numerical inve stigation of recirculation flow tn a draft tube kofi k. adane

131 Pages·2013·8.13 MB·English

NUMERICAL INVE STIGATION OF RECIRCULATION FLOW
TN A DRAFT TUBE
BY
KOFI K. ADANE
A Thesis
Presented to the Faculty of Graduate Studies
In Partial Fulfilment of the Requirements for the Degree of
MASTER OF SCIENCE
Department of Mechanical and Manufacturing Engineering
University of Manitoba
Winnipcg, Manitoba
@ Kofi K. Adane, 2005
THB UNIVERSITY OF MANITOBA
FACULTY OF GRADUATE STUDIES
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COPYRIGHT PERMISSION
"Numerical Investigation of Recirculation Flow in a Draft Ttbe,,
BY
Kofi K. Adane
A ThesisÆracticum submitted to the Faculty of Graduate Studies of The University of
Manitoba in partial fulfillment of the requirement of the degree
of
MASTER OF SCIENCE
Kofi K. Adane O 2005
Permission has been granted to the Library of the University of Manitoba to lend or sell copies of
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ABSTRACT
This thesis presents a numerical investigation of turbulent flow in a typical draft tube at
Manitoba Hydro. The draft tube geometry includes a conical inlet section prior to the
pier nose and three outlet channels. Each of the outlet channels has a slot or an opening
in the ceiling to allow placement of stoplog. These slots allow recirculation of flow back
into the diffuser and the goal of this study is to evaluate the effects of the slot flow on the
flow characteristics in the draft tube.
The computation was performed using a commercial code, CFX-5, to solve the
conventional Navier-Stokes equations and two-equation eddy viscosity turbulence model.
A scalable wall function version of k-t was used as near-wall treatment to model the
near-wall region of the flow. CFX-5 is a computer code that uses a finite volume method
of solution based on a finite element approach representing the geometry. Prior to the
draft tube computation, the commercial code was validated using two different diffusers
and various turbulence models.
Because the exact amount of flow through the slot is not known, the computation was
performed using 3olo, 6Yo and 9o/o of the inlet mass flow rate through the channels.
Computation was also performed with no slot (0%) and this case was used as the
reference for comparing the effects of slot flow on the draft tube performance. The
pressure coefficient and kinetic head are the principal indicators used to evaluate the draft
tube performance.
The draft tube results show that approximately 40 %ó of the inlet flow goes through each
of the side channels and only 20 o/o goes through the middle channel. The results clearly
demonstrate that values of the pressure coefficient and velocity head obtained for the
various slot mass flow rates and the particular draft tube geometry investigated in this
study are not significantly different. The flow through the slots, however, creates
different amounts of localised recirculation zones and backflow in the individual
channels.
lll
ACKNOWLEDGEMENT
I would like to express my profound gratitude to my advisors, Drs S. J. Ormiston and M.
F. Tachie, for their excellent professional guidance and impressive help with all aspects
of this thesis as well as with my graduate coursev/ork. I would also like to thank Drs R.
W. Derksen and Abba Gumel for their participation on the examining committee. I also
appreciate the effort from Mr Reed Winstone, the Manitoba Hydro line advocate, for
providing all relevant information to make this thesis a successful one. I am grateful to
Manitoba Hydro and the Natural Sciences and Engineering Research Council of Canada
for their financial support of this work.
Also I would like to thank my three loving sisters, my two nieces, and my uncle for their
invaluable support. Thanks to Seth Osei-Fosu, Robyn Tully, Kim Melissa Chandler,
Siobhán Stewart, Lucious Delice, Martin Agelinchaab, Jeffery Berg, Samuel Sunday
Paul, Mohammad Khalid Shah, Meghan Groff, and everyone who directly or indirectly
contributed to the success of this thesis. Special thanks to Him through whom all things
are completed.
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TABLE OF CONTENTS
ABSTRACT.... ........ii
.. ...
ACKNOWLEDGEMENTS. .iv
TABLEOFCONTENTS... ......v
LISTOFFIGURES ....viii
LISTOFTABLES ......xii
NOTATIONS.. .......xiii
ACRONYI\4S... .....xvi
I
Chapter INTRODUCTION
1.1 Overview ....
I
1.2 ManitobaHydroPowerPlant:DraftTube. .......3
1.3 Objectives ........4
1.4 LayoutoftheThesis .......4
2
chapfer LITERATURE REVIEW
2.1 Overview .........5
2.2 Experimentallnvestigations .....6
2.3 NumericalStudiesonDraftTube. .......8
2.4 Summary ... .....14
3
chapter PROBLEM DESCRIPTION
3.1 ProblemDefinition ......16
3.2 Assumptions.... .......19
3.3 MathematicalModel ....19
3.3.1 Governing Equation . .. . . .19
3.3.2 TurbulenceClosures. ....20
3.3.3 Boundary Conditions. .. . . 23
Chapter 4 NUMERICAL SOLUTI ON PROCEDURE
4.1 Introduction.... ........27
4.2 GridGeneration. .......27
4.3 NumericalMethod .......30
4.4 .
Overview of Commercial Codes Used . . . .. . . .. 3l
Chapter 5 CODE VALIDATION AND TEST PROBLEMS
5.1 Introduction
.. .. . .. .33
5.2 Asymmetric Plane Diffuser .. . . .34
5.2.1 FlowGeometryandDescription .........34
5.2.2 Prior Computations . .35
5.2.3 Numerical Procedure .. .. . .36
5.2.4 Comparison of Present Numerical results with Previous Results.
.39
5.2.5 Concluding Remarks for Asymmetric Plane Diffuser . . .42
5.3 ConicalDiffuser .........42
5.3.1 Flow Geometry and Description
5.3.2 Prior Computations .. . . . 43
5.3.3 Numerical Procedure . .. .. .44
5.3.4
Present Numerical Results Compared with Previous Results . . 46
5.3.5 Concluding Remarks for Conical Diffuser . . .. .. ..50
5.4 Tube
Validity Checks for the Draft . . . . .51
vl
5.4.1 Definitions .......51
5.4.2 GridlndependenceTests. .......55
5.4.3 MassConservationChecks. .....58
5.4.4 Effects of Eddy Length Scale on Flow Parameters . . . . ..59
5 Results.
5.4 Comparison between k-e and k-a¡model .. . . . . . 61
Chapter 6 RESULTS AND DISCUSSION
6.1 Introduction ......63
6.2 Mass
Effects of Varying Slot . . . . .63
6.3 VelocityQuantities. ......68
6.3.I VelocityContours .......68
6.3.2 Mean Velocity Profiles . . .72
6.4 Distribution
Pressure Coefficient - . .76
6.5 Comparison of Kinetic Head with Pressure Coefficient. .. . . . . .82
6.6 .
The Effect of Inlet Mass Flow Rate . . . . .85
Chapter 7 SUMMARY AND CONCLUSIONS
7.1 Summary .........91
7.2 Conclusions.... ........92
REFERENCES. ......
.93
DRAFTTUBECADDRAWINGS.
APPENDIX A .....99
APPENDIX B cFX-s (s.7) /CFX-TASCFLOW PARAMETERS. . . . .10s
.
APPENDIX C OVERALL FLOW FEATURES. . . . . . . . . . . .I 09
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LIST OF FIGURES
Figure Title Page
l.l
1.2
3.i
3.2
4.1
4.2
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
5.10
5.11
YIII
5.12 Boundaries of mid plane and nomenclature for arc lengths along top and bottom
tube.
walls of the draft ......52
5.13 tube..
Selected planes in draft ...........54
6.1 Comparison of absolute velocity contours at mid-plane of the Right channel
flow).
(a) case A (no slot flow) and (b) case C.(6%o slot .......69
6.2 Comparison of absolute velocity contours at mid-plane of the Left channel
C........
(a) Case A and (b) Case ............70
6.3 Comparison of absolute velocity contours at mid-plane of the Middle channel
C.....
(a) Case A and (b) Case .........71
6.4 Comparison of axial velocity contours at plane P10 (0.55 m before the slot)
C......
(a) Case A and (b) Case ..................73
6.5 Comparison of axial velocity contours at exit plane: (a) Case A and (b) Case
c.....
...............74
6.6 Comparison of outflow a velocity at the top (Line l) of the exit (drawn from Left
end-walls).
to Right ..............75
6.7
Comparison of outflow ø velocity at the bottom (Line 2) of the exit (drawn from
end-walls).
L to R ............75
6.8
Comparison of outflow v velocity at the top (Line 1) of the exit (drawn from L to
Rend-walls)........
..............77
6.9
Comparison of outflow v velocity at the bottom (Line 2) of the exit (drawn from L
end-walls)...
to R ..................77
6.10 Comparison of outflow w velocity at the top (Line 1) of the exit (drawn from L to
...
R end-walls).. .. . ...... . ...... ....78
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