and 6 was varied from 15° to 75°. In the third series with the 152.4 mm jet, U0 was varied from 4.93 to 5.46m/s and 6 was equal to 15°, 30°, 45°, and 60°. In the second and third series, the thickness of the deflected jet (or stream) was measured in the forward flow region, in the centerplane for all experiments as well as in the transverse direction at a number of sections for a number of experiments (see Table A.l). The velocity profiles in the deflected jet were also measured in the vertical centerplane for two experiments in the second series and three experiments in the third series. In these velocity measurements, when the Prandtl tube was placed on the plate, it was also used as a Preston tube (Preston 1954) to measure the bed shear stress, using the calibration curves of Patel (1965). The thickness of the deflected jet in the backward flow region was generally very small except (possibly) for 0=15°. It was observed that the flow rate in the backward flow region was negligible for 6 < 45° degrees whereas it was about 5-10 % of the total flow for the two larger values of 9, and these observations are somewhat similar to those of Naib (1974) on the obliquely impinging air jets. Figures A. 3(a- d) show (typical pictures of) the deflected jet for d = 50.8 and 101.6mm, with 6= 15° and 30°. Because the deflected jets were generally in the supercritical state, the flow in the deflected jet region was not affected by the presence of the sidewalls of the flume. 156 A.3 Experimental Results and Analysis A.3.1 Water depth profiles The water jet, obliquely impinging on the horizontal plate, is deflected to form a radially asymmetric flow, with the depth of flow decreasing rapidly in the impingement region. The variation of the thickness tm of the deflected jet in the centerplane with the longitudinal distance x from the impingement point is shown in Fig. A.4 (a-c) for some typical cases, from the three series. These and other profiles (not reproduced herein) showed that the jet thickness decreased rapidly in the impingement region and the variation was rather minimal after some distance. Figure A. 5(a-c) shows typical transverse thickness (z) profiles, for the jet with d =101.6 mm, for three values of G =15°, 30° and 45°. Considering the variation of the thickness of the deflected jet in the centerplane, the results of an attempt to describe them in a generalized non-dimensional form are shown in Fig. A. 6(a-c). In Fig. A. 6(a), wherein the diameter of the jet d is used as the scale to normalize both the jet thickness as well as the distance from the impingement point, it may be observed that the thickness profiles are not similar. However, Fig. A. 6(b, c) indicates that these profiles are similar if the thickness is normalized by either tx to t for x/d =1 .0 or t5 equal to the thickness at x/d=5.0, except for x/d less than about 0.5. From Fig. A. 6(a), it appears that the thickness of the jet at the impingement point in terms of the jet diameter d varies from 0.6 to 1.4. Concerning the scales tt and t5 in terms of d, the experimental results are shown in Fig. A. 7(a, b), without the results for the smallest nozzle for 9=75° for tx (which was difficult to measure precisely). Figure A. 7(a, b) also show the calculated points for 0=90°, using Eq. (6.1). In Fig. A. 7(c), wherein the average values for each angle 157 (from Fig. A. 7(a, b)) are shown, it was observed that the normalized length scales tt/d and t5/d decreased continuously as 0 increased, respectively from about 0.46 and 0.17 for 0=15° to about 0.13 and 0.025 for 6>=90°. These variations are described by the equations tl _5 2 2 /d = -3(1O )0 - 0.00140 + 0.4652 (r = 0.969) (A.2) c _6 2 2 5/d = 7(10 )6» - 0.00220 + 0.1694 (r = 0.998) (A.3) If tmo is the depth of the jet at the impingement point, it was found that tmo/d increases almost linearly from about 0.72 for 0=15° to 1.21 for 0=60°. As mentioned earlier, for the second and third series of experiments, the variation of thickness in the transverse direction was measured and Fig. A. 8(a) shows that these profiles are approximately similar if they are normalized with the central thickness tm and the length scale L which is equal to z where t =0.5tm. This similarity profile is described well by the exponential equation 693(f)2 7tm = e-°' (A-4) for z/L less than about 1.5. The variation of L/d with x/d is shown in Fig. A. 8(b) where it appears that L/d increases almost linearly with x/d and may be described by the equation L /d = 0.45 + 0.45 (%) (A.5) with a value of 0.9 for the correlation coefficient r2. 158 A.3.2 Velocity profiles The velocity profiles in the centerplane of the deflected jet are shown in a U y normalized form with /Um versus /s for several sections, for five experiments with the two larger jets in Figures. A. 9(a-e). From these profiles, it may be seen that in all cases, in the boundary layer region on the plate, the velocity u increases with the distance y from the plate to reach a maximum value of um at y = S and then decrease as y increases further. Except for small values ofx/d, the velocity distribution in the boundary layer is approximately similar and the familiar power law could describe this similarity profile with the exponent varying from about 1/6 to 1/10 for the different experiments. In the region above the boundary layer, the velocity profiles are perhaps similar for some distance beyond which the experimental results fall of the general profile. Because of the lack of mixing with the ambient fluid as in the case of submerged impinging jets, the wall jet-like profiles do not develop. In Fig. A. 10(a), it is interesting to observe that the thickness of the boundary layer remains approximately constant in the region under consideration, very much as in the case of stagnation flows (Schlichting and Gersten, 2000). For axisymmetric (perpendicular) stagnation flows, S = 2.8V% (A.6) where a is a constant for the approaching potential flow and v is the kinematic viscosity of the fluid, for laminar motion in the boundary layer and perhaps equal to the turbulent kinematic viscosity for turbulent motion in the boundary layer. Taking an average value of 8mm for the thickness of the boundary layer in Fig. A. 10(a) would be equal to 0.0028. The velocity scale for the boundary layer would be the Um maximum velocity um and the variation of /y- where U'0 is the velocity of the jet at 159 the source adjusted for the fall through the vertical distance ofh, using the Bernoulli Equation, with x/d is shown in Fig. A. 10(b). It may be observed in Fig. A. 10(b) that this normalized velocity scale, with values in the range of 0.95-1.1, remains approximately constant in the longitudinal direction, for x/d up to about 8.0. A.3.3 Bed shear stress The variation of the shear stress r0 on the bed along the centerline in the deflected jet, obtained with the Preston tube, is shown in Fig. A. 11(a) for the two larger jets and 0=15°, 30° and 45°. In Fig. A. 11(a), it appears that at least for 0=30° and 45°, r0 increases with the distance from the impingement point to reach a maximum value and then decreases as x increases as in the case of submerged impinging jets. Figure A. 11(b) shows the variation of the normalized shear stress r0 /(O.SpUl) with x/d which indicates the spread of the normalized shear stress between 0.003 and 0.006. A.4 Conclusions Based on the experimental observations of the oblique impingement of three turbulent water jets of diameter d equal to 50.8, 101.6 and 152.4 mm, placed above a horizontal plate at vertical distances varying from 45 to 255 mm and at angles with the plate of 9 equal to 15°, 30°, 45°, 60° and 75° , the following conclusions may be formulated. The deflected jet was mostly in the forward direction with very little backward flow for #<45°, which increased to an estimated value of about 5-10% for the larger angles of impingement. The forward flow in the deflected jet or stream was in the supercritical state. The thickness profile of the deflected jet in the centerplane was similar for all the experiments if plotted in terms of a suitable scale which was either 160 the thickness at x/d = 1.0 (tx ) or x/d = 5.0 (t5 ) for x/d up to about 20, which was the range of measurement. These scales in terms of the jet diameter varied mainly with the angle of jet impingement. The transverse thickness profiles in the deflected jet were also found to be similar, with the length scale L in the transverse direction varying mainly with x/d for 0=15°, 30° and 45°. The velocity profiles in the deflected jet clearly showed the boundary layer in which the velocity profiles were similar and its thickness 8 remained constant for x/d up to about 7.5 as in the case of stagnation flows. The boundary shear stress r0 appeared to increase first with the distance from the impingement point and then decrease as in the case of the impingement of submerged impinging jets. This study has shown that the oblique impingement of water jets has some similarities to impinging submerged jets but there are many important differences. 161 Table A.l Details of the experiments Jet Series Experiment Jet Reynolds Angle Jet Comments Diameter No. No. Discharge Velocity Number of jet height (mm) (L/sec) (m/sec) R=U0d/v ( (mm) d Q u„ degrees) h e 1 1115 16 7.88 382,351 15 63 Every experiment 50.8 1130 16 7.88 382,351 30 60 includes measurement 1145 16 7.88 382,351 45 56 of depth profile on 1160 16 7.88 382,351 60 51 centerplane 1175 16 7.88 382,351 75 45 1215 18 8.87 430,388 15 63 1230 18 8.87 430,388 30 60 1245 18 8.87 430,388 45 56 1260 18 8.87 430,388 60 51 1275 18 8.87 430,388 75 45 1315 20 9.85 477,939 15 63 1330 20 9.85 477,939 30 60 1345 20 9.85 477,939 45 56 1360 20 9.85 477,939 60 51 1375 20 9.85 477,939 75 45 2 2115 25 3.1 273,878 15 155 Every experiment 101.6 2130 25 3.1 273,878 30 85 includes measurement 2145 25 3.1 273,878 45 71 of depth profile on 2160 25 3.1 273,878 60 165 centerplane 2175 25 3.1 273,878 75 155 2215 30 3.7 326,887 15 155 2230 30 3.7 326,887 30 85 2245 30 3.7 326,887 45 71 2260 30 3.7 326,887 60 165 2275 30 3.7 326,887 75 155 2315 35 4.32 381,663 15 155 2330 35 4.32 381,663 30 85 2345 35 4.32 381,663 45 71 2360 35 4.32 381,663 60 165 2375 35 4.32 381,663 75 155 2415 40 4.93 435,555 15 142 Includes 2430 40 4.93 435,555 30 115 measurements 2445 40 4.93 435,555 45 138 of centerplane depth, transverse depth, and velocity profiles 3 3115 100 5.46 723,569 15 150 Includes 152.4 measurements 3230 96 5.26 697,064 30 185 of centerplane depth, 3345 90 4.93 653,332 45 222 transverse depth, and velocity profiles 3460 90 4.93 653,332 60 255 includes measurement of depth profile on centerplane 162 Impinging jet /77777777777777777777777777777777777777K777 ;//;;;;///;//;;; //2 V7777 +• v gement point y'\ (c) f\ S-v • LZ J Backward Forward flovV flow region region Figure A.l (a) Normal and (b) Oblique impingement of a circular water jet on a flat plate, (c) Plan view of obliquely impinging jet. 163 "!P*.v 4,1 t i Figure A.2 Experimental arrangement. /j -:. ^ '/7Miirii\ (C) (d) Figure A.3 Flow in the impingement region of water jets (a, b) 50.8 mm jet at 0= and 30° and (c, d) 101.6 mm jet at 9=15° & 30°. 164 160 0.2 0.4 0.6 0.8 Distance x from the impingement point (m) 160 0.2 0.4 0.6 0.8 1.2 Distance x from the impingement point (m) 160 -i 1 1- 0.2 0.4 0.6 0.8 1 Distance x from the impingement point (m) Figure A.4 Variation of jet thickness in the centerplane for (a) d=50.8 mm (b) d=101.6 mm and (c) d=152.4 mm, for several values of 9. 165 0.2 0.3 0.S Transverse distance z(m) 100 E E ! 0.1 0.2 0.3 0.4 0.5 Transverse distance z(m) 100 90 exp.2445 80 \ (c) E >—x=0m E 70 —CJ— x-u.uo ••• —A—x=0.18 m 60 —o— x=U.Z8 m —•— x=0.38 m 50 A x=0.48 m 40 —•— x=0 58 m * —•— x=0.68 m 30 —(— x=0.88 m 20 "K ^ 10 c^^^^*"^™^^ h —=* -=^ 1 1F 1F 0.1 0.2 0.3 0.4 0.5 Transverse distance z(m) Figure A.5 Typical thickness profiles of the deflected jet in the transverse direction for d=101.6 mm for (a) 0=15° (b) 0=30° and (c) 0=45°. 166 1 1 1 D 9=15, d= 50.8 mm (a) A 6=45, d=50.8 mm 1.2 - X X 9=75, d= 50.8 mm • 9=30 ,d= 101.6 mm T3 no? A 0=45 d= 101 6 mm 8 • 8=60 ,d= 101.6 mm E ° 53 9=75. d= 101.6 mm "0.6 o 8=15, d= 152.4mm O 9=30, d= 152.4 mm J&lflft^ A 9=45, d= 152.4 mm 0.2 o 9=60, d= 152.4 mm 0 ^%^*^H3^I ifotk&t^&K&i&l&iA* A Y 10 15 20 25 x/d 10 15 20 25 x/d :50.8 mm -50.8 mm '50.8 mm '50.8 mm :50.8 mm = 101.6 mm 101.6 mm 101.6 mm : 101.6 mm 101.6 mm :152.4 mm :152.4 mm :152.4 mm :152.4 mm •X'.nnA Figure A.6 Variation of the normalized thickness in the deflected jet with x/d with three different thickness scales of (a) diameter of jet d (b) thickness of the jet tx at x/d = 1 and (c) thickness of the jet t5 at x/d = 5. 167 u. / - od= 50.8 mm /a\ <> laJ 3 d=101.6 mm Pt P o id=152.4mm - <• R X 0 » calculated • B ia a B G < 0 10 20 30 40 50 60 70 80 90 Impingement angle of the jet 6 (degrees) 0.25 © od= 50.8 mm 0.2 (I >) • d=101.6 mm A <> Ad=152.4mm 0.15 a • calculated a I a 0.1 8o 0.05 B i 10 20 30 40 50 60 70 80 90 Impingement angle of the jet 6 (degrees) 0.5 a ave 'age data for t1/d 0.45 ^ A average data for t5/d 0.4 • c (c) ^ ^ o ^ 0.35 «^^ - ' Equation (4) 2} 0.3 sO 0.2„5 a 0.15 A . . * -i ^>4> 0.1 r* * » * - A » , " i 0.05 r " 10 20 30 40 50 60 70 80 90 Impingement angle of the jet 6 (degrees) Figure A.7 Variation with x/d of the normalized jet thickness scales (a) t±/d (b) t5/d and (c) average values of tr/d and t5/d. 168 1.2 (a) a 6=15 , d = 101.6 mm o o 6=30 , d = 101.6 mm |LS*A A 6=45 , d= 101.6 mm • 6=15 , d= 152.4 mm • 6=30 , d= 152.4 mm 0.8 A 6=45 , d= 152.4 mm Equation (4) Jo.6 0.4 ^^ 0.2 • ^* W *0ft,o »• *0i A<> o 10 z/L a 6=15 , d=- 101.6 mm (b) o 6=30 , d== 101.6 mm A 6=45 , d== 101.6 mm a • 6=15 , d== 152.4 mm O • - • 6=30, d= • ^*>^** • 6=45 , d== 152.4 mm A ° Equatior 1(5) 5 3 A m *^+ • • • A • 10 x/d Figure A.8 (a) Normalized thickness profile in the deflected jet in the transverse direction and (b) variation of the length scale L for the transverse thickness profiles in terms of jet diameter d. 169 5 5 4.5 -(a)- 4.5 — (b) 4 4 a \ 3.5 _ exp. 2415 3.5 - exp. 2530 • O x/d= 0.39 Ox/d=0.2C • 3 3 • x/d=1.38 • x/d=1.1J ^t A • £?2.5 ^2.5 \t\ D x/d= 2.36 ax/d=2.17 A • { A • • x/d= 3.35 2 • x/d=3.1J h 2 A A x/d= 4.33 1.5 1.5 . Ax/d=4.13 ii A x/d= 5.31 Ax/d=5.12 ^•* U/Um U/Um 5 4.5 (C) 4.5 —(d) 4 0 4 • i 3.5 exp. 3115 3.5 0 3 Ox/d=1.31 3 Ox/d=1.44 D • • x/d=1.97 • x/d=2.10 „ a «2.5 D a x/d= 2.62 £©2.5 u x/d= 2.76 • x/d= 3.28 • x/d= 3.41 2 A x/d= 3.94 * 2 A AII no Ax/d=4.07 • o aci> 1.5 A x/d= 4.59 1.5 o x/d= 5.25 Ax/d=4.72 ? 1 • x/d= 5.91 1 o x/d= 5 38 • x/d=6.04 ^s? 0.5 X x/d= 6.56 + x/d=7.22 0.5 Xx/d=6.69 *b^" 0 h- 0 1 1 0.65 0.75 1.05 0.65 0.75 0.85 0.95 1.05 u/um 5 • 4.5 (e) • • 4 exp. 334 5 > *.\ 3.5 o x/d= 1 05 0 • x/d=1.7 1 * 3 D a x/d= 2.3 6 • • x/d=3 .02 .. \ £?2.5 u Ax/d=3 .67' 3 — Ax/d=4 • i 9 2 .33 4, D ox/d=4 o 1.5 •99 • ,,, ** \ "A ""7; • x/d=5 .64 • •° :-*< »" (a) d=101.6 mm, 0=15° and U0 =4.93 m/s (b) d=101.6 mm, 0=30° and U0 =4.93 m/s (c) d=152.4 mm, 0=15° and U0 =5.46 m/s (d) d=152.4 mm, 0=30° and U0 =5.46 m/s (e) d=152.4 mm, 6>=45° and U0 =4.93 m/s. 170 0.6 0.8 x(m) 0.8 -0—6=15, d=101.6mm -0—6=30, d=101.6 mm P 0.6 -A—6=15, d=152.4mm -o—e=30, d=152.4mm -•—8=45, d=152.4 mm 0.4 0.2 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 x/d Figure A. 10 Variation of the (a) boundary layer thickness in the deflected jet with the distance x from the impingement point (b) normalized maximum velocity um in terms of U'0 with x/d. 171 80 • • A • (a) 70 * ?• n- A i: - • • . . 60 • .".t • 50 O o " A ° O o o 40 v o k. 30 (0 o8=15, d=101.6 mm • 8=30, d=101.6 mm 20 a 8=15, d=1S2.4 mm • 0=30, d=152.4 mm 10 A 0=45 a=is^.4 mm 0 0.2 0.4 0.6 0.8 1 1.2 1.4 distance along the jet x (m) 0.007 (b) 0.006 • A • A • • 0.005 1 • • A " • • t V D A • o D D D D 0.004 A o a O • D O 0 o O s 0.003 o o9=1 5, d=101. 6 mm 0.002 • 9=3 0, d=101. 6 mm • 9=15, d=152. 4 mm • 9=30, d=152. 4 mm 0.001 A 9=4 5, d=152. 4 mm 0 4 x/d Figure A. 11 Variation of the (a) bed shear stress on the centerline with longitudinal distance and (b) centerline normalized bed shear stress with x/d. 172 References Araujo, S. B. R., Durao, D. F. G. and Firmino, F. J. C. (1981). "Jets impinging normally and obliquely to a wall". Fluid Dynamics of Jets with applications to V/STOL, AGARD, Proceedings No 308, pp 5.1-5.10. Beltaos, S. (1976). "Oblique impingement of circular turbulent jets." IAHR, Journal of Hydraulic Research., 14(1), 17-36. Beltaos, S. and Rajaratnam, N. (1974). "Impinging Circular Turbulent Jets." Journal of the Hydraulic Engineering, ASCE, 100(10), 1313-1328. Beltaos, S. and Rajaratnam, N. (1977). "Impingement Axisymmetric Developing Jets". Journal of Hydraulic Research, 15(4), 311-325 Borges, A. R. J. and Viegas, D. X. (1981). "Interaction of Single and Multiple Jets with a Plane Surface." Fluid Dynamics of Jets with applications to V/STOL, AGARD Proceedings No. 308, pp 3.1-3.13. Bradshaw, P. and Love, E. M. (1959). "The Normal Impingement of a Circular Jet on a Flat Surface." Aero Research Council, UK, R & M 3205. Foss, J. F. (1979). "Measurements in a large angle oblique jet impingement flow." AIAA Journal, 14, 801-802. Gauntner, J. W., Livingood, N. B. and Hrycak. P. (1970). "Survey of Literature of Flow Characteristics of a Single Jet Impinging on a Flat Plate". NASA TND- 5960. Naib, S. K. A. (1974). "Deflection of a Round Jet to Increase Lateral Spreading." La Houille Blanche, 6, 455-461. 173 Patel, V. C. (1965). "Calibration of Preston Tube and Limitations on its Use in Pressure Gradients." Journal of Fluid mechanics, 58, 185-208. Poreh, M, and Cermak, J. E (1959). "Flow Characteristics of a Circular Submerged Jet Impinging Normally on a Flat Boundary." Proceeding of the Sixth Midwestern Conference on Fluid Mechanics, University of Texas, Austin, Texas, USA, pp.198-212. Poreh, M, Tsuei, Y. G and Cermak, J. E. (1967). "Investigation of a Turbulent Radial Wall Jet". Journal of applied Mechanics, 89, 457-463. Preston, J. H. (1954). "The Determination of Turbulent Skin Friction by Means of Pitot Tubes." Journal of Royal Aero Society, 58, 109-121. Rajaratnam, N. (1976). "Turbulent Jets." Elsevier, The Netherlands, 304 pp. Schlichting, H and Gersten, K. (2000). "Boundary-Layer Theory." 8th ed., Springer, Heidelberg, 799 pp. Yakovlevsky, O. V, and Krasheninnicov, S. Y. (1966). "Spreading of a Turbulent Jet on a Flat Surface". Fluid dynamics, 1, 136-139. 174 Appendix B CFD Modelling of Oblique Water Circular Jet Impingement on a Flat Surface B.l Introduction The impingement of plane circular water jets or air jets on solid and erodible surfaces finds applications in many industrial or engineering works. Impinging air jets are used extensively in installations of heating, spraying, cooling, drying, cleaning, pulverization, containment of polluted environments, and recently in fan-powered short/vertical-take-off-and-landing (S/VTOL) aircraft. The water jets can be found in hydraulic outlet structures such as weirs, culverts, dams, water jet drills, stilling basins at the end of chutes, and some types offish passage. Several investigators have extensively researched the normal impingement of a plane and circular submerged jet (air jets in air or water jets in water) on flat surfaces. Gaunter et al. (1970) and Beltaos and Rajaratnam (1974 and 1977) used Pitot tubes to study the influence of jet Reynolds numbers, and the distance from the wall on the main velocity profiles. Porch and Cermak (1959), and Bradshaw and Love (1959) reported experimental results mainly concerning static pressure and skin friction at the impingement region. Porch et al. (1967) used hotwire anemometry to measure the turbulent intensity in impingement regions. In comparison to the normal jets, the oblique impinging jets received relatively less interest for study. Yakovlesky and Karasheninnicov (1966) studied the oblique impingement of the circular air jet (submerged) on a plain surface experimentally, which presented experimental and analytical results concerning the velocity field in 175 the wall jet region of the circular jets. Donaldson and Snedeker (1971) presented measurements of wall pressure and mean velocity obtained with Pitot tubes for different impingement angles. Naib (1974) investigated the spreading of the deflected jet and velocity of the air jet placed on the plate with the angle of the jet equal to 0°, 15°, 30°, and 45°. Beltos (1976) developed a semi-empirical method to predict wall pressure and shear stress along the symmetry plane for oblique impingement of a circular air jet. Foss and Kleis (1976) examined a very small impingement angle almost tangential to the surface (0=9°) while Foss (1979) investigated a large impinging angle (0=45°). Borges and Viegas (1981) studied the shear stress field that is produced by normal or oblique circular air jets on a plane surface. Araujo et al. (1981) used LDA (Laser Doppler Anemometry) to study the flow characteristics of a circular jet impinging normally and obliquely on a large plate. Examination of the relevant literature reveals only a few theoretical studies on obliquely impinging, axisymmetric free liquid jets. Schach (1963) studied the oblique impingement of a free surface liquid plane jet. This study was limited to two- dimensional plane flows for an ideal fluid by assuming the inlet jet velocity is uniform to satisfy the irrotational condition for potential flow. Solutions for free surface and stagnation point locations were reported along numerical results on the stagnation point and jet thickness at several inclination angles. Rubel (1981) formulated a two- dimensional, axisymmetric, inviscid, rotational flow model for incompressible oblique jet impingement angles of 90°, 75°, and 60°. The numerical solutions were limited to the use of stream function-vorticity for solving Navier-Stocks Equations. Advances in computer technology play an important role in developing computational fluid dynamics (CFD) modelling research. The first trials numerically solving the full Navier-Stocks Equations for the entire flow region have been done in 176 several studies. Deshpande and Vaishnav (1982) considered the impinging laminar axisymmetric jet while Agarwal and Bower (1982) and Looney and Walsh (1984) used the Jones-Launder k — e two-equation turbulence model with compressible equations to predict impinging jet flow and found the result in good agreement with the experimental results. Hwang and Liu (1989) employed the same equations to simulate the impingement jet flow fields relevant to VTOL aircraft ground effect problems. Bouainouche et al. (1997) solved the Navier-Stokes continuity and energy equations for a two-dimensional turbulent compressible flow with a k — e turbulence model by using the finite volume method. The major concern was the wall function influence on the calculation of wall shear stress generated by the action of a normal plane impinging jet on a flat plate. The numerical simulation of liquid jet impingement in air is even more difficult. The main complexity is the dynamics of the rapidly changing shape of the free surface profile and the supercritical flow of the jet. The difficulty is to achieve a good representation of the free surface interface. The simulation of the free surface flow is performed using different methods such as a volume of fluid (VOF), marker-and-cell, and level set technique. The VOF method has been implemented as a free surface option in multiphase flow modelling in the CFX commercial CFD package. In this method, the two phases are considered to make up one single fluid. The position of each phase is described by assigning a volume fraction of either 0 or 1. The free surface is then identified with the value of 0.5 within the region of rapid change in the volume fraction. The aim of this work to is to examine computational fluid dynamics commercial software (CFX) as a supplement to experimental studies particularly the oblique impingement of circular water jets on plane surface boundaries. The modelling 177 involved comparisons by undertaking a series of experiments. The outline of this work is as follows. The numerical formulation of solving the full Navier-Stock Equations for the entire flow region utilizing the homogeneous model is elaborated. The flow domain and the boundary conditions used in this simulation are explained. The results of the numerical simulation for the water depth and velocity profiles, pressure field and shear stress are presented with a focus on the centerline plane along the jet pipe. The numerical simulation results are further validated by the experimental data. B.2 Homogeneous Model The numerical simulation for the flow in oblique water circular jet impingement on a flat surface involves two-phase (air and water) free surface flow. Each phase behaves as a continuous media occupying the entire domain where the amount of each phase present is given by the volume fraction. The model refers to the liquid phase (water) as a and to the gaseous phase (air) as p. A particular case of Eulerian-Eulerian approach for two-phase flow where there is no momentum transfer between phases is called a homogeneous model. In this model, the phases are assumed to be in mechanical equilibrium, and the transported quantities for each phase are the same. The Continuity Equation for both phases in the control volume is solved in order to determine the individual volume fraction. lt(rapa) + \7-(raPaUa) = 0 (B.l) ^(n»P/») + V-(r/?P/?i//,) = 0 (B.2) The momentum conservation equation for the mixture of phases in the control volume is given by: 178 T jt{pMUM) + ^- (pMUM ®UM) = V- [fiM (VUM + {VUM) )] - VpM + pMg (B.3) pM, UM, and [iM represent respectively the density, velocity and viscosity of the mixture of phases in the control volume that is given by: PM = raPa + rp pp UM = -i- (ra pjja + rp ppUp) \iM =rana + rp \ip PM where r represents the volume fractions of each phase in the control volume, g is the gravitational force, and pM is the mixture pressure. It is assumed that all phases share the same pressure field in the control volume. Therefore, only one pressure is solved (Ansys 2006), so the pressure constraint is: PM=Pa= Pp The summation of the volume faction over the phases is constant and equal to one. ra + rp = 1 (B.4) Turbulence is simulated by using the traditional k — s model, and it is assumed to be the same as that of the single phase except that the mixture density and the mixture viscosity are used. B.3 Computational Geometry A three-dimensional calculation domain was chosen in order to capture the flow characteristics of oblique water jet impinging on a flat plate. The dimensions of the numerical geometry were taken to be similar to the experimental setup for numerical simulation validation. The water jet pipe diameter was 152.4mm and 500mm in length. The plate has a dimension of 200cm in length by 100cm in width. The intersection of centerline of the jet pipe with the plate centerline represents the origin (0, 0, 0) of coordinates. The angle of the jet pipe with the center plane of the plate (0) was changed from 15° to 90° at 15° increments. The flow was found to be 179 symmetrical about the centerline of the jet (x-axis) so only half of the domain was modeled to save computational time and memory. The details of the domain used in the numerical simulations are shown in Fig. (B.l). Three series of numerical simulations were done. The first series has a fixed jet height (h) of 200mm so the impingement length (H) will be variable according to the jet impingement angle (the constant jet height series). In the second series, the impingement length (H) was fixed at 300mm for all jet impingement angles so the jet height (h) was variable according to the impingement angle (the constant jet length series). In the third series for numerical simulation validations (validation series), the jet height was the same as the experimental work that was done by Jalil and Rajaratnam (2006) (exp.3115, exp.3230, and exp.3345). B.4 Boundary Conditions In the numerical simulations, boundary conditions needed to be specified for all external faces of the domain geometry. The inlet pipe was assumed to be running full by setting the volume fraction of water to unity, and an average velocity boundary condition was used. Three different average velocity values (3.5, 5.5 and 7.5 m/sec) were used for the first two series of the numerical simulations. Additional average velocity (10 m/sec) was used for the impingement angle of 15°. The average velocity for the validation series was taken to be the same as the experiments. The three sides of the flow domain were specified as outlets. A static pressure boundary condition was used for the outlet. The reference pressure was set to be atmospheric so the relative static pressure at the outlet boundary was given as zero. In this case, it was not necessary to specify the water depth in the outlet. An opening type boundary condition was used at the top faces of the flow domain to allow the air to cross the 180 boundary condition in both directions. A symmetry boundary condition was used along the centerline of the domain along the jet pipe. At the face of the symmetry, the normal velocity was zero and the gradient of other variables in the transverse coordinate direction were taken to be zero. A scalable wall-function for near wall modeling was used for the jet pipe and for the bottom face of the domain (the flat plate). The turbulence models require estimates for k and s at the inlet and opening boundary conditions. In these numerical simulations, k and s estimates for turbulence at the inlet and opening were provided in terms of turbulent intensity (3.7 %), and length scale (0.3 * d) estimates. B.5 Gird Generation and Mesh Refinement Grid convergence requires that at a certain grid size the numerical result will not change significantly as the grid size decreases. The CFX mesh generator creates an unstructured mesh of tetrahedral elements. The minimum edge length was set as 2mm whereas the maximum edge length and the maximum body spacing length were set as 10mm. In the near wall regions, a boundary layer development requires a fine mesh to capture the high velocity gradient and the shear effects. The total thickness of the boundary layer mesh for all cases was 10mm. The dimension (normal to the wall) of prism elements adjacent to the surface is set so that the y+ restriction is met. Moving away from the wall, five layers were placed with the expansion factor set to 1.2. The number of the initial grid that was generated came approximately to between 200000 to 250000 nodes according to the impingement angle. The numerical domain was relatively large so due to the computer memory limitation it was not able to increase the initial number of nodes, and relatively coarse meshes were used; in particular for the area expected to be filled with air. 181 Through mesh analysis, the initial grid showed a significant numerical diffusion in the air-water interface, and the maximum pressure (at the stagnation point) on the flat plate changed significantly as the grid size decreased especially for small impingement angles. In order to achieve a good representation of the free surface interface, adaptive mesh refinement was used in the area where volume fraction and the area of high-pressure gradient changes. The high-resolution discretization schemes were used for all equations. Using this mesh refinement, the run times on a 2.6 GHz Xeon dual processors with 3 GBytes of RAM took about 2-3 hours. B.6 Numerical Simulation Results and Quality Assurance B.6.1 Simulation error The quality assurance was examined during the evaluation of the numerical simulation results for the selected target variables, the pressure, and volume fraction. The pressure coefficient Cp at the stagnation point for an ideal, inviscid fluid would be unity. The difference to the unity is therefore a measure of physical (viscosity, turbulent) and numerical diffusion. The pressure coefficient Cp at the stagnation point is defined as: c>=^k The iteration error was reduced in the first step, and then the discretization error was investigated by comparing the results of the mesh refinement steps. The iteration errors were plotted with the pressure coefficient at the stagnation point as a function 182 of the convergence criteria for the initial mesh for impingement angles 15° and 90° for the constant jet height series (h/d=1.31, U0= 7.5 m/sec) that is shown in Fig. B.2. The chosen convergence criteria are based on the maximum normalized residuals for mass and momentum in the flow domain. Figure B.2 shows the estimation of iteration error on the grid before mesh refinement. The pressure coefficient at the stagnation point significantly changed when the convergence criterion was reduced from 10-2 to 10-3, whereas insignificant change was noted when it was reduced to 10-4 or less. Figure B.2 confirmed that the solution does not change at all for a convergence criteria of less than 10~4. The convergence criterion of 10-4 is a good compromise between the iteration accuracy and computational effort for the tested case. The comparison of the pressure coefficient at the stagnation pressure as a target variable on the number of nodes at three mesh refinement steps is shown in Fig. B.3 for different impingement angles for the constant jet height series (h/d=1.31, Uo= 7.5 m/sec). Figure B.3 also gives some information on the solution errors. As the grid resolution increases, the pressure coefficient changes because the discretization error is reduced. In addition, the differences between mesh refinement steps 2, and 3 are smaller than the difference between mesh refinement steps 1, and 2. It is clear from Figure B.3 that a grid independent solution was achieved for large impingement angles (0> 45°), whereas further refinement was needed for the small impingement angles (9< 45°). The maximum number of nodes can be reached after mesh adaption from 1.10 to 1.28 million nodes were used in this study, and that depends on the computer memory limitation and the angle of the impinging jet. 183 B.6.2 Water depth and velocity profiles When a circular water jet impinges with a flat surface, the water flow transforms into a water sheet mainly in the outward radially flow and backward radially flow. For the normal circular water jet, the radially flow is an axisymmetric flow and the backward radially flow decreases with decreasing the jet impingement angle. The high pressure at the impact region changes the streamlines direction from the jet direction to a spread out in radial direction. The stagnation point is considered to be the point of intersection of the separation streamline with the plane of impinging surface where the maximum pressure is located. The streamlines exhibit a deflection outwards to the stagnation streamline in the vicinity of the stagnation point. Observations of the streamlines pattern within the symmetry plane of oblique impingement flow field revealed some aspects as shown in Fig. B.4 for the same jet height series. Increasing the jet impingement angle results in an increasingly asymmetric flow pattern. The stagnation streamline coincides with the jet centerline for the normal jet, and follows a trajectory parallel to, and displaced backwards for the oblique angles. The displaced distance (xs) between the impingement point and stagnation point increased with increasing the inclination of the impingement jet. For the impingement angle 15°, the stagnation streamline deflection was found only towards the main direction of the jet. The stagnation displacements are normalized by the jet diameter for different impingement angles as shown in Fig. B.5. Figure B.5 revealed that for a small impingement angle (0<45°), the stagnation displacement increased with decreasing the jet velocity for the same impingement length. The stagnation displacement is also increased by decreasing the impingement angle. The stagnation displacement was also found to increase by increasing the impingement length for the same jet velocity. These results were expected since the y component of 184 momentum of the jet (p UQ sin 9 ) has great effect on the location of the stagnation point. The increase in y momentum could be obtained by increasing the jet velocity U0 or by increasing the impingement angle 9, which will decrease the displacement of the stagnation point from the impingement point. The thickness of the deflected jet decreases rapidly in the impingement region. The variation of the jet thickness with a distance along the centerline of the deflected jet is increased with increasing the impingement angle. It is expected that the jet thickness for a small impingement angle will be higher than the large impingement angle since most the flow is in the forward direction. Figure B.6 shows the variation of the thickness of the deflected jet in the centerplane with the longitudinal distance from the impingement point, which is normalized by jet diameter for the constant jet length series. As seen in Fig. B.7, the numerical simulation of the water depth results shows reasonable agreement with the experimental data. The ratio between the backflow to the forward flow along the jet for different impingement angles are plotted in Fig. B.8 for the constant jet height series and the constant jet length series. The perpendicular plane on the surface through the impingement point separates the backflow and forward flow. The results revealed that the backflow ratio increased with increasing the impingement angle, and for a normal jet became constant with a value of 0.5, where the flow is axisymmetric. The backflow ratio slightly increased with increasing the jet velocity, in particular for a small impingement angle as seen in Fig. B.8. The backflow ratio results were also compared with the oblique plane jet that was investigated by Schach (1934). The comparison showed that the circular oblique water jet has a higher backflow than the oblique water plane jet as shown in Fig. B.8 185 The velocity contours profiles of a 10% interval difference of the normalized velocity with the maximum velocity along the symmetry plane for different impingement angles for the constant impingement length series (U0=7.5 m/sec) are plotted in Fig. B.9 (a-f). Since the flow is turbulent, the velocity distribution along the outlet jet pipe is fairly flat in the turbulent core. It is interesting to note that for the normal impingement (Fig. B.9 (f)), the stagnation point is along the centerline of the maximum velocity core, which means the streamline of the stagnation point has the maximum velocity of the turbulent core at the outlet pipe section. As mentioned before, the stagnation point streamline moved backwards away from the centerline of jet pipe when the impingement angle of the jet decreased, and the stagnation streamline was located at the edge of 90% of the maximum velocity contour for 75°. As the impingement angle of the jet decreased further, the velocity of the streamline at the outlet of the jet pipe decreased due to the stagnation streamline located further away from the maximum velocity core. As seen in Fig. B.9 (a), for an impingement angle of 15°, the stagnation point was approximately located within 20% of the maximum velocity contour. The velocity profiles along the centerline of the deflected jet for different impingement angles of the constant jet height series are plotted in Fig. B.10 (a-f). Figure B.10 showed clearly that the location where the flow becomes fully developed along the flat surface depends on the impingement angle of the jet. The distance of a fully developed velocity profile from the impingement point increased with decreasing the impingement angle. The location of the fully developed velocity profile is about x/d=l for an impingement angle of 90°, whereas the impingement angle of 15° was found to be at x/d>6. From these velocity profiles it may be seen that in all impingement angles in the boundary layer region, the velocity U increased with 186 the distance y measured from the bed surface to reach a maximum value of Um at y=8 and decreased as y increased further. The development of the boundary layer along the centerline of the jet was plotted in normalized form as seen in Fig. B.ll. The relation between 8/d with x/d was expected to become constant for a fully developed flow for a certain distance very much as in the case of the stagnation flows (Schlichting 2000). Because the water jet is not fully developed in the simulated geometry, this linear relation is not clear except for higher impingement angles of 75°, and 90°. Figure B.l 1 reveals that for a particular value of x/d, the 5/d decreased with increasing the impingement angle. The velocity scale for the boundary layer would be the maximum velocity Um normalized with U'0 where U'0 is velocity of the jet at the source adjusted for the fall through the jet height (h). The variation of Um/ U'0 with x/d is shown in Fig. B.12. It may be observed in Fig. B.12 that the normalized velocity scale for small impingement angles remains approximately constant (Um/U'0 = 1) up to x/d =6 along the jet centerline since the main flow is in the forward direction along the centerline of the jet. As seen in Fig. B.12, it is expected for an impingement angle of 9> 45°, the rate of decay of the maximum velocity is much faster than the small impingement angle due to the greater rate of spreading around the impingement area. The comparison between experimental and numerical simulations of the velocity profiles along the centerline of the deflected jet is plotted in Fig. B.13(a-f). In general, the simulated profiles are shown to be in some agreement with the experimental profiles especially close to the impingement area. However, there is some difference near the locations of maximum velocity with a further distance. This may be caused by inaccuracy of the measurements in the regions where water depth is small. 187 B.6.3 Pressure field The typical contour plots of the simulated values of the normalized static pressure P with stagnation pressure Ps (maximum pressure) on the flat surface for the same jet height (h) series and for the same jet length (H) series for U0=7.5 m/sec are provided in Fig. B.14 (a-f). The counter plot of constant pressure contours for the normal impingement takes a circular shape as seen in Fig. B.14 (f). When the impingement angle increased measured from the normal jet, the constant pressure contours started to form an egg-shape as seen Fig. B.14 (e-d). The major axis of this egg-shape is along the centerline of the flow of the jet, and the minor axis is located at the stagnation point. The stagnation point (maximum pressure) lies along the symmetry plane, coincides with the jet impingement point at the normal jet, and shifts backwards from the jet impingement point as the jet angle decreases as mentioned before. The impingement of 90% of maximum pressure occurred approximately in a circular area with a diameter equal to half of the diameter of the jet, and the center was the stagnation point while 10% of the maximum pressure for the normal jet occurred at a circular area with a diameter equal to twice that of the jet diameter. The curvature of the egg-shaped curve started to increase with decreasing the impingement angle. The main changes in the pressure contour area occurred at the impingement angle of 15°, where 10% of the maximum pressure extended to five times that of the jet diameter as seen in Fig. B.15 (a-b). These results were expected due to the increase in the projection area of impingement of the jet on the flat surface when the impingement angle decreased. The pressure along the x-axis at the symmetry plane was normalized with the maximum pressure at the stagnation point that is presented in Fig. B.16 (a-b) for all impingement angles for a constant jet height series for the jet velocity (7.5 and 3.5 188 m/sec). The pressure distribution is symmetrical around the stagnation point for the normal impingement and it began to have a positive skew distribution along the x- axis. The degree of the skewness of the distribution increased with decreasing the impingement angle of the jet. In the negative direction of the x-axis from the stagnation point, the pressure distribution shifted inwards to the impingement point and the change in skewness was small in comparison with the positive direction. The stagnation pressure can be estimated by assuming the velocity at the stagnation streamline will be reduced to zero, and the momentum normal to the surface destroyed. Therefore, the pressure force exerted between the jet and the surface is equal to the rate of change in momentum normal to the surface so the pressure at the stagnation point can be predicted by using Bernoulli Equation taking the effect of the jet height equal to%pUo2. The relation between the simulated and predicated stagnation pressure data for the same jet height (h) series, and for the same jet length (H) series for the simulated impingement angles at two different jet velocities (3.5 and 7.5 m/sec) are shown in Fig. B.17. It is clear from Fig. B.17 that for larger impingement angles (0> 45°), the simulated stagnation pressure value is slightly overestimated as compared to the predicated value (approximately 3%). This difference is due to the numerical simulation solving Navier-Stocks Equations, which calculates the actual velocity of the stagnation streamline, and the effects of the viscosity, whereas using Bernoulli Equation for predicting the stagnation pressure neglects the viscosity and uses the average velocity of the jet. On the other hand, for small impingement angle (9<45°), the simulated stagnation pressure is underestimated as compared to the predicated value, and the difference increases with decreasing the impingement angle i.e. for 30° about 8%, and for 15° about 40%. Neglecting the viscous and gravity effects, the stagnation streamline velocity has the most significant 189 effect on the stagnation pressure. As mentioned before, the stagnation streamline velocity depends on the location of this streamline on the velocity distribution profile at the outlet of the jet pipe, which is merely proportional with the impingement angle of the jet. For small impingement angles (0< 45°), the stagnation streamline is located very close to the wall of the jet pipe where the velocity gradient in this area is very high. Therefore, in this case, the error source is mainly due to the discretization error, and a very fine mesh will reduce the error, which is beyond the capability of the computer being used for this numerical simulations. B.6.4 Shear stress The simulation results of shear stress (x) on the surface are plotted in Fig. B.18 (a- f) for the constant jet length series, and Fig. B.19 (a-f) for the constant jet height series. The shape of constant shear stress contour lines are very similar to the constant pressure contour lines in the impingement area, in particular from the stagnation point where the zero shear stress occurs at the stagnation pressure. The contour lines take an almost circular shape in normal impingement (see Fig. B.18 (f) and Fig. B.19 (f)) and start to form an egg- shape with the decrease in the impingement angle. The egg- shape increases in size with decreasing the impingement angle. From Fig. B.18 and Fig. B.19, it can be seen that the shear stress increases rapidly with a short distance from the stagnation point up to the maximum value which is approximately x/d=l for a large impingement angle (9 > 45°). The maximum value of shear stress on the surface is associated with the extreme interaction between the jet and the surface so it is of great practical importance for predicting the value. For impingement angles 15° and 30°, it can be seen that the maximum shear stress (tmax) occurred only along the jet pipe direction and at a distance depending on the H/d and jet velocity. When the 190 shear stress rapidly reached the maximum value from zero at the impingement point, the shear stress started to decrease gradually with the distance. Figures B.18 and B.19 also reveal that the shear stress depends on the H/d, which increases with decreasing the H/d, in particular for a small impingement angle. Figure B.20 (a-d) shows the effect of jet velocity on shear stress contour lines for four different jet velocities for the impingement angle 15°. The normalized shear stress with the maximum shear stress along the surface in the symmetry plane for 3.5 and 7.5 m/sec jet velocity are provided in Fig. B.21 (a-b) for the constant jet length series. The rate of decay in shear stress after reaching the maximum value as seen in Fig. B.21 (a-b) depends on the impingement angle. It is clear that the rate of shear stress decay is higher with the normal jet, and starts to decease with decreasing the impingement jet. The rate in shear stress decay also increases with decreasing the jet velocity. Following the pressure coefficient, the shear stress value can be expressed in dimensionless form as: c' = v^I B.22. Figure B.22 reveals that the dimensionless maximum shear stress distribution increases with increasing impingement angle 6, and increases with decreasing the jet velocity. For a given impingement angle 9, the dimensionless shear stress is a function of jet Reynolds number (Re) and jet length (H). Following the works done by Porch et al. (1967) and Phares et al. (2000) for the normal impingement jet, the 191 maximum shear stress can be scaled in terms of the jet Reynolds number yielding this function. ^Re% = f(f.e) (B.7) For the range H/d used in the numerical simulation (1.31 ma 1 2 parameter J *2 Re / is plotted with the impingement angle 9 in . B.23, where it ma 1/z appears the parameter J *2 Re increases with increasing 9, and the best fit for this relation may be described by the Equation: -T^ReVz = -le-593 + 0.00192 - 0.0479 + 2.422 (B.8) with a correlation coefficient value of r2 = 0.984. The comparison between the experimental data and numerical results for the shear stress along the centerline of the symmetry plane for the impingement angles 30° and 45° are plotted in Fig. B.24. Figure B.24 reveals there is fair agreement between the experimental and numerical simulations for shear stress results. B.7 Summary and Conclusions The aim of this study is an understanding of water circular jet impinging on a flat surface at different angles of obliquity in terms of water depth profiles, velocity profiles, pressure distribution, and shear stress distribution. Three-dimensional computational simulations were carried out for the different angles of impingement of circular water jets by using the commercial software package CFX11.0. A homogeneous multiphase flow model that is incorporated with the CFX11.0 combined with the k — E turbulence model was applied. At the same time, the 192 numerical simulation results were validated, and compared with the experimental data including the water surface profile, velocity profile, and the shear stress along the centerline of the deflected jet. The discretization error was quantified by refining the numerical grid size using the automatic adaptive mesh refinement. Overall, the homogenous model and the turbulence model were found to be suitable for simulating the flow of the jet with good accuracy except for small impingement angle (6<45°) of the jet that required a very fine mesh size. The change of the jet water surface profiles, and velocity profiles at different impingement angles were analyzed. Observations of the streamlines pattern within the symmetry plane showed that the stagnation streamline coincides with the centerlines for the normal jet while it displaced backwards as the impingement angle decreased. The stagnation displacements were normalized by the jet diameter. It was found that for small impingement angles, the stagnation displacement increased with decreasing the jet velocity for the same jet length, and increased with increasing the jet length for the same jet velocity at a particular impingement angle. The jet thickness along the centerline of the deflected jet increased with increasing the impingement angle. The ratio of backward flow to the total flow was presented, and it was found to decrease with decreasing the impingement angle of the jet. For small impingement angles, this ratio increased with decreasing the jet velocity for a particular angle. The velocity profiles along the centerline of the deflected jet for different impingement angles showed that the location of fully developed velocity profiles increased with decreasing the impingement angle. The contour plots of the pressure distribution on the surface were found to take a circular shape for the normal impingement, and started to take an egg-shape with the major axis along the deflected jet centerline and the minor axis at the stagnation point. 193 The normalized pressure distribution along x-axis at the symmetry plane for normal impingement had the normal distribution shape with the center at the stagnation point, and the distribution began to have a positive skewness that increased in value with decreasing the impingement angle. The comparison of the pressure at the stagnation point between the calculated pressures using Bernoulli Equation with the simulated pressure showed that the CFX could predict the pressure very well for larger impingement angles, whereas for small angles, it underestimated the pressure at the stagnation point, and it was found that a very fine mesh was needed for accurate results. The maximum shear stress is important due to the extreme interaction between the jet and the surface. The results of normalized maximum shear stress along the centerline of the deflected jet showed that the shear stress increased with increasing the impingement angle, and it decreased with decreasing the jet velocity. The location of maximum value was found to be approximately x/d=l for large impingement angle (9> 45°). A general equation for maximum shear stress proposed including the Reynolds numbers and impingement angle. Further study is needed to examine the effect of H/d on the maximum shear stress. 194 igure B.l Jet impingement layout of CFD Figi 195 1.2 0- -e- -© 0.8 •15deg. 0.6 •90deg. 0.4 0.2 0 1.00E-03 1.00E-04 1.00E-05 1.00E-06 1.00E-07 Max. residual of mass and momentum B.2 Estimation of iteration error of pressure coefficient at the stagnation point for the initial mesh for impingement angles 15° and 90° (constant jet height series, Uo= 7.5 m/sec). 200000 400000 600000 800000 1000000 Number of nodes Figure B.3 Change of the pressure coefficient at the stagnation point for different impingement angles with the number of nodes (constant jet height series, Uo= 7.5 m/sec). 196 (e) 6 = 75c jiflK^i:- (f) 9 = 90° ^AeA 4s. Figure B.4 (a-f) Change of streamline patterns at the symmetry plane for different impingement jet angles (constant jet height series, U0=5.5 m/sec). 197 3.0 • 2.5 • A Uo=3.5m/s,h/d=1.31 9 • Uo=5.5m/s,h/d=1.31 2.0 o • Uo=7.5m/s,h/d=1.31 a A Uo=3.5m/s,H/d=1.97 p 1-5 Ouo-o.o m/s , H/a in =1.97 X DUo=7.5m/s,H/d 1.0 £ —8— 0.5 a Q 0.0 D 10 20 30 40 50 60 70 80 90 Impingement angle (6) degree Figure B.5 Change of normalized stagnation point displacement from the center of impingement with the impingement angle of the jet. 0.50 1 < f ! n • 15 deg. 0.40 V —•—30 deg. X ,y —*—45 deg. X —•— 60 d AM 0.30 • < eg. 1 1 9 *\ V ~~*— 75 deg. "5» T 1 * 90 deg. 0.20 \ L ' m 0.10 \ ^ 0.00 -7.00 -5.00 -3.00 -1.00 1.00 3.00 5.00 7.00 x/d Figure B.6 Change of normalized water depth profiles with x/d in the symmetry plane for different impingement angles (constant impingement length series, Uo= 7.5 m/sec) 198 012345678 x/d Figure B.7 Comparison between experimental and numerical simulations for the normalized water surface profile with x/d (6=15°, h= 150mm, U0=5.46 m/sec (exp.3115); 9=30°, h=185mm, U0=5.26 m/sec (exp.3230); 9=45°, h=222mm, U0 =4.93 m/sec (exp.3345)). 0.6 0.5 AUO= 3.5 m/sec, h/D=1.31 • Uo= 5.5 m/sec, h/D=1.31 • Uo=7.5 m/sec , h/D=1.31 A Uo= 3.5 m/sec , H/D=1.97 ollo= 5.5 m/sec , H/D=1.97 DUo=7.5 m/sec, H/D=1.97 }" X plane jet (Schach 1934) I 0.2 0.1 0 -I 15 30 45 60 75 90 Impingement angle (6) degree Figure B.8 Change of ratio of the backflow to the total inflow at the impingement point section with the impingement angle of the jet for the constant impingement length series and the constant jet height series. 199 Figure B.9 (a-f) Change of velocity contours (10% normalized velocity interval) at the symmetry plane for different impingement angles (constant impingement length series U0=7.5 m/sec). 200 U (m/sec) Fig.|d) x/d=4 1 —•—15deg. —*—45 deg. ^^ —••—75deg. ^^•L "O - 90 deg- ^^* n t- ""• n '" .'I,, ii ^ U (m/sec) Fig-(e) x/d=5 35 ^^^ —•— IS deg. 30 —#—45 deg. —•—60 deg. —•—75 deg. O 90 deg. 20 7Z!*«!( 15 .Sfc^^— in 5 .- 1 _ 6 U (m/sec) U (m/sec) Figure B.10 (a-f) Change of velocity profile of the deflected jet at different locations along the symmetry plane for different impingement angles (constant impingement length series, U0=7.5 m/sec) 201 01234567 x/d Figure B.ll Change of the normalized boundary layer thickness in the deflected jet with x/d at different impingement angles (constant impingement length series, U0=7.5m/sec). x/d Figure B.12 Change of the normalized maximum velocity Um in terms of U'0 with x/d at different impingement angles (constant impingement length series, U0=7.5 m/sec). 202 U„ (m/sec) 4 6 U„ (m/sec) 45 40 35 Fig. (C) \ 30 x= 40 cm **\ —*— Exp. ^ ^ ?25 !» CFD Y\ 15 10 5 0 U„ (m/sec) U0 (m/sec) 2 4 U„ (m/sec) U„ (m/sec) 2 4 U„ (m/sec) " U0 (m/sec) Figure B.13 (a-f) Comparison between experimental and numerical simulation velocity profiles along the centerline of the deflected jet (6=15°, h = 150mm, U0=5.46 m/sec, d= 152.4 mm (exp. 3115)). 203 S0.5 Figure B.14 (a-f) Pressure distribution contours (10% normalized pressure intervals) for different impingement angles for the constant impingement length series and the constant jet height series, (U0=7.5 m/sec). 204 0.75 5 0.5 0.25 -4 -3 -2 -1 x/d 0.75 1. 05 0.25 -1 1 x/d Figure B.15 (a-b) Change of the pressure distribution contours (10% normalized pressure intervals) for the impingement angle 15°, and for different jet flow velocities (constant impingement length series). 205 1 0.9 Hg. (a) jl 0.8 U0=7.5m/sec,h/d=1.31 if » 15 deg. II 0.7 —•— 30 deg. f| 0.6 —+— 45 deg. I£ a. —•— 60 deg f I £ 0.4 —©—75 deg. II 0.3 o 90 dog [• 0.2 0.1 0 ^^^^^^^^^^^^^^^^^^^^^^^^^"^ i -8 0 10 (x-xs)/d Figure B.16 (a-b) Normalized pressure distribution at the surface on the symmetry plane for different impingement angles, and for different jet flow velocities (constant impingement length series). 206 1.1 ^ H A s H 0.9 s i 0.8 DUo=7.5m/s,H/d=1.97 £L 0.7 &Uo=3 5 m/s H/d=1 97 • Uo=7.5m/s,h/d=1.31 A 0.6 — B 0.5 10 20 30 40 50 60 70 80 90 Impingement angle (6) degree Figure B.17 Change of the normalized stagnation pressure for different impingement angles and for different jet flow velocities (constant impingement length series and the constant jet height series). 207 3 Fig. a 6=15° Hfd= w////^- 2.5 I;I =O,I if/ 2 M //// // ( / / ) / f ( 1 //// ( 0.5 (I I { , \ \ 0 \\\\v -3-2-10 1 2 3 4 5 6 x/d Figure B.18 (a-f) Shear stress distribution contours (10% normalized shear stress intervals) for different impingement angles (constant impingement length series (U0=7.5 m/sec)). 208 3 ? 7—/ V; / ' 3 Fig. a k=\S°/dl4 £07/ / / 2.5 / / / 2.5 2 '••/•"V///1 /////, / / <' V'0'' 2 7 ' /.-'/,- ! / I i z! / ./ mw 5 1.5 •o 1.5 urn 1 wn 1 0.5 0.5 -fntiiffifc-----—Ml' b^?^—- \\\\ ^. / / |l»,N\ 0 w 0 1 2 -4-3-2-10 1 2 3 4 5 6 x/d x/d 3 3 JFig.c;e=-i5° h/d>1.45 / JFig.dj 9=$0° lj/d=^51 / 2.5 I f *—1—i—i—r— 2.5 2 2 1-1 \\l I k ( f ,1.5 CO- -MiI / 1 1 i \ Ml,\i, a 0.5 0.5 -t—r HM \ \ / mm aii 0 am 0 \ \(iwm •6-5-4-3-2-10123456 -5-4-3-2-10123456 x/d x/d 'iFigie-^H/W / Fig. f ^=90° HCd=1.31 25 2.5 2 cw 2 r-rr -\ V- 1.5 ] ,1.5 •*#—/—i—^ >• • \ \ \ 1 J*SX 1 ' / / / 0.5 0.5 -i—t V-rt 0 I i I/H«I 0 /sin 11 -5-4-3-2-10123456 -5-4-3-2-10123456 x/d x/d Figure B.19 (a-f) Shear stress distribution contours (10% normalized shear stress intervals) for different impingement angles (constant jet height series (U0 =7.5 m/sec)). i 209 Figure B.20 (a-b) Shear stress distribution contours (10% normalized shear stress intervals) at impingement angle 15°, and for different jet flow velocities (constant impingement length series). 210 Figure B.21 (a-b) Normalized shear stress distribution on the surface at the symmetry plane, and for different impingement angles (constant impingement length series). 211 0.007 0.006 * • 0.005 « i II = 0.004 * e • • 1 0.003 • H/d=1.97 , Uo=3.5 m/sec B B 0.002 • H/a=i.a/, uo=/.b m/sec • h/d=1.31, Uo=3.5 m/sec 0.001 D h/d=1.31, Uo=7.5 m/sec 0 i i i i i 15 30 45 60 75 90 Impingment angle (6) degree Figure B.22 Change of the dimensionless maximum shear stress with the impingement angle, and for different jet velocities (constant impingement length series, and the constant jet height series). 4.5 2 2 Tm.,Re»/(>4pU J= _le-o563 + o.ooie - 0.0479 + 2.422 4 r2 = 0.984 3.5 ^S^> r« 3 E 25 X n E • H/d-1 97 Uo-3 5 m/sec H 1.5 m H/d=1.97, Uo=7.5 m/sec O h/d=1.31, Uo=3.5 m/sec 1 • h/d=1.31,Uo=7.5 m/sec 0.5 -•- r l i i i 0 15 30 45 60 75 90 Impingment angle (6) degree Figure B.23 Change of the normalized maximum shear stress with impingement angles, and for different jet flow velocities (constant impingement length series and the constant jet height series). 212 90 80 70 60 a 50 40 30 JLcFD } 0= 30°, h =185 mm, U0=5.26 m/sec 20 A Exp. -j w -*^CFD ) 9= 45°, h =222 mm, U0=4.93 m/sec 10 0 20 40 60 80 100 120 Distance along the centerline x (cm) Figure B.24 Comparison between experimental and numerical simulation results for the shear stress along the centerline of the deflected jet (9=30°, h=185 mm, U0 =5.26 m/sec (exp.3230), and 0=45° h= 222 mm, U0 =4.93 m/sec (exp.3345)). 213 References Agrwal, R.K. and Bower, W.W. 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