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UBC Theses and Dissertations

Air-actuated pumping technology in urban drainage Bohnen, D. Aaron 2004

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A I R - A C T U A T E D P U M P I N G T E C H N O L O G Y IN U R B A N D R A I N A G E  by D. Aaron Bohnen B . A S c , T h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1996  A THESIS S U B M I T T E D IN P A R T I A L F U L F I L M E N T OF THE REQUIREMENTS FORT H ED E G R E E OF M A S T E R OF APPLIED SCIENCE in ' T H E F A C U L T Y OF G R A D U A T E STUDIES CIVIL ENGINEERING  W e accept this thesis as c o n f o r m i n g to the required standard  THE UNIVERSITY OF BRITISH C O L U M B I A A p r i l 2004 © D . A a r o n Bohnen, 2004  Library Authorization  In presenting this thesis in partial fulfillment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.  Name of Author (please print)  Title of Thesis:  Date ~(dd/mm/yyyy)  4'/g^/}^fU/tT&h  PUH4P'AJ6r  Degree: Department of  Year: CWlL-  &KT&?  The University of British Columbia Vancouver, B C  TS^A/rJiFLO  Canada  I K I S . ^ : fZ ?r4 ^  fry  ABSTRACT A i r l i f t P u m p t e c h n o l o g y is b r i e f l y s u m m a r i z e d and the potential a p p l i c a t i o n o f airlift t e c h n o l o g y to l o w - l i f t , l o w - s u b m e r g e n c e , h i g h - f l o w applications s u c h as o p e n c h a n n e l f l o w i n urban s t o r m drainage, is e x p l o r e d . F o u r e x p e r i m e n t a l setups are d e s c r i b e d , i n c l u d i n g one prototype urban storm drainage installation. T h r e e d e s c r i p t i v e m o d e l s for airlift p u m p operation are d e v e l o p e d and one adopted for a p p l i c a t i o n i n l o w - l i f t , l o w submergence, h i g h - f l o w applications. T h e m o d e l a l l o w s a s i m p l e d e s i g n p r o c e d u r e for airlift p u m p s i n this r e g i m e . A s i m p l e design hand-calculations procedure is d e v e l o p e d , and t w o p e r s o n a l computer-based i m p l e m e n t a t i o n s are described. A s i m p l e d e s i g n e x a m p l e is presented and r e c o m m e n d a t i o n s for further research and d e v e l o p m e n t d i r e c t i o n s are made.  TABLE OF CONTENTS Abstract  ii  T a b l e o f Contents  iii  List o f Figures  v  List o f Tables  vi  Acknowledgements  vii  CHAPTER 1  Overview & Summary  1.1  I n t r o d u c t i o n to A i r l i f t P u m p s  1  1.2  Description o f an Airlift P u m p  6  1.3  Applications o f Airlift Pumps  9  1.4  Project S c o p e and R a t i o n a l e  11  1.5  Two-Phase F l o w Regimes  14  1.6  Operational Efficiency o f Airlift Pumps  17  1.7  Summary  20  CHAPTER 2  Literature R e v i e w  2.1  Introduction  22  2.2  D e v e l o p m e n t o f A i r l i f t P u m p T h e o r y , 1797 to Present  22  2.3  Summary  30  CHAPTER 3  Experimental Program  3.1  O v e r v i e w o f the E x p e r i m e n t a l P r o g r a m  32  3.2  T h e E x p e r i m e n t a l Setups  36  3.2  R e s u l t s o f the E x p e r i m e n t a l P r o g r a m  56  iii  T A B L E O F C O N T E N T S (cont'd)  CHAPTER 4  Three Airlift Pump Theoretical M o d e l s  4.1  A i r l i f t P u m p M o d e l for F i x e d B u b b l e V e l o c i t i e s  57  4.2  A i r l i f t P u m p M o d e l for V a r i a b l e B u b b l e S l i p V e l o c i t i e s  65  4.3  A i r l i f t P u m p M o d e l for T u r b u l e n t M i x i n g  72  4.4  S u m m a r i z i n g the T h r e e M o d e l s  79  CHAPTER 5  Preliminary Design o f Airlift Pumps  5.1  Preliminary Design Procedure Calculations  81  5.2  D e s i g n C a l c u l a t i o n s for P e r s o n a l C o m p u t e r  86  5.3  P r a c t i c a l C o n s i d e r a t i o n s for P r e l i m i n a r y A i r l i f t P u m p D e s i g n .  91  CHAPTER 6  C o n c l u s i o n s and R e s e a r c h  Recommendations  6.1  Conclusions  94  6.2  Research Recommendations  95  REFERENCES  96  APPENDLX 1  99  LIST O F FIGURES F i g u r e 1 - S c h e m a t i c A i r l i f t P u m p L a y o u t and T e r m i n o l o g y  7 (also 57)  Figure 2 - Two-Phase Air-Water F l o w Regimes  15  F i g u r e 3 - T w o - P h a s e F l o w R e g i m e s characterized b y G a s F l u x and M i x t u r e  16  V o i d Fraction  Figure 4 - First Laboratory Airlift Pumping System  37  F i g u r e 5 - F i r s t L a b o r a t o r y A i r l i f t P u m p i n g S y s t e m Results  38  Figure 6 - Prototype Scale Laboratory Airlift P u m p i n g System  39  F i g u r e 7 - G i l b e r t R o a d Prototype A i r l i f t S y s t e m L a y o u t  42  F i g u r e 8 - G i l b e r t R o a d Prototype A i r l i f t S y s t e m C o m p o n e n t s  43  Figure 9 - Gilbert R o a d Compressed A i r Supply Subsystem  45  F i g u r e 10 - G i l b e r t R o a d Prototype A i r l i f t S y s t e m i n O p e r a t i o n  46  F i g u r e 11 - S l o t - c o n f i g u r e d A i r l i f t P u m p S y s t e m i n O p e r a t i o n  51  F i g u r e 12 - R i c h m o n d P u b l i c W o r k s E x p e r i m e n t a l Setup  54  F i g u r e 13 - B u b b l e R i s e V e l o c i t i e s i n S t i l l W a t e r  61  F i g u r e 14 - M i x t u r e and G a s F l u x Rates  65  F i g u r e 15 - C o m p a r i s o n o f E x p e r i m e n t a l and C a l c u l a t e d P e r f o r m a n c e  78  v  L I S T O F F I G U R E S (cont'd)  F i g u r e 16 - S i m p l e D e s i g n E x a m p l e L a y o u t  82  F i g u r e 17 - A i r l i f t P u m p C h u r n F l o w W o r k s h e e t  87  F i g u r e 18 - V B A C o d e for C h u r n F l o w A i r l i f t P u m p D e s i g n  89  F i g u r e 19 - V B A C o d e for C h u r n F l o w A i r l i f t P u m p D e s i g n  90  LIST OF TABLES T a b l e 1 - A i r l i f t P u m p N o m e n c l a t u r e and V a r i a b l e s  8  Table 2 - Prototype Scale Laboratory Airlift P u m p i n g System Results  40  T a b l e 3 - G i l b e r t R o a d Prototype A i r l i f t S y s t e m S a m p l e E x p e r i m e n t a l D a t a  48  T a b l e 4 - G i l b e r t R o a d Prototype A i r l i f t S y s t e m S a m p l e E x p e r i m e n t a l  48  Results T a b l e 5 - G i l b e r t R o a d Prototype A i r l i f t S y s t e m L e a k a g e Tests  49  T a b l e 6 - G i l b e r t R o a d Prototype A i r l i f t S y s t e m S a m p l e E x p e r i m e n t a l  50  Results 2 Table 7 - R i c h m o n d Public W o r k s Sample Experimental Data  55  vi  A C K N O W L E D G E M E N T S  I w o u l d l i k e to gratefully a c k n o w l e d g e m y research supervisor, D e n i s S. O . R u s s e l l , Professor E m e r i t u s o f the U n i v e r s i t y o f B r i t i s h C o l u m b i a D e p a r t m e n t o f C i v i l E n g i n e e r i n g , for his continuous support throughout this project. T h a n k s also to Professor J i m A t w a t e r a n d Professor A l a n R u s s e l l , also o f the U n i v e r s i t y o f B r i t i s h C o l u m b i a Department o f C i v i l E n g i n e e r i n g . T h e i r assistance and encouragement w a s p a r t i c u l a r l y v a l u a b l e . T h a n k s also to the E n g i n e e r i n g D e p a r t m e n t at the C i t y o f R i c h m o n d , a n d M r . A r t h u r L o u i e w h o s e interest i n the a p p l i c a t i o n o f airlift p u m p s to u r b a n drainage m a d e this study p o s s i b l e . F i n a l l y , thanks also to the N a t i o n a l S c i e n c e a n d R e s e a r c h C o u n c i l o f C a n a d a for their c o n t r i b u t i o n d u r i n g the e a r l y phases o f this project.  CHAPTER 1  1.1 - I n t r o d u c t i o n t o A i r l i f t P u m p s A i r l i f t p u m p s are c o m m o n l y c o n s i d e r e d to be part o f a u n i q u e class o f "alternate" p u m p i n g technologies. T h e s e alternate p u m p i n g technologies are r e q u i r e d w h e n c o m m o n r o t o d y n a m i c p u m p s are unsuitable for a g i v e n project or a p p l i c a t i o n . S o m e a p p l i c a t i o n s that c o m m o n l y benefit f r o m alternate p u m p i n g technologies i n v o l v e f l u i d / s o l i d m i x t u r e s , v e r y v i s c o u s fluids, hazardous fluids, l i v e organisms suspended i n fluids, l o w - h e a d or l o w - s u b m e r g e n c e situations, scenarios w i t h variable inlet water surface l e v e l s , etc. A i r l i f t and other alternate p u m p i n g technologies p r o v i d e a means for engineers to a p p r o a c h these scenarios.  D e s p i t e the success o f the airlift p u m p i n several other areas, the airlift p u m p has not g a i n e d acceptance i n c i v i l engineering applications. S p e c i f i c a l l y it has not been u s e d for management o f s t o r m waters, p u m p i n g fluids i n open channels, n o r i n any other h i g h discharge, l o w lift, l o w head applications despite the fact that i n s o m e cases it m a y p r o m i s e s o m e advantages i n these settings. In fact, an extensive literature search o n airlift p u m p research and d e v e l o p m e n t f o u n d no references at a l l to airlift p u m p s u s e d i n h i g h discharge, l o w - h e a d , l o w - l i f t capacities i n c i v i l engineering applications or otherwise. N e v e r t h e l e s s , there are potential applications for l o w head, h i g h c a p a c i t y p u m p i n g o f water i n o p e n channels, and s p e c i f i c a l l y o f storm r u n o f f i n drainage c o n d u i t s . T h i s research p r o g r a m is f o c u s e d on investigating those p o s s i b i l i t i e s .  1  T h e m a i n feature o f an airlift p u m p is a vertical tube w i t h the l o w e r end s u b m e r g e d i n water a n d a s u p p l y o f c o m p r e s s e d air p r o v i d e d to the l o w e r end. A s the c o m p r e s s e d air f l o w s into the l o w e r e n d o f this tube bubbles are f o r m e d and a m i x t u r e o f water a n d air b u b b l e s results. S i n c e this m i x t u r e o f air a n d water is less dense and thus l i g h t e r than water, the l e v e l o f the air and water m i x t u r e i n the vertical tube rises above that o f the s u r r o u n d i n g water surface. W i t h a suitable p h y s i c a l arrangement, this results i n c o n t i n u o u s " l i f t i n g " o f the water to a higher l e v e l than the o r i g i n a l water surface - i n effect c r e a t i n g an "airlift p u m p " .  C a r l L o e s c h e r , a G e r m a n m i n i n g engineer, reportedly d e v e l o p e d the o r i g i n a l airlift p u m p concept i n 1797 a n d the t e c h n o l o g y began to g a i n w i d e s p r e a d acceptance i n the m i d d l e 1 8 0 0 ' s ( W a r d 1924). B y the early 1900's several patents h a d been i s s u e d for v a r i o u s arrangements o f airlift p u m p s and they were w i d e l y u s e d for p u m p i n g water, often f r o m quite deep w e l l s , u n t i l b e i n g superceded b y reliable e l e c t r i c a l l y - d r i v e n s u b m e r s i b l e r o t o d y n a m i c p u m p s . T h e r e was a considerable amount o f early research into the airlift concept, but b r o a d interest o n the t o p i c w a n e d as airlift p u m p s were superceded i n the early 1 9 0 0 ' s . D e s p i t e h a v i n g been replaced i n c o m m o n use, airlift p u m p s have c o n t i n u e d to be u s e d i n several s p e c i a l i z e d applications, w h i c h are d e s c r i b e d i n m o r e detail later i n this chapter.  2  T h e c i t y o f R i c h m o n d i n B r i t i s h C o l u m b i a , C a n a d a is situated i n the m o u t h o f the F r a s e r R i v e r a n d experiences an average 1100 m m o f rainfall per y e a r . T h e average e l e v a t i o n o f 1  the c i t y is a p p r o x i m a t e l y one metre above mean sea l e v e l . B e c a u s e o f this v e r y l o w e l e v a t i o n , m u c h o f the c i t y w o u l d be s u b m e r g e d under tidal or r i v e r water d u r i n g v a r i o u s parts o f the year w e r e it not for the extensive s y s t e m o f levees p r o t e c t i n g R i c h m o n d f r o m the F r a s e r R i v e r a n d the ocean waters o f G e o r g i a Strait. R e c e n t i n i t i a t i v e s to further i m p r o v e the c i t y ' s p r o t e c t i o n f r o m r i v e r and sea f l o o d waters have been to p l a n for the i n s t a l l a t i o n o f a s o - c a l l e d m i d - i s l a n d d i k e to help prevent F r a s e r R i v e r waters f r o m i n u n d a t i n g central R i c h m o n d i n the event o f a levee breach i n the E a s t e r n r e g i o n o f the municipality.  T h e average g r o u n d slope i n R i c h m o n d is zero and thus the m u n i c i p a l stormwater management s y s t e m is constrained to v e r y l o w slopes i n its' m a i n c o n d u i t s . T h e p r o b l e m o f l o w slopes is c o m p o u n d e d b y the necessary levee s y s t e m used to protect the c i t y . T h e levees create a n e e d to p u m p stormwater out o f R i c h m o n d w h e n tides are u n f a v o r a b l e , p a r t i c u l a r l y i n the w i n t e r w h e n the tides are r e l a t i v e l y h i g h and constant. T h e stormwater m a n a g e m e n t s y s t e m i n R i c h m o n d relies on l o w tides to a l l o w the outfall flapgates to o p e n . In the w i n t e r months the tides tend to be h i g h and constant, w i t h the d a i l y s e c o n d l o w tide s t i l l v e r y h i g h . T h i s is unfortunate t i m i n g since the w i n t e r months are often v e r y rainy i n the L o w e r M a i n l a n d . T h e s e factors result i n a real and o n g o i n g danger o f w i n t e r f l o o d i n g i n the c i t y o f R i c h m o n d .  City of Richmond Engineering staff graciously provided the background information on their stormwater drainage system as presented in this brief section during various site visits, meetings and conversations that took place from 1997 to 1999 throughout the development of this research project. 1  3  D u r i n g h e a v y rains, p u m p i n g stations at the perimeter outfalls o f the s y s t e m c a n p u l l the l o c a l water l e v e l s d o w n to shutoff but there can still be f l o o d i n g i n central R i c h m o n d because o f the i n a b i l i t y to m o v e s t o r m water q u i c k l y enough to the outfalls. R e c e n t e x p e r i e n c e has s h o w n that R i c h m o n d experiences unacceptable s t o r m water l e v e l s and f l o o d i n g i n s o m e areas as frequently as once every t w o or three years.  B e c a u s e o f these concerns and i n c r e a s i n g high-density d e v e l o p m e n t i n the u r b a n i z e d core o f R i c h m o n d , the c i t y has been c o n s i d e r i n g options for i m p r o v i n g the c a p a c i t y o f their stormwater management system. C o n c e n t r a t i o n times are short so either faster r e m o v a l o f r u n o f f or detention and storage is required. D e t e n t i o n and storage is p r o b l e m a t i c g i v e n the h i g h water table i n R i c h m o n d , so the approach has been to c o n s i d e r options f o c u s e d o n i n c r e a s i n g the rate o f r u n o f f r e m o v a l .  T h e first o p t i o n presented was to introduce more and larger conduits. U n f o r t u n a t e l y this strategy w o u l d be e x t r e m e l y e x p e n s i v e and v e r y p r o b l e m a t i c i n p u b l i c i n c o n v e n i e n c e since m a n y o f the m a i n stormwater conduits are i n s t a l l e d i n b u i l t - u p areas and under m a i n c i t y roads. A d d i t i o n a l l y , installation o f large concrete b o x culverts has b e c o m e v e r y unattractive since B r i t i s h C o l u m b i a w o r k e r ' s protection l e g i s l a t i o n c o n c e r n i n g the c o n d i t i o n s r e q u i r e d for their maintenance is so strict that it makes the u p k e e p o f s u c h c o n d u i t s i m p r a c t i c a l and v e r y expensive.  T h e s e c o n d alternative was to investigate means o f i n c r e a s i n g the effective slope o f the s y s t e m b y i n c r e a s i n g the water surface grade w i t h i n the conduits b y p u m p i n g . T h i s  4  s e c o n d a p p r o a c h w o u l d accelerate the m e a n flow v e l o c i t i e s a n d thus r e m o v e stormwater f r o m the c i t y c o r e at an increased rate.  A need for h i g h c a p a c i t y , l o w head p u m p s that c o u l d be i n s t a l l e d i n s t o r m drainage c o n d u i t s to lift s t o r m water between 1 and three feet (0.3 to 1.0 m ) h a d d e v e l o p e d . S u c h p u m p s w o u l d increase the effective slope and hence the discharge c a p a c i t y o f the e x i s t i n g s t o r m drainage infrastructure. T h e s e p u m p s w o u l d o n l y be r e q u i r e d for short durations under the c o m b i n a t i o n o f h e a v y rainfalls and h i g h tides.  C o m m o n r o t o d y n a m i c p u m p s do not c o n f o r m to this h i g h - f l o w , l o w - h e a d requirement and i f p u m p units c o u l d be f o u n d to satisfy these requirements they w o u l d s t i l l be e x p e n s i v e to install and house i n the R i c h m o n d system. T h i s is because o f their n e e d for m i n i m u m submergence l e v e l s at their inlets, necessitating substantial e x c a v a t i o n a n d p l a c e m e n t o f infrastructure i n an area w i t h sandy soils and a h i g h watertable.  T h e difficulties a n d i m p r a c t i c a l i t i e s i n both o f the p r o p o s e d s o l u t i o n strategies have e f f e c t i v e l y stopped R i c h m o n d ' s progress towards an i m p r o v e d stormwater m a n a g e m e n t system. D e s p i t e the i m p a s s e h o w e v e r , the danger o f f l o o d i n g i n central R i c h m o n d is real and i n c r e a s i n g as urban d e v e l o p m e n t continues.  R e a l i z i n g the need for a w a y f o r w a r d , a h alternative p u m p i n g t e c h n o l o g y was sought a n d this requirement spurred R i c h m o n d into s p o n s o r i n g the a p p l i e d research p r o g r a m that is d e s c r i b e d i n this thesis.  5  1.2 - Description of an Airlift Pump A n airlift p u m p i t s e l f is c o m p r i s e d o f five major c o m p o n e n t s , n a m e l y the air s u p p l y apparatus, the air i n j e c t i o n or aeration system, the water intake, the riser p i p e a n d the p u m p outlet. F i g u r e 1 s h o w s the m a i n elements o f an airlift p u m p . N o m e n c l a t u r e u s e d i n that figure a n d other variables o f interest are defined i n T a b l e 1.  A n airlift p u m p m a y also feature a s o - c a l l e d "foot p i e c e " , a lengthened s e c t i o n o f the m a i n riser p i p e l o c a t e d b e l o w the aeration p o i n t and i n w h i c h o n l y single-phase water f l o w s . A foot p i e c e a l l o w s an airlift p u m p to entrain water f r o m a depth greater than i t s ' aeration depth. T h i s a l l o w s a means for p u m p units w i t h l o w head a i r - s u p p l y apparatus to successfully p u m p l i q u i d f r o m m u c h deeper l e v e l s than they w o u l d o t h e r w i s e be c a p a b l e of. S i n c e foot pieces are required o n l y i n scenarios i n w h i c h the water to be p u m p e d is to rise f r o m a great depth not a l l airlift p u m p s feature foot pieces. In fact, most short airlift p u m p s s u c h as those i n this study, do not use foot pieces.  6  F I G U R E 1 - Schematic Airlift P u m p Layout  T A B L E 1 - Airlift P u m p Nomenclature and Variables Area  = cross-sectional area o f airlift p u m p tube  b  = t u n i n g parameter i n air phase v e l o c i t y / m i x t u r e v e l o c i t y r e l a t i o n s h i p  A ir  = area o f f l o w m i x t u r e cross section o c c u p i e d b y air  A  = area o f f l o w m i x t u r e cross section o c c u p i e d b y water  a  w  c  = t u n i n g parameter i n air phase v e l o c i t y / m i x t u r e v e l o c i t y r e l a t i o n s h i p  d  = t u n i n g parameter i n head loss equation  Diam  = diameter o f airlift p u m p tube  Dens  = relative density o f the air-water m i x t u r e i n the airlift p u m p tube  e  = t u n i n g parameter i n head loss equation  g  = a c c e l e r a t i o n due to g r a v i t y  Hdrive  = d r i v i n g head a p p l i e d to airlift p u m p  Hlift  = lift height o f air-water m i x t u r e i n airlift p u m p tube  Hioss  = head loss i n airlift p u m p tube  Htota  = height o f p u m p lift a b o v e aeration p o i n t  Hfoot  = height o f p u m p tube footpiece b e l o w aeration p o i n t  H b  = height o f standing water surface a b o v e aeration p o i n t  Kent  = p u m p tube entrance loss factor  Kexit  = p u m p tube e x i t loss factor  Kpipe  = p u m p tube p i p e loss factor  Ktotal  = total p u m p loss factor  Qair  = v o l u m e f l o w rate o f air i n airlift p u m p tube  Qmix  = v o l u m e f l o w rate o f the air-water m i x t u r e i n airlift p u m p tube  Qwater  = v o l u m e f l o w rate o f water i n the airlift p u m p tube  V  = v e l o c i t y o f the air fraction i n the air-water m i x t u r e i n airlift p u m p tube  s u  V v  a i r  mix  = v e l o c i t y o f the air-water m i x t u r e i n airlift p u m p tube  V l  = r e l a t i v e v e l o c i t y o f the air phase to the water phase i n the airlift p u m p tube  Vwater  = v e l o c i t y o f the water fraction i n the air-water m i x t u r e i n airlift p u m p tube  Tlsystem  = airlift p u m p s y s t e m e f f i c i e n c y  Tlairdelivery  = airlift p u m p air d e l i v e r y s u b s y s t e m e f f i c i e n c y  Tlriser  = airlift p u m p riser tube subsystem e f f i c i e n c y  Pair  = density o f gas phase  Pwater  = density o f l i q u i d phase  r e  8  A s m e n t i o n e d p r e v i o u s l y , i n this study o n l y airlift p u m p s w i t h zero-length footpieces are c o n s i d e r e d , so H f t = 0 and the total length o f the p u m p riser tube is e q u a l to the s u m o f 00  the s u b m e r g e d and u n s u b m e r g e d lengths, H b and Hijf . S U  t  1.3 - Applications of Airlift Pumps D e s p i t e h a v i n g been superceded b y submersible r o t o d y n a m i c p u m p s i n m o s t c o m m o n a p p l i c a t i o n s , airlift p u m p s are s t i l l used i n several s p e c i a l i z e d settings. T y p i c a l m o d e r n a p p l i c a t i o n s o f e x i s t i n g airlift p u m p t e c h n o l o g y i n c l u d e use o f these p u m p s i n deep water w e l l s , where a related s y s t e m k n o w n as a "geyser p u m p " is also b e c o m i n g i n c r e a s i n g l y c o m m o n where s m a l l - d i a m e t e r p u m p tubes are feasible. A i r l i f t p u m p s also s t i l l frequently serve deep shaft and w e l l d r i l l i n g applications. A i r l i f t p u m p s are also u s e d i n m o d e r n w i n d m i l l - d r i v e n p n e u m a t i c a l l y - o p e r a t e d waterw e l l p u m p i n g a p p l i c a t i o n s , such as those a v a i l a b l e as turnkey systems f r o m A i r l i f t Technologies of Redlands, C A .  D e s p i t e the fact that m i n i n g t e c h n o l o g y has d e v e l o p e d d r a m a t i c a l l y , airlift p u m p s are s t i l l a staple i n m i n e d e w a t e r i n g , and m o d e r n e x a m p l e s are r e m a r k a b l y s i m i l a r to the o r i g i n a l s y s t e m d e v e l o p e d b y L o e s c h e r i n 1797. A i r l i f t p u m p s are also often u s e d i n process a p p l i c a t i o n s i n w h i c h c o r r o s i v e or v i s c o u s l i q u i d s such as sand-water slurries, salt s o l u t i o n , o i l s and v a r i o u s other waste products m a k e traditional r o t o d y n a m i c p u m p s less suitable. ( G i o t , 1982) T h e o i l industry uses airlift p u m p s i n r e t r i e v i n g crude o i l f r o m dead w e l l s . T h e n u c l e a r industry uses c a r e f u l l y calibrated s m a l l diameter airlift units to p u m p fluids i n n u c l e a r fuel retreatment ( C l a r k & D a b o l t 1986).  9  W a s t e w a t e r treatment plants are currently the most c o m m o n a p p l i c a t i o n for airlift p u m p s , w h e r e e x c e l l e n t aeration and subsequent o x y g e n a t i o n o f the p u m p e d m i x t u r e that is d e r i v e d f r o m the injected air is a strong benefit. T h e Sanitaire c o m p a n y o f B r o w n D e e r , W I b u i l d s stainless steel airlift p u m p s for this a p p l i c a t i o n .  A i r l i f t p u m p s are often u s e d i n aquaculture a n d fish f a r m i n g operations w h e r e their l a c k o f m o v i n g parts p r o v i d e s necessary safety for fish and the air i n t r o d u c e d into the water c o l u m n i m p r o v e s o x y g e n a t i o n ( W u r t s , M c N e i l l & O v e r h u l t s , 1994). T h e A q u a c a r e c o m p a n y o f B e l l i n g h a m , W A manufactures airlift p u m p s for fish f a r m i n g a p p l i c a t i o n s . T h e c o m p e t i n g t e c h n o l o g i e s used i n fish f a r m i n g , n a m e l y geyser p u m p s a n d p r o p e l l e r p u m p s , have the respective disadvantages o f n o i s e and p o s s i b l e damage to fish safety i n aquaculture a p p l i c a t i o n s .  Offshore m i n e r a l e x c a v a t i o n a n d d i a m o n d m i n i n g is an e m e r g i n g a p p l i c a t i o n for airlift p u m p s , w h e r e the l a c k o f m o v i n g parts and a b i l i t y to handle particulates m a k e t h e m p a r t i c u l a r l y suitable. A i r l i f t p u m p s are also sometimes used i n a s i m i l a r m a n n e r for underwater r e c o v e r y a n d salvage operations, where an airlift tube m a y be r i g g e d a n d p o w e r e d f r o m the surface, a l l o w i n g divers to p l a c e s m a l l items at the intake o f the p u m p and have the items c a r r i e d to the surface. A i r l i f t p u m p s for use i n deepwater salvage often feature tapered riser pipes, p r e s u m a b l y so that as air bubbles increase i n size d u r i n g their rise f r o m the aeration p o i n t towards the surface the v o i d ratio o f the m i x t u r e i n the p u m p tube does not increase too m u c h and reduce e f f i c i e n c y . T h e airlift p u m p is v e r y w e l l suited to underwater r e c o v e r y purposes since c o m p r e s s e d air is a staple a b o a r d salvage  10  vessels and the turbulent nature o f the f l o w i n the airlift p u m p tube as w e l l as the u p w a r d s - o p e n i n g shape o f the c o m m o n l y - u s e d airlift p u m p barrels i n this a p p l i c a t i o n are doubtless h e l p f u l i n a v o i d i n g any potential j a m m i n g i r r e g u l a r l y shaped items m a y experience i n the p u m p risers.  T h e f i n a l c o m m o n a p p l i c a t i o n o f airlift p u m p s is i n l a k e turnover, where these p u m p s are used to counter the effects o f lake stratification (Parker & Suttle 1987). In l a k e destratification applications airlift p u m p s often float o n s m a l l b u o y s w i t h their outlets at the water surface and c o m p r e s s e d air d e l i v e r e d b y f l o a t i n g s u p p l y lines ( W u r t s , M c N e i l l & O v e r h u l t s 1994).  1.4 - Project Scope a n d Rationale T h i s research project aims to investigate the s u i t a b i l i t y and b e h a v i o u r o f airlift p u m p s i n a n e w class o f applications - n a m e l y l o w - l i f t , h i g h - f l o w , l o w - s u b m e r g e n c e scenarios s u c h as p u m p i n g i n open channels and management o f urban storm drainage. D e s p i t e the u n o r t h o d o x concept, airlift p u m p s p r o m i s e m a n y advantages i n s u c h a p p l i c a t i o n s . Installed costs are l o w since the p u m p s are s i m p l e , c o m p o s e d p r i m a r i l y o f c o m m o n l y a v a i l a b l e P V C or steel p i p e fittings. A i r l i f t p u m p s are v e r y robust and nearly maintenance-free since they have no underwater m o v i n g parts (de C a c h a r d & D e l h a y e 1996). A d d i t i o n a l l y , their air s u p p l y systems c a n be located c o n v e n i e n t l y a b o v e g r o u n d to m i n i m i z e i n s t a l l a t i o n costs and facilitate i n s p e c t i o n and maintenance.  11  The following discussion of airlift pump efficiency suggests that the low-head, lowsubmergence, high-flow, necessarily large diameter airlift pumps that would be required in open-channel and urban storm drainage applications would be energy inefficient units. Despite this inefficiency, the author believes that airlift pumps may offer enough other cost and service advantages to offset the operational inefficiency of the airlift pumps that would be applied in these settings.  Some of the advantages airlift pumps may offer to urban drainage applications include low installation cost and maintenance cost, very low supporting infrastructure cost, and a possibly huge placement benefit in the potential option for portable pump units and/or portable power units, thus potentially eliminating entirely the need for a pump house or similar infrastructure.  The aeration of storm runoff may also be a reason to consider the application of airlift pumps to urban drainage applications. Urban storm runoff often contain high levels of heavy metals, petrocarbons, chemicals from spills, and other roadwash pollutants and tend to create potentially significant environmental impacts to the bodies of water into which they discharge. (Turer, Maynard & Sansalone, 1996). Airlift pumps are used routinely in aquaculture and wastewater treatment because of their significant benefit in aerating the pumped liquid. Using airlift pumps for urban drainage could provide the additional benefit of aerating the storm runoff, thereby mimicking the aeration process used in many municipal mixed-sewage treatment plants, potentially accelerating  12  o x i d a t i o n o f the r o a d w a s h a n d other stormwater pollutants, a n d a l l o w i n g for a decrease i n r e s u l t i n g e n v i r o n m e n t a l impacts.  T h i s c o m p e l l i n g array o f advantages, p a r t i c u l a r l y the v e r y l o w cost o f i n s t a l l a t i o n a n d maintenance o f airlift p u m p s , the lack o f a need for permanently i n s t a l l e d p o w e r and c o n t r o l systems w i t h their attendant h o u s i n g infrastructure, and the potential benefit o f aerating the r u n o f f waters m a k e the i n v e s t i g a t i o n o f airlift p u m p s for these a p p l i c a t i o n s v e r y attractive.  13  1.5 - Two-Phase Flow Regimes A i r l i f t p u m p s are two-phase f l u i d f l o w d e v i c e s . G a s and l i q u i d ( i n most cases air and water) f l o w u p w a r d s together i n a v e r t i c a l pipe. T h i s two-phase f l u i d m i x t u r e c a n take several different forms, a n d the v a r i o u s f l o w patterns o f the t w o phases i n these f o r m s have s i g n i f i c a n t l y d i f f e r i n g h y d r a u l i c behaviours. T h i s is significant to the science and d e s i g n o f airlift p u m p i n g systems since any o f these forms o f air-water m i x t u r e s are p o s s i b l e , and the f o r m f o u n d i n the system o f interest is a v e r y important v a r i a b l e since p h y s i c a l relationships and d e r i v e d mathematical relationships are u n i q u e for each f o r m . T h e exact descriptions o f the f l o w patterns v a r y somewhat b y author, t e r m i n o l o g y is not a l w a y s c o m m o n , and s o m e f l o w s are described as c o m b i n a t i o n s o f patterns ( S h e l t o n & Stewart, 2 0 0 2 ) .  A s u m m a r y o f the f i v e basic forms observed i n the two-phase f l o w o f water and air i n vertical pipes, a l o n g w i t h their most c o m m o n names are s h o w n i n F i g u r e 2. ( m o d i f i e d f r o m T a i t e l , B o r n e a & B u c k l e r , 1980). F i g u r e 3 s h o w s the same f l o w r e g i m e s c h a r a c t e r i z e d b y gas f l u x and m i x t u r e v e l o c i t y .  14  F I G U R E 2 - Two-Phase Air-Water Flow Regimes  Bubbly Flow  Churn "Froth" Flow  Slug Flow  Dispersed Annular "Ripple" Flow  Annular "Film" Flow  15  F I G U R E 3 - Two Phase Flow Regimes characterized by Gas Flux and Mixture Void Fraction, adapted from Wallis (1969)  PERFORATED NO. OF ORIFICES' I 30  U  PLATES  DIAMETER(cm) 4.06  X  10  X  10  o •  49  4.06  100  1.52  x  289  0.41  X 10  SQUARE ARRAY SPACINGfcm^  -l -l  6.25  X  10  9.50  X  10  6.25  X 10  X  10  25  -I I  -I  z  UJ _l  X  20  QC  Z>  X  X  o  E o  X X  o  XX X X X XX X  15  X X X X  CHURN TURBULENT REGIME «  X ID  UJ  x  x  XX X * X X x  10  x A  XXX X XX XX XX  cc  z o z  X  CO < CD  Z  o u  <t cc  X  IDEAL BUBBLING REGIME  0.1  0.2  VOID  0.3  €.4  FRACTION - oc  16  1.6 - O p e r a t i o n a l Efficiency of A i r l i f t P u m p s A i r l i f t p u m p e f f i c i e n c y c a n be defined as the ratio o f energy d e l i v e r e d to the p u m p u n i t to the unit energy output i n the f o r m o f v e l o c i t y and head o f the p u m p e d l i q u i d . T h e o v e r a l l s y s t e m e f f i c i e n c y c a n be c o n s i d e r e d a product o f the air d e l i v e r y a n d airlift riser s u b s y s t e m efficiencies. T h e efficiency o f the air d e l i v e r y subsystem depends o n the type and c o n f i g u r a t i o n o f the air s u p p l y equipment, p i p i n g , conduits and c o n t r o l s . E f f i c i e n t d e l i v e r y o f air t h r o u g h i n s t a l l e d conduits at desired pressures and f l o w rates is a w e l l e x p l o r e d a n d mature b r a n c h o f m e c h a n i c a l e n g i n e e r i n g .  C o m m o n w i s d o m i n the design a n d use o f airlift p u m p s suggests the e f f i c i e n c y o f an airlift p u m p riser s u b s y s t e m is m a x i m i z e d w h e n deep submergence is a v a i l a b l e , the lift height is l o w , a n d l i q u i d and air f l o w rates are l o w . D e C a c h a r d & D e l h a y e (1995) a n d D e C a c h a r d (1989) also suggest a v e r y strong c o n t r i b u t i n g effect i n the length-todiameter ratio, n a m e l y that slender p u m p s w i t h h i g h length-to-diameter ratios are greatly m o r e efficient than their l o w length-to-diameter ratio counterparts.  T h e m o s t efficient airlift p u m p s feature a situation i n w h i c h the air a n d water phases h a v e v e r y s i m i l a r v e l o c i t i e s , air bubbles are either s p h e r i c a l and v e r y s m a l l or are large, dartshaped T a y l o r b u b b l e s w i t h a cross section near the entire p i p e diameter. In b o t h o f these m a x i m a l l y efficient cases, the s l i p v e l o c i t y between the air bubbles a n d water is minimized.  17  A i r l i f t p u m p e f f i c i e n c y is further enhanced b y use o f the smallest p o s s i b l e stable v o i d fraction - thus p u m p i n g the m a x i m u m amount o f water per amount o f air injected. A e r a t i o n e f f i c i e n c y is also an important factor i n d e t e r m i n i n g the e f f i c i e n c y o f short airlift p u m p s a l t h o u g h it matters less i n l o n g p u m p s ( W a l l i s 1968). T h i s p h e n o m e n o n appears to o c c u r because the l o n g airlift p u m p s tend to operate i n s l u g f l o w . S l u g f l o w o c c u r s i n p u m p s l o n g e n o u g h that s m a l l bubbles can accrete together to f o r m h o m o g e n e o u s l y spaced large T a y l o r bubbles c l o s e i n cross section to the p i p e diameter ( T a i t e l & a l . 1980). In this f l o w r e g i m e the f l u i d f l o w s c o n t i n u o u s l y i n contact w i t h the p i p e w a l l s creating losses d i r e c t l y dependent on the f l u i d v e l o c i t y .  A t the entrance o f l o n g p u m p s (and i n shorter airlift p u m p s i n w h i c h s m a l l b u b b l e s d o not have the o p p o r t u n i t y to accrete into T a y l o r bubbles before e x i t i n g the p u m p riser) the air and water m i x t u r e f l o w is turbulent and recirculatory. T a i t e l & al (1980) characterize this f l o w r e g i m e as " f r o t h " or " c h u r n " f l o w a n d identify it b y the o s c i l l a t o r y nature o f the l i q u i d ' s u p w a r d a n d d o w n w a r d m o t i o n between a n d a r o u n d bubbles. A n aerator a s s e m b l y that diffuses m a n y s m a l l e v e n l y distributed bubbles into the f l o w f i e l d helps reduce this turbulence a n d r e c i r c u l a t i o n , r e d u c i n g losses and i n c r e a s i n g e f f i c i e n c y . M o r r i s o n & a l . (1987) suggest that this is also true for the b u b b l y f l o w r e g i m e w h e r e " m u l t i p o r t i n j e c t i o n is m o r e efficient".  D e s p i t e early a n d c o n t r a d i c t o r y observations such as those b y W a r d (1924) and B a u e r & P o l l a r d (1945) o n large diameter airlift p u m p systems, riser diameter also p l a y s a r o l e i n airlift p u m p e f f i c i e n c y for a g i v e n lift height since larger diameter airlift p u m p s tend to be  18  less efficient than their s m a l l e r counterparts. T h i s is because the larger diameter p u m p s must be v e r y l o n g before the efficient T a y l o r b u b b l e - i n d u c e d s l u g f l o w r e g i m e c a n s t a b i l i z e ( D e C a c h a r d & D e l h a y e 1995). In fact, as the p i p e diameter increases the cross sectional area increases e v e n m o r e r a p i d l y , thus d i m i n i s h i n g the a b i l i t y o f surface tension forces to h o l d large bubbles intact against the i n f l u e n c e o f a c o m p l e x turbulent shear f i e l d i n the air/water m i x t u r e c o l u m n . D e C a c h a r d & D e l h a y e (1995) also suggest that surface tension forces i n bubbles reduce s l i p v e l o c i t i e s between the air water phases. In that case since b u b b l e surface tension forces are increased i n s m a l l diameter pipes, the r e d u c e d e f f i c i e n c y o f large diameter p u m p s m a y be due to greater s l i p v e l o c i t i e s , themselves due to the r e d u c e d relative effect o f surface tension forces.  O b s e r v a t i o n suggests that as the p i p e diameter increases above a m a x i m u m feasible b u b b l e diameter the thickness o f the f i l m i n the annular r e g i o n s u r r o u n d i n g the T a y l o r bubbles i n the s l u g f l o w m i x t u r e m a y b e g i n to t h i c k e n r a p i d l y . T h i s r a p i d l y t h i c k e n i n g f i l m c o u l d then p r o v i d e a d r a m a t i c a l l y increased f l o w path area for l i q u i d f r o m the r e g i o n ahead o f any T a y l o r b u b b l e to s l i p d o w n w a r d s through the annular-shaped r e g i o n , past the T a y l o r b u b b l e and into the r e g i o n b e h i n d the b u b b l e . A s the f l o w rate o f the d o w n w a r d - t r a v e l i n g f l u i d i n the annulus regions increases, the o v e r a l l frictional shear o n the p i p e tube m a y b e c o m e d o w n w a r d ( W a l l i s 1968). In such cases the o v e r a l l lift e f f i c i e n c y falls r a p i d l y . T h u s , i n c r e a s i n g p i p e diameter above the stable b u b b l e diameter for a g i v e n f l o w f i e l d m a y reduce efficiencies for l o n g airlift p u m p s operating i n the s l u g flow regime.  19  1.7 - Summary T h e m o t i v a t i o n for this w o r k is " C a n a p p l y airlift p u m p t e c h n o l o g y be p r a c t i c a l l y a p p l i e d to c i v i l e n g i n e e r i n g w o r k s such as open c h a n n e l drainage o f urban s t o r m w a t e r ? "  A n airlift p u m p is a d e c e p t i v e l y s i m p l e two-phase f l o w d e v i c e than can operate i n several f l o w r e g i m e s , d e p e n d i n g o n several geometric and f l o w parameters. A i r l i f t p u m p s have been the subject o f a s m a l l amount o f research since their i n v e n t i o n i n 1797 b y C a r l L o e s c h e r . S i n c e then they have been a p p l i e d e x t e n s i v e l y i n a s m a l l n u m b e r o f s p e c i a l i z e d a p p l i c a t i o n s but not to h i g h - f l o w , l o w - l i f t , l o w - s u b m e r g e n c e c i v i l e n g i n e e r i n g a p p l i c a t i o n s s u c h as o p e n - c h a n n e l drainage and s t o r m water management. A i r l i f t p u m p e f f i c i e n c y is m a x i m i z e d i n scenarios i n w h i c h submergence is h i g h , gas a n d l i q u i d f l o w rates are l o w a n d aeration efficiency is h i g h . D e s p i t e the fact that l o w - h e a d h i g h - f l o w a p p l i c a t i o n s do not p r o m i s e v e r y efficient operation o f airlift p u m p s there are s i g n i f i c a n t reasons s u c h as l o w i n s t a l l e d cost, ease o f maintenance, reduction o f e n v i r o n m e n t a l i m p a c t o f r u n o f f water, etc. to investigate t h e m for these uses.  T h i s thesis considers the a p p l i c a t i o n o f airlift p u m p s to these c i v i l e n g i n e e r i n g a p p l i c a t i o n s a n d outlines a four-stage e x p e r i m e n t a l p r o g r a m undertaken at the U n i v e r s i t y o f B r i t i s h C o l u m b i a and the C i t y o f R i c h m o n d , B r i t i s h C o l u m b i a . T h i s study h a d s e v e r a l objectives. T h e s e w e r e n a m e l y : to first evaluate the potential for airlift p u m p s i n urban drainage a n d other l o w - s l o p e open-channel a p p l i c a t i o n s , to create a m a t h e m a t i c a l d e s c r i p t i v e m o d e l o f l o w - h e a d , h i g h discharge airlift p u m p systems, to d e v e l o p a p r a c t i c a l d e s i g n m e t h o d for such p u m p s u s i n g the m a t h e m a t i c a l m o d e l a b o v e , a n d to  20  illustrate the use of that method. To these ends, small-scale and full-scale models were built and tested. Water and air flows and levels were recorded. A broad literature study was undertaken. From this theoretical background and experimental observations, three mathematical models for predicting airlift pump behaviour in these settings are developed. One is suggested as representative. A simple hand-calculator design procedure is explained and two personal computer-based solutions are suggested. A practical design example is presented, and conclusions and recommendations for further development are made.  21  CHAPTER 2  2.1 - Introduction - Literature Review T h i s chapter describes a b r i e f history o f the open literature o n airlift p u m p s , p r o v i d i n g an o v e r v i e w o f the d e v e l o p m e n t and theory b e h i n d their operation as w e l l as an o v e r v i e w o f airlift theory d e v e l o p m e n t to the present day. T h i s literature search first i n v e s t i g a t e d the h i s t o r i c a l use o f airlift p u m p s i n c i v i l e n g i n e e r i n g applications. N o m e n t i o n was f o u n d . B r o a d e n i n g the scope o f the search revealed a n i c h e b o d y o f literature c o n c e r n i n g airlift p u m p s i n the process e n g i n e e r i n g f i e l d , d o c u m e n t e d m a i n l y i n the d i s c i p l i n e s o f A q u a c u l t u r e and C h e m i c a l E n g i n e e r i n g .  2.2 - Development of Airlift Pump Theory, 1797 to Present A s n o t e d i n C h a p t e r 1, C a r l L o e s c h e r , a G e r m a n m i n i n g engineer, is thought to have been first i n v e n t e d the airlift p u m p i n 1797 ( G i o t 1982). L o e s c h e r ' s i n v e n t i o n was an attempt to s i m p l i f y the p u m p i n g tasks i n deep m i n e s . S u b m e r s i b l e r o t o m a c h i n e r y was not a v a i l a b l e i n the late 1 7 0 0 ' s and the benefits o f a p n e u m a t i c a l l y - o p e r a t e d s y s t e m are i m m e d i a t e l y evident i n that context.  A i r l i f t p u m p s b e c a m e p o p u l a r several decades after L o e s c h e r ' s first m o d e l s , d u r i n g the m i d d l e 1 8 0 0 ' s ( W a r d 1924). A t this t i m e direct pneumatic p o w e r was w i d e l y a v a i l a b l e i n the f o r m o f b o i l e r steam w h i c h was e a s i l y generated at h i g h pressure. P n e u m a t i c p o w e r was also a v a i l a b l e f r o m steam-powered compressors. F a r a d a y ' s d i s c o v e r y o f e l e c t r o m a g n e t i c i n d u c t i o n i n 1831 l e d the w a y to the i n v e n t i o n o f the e l e c t r i c m o t o r . T h i s  22  and the appearance o f the internal c o m b u s t i o n engine p i o n e e r e d b y R u d o l f D i e s e l a n d others at the e n d o f the same century made c o m p r e s s e d air a v i a b l e source o f p o w e r .  S h a w (1920) first suggested a v o l u m e ratio for the gas a n d l i q u i d phases i n a l o n g airlift p u m p riser tube operating at 1 0 0 % efficiency:  Volume  air  Q g-H,  =  WMer  f  \7~1  Volume  P  ( waler  discharge  In  (1)  rt  aerati aerationdepth  P  discharge  J  S h a w ' s is the first attempt f o u n d i n the open literature to quantify airlift p u m p b e h a v i o u r o n a p h y s i c a l basis. E v i d e n t l y his relationship w a s successfully used i n d e s i g n w i t h an e f f i c i e n c y m u l t i p l i e r added, o n the order o f 5 0 % ( Z e n z 1993).  W a r d at the U n i v e r s i t y o f W i s c o n s i n d i d the first serious e x p e r i m e n t a l study o f airlift p u m p s f o u n d i n 1924. T h i s study focused o n the b e h a v i o u r o f l o n g airlift p u m p s a n d attempted to create f u n c t i o n a l relationships between the a i r a n d water phase f l o w rates, e f f i c i e n c y a n d p u m p riser geometry such as p u m p length a n d diameter. W a r d d e v e l o p e d an elaborate c u r v e - f i t t i n g a l g o r i t h m for use i n design but w a s o n l y m o d e r a t e l y satisfied w i t h the results a n d q u a l i f i e d the t e c h n i q u e ' s a p p l i c a t i o n to the l o n g p u m p risers i n h i s study.  23  W a r d presented sixteen s u m m a r y c o n c l u s i o n s i n his study. M a n y o f W a r d ' s results a n d suggestions f o r m the o n g o i n g c o m m o n basis for subsequent use and u n d e r s t a n d i n g o f airlift p u m p i n g systems. H e r e is a s u m m a r y o f W a r d ' s eight most salient c o n c l u s i o n s :  1.  T h e e f f i c i e n c y o f l o n g airlift p u m p s depends p r i m a r i l y o n f l o w c o n d i t i o n s i n the riser p i p e , a n d thus great refinement i n aeration and foot p i e c e design b e y o n d e n s u r i n g m i n i m u m f l o w restriction at the entrance are not necessary i n m o s t cases.  2.  T h e r e is a m a x i m u m e f f i c i e n c y for e v e r y c o m b i n a t i o n o f p u m p g e o m e t r y a n d s u b m e r g e n c e that depends o n water f l o w rate.  3.  M a x i m u m efficiency occurs at submergence ratios o f greater than 7 0 % i n m o s t cases, (ie: w h e n o v e r 7 0 % o f the total length o f the riser tube is submerged) a l t h o u g h v e r y s m a l l diameter p u m p s can operate w i t h r e l a t i v e l y h i g h e f f i c i e n c y at l o w e r s u b m e r g e n c e ratios.  4.  H i g h e f f i c i e n c y is p o s s i b l e at l o w e r submergence ratios i f the aeration depth is deep.  5.  T h e c o m b i n e d f r i c t i o n and s l i p losses due to the f l o w i n airlift riser pipes f o l l o w a different l a w than those that g o v e r n the f l o w o f water or air i n a p i p e .  6.  T h e r e is a r e l a t i v e l y s i m p l e relation between frictional losses a n d v e l o c i t y o f f l o w i n an airlift riser p i p e for any particular m i x t u r e o f air and water.  7.  S m o o t h j o i n t s i n airlift riser pipes are necessary to a v o i d unnecessary losses. S u d d e n e x p a n s i o n o r contraction is v e r y detrimental to efficient operation.  8.  A i r lift p u m p s o f less than forty feet i n length are l i k e l y to g i v e results m u c h different to those encountered i n l o n g p u m p s . L o s s e s that are r e l a t i v e l y i n s i g n i f i c a n t i n large p u m p s b e c o m e important i n short airlift p u m p s .  24  E i g h t years later i n 1932, P i c k e r t p u b l i s h e d " T h e T h e o r y o f the A i r l i f t P u m p " i n an attempt to elaborate o n the m e c h a n i c s o f the f l o w i n these units. H i s study d i d not present results greatly c o n t r i b u t o r y to the b e h a v i o u r o f the large diameter, l o w lift, l o w s u b m e r g e n c e h i g h f l o w p u m p s o f interest i n this study.  M o r e than 2 5 years passed u n t i l G o v i e r , R a d f o r d & D u n n ' s " T h e U p w a r d s V e r t i c a l F l o w o f A i r - W a t e r M i x t u r e s " appeared i n 1957. T h e i r e x p e r i m e n t a l study w a s based o n a 1.025" diameter p u m p riser 3 0 ' l o n g (ie: length-to-diameter ratio a p p r o x i m a t e l y 3 5 0 : 1 ) . T h e y w e r e able to accurately predict f l o w pattern, head loss a n d s l i p v e l o c i t y but restricted the a p p l i c a t i o n o f their results to the b e h a v i o u r o f p u m p units o f s i m i l a r riser tube diameters w h e n p u m p i n g m i x t u r e s o f s i m i l a r gas a n d l i q u i d properties.  D J N i c k l i n ' s " T h e A i r l i f t P u m p : T h e o r y a n d O p t i m i z a t i o n " o f 1963 presented the first satisfactory e x p l a n a t i o n o f the b e h a v i o u r o f s m a l l - d i a m e t e r airlift p u m p s i n the b u b b l y and m o r e i m p o r t a n t l y , the s l u g - f l o w regimes. N i c k l i n ' s m o m e n t u m balance, 2-phase drift f l u x m o d e l based o n mass f l o w forms the basis o f the b u l k o f subsequent research into airlift p u m p s a n d s l u g f l o w theory a n d b e h a v i o u r . T h e most b r o a d l y u s e d o f N i c k l i n ' s c o n c l u s i o n s (recast here i n consistent t e r m i n o l o g y for this study) is u s e d to characterize the v e l o c i t y o f T a y l o r bubbles i n the s l u g f l o w r e g i m e i n still water:  (2)  V„ taylorbuhble ~ 0.35 • g • Diam  25  N i c k l i n also o b s e r v e d ( l i k e W a r d ) that although m a n y aerators have been d e s i g n e d to m i n i m i z e b u b b l e size and m a x i m i z e bubble d i s t r i b u t i o n , none were successful i n l o n g airlift p u m p s . H e also first c l a r i f i e d the one-to-one relationship between the s u b m e r g e n c e ratio and the average pressure gradient i n the p u m p riser tube.  M u l t i p h a s e f l o w was s t i l l a nascent f i e l d i n the 1960's and d e v e l o p m e n t s i n this area were h a p p e n i n g r a p i d l y . In 1964, D u c k l e r , W i c k s & C l e v e l a n d p u b l i s h e d a two-part study " F r i c t i o n a l pressure drop i n two-phase f l o w " . T h e i r results are i l l u s t r a t i v e o f the s t i l l d e v e l o p i n g nature o f two-phase f l o w theory at that t i m e . T h e y f o u n d the e x i s t i n g c o r r e l a t i o n s for pressure loss i n two-phase p i p e f l o w to be inadequate and asserted that " T h e r e is not e v e n a p h e n o m e n o l o g i c a l understanding o f this type o f f l o w . "  A s two-phase f l o w theory was further d e v e l o p e d , and due p o s s i b l y to the e x p l i c i t s o l u t i o n for s l u g f l o w operation as suggested b y N i c k l i n , the study o f airlift p u m p s c o n t i n u e d to focus i n c r e a s i n g l y o n the m e c h a n i c s o f T a y l o r bubbles i n the s l u g f l o w r e g i m e , and to an i n c r e a s i n g l y lesser degree o n the b u b b l y f l o w , c h u r n i n g f l o w and annular f l o w r e g i m e s .  W a l l i s ' d e f i n i t i v e w o r k , One Dimensional  Two-Phase Flow, appeared i n 1969. W a l l i s '  text is s t i l l one o f the best sources for a b r o a d l y - f o c u s e d c o l l e c t i o n o f most o f the o p e n theory o f o n e - d i m e n s i o n a l two-phase f l o w . W a l l i s ' w o r k exposes the tremendous c o m p l e x i t y i n m u l t i p h a s e f l o w b e h a v i o u r and p r o v i d e s m u c h o f the f o u n d a t i o n for t w o phase f l o w as u s e d today. M a n y frictional and v e l o c i t y relationships d e v e l o p e d b y W a l l i s are s t i l l state o f the art i n m o d e r n two-phase f l o w theory.  26  T o d o r o s k i , Sato and H o n d a f o l l o w e d N i c k l i n ten years later i n 1973 w i t h " P e r f o r m a n c e o f A i r l i f t P u m p s " , w h i c h elaborated s l i g h t l y o n N i c k l i n ' s approach to the s l u g - f l o w r e g i m e f l o w o f these devices. T o d o r o s k i , Sato and H o n d a m o d i f i e d N i c k l i n ' s e x p e r i m e n t a l basis for determination o f the slip velocities i n s l u g f l o w .  T h e interpretation o f the various regimes o f vertical two-phase f l o w was m a i n l y d e s c r i p t i v e i n nature u n t i l 1980 w h e n T a i t e l , B a r n e a & D u c k l e r p u b l i s h e d " M o d e l i n g F l o w Pattern T r a n s i t i o n s for Steady U p w a r d G a s - L i q u i d F l o w i n V e r t i c a l T u b e s " . T h e i r study undertook m a t h e m a t i c a l l y p r e d i c t i n g the transitions between these patterns. T h e y were able to predict w h i c h pattern or r e g i m e o f two-phase f l o w w o u l d o c c u r under a g i v e n set o f c o n d i t i o n s , and their approach is still used today. T a i t e l , B a r n e a & D u c k l e r also p r o v i d e the best o f the v i s u a l descriptions o f two-phase f l o w regimes ( w h i c h s u p p l i e d the basis for F i g u r e 2 i n chapter 1). T h e i r most useful f i n d i n g for this current study suggests that (in cases i n w h i c h s l u g f l o w c a n develop) the length o f the turbulent entrance or transition z o n e r e g i o n f r o m the aeration p o i n t to the p o i n t where s l u g f l o w c a n d e v e l o p depends o n the m i x t u r e v e l o c i t y and p i p e diameter:  France = 40.6  Diam  yjg  Diam  + 0.22  (3) J  In 1982, M a r k a t o s & S i n g h a l p r o d u c e d a n u m e r i c a l analysis process for two-phase f l o w . T h i s study was focused o n b u b b l y and s l u g f l o w , m u c h the same as those that had preceded it. It appears that i n the b u b b l y and p a r t i c u l a r l y the s l u g f l o w r e g i m e s the m a t h e m a t i c a l f o r m u l a t i o n for the friction and loss terms is easier to a c c o m p l i s h since the  27  r e l a t i v e l y f i x e d geometry o f the r o u n d or T a y l o r bubbles a l l o w a s o l u t i o n that requires less e x p e r i m e n t a l data for c o r r e l a t i o n . M a r k a t o s & S i n g h a l ' s technique was d e v e l o p e d for use i n deep water w e l l s and depends on the b r e a k d o w n o f l o n g v e r t i c a l risers into s m a l l e r c o n t i g u o u s segments, i n effect creating a " g r a d u a l l y v a r y i n g f l o w " f o r m u l a t i o n . It is suitable o n l y to l o n g riser pipes.  L o n g , s m a l l diameter airlift p u m p s are w i d e l y used i n nuclear fuel reprocessing. V e r y accurate estimates o f f l o w rates are r e q u i r e d i n those settings. In 1986 C l a r k & D a b o l t d e v e l o p e d a general set o f design equations for airlift p u m p s i n s l u g f l o w for use i n the nuclear industry. T h e y focused p r i m a r i l y on accurately p r e d i c t i n g the f l o w rate b e h a v i o u r i n their a p p l i c a t i o n s . D e s p i t e their admitted i n a b i l i t y to accurately calculate the o v e r a l l f r i c t i o n a l losses i n pipes o f 38 m m diameter they d i d p r o v i d e an accurate d e s i g n m o d e l for s u c h p u m p s i n the s l u g f l o w regime. Interestingly they also attempted to a p p l y N i c k l i n ' s m o d e l to a short p u m p and f o u n d that N i c k l i n ' s m o d e l o v e r p r e d i c t e d the p u m p e f f i c i e n c y , u n l i k e its' better agreement w h e n a p p l i e d to longer units. C l a r k & D a b o l t ' s general d e s i g n equation for l o n g , small-diameter p u m p s does not address p u m p e f f i c i e n c y i n great detail but does p r o v i d e an accurate and p r a c t i c a l means o f d e s i g n for v e r y l o n g slender airlift p u m p s .  In 1993 Z e n z p r o d u c e d " E x p l o r e Potential o f A i r l i f t P u m p s and M u l t i p h a s e S y s t e m s " p r i m a r i l y e x p l o r i n g airlift p u m p s i n three-phase scenarios. Z e n z ' study was c o n c e r n e d m a i n l y w i t h s l u g f l o w and particulate entrainment, again i n l o n g pipes. A i r l i f t p u m p riser pipes are g e n e r a l l y c o n s i d e r e d l o n g w h e n length to diameter ratios are 50:1 or m o r e .  28  W u r t s , M c N e i l l and O v e r h u l t s (1994) p r o v i d e d a s i m p l e c u r v e - f i t t i n g approach to airlift p u m p performance for near-100% submergence i n aquaculture and destratification applications.  In 1995 T r a m b a , T o p a l i d o u , K a s t r i n a k i s , N y c a s , F r a n c o i s & S c r i v e n e r c o m p l e t e d their " V i s u a l S t u d y o f an A i r l i f t P u m p O p e r a t i n g at L o w S u b m e r g e n c e R a t i o s " w h i c h is not p a r t i c u l a r l y h e l p f u l for this present study since it is m a i n l y c o n c e r n e d w i t h b u b b l e f o r m a t i o n at a jet inlet and includes no performance data for n o n - s l u g f l o w s .  F o l l o w i n g C l a r k & D a b o l t i n the nuclear fuel reprocessing industry, D e C a c h a r d & C a l h a y e created a steady-state m o d e l for v e r y s m a l l diameter, l o n g lift p u m p s i n 1995. D e C a c h a r d & C a l h a y e ' s is certainly the most extensive study f o u n d . It is c o n c e r n e d p r i m a r i l y w i t h creating an accurate m o d e l for gravitational and f r i c t i o n a l c o m p o n e n t s o f the airlift p u m p riser pressure gradient. L i k e C l a r k & D a b o l t ' s w o r k , it is f o c u s e d o n v e r y l o n g "slender" airlift p u m p s i n the s l u g f l o w regime. D e C a c h a r d & D e l h a y e are not c o n c e r n e d w i t h o p t i m i z a t i o n o f energy e f f i c i e n c y since energy inputs are v e r y s m a l l i n their cases o f interest. D e C a c h a r d & D e l h a y e observed c h u r n i n g f l o w i n the l o w e r sections o f their study p u m p units and c o n c u r w i t h p r e v i o u s researchers that c h u r n f l o w is a d e v e l o p m e n t phase for the s l u g f l o w pattern. H o w e v e r , they also f o u n d that c h u r n f l o w c o u l d exist as a stable f l o w pattern at h i g h gas f l o w rates. D e C a c h a r d & D e l h a y e d e v e l o p e d the m o s t detailed and accurate analysis f r a m e w o r k a v a i l a b l e for airlift p u m p s o f under 4 0 m m diameter and w i t h length-to-diameter ratios above 2 5 0 : 1 .  29  M o s t recently N e n e s , A s s i m a c o p u l o s , M a r k a t o s , & M i t s o u l i s c o m p l e t e d " S i m u l a t i o n o f A i r l i f t P u m p s for D e e p W a t e r W e l l s " i n 1998. T h e i r a n a l y t i c a l f r a m e w o r k i n v o l v e s an interspersed c o n t i n u a m o d e l and solves a system o f differential equations per M a r k a t o s (1982). R e s u l t s f r o m their system are v e r y accurate but unfortunately suitable o n l y for v e r y t a l l p i p e units i n w h i c h the p u m p riser tube m a y be b r o k e n into tens o f i n t e r n a l l y c o n t i g u o u s discrete elements.  2.3 - S u m m a r y o f L i t e r a t u r e R e v i e w A i r l i f t p u m p s have been a n i c h e interest area i n process, c h e m i c a l and m e c h a n i c a l e n g i n e e r i n g as w e l l as aquaculture. P u b l i c a t i o n on the topic has been sparse and the literature has tended towards attempts to e x p l a i n the b e h a v i o u r o f these devices i n t w o distinct f l o w regimes. N i c k l i n ' s m o d e l (1963) continues as the base for almost a l l theoretical d e v e l o p m e n t whereas the n u m e r i c a l techniques o f M a r k a t o s , N e n e s et a l . (1992) p r o m i s e a p o w e r f u l toolset for e v a l u a t i n g the b e h a v i o u r o f l o n g airlift units.  T h e r e has been l i t t l e reason to evaluate the h i g h - f l o w , l o w - h e a d , l o w - s u b m e r g e n c e airlift systems and subsequently those applications are still u n e x p l o r e d f r o m theoretical and d e s i g n standpoints. T h i s has not stopped such p u m p s f r o m b e i n g u s e d s p o r a d i c a l l y and often u n i n t e n t i o n a l l y since i n a p r a c t i c a l sense, s i m p l i c i t y i n f i e l d use has tended towards i n s t a l l i n g a p i p e at an appropriate depth, a d d i n g air i n an appropriate v o l u m e and at an appropriate depth to p r o d u c e the desired results i f p o s s i b l e . In a research sense, the i n a b i l i t y to accurately measure the relative v e l o c i t i e s o f the air and water phases except i n the b u b b l y and s l u g f l o w regimes have tended towards t u n i n g a theory f o c u s e d o n those  30  regimes alone. H i g h submergence, s m a l l diameter, short lifts have been t r a d i t i o n a l l y i n v e s t i g a t e d since l o w - s u b m e r g e n c e , high-lift units p r o v i d e decreasing e f f i c i e n c i e s .  A s W a r d (1924) c o n c l u d e d , there r e m a i n inherent gaps i n our u n d e r s t a n d i n g o f theory that m a i n l y arise f r o m the fact that the sizes, speeds and d i s t r i b u t i o n o f the air bubbles are not k n o w n , yet the s i z e and the rate o f ascent o f the bubbles t h r o u g h the air-water m i x t u r e are c r i t i c a l variables.  R e c e n t research w o r k o n air entrainment i n fast f l o w i n g water u s i n g laser o p t i c a l probe t e c h n o l o g y w i t h the a b i l i t y to measure the b e h a v i o u r o f the air fraction i n a two-phase air-water f l o w m i x t u r e as distinct f r o m the o v e r a l l air-water f l u i d m i x t u r e has recently b e c o m e a v a i l a b l e . T h i s technique was e m p l o y e d first b y C a r t e l l i e r (1992) and later refined b y S e r d u l a & L o e w e n (1998), w h o s e techniques m i g h t seem to p r o m i s e a m o r e r i g o r o u s approach to air lift p u m p design b y the direct measurement o f gas and l i q u i d phase v e l o c i t i e s and v o i d ratio. U n f o r t u n a t e l y , i n v e s t i g a t i o n o f the e x p e r i m e n t a l e q u i p m e n t and personal conversations w i t h L o e w e n suggest that since the laser s y s t e m e m p l o y e d is a'point measurement system it is not suitable for air-water m i x t u r e s w i t h r e c i r c u l a t o r y m o v e m e n t . It cannot resolve differences between u p w a r d - m o v i n g and r e c i r c u l a t i n g air bubbles and does not function w e l l w i t h o u t distinct boundaries b e t w e e n the air and water phases at the b u b b l e boundaries such as are f o u n d i n b u b b l y and s l u g f l o w . U n f o r t u n a t e l y this means that at least currently the laser measurement t e c h n o l o g y is i n a p p l i c a b l e to the study o f airlift p u m p s i n the c h u r n f l o w regime.  31  CHAPTER 3  3.1 - Overview of the experimental program F o r airlift p u m p s to be u s e d effectively i n short lift, h i g h f l o w a p p l i c a t i o n s s u c h as s t o r m drainage c o n d u i t s , the airlift p u m p must be able to "lift" large v o l u m e s o f water t h r o u g h a height o f about 0.3 to 0.6 m . F o r e x a m p l e , such an increase i n head o v e r a run o f 5 0 0 0 feet i n r e l a t i v e l y flat terrain such as exists i n R i c h m o n d , B . C i n the 5 ' b y 9 ' concrete b o x c u l v e r t l e a d i n g f r o m G r a n v i l l e Street to the G i l b e r t R o a d outfall c o u l d e a s i l y result i n a d o u b l e d water surface slope and subsequent dramatic i m p r o v e m e n t s i n water f l o w v e l o c i t y , a n d subsequent reduction o f l o c a l f l o o d i n g d u r i n g extreme r a i n f a l l events.  A p u m p s y s t e m for o c c a s i o n a l use i n e m e r g e n c y situations such as m i g h t be e x p e r i e n c e d b y R i c h m o n d d u r i n g the 10-year d e s i g n f l o w s h o u l d i d e a l l y be i n e x p e n s i v e a n d m a i n t e n a n c e - f r i e n d l y . S i n c e the p u m p units w o u l d run o n l y d u r i n g extreme c o n d i t i o n s , and s i n c e o p e r a t i n g costs i n extreme c o n d i t i o n s are often accounted for differently than o n g o i n g costs, e f f i c i e n c y is o n l y important i n so m u c h as it affects the first cost o f the i n s t a l l a t i o n . R u n n i n g costs are less important as the p u m p s are o n l y u s e d d u r i n g extreme s t o r m events - i n the order o f once every t w o or three years. H o w e v e r , i n s t a l l e d cost is important - o f course less e x p e n s i v e is preferred. A i r l i f t p u m p s p r o m i s e a v e r y attractive m a t c h to these criteria. T h e c o m p r e s s e d air s u p p l y can be d r y and out o f the w a y , i n fact there is n o need for the s u p p l y apparatus to be p e r m a n e n t l y located since air c a n be s u p p l i e d t h r o u g h a f l e x i b l e pipe. T h i s means that a permanent p u m p h o u s e need not necessarily be u s e d w i t h an airlift system. T h e p u m p s themselves c a n be b u i l t quite  32  i n e x p e n s i v e l y as they o n l y consist o f sets o f tubes and aerators w i t h an air s u p p l y . B e c a u s e airlift p u m p s are n o t o r i o u s l y inefficient c o m p a r e d w i t h their r o t o d y n a m i c counterparts and air compressors are e x p e n s i v e , it is very desirable to have the ratio o f water lifted to c o m p r e s s e d air used be as h i g h as p o s s i b l e .  T h e s e d e s i g n considerations and potential benefits were investigated, m o t i v a t i n g the current study. P r e l i m i n a r y c a l c u l a t i o n s were m a d e and t w o series o f p r e l i m i n a r y qualitative experiments were run at the U n i v e r s i t y o f B r i t i s h C o l u m b i a C i v i l E n g i n e e r i n g H y d r a u l i c s L a b o r a t o r y to c h e c k the concept. C l a s s i c a l airlift p u m p c o m p o n e n t s a n d layouts w e r e c o n s i d e r e d and adapted for use i n a l o w - l i f t situation. S i n c e the desire was to determine whether a v i a b l e airlift p u m p c o u l d be d e v e l o p e d for these a p p l i c a t i o n s it was reasonable to start w i t h a system that was c o n f i g u r e d s i m i l a r l y to what a w o r k i n g unit m i g h t be.  F i r s t a s m a l l - s c a l e airlift unit was b u i l t u s i n g the f u l l w i d t h o f a 6 i n c h w i d e undergraduate student h y d r a u l i c s lab f l u m e , e x p l o r i n g the conceptual l a y o u t for a f u l l w i d t h b o x c u l v e r t installation.  S u b s e q u e n t l y a s i m i l a r larger-scale airlift unit was b u i l t u s i n g the f u l l 20-inch w i d t h o f a large h y d r a u l i c s lab f l u m e to c h e c k i f the system w o u l d be functional on a larger scale.  33  T h e laboratory experiments p r o v i d e d some v a l u a b l e insights into the nature o f airlift p e r f o r m a n c e at l o w lifts, l o w submergence and l o w v o i d ratios. T h e y also s h o w e d that airlift p u m p s o f this type c o u l d be p r a c t i c a l .  N e x t a sequence o f full-scale prototype experiments was c a r r i e d out at the G i l b e r t R o a d s t o r m drainage outfall i n R i c h m o n d . S e v e r a l full-scale e x p e r i m e n t a l prototype l a y o u t s and systems w e r e p l a n n e d a n d tried. V a r i o u s c o m b i n a t i o n s o f upstream a n d d o w n s t r e a m water l e v e l s w e r e investigated w i t h v a r y i n g rates o f air injection. R i s e r p i p e diameter w a s investigated, as was aerator geometry.  S i n c e e v a l u a t i n g and m a x i m i z i n g water f l o w for these p u m p systems w a s the e n d g o a l o f this study, i n a l l cases it was attempted to determine the water flowrate p o s s i b l e for a g i v e n u p s t r e a m a n d d o w n s t r e a m depth, rate o f air injection, p u m p riser diameter a n d aerator geometry.  T h e r e w e r e m a n y p r a c t i c a l difficulties such as u n u s u a l l y l o w f l o w s a n d water l e v e l s i n the drainage c o n d u i t that was used as the site. H o w e v e r , these experiments p r o d u c e d several v e r y useful results. T h e y demonstrated that l o w - h e a d , h i g h - f l o w , l o w submergence airlift systems d i d p r o v i d e a v i a b l e a n d p r a c t i c a l alternative i n an i n s t a l l e d s t o r m drainage system. H o w e v e r , they also s h o w e d that there was c o n s i d e r a b l e c i r c u l a t i o n i n the p u m p tubes a n d as a result, the water was b e i n g lifted several times w i t h r e s u l t i n g l o w o v e r a l l e f f i c i e n c y . T h e y also s h o w e d that there was never a steady state situation s u c h as is u s u a l l y assumed i n d e r i v i n g theory a n d f o r m u l a e . T h e air-water  34  m i x t u r e was v e r y turbulent and the air bubbles were i n c r e a s i n g and decreasing i n s i z e b y shearing and coalescence as they rose, i n effect a l w a y s i n a transient c o n d i t i o n .  H a v i n g i d e n t i f i e d the major p r o b l e m o f c i r c u l a t i o n and r e - c y c l i n g , a f i n a l set o f e x p e r i m e n t s were set up at the R i c h m o n d P u b l i c W o r k s Y a r d , u s i n g b a n k s o f tubes 7 5 to 2 0 0 m m i n diameter, as o p p o s e d to the 2 5 0 and 3 0 0 m m tubes used i n the G i l b e r t R o a d prototype experiments. T h e o r y suggested that s m a l l e r diameter pipes w o u l d a l l o w less c i r c u l a t i o n due to a m o r e e v e n l y distributed air phase. A l s o , the riser p i p e w a l l s w o u l d have a m u c h greater i n f l u e n c e over a larger cross-sectional f l o w area. T r i a l s were also m a d e w i t h the tubes i n c l i n e d instead o f v e r t i c a l , as i n c l i n e d tubes w o u l d be easier to install and c o u l d be p o t e n t i a l l y less c o s t l y due to a reduced n u m b e r o f fittings r e q u i r e d for c o n s t r u c t i o n .  T h e results f r o m the fourth e x p e r i m e n t a l setup were successful and s h o w e d l i t t l e c i r c u l a t i o n , a l t h o u g h there was still considerable uncertainty as a result o f the transient nature o f the u n d e r l y i n g p h e n o m e n o n o f the air bubbles r i s i n g , e x p a n d i n g , shearing and c o a l e s c i n g . S i n c e the e x p e r i m e n t a l "pumps" were s i m i l a r to the p r o p o s e d f i n a l d e s i g n the results were c o n s i d e r e d acceptably accurate. T h e design concept was thus c o n s i d e r e d p r o v e n and the relationships d e v e l o p e d sufficient for design o f a p r a c t i c a l operating airlift pump.  35  3.2 - T h e E x p e r i m e n t a l S e t u p s T h e first e x p e r i m e n t a l laboratory setup is s h o w n i n F i g u r e 4. T h e purpose o f this first setup was to b u i l d a v i s u a l m o d e l o f the airlift p u m p as a f u l l - w i d t h element i n a s t o r m d r a i n scenario. B e c a u s e o f k n o w n l i m i t a t i o n s i n w i d t h , discharge rate, f l o w rate measurement e q u i p m e n t and theoretical k n o w l e d g e , this first setup was intended to serve as a base for e x p e r i m e n t a t i o n to a i d i n understanding airlift p u m p b e h a v i o u r , rather than as an instrumented data c o l l e c t i o n experiment. T h i s system was d e s i g n e d to s i m u l a t e o n a v e r y s m a l l scale the o r i g i n a l p r o p o s e d l a y o u t o f an i n - c u l v e r t airlift p u m p i n g s y s t e m . U p s t r e a m water f l o w e d into the system under a baffle. A n aerator i n s t a l l e d on the base o f the c h a n n e l s u p p l i e d bubbles to the water c o l u m n . T h e air-water m i x t u r e then f l o w e d between the upstream baffle and a d o w n s t r e a m baffle, e x i t i n g the p u m p unit at the h i g h e r downstream level.  T h e s m a l l - s c a l e s y s t e m was i n s t a l l e d i n a s i x - i n c h w i d e student h y d r a u l i c s lab f l u m e to test the concept o f a f u l l - w i d t h airlift system i n a rectangular c h a n n e l . V a r i o u s c o m b i n a t i o n s o f upstream and d o w n s t r e a m water levels and air v o l u m e inputs were t r i e d i n order to m a x i m i z e the water flowrate g i v e n any c o m b i n a t i o n o f upstream and d o w n s t r e a m l e v e l s . S e v e r a l geometries were tried since a l l o f the v a r i o u s s y s t e m elements were m o d u l a r . T h e most effective l a y o u t f o u n d is s h o w n i n F i g u r e 4.  36  F I G U R E 4 - First Laboratory Airlift P u m p i n g System  Preliminary Lab Airlift Pumping System 1  n  ,  o to  all dimensions in mm  S e v e r a l aerator designs were also tried, w i t h little i m p r o v e m e n t i n e f f i c i e n c y . C i r c u l a t i o n was evident as a v e r y important (and p r e v i o u s l y m u c h under-estimated) effect i n these h i g h - f l o w , l o w - s u b m e r g e n c e scenarios.  T h e best p e r f o r m i n g setup i n the p r e l i m i n a r y experiment was m e a s u r e d for p e r f o r m a n c e and p r o v i d e d the first clues to the shapes o f p u m p discharge curves for systems o f this nature. F i g u r e 5 s h o w s the sample data set and resulting discharge c u r v e for this s y s t e m .  T h e s e c o n d e x p e r i m e n t a l setup was a s i m p l e test intended to determine the p o s s i b i l i t y o f a larger-scale s y s t e m based o n the same c o n c e p t u a l l a y o u t as the first s m a l l - s c a l e system. T h e larger scale s y s t e m b u i l t i n a large 2 0 - i n c h w i d e h y d r a u l i c s f l u m e at the U n i v e r s i t y o f B r i t i s h C o l u m b i a D e p a r t m e n t o f C i v i l E n g i n e e r i n g . T h i s system was d e s i g n e d to determine the f e a s i b i l i t y o f airlift p u m p t e c h n o l o g y at prototype scale for v e r y s h a l l o w  37  F I G U R E 5 - First Laboratory Airlift Pumping System Results Preliminary Airlift Pump Curve 0.800 •  0.700 0.600 0.500  $ 5  • 0.400  Q, gpm Poly- (Q. gpm)  s  x  4  0.300 0.200  y - O.O003x + 0.O< 24x+0.719-\ J  0.000 0.100 0.000  10.000  20.000  30.000  40.000  50.000  Flow Rate, gpm  These operating characteristics are for the model pump which has a width of 156mm and hence art operational lift chamber plan area of 29640 mm . 2  Lift, mm 226.000 205.000 182.000 162.000 116.000 139.000 67.000 89.000 39.000 7.000  Q, 1/s 0.333 0.714 1.176 1.667 2.222 2.353 2.500 2.500 2.857 3.077  Lift, feet 0.753 0.683 0.607 " 0.540 0.387 0.463 0.223 0.297 0.130 0.023  Q, gpm 5.283 11.321 18.647 26.417 35.222 37.294 39.625 39.625 45.286 48.769  insertion depths. S e v e r a l tests were r u n and results were p r o m i s i n g . C i r c u l a t i o n was v e r y s t r o n g l y e v i d e n t i n the large 1 8 " x 2 0 " lift chamber. A c c u r a t e instruments for m e a s u r i n g the a i r f l o w i n the s y s t e m were not a v a i l a b l e and therefore direct n u m e r i c a l results for  38  a i r f l o w were not c o l l e c t e d . T h i s was not c o n s i d e r e d a d r a w b a c k because the larger scale laboratory airlift unit d i d p r o v e the concept at the prototype scale despite serious submergence l i m i t a t i o n s and l i m i t a t i o n s i n the air f l o w rate p o s s i b l e f r o m the i n s t a l l e d s c r e w c o m p r e s s o r - b a s e d air d e l i v e r y system. F i g u r e 6 s h o w s the s e c o n d e x p e r i m e n t a l setup and T a b l e 2 s h o w s n u m e r i c a l results o f this phase o f the study.  F I G U R E 6 - Prototype Scale Laboratory Airlift Pumping System  lift chamber length 18"  V Hd/s  Qwater i  ^>  H u/s  If Qair S e c o n d P h a s e A i r l i f t P u m p T e s t Setup  lift chamber plan view with aerator  T  U B C C i v i l Engineering Hydraulics Laboratory  18"  _L  flume width 20" three-tined 3/4" brass aerator, 3 x 30 ea. orifices 1 mm dia. 20"  39  T A B L E 2 - Prototype Scale Laboratory Airlift Pumping System Results Airlift Flow Test 2 Aaron Bohnen UBC Civil Engineering Hydraulics Lab Flow baffle height Weir crest height Weir crest width  Hds Pweir Wweir  25.5 in 23 in 19.5 in  0.65 m 0.59 m 0.50 m  Coefficient of Discharge = 0.63 for this test. Q=Cd*(2/3)*L*H (3/2)*SQRT(2*g) A  Head d/s  Head u/s  Weir head  (Hds, in)  (Hus, in)  (Hweir, in)  25.5 25.5 25.5 25.5 25.5 25.5 25.5 25.5 25.5 25.5 25.5 25.5 25.5 25.5  26.0 24.5 24.0 23.0 22.5 22.0 21.5 20.3 18.5 17.0 16.0 15.0 14.5 14.0  5.5 5.3 5.0 4.5 4.3 4.3 4.0 3.5 2.8 2.0 1.5 1.0 0.5 0.3  Flow lift (delta (m 3/s) H, in) A  -0.5 1.0 I. 5 2.5 3.0 3.5 4.0 5.3 7.0 8.5 9.5 10.5 II. 0 11.5  0.050 0.046 0.043 0.037 0.034 0.034 0.031 0.025 0.018 0.011 0.007 0.004 0.001 0.000  Flow  Flow  (l/s)  (cfs)  49.5 46.2 42.9 36.6 33.6 33.6 30.7 25.1 17.5 10.9 7.1 3.8 1.4 0.5  1.75 1.63 1.52 1.29 1.19 1.19 1.09 0.89 0.62 0.38 0.25 0.14 0.05 0.02  Notes: Pressure at 100 psi delivered, approx. 4 psi at aerator 20" wide in 39" tall flume four-tined 3/4" diam aerator -1 mm holes  T h e l i m i t e d a i r f l o w a v a i l a b l e f r o m the screw-based c o m p r e s s o r s l o w e d d e v e l o p m e n t u n t i l a four h o r s e p o w e r gasoline e n g i n e - p o w e r e d centrifugal b l o w e r was o b t a i n e d f r o m the u n i v e r s i t y e q u i p m e n t salvage p r o g r a m . T h e b l o w e r was o v e r h a u l e d , p e r f o r m a n c e w a s e v a l u a t e d and fittings w e r e designed to adapt it to the e x p e r i m e n t a l setup. T h e c e n t r i f u g a l  40  b l o w e r was not i n s t a l l e d i n the s e c o n d laboratory e x p e r i m e n t a l setup since at this t i m e a full-scale prototype l o c a t i o n was selected i n the C i t y o f R i c h m o n d a n d the e x p e r i m e n t a l p r o g r a m shifted focus to that l o c a t i o n .  T h e t h i r d set o f prototype e x p e r i m e n t a l equipment w a s d e v e l o p e d , a s s e m b l e d and i n s t a l l e d j u s t upstream o f one o f the f l o o d b o x e s at the outlet o f a drainage c o n d u i t at the G i l b e r t R o a d storm water outfall i n R i c h m o n d . T h e e x p e r i m e n t a l setup w a s i n s t a l l e d over the w i n t e r o f 1997 to 1998. It o r i g i n a l l y consisted o f three different p u m p designs a i m e d at i n v e s t i g a t i n g k e y features o f the p r o p o s e d p u m p s . T h e o r i g i n a l e q u i p m e n t w a s c o m p r i s e d o f t w o , t e n - i n c h diameter p u m p units and one, t w e l v e - i n c h diameter unit. O n e o f the t e n - i n c h diameter p u m p units was constructed f r o m clear a c r y l i c p i p e , a l l o w i n g v i s u a l i n s p e c t i o n o f the m i x t u r e f l o w r e g i m e w i t h i n the p u m p riser p i p e .  W a t e r was i n t r o d u c e d f r o m an upstream c h a m b e r over a V - n o t c h w e i r a n d p u m p e d b y the e x p e r i m e n t a l airlift units into a d o w n s t r e a m chamber. A n o t h e r V - n o t c h w e i r at the output o f the d o w n s t r e a m c h a m b e r enabled the water p u m p i n g flowrate to be measured. W a t e r levels were read f r o m staff gauges.  Tests were r u n u n t i l the s y s t e m h a d s t a b i l i z e d , at w h i c h p o i n t measurements o f a l l the water l e v e l s and a i r f l o w rates were taken. T h e water levels were u s e d to find the flowrates b y c o n v e n t i o n a l V - n o t c h w e i r analysis. F i g u r e s 7 and 8 s h o w the o r i g i n a l prototype l a y o u t at the G i l b e r t R o a d l o c a t i o n . A d d i t i o n a l large-scale s y s t e m a n d site d r a w i n g s c a n be f o u n d i n A p p e n d i x 1.  41  F I G U R E 7 - G i l b e r t R o a d Prototype A i r l i f t System L a y o u t  F I G U R E 8 - Gilbert Road Prototype Airlift System Components  C o m p r e s s e d air w a s s u p p l i e d to diffusers located beneath each p u m p u n i t b y a 28 h o r s e p o w e r C o m a i r - R o t r o n p o s i t i v e displacement b l o w e r u n i t and p i p e d i s t r i b u t i o n system. T h i s unit w a s i n s t a l l e d i n a soundproofed shed and e q u i p p e d w i t h intake and discharge filters a n d silencers. S i n c e p o s i t i v e displacement b l o w e r s p r o v i d e a constant rate o f a i r f l o w , i n d i v i d u a l v a l v e s were i n s t a l l e d at each p u m p u n i t and a b y p a s s added. I n this w a y each p u m p unit c o u l d be tested i n d i v i d u a l l y . V e n t u r i - s t y l e air v e l o c i t y meters w e r e also i n s t a l l e d to a l l o w air f l o w to each p u m p unit to be i n d i v i d u a l l y m o n i t o r e d . F i g u r e 9 s h o w s the air s u p p l y system at the G i l b e r t R o a d site. F i g u r e 10 s h o w s the prototype s y s t e m i n operation. L a r g e - s c a l e site d r a w i n g s i n A p p e n d i x 2 s h o w the i n s t a l l a t i o n o f the air s u p p l y subsystem at the G i l b e r t R o a d l o c a t i o n .  44  F I G U R E 9 - Gilbert Road Compressed A i r Supply Subsystem  STEEL LADDER  2"«> LONG RADIUS 90" ELBOW (TYP.)  3"0 AIR FLOW METER  2"x3" REDUCER  AIR FLOW  2 0 CONTROL VALVE  3"0 AIR PIPE  3 0 3-WAY WYE 4"x3" REDUCER 4 0 AIR SUPPLY  4 « LONG RADIUS 90' ELBOW DETAIL  Y  45  F I G U R E 10 - G i l b e r t R o a d P r o t o t y p e A i r l i f t S y s t e m i n O p e r a t i o n  T h e o r i g i n a l system as tested w a s moderately successful at p u m p i n g water and p r o v i d e d tremendous i n s i g h t into the operation o f the p u m p units, p a r t i c u l a r l y b y the a b i l i t y to observe the m i x t u r e flow pattern i n the a c r y l i c t e n - i n c h diameter unit (the centre u n i t s h o w n i n F i g u r e s 9 and 10). T h e o r i g i n a l prototype setup i d e n t i f i e d several weaknesses i n the p h y s i c a l layout a n d c o n s t r u c t i o n o f the layout at the prototype site. L e a k a g e b e t w e e n upstream a n d d o w n s t r e a m chambers w a s f o u n d to be p a r t i c u l a r l y p r o b l e m a t i c . A d d i t i o n a l l y , the a b n o r m a l l y l o w l e v e l s o f water i n the drainage c o n d u i t l e a d i n g to the site o v e r the w i n t e r o f 1997/1998 made testing at o n l y one l e v e l o f upstream f l o w p o s s i b l e . A portable p u m p was i n t r o d u c e d to increase the l e v e l i n the upstream c o n d u i t but this h a d o n l y l i m i t e d success.  46  T h e s e difficulties l e d to d e l a y i n this phase o f the p r o g r a m as several r e v i s i o n s to the site s y s t e m l a y o u t and air d i s t r i b u t i o n l a y o u t were d e v e l o p e d , drafted a n d i m p l e m e n t e d . T h i s w o r k progressed o v e r m u c h o f the S p r i n g o f 1998.  T h e results f r o m the tests o f these prototype units were m o r e scattered than e x p e c t e d but c l e a r l y s h o w e d the i m p o r t a n c e o f d e s i g n details. A l t h o u g h reduced, leakage b e t w e e n chambers c o n t i n u e d to be p r o b l e m a t i c despite the system r e v i s i o n s , and a b r e a k d o w n o f the c o m p r e s s e d air d e l i v e r y system created further difficulties.  S o m e o f the data a n d c a l c u l a t i o n s f r o m the t h i r d e x p e r i m e n t a l setup are s h o w n i n T a b l e 3. T a b l e 4 s h o w s s a m p l e v e l o c i t y and loss c a l c u l a t i o n s for the data s h o w n i n T a b l e 3. T a b l e 5 s h o w s the leakage test data c o l l e c t e d at this site. T a b l e 6 s h o w s a s a m p l e o f later data and also c a l c u l a t i o n s for the loss coefficients o f the three o r i g i n a l prototype p u m p systems at the G i l b e r t R o a d site.  W h e n a n a l y z e d , the results o f this phase o f testing i n d i c a t e d s y s t e m i c p r o b l e m s w i t h the alternatives b e i n g investigated. T h e large diameters pipes h a d v e r y l o w p a c k i n g d e n s i t y i n the space-constrained s t o r m d r a i n scenario. A l s o n o aerator geometry w a s f o u n d to be h i g h l y successful i n sharply m a x i m i z i n g efficiency. T h i s was l i k e l y due to several factors, p r i m a r i l y the p r a c t i c a l issue o f leakage and the prevalent r e c i r c u l a t i n g f l o w patterns i n the p u m p risers.  47  T A B L E 3 - Gilbert Road Prototype Airlift System Sample Experimental Data Results march 9,1998 Outside wl = 33 Vee notch = 34 U/wl d/swl aircfm Flow  Pump  35.000 34.500 34.500 39.000  40.25 39.75 39 41.5  38.750 35.250 35.000  250 250 250 250  pipe dia  area  qmix  vmix  inches headless 2.5 35.7942 35.313 33.44365 41.45398  Mix density vwat vair vrel 8 0.391054 0.485614 12.55535 12.06974 0.395151 0.419289 12.64>t 12.22111 0.411212 0.340279 12.98521 12.64493 0.413587 0.739413 13.0378 12.29839  0 676762 0 578271 0 450973 0 974318  0 833 0 833 0 833 0 833  0 54498 0 54498 0 54498 0 54498  41.25 40.75 40.5  200 0 908704 200 0 786746 200 0 730287  0 833 0 833 0 833  0 54498 4.242037 7.783834 28.22426 0.500209 0.834052 12.23798 11.40393 0 54498 4.120079 7.56005 26.6247 0.45895 0.66255 11.30473 10.64218 0 54498 4.06362 7.456452 25.9 0.462329 0.619532 11.37578 10.75624  35.000 35.000 37.750  40.5 40.75 41.62  150 0 730287 150 0 786746 150 1 006934  0 833 0 833 0 833  0 54498 3.230287 5.927345 16.3665 0.552526 0.740398 10.25159 9.511189 0 54498 3.286746 6.030943 16.94361 0.543329 0.784363 10.04514 9.26078 0 54498 3.506934 6.434972 19.28984 0.562277 1.038892 10.47997 9.441076  38.000 34.500  41.5 40  100 0 974318 100 0 626111  0 833 0 833  0 54498 2.640985 4.846018 10.9397 0.675072 1.206897 9.411976 6.205079 0 54498 2.292777 4.207082 8.245128 0.658465 0.756489 8.954315 8.197826  40.250 33.500 35.000 39.750 37.000 35.500  41 38 38 41 40 39  250 250 200 200 150 150  0 833 0 833 0 833 0 833 0 833 0 833  0 54498 0 54498 0 54498 0 54498 0 54498 0 54498  .  0 846199 0 316525 0 316525 0 846199 0 626111 0 450973  4.843429 8.887344 4.744937 8.70662 4.617639 8.473037 5.140985 9.433339  5.012866 4.483191 3.649858 4.179532 3.126111 2.950973  9.198249 8.226335 6.697228 7.669142 5.736189 5.414823  39.41356 31.5245 20.89419 27.39864 15.32789 13.65853  0.406102 0.356521 0.443392 0.471078 0.524148 0.5125  0.63056 0.207068 0.257522 0.731449 0.602177 0.424095  12.87348 11.88156 10.98875 11.56395 9.640225 9.40989  12.24292 11.6745 10.73123 10.8325 9.038048 8.985795  T A B L E 4 - Gilbert Road Prototype Airlift System Sample Experimental Results Results March 9,1998 2 3 Us/wl d/s wl ins. ins. 2 35.00 57.75 34.50 57.75 34.50 57.75 39.00 57.75  1 Pump  4 Air cfs 4.17 4.17 4.17 4.17  5 Water cfs 0.68 0.58 0.45 0.97  6 Vmix ft/sec 8.96 8.78 8.54 9.51  2  38.75 35.25 35.00  57.75 57.75 57.75  3.33 3.33 3.33  0.91 0.79 0.73  7.83 7.61 7.51  2  35.00 35.00 37.75  57.75 57.75 57.75  2.5 2.5 2.5  0.73 0.79 1.01  5.97 6.08 6.48  2  38.00 34.50  57.75 57.75  1.67 1.67  0.97 0.63  4.89 4.24  1  40.25 33.50 35.00 39.75 37.00 35.50  54.5 54.5 54.5 54.5 54.5 54.5  4.17 4.17 3.33 3.33 2.5 2.5  0.85 0.32 0.32 0.85 0.63 0.45  9.27 8.29 6.74 7.72 5.78 5.45  Outside wl = 33  Vee notch = 34  7 Dens 0.23 0.21 0.19 0.27 1.00 0.30 0.29 0.28 i nn. 1 .UU 0.34 0.35 0.38 1.00 0.48 0.41 1.00 0.25 0.17 0.20 0.29 0.32 0.28  8 9 Vw Head loss ft/sec feet 1.44 5.53 5.05 1.46 4.34 1.55 6.76 1.60  10 11 t W m 2 Vm 2*Den A  A  12 13 U V w 2 -exit/vw 2 A  A  1.16 1.22 1.36 1.14  5.12 5.78 7.10 4.28  3.03 3.69 5.29 2.26  2.44 3.05 4.55 1.73  5.54 5.10 4.89  1.42 1.21 1.23  1.49 1.34 1.40  4.92 4.71 5.07  2.98 2.99 3.31  2.38 2.36 2.65  4.00 4.19 4.87  0.96 0.92 1.00  1.74 1.61 1.53  5.16 4.63 3.99  3.87 3.37 2.71  3.12 2.65 2.03  3.79 2.81  0.62 0.60  1.66 2.15  3.49 5.22  2.76 4.89  1.97 3.95  6.27 3.43 2.86 5.32 3.64 2.93  1.85 1.60 1.59 1.62 1.30 1.31  1.38 1.50 2.25 1.76 2.50 2.84  5.54 8.80 11.00 5.97 7.86 9.98  3.03 8.77 12.54 3.70 6.32 9.80  2.48 7.77 11.40 3.08 5.51 8.82  1.48 2.04 0.28 0.58 0.19 0.29  4.96 8.19 0.91 2.17 0.18 0.26  3.43 7.36 0.89 3.69 0.26 0.50  2.74 6.51 0.82 3.46 0.30 0.53  Average #2 Av. #1 Sdev #2 Sdev #1 CV#2 CV#1  48  T A B L E 5 - G i l b e r t R o a d Prototype A i r l i f t System Leakage Tests Pump Data from May 1 tests No 3 p u m p - 1 2 " Air U/sW,L D/SW.L  Weir  Weir flow Leaks  Total  250 250 250 250 250 250 200 200 150 150 150 100  46.5 44.5 37.5 38 46 42.5 45 38.25 47 44.5 38 45.5  50.5 50 48 48.75 50 49.5 50 48 50 50 48 49  41.75 41.75 41.75 41.25 41.25 41,25 41.75 41.75 41.75 41.75 41.75 41.75  1.127673 0.974561 0.489537 0.769405 1.127673 0.974561 0.974561 0.489537 0.974561 0.974561 0.489537 0.707362  0.33775 0.334608 0.321734 0.326621 0.334608 0.331436 0.334608 0.321734 0.334608 0.334608 0.321734 0.328234  1.465423 1.309169 0.811271 1.096026 1.462281 1.305998 1.309169 0.811271 1.309169 1.309169 0.811271 1.035596  No 2 pump 250 250 250 220 200 150 150 150 100  48 45 37.5 39 45.5 48.5 45.5 39 45.5  49 48 47 48 48.5 49 48.5 47 48  41.75 41.75 41.75 41.25 41.75 41.75 41.75 41.75 41.75  0.707362 0.489537 0.317686 0.592484 0.592484 0.707362 0.592484 0.317686 0.489537  0.328234 0.321734 0.315099 0.321734 0.325 0.328234 0.325 0.315099 0.321734  1.035596 0.811271 0.632785 0.914218 0.917484 1.035596 0.917484 0.632785 0.811271  No 1 pump 250 250 250 200 200 150 150 150 100  48 45 38.5 46 38 49 46 39.5 46.5  49 48 47 48.5 47 49 49 47 48.5  41.75 41.75 41.75 41.75 41.75 41.75 41.75 41.75 41.75  0.707362 0.489537 0.317686 0.592484 0.317686 0.707362 0.707362 0.317686 0.592484  0.328234 0.321734 0.315099 0.325 0.315099 0.328234 0.328234 0.315099 0.325  1.035596 0.811271 0.632785 0.917484 0.632785 1.035596 1.035596 0.632785 0.917484  49  T A B L E 6 - Gilbert Road Prototype Airlift System Sample Experimental Results 2 Tests May 1,1998 2 3 U/Swl d/swl ins. ins. 3 46.50 53.50 3 44.50 53.50 37.50 53.50 3 3 38.00 53.50 53.50 3 46.00 53.50 3 42.50 53.50 3 45.00 3 38.25 53.50 47.00 53.50 3 3 53.50 44.50 53.50 38.00 3 45.50 53.50 3  1 Pump  2 2 2 2 2 2 2 2 2  !  1 1 1 1  1  1 1 1  4 Air cfs 4.17 4.17 4.17 4.17 4.17 4.17 3.33 3.33 2.50 2.50 2.50 1.67  5 6 Water Pipe area cfs sq. ft. 1,80 0.79 1,31 0.79 0.81 0.79 1.10 0.79 1.46 0.79 1.31 0.79 1.70 0.79 1.20 0.79 1.31 0.79 1.31 . 0.79 0.79 0.81 1.04 0.79  7 V mix ft/sec 7.60 6.97 6.34 6.70 7.17 6.97 6.41 5.77 4.85 4.85. 4.22 3.44  8 Dens 0.38 0.33 0.28 0.31 0,35 0.33 0.43 0.37 0.46 0.46 0.390.52  .  9 10 Vw Head loss ft/sec feet 5.99 1.86 4.98 1.88 3.73 1.53 4.49 1.44 5.31 1.95 4.98 1.72 5.07 1.56 1.21 4.09 3.66 1.61 3.66 1.40 .2.65 1.12 2.53 1.22  11  12  UVm*2 Ud"vm 2 A  13 UVw»2  2.07 2.50 2.45 2.06 2.44 2.28 2.44 2.34 4.41 3.84 4.07 6.66  5.42 7.46 8.84 6.62 6.96 6.82 5.72 6.27 9.68 8.43 10.45 12.76  4.44 4.47 3.91 4.65 7.77 6.76 10.30 12.37  3.34 4.89 7.08 4.59  57.75 57.75  4.17 4.17 4.17 3.67 3.33 2.50 2.50 2.50 1.67  1.04 0.81 0.63 0.91 0.92 1.04 0.92 0.83 0.81  0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55  9.55 9.13 8.81 8.41 7.80 6.49 6.27 5.75 4.55  0.28 0.2S 0.22 0.28 0.30 0.39 0.37 0,32 0.45  6:916.06 S.27, 5.89 5.52 4.91 4.56 3.63 3.32  2.31 2.19 1.67 1.52 1.98 1.87 1.70 1.37 1.36  1.64 1.69 1.39 1.39 2.09 2.86 2.78 2.67 4.23  5.95 6.89 6.31 4.87 6.86 7.39 7.54 8.33 9.42  3.12 3.84 3,89 2.82 4.18 5.01 5.26 6.71 7.94  54.50 54.50 54.50 54.50 , 54.50 54.50 54.50 54.50 54.50  4,17' 4.17 4.17 3.33 3.33 2.50 2.50 2.50 1,67  1.04 0.81 0.63 0.92 0.63 1.04 1.04 0.63 0.92  0.55 0.55 0.55  9.55 9.13 8.81 7.80 7.28 6.49 6.49 5.75 4.74  0.28 0.25 0.22 0.30 0.26 0.39 0.39 0.32 0.47  6.91 6.06 5.27 5.52 4.45 4.91 4.91 3.63 3.60  2.39 2.26 1.82 2.10 1.61 2.02 1.77 1.50 1,49  1.69 1.74 1.51 2.22 1.96 3.09 2.71 2.92 4.26  6.14 7.10 6.85 7.29 7.51 7.97 6.98 9.11 9.11  3.22 3.96 4.22 4.44 5.25 5.40 4.73 7.34 7.38  Average #3 Stdsv #3 CV#3  3.13 1.38 0.44  7.95 2.17 0.27  6,21 2.77 0.45  Average #2 Std#2 CV#2  2.30 0.93 0.40  7.06 1.33 0:19  4.75 1.68 0.35  Average #1 Std #1 CV#1  2.45 0.88 0.36  7.56 1.01 0.13  5.10 1.44 0.28  48.00 45.00 37.50 39.00 45.50 48.50 45.50 39.00 45.50  57.75 57.75  48.00 45.00 38.50 46.00 38.00 49.00 46.00 39.50 46.50  57.75  57.75 57.75 57.75  57.75  0.55  0.55 0.55 0.55 0.55 0.55  1  :  A second prototype concept was then designed and built at the Gilbert Road location. This system was conceived in an attempt to maximize the use o f the available plan area i n the constrained space o f a drainage conduit. The concept was based on the original lab model that used the full width o f a small flume. A full-width built-in pump assembly was designed. It formed a continuous side-to-side element in the base o f the drainage conduit.  50  S u c h a unit w o u l d have superior aeration density and m a k e m a x i m a l l y - e f f i c i e n t use o f the l i m i t e d p l a n area i n the base o f the conduit. T h e result was a lateral slot-based p u m p and aerator. T h i s unit w a s b u i l t i n the f o r m o f a slot four feet l o n g b y one foot w i d e for the air-water m i x t u r e . A h o r i z o n t a l l y oriented c y l i n d r i c a l aerator was designed and i n s t a l l e d at the base o f the unit. I f this p r o v e d successful the intention was to adopt the d e s i g n concept and b u i l d airlift p u m p units that c o u l d span across the entire w i d t h o f rectangular b o x c u l v e r t . L a r g e - s c a l e d r a w i n g s o f the slot-configured airlift p u m p system c a n be f o u n d i n A p p e n d i x 2. F i g u r e 11 s h o w s the slot-configured airlift p u m p i n operation.  F i g u r e 11 - Slot-Configured A i r l i f t P u m p i n Operation  51  This system was tested under adverse conditions with very little upstream depth available. Nevertheless, it identified an unanticipated and major problem with the "slot" design. Water tended to "slosh" from side to side in the pump unit body, but very little was effectively lifted. It was observed that when the water was high at one end of the slot it gave a large enough back pressure to the orifices there to create an increased flow of air from the orifices at the other end. In this way the air tended to escape from the system. When the water sloshed back to the other end of the system the air escaped from the first end. Thus, although a considerable amount of spray was created very little water was pumped. The immediate failure of this design showed convincingly that large capacity airlift pump systems must be designed to prevent this sloshing behaviour, effectively a one-dimensional recirculation effect analogous to that which had been observed in the cylindrical units. This test confirmed thefindingsof the first test, namely that circulation could easily develop within the pump riser pipes, greatly reducing pump efficiency.  The third experimental phase was successful in pointing the way forward. The design concept was revised to minimize the two most severe problems encountered at the Gilbert Road site, namely circulation within the riser pipes and leakage between the test chambers. The large ten and twelve-inch diameter pump barrels were replaced with eight, six, four, and three-inch units. This was considered a useful means of reducing circulation and turned out to be very effective. It was also decided to test the effect of inclining the pump tubes. Wallis (1969) asserts that inclination up to approximately 40 degrees from the vertical does not adversely affect bubble velocity, and inclining the pump riser tubes in this way promised reduced construction costs by requiring fewer pipe fittings.  52  This fourth phase o f the experimental program was carried out over the course o f several months at the Richmond Public Works Yard. Plastic pipes were set up i n a tank with a metered water supply and metered compressed air supplied from a single jet at the bottom o f each pump's riser tube. Since aerator configuration had little discernible effect i n previous phases o f the project, aerator designs were not tested i n this phase. The pipes were inclined from zero to thirty degrees from the vertical. The flow of air and water were set and when the water level stabilized in the tank, the stable depth o f water in the tank was read. Figure 12 shows the experimental setup for this phase of the project.  Various combinations o f air and water flow and pipe diameters were tested i n an "evolutionary" manner - starting with one pipe at one upstream water level and varying downstream water levels for a given air flow rate. The tests showed that for a given flow of air the inclination away from the vertical of the pump riser pipes within the range o f zero to thirty degrees did not seem to affect the water flow rates. The overall results still evidenced some scatter but this was at least partly due to unavoidable variations i n the position o f the air jets i n the bottom of each pipe riser tube and other minor factors such as the resolution of the meters used, etc.  Data from this experimental phase was far more consistent than that from the third experimental setup since upstream and downstream water levels could be precisely controlled and there was no leakage from the sealed tanks. Table 7 shows sample experimental data from this series of experimental tests.  53  F I G U R E 12 - Richmond Public Works Experimental Setup  f m +-> CO  (D  T3  H OH H 3  4H  >H CO  •a o  a  O  < I CO  PH  IT)  PH  o  CN CN CN  X CN  m  S-H  *->  GO  O PH  "5b PH  1  *S  '5  54  T A B L E 7 - R i c h m o n d Public W o r k s Sample Experimental Data  o  1  3 .a  s  I I  5? PO ^  ?5 ^  ssss  Si  d o o o  w u> w w N N N K flCtcooq«p N  N  N  IO  in i d »  CD <D (O <£>  «  J: e  2  QJ  w w  CD CD CD O S N N N  PJ  O) N  *r v d 6 o' o* d <r  V V f  o o o o o o  jp jn ip jp i n  i° SP  N. K J*. |s. iri i r i i n i r i tn  IP  ^  V  d d d d  d  IP  fx. f— N- r— N- hs s N s N N  tr t  IA  n tf) i o i n «  V  "t V  h~ f»  W  <o u> m to  i i  n  i n trj i n i n vn i n K f*. K p» l*« co co <o co" co co  in ifl i n in in ui  13  1 l«  n  d o d d d d  <3 13 pi  <o <x> m i n  m  tn in m w to  <8  S$  •«  N  w n  w in « « j w w  i8  r  !3 UJ  u>  5$  $5 S  >q «  rs.^r*.  ^-  cn p s  m  ?S?  CQ  2 to!  m o  ^  3 8 8  8 3 8 8 8 8  8 3 8 8 8  S8 3 8 88  S8 8  88 8  d o* © d  o o d d d o  d d d d  d d d d d d  ddd  d  pj n n n  v « n ^ < v  10 n o o o  <o co to 03 to co  1  in  £> «o M  d o d o  ;*» ro  P - r*  88  do  A t this p o i n t the head loss relationships described i n equation s (35) and (36) i n chapter 3 w e r e created a n d u s e d to characterize the system b e h a v i o u r . A f i n a l set o f tests w e r e m a d e w i t h a b u n d l e o f n i n e , f o u r - i n c h diameter p l a s t i c pipes at a n i n c l i n a t i o n o f 0 to 4 0 degrees from the v e r t i c a l . C o m p r e s s e d air was s u p p l i e d t h r o u g h a m a n i f o l d o f p i p e s w i t h a one i n c h j e t at the centre o f each p u m p riser p i p e .  A l t h o u g h s o m e p r a c t i c a l p r o b l e m s r e m a i n e d , the performance o f this e x p e r i m e n t a l setup c o n f i r m e d that the relationships d e v e l o p e d i n the m o d e l for turbulent m i x i n g f o r m e d a reasonable basis for airlift p u m p d e s i g n i n the c h u r n turbulent r e g i m e . T h i s successful phase o f the p r o g r a m resulted i n a reliable data set, p r o v i d i n g the basis for c a l i b r a t i o n o f the theoretical m o d e l and p o i n t e d the w a y towards a v i a b l e airlift p u m p d e s i g n for the situation i n R i c h m o n d .  3.3 - Results o f the E x p e r i m e n t a l P r o g r a m T h e lessons f r o m the first t w o laboratory-based phases o f the e x p e r i m e n t a l p r o g r a m i n d i c a t e d the v i a b i l i t y o f the concept o f l o w - l i f t h i g h - f l o w l o w - s u b m e r g e n c e airlift p u m p s for u r b a n s t o r m drainage. T h e G i l b e r t R o a d prototype s y s t e m suggested several p r a c t i c a l considerations for full-scale applications and l e d the w a y to the f i n a l e x p e r i m e n t a l phase. T h e f i n a l phase p r o d u c e d the reliable data set used to calibrate the h e a d loss r e l a t i o n s h i p s d e v e l o p e d i n the t h i r d theoretical m o d e l . T h i s e x p e r i m e n t a l p r o g r a m also l e d to a v i a b l e p r a c t i c a l d e s i g n . T h e results were also u s e d to v e r i f y the theoretical m o d e l d e v e l o p e d to e x p l a i n l o w - l i f t , l o w - s u b m e r g e n c e , h i g h - f l o w airlift p u m p b e h a v i o u r i n these scenarios, w h i c h i n t u r n l e d to a v i a b l e p r a c t i c a l engineering d e s i g n procedure.  56  CHAPTER 4  4.1 - Airlift Pump Model for Fixed Bubble Slip Velocities Refer again to Figure 1, reproduced here for convenience:  'jjQwater  In static conditions, the pressures inside and outside of the airlift pump tube are equal at the point o f aeration.  H  sub =  H  t e a l '  D  e  n  S  (4)  Under dynamic conditions air bubbles are rising through the water column within the airlift pump tube and a driving head must be added to the system as described in (4) to maintain the pumping action:  57  sub  H  drive  H  =  total •  H  =H  -H  xllh  which can be rearranged to form  + Hdrive  lolal  -Dens  (5)  For equilibrium, the driving head must be equal to the losses in the system.  drive  H  (6)  ~ hss H  Fluid flow losses are commonly expressed in the form of:  V  2  headloss = K  (7) 2g  so for the case o f entrance, pipe and exit losses in the airlift pump system, and assuming that the entrance, pipe and exit losses due to viscosity and fluid friction due to air w i l l be much less than those due to water:  v  V  2  TT T/' water . js ^ loss ~ ^entrance ' ^ pipe +  2  water , jy2g  V '  2  water 2g  /o\  or for the case i n which loss factors for various entrance, pipe and exit geometries are not explicitly considered separately, a combined loss factor can be used:  Kate' loss  H  = ,o,al K  -  () 9  2g  58  C o m b i n i n g (3) a n d (2) and rearranging, get  H -H Dens suh  = K,total  lolar  viwater  (10)  2g  T h e g o a l i s to determine the c o m b i n e d loss factors K i tota  for representative geometries so  that airlift p u m p performance c a n be m o d e l e d s i m p l y b y (7). W e w a n t to determine the loss factor, so rearrange:  suh  H  «„ ,  K  a  =8 • 2  ~  H  „tolal  •Dens  viwater  (11)  E q u a t i o n (11) p r o v i d e s the total loss factor for the airlift p u m p , dependent o n the submergence a n d total p u m p length, as w e l l as the density o f the air-water m i x t u r e a n d the v e l o c i t y o f the water phase.  T o s o l v e (11) for the total loss factor w e need the density o f the air-water m i x t u r e i n the airlift p u m p tube a n d the v e l o c i t y o f the water phase i n the airlift p u m p tube. C o n s i d e r i n g a representative cross-section o f the air-water m i x t u r e f l o w i n g i n the airlift p u m p tube, the relative density o f the air-water m i x t u r e i n the airlift p u m p tube i s g i v e n b y :  Dens =  water  Area  (12)  59  T o s o l v e (11), the area o f the p u m p cross section o c c u p i e d b y the water phase i s also needed. T o o b t a i n the area o c c u p i e d b y the water phase, the v e l o c i t y o f the water phase and the v e l o c i t y a n d area o c c u p i e d b y the air phase are required.  T o get the v e l o c i t y o f the water fraction o f the m i x t u r e , c o n s i d e r c o n t i n u i t y o f the v o l u m e flow rates o f the m i x t u r e a n d o f each phase i n the airlift p u m p tube:  Qmix  ^ mix  Qair  ^air  ^mix  r  Q water  (13)  ^air  ^water  0  4)  ^water  0^)  also the v o l u m e flow rate o f the m i x t u r e is c o m p o s e d o f the s u m o f the v o l u m e f l o w rates o f the a i r a n d water phases:  Qmix  ^mix  ^mix  water  ^water  0^)  and the total cross-sectional area i n the airlift p u m p tube is s i m p l y c o m p o s e d o f the s u m o f the areas o c c u p i e d b y the air a n d water phases:  —A  A mix  water  +A  air  V  /  N i c k l i n (1962) suggests that i n the s l u g flow r e g i m e for s t i l l water a n d w h e r e T a y l o r b u b b l e diameter a n d p i p e diameter are v e r y s i m i l a r ,  60  (2)  If Taylor bubbles were to be found in the 3 to 12-inch diameter airlift pump riser tubes in this study, Nicklin (1962)'s equation (2) would suggest their rise velocities to be within the 1.1 to 2 foot per second range. Classical observations of bubble rise speeds outside the slug flow regime (i.e.: smaller bubbles not constrained directly by pipe boundaries) suggest the terminal velocity of a single bubble is relatively constant between 25 to 45 cm/s over a broad range of bubble diameters, as shown in Figure 12, here reproduced from Wallis (1969):  F I G U R E 13 - Bubble Rise Velocities in Still Water, from Wallis (1969)  /  I  O.OI  1  1  0.02  II  I  I I I I I ••!-•• I •'• I  0.04 0.04,0.01,0.1  L  l  l  O.Z  'I  l l  II  III  II  I  O.H OA 0.&/.O  I  I  2.0  I  I  I I  4.0  Equivalent Radius in centimeters Ry  61  T a i t e l & al.(1980) suggest that above a c r i t i c a l diameter ( a p p r o x i m a t e l y 1.5 m m ) air b u b b l e s tend to d e f o r m and adopt a n erratic path. T h u s the s l i g h t l y s l o w e r effective b u b b l e rise speeds o f the unconstrained n o n - T a y l o r bubbles m a y be e x p l a i n e d b y the i r r e g u l a r i t y o f the s m a l l e r b u b b l e s ' rise trajectories c o m p a r e d w i t h the c o n s t r a i n e d v e r t i c a l rise trajectories o f the T a y l o r bubbles i n the s l u g f l o w r e g i m e .  U s i n g the concept o f a constant t e r m i n a l rise v e l o c i t y for bubbles i n s t i l l water, w e i n t r o d u c e the relative v e l o c i t y o f the air phase to the water phase i n the airlift p u m p tube,  water  (18)  rel  substituting (18) into (14) results i n :  (19)  Qair = (Kwater  substituting (17) into (19) results i n :  Qair =  'water + Kel  X ° Are  "4 ) water  (20)  r e a r r a n g i n g (15) a n d substituting into (20):  (21)  62  E q u a t i o n (21) p r o v i d e s a functional relationship between the m e a s u r e d f l o w rates o f the air a n d water phases Q  and Q  air  ,  the k n o w n cross-sectional area o f the airlift p u m p  waler  tube Area, the k n o w n relative v e l o c i t y o f the air phase to the water phase V i, a n d the re  unknown velocity V  waler  o f the water phase. Therefore, under these assumptions the  v e l o c i t y o f the water phase i n the airlift p u m p tube c a n be c a l c u l a t e d for any c o m b i n a t i o n o f the m e a s u r e d values. T h i s water phase v e l o c i t y c a n then be used to s o l v e (11) for the d e s i r e d o v e r a l l loss factor  K i. tota  H o w e v e r , to s o l v e (11) w e also need the density o f the air-water m i x t u r e i n the airlift p u m p tube. R e a r r a n g i n g (15) and substituting into (12):  Dens = — water  V  (22) '  A  r  e  a  substituting (22) into (11) and rearranging, get:  (  _  v  V  ™*  H  0  *  XL. water  x  total  ^  (23)  water'Ar™;  v  water  E q u a t i o n (23) g i v e s the p u m p loss factor as a f u n c t i o n o f the water phase v e l o c i t y , diameter, total l e n g t h a n d submergence o f the p u m p tube, v o l u m e flow rate o f water a n d v e l o c i t y o f the water phase i n the airlift p u m p tube. T h e v e l o c i t y o f the water phase c a n be d e t e r m i n e d f r o m (21) and thus the p u m p loss factor determined for a v a r i e t y o f flow a n d submergence c o n d i t i o n s .  63  In this w a y it w a s h o p e d the characteristic b e h a v i o u r o f the airlift p u m p s y s t e m c o u l d be d e t e r m i n e d f r o m the p u m p loss coefficient, e n a b l i n g a clear understanding o f the p u m p s y s t e m o p e r a t i o n a n d as w e l l creating a s i m p l e d e s i g n procedure.  W h e n the e x p e r i m e n t a l data was c o m p a r e d w i t h this m o d e l it b e c a m e apparent that losses f o u n d i n the p u m p units i n this study w e r e not accurately predicted. T h e s u m m a r y v a l u e s i n c o l u m n 13 o f T a b l e 6 correlate the measured system losses w i t h the water phase v e l o c i t y . T h e w i d e spread i n the d e r i v e d loss factors as w e l l as the large coefficients o f v a r i a t i o n i n d i c a t e c l e a r l y that this m o d e l is not a p p l i c a b l e to the p u m p s i n this study.  F u r t h e r observations o f the e x p e r i m e n t a l units i n operation and m o r e research suggested that the a s s u m p t i o n o f a t e r m i n a l b u b b l e v e l o c i t y as e x p l a i n e d b y F i g u r e 13 w a s not a p p l i c a b l e i n this case.  T h e a s s u m p t i o n o f a t e r m i n a l b u b b l e speed relative to still water m a k e s this m o d e l p o s s i b l y m o r e suitable for l o w v o i d -ratio f l o w s a n d l o w m i x t u r e f l o w v e l o c i t i e s , s u c h as m i g h t be encountered i n a l o n g , large diameter riser s u c h as u s e d i n l a k e aeration or destratification or harbour d e - i c i n g . A l t h o u g h this m o d e l for airlift p u m p p e r f o r m a n c e is not h e l p f u l i n the case o f l o w - l i f t , l o w - h e a d h i g h f l o w p u m p s s u c h as are c o n s i d e r e d here it does have p r o m i s e and m a y p r o v e useful i n analysis o f cases s u c h as those m e n t i o n e d above.  64  4.2 - Airlift Pump Model for Variable Bubble Slip Velocities W a l l i s ( 1 9 6 8 ) ' s F i g u r e (9.5) i n the section c o n c e r n i n g c h u r n i n g f l o w presents the m i x t u r e and gas phase m a s s f l u x rates i n terms o f the m i x t u r e mass f l u x rate a n d a gas phase "drift flux"  rate relative to the mixture flux. W a l l i s ' figure is r e p r o d u c e d as F i g u r e 13 here.  F I G U R E 14 - Mixture and Gas Flux Rates, Wallis (1969  OVERALL FLUX  Jt  m/sec  65  It indicates the r e l a t i o n s h i p between the mass f l o w rate o f the gas and the m a s s f l o w rate o f the m i x t u r e , expressed as a m a s s f l u x rate per unit area for the m i x t u r e a n d a relative, or " d r i f t " m a s s f l u x rate per unit area for the gas phase. Inspection o f F i g u r e 13 suggests that the gas phase average v e l o c i t y is dependent o n the flux rate o f the m i x t u r e .  C o n s i d e r a case s u c h as ours i n w h i c h the densities o f the gas and l i q u i d phases are k n o w n f i x e d quantities, the p u m p geometry is k n o w n and the density o f the gas phase is n e g l i g i b l e c o m p a r e d to that o f b o t h the l i q u i d phase and that o f the m i x t u r e . In s u c h a case F i g u r e 9 suggests that the drift f l u x rate and m i x t u r e flux rate are dependent o n the m i x ratio a n d c o m p o n e n t phase v e l o c i t i e s o n l y . S o for a n y g i v e n m i x ratio the straightl i n e r e l a t i o n s h i p i n the ratio o f the gas drift flux and m i x t u r e f l u x rate s h o u l d be e q u a l l y representative o f the gas and m i x t u r e fraction v e l o c i t i e s . In that case for k n o w n  fixed  densities o f l i q u i d (water) a n d gas (air) phases, a n d for a k n o w n v o i d f r a c t i o n , the v e l o c i t y o f the gas phase o f the m i x t u r e i n a churn-turbulent two-phase flow depends not o n the v e l o c i t y o f the water phase as suggested b y F i g u r e 8 and as f o u n d i n l o w v o i d fraction s t i l l water and b u b b l y f l o w , but rather depends o n the v e l o c i t y o f the m i x t u r e instead.  W a l l i s ' e q u a t i o n 9.36 suggests a different f o r m o f this relationship. T h a t is expected since h i s flow a n a l y s i s w a s m o m e n t u m - b a s e d and d i d not require the relative v e l o c i t i e s o f the c o m p o n e n t m i x t u r e phases.  66  N e v e r t h e l e s s , the c o n c l u s i o n is p o w e r f u l - n a m e l y that i n cases where the gas d e n s i t y is n e g l i g i b l y l o w i n c o m p a r i s o n w i t h the m i x t u r e density the gas phase v e l o c i t y is greater than, a n d rises l i n e a r l y w i t h the m i x t u r e v e l o c i t y . T h i s p r o v i d e s a v a l u a b l e c o m p o n e n t m i s s i n g so far i n the a n a l y s i s o f these short-lift systems. It is reassuring to note that D e C a c h a r d & D e l h a y e (1995) also f o u n d a s i m i l a r result for m i x t u r e and gas phase v e l o c i t i e s u p to a p p r o x i m a t e l y 6 m/s i n s m a l l diameter, l o n g lift p u m p risers.  S o , e x p r e s s i n g the air phase v e l o c i t y as a linear f u n c t i o n o f the m i x t u r e v e l o c i t y :  (24)  and fitting the l i n e a r r e l a t i o n s h i p i n (25) to W a l l i s ' data i n F i g u r e 13 suggests:  (25)  E q u a t i o n (25) m o d e l s F i g u r e 13 to r e m a r k a b l y g o o d agreement i n units o f feet per second. T h i s e q u a t i o n fit corresponds w i t h the b u b b l e t e r m i n a l v e l o c i t y o f a p p r o x i m a t e l y 30 c m / s , w h i c h is a p p r o x i m a t e l y e q u a l to 1 foot per s e c o n d as i n F i g u r e 12 a n d suggested b y W a l l i s for s t i l l water a n d used i n the first m o d e l . T h e \ 2V  mix  t e r m is also f a m i l i a r  since it represents the ratio o f the centreline v e l o c i t y to the average v e l o c i t y i n the f u l l y d e v e l o p e d turbulent flow field w i t h i n a c l o s e d p i p e .  67  T h e f o r m a n d v a l u e s o f (25) as interpreted here f r o m W a l l i s ' data are v e r y s i m i l a r to those suggested b y N i c k l i n (1962) before h i s w o r k o n airlift p u m p s . N i c k l i n suggested f o r the v e l o c i t y o f a s l u g b u b b l e r i s i n g i n a two-phase m i x t u r e at R e y n o l d ' s n u m b e r s u n d e r 8000:  V =\.2V +0.35jg-Diam air  (26)  mix  In consistent units f o r a representative p u m p riser tube o f s i x - i n c h i n t e r n a l diameter, e q u a t i o n (26) b e c o m e s  (27)  N i c k l i n ( 1 9 6 2 ) qualifies (28) above as b e i n g accurate for R e y n o l d ' s n u m b e r s b e l o w 8 0 0 0 a n d a p p r o x i m a t e f o r R e y n o l d ' s numbers o v e r 8 0 0 0 .  F u r t h e r m o r e , Fernandes, S e m i a t & D u c k l e r (1983) i n d e p e n d e n t l y suggest that the T a y l o r b u b b l e rise v e l o c i t y i n larger diameter pipes than those studied b y T a i t e l et a l . ( 1 9 8 0 ) i s given b y  V = \.2W air  mix  +0.35  Jg-Diam  (28)  E q u a t i o n s (27) a n d (28) are v e r y s i m i l a r to one another a n d suggest v a l u e s for the a i r phase v e l o c i t y for s l u g f l o w j u s t s l i g h t l y greater than suggested b y W a l l i s ' e x p e r i m e n t s  68  for b u b b l y f l o w as g i v e n i n (25). These findings inspire confidence i n this study that the , f o r m a n d v a l u e s i n equation (25) are reliable.  Therefore, substituting (25) into (14):  a,>=(i.o+i.2F;, R fc  (29)  S u b s t i t u t i n g (13) into (25):  1.0 +  1 . 2 ^  (30)  ^mix J  R e a r r a n g i n g (30) to s o l v e for the cross sectional area o c c u p i e d b y the air phase,  A  -  (31)  Qair  1.0 +  1.2^ ^mix J  V  substituting (13) into (28): :  ( V,, = 1 . 0 + 1.2  'mix  Area.  (32)  69  also substituting (32) into (14):  (33)  f 1.0 + 1.2 0,,  Area  and substituting (33) into (15) and u s i n g (16):  V , =Q water  (34)  w  Area - Q water  1.0 + 1.2  Area  Qair J)  E q u a t i o n (34) w i l l then g i v e the v e l o c i t y o f the water phase i n the airlift p u m p tube as a f u n c t i o n o f the m e a s u r e d f l o w rates o f air and water, and the cross s e c t i o n a l area o f the airlift p u m p tube for churn-turbulent f l o w s , a s s u m i n g the air and water phase f l o w v e l o c i t i e s are accurately represented b y equation (22) w h i c h was d e r i v e d f r o m a f i x e d densities a n d m i x ratios analysis o f W a l l i s (1968) data i n F i g u r e 14 and b o l s t e r e d b y N i c k l i n (1962).  H a v i n g d e t e r m i n e d the v e l o c i t y o f the water phase i n the airlift p u m p tube f r o m e q u a t i o n (34), a n d k n o w i n g the water phase v o l u m e f l o w rate and p u m p geometry, the v a l u e s c a n be u s e d to f i n d the v a l u e for the p u m p loss coefficient as d e t e r m i n e d b y e q u a t i o n (23):  K total  H  2g suh  H  water \  total  water  (23)  ~ water '  V  A  r  e  a  J  70  T h i s a p p r o a c h h o l d s m o r e p r o m i s e than the first for i m p r o v e d a n d m o r e r e l i a b l e results.  T h e e x p e r i m e n t a l data w a s r e a n a l y z e d . H o w e v e r , e v e n w i t h this m o r e r e l i a b l e a p p r o a c h for c a l c u l a t i n g the v e l o c i t y o f the water phase a n d despite g o o d e v i d e n c e to support e q u a t i o n (29), the h e a d losses w e r e s t i l l f o u n d not to be p r o p o r t i o n a l to the square o f the water phase v e l o c i t y .  D e s p i t e the fact that this m o d e l cannot be used to e x p l a i n the b e h a v i o u r o f the l o w s u b m e r g e n c e , l o w - l i f t , h i g h - f l o w p u m p units i n this study it does h o l d p r o m i s e for use i n m i d - v e l o c i t y b u b b l y f l o w p u m p units. In s u c h units head losses are p r i m a r i l y due to p i p e f r i c t i o n as suggested b y W a r d (1924) a n d this m o d e l m a y h e l p p r o v i d e a s i m p l e a n a l y s i s t o o l for that class o f airlift p u m p systems.  71  4.3 - Airlift Pump Model for Turbulent Mixing G i v e n the i n a b i l i t y o f the s e c o n d m o d e l to accurately predict the h e a d losses u s i n g the i m p r o v e d m e t h o d for c a l c u l a t i n g the water phase v e l o c i t y , a n e w a p p r o a c h is c l e a r l y necessary. E v i d e n t l y the a s s u m p t i o n that the losses are p r i m a r i l y due to p i p e f r i c t i o n , entrance a n d e x i t losses a n d are dependent o n the v e l o c i t y o f the water phase m u s t be reexamined.  T h e f l o w o f the m i x t u r e i n the airlift p u m p tube is v e r y turbulent w i t h s i g n i f i c a n t v i s u a l e v i d e n c e o f c h u r n i n g . a n d r e c i r c u l a t i o n , so the a s s u m p t i o n that the i n f l u e n c e o f the air phase is n e g l i g i b l e m a y be suspect. W a l l i s (1968) suggests i n p a s s i n g that the m a j o r i t y o f e n e r g y d i s s i p a t e d i n the p i p e f l o w o f c h u r n i n g two-phase m i x t u r e s results f r o m internal losses rather t h a n pipe-friction-related causes. C l a r k & D a b o l t (1986) also argue that the f r i c t i o n a l h e a d losses are a second-order effect w i t h i n p r a c t i c a l lengths for n o n - s l u g f l o w s a l t h o u g h t h e y do not quantify what the frictional head losses are.  F u r t h e r research a n d p a s s i n g suggestions i n several other references p r o v i d e s o m e clues to the m e c h a n i s m o f these losses. W a l l i s (1968) mentions that i n c h u r n i n g f l o w the c h a o t i c m o v e m e n t o f water i n the f l o w m i x t u r e causes the m o s t energy l o s s , a n d furthermore, that i n the m a j o r i t y o f p r a c t i c a l cases b u b b l y f l o w never b e c o m e s f u l l y d e v e l o p e d a n d entrance effects dominate the r e g i o n before s l u g f l o w d e v e l o p s . W a r d (1924) m e n t i o n s that short p u m p s have losses not important i n l o n g p u m p s . M o r r i s o n & a l . (1987) suggest that c h u r n i n g f l o w is i n fact a t r a n s i t i o n r e g i m e u s u a l l y e x i s t i n g f r o m 15 to 35 p i p e diameters a w a y f r o m the aeration point, before s i g n i f i c a n t e n o u g h b u b b l e  72  a c c r e t i o n c a n o c c u r to create s l u g f l o w . D e C a c h a r d & D e l h a y e (1995) suggest that the l e n g t h effects f r o m the d e v e l o p m e n t a l r e g i o n o f c h u r n flow l e a d i n g to s t a b i l i z e d s l u g flow m a y create h i g h e r than p r e d i c t e d head losses up to lengths several h u n d r e d t i m e s the p i p e diameter a w a y f r o m the entrance. T h u s a fully s t a b i l i z e d s l u g flow r e g i m e m a y not d e v e l o p w i t h i n a length u p to e v e n t w o hundred times the p i p e diameter. T a i t e l & a l (1980) q u a n t i f i e d a m i n i m u m length for the turbulent entrance t r a n s i t i o n z o n e as  f  Lauras  =  4  0  -  6  -  D  i  a  v.  m  yjg • Diam  ^  + 0.22  (35)  It o c c u r s that the short p u m p losses m e n t i o n e d b y W a r d (1924) m u s t be due to the entrance a n d t r a n s i t i o n z o n e turbulence. T h e p u m p s i n this study are c o n c l u s i v e l y " s h o r t " - s u b s t a n t i a l l y shorter t h a n 15 to 35 to several h u n d r e d diameters l o n g , a n d s u b s t a n t i a l l y shorter t h a n the entrance lengths suggested b y T a i t a l & a l . (1980) b y e q u a t i o n (35) a b o v e .  Therefore it is reasonable to assume that the m i x t u r e i n the entire p u m p riser tubes is e x c l u s i v e l y e x p e r i e n c i n g the turbulent transition z o n e f l o w r e g i m e . I n that case, the losses i n short airlift p u m p s s u c h as those i n this study m u s t be p r i m a r i l y turbulent i n nature and not p i p e f r i c t i o n losses dependent o n the water phase v e l o c i t y as w a s a s s u m e d i n the first t w o m o d e l s , a n d as c o m m o n l y assumed i n the p r i m a r i l y s l u g - f l o w m o d e l s d e v e l o p e d , to date.  In this case the c h a l l e n g e then becomes h o w to quantify the m i x t u r e turbulence a n d relate the p u m p h e a d losses to that turbulence.  73  It w a s o b s e r v e d i n e x p e r i m e n t a l trials that the air-water m i x t u r e b e c a m e i n c r e a s i n g l y turbulent w i t h i n c r e a s i n g m i x t u r e v e l o c i t i e s , a n d that v e r y h i g h gas phase v e l o c i t i e s at h i g h v o i d fractions resulted i n large losses a n d v e r y little l i q u i d f l o w . T h e s e observations suggest that m i x t u r e v e l o c i t y i n the c h u r n i n g r e g i m e is a g o o d i n d i c a t o r o f m i x t u r e turbulence a n d hence o f losses i n these short p u m p units.  F u r t h e r research d i s c o v e r e d I s h i i a n d Z u b e r ' s (1979) c l a i m that i n turbulent f l o w r e g i m e s the b u b b l e s i n f l u e n c e the s u r r o u n d i n g f l u i d and also other b u b b l e s , a n d that thus b u b b l e s can be entrained i n e a c h others' w a k e s , a n d therefore the losses i n s u c h f l o w s s h o u l d be c o n s i d e r e d relative to the m i x t u r e v e l o c i t y rather than that o f the l i q u i d phase. W a l l i s (1968) also suggests a s i m i l a r general f o r m .  W e therefore propose a functional f o r m for the turbulent head losses i n these short airlift p u m p s , dependent o n the m i x t u r e density a n d turbulence, a n d represented b y the d e n s i t y and v e l o c i t y o f the entire m i x t u r e rather than the v e l o c i t y o f the water phase alone:  H =d-Dens-V; lms  iix  (36)  The t u n i n g parameters d a n d e w i l l be e x p e r i m e n t a l l y d e t e r m i n e d f r o m the research p r o g r a m data.  T h e f o r m o f e q u a t i o n (36) w i l l effectively parameterize the head losses but does not p r o m i s e a great advancement i n terms o f the details o f the head loss m e c h a n i s m . T h i s i s  74  not e n t i r e l y s u r p r i s i n g since D e C a c h a r d & C a l h a y e (1995) e x p l a i n that a m o d e l f o r w a l l f r i c t i o n i n c h u r n i n g flow is n o t yet a v a i l a b l e , a n d that the chaotic m o t i o n i n c h u r n i n g  flow  m a k e s e m p i r i c a l considerations for w a l l f r i c t i o n losses a necessity. G o v a n et a l (1991) agree, suggesting that creating a realistic m o d e l for c h u r n flow m e c h a n i c s i s " p a r t i c u l a r l y challenging".  D e C a c h a r d & C a l h a y e (1995) r e c o m m e n d a f o r m u l a t i o n s i m i l a r to e q u a t i o n (36) f o r l o n g slender p u m p s , based o n the l i q u i d phase v e l o c i t y . F o l l o w i n g their s u g g e s t i o n a n d u s i n g their e q u a t i o n [48] a n d B l a s i u s ' f o r m u l a for frictional losses i n the b o u n d a r y l a y e r as g i v e n i n their e q u a t i o n [11] their s o l u t i o n proposes a f r i c t i o n loss t e r m for c h u r n flow as:  - 0 . 3 1 6 - Dens  l i q u i d  Hhss  =  Hlolal  IDiam  _„.  2S  2  (37)  liquid ^liquid  for the R e y n o l d ' s N u m b e r R e based o n the v e l o c i t y o f the l i q u i d phase Vn d. T h e f o r m qui  o f e q u a t i o n (37) i s r e a s s u r i n g l y s i m i l a r to the f o r m o f equation (36), a r r i v e d at i n d e p e n d e n t l y . T h e p r i m a r y difference between D e C a c h a r d & D e l h a y e ' s f o r m a n d that suggested i n this study i s that their e x p r e s s i o n is calibrated for s m a l l diameter t a l l risers and uses the l i q u i d phase v e l o c i t y as w a s suggested i n the s e c o n d m o d e l a b o v e , whereas e q u a t i o n (36) relies o n the m i x t u r e v e l o c i t y as a n i n d i c a t o r o f turbulence.  T o use (36), w e substitute (6) into (5):  H =H -H Dens loss  suh  lolar  (38)  75  a n d substitute (36) into (38):  d • Dens • V  e mix  =H  suh  - H  • Dens  lolal  (39)  n o w substituting (13) into (38):  d  (^water ^ l y e ' mix  sub  n  V Area j  n  total  (A  \  \Area  j  (40)  T h i s t h i r d m o d e l for airlift p u m p s continues to m a k e use o f the relative v e l o c i t y o f the a i r phase to the v e l o c i t y o f the m i x t u r e as g i v e n b y the e x p e r i m e n t a l l y d e t e r m i n e d e q u a t i o n (26) a n d suggested f r o m W a l l i s ( 1 9 6 8 ) ' s data a n d reflected i n F i g u r e 13.  S o , u s i n g (29) for the water phase cross sectional area, a n d substituting into (40):  Qa  Area-  1 + 1.2  V  Qm  = M  ' mix  n  —M  sub  n  total  Qa,  Area-  1 + 1.2  Area J  (41)  Qm Area  F i n a l l y , b y substituting (11) into (41), get:  Area —  a,  1 + 1.2  Qair  Qm Area  Qwater  Area  Y  =  H„,h-H, sub total 1  Area - -  1  V  1 + 1.2  Qm  (42)  Area  76  B y u s i n g the m e a s u r e d water a n d air phase f l o w rates a n d p u m p geometry, e q u a t i o n (42) a l l o w s the t u n i n g parameters d a n d e to be d e t e r m i n e d f r o m the e x p e r i m e n t a l results.  T h e s u m m a r i e s o f c o l u m n s 10 a n d 11 i n T a b l e 4 a n d c o l u m n s 11 a n d 12 i n T a b l e 6 s h o w g o o d c o r r e l a t i o n b e t w e e n the head losses i n the p u m p s a n d the m i x t u r e v e l o c i t y as a measure o f turbulence. T h i s c o r r e l a t i o n w a s f o u n d throughout the e x p e r i m e n t a l results, albeit m o r e c o n v i n c i n g l y f r o m the last phase o f the p r o g r a m i n w h i c h results w e r e m o r e r e l i a b l e t h a n those p r e v i o u s due to factors already discussed.  F i g u r e 15 s h o w s a s u m m a r y o f the e x p e r i m e n t a l data a n d m o d e l p r e d i c t i o n s . T h e l i n e o f best fit for the e x p e r i m e n t a l data leads to the f o l l o w i n g r e l a t i o n s h i p for the h e a d loss as a f u n c t i o n o f the m i x t u r e f l o w v e l o c i t y :  (43)  c o n s t r u c t i n g a s l i g h t l y m o r e conservative c u r v e fit f r o m the data l e a d to the f o l l o w i n g r e l a t i o n s h i p for the h e a d loss as a f u n c t i o n o f the m i x t u r e f l o w v e l o c i t y ,  H =0.62-dens-V loxs  n  (44)  E q u a t i o n (44) c o u l d be m o r e suitable for d e s i g n since it predicts a s l i g h t l y h i g h e r h e a d loss t h a n the l i n e o f best fit and w o u l d thus be a conservative estimate for p u m p c a p a c i t y .  77  Figure 15 - Comparison of Experimental and Calculated Performance: Log(head loss/density) vs. Log(Mixture velocity)  T h i s m o d e l f o r airlift p u m p performance performs w e l l i n p r e d i c t i n g the p e r f o r m a n c e o f the l o w - s u b m e r g e n c e , l o w - l i f t , h i g h - f l o w units investigated i n this project. It also p r o v i d e s the basis for a s i m p l e a p p r o a c h to e v a l u a t i n g the b e h a v i o u r o f these units a n d leads to a r e a s o n a b l y direct a n d p r a c t i c a l d e s i g n approach.  4.4 - Summarizing the three models T h e first m o d e l d e s c r i b e d i n 4.1 - Airlift Pump Model for Fixed Bubble Slip Velocities relies o n the a s s u m p t i o n o f a r e l a t i v e l y constant bubble rise speed, a n d f r i c t i o n a l p u m p losses g o v e r n e d b y the v e l o c i t y o f the water phase i n the air-water m i x t u r e . Investigations o f the e x p e r i m e n t a l results a n d further research indicate that this a s s u m p t i o n i s n o t v a l i d i n the c h u r n f l o w r e g i m e e x p e r i e n c e d b y the p u m p units i n this study. T h i s m o d e l does have p r o m i s e i n a p p l i c a t i o n s where the constant b u b b l e rise speed i s supported, a n d m a y find use i n large diameter systems s u c h as are used for lake destratification a n d harbour de-icing.  T h e s e c o n d m o d e l d e s c r i b e d i n 4.2 -Airlift Pump Model for Variable Bubble Slip Velocities also assumes losses g o v e r n e d b y the v e l o c i t y o f the water phase i n the a i r water m i x t u r e . It features a refined estimate for the m e a n b u b b l e v e l o c i t y as a f u n c t i o n o f the m i x t u r e v e l o c i t y , a refinement based o n the e x p e r i m e n t a l w o r k o f several p r e v i o u s researchers. T h i s m o d e l does not accurately describe the b e h a v i o u r o f the l o w - l i f t , h i g h f l o w , l o w - s u b m e r g e n c e p u m p s i n this study but does h o l d p r o m i s e for use i n m o r e energetic b u b b l y f l o w r e g i m e p u m p s s u c h as those used i n aquaculture a n d wastewater treatment a p p l i c a t i o n s .  79  T h e t h i r d m o d e l as d e s c r i b e d i n 4.3- Airlift Pump Model for Turbulent Mixing is specific to the c h u r n flow r e g i m e . T h e refinement introduced i n the s e c o n d m o d e l is retained, but a n e w f o r m u l a t i o n for the nature o f the head losses is u t i l i z e d . H e a d losses i n the t h i r d m o d e l are a s s u m e d to be p r o p o r t i o n a l to the turbulent m o t i o n o f the air a n d water phases i n the m i x t u r e . M i x t u r e v e l o c i t y is f o u n d to be a g o o d i n d i c a t o r for m i x t u r e turbulence a n d is thus u s e d as a basis for c a l c u l a t i n g the turbulent h e a d losses. T h i s m o d e l predicts the b e h a v i o u r o f the p u m p s i n this study w i t h g o o d a c c u r a c y a n d f o r m s the basis o f the s i m p l e d e s i g n procedure presented i n C h a p t e r 5.  N o n e o f the procedures suggested i n the o p e n literature are p r a c t i c a l for the engineer w i s h i n g to d e s i g n a l o w - s u b m e r g e n c e , l o w - l i f t , h i g h - f l o w airlift p u m p s y s t e m . W a r d ' s (1924) a p p r o a c h to d e s i g n o f v e r y l o n g airlift p u m p s b y c u r v e m a t c h i n g i n c l u d e s n o data for short l e n g t h p u m p s a n d h i g h v o i d fractions. N i c k l i n ' s (1963) technique for d e s i g n o f airlift p u m p s i n s l u g flow, and a l l o f the suggested refinements to N i c k l i n ' s w o r k suggested b y subsequent researchers do not describe turbulent losses i n a c h u r n i n g system. T r a m b a ' s (1982) and N e n e s & a l ' s (1995) m u l t i - c e l l e d s i m u l a t i o n - b a s e d n u m e r i c a l approaches for d e e p - w e l l airlift p u m p analysis relies o n d i v i d i n g the p u m p p i p e riser b o d y into d i f f e r i n g c o n t i g u o u s sections, each w i t h i n d i v i d u a l f l o w characteristics, a process not feasible for the short p u m p s described here.  H o w e v e r , 4.3 - Airlift Pump Model for Turbulent Mixing d e s c r i b e d i n the p r e v i o u s chapter, p r o v i d e s the m i s s i n g basis for a s i m p l e a n d p r a c t i c a l d e s i g n procedure a l o w submergence, l o w - l i f t h i g h - f l o w airlift p u m p system.  80  CHAPTER 5  5.1 - A Preliminary Design Procedure for Low-lift, Low-Submergence Airlift Pumps in the Churn Flow Regime  T h i s p r o c e d u r e a l l o w s a designer to q u i c k l y c o m p l e t e the p r e l i m i n a r y c a l c u l a t i o n s for a n airlift p u m p i n a l o w - h e a d , h i g h - f l o w , l o w - s u b m e r g e n c e a p p l i c a t i o n for p r a c t i c a l p u m p diameters i n the a p p r o x i m a t e l y 3 i n c h to 12 i n c h range. S i n c e airlift p u m p s are i n e x p e n s i v e to construct, a prototype unit m a y then be b u i l t and the p e r f o r m a n c e v e r i f i e d .  B e c a u s e this d e s i g n a p p r o a c h is s i m p l e and based o n the f r i c t i o n and v e l o c i t y c o r r e l a t i o n s d e v e l o p e d i n this research p r o g r a m it s h o u l d be used w i t h care i n cases o f m u c h h i g h e r lift a n d m u c h deeper submergence. I n those cases the p i p e - f l u i d f r i c t i o n losses w i l l b e g i n to p l a y a larger part i n o v e r a l l system b e h a v i o u r as the bubbles i n the c h u r n f l o w b e g i n to coalesce into T a y l o r b u b b l e s and arrange themselves into a s l u g f l o w pattern. T h e d e s i g n procedure o f C l a r k & D a b o l t (1986) is r e c o m m e n d e d for use i n s u c h cases.  T h i s d e s i g n procedure is used to predict the v o l u m e f l o w rate o f water e x p e c t e d f r o m a l o w - h e a d , h i g h - f l o w , l o w - s u b m e r g e n c e airlift p u m p operating i n the c h u r n f l o w r e g i m e . T h e d e s i g n parameters r e q u i r e d are:  •  Qair = the intended v o l u m e f l o w rate o f air, i n c u b i c feet per s e c o n d  •  Qwater = the intended water f l o w rate, i n c u b i c feet per s e c o n d  81  •  U p s t r = the upstream water l e v e l , i n feet  •  D n s t r d e s = the desired d o w n s t r e a m water l e v e l , i n feet  T h e d e s i g n procedure w i l l be illustrated b y a s i m p l e e x a m p l e . I n this e x a m p l e a n engineer desires to aerate a n d p u m p 10 c u b i c feet per s e c o n d o f water o v e r a 1.5 foot lift u s i n g a s i n g l e or m u l t i p l e - p i p e airlift p u m p s y s t e m w i t h 8 i n c h diameter riser tubes. T h i s p u m p i n g s y s t e m is set i n a s m a l l concrete drainage c h a n n e l 8 feet w i d e b y 5 feet deep. F i g u r e 16 s h o w s the p r o p o s e d l a y o u t o f the system.  F I G U R E 16 - Simple Design Example Layout  Qwater  A Simple 10-Step Design Process: 1.  T h i s d e s i g n appears to require several p u m p units to a c c o m p l i s h the r e q u i r e d  flow  rate a n d lift. I n s u c h a case, assume an air flow rate a n d water flow rate for a  82  single pipe. W i t h n o other i n f o r m a t i o n a v a i l a b l e , 5 0 % o f the a i r f l o w rate i s f o u n d to be a reasonable starting estimate o f the water f l o w rate. A s s u m i n g 2.5 cfs o f air, a n d 1.25 cfs o f water:  a,>=2.5cfs,  2.  e ^=1.25cfs  (DI)  w  F o r l o w i n s e r t i o n depths air c a n be considered i n c o m p r e s s i b l e , so calculate the v o l u m e f l o w rate o f the m i x t u r e b y a d d i n g the v o l u m e f l o w rates o f the a i r a n d water:  & *  3.  -  Qair  + Q a,er W  = (2.5)  + ( l .25)  = 3.75  cfs  (D2)  D e t e r m i n e the m i x t u r e v e l o c i t y b y d i v i d i n g the m i x t u r e f l o w rate b y the crosssectional area o f the riser p i p e :  Qmix  (3.75 cfs) 0.785 • (0.75 f t )  4.  • = 10.7fps  (D3)  :  D e t e r m i n e the v e l o c i t y o f the air phase i n the p u m p riser p i p e f r o m equation (25):  V  air  = 1 + 1.2-V  mix  = 1 + 1 . 2 • (10.7) = 13.9 fps  (D4)  83  5.  D e t e r m i n e the sectional area o c c u p i e d b y the air phase i n the p u m p riser p i p e :  V  air  6.  )  D e t e r m i n e the relative density o f the air-water m i x t u r e i n the p u m p riser p i p e :  Dens = 1  7.  (13.9 fps)  \Area)  (0.35 s f j  D e t e r m i n e the system head loss f r o m equation (44):  -0.56-=0.48-(10.7fps)  8.  =1.18ft  (D7)  C a l c u l a t e the expected d o w n s t r e a m water l e v e l f r o m equations (4) and (5):  ,,  fc ra c  9.  2  =  fc^) Dens  =  MzM) 0.48  =  4  .78ft  (D8)  C o m p a r e the c a l c u l a t e d d o w n s t r e a m water depth f r o m equation ( D 8 ) i n Step 8 to the desired d o w n s t r e a m water depth. I f the c a l c u l a t e d water l e v e l f r o m Step 8 is b e l o w the desired l e v e l the p u m p unit cannot p r o v i d e the desired f l o w rate at the desired lift and g i v e n air f l o w rate. I n s u c h a case the water f l o w rate must be  84  decreased and/or the air f l o w rate must be increased. T h e reverse is true i f the c a l c u l a t e d d o w n s t r e a m l e v e l is above the desired height.  10. I n this e x a m p l e w e select a l o w e r water f l o w rate, leave the a i r f l o w rate as i s a n d re-enter the process at step 1, n o w decreasing our a s s u m p t i o n o f the water f l o w rate to Q r wate  = 1.15 cfs for this p u m p unit at this a i r f l o w . C a r r y out the steps a g a i n  starting at step 1 and c h e c k the n e w result for the d o w n s t r e a m w a t e r l e v e l . O n c e reasonable agreement has b e e n reached the p r e l i m i n a r y d e s i g n i s c o m p l e t e . I n t h i s case the s e c o n d t r i a l for the water f l o w rate w a s a l m o s t exact a n d thus a p r e l i m i n a r y estimate o f the p u m p unit performance has b e e n m a d e .  I n this e x a m p l e a p r a c t i c a l operating p o i n t o f 1.15 cfs o f water a n d 2.5 cfs o f air i n a s i n g l e 8" diameter p u m p w i t h a lift o f 1.5 feet has been established. O t h e r o p e r a t i n g p o i n t s m a y be e x p l o r e d u s i n g the same technique u n t i l a satisfactory o p e r a t i n g p o i n t is selected. A s s u m i n g the p r e l i m i n a r y d e s i g n g i v e n a b o v e is satisfactory, a n d g i v e n the d e s i g n requirement for 10 cfs o f water, a reasonable suggestion w o u l d be to i n s t a l l 9 o f the p u m p s as d e s c r i b e d , for a total water flowrate o f a p p r o x i m a t e l y 10.5 cfs o f water r e q u i r i n g a p p r o x i m a t e l y 23 cfs o f air.  G i v e n that step 7 as s h o w n uses the fit values for the parameters i n e q u a t i o n (43) rather t h a n the c o n s e r v a t i v e v a l u e s o f equation (44) it is reasonable to b u i l d a prototype u n i t based o n these s p e c i f i c a t i o n s to c h e c k performance. A m o r e c o n s e r v a t i v e a p p r o a c h w o u l d be to use the " e n v e l o p e c u r v e " parameters f r o m e q u a t i o n (44) i n step 7 instead. D o i n g so  85  results i n a p r e d i c t e d water f l o w rate for the e x a m p l e p u m p o f 1.05 cfs, i n d i c a t i n g that 10 rather than 9 units c o u l d be required.  A l t e r n a t e p i p e diameters c a n be investigated easily, as c a n the influence o f a greater aeration depth, p o s s i b l y d e v e l o p e d t h r o u g h e x c a v a t i n g a s u m p at the site, etc. F o r e x a m p l e , the m o d e l suggests that the same p u m p c o u l d p r o d u c e a water flowrate o f 2.14 cfs i f the aerator were p l a c e d i n a three-foot deep s u m p . H o w e v e r , this increase i n water flowrate at the same air flowrate is not entirely free since the air m u s t be d e l i v e r e d at a c o n s e q u e n t l y h i g h e r pressure, and subsequently a p o s s i b l y higher cost.  T h i s d e s i g n a p p r o a c h is c l e a r l y suitable for h a n d c a l c u l a t i o n and c a n e a s i l y be automated b y p r o g r a m m i n g into a p o c k e t c a l c u l a t o r s u c h as the H e w l e t t - P a c k a r d 48 series or others o f similar capability.  5.2 - Design Calculations for Personal C o m p u t e r T h e d e s i g n procedure o u t l i n e d above is also suitable for i m p l e m e n t a t i o n i n a c o m m o n spreadsheet software s u c h as M i c r o s o f t E x c e l © . F i g u r e 17 s h o w s a s i m p l e formatted spreadsheet i m p l e m e n t a t i o n o f this d e s i g n technique. T h e user enters d e s i g n v a l u e s i n the b o x e d c e l l s m a r k e d as " I n p u t " and the spreadsheet automates the subsequent c a l c u l a t i o n steps d e s c r i b e d above. S i m p l e changes to the system characteristics c a n be m a d e a n d effects investigated. F i t parameters for the air phase v e l o c i t y to m i x t u r e v e l o c i t y r e l a t i o n s h i p c a n also be adjusted i f desired, as c a n the fit parameters for the head loss to m i x t u r e v e l o c i t y r e l a t i o n s h i p . I n this w a y the performance p r e d i c t i o n s r e s u l t i n g f r o m the  86  direct fit a n d c o n s e r v a t i v e parameters c a n be investigated. T h e spreadsheet s o l u t i o n also a l l o w s for automated fast iteration to accurate solutions b y means o f the M i c r o s o f t E x c e l © " S o l v e r " , " G o a l Seek", or equivalent u s e r - i m p l e m e n t e d system.  Figure 17 - Airlift Pump Churn Flow Worksheet Sample Airlift Pump Churn Flow Worksheet AB December 2003 = volume flow rate of air volume flow rate of water = diameter of airlift pump tube = upstream water level above aerator = desired downstream water level above aerator = acceleration due to gravity = curve fitting parameter in Vair=a+b*Vmix = curve fitting parameter in Vair=a+b*Vmix = curve fitting parameter in Hloss = d*Dens*Vmix e = curve fitting parameter in Hloss = d*Dens*Vmix e =  Qair Qw Diani Upstr Dnstrdes grav a b d e  = = = = = = = = = =  athy  theoretical value for a above given slug flow = 0.35*sqrt(grav*Diam)  -  1.61 fps  Calculated  Qmix  volume flow rate of the mixture = Qair+Qw  =  3.660 cfs  Calculated  Area  cross sectional area of the airlift pump tube = PI()/4*Diam 2  =  0.349 sf  Calculated  Vmix  velocity of the mixture = Qmix/Area  = 10.486 fps  Calculated  Vair  velocity of the air phase in the airlift pump tube = a+b*Vmix  = 13.583 fps  Calculated  Aair  cross sectional area occupied by the air phase = Qair/Vair  =  Calculated  A  A  A  2.50 1.16 0.67 3.50 5.00 31.90 1.00 1.20 0.56 0.62  cfs cfs ft ft ft fpss fps n/a n/a n/a  0.184 sf  Input Input Input Input Input Parameter Parameter Parameter Parameter Parameter  Dens  relative density of the mixture in the airlift pump tube l-(Aair/Area) =  0.473 n/a Calculated  Hloss  head loss from curve fitting experimental data d*Dens*Vmix e  =  1.136 ft  Calculated  =  5.000 ft  Calculated  difference in calculated and desired downstream water levels Dnstrdiff = Dnstrcalc-Dnstrdes = 0.000 ft  Calculated  A  calculated downstream water level Dnstrcalc = (Upstr-Hloss)/Dens  low 1  high 3  fit 1  1.2  1.29  1.2  0.56  0.62  0.56  0.62  0.64  0.62  87  T h e user selects values for the system inputs and parameters and c a n e x p l o r e v a r i o u s aspects o f the p u m p u n i t ' s predicted performance. Iteration is s i m p l e as the user adjusts the air and/or water f l o w rate u n t i l the desired d o w n s t r e a m a n d c a l c u l a t e d d o w n s t r e a m depths are e q u a l . T h e difference i n these depths is calculated at the b o t t o m o f the w o r k s h e e t to facilitate the process. A g o a l - s e e k i n g a l g o r i t h m or s y s t e m m a y also be used.  T h e d e s i g n procedure c a n also be c o d e d into a functional f o r m for i n c l u s i o n i n other spreadsheets. T h i s a p p r o a c h makes the c a l c u l a t i o n o f airlift p u m p b e h a v i o u r i m m e d i a t e . T h i s a p p r o a c h i s also w e l l suited for tabulating predicted airlift p u m p b e h a v i o u r and generating p r e d i c t e d performance values for v a r i o u s c o m b i n a t i o n s o f d e s i g n v a r i a b l e s .  T h e d e s i g n procedure w a s c o d e d into a set o f M i c r o s o f t V i s u a l B a s i c for A p p l i c a t i o n s © functions for use w i t h M i c r o s o f t E x c e l © spreadsheets..  F i g u r e s 18 a n d 19 s h o w the M i c r o s o f t V i s u a l B a s i c for A p p l i c a t i o n s functions.  88  F i g u r e 18 - V B A © C o d e f o r C h u r n F l o w A i r l i f t P u m p D e s i g n Function Dnstrcalc ( B y V a l Qair A s Single, B y V a l Q w A s Single, B y V a l D i a m A s Single, B y V a l Upstr A s Single) A s Single ' T h i s f u n c t i o n c o m p u t e s the d o w n s t r e a m water l e v e l g i v e n the f l o w o f w a t e r ( i n cfs), ' f l o w o f air ( i n cfs), the p i p e riser diameter, and the upstream water l e v e l (both i n feet)  D i m Q m i x A s Single, V m i x A s Single, V a i r A s Single, Dens A s Single D i m Hloss A s Single, A r e a A s Single, A i r A s Single  Q m i x = Q a i r + Q w a t e r : A r e a = 0.785 * ( D i a m )  A  2  A a i r = Q a i r / V a i r : D e n s = 1 - ( A a i r / A r e a ) : H l o s s = 0.56 * D e n s * ( V m i x  A  0.62)  Dnstrcalc = (Upstr - Hloss) / Dens End Function  89  F i g u r e 19 - V B A © C o d e f o r C h u r n F l o w A i r l i f t P u m p D e s i g n Function Q w a t e r ( B y V a l Qair A s Single, B y V a l D i a m A s Single, B y V a l Upstr A s Single, B y V a l Dnstr A s Single) A s Single ' T h i s f u n c t i o n computes the f l o w o f water g i v e n the f l o w o f air ( i n cfs), the p u m p riser ' d i a m e t e r , the upstream water l e v e l and the d o w n s t r e a m water l e v e l ( a l l i n feet). It sets 'the w a t e r f l o w rate to zero and raises it i n s m a l l steps u s i n g D n s t r c a l c u n t i l the c a l c u l a t e d ' a n d d e s i r e d d o w n s t r e a m levels are e q u a l .  D i m Q w l A s Single, D n s t r l A s Single  Q w l = 0: D n s t r l = D n s t r c a l c ( Q a i r , Q w , D i a m , U p s t r ) I f D n s t r l <= D n s t r T h e n Q w a t e r = 0 D o U n t i l D n s t r l <= D n s t r Q w l = Q w l + 0.01: D n s t r l = D n s t r c a l c ( Q a i r , Q w , D i a m , U p s t r ) Loop Qwater = Q w l End Function  T h e disadvantage to the functional f o r m described here is that it isolates the user f r o m the intermediate values o f m i x t u r e density, air, water, and m i x t u r e v e l o c i t y , etc. T h e r e is a greater o p p o r t u n i t y for the user to trust p o s s i b l y questionable results because o f this disconnect.  90  5.3 - Practical Considerations for Preliminary Airlift Pump Design.  Mixture Density: T h e r e are several p r a c t i c a l considerations w h e n u s i n g this approach. It w i l l b e c o m e evident b y u s i n g this d e s i g n technique that the l o w - l i f t , l o w - s u b m e r g e n c e c h u r n f l o w airlift p u m p system is sensitive to the m i x t u r e relative density Dens. W h e n the m i x t u r e relative d e n s i t y falls m u c h b e l o w 0.5, d i m i n i s h i n g returns set i n q u i c k l y i n terms o f increased water f l o w rate w i t h increased a i r f l o w rate. O n c e the m i x t u r e r e l a t i v e d e n s i t y has f a l l e n m u c h b e l o w 0.45, i n c r e a s i n g the a i r f l o w rate e v e n d r a m a t i c a l l y w i l l p r o d u c e v e r y l i t t l e increase i n f l o w o f water. In practice, i n c r e a s i n g a i r f l o w past this l e v e l w i l l e v e n t u a l l y reduce the f l o w o f water since the air is d i s p l a c i n g water i n the p i p e riser tube. T h e m o d e l presented here does not capture this b e h a v i o u r at v e r y h i g h air f l o w rates. H o w e v e r , that is not c o n s i d e r e d a f a i l i n g because the p h e n o m e n o n o c c u r s far outside the p r a c t i c a l range o f d e s i g n . I f a designer finds h i m or h e r s e l f attempting to b u i l d a n airlift s y s t e m to operate i n s u c h a scenario, prototype testing w i l l be r e q u i r e d since the p u m p u n i t w i l l l i k e l y be operating i n the annular or m i s t f l o w regimes, w h i c h e x i s t i n g airlift p u m p theory cannot quantify.  Air Pressure Required: T h e air pressure r e q u i r e d for a n airlift p u m p system is t h e o r e t i c a l l y equal to the static water pressure at the aeration depth and a n a l l o w a n c e for losses i n the air d i s t r i b u t i o n system. I n practice, i f u s i n g a m u l t i - p o r t aerator the aerator ports s h o u l d contribute a reasonable h e a d loss themselves. P r o v i d i n g a notable pressure drop across the ports helps  91  ensure that a l l ports p r o v i d e equal a i r f l o w , thus m a x i m i z i n g the aeration e f f i c i e n c y o f the m u l t i - p o r t aerator. T h u s the system designer s h o u l d be prepared to p r o v i d e a i r f l o w at a p p r o x i m a t e l y 0.5 to 1 p s i greater than p r e d i c t e d b y the aerator submergence and air s y s t e m d i s t r i b u t i o n losses.  C o m p r e s s o r Types C o m p r e s s e d air at l o w pressures and h i g h v o l u m e f l o w rates s u c h as is r e q u i r e d b y a n airlift p u m p s y s t e m o f this type c a n be obtained b y several means. E n e r g y e f f i c i e n c y o f these systems i s l o w since m u c h is lost i n turbulence and m i x i n g . B e c a u s e o f this e n e r g y i n e f f i c i e n c y , requirements for p o w e r are reasonably h i g h . (Fortunately, portable gasp o w e r e d sources are a v e r y v i a b l e alternative and c a n be used o n l y w h e n necessary).  C e n t r i f u g a l b l o w e r s are the most e c o n o m i c a l means o f s u p p l y i n g c o m p r e s s e d air to a n airlift p u m p s y s t e m , p r o d u c i n g h i g h rates o f f l o w at l o w heads, t y p i c a l l y b e l o w 3 to 4 p s i . T h e V o r t r o n Z 4 0 , for e x a m p l e c a n e a s i l y generate 1000 s c f m at 3 p s i w i t h a 4 0 h p m o t o r . T h e centrifugal units operate at v e r y h i g h rotational rates, o n the order o f 25 0 0 0 r p m , and must be m u f f l e d appropriately to a v o i d e x c e s s i v e noise output. R e g e n e r a t i v e b l o w e r s are s o m e w h a t m o r e e x p e n s i v e than centrifugal b l o w e r s but have the potential for a multistage d e s i g n . I n s u c h systems operating pressures o f u p to 9 p s i i n the 2 0 0 to 2 5 0 s c f m range c a n be reached. T h e F P Z S C L - 1 1 5 - D H , for e x a m p l e , c a n generate 4 7 5 s c f m at 9 p s i w i t h a 4 0 hp m o t o r . T h e last type o f air s u p p l y m a c h i n e r y suitable for use i n airlift p u m p i n g systems is the p o s i t i v e d i s p l a c e m e n t b l o w e r . B e c a u s e o f their d e s i g n these units d e l i v e r a r e l a t i v e l y constant s u p p l y o f air g o v e r n e d b y displacement o f their internal lobes and the  92  rotational speed o f their i m p e l l e r s . D e l i v e r y pressures up to 15 p s i are p o s s i b l e w i t h single-stage units. F o r e x a m p l e , the S u t o r b i l t 8 D H c a n generate 300 s c f m at 15 p s i w i t h a 36 h p m o t o r . A n airlift p u m p system r e q u i r i n g a n air s u p p l y w i t h d e l i v e r y pressure a b o v e 15 p s i w o u l d feature a n aerator submergence m u c h greater than those treated i n this study. I n s u c h a case air s u p p l y w o u l d l i k e l y be s u p p l i e d b y a rotary s c r e w c o m p r e s s o r ( s u c h as that u s e d i n the s e c o n d e x p e r i m e n t a l phase o f this project). I n s u c h a case the d e s i g n p r o c e d u r e o f C l a r k & D a b o l t (1986) w o u l d be r e c o m m e n d e d .  93  CHAPTER 6  6.1 - C o n c l u s i o n s .  Interest in low-head, high-flow, low-submergence airlift pump units has historically been low since such pumps are not particularly energy efficient and have been superceded by submersible electric rotomachinery for many decades.  Despite having been replaced with more modern technology, airlift pumps are still used in several niche applications and offer some promising potential benefits in the field of urban stormwater management and other open-channel civil-engineering applications.  Existing theory was evaluated and found inadequate to describe the behaviour of the lowhead, high-flow, low-submergence airlift pumps. A four-stage experimental program was developed and implemented, including a full-scale prototype application in an urban storm drainage application in the city of Richmond, British Columbia. Performance data was collected.  Three theoretical models were developed, with one satisfactorily fitting the experimental data. The model was translated into a practical procedure that an engineer may easily use to develop preliminary designs for airlift pumps operating in the churn flow regime. The design procedure was implemented in two personal-computer-based applications and thus can be quickly and easily completed. Some practical considerations for design of airlift pumps operating in the churn flow regime are given.  94  6.2 - R e s e a r c h R e c o m m e n d a t i o n s  Now that the behaviour of airlift pumps in the churn flow regime has been modeled, the potential for uses of these systems in other low-lift, high-flow, low-submergence applications than those mentioned in this project should be explored. For example, airlift pumps may be useful in irrigation and other pumping in open channels. If so, methods of optimizing their performance in those scenarios must be developed. Additionally, the aquaculture potential of airlift pumping in shrimp and other invertebrate farming drainage applications should be investigated - the range of lift and flow rates are similar to those in urban drainage and aeration of the water may provide additional productivity benefits and cost savings through reducing the need for aeration equipment.  The airlift pump seems to offer many advantages in the urban drainage setting, and the details of those advantages deserve to be investigated. Portable airlift pump units for local flood control may be practical, as might portable or "emergency only" trailer-mounted gasoline-powered air supply subsystems for permanently-installed units. The possibility of reduced environmental impacts in urban drainage subject to aeration as a side effect of airlift pumps should be investigated and subsequent benefits quantified.  More work is also needed to better understand the underlying phenomena of the twophase churn flow regime. Details such as the turbulent fluid behaviour at high void fractions, the manner in which bubbles accrete at high void fractions and the influence of aeration efficiency on regime stability are all unexplored. The development of high-speed 3-dimensional laser imaging technology may provide the necessary tools.  95  References C a r t e l l i e r , A . " S i m u l t a n e o u s V o i d F r a c t i o n M e a s u r e m e n t , B u b b l e V e l o c i t y , and S i z e Estimate U s i n g a Single Optical Probe i n G a s - L i q u i d Two-Phase F l o w s " , R e v i e w o f S c i e n t i f i c Instruments 63(11), (1992) C l a r k , N . N . & R . J . D a b o l t , " A general d e s i g n equation for air lift p u m p s operating i n s l u g f l o w " , A m e r i c a n Institute o f C h e m i c a l E n g i n e e r s J o u r n a l 32(1), (1986) D e C a c h a r d , F . & J . M . 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O v e r h u l t s , " P e r f o r m a n c e and d e s i g n characteristics o f airlift p u m p s for f i e l d a p p l i c a t i o n s " , W o r l d A q u a c u l t u r e 25(4) (1994) Z e n z , F . A . , " E x p l o r e the P o t e n t i a l o f A i r - L i f t P u m p s and M u l t i p h a s e S y s t e m s " , C h e m i c a l E n g i n e e r i n g Progress, 89(8), A u g u s t (1993)  98  —Si —a  C: /AIRPUMP/AIRPUMP- 3.DWG  -7  •!'!<i  <5<5<  <5<5< <5<5< FLOW  -a  o  > O "O  n XI  > zi O z  o  > o X) >  1 1 1 1 1 1 1 1 1 1 1 1 1  mJIM  nn HI  null  ill"™™"  ill'  ilF"|||i" ,1111111111  IIIIIIIIIIII iiiinni  1  "llllllllllllll  can illiiiiiill  1  lllllllllljl III  ill'  llll"l»lll IIIIIINllllllll  >  o  o<5< <<<<< •<5<5<  TYPE 4 <<<<< <<<<<  12"x4' P V C  k I  <<<< <<<<  <<<<<  <<<<  <<<<<  <<<<'  .I  

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