UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Cavitation and entrainment in a downcomer entrance Ryan, James Arthur 1983

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1983_A7 R93.pdf [ 6.37MB ]
Metadata
JSON: 831-1.0095668.json
JSON-LD: 831-1.0095668-ld.json
RDF/XML (Pretty): 831-1.0095668-rdf.xml
RDF/JSON: 831-1.0095668-rdf.json
Turtle: 831-1.0095668-turtle.txt
N-Triples: 831-1.0095668-rdf-ntriples.txt
Original Record: 831-1.0095668-source.json
Full Text
831-1.0095668-fulltext.txt
Citation
831-1.0095668.ris

Full Text

CAVITATION AND ENTRAINMENT IN A DOWNCOMER ENTRANCE by JAMES ARTHUR RYAN B.A.Sc, University Of B r i t i s h Columbia, 1978 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES Department Of Mechanical Engineering We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l 1983 © James Arthur Ryan, 1983 In presenting t h i s thesis in p a r t i a l fulfilment of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t free l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the Head of my Department or by his or her representatives. It i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Mechanical Engineering The University of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date: A p r i l 20, 1983 i i Abstract Two-phase i n s t a b i l i t i e s have been observed at a downcomer entrance in an experimental r i g that drains near-saturated Freon-11 from a vessel. The regimes have been characterized using dimensionless parameters describing the pool depth, downcomer flowrate and the subcooling at the l i q u i d interface in the pool. The two primary mechanisms involved in the i n s t a b i l i t y were entrainment and c a v i t a t i o n . The entrainment regimes observed in th i s study can be correlated with the previously documented occurrence of air-water incipient drawdown. Drawdown was observed at higher pool depths than expected (for a given flowrate) when vapour bubbles were present at the entrance. Cavitation, the mechanism responsible for bubble formation and growth, has been found to be very susceptible to the presence of nucleation s i t e s and to the amount of subcooling at the pool interface. Severe i n s t a b i l i t y may occur at a flowrate where the l o c a l v e locity at the entrance i s equal to the r i s e v e l o c i t y of a p a r t i c u l a r vapour bubble. Due to the generation of vapour through entrainment and c a v i t a t i o n , bubbles conglomerate at the entrance, with the vapour having no mechanism for escape. Some segregation occurs, with small bubbles discharging downwards and l a r g e bubbles r i s i n g upwards. Downcomer entrance geometry was v a r i e d as an independent parameter . In g e n e r a l , the observed regimes i n the r e - e n t r a n t and sharp-edged geometr ies were s i m i l a r . The f low regimes in the rounded geometry were unique due to the e f f e c t of the s t r e a m l i n e d cu rva tu re reduc ing c a v i t a t i o n at the e n t r a n c e . iv Table of Contents Abstract i i L i s t of Figures v i Acknowledgements v i i Nomenclature v i i i Chapter I INTRODUCTION 1 1.1 Preliminary Remarks 1 1.2 Review Of The Terminology 2 1.2.1 Dimensionless Parameters 2 1.2.2 Descriptive Terms 5 1.3 Review Of Previous Work 9 1.3.1 I n s t a b i l i t i e s In Two-Phase Systems 9 1.3.2 Cavitation 10 1.3.3 Incipient Drawdown 10 1.3.4 Miscellaneous Studies 12 1.4 Scope Of The Present Investigation 13 Chapter II EXPERIMENTAL APPARATUS 14 2.1 General Concept 14 2.2 Working F l u i d 15 2.3 Pipe, Tubing, Hose, And F i t t i n g s 17 2.4 Vacuum Chamber And Vessels 18 2.5 Pumps 20 2.6 Instrumentation 20 2.6.1 Temperature Measurement 20 2.6.2 Pressure Measurement 21 2.6.3 Depth Measurement 21 2.6.4 Flowrate Measurement 22 2.6.5 Data Acquisition System 23 2.6.6 Photographic Studies 24 2.7 Assembly And I n i t i a l Testing 25 Chapter III PROCEDURE 27 3.1 Routine Experimental Preparation 27 3.2 C a l i b r a t i o n 30 3.3 Measurements With Fixed Pool Depth 31 3.4 Measurement Of Downcomer Flowrate Fluctuations ....32 Chapter IV EXPERIMENTAL RESULTS 34 4.1 Flow Mapping 34 4.1.1 Incipient Drawdown 35 4.1.2 Onset Of Cavitation Bubbles (OCB) 36 4.1.3 Requirements For A Violent I n s t a b i l i t y 38 4.2 C r i t i c a l Pool Depth (CPD) 39 V 4.3 Video Cassette 40 4.4 Downcomer Flowrate Fluctuation ' 41 Chapter V DISCUSSION OF RESULTS 43 5.1 Qualifying Remarks 43 5.2 Experimental Error 46 5.3 Incipient Drawdown 47 5.4 Onset Of Cavitation Bubbles (OCB) 50 5.5 Requirements For A Violent I n s t a b i l i t y 53 5.6 The Up-Down Transition 54 5.7 C r i t i c a l Pool Depth (CPD) 55 5.8 Bubble Rise Velocity In The Fu l l y Developed Region 57 5.9 Expected Behaviour At High Values Of Subcooling ...58 5.10 Downcomer Flowrate Fluctuation 58 Chapter VI CONCLUSIONS 60 6.1 General 60 6.2 Incipient Drawdown 61 6.3 Onset Of Cavitation Bubbles (OCB) 62 6.4 Requirements For A Violent I n s t a b i l i t y 63 6.5 C r i t i c a l Pool Depth (CPD) And The Up-Down Transition 63 6.6 Sample Theoretical Curves 64 6.7 Downcomer Flowrate Fluctuation 64 Chapter VII RECOMMENDATIONS 65 7.1 Industrial Design 65 7.2 Further Work 66 7.2.1 Modifications To The Apparatus And Instrumentation 66 7.2.2 Further Areas Of Study 68 BIBLIOGRAPHY 100 APPENDIX A - DIMENSIONAL ANALYSIS 102 APPENDIX B - SAMPLE CALCULATIONS AND ERROR ANALYSIS 105 APPENDIX C - INDEX TO VIDEO CASSETTE 108 v i L i s t of Figures 1. Industrial Example Of The I n s t a b i l i t y (Steam and Condensate) 70 2. Incipient Drawdown With Liquid Level At Downcomer Entrance (Air-Water) 71 3. Incipient Drawdown With Liquid Level Below Downcomer Entrance (Air-Water [9]) 72 4. Experimental Schematic 73 5. Pictures Of Apparatus And Instrumentation 74 6. Det a i l s Of Vacuum Chamber 75 7. Downcomer Entrance Geometries 76 8. Constant Temperature Anemometer Schematic 77 9. Data Acquisition System Schematic 78 10. The Effe c t Of Subcooling On Incipient Drawdown For The Re-entrant Geometry 79 11. Incipient Drawdown For Rounded And Sharp-edged Geometries 80 12. The Effect Of Subcooling On The Onset Of Cavitation Bubbles (OCB) For The Re-entrant Geometry 81 13. The Effe c t Of Subcooling On The Onset Of Cavitation Bubbles (OCB) For The Sharp-edged Geometry 82 14. Violent Region For The Re-entrant, Rounded And Sharp-edged Geometries ' 83 15. C r i t i c a l Pool Depth (CPD) For The Re-entrant Geometry 84 16. C r i t i c a l Pool Depth (CPD) For The Rounded Geometry. ..85 17. The Effect Of Subcooling On CPD For The Sharp-edged Geometry 86 18. Pictures Of Incipient Drawdown, Spouting And OCB In The Re-entrant Geometry ..87 19. Froude Number Fluctuation And Frequency Analysis For The Re-entrant Geometry 88 20. Froude Number Fluctuation And Frequency Analysis For The Rounded Geometry 89 21. Froude Number Fluctuation And Frequency Analysis For The Sharp-edged Geometry 90 22. Froude Number Fluctuation In The Re-entrant Geometry During Bridging 91 23. Miscellaneous Pictures Of The Re-entrant Geometry. ...92 24. Streamline Pattern In Liquid-Only Flow 93 25. Theoretical OCB Curves 94 26. Violent Spouting In The Re-entrant Geometry 95 27. Expected Behaviour At Different Values Of Subcooling 96 28. Idealized CPD For The Re-entrant Geometry At SC = 9. .97 29. Idealized CPD For The Rounded Geometry At SC = 9 98 30. Idealized CPD For The Sharp-edged Geometry At SC = 9 99 v i i Acknowledgement The author wishes to express his sincere gratitude to Professor E.G. Hauptmann, for his invaluable advice and guidance throughout a l l phases of the investigation. Thanks are due to the technical s t a f f of the mechanical engineering department for their assistance in the construction of the experimental apparatus. Special thanks to my fellow graduate students for their helpful advice and suggestions, to Chien Wei Jang for his help performing the experiments, and to my wife, Janin, who helped proof-read the thesis and who was a constant source of moral support and motivation during my graduate work. Financial support for th i s research by the Natural Sciences and Engineering Research Council of Canada i s g r a t e f u l l y acknowledged. v i i i Nomenclature B ca l i b r a t e d y-intercept (see Ch. I l l , p. 30) D downcomer inside diameter (m) Fr Froude number (dimensionless flowrate) V(gD)' V2 AFr* Froude number peak-to-peak fluctuation expressed as a percentage of the mean Froude number H chamber pool depth above the top of the entrance (m) H/D dimensionless pool depth K linear c a l i b r a t i o n constant (see Ch. I l l , p. 30) N number of data points Pch chamber pressure (Pa) PV chamber pressure signal voltage Psat saturation pressure at temperature Tch (Pa) Q siphon loop flowrate ( l i t r e s / s ) QV siphon loop flowrate signal voltage SC dimensionless subcooling (Pch - Psat)/pgD SCAVG average value of subcooling SD standard deviation Tch chamber temperature (°C) TV chamber temperature signal voltage ix V average l i q u i d phase v e l o c i t y in the tube (m/s) Vn valve number "n" as shown on Figure 4 g g r a v i t a t i o n a l acceleration (m/s2) p l i q u i d density (kg/m3) Abbreviations rd rounded entrance re re-entrant entrance shp sharp-edged entrance CPD c r i t i c a l pool depth ID i n c i p i e n t drawdown OCB onset of c a v i t a t i o n bubbles 1 I. INTRODUCTION 1.1 Preliminary Remarks Much e f f o r t has been devoted in the last forty years to the study of two-phase flow regimes and their r e l a t i o n s h i p to heat and mass transfer phenomena. Such previous work has been an integral part of the development of sophisticated power generation and process industry technologies, where two-phase flows occur frequently. The present study i s concerned with the l i q u i d -vapour flow of a one-component f l u i d , near saturation temperature and pressure. The l i q u i d drains from a vessel through an . entrance into a v e r t i c a l tube or "downcomer". An example of t h i s type of flow i s shown in Figure 1. The l i q u i d i s draining from the chamber into a region of increasing hydrostatic pressure, but in the d i r e c t i o n of decreasing piezometric pressure. Other common examples of t h i s type of near-saturated flow are in package b o i l e r i n s t a l l a t i o n s and in several types of evaporators used in industry. When vapour phase i s present, the resulting tube flowrate turns out to be much less (and the f r i c t i o n a l head loss much greater) than that predicted in the conventional single-phase analysis. The existence of t h i s type of i n s t a b i l i t y has been 2 hinted at several times in the l i t e r a t u r e , for example by Simpson [1], but i t seems that i t has not been v i s u a l i z e d or systematically studied. Simpson made a vague, and i t seems misleading postulate as to the mechanisms involved, suggesting c e r t a i n design guidelines be followed to minimize the e f f e c t of the i n s t a b i l i t y . In essence he stated that one should avoid Froude numbers from 0.31 to 1.0 in v e r t i c a l two-phase pipe flow. In the past t h i s guideline has been used by engineers in industry. However, very inconsistent results have been obtained, p a r t i c u l a r l y in flows with near-saturated l i q u i d s . Often t r i a l and error solutions have been attempted in e f f o r t s to control the i n s t a b i l i t y (for example a i r - i n j e c t i o n into the downcomer) without any basic understanding of the flow regimes involved. 1.2 Review Of The Terminology 1.2.1 Dimensionless Parameters In characterizing two-phase flow regimes, dimensionless parameters are sometimes used to describe the flow of one f l u i d under a p a r t i c u l a r set of conditions. Then, using the p r i n c i p l e of dynamic s i m i l a r i t y , t h i s description can be applied to other 3 f l u i d s and other sets of conditions. In l i q u i d flow with a liquid-vapour interface, the Froude number (abbreviated Fr) i s a s i g n i f i c a n t dimensionless group. In pipe flow i t i s usually defined as the square root of the r a t i o of i n e r t i a l to buoyancy forces, given by F r ( l i q u i d ) = V(gD)" ^  ( p/( p - p v ) ) 1 / 2 Here V i s the average l i q u i d v e l o c i t y in the tube, D i s the tube diameter, g i s g r a v i t a t i o n a l acceleration, and p and pv are the respective l i q u i d and vapour d e n s i t i e s . Since at low pressures, the vapour density is n e g l i g i b l e when compared to that of the l i q u i d , t h i s term s i m p l i f i e s to Fr = V(gD)" 1/ 2 = "dimensionless flowrate" It i s assumed that when the p r i n c i p l e of dynamic s i m i l a r i t y of Froude numbers i s applied to other f l u i d s and sets of conditions, other forces on the f l u i d such as those involved with surface tension and v i s c o s i t y , are small r e l a t i v e to i n e r t i a l and buoyancy forces. The pool depth H, defined as the v e r t i c a l distance from the vapour-liquid interface in the chamber to the 4 top of the downcomer entrance, is another important parameter. It i s a measure of the suppression of vapour formation at the downcomer entrance due to hydrostatic pressure e f f e c t s . H can be non-dimensionalized by dividing by the tube diameter D, to give H/D = "dimensionless pool depth" The t h i r d dimensionless parameter used in thi s project describes the magnitude of l i q u i d subcooling in the chamber. The subcooling number, defined here as SC = (Pch - Psat)/pgD = "dimensionless.subcooling" is the difference between the chamber pressure Pch and saturation pressure Psat of the l i q u i d in the chamber (at the chamber temperature Tch), non-dimensionalized by di v i d i n g by pgD. The s u i t a b i l i t y of non-dimensionalizing by pgD w i l l have to be examined in the future with experimental studies using several other tube diameters. APPENDIX A contains a brief dimensional analysis used to j u s t i f y the use of these dimensionless groups. 5 1.2.2 Descriptive Terms Three terms used in the hydraulic study of downcomers, with the d e f i n i t i o n s in the context used in the present study are: 1. "flow i n s t a b i l i t y " - a spontaneous occurrence of rapidly changing two-phase flow regimes in a tube, accompanied by fluctuations in the tube flowrate. For' a more general d e f i n i t i o n of two-phase flow i n s t a b i l i t i e s , the reader i s referred to a review done on t h i s subject by Bergles [2]. 2. "cavitation" - v a p o u r - f i l l e d bubble formation and collapse in a l i q u i d caused by dynamic (flow-induced) pressure reduction in an adiabatic flow. Knapp [3] has defined the term " i n c i p i e n t " c avitation as the stage of ca v i t a t i o n that i s barely perceptible as the l i q u i d pressure i s lowered, with "desinent" c a v i t a t i o n describing the stage where the cavitation disappears with increasing pressure. Theoretically cavitation occurs when the normal stresses on an i n f i n i t e s i m a l p a r t i c l e of l i q u i d are reduced to 6 the vapour pressure of the l i q u i d (at the p a r t i c l e temperature). The presence of surface tension forces, boundary layers, turbulence, undissolved gas and dust p a r t i c l e s (which act as nucleation s i t e s ) , d i s t o r t the requirement of zero net normal stress at a point in the l i q u i d . Since bubble formation and collapse are time-dependent phenomena, the time a l i q u i d p a r t i c l e remains trapped in a low pressure eddy w i l l be an important factor in determining i f and to what extent ca v i t a t i o n w i l l occur. In the absence of any nucleation s i t e s , the formation of vapour after pressure reduction i s delayed due to the existence of a "thermodynamically metastabl.e" state. 3. "incipient drawdown" - the point of incipient entrainment. Consider the " i r r o t a t i o n a l " downflow (without swirl) of a l i q u i d from a pool, through a v e r t i c a l drain or downcomer. For each pool depth there exists a c r i t i c a l flowrate at which the l i q u i d interface suddenly breaks down, and a cone-shaped interface forms above the entrance. The s t r a t i f i e d gas or vapour above the l i q u i d surface becomes entrained in the l i q u i d at the vertex of the cone. 7 This c r i t i c a l flowrate, defined as incipient drawdown (abbreviated ID), i s i l l u s t r a t e d in Figure 2 for the case of air-water flow into a l i q u i d l e v e l at or near the tube entrance. With water flowing at very low depths above the entrance (1 or 2 mm), the flowrate i s susceptible to surface tension e f f e c t s . At low pool depths (H/D less than 0.25 as suggested by Souders [4]) the maximum water flow i s limited by a c i r c u l a r weir phenomenon (Figure 2a), where the l i q u i d flows down to the l i q u i d l e v e l in an annular or f a l l i n g f i l m regime. For every pool depth, there i s a maximum flowrate given by the lower part of the " c i r c u l a r weir" curve on Figure 2. The magnitude of a i r entrainment i s ne g l i g i b l e in t h i s regime as any bubbles present in the tube quickly r i s e upwards. At higher pool depths (H/D greater than 0.25) the maximum flowrate at a given pool depth i s governed by incipient drawdown, shown on the upper part of the same curve (Figure 2b). Any attempt to increase the flowrate above values given by the curve (by increasing the chamber pressure Pch) w i l l result in the large scale entrainment of the a i r from above the interface, with no net increase in the l i q u i d flowrate. Figure 2 i s arrived at based on the assumption that the t r a n s i t i o n from weir flow to incipient drawdown i s continuous, which happens only when the flow i s into a l i q u i d l e v e l at or near the tube entrance. In t h i s 8 study the phenomena of weir flow and incipient drawdown are described solely, by the term incipient drawdown, with the implication that the curve joining the two phenomena i s continuous. The t r a n s i t i o n from weir flow to incipient drawdown i s not well defined when the l i q u i d l e v e l in the tube is much lower than the entrance. An example of water draining from a vessel (under the effects of gravity only) i s shown in Figure 3. As the flowrate into the upper chamber i s increased the following sequence i s observed. I n i t i a l l y a thin f i l m of water runs down the wall of the tube in an annular or weir regime (Figure 3a). Eventually as the pool depth r i s e s , necking occurs at the vena contracta (Figure 3b). As the depth ri s e s further, the vapour core bridges with l i q u i d (Figure 3c). The Froude number does not increase s i g n i f i c a n t l y after bridging, and the pool depth diverges from the drawdown curve (Figure 3d). Despite the bridging of the annular a i r - f i l l e d region, annular flow w i l l p e r s i s t in the tube well below the pool interface. Any mechanism for increasing the flowrate by increasing the pressure in the upper vessel w i l l again be limited by the drawdown curve. At very high flowrates, "flooding" w i l l occur in the tube, irrespective of drawdown (Figures 3e and 3 f ) . During flooding, the l i q u i d f i l m bridges throughout i t s whole 9 v e r t i c a l extent, and the tube flows f u l l for i t s entire length. Both bridging (Froude number observed at approximately 0.5 for .Freon-11) and flooding (Froude number approximately 2.0 from [1]) phenomena occur above a dimensionless pool depth of 0.25. However, i f the l i q u i d l e v e l i s maintained at the tube entrance independent of flowrate (by lowering the pressure in the upper vessel), a smooth but d e f i n i t e t r a n s i t i o n without bridging w i l l be observed, as shown previously in Figure 2. 1.3 Review Of Previous Work A l i t e r a t u r e search was conducted and i t was concluded that no systematic study of t h i s i n s t a b i l i t y could be found. However, various authors have published work on related topics. 1.3.1 I n s t a b i l i t i e s In Two-Phase Systems Bergles [2] has published a review of previous work done in th i s area. This review included both thermal and hydrodynamic i n s t a b i l i t i e s characterized as either s t a t i c or dynamic, and of a primary, secondary or compound nature. No mention was 10 made of any cavitation-induced entrance i n s t a b i l i t y . 1.3.2 Cavitation Oba [5] studied c a v i t a t i o n in water flowing through a horizontal m i c r o - o r i f i c e , under prescribed nuclei condition. The e f f e c t of o r i f i c e diameter on the desinent cavitation number, given by (Pch - Psat)/(pV 2/2) was investigated. Lienhard [6] did a similar study varying the magnitude of the orifice-to-pipe-diameter r a t i o and the r a t i o of orifice-diameter-to-nucleation-site-spacing in a horizontal submerged o r i f i c e . The c a v i t a t i o n number at desinence was correlated to the product of these two r a t i o s . 1.3.3 Incipient Drawdown Souders [4] experimentally studied incipient drawdown as i t related to rotational flow in a fractionation column. The downcomer was modelled under three d i s t i n c t conditions of f l u i d head. These were; operating as a c i r c u l a r weir at low depths, operating as 11 a free running o r i f i c e at intermediate depths, and operating as an o r i f i c e running f u l l at high depths. Davidian [7] did experimental work on the development of a non-circulatory waterspout. This phenomenon i s e s s e n t i a l l y incipient drawdown reversed, with the l i q u i d entrained upwards by the flow of a gas into a tube, rather than gas entrained downward by the flow of a l i q u i d . The results seem to agree well with other published air-water incipient drawdown experiments. Harleman [8] analyzed i r r o t a t i o n a l i ncipient drawdown using potential flow, modelling the entrance as a point sink. An experimental study was then performed using two v e r t i c a l l y s t r a t i f i e d l i q u i d s , testing for the c r i t i c a l entrainment point. Re-entrant, sharp-edged and rounded entrance geometries were tested for a 2.54 cm diameter tube. Kalinske [9] used re-entrant and sharp-edged pipes of various diameters and lengths in a study of incipient drawdown. While draining an air-water mixture from a closed vessel with a metered a i r i n l e t , the a i r entrainment rate at incipient drawdown was measured. Simpson [1], reviewed previous work done on inci p i e n t drawdown. Also reviewed was work done on the dependence of bubble r i s e v e l o c i t y on Froude number in v e r t i c a l pipe flow. Bubble r i s e v e l o c i t y i s usually 1 2 defined in a stagnant pool of l i q u i d and is a function mainly of l i q u i d surface tension, v i s c o s i t y , bubble size and shape, and the diameter of the constraining tube. In a downflowing l i q u i d , a bubble w i l l r i s e where the l o c a l l i q u i d v e l o c i t y at the bubble i s less than the calculated r i s e v e l o c i t y . Simpson stated that Froude numbers ranging from 0.31 to 1.0 should be avoided (to prevent pressure pulsation and vibration) in a l l v e r t i c a l pipe flow where entrainment of a i r or vapour might be possible. 1.3.4 Miscellaneous Studies It seems that the flow f i e l d in an o r i f i c e has not been solved numerically (at high Reynolds numbers) using the Navier-Stokes equations. However, using two-dimensional hydrodynamic flow theory, solutions have been obtained for both re-entrant (Borda's mouthpiece) o r i f i c e s and sharp-edged o r i f i c e s (for example Vallentine [10]). These solutions neglect boundary layer e f f e c t s , but give an order of magnitude estimate of the l o c a l v e l o c i t y (and pressure from Bernoulli's equation) throughout a downcomer entrance. Kelly [11], studied extensively the operation of siphons. In p a r t i c u l a r , the e f f e c t of dissolved a i r and gases in the siphon flow of water was investigated. 13 Several postulates were made as to the source of high frequency vibrations (noise) often found in siphons. Bharathan [12] and Wallis [13] have conducted several experimental studies into the subject of countercurrent annular flow. Bharathan was concerned with flooding and i n t e r f a c i a l shear stress phenomena in air-water flow, while Wallis studied additional condensation e f f e c t s in steam-subcooled water flow. 1.4 Scope Of The Present Investigation After conducting t h i s l i t e r a t u r e search, i t was decided to conduct a systematic experimental study of the flow i n s t a b i l i t y that was presumed to exist when draining (without swirl) near-saturated f l u i d s from a chamber or vessel. Accordingly, an experimental r i g was designed and constructed to model t h i s occurrence. Flow v i s u a l i z a t i o n , and flow mapping of any regimes by the measurement of the dimensionless flowrate, pool depth and subcooling constituted the scope of the experimental work. The measurement of subcooling entailed the measurement of the chamber pressure and temperature. The results of the investigation hopefully can be applied by engineers in attempts to predict and/or control the occurrence of the i n s t a b i l i t y . 1 4 II. EXPERIMENTAL APPARATUS 2.1 General Concept The apparatus depicted on the flowsheet in Figure 4 was used to investigate the flow regimes. Pictures of the experimental r i g and instrumentation are shown in Figure 5. Two loops are shown on the flowsheet; a c i r c u l a t i o n loop and a siphon loop. In the c i r c u l a t i o n loop, the l i q u i d was extracted from the lower vessel by a c i r c u l a t i o n pump and passed through a co-axial heat exchanger into the overflow vessel. A constant l e v e l was maintained in t h i s vessel by an overflow l i n e passing back into the lower vessel. In the siphon loop, the f l u i d was extracted from the overflow vessel up into the vacuum chamber (Figure 6) where i t drained through an attached entrance geometry (Figure 7) into the downcomer test section. The downcomer emptied into an overflow weir in the lower vessel. Both the i n l e t and discharge of the siphon were kept submerged. The siphon loop was primed from a vacuum accumulator tank, which was evacuated p e r i o d i c a l l y by a vacuum pump. Compared to alternative methods, advantages of using t h i s system to achieve near-saturated conditions in the vacuum chamber were: 15 (a) - regulation of the l i q u i d temperature in the siphon loop by simply c o n t r o l l i n g the cooling water flowrate through the heat exchanger. Then by c o n t r o l l i n g the pressure in the apex of the siphon (the vacuum chamber), the l i q u i d properties could be adjusted to achieve near-saturation. (b) - saturated vapour conditions could be maintained in the vacuum chamber despite the presence of any non-condensibles ( i e . a i r leaks) that may have i n f i l t r a t e d the system, by continuously evacuating a small amount of vapour from the vacuum chamber and generating additional saturated vapour. (c) - pressure control in the vacuum chamber was independent of any fluctuations due to pumping, as a siphon (with a nominal dri v i n g head of 60 cm) was used to provide the flow through the test section. 2.2 Working F l u i d As water was readily available and non-toxic i t was f i r s t considered for the working f l u i d . However, operating the siphon loop with water (at ambient temperature) would have required a difference in elevation of approximately 10 m (between the overflow vessel and vacuum chamber) for the siphon apex pressure 1 6 to reach the saturation vapour pressure of water. Running at higher water temperatures would have decreased this height, but heating elements and insulation would have added to the o v e r a l l complexity. The most serious problem would have been the ef f e c t s of dissolved a i r in the water, as revealed by Kelly [11]. Air may have come out of solution near the apex of the siphon, lowering the average f l u i d density and preventing saturation from occurring at a given apex height. This phenomenon would have required apex heights for water, measured on the r i s i n g leg of the siphon, to be considerably larger than 10 m. Freon-11 1, a common refrigerant, was eventually chosen as the working f l u i d . It has the following c h a r a c t e r i s t i c s : (a) - a poor solvent of both a i r and water (b) - low t o x i c i t y under normal conditions of handling and usage (group 5a - Underwriter's Laboratories C l a s s i f i c a t i o n of Comparative L i f e Hazard of Gases and Vapours [14]) (c) - low b o i l i n g point at atmospheric pressure of 23.8 °C 'Freon-ll, CCL 3F (trichlorofluoromethane) i s a registered trademark of the Du Pont corporation 1 7 -(d) - r e l a t i v e l y low cost (the least expensive of the Freons) (e) - low v i s c o s i t y and surface tension (f) - excellent thermal and chemical s t a b i l i t y (g) - inflammable, non-conductive and non-corrosive (h) - well documented thermodynamic properties There were some disadvantages to using Freon-11 as the working f l u i d . It was s t i l l very expensive to purchase compared to water, and i t s peculiar chemical properties necessitated careful choice of apparatus material. For example, the p l a s t i c polyethylene and the elastomer neoprene both react unfavourably with Freon-11. It was very important to keep the. apparatus clean as Freon-11 has a great a f f i n i t y for grease and o i l s . The presence of these substances in s u f f i c i e n t quantities would have s i g n i f i c a n t l y affected the Freon's saturation properties. 2.3 Pipe, Tubing, Hose, And F i t t i n g s 1.3 and 2.5 cm PVC pipe and f i t t i n g s were used for the Freon c i r c u i t because they were readily available and easy to assemble. PVC b a l l valves with te f l o n seats were used for t h r o t t l i n g and shutoff purposes. 18 The tubing i n i t i a l l y chosen for the downcomer test section was 3.2 cm I.D. by 1.8 m long polycarbonate tubing. It was found that when the tubing was exposed to Freon-11 under a s l i g h t vacuum, severe crazing (micro-cracking) occurred. Glass tubing of 2.54 cm I.D. was chosen as a replacement. Brass c o l l a r s were fastened to the tube where the vacuum chamber O-ring seal f i t t e d over the tube. To allow v i s u a l i z a t i o n of vapour formation, the top portion of the r i s i n g leg of the siphon was also fabricated out of glass tube. The heat exchanger was a simple co-axial s h e l l and tube type made from 2.5 cm copper pipe (shell) and 1.3 cm copper pipe (tube), with brass Swagelok heat exchanger f i t t i n g s sealing the ends of t h e , s h e l l . Cold building supply water was used as the cooling medium. 2.4 Vacuum Chamber And Vessels The vacuum chamber used was a 17 l i t r e Nalgene polycarbonate b e l l jar (Figure 6) placed over a mounting plate, with an O-ring providing the s e a l . Any a i r present in the chamber during the experiments would have risen to the top of the vacuum chamber, since Freon vapour i s denser than a i r . Therefore the extraction i n l e t to the vacuum pump was located at the top of the chamber, where i t would keep the liquid-vapour interface 19 clear of non-condensibles. A false floor made from two perforated aluminum plates (with a fine brass screen sandwiched between) was located around the test section entrance. Three equally spaced v e r t i c a l straightening vanes were attached to th i s false f l o o r . The arrangement was intended to remove large scale turbulence from the pool and to prevent the buildup of s w i r l . The incoming jet of Freon was dissipated d i r e c t l y at the chamber i n l e t by a wire basket f i l l e d with brass wool. Some crazing problems were encountered with the b e l l jars, but these were minimized by taking care when mounting the jars so as not to form any small cracks in the walls of the j a r . When present, these cracks (with their inherent stress concentrations) would rapidly propagate upon further exposure to the Freon. An aluminum container with 2.5 cm threaded nipples attached was used for the overflow vessel, while a spare b e l l jar was used for the lower vessel. Loose f i t t i n g l i d s were placed over these vessels to minimize evaporation losses. A 51 cm diameter by 152 cm high mild steel pressure vessel was used for the vacuum accumulator tank. It was equipped with an analog pressure gauge for l o c a l vacuum indic a t i o n . 20 2.5 Pumps An Eastern Model MD-80 magnetic drive pump was used to c i r c u l a t e the Freon. This was a seal-less pump with a polypropylene casing and impellor. Maximum capacity was rated at 1.0 l i t r e s / s with a shut-off head of 10 m. The pump was driven by a 249 W at 3450 rpm motor. A Bendix Model AAF vacuum pump was used d i r e c t -coupled to a 373 W at 1800 rpm motor. 2.6 Instrumentation The instrumentation measured the chamber pressure, temperature, and pool depth, the average flowrate through the siphon loop, and the peak-to-peak amplitude of downcomer flowrate fluctuations (see Figure 4). 2.6.1 Temperature Measurement Temperature was measured with an Omega Type PR-11 general purpose platinum resistance thermometer probe (RTD) coupled with an, Omega Model 199p2 d i g i t a l indicator. The indicator had an analog output option (± 0.1°C resolution) for interfacing with the data a c q u i s i t i o n system. 21 2.6.2 Pressure Measurement Chamber pressure was i n i t i a l l y measured with a Bourns Model 441 bellows/potentiometer type absolute pressure transducer, with a range of 0-101 kPa. The transducer had a s t a t i c error band of 1.2% f u l l scale, including the effects of l i n e a r i t y , f r i c t i o n , hysteresis, resolution and r e p e a t a b i l i t y . It was found that t h i s instrument was not s u f f i c i e n t l y accurate to measure the small pressure differences necessary to characterize the subcooling. A simple water manometer was then connected to the system. It was found to be accurate for steady-state measurements but clumsy to use i f the chamber pressure fluctuated. The transducer was then used only for transient measurements when the operating c h a r a c t e r i s t i c s of the system were being studied. 2.6.3 Depth Measurement Pool depth in the vacuum chamber was measured (± 1.0 mm) against a st a i n l e s s steel graduated scale mounted on the fal s e f l o o r . 22 2.6.4 Flowrate Measurement Average flowrate in the siphon loop was measured with a Signet MK 315 paddlewheel "flosensor", with an open paddle design that minimized cavitation e f f e c t s . The sensor was mounted in a 1.3 cm diameter PVC f i t t i n g with 30 pipe diameters length of straight pipe preceding the sensor. The sensor was coupled with a Signet MK 309 analog "flometer" for l o c a l indication and a MK 314-6 signal conditioner for inte r f a c i n g with the data a c q u i s i t i o n system. This method of flowrate measurement was chosen because cavitation occurs when near-saturated l i q u i d flows through an o r i f i c e plate or a venturi. It was found that t h i s instrument gave repeatable and accurate results (± 0.003 l i t r e s / s ) providing the f l u i d v e l o c i t y in the sensor was kept above 30 cm/s (Froude number of 0.17). Fluctuations in downcomer flowrate were measured with a ThermoSystem Inc. Model 1010-A constant temperature anemometer coupled with a DISA Model 55D10 l i n e a r i z e r and a Nicolet Model 660A FFT 1 spectrum analyzer. The analyzer used a Tektronix Model 4662 d i g i t a l p lotter for hardcopy output. A TSI Model 1230 hot f i l m sensor was used as the 1Fast Fourier Transform 23 anemometer probe. This conical shaped sensor was constructed from a quartz rod with a quartz-coated platinum f i l m band at the cone t i p , and was chosen because of i t s ruggedness, s p a t i a l resolution and r i g i d i t y . The probe was placed at the discharge of the downcomer, in the f u l l y developed region of the flow. The TSI anemometer unit c i r c u i t consisted of a Wheatstone bridge arrangement with the probe as one variable leg and a decade resistance as the other variable leg (Figure 8). The bridge had a feedback loop which supplied s u f f i c i e n t power to raise or lower the probe resistance so that the bridge was kept in balance. Varying the decade resistance varied the probe operating resistance, and therefore the probe temperature. Since the heat transfer rate from the probe varied non-l i n e a r l y with the l i q u i d v e l o c i t y at the probe, the l i n e a r i z e r was used to create a linear r e l a t i o n s h i p between flowrate and output voltage. 2.6.5 Data Acquisition System The signals from the pressure, temperature and average flowrate measurement devices were then interfaced with the department's Neff Model 620 data a c q u i s i t i o n system and processed by a PDP-11/34 minicomputer. 24 Provision was made for the two types of sampling shown in Figure 9. The f i r s t type was at a constant pool depth, prompting for the pool depth and manometer reading and then sampling the temperature, and flowrate for five seconds at a sampling rate of 10 Hz. The second type was while lowering or ra i s i n g the depth of the pool, sampling the pressure (from the transducer), temperature and flowrate for 50 seconds at a sampling rate of 1 Hz. 2.6.6 Photographic' Studies Film footage was shot of the regimes using a Bolex 16 mm cine camera (at 24 frames per second). This f i l m was used for i n i t i a l analysis of the regimes, with s p e c i f i c frames of interest developed for presentation purposes. A HaRco Mini-Max Model CTC-3000 black and white video camera was used for the preparation of a video cassette describing the regimes. S t i l l pictures of some regimes were taken with a standard 35 mm camera using 400 ASA black and white f i l m . 25 2.7 Assembly And I n i t i a l Testing The components of the c i r c u l a t i o n loop were assembled and the loop f i l l e d with tap water. The heat exchanger response was tested with the c i r c u l a t i o n pump running. Leaks in the system were noted and subsequently repaired. A small amount of Freon was then tested in the c i r c u l a t i o n loop to observe whether vapour-locking and cav i t a t i o n would seriously impair pump performance. Some problems occurred when the Freon flowrate was reduced for a lengthy period of time, when the l i q u i d temperature was near ambient. Occasionally the pump would seize, but i t was repaired simply by dismantling the l i q u i d end of the pump and prying loose the p l a s t i c impellor assembly from the casing. The roughened surfaces were then sanded smooth" and the pump re-assembled. Subsequently the siphon loop was assembled and tested with both water and Freon. After running water in the apparatus, i t was found that i t was impossible to completely drain the system. Condensation alone would leave small amounts of water in the piping. This water then could then f i n d i t s way to the vapour-liquid interface in the vacuum chamber (Freon-11 and water are immiscible) where i t s entrainment would grossly a f f e c t 26 a n y o b s e r v e d f l o w r e g i m e s . I t was f o u n d a t t h i s s t a g e t h a t u s i n g a n a c c u m u l a t o r t a n k a s a b u f f e r p r o v i d e d much b e t t e r v a c u u m c o n t r o l t h a n d i r e c t - c o u p l i n g t h e v a c u u m pump t o t h e v a c u u m c h a m b e r . T h e i n s t r u m e n t a t i o n was t h e n i n s t a l l e d a n d t h e d a t a a c q u i s i t i o n p r o g r a m w r i t t e n . F i n a l l y t h e f l o w c o n d i t i o n i n g e l e m e n t s w e r e p l a c e d i n t h e v a c u u m c h a m b e r , a n d t h e a p p a r a t u s was r e a d y f o r t h e c o l l e c t i o n o f d a t a . 27 III . PROCEDURE 3.1 Routine Experimental Preparation After several test runs using water as the working f l u i d , a routine procedure was developed for placing the Freon into the system while minimizing the presence of water and other contaminants. The procedure, r e f e r r i n g to Figure 4, was to: (1) - drain the piping. (2) - disconnect the unions coupling the piping to the vessels, and empty a l l vessels. (3) - remove any residual s o l i d s from the vessels, ( i e . rust and chips of p l a s t i c ) and wipe clean a l l surfaces of any grease and d i r t with rags soaked in Freon. (4) - disconnect the heat exchanger and blow out residual water from any low spots that did not drain completely. (5) - reconnect the piping. (6) - pour the Freon through a clot h f i l t e r placed in a p l a s t i c funnel, into the overflow vessel. Gravity causes the l i q u i d to flow down through the c i r c u l a t i o n loop to the lower vessel, priming the pump. 28 (7) - turn on the heat exchanger by opening valve V5 (Figure 4). This allows the Freon to pick up some i n i t i a l subcooling, which minimizes evaporation in the vessels and prevents c a v i t a t i o n and vapour-lock during pump startup. (8) - c i r c u l a t e the Freon u n t i l i t achieves i t s maximum possible subcooling. (9) - shut the c i r c u l a t i o n pump down and skim off any v i s i b l e water and contaminants present in the lower vessel, where they have now accumulated. It was found that most of the v i s i b l e s o l i d contaminants were attracted to thi s thin f i l m of water, and were e a s i l y removed. It soon became evident that complete removal of the water was not required as the pump suction tended not to entrain and c i r c u l a t e these impurities when the amounts present were very small. It was necessary to externally prime the pump during water runs using the priming connection at valve V3. Air - l o c k s prevented the gravity flow of water from the overflow vessel down to the lower vessel. However, as mentioned previously i t was not required to externally prime the pump when running Freon, probably due to i t s lower surface tension. The vacuum chamber and test section were aligned 29 and l e v e l l e d and the video equipment and l i g h t i n g given f i n a l preparation. The data ac q u i s i t i o n system was "signed on" and the computer program prepared for execution. The vacuum accumulator tank was then evacuated with the vacuum pump to approximately 50 kPa. The siphon loop was then primed to the desired pool depth by closing valve V8 and opening needle valve V7. A large amount of vapour was generated and lo s t (through the vacuum pump) during t h i s i n i t i a l period as the vacuum chamber and test section were cooled to the temperature of the Freon. Subsequently a small amount of gas was bled continuously from the vacuum chamber to account for the removal of any non-condensibles i n i t i a l l y present, a i r leaks, and any steady-state vapour generation. Great care had to be taken to ensure that both ends of the siphon remained submerged below the l i q u i d Freon l e v e l . If either end became uncovered due to a low lev e l in either the overflow or lower vessels, an a i r -Freon charge would shoot up into the vacuum chamber as i t became pressurized. The cooling water flowrate was adjusted by t h r o t t l i n g valve V5 to control the amount of subcooling within the vacuum chamber. The variation of cold building supply water temperature with season allowed minimum Freon temperatures of 11°C in winter months, but 3 0 only 13°C in summer months. The maximum Freon temperature observed in the vacuum chamber was 16°C. Higher temperatures caused excessive vapour generation, which caused stoppage of the siphon flow at the apex due to the absence of l i q u i d . 3.2 Calibration The data a c q u i s i t i o n system used for thi s experiment measured chamber pressure Pch, chamber temperature Tch, and siphon loop flowrate Q, with the chamber pool depth H measured manually. Assuming device l i n e a r i t y , the following relationship existed between the measured voltages read by the data a c q u i s i t i o n system and the variables measured: Pch(Pa) = K1xPV + B1 Tch(°C) = K2xTV + B2 Q( l i t r e s / s ) = K3xQV.+ B3 where PV, TV, and QV were the voltage signals read by the data acqu i s i t i o n system (after attenuation into the 0-1.0 volt D.C. range) and Pch, Tch, and Q were the calculated values (in real units) output to the data f i l e by the computer. K1, K2, and K3 were the 31 c a l i b r a t e d proportionality constants and B1, B2, and B3 were the c a l i b r a t e d y-intercepts. By running the data a c q u i s i t i o n system with several known 'values of Pch, Tch, and Q, the measured values of PV, TV, and QV were entered into a "best f i t " l i n e a r regression program to solve for the six c a l i b r a t i o n constants. 3.3 Measurements With Fixed Pool Depth For the purposes of flow mapping, a reading of chamber pressure, temperature, pool depth and siphon flowrate (or Froude number) was required for each measurement at constant pool depth. For these measurements the pressure transducer signal was neglected and the manometer-indicated value of chamber pressure was used. This calculated value took into account the day-to-day va r i a t i o n in atmospheric pressure. The Freon l e v e l was raised to a desired pool depth where a c h a r a c t e r i s t i c flow regime was occurring by adjusting the chamber pressure using valve V7 and the Froude number using valve V4. Valve V6 was opened to lower the pool depth i f an overshoot had occurred. The cooling water flow was then adjusted u n t i l a small amount of vapour generation had occurred and the Freon reached the desired l e v e l of subcooling. The pool depth 32 and the manometer reading were then entered into the computer. After waiting approximately 30 seconds for any transients to die out, the data ac q u i s i t i o n system (Figure 9) was instructed to record the chamber temperature and siphon flowrate. Time averaged values of the temperature and flowrate were then calculated by the computer. A descriptive code was then entered into the computer which described q u a l i t a t i v e l y the par t i c u l a r regimes observed during the measurement. The presence was noted of entrainment, c a v i t a t i o n , i n c i p i e n t drawdown, upward or downward discharge of vapour and any special c h a r a c t e r i s t i c s of the observed regimes. Comments as to the quality of the p a r t i c u l a r measurement were also recorded. A video recording of each regime was made during t h i s period. 3.4 Measurement Of Downcomer Flowrate Fluctuations The overflow weir in the lower vessel was removed for these measurements and a hot film probe was inserted into the discharge of the test section. The l i n e a r i z e r , spectrum analyzer, and anemometer unit were then turned on and warmed up for at least two hours prior to the taking of data. The Freon was c i r c u l a t e d through the system u n t i l i t reached a temperature of approximately 13°C. The 33 "cold" resistance of the hot fi l m probe was then measured and the operating resistance set at a value of 0.2 ohms higher. The probe was not temperature compensated, therefore care had to be taken to ensure the temperature of the Freon did not vary far from 13°C when measurements were taken. The probe and l i n e a r i z e r were cal i b r a t e d with Freon flowing through the c i r c u l a t i o n loop in a stable l i q u i d phase regime, with the flosensor providing the known flowrate. The l i n e a r i z e r was calibrated by setting the "zero", the "gain", and the "exponent" so that the output voltage from the l i n e a r i z e r was l i n e a r l y proportional to flowrate in the downcomer, with zero flowrate giving zero voltage. The flowrate, pool depth and subcooling were then adjusted in the downcomer u n t i l the largest real time fluctuation was observed on the analyzer. Hardcopy output of the flowrate in the time domain (Froude number vs. time) and in the frequency domain (RMS power vs. frequency) was produced. The frequency domain plot was produced after ensemble averaging 16 time domain plots and performing a spectral analysis for dominant frequencies. The RMS power was formed from the square root of the ensemble average of the squared spectral magnitudes. 34 IV. EXPERIMENTAL RESULTS 4.1 Flow Mapping Typical measurements of regimes obtained at constant pool depth are shown in Figures 10 to 14. The flow regimes are grouped according to the mechanism responsible for the presence of vapour in the entrance, with Figure 14 showing the locus of the most "violent" regime observed. The regimes are mapped on diagrams of dimensionless pool depth vs. Froude number. The subcooling SC present during the measurements i s described s t a t i s t i c a l l y on the diagrams by stating the number of data points N, the range of subcooling of the points ( i f applicable), the average value of subcooling SCAVG and the standard deviation of the values SD. An inset i s included on the diagrams to i l l u s t r a t e the regime being mapped. The results presented cover a range of values for near-saturated Freon-11 (SC less than 45). Re-entrant, rounded, and sharp-edged entrances have been tested. The re-entrant entrance was investigated extensively because i t was the f i r s t geometry tested, when the regimes involved were completely unknown. Also, the re-entrant shape allowed unobstructed flow v i s u a l i z a t i o n at the vena contracta. Figures 10 to 17 show a reference curve from 35 experimental incipient drawdown data of Kalinske [9]. The points c i t e d were from his experiment with air-water flow in a 4.4 cm diameter tube with a sharp-edged entrance. This curve i s an i d e a l i z a t i o n of the drawdown phenomenon as i t applies to air-water flow into a l i q u i d l e v e l below the tube entrance, but at Froude numbers below the bridging flowrate of water. 4.1.1 Incipient Drawdown Figure 10 shows the occurrence of incipient drawdown into the re-entrant geometry, for both low and high ranges of subcooling. The drawdown cone often penetrated into a region containing vapour that had accumulated at the entrance, which caused s i g n i f i c a n t variation in the results (compared to data from previous air-water experiments). The points exhibit a large amount of scatter, p a r t i c u l a r l y at low values of subcooling. Figure 11 shows similar incipient drawdown data for the rounded and sharp-edged entrances. No d i s t i n c t i o n i s made between high and low values of subcooling. The diagram shows a d e f i n i t e trend in that drawdown occurs at lower pool depths for a given flowrate in the rounded geometry than in the sharp-edged geometry. When compared to Figure 10, i t seems that re-entrant drawdown 36 occurs at higher pool depths than rounded and sharp-edged drawdown. The scatter for rounded and sharp-edged entrances i s also s i g n i f i c a n t l y less than for the re-entrant case. Drawdown for the sharp-edged geometry follows very closely the sharp-edged air-water data of Kalinske [9]. Figure 18a shows a picture of the re-entrant geometry during incipient drawdown (at low values of subcooling) with bubbles present at the entrance. The drawdown cone i s well defined despite the presence of bridged annular flow downstream from the entrance. 4.1.2 Onset Of Cavitation Bubbles (OCB) In the flow of a near-saturated l i q u i d in a region above the drawdown curve (in the i n i t i a l absence of vapour), there i s a l i m i t i n g flowrate at a given pool depth where incipient c a v i t a t i o n w i l l occur. An i n f i n i t e s i m a l l y small vapour bubble w i l l nucleate at the vena contracta of the tube entrance. At a given value of subcooling, incipient c a v i t a t i o n is dependent on both the Froude number and the dimensionless pool depth. A curve defining t h i s relationship can be derived after making a few simplifying assumptions (APPENDIX A). Once the f i r s t bubble has formed i t grows in size , eventually forming a ring-shaped cavity of bubbles 37 (similar in shape to a "string of beads") that surrounds the periphery of the tube. The i n i t i a l nucleation sequence is defined here as the "Onset of Cavitation Bubbles" (abbreviated OCB). Successive pictures of t h i s regime in the re-entrant entrance (taken from 16 mm film) are shown in Figures I8d, 18e and I8f. On Figure 12, experimental OCB points have been plotted for the re-entrant geometry, with low and high subcooling as the distinguishing parameter. As expected, nucleation points with high subcooling tend to occur at higher flowrates for a given pool depth than those with low subcooling. There is a large amount of scatter in the points. Figure 13 shows OCB for the sharp-edged entrance, with the parameters of high and low subcooling. Again, points with high subcooling tend to be further to the right (at higher flowrates) on the diagram than those with low subcooling. No evidence of pure c a v i t a t i o n (OCB) from a l i q u i d -only regime was found in the rounded geometry at the flowrates possible in the present study. However, o s c i l l a t i n g vapour bubbles were observed and often persisted at the entrance long after entrainment had occurred. Cavitation was observed at the periphery of the bubbles. 38 4.1.3 Requirements For A Violent I n s t a b i l i t y At the same c h a r a c t e r i s t i c area on the flow map a l l three entrances showed a regime where the i n s t a b i l i t y was subjectively judged to be "violent". Rapid bubble formation, o s c i l l a t i o n , and collapse occurred, accompanied by the r i s i n g and spouting of large bubbles at the pool interface. This general region (but not the boundary) i s shown on Figure 14 as between Froude numbers 0.25 to 0.65 at dimensionless pool depths less than 0.8. In the rounded entrance a large bullet-shaped bubble would move every few seconds between a position at the tube entrance and a position several diameters downstream during t h i s "violent" regime. Vapour would form at the bubble's periphery or wake. When at the upper position vapour would be ejected from the bubble in the form of smaller bubbles which would spout v i o l e n t l y upwards against the roof of the vacuum chamber. Spouting with the re-entrant and sharp-edged geometries was much less severe and the bubbles involved were smaller. Figure 18b shows a picture of this violent regime interacting with a drawdown cone in the re-entrant geometry, and Figure 18c shows a picture from above the re-entrant geometry during spouting. 39 Vapour phase existed everywhere on the diagram where flowrates were higher and pool depths lower than at a previous OCB occurrence. The regime present and the severity of any i n s t a b i l i t y was found to be a function of the p a r t i c u l a r location on the flow map and the value of subcooling at that point. 4.2 C r i t i c a l Pool Depth (CPD) Despite OCB having not yet occurred (due to high subcooling), a regime with o s c i l l a t i n g bubbles was often observed at the various entrances. Entrained bubbles passing through the vena contracta usually triggered t h i s i n s t a b i l i t y . However by r a i s i n g the pool depth (keeping the flowrate constant) a depth was reached where these "semi-trapped" bubbles would r i s e into the chamber or exit down the tube, leaving the entrance free of vapour. The point at which th i s event occurred i s defined here as the " C r i t i c a l Pool Depth" (abbreviated CPD). CPD i s shown for each entrance on Figures 15 to 17. Therefore CPD does not define a flow regime as such, but a region on the flow map that i s path dependent. The CPD region i s a region that must be avoided to ensure that no vapour phase w i l l be present at the tube entrance. Sometimes at high Froude numbers and low values of subcooling (Fr greater than 0.06 and 40 SC less than 20) OCB would occur at higher pool depths than CPD. Physically this meant any unattached bubbles would s t i l l e x i t the tube at CPD, but a small and stable cavitation bubble (OCB) would reappear at the entrance. Figures 15 and 16 show CPD for the re-entrant and rounded entrances at r e l a t i v e l y constant values of subcooling. A "resonant" peak exists for the rounded entrance (Figure 16) at the t r a n s i t i o n between "bubble-up" and "bubble-down" flowrates (at approximately the same flowrates as for the previously mentioned violent i n s t a b i l i t y ) . However in Figure 15, CPD for the re-entrant geometry reached a plateau at the "bubble-up" flowrate and did not decrease rapidly. Figure 17 shows thi s s i t u a t i o n in the sharp-edged entrance, for low and high ranges of subcooling. Subcooling has l i t t l e apparent effect on the size of the region. 4.3 Video Cassette A video cassette was recorded showing these regimes in the three entrances. See APPENDIX C for an index to and a brief description of the regimes, and nominal values of the Froude number, pool depth and subcooling (where applicable). 41 4.4 Downcomer Flowrate Fluctuation A real time plot of downcomer flowrate fluctuation (peak-to-peak) i s shown in Figure 19a. This measurement was taken during the "violent" regime for the re-entrant geometry. The magnitude of fluctuation (as a percentage of the mean Froude number) i s approximately 10%. Figure 19b shows a spectral analysis of the same regime. Taken over a 64 second sampling period, i t shows no dominant spectral frequency other than 60 Hz noise. Figures 20a and 21a show real time plots for the rounded and sharp-edged entrances during the violent regime. Fluctuations of approximately 27% and 15% are shown here. Figures 20b and 21b show a spectral analysis for these two respective entrances, and again no dominant frequencies other than 60 Hz noise are evident. Figure 22a shows steady-state flowrate fluctuation of 80% for the re-entrant entrance. This measurement was of a periodic change between a bridged incipient drawdown regime and a bridged annular flow regime (see Figures 22b and 22c). The low frequency component (0.4 Hz) i s the rate at which the regimes are changing. The type of bridging observed varied from that with a l i q u i d core and vapour annulus, to that with a vapour core and a l i q u i d annulus. The presence of the large 42 vapour space in the regime disqualifies it from further analysis in this project, but it does illustrate how large hydraulic fluctuations (without phase transition) can occur in downcomer flow. 43 V. DISCUSSION OF RESULTS 5.1 Qualifying Remarks A clear statement of the l i m i t a t i o n s of the experimental method used must be made before a detailed quantative or q u a l i t a t i v e description of the observed regimes can be undertaken. This i s p a r t i c u l a r l y true for the material of any investigation where subjective observations of a new or pioneering nature are being made. The experimental data presented in t h i s report represents an attempt to locate the boundaries of certain observed flow regimes on a flow map. The existence of the regimes in the areas adjacent to the boundaries has been v e r i f i e d v i s u a l l y to a much greater degree of certainty than s t a t i s t i c a l l y indicated by the number of data points taken. The quantitative measurement of instantaneous f l u i d properties during an unstable phenomenon, such as a two-phase i n s t a b i l i t y in near-saturated f l u i d , i s very d i f f i c u l t to do accurately. The regimes can change very quickly due to small perturbations in flowrate and pool depth, allowing non-equilibrium regimes to be observed. These regimes would not have been seen i f the changes were made systematically and slowly. A certain amount of swirl was always evident in the 44 chamber pool. A f i n i t e amount of v o r t i c i t y was generated in the f l u i d at the i n l e t to the chamber and any swirl not removed by the flow conditioning elements would grow with time into a large and unpredictable vortex, or whirlpool. Depending on i t s size, the rotational core of the whirlpool could penetrate well down into the downcomer entrance where i t would affect any regimes occurring there. Early in the project a straightening cross was placed over the tube entrance to eliminate t h i s s w i r l . However the boundary layers developed at the cross walls caused s i g n i f i c a n t v a r i a t i o n in regimes (see Figure 23a) as compared to those observed in flow without the straightening cross. Therefore, i t was decided to use straightening vanes located r a d i a l l y away from the tube entrance to minimize (but not eliminate) s w i r l . Measurements taken of regimes where the whirlpool e f f e c t seemed large or s i g n i f i c a n t were neglected. The e f f e c t of trace contaminants in the Freon was an uncontrolled parameter that was watched c l o s e l y . Losses of Freon from the operating batch were made up from a container of unused, "clean" Freon. Thus, contaminants continually accumulated in the system, and by the end of the experimental work the Freon had become " d i r t i e r " , with a s l i g h t yellow tinge not o r i g i n a l l y observed. Contaminants that act as surface-active 45 agents are thought to i n h i b i t bubble coalescence, however there seemed to be no systematic va r i a t i o n of the degree of saturation observed (at a given chamber pressure and temperature) over the time period. The presence of a large bridged vapour cavity trapped at the entrance required an extra parameter (the size of the cavity) to characterize f u l l y the regimes. The flowrate became dependent on the shape and size of the vapour region, and independent of chamber pressure. This cavity usually formed at high flowrates, when the chamber pressure became high enough to force the tube l i q u i d l e v e l (defined at zero flowrate at the same chamber pressure) below the tube entrance. This cavity nucleated as a normal ring-shaped set of c a v i t a t i o n bubbles (OCB), but after a short period of growth i t became attached to the tube wall (Figure 23b). The cavity grew a x i a l l y down the tube u n t i l the vapour detached from the wall, forming a large bubble in the center of the tube. Measurements were neglected when the vapour cavity became large enough that a decrease in chamber pressure did not cause an increase in pool depth. When the vapour cavity occupied the core of the tube, violent up-venting of large bubbles was observed (Figure 23c) over a wide range of flowrates. A stationary vapour cavity was not observed in the 46 rounded entrance but was seen frequently in the re-entrant and sharp-edged geometries. 5.2 Experimental Error It i s important in the measurement of these regimes to have a good estimate of the type and size of the experimental error involved. The three types of error involved in this work were instrumentation errors, time lapse errors, and judgement errors. Instrumentation errors were those which described the accuracy of measurement of the p a r t i c u l a r transducers and measuring devices. Included were the assumptions of l i n e a r i t y made during the c a l i b r a t i o n process. These errors were r e l a t i v e l y easy to determine using both the manufacturers' figures and errors estimated during the c a l i b r a t i o n procedure. In APPENDIX B an estimate of th i s type of error (using uncertainty analysis equations quoted in [15]) i s ; Fr ± 0.01, SC ± 1.17, and H/D ± 0.04. Time lapse errors resulted from a delay in taking a measurement of a f l u i d property. This usually happened when a pool depth and manometer reading were taken manually, just before the data a c q u i s i t i o n system recorded the chamber temperature and Froude number. Although hard to quantify, t h i s type of error was 47 thought to be quite small. Inconsistencies in judgement were inevitable when attempting to distinguish the t r a n s i t i o n from one regime to another. This t h i r d type of error was also hard to quantify and at times was probably large. The experimenter who made the observations and judgements, also turned on the l i g h t i n g , activated the video recorder and adjusted the flowrate, pool depth, chamber pressure and temperature. Performance of these tasks while c o n t r o l l i n g an extremely unstable flow regime made a compromising of the qual i t y of subjective measurement inevitable. 5.3 Incipient Drawdown . Pinpointing the location of drawdown entrainment was a very important objective since entrainment of saturated vapours was one of the mechanisms responsible for triggering the i n s t a b i l i t y . Incipient drawdown has been idea l i z e d as a regime where the liquid-vapour interface changes instantaneously from a planar surface into a pointed cone as the downcomer flowrate i s increased. Actually (for a given pool depth) a drawdown cone of some type existed over a small range of flowrates. To consistently determine the exact location of the f i r s t 48 entrainment requires sophisticated procedures (for example those used by Harleman [8]) which did not seem warranted for thi s project. The measurement of incipient drawdown in f l u i d s with low values of subcooling was much more complicated than in the standard case of air-water flow (with high values of water subcooling). Because of the presence of vapour in the downcomer, the flow "saw" a lower e f f e c t i v e pool depth* than a c t u a l l y existed. This gave ri s e to incipient drawdown (entrainment) at much higher pool depths than otherwise expected. The e f f e c t of subcooling on incipient drawdown for the re-entrant geometry can be interpreted from Figure 10. When incipient drawdown occurs, higher pool depths (at a given flowrate) can be expected at low values of subcooling. The drawdown curve for the rounded entrance (Figure 11) was much lower (higher flowrates for a given pool depth) than for the other geometries. This c o n f l i c t s with the data presented by Harleman, who reported no s i g n i f i c a n t difference between the curve for rounded and sharp-edged geometries. However, Harleman used a much sharper parabolic entrance curvature. Since a rounded entrance w i l l carry a larger flowrate (at a given pool depth) than a sharp-edged entrance, i t seems probable the same tendency should occur for drawdown. 49 The drawdown cone was much "wider" in the rounded entrance than in the other geometries since the drawdown cone tended to follow the entrance curvature. This again c o n f l i c t s with the findings of Harleman who stated the cones were geometrically similar in a l l entrances. Kalinske [9] has reported that the re-entrant entrance has a lower drawdown curve than the sharp-edged entrance. This does not seem to be confirmed by the data presented in Figures 10 and 11, although the presence of vapour phase (in near-saturated flow) makes any dir e c t comparison of l i t t l e use. A sketch of the streamlines in the three respective entrances (liquid-only flow) i s shown in Figure 24. Of par t i c u l a r significance are the large separation eddies present at the vena contracta for the re-entrant and sharp-edged geometies but not for the rounded geometry. The lack of eddies in the rounded entrance explains why bubbles did not become attached at the vena contracta. There was a much greater tendency for bubbles to become trapped (at a l l entrances) in Freon-11 flow than in air-water flow. This was due p a r t i a l l y to the lower v i s c o s i t y and surface tension of the Freon and to cavitation effects at the vena contracta. 50 5.4 Onset Of Cavitation Bubbles (OCB) Cavitation i s the mechanism that distinguishes the v e r t i c a l downflow of near-saturated l i q u i d from that of l i q u i d at higher values of subcooling. As mentioned in the introduction, the s t a t i c pressure gradient in the downflowing l i q u i d can have a minimum value at the vena contracta. This occurrence depends on the value of the l o c a l v e l o c i t y head at t h i s point. The v e l o c i t y gradient at the entrance could be obtained by potential flow methods or by solving the Navier-Stokes equations numerically for each entrance geometry. The amount of approximations made necessary to solve for the flow f i e l d may make the f i n a l result of l i t t l e p r a c t i c a l s i gnificance when small amounts of vapour are present. However, by making the same simplifying assumptions as stated in APPENDIX A one can predict the general shape of an OCB curve on a diagram of dimensionless pool depth vs. Froude number (at a given value of subcooling and chamber pressure). Theoretical curves for d i f f e r e n t values of subcooling are shown for the case without entrainment in Figure 25a and the case with entrainment in Figure 25b. Note the predicted s e n s i t i v i t y of OCB to changes in subcooling that are small compared to the experimental error (SC ± 1.17). There were several factors that caused deviations 51 from these theoretical curves. At the vena contracta the pressure was higher at the tube centerline. than at the - tube wall. This gradient channelled the f l u i d into the v e r t i c a l d i r e c t i o n and explained why OCB occurred close to the tube wall (Figure I8d). As expected, OCB was very sensitive to the presence of nucleation s i t e s . Small undissolved vapour or gas bubbles (previously entrained by the flow in a drawdown or whirlpool) caused OCB while t r a v e l l i n g into the vena contracta. The s e n s i t i v i t y of OCB to nucleation s i t e s explains the large amount of scatter near the drawdown curve observed for a l l three entrances. It was found that OCB was very sensitive to non-equilibrium e f f e c t s . It was d i f f i c u l t to increase the flowrate (at constant pool depth) slowly enough to pinpoint the location of OCB. This was p a r t i c u l a r l y true at high values of subcooling where v e l o c i t i e s became very large at the vena contracta. The f i r s t bubble quickly grew in size after i t was generated at the vena contracta. A rapid conglomeration of other bubbles quickly formed and converged around the inside of the tube, without any s i g n i f i c a n t change in pool depth or flowrate. In a few seconds the equilibrium conditions changed from a liquid-only regime to one where a ring-shaped vapour cavity surrounded the periphery of the tube. The vapour region grew larger as 52 the flowrate increased. Eventually some of the bubbles detached from the ring and moved either up or down the tube. After an OCB occurrence the bubbles did not necessarily collapse at the same flowrate where they i n i t i a l l y formed. Hysteresis of this type, between desinent and incipient c a v i t a t i o n has been reported previously, for example Knapp [ 3 ] . It would seem that OCB should occur at s l i g h t l y lower flowrates for the re-entrant than for the sharp-edged geometry. The more pronounced change in d i r e c t i o n (as the l i q u i d flows over the protruding tube) causes a more severe vena contracta. This trend lacks s t a t i s t i c a l significance considering the number of data points taken. The re-entrant geometry protruded well above the false floor and allowed unobstructed v i s u a l i z a t i o n of OCB. There was a s i g n i f i c a n t amount of obstruction when looking hor i z o n t a l l y at the rounded entrance. However from a viewpoint well above the false floor the complete entrance could be seen, and no evidence of OCB was observed at the flowrates tested. The absence of ca v i t a t i o n was not surprising considering the smooth curvature of the entrance. The sharp-edged entrance was the most d i f f i c u l t to work with although OCB could s t i l l be seen e a s i l y from above. 53 5.5 Requirements For A Violent I n s t a b i l i t y A l l three entrances displayed a regime where several small bubbles (from previous entrainment or cavitation) o s c i l l a t e d up and down at the tube entrance. This regime occurred in the up-down t r a n s i t i o n a l range of flowrates for bubbles at the entrance. Some bubbles would r i s e out of the entrance, to be replaced by vapour generated at the periphery of bubbles already present. V e r t i c a l segregation of bubbles would take place according to the size , shape and location of the bubbles. Small bubbles tended to be spherical and had small r i s e v e l o c i t i e s while large bubbles tended to be bullet-shaped and had large r i s e v e l o c i t i e s . The location of the ca v i t a t i o n varied and was hard to discern as there was no fixed cavity attached to the wall. The regime looked similar to nucleate b o i l i n g but without the temperature gradient in the tube. This o s c i l l a t i o n was observed at Froude numbers between 0.25 and 0.50 at pool depths s l i g h t l y above the drawdown curve. Raising the pool depth usually resulted in a lowering of the frequency of o s c i l l a t i o n , but also caused an increase in the size of the bubbles and the severity of the regime. Often a drawdown cone could be seen p e r i o d i c a l l y interacting with the o s c i l l a t i n g bubbles. The drawdown cone would appear as a r i s i n g 54 bubble h i t the pool interface, and then would disappear. When at i t s greatest severity t h i s regime was the primary component observed in the regimes subjectively judged to be "violent". 5.6 The Up-Down Transition The t r a n s i t i o n a l flowrate between bubbles being expelled upwards (bubble-up) or expelled downwards (bubble-down) i s defined here as the "up-down" t r a n s i t i o n . This t r a n s i t i o n has been observed to move to the right (to higher flowrates) with increasing pool depth. This trend can be explained by the larger hemispherical area made available to the flow as the depth increases, which results in lower downward v e l o c i t i e s in the pool. This in turn allows upward buoyancy forces on the bubbles to predominate at higher flowrates. Negligible bubble penetration down the tube was observed at flowrates below the up-down t r a n s i t i o n , while at higher flowrates penetration depended upon the p a r t i c u l a r entrance regime. The v e l o c i t y of the spouting bubble at the pool interface tended to be greater for larger pool depths, as the bubble had more time to accelerate upwards to i t s terminal v e l o c i t y . 55 5.7 C r i t i c a l Pool Depth (CPD) CPD was s i g n i f i c a n t as i t emphasizes the importance of the up-down t r a n s i t i o n on the presence of vapour in the tube. In a constant l e v e l process (with increasing flowrate) vapour phase i n i t i a l l y forms at OCB, but to eliminate vapour completely the process must f i r s t pass outside the OCB and CPD regions. At high values of subcooling a tendency for the vapour bubbles to collapse and/or shrink in size should e x i s t . In the l i m i t (at very high values of subcooling) bubbles should readily collapse. Those that do not (due to the presence of non-condensibles) should readily self-vent as in the case of air-water flow. Yet at low values of subcooling excess vapour would ac t u a l l y be generated. These tendencies should cause a shrinkage of the CPD region at high values of subcooling. This is not shown by the data in Figure 17, perhaps due to the r e l a t i v e l y small range of subcooling examined, or to the large amount of non-condensibles present at high values of subcooling. In the re-entrant entrance with i t s pronounced vena contracta (Figure 24a), only bubbles on streamlines d i r e c t l y above the entrance w i l l be affected by the maximum l i q u i d v e l o c i t y . Therefore at a given flowrate the tendency is smaller for bubbles in the general area 56 above the entrance to be swept down the tube. The plateau observed on the CPD curve in Figure 15 is explained by this phenomenon. The opposite of th i s e f f e c t explains why the up-down t r a n s i t i o n seems to occur at lower flowrates in the rounded entrance (Figure 16). As mentioned in the previous chapter CPD i s p a r t i c u l a r l y s i g n i f i c a n t for the rounded entrance near the up-down t r a n s i t i o n . As the pool depth i s raised near the CPD curve, a large bullet-shaped bubble (with a diameter nearly that of the tube) formed from merging smaller bubbles. The bubble would o s c i l l a t e (every few seconds) between two positions; one several diameters downstream from the entrance and one at the entrance (Figures 26a and 26b). Severe spouting took place when the bubble was at the upper position (low hydrostatic pressure). Liquid droplets were thrown up against the roof of the chamber by r i s i n g bubbles generated in and ejected from the large bubble. A smaller amount of vapour was also evolved in the lower position but most bubbles coalesced or were swept through the tube. This regime continued i n d e f i n i t e l y as long as vapour was generated from the lower periphery or wake of the bubble. T a i t e l [16] observed a similar regime in upward co-current gas-liquid flow. This entry region phenomenon, described as an o s c i l l a t o r y motion of 57 "Taylor" bubbles, was c l a s s i f i e d as "churn" flow. 5.8 Bubble Rise Velocity In The F u l l y Developed Region Simpson [1] has reported that for bubbles roughly the size of the tube diameter, the up-down t r a n s i t i o n in the f u l l y developed region of the tube should occur at approximately Froude number 0.31. During the project t h i s phenomenon was v e r i f i e d for the case of air-water flow, but i t did not correlate well with the observed flow of Freon-11. Large bubbles were frequently trapped in the tube around Froude number 0.46. A large amount of segregation occurred at th i s Froude number with only the very large bubbles remaining stationary. The difference in flowrates could be explained by the fact that (in near-saturated Freon) i t was impossible to iso l a t e a large bubble in the tube. The constant merging and separation of larger bubbles with smaller bubbles, and the momentum interchange during c o l l i s i o n , probably had a s i g n i f i c a n t effect on the buoyancy forces involved. The difference in v i s c o s i t y between Freon-11 and water should have been i n s i g n i f i c a n t since the flow was turbulent (Reynolds numbers varied from 9500 to 57,000 as the Froude number ranged from 0.2 to 1.2). 58 5.9 Expected Behaviour At High Values Of Subcooling When the i n s t a b i l i t y i s plotted on three dimensional axes of dimensionless pool depth vs. Froude number vs. dimensionless subcooling, a three-dimensional volume (bounded by OCB and incipient drawdown surfaces) similar to Figure 27 i s expected to e x i s t . Only at low values of subcooling i s the up-down tr a n s i t i o n under the surface of the OCB curve, where the vapour phase can readily accumulate at the entrance. The OCB surface moves to higher Froude numbers as the subcooling i s increased. Incipient drawdown has been ideal i z e d as independent of subcooling. 5.10 Downcomer Flowrate Fluctuation Interpretation of the anemometer signals must account for the low frequency o s c i l l a t i o n produced by the experimental procedures. Therefore, the real time plots were usually quite indicative of the true ve l o c i t y f l u c t u a t i o n , but the frequency analysis (performed over 64 seconds) may have picked up some of these low frequency components. With the exception of Figure 20 the amount of vapour that . penetrated down the tube was n e g l i g i b l e in these measurements. In Figure 20 vapour bubbles passing 59 by the anemometer probe caused fluctuations in the l i q u i d v e l o c i t y at the probe, especially i f the bubble was large. These fluctuations generally occurred randomly at low frequencies and were neglected in the frequency analysis. A "violent" regime was picked for th i s measurement for each entrance. The magnitude of fluctuation was found to be less than 27% of the mean Froude number in each case, thus suggesting that the e f f e c t of the entrance i n s t a b i l i t y on the l i q u i d phase flowrate was small. A large amount of t h i s fluctuation may have been free stream turbulence present in any pipe flow at the same Reynolds number. However as mentioned in the previous chapter, t h i s does not mean that hydraulic i n s t a b i l i t i e s due to p e r i o d i c a l l y changing regimes could not cause fluctuation of up to and greater than 80% of the mean flowrate. Inferences cannot be drawn as to the r e l a t i v e magnitude of the regime i n s t a b i l i t i e s in each geometry without further measurements, but the preliminary findings suggest the rounded entrance as the most prone to flowrate fluctuation. 60 VI. CONCLUSIONS 6.1 General Two-phase i n s t a b i l i t i e s have been observed at a downcomer entrance in an experimental r i g that drains near-saturated Freon-11 from a vessel. Regimes studied have been r e s t r i c t e d to those without noticeable swirl and without a large bridged vapour space. In t h i s study the regimes have been characterized for the f i r s t time, using dimensionless parameters describing the pool depth, downcomer flowrate and the subcooling at the l i q u i d interface in the pool. Downcomer entrance geometry has been varied as an independent parameter. A video recording has been made of the regimes for future reference. The two primary mechanisms involved in the i n s t a b i l i t y were entrainment and c a v i t a t i o n . The entrainment regimes observed in t h i s study can be correlated with the previously documented occurrence of air-water incipient drawdown. Drawdown was observed at higher pool depths than was expected (at a given flowrate) when vapour bubbles were present at the entrance. Cavitation, the mechanism responsible for bubble formation and growth, has been found to be very susceptible to the presence of nucleation s i t e s and to the amount of subcooling at the pool interface. 61 The up-down t r a n s i t i o n , at flowrates where the lo c a l v e l o c i t y at a point in the entrance i s equal to the r i s e v e l o c i t y of a pa r t i c u l a r vapour bubble, has been found to be a very important physical phenomenon. When coupled with the generation of vapour through entrainment and ca v i t a t i o n , a flowrate near th i s t r a n s i t i o n makes the i n s t a b i l i t y very severe. Bubbles conglomerate at the entrance, with the vapour having no mechanism for escape from the region. Some segregation occurs, with small bubbles expelled downwards and large bubbles expelled upwards. In general, the observed regimes in the re-entrant and sharp-edged geometries were s i m i l a r . The flow regimes in the rounded geometry were unique due to the effe c t of the streamlined curvature reducing ca v i t a t i o n at the entrance. 6.2 Incipient Drawdown The experimental results for inc i p i e n t drawdown show considerable scatter with the re-entrant geometry, p a r t i c u l a r l y at low values of subcooling. This i s explained by the interaction between the drawdown cone and vapour bubbles, commonly found at the entrance at low subcooling. 62 The incipient drawdown curve for the sharp-edged geometry behaves roughly as predicted in previous a i r -water work [9], while the rounded geometry exhibits a lower curve than was expected. Bubbles rarely attached themselves to the tube in the rounded entrance because i t had a much less severe vena contracta than the re-entrant and sharp-edged geometries. 6.3 Onset Of Cavitation Bubbles (OCB) It was d i f f i c u l t to delineate a complete OCB curve at a given value of subcooling. The s e n s i t i v i t y to subcooling, nucleation s i t e s , and experimental error explain the large amount of scatter. For a given pool depth, ca v i t a t i o n occurs at higher flowrates with higher values of subcooling. The general shape of an OCB curve can be predicted from th e o r e t i c a l considerations. Cavitation from an i n f i n i t e s i m a l nucleation s i t e (OCB) was not observed in the rounded entrance at the flowrates attempted in t h i s study. 63 6.4 Requirements For A Violent I n s t a b i l i t y The i n s t a b i l i t y was most severe in the v i c i n i t y of the up-down t r a n s i t i o n for a l l three entrances. During this regime, a high head loss due to f r i c t i o n can be expected in the tube. Severe spouting up into the vacuum chamber has been observed, p a r t i c u l a r l y in the rounded geometry. 6.5 C r i t i c a l Pool Depth (CPD) And The Up-Down Transition Flow mapping of the previously mentioned regimes by i t s e l f cannot predict f u l l y the occurrence of the i n s t a b i l i t y . Some regimes can be triggered by a large disturbance or entrained bubble. This may occur at subcooling higher than normally expected for OCB. To clear the tube of thi s disturbance the flowrate or pool depth must.be changed so that i t no longer f a l l s in the region enclosed by the CPD and OCB curves. This i s a p a r t i c u l a r l y important requirement for the rounded entrance, where OCB does not e x i s t . The CPD curve i s s i g n i f i c a n t in that the peak occurs at the up-down t r a n s i t i o n . This peak seems to occur at lower flowrates and pool depths for the rounded geometry than for the sharp-edged and re-entrant geometries. Because of i t s narrow vena contracta, the 64 re-entrant geometry exhibits more of a "plateau" at high flowrates. The CPD- region should shrink in size at high values of subcooling. This shrinkage was not evident over the small range of subcooling tested. Freon vapour bubbles in the f u l l y developed region of the tube were not trapped at Froude number 0.31 as expected, but at a higher Froude number of around 0.46. 6.6 Sample Theoretical Curves Idealized flow diagrams are shown on Figures 28, 29 and 30 for the re-entrant, rounded and sharp-edged geometries at a common value of subcooling. At higher values of subcooling the OCB curve moves to the right (to higher flowrates) while the CPD and "violent" regions do not move but shrink in s i z e . 6.7 Downcomer Flowrate Fluctuation Fluctuations in downcomer flowrate of up to 27% of the mean Froude number have been observed in the "violent" regime. However, much larger low frequency hydraulic fluctuations can be expected during a periodic change of regimes such as intermittent bridging. 65 VII. RECOMMENDATIONS 7.1 Industrial Design The following guidelines may prove helpful in c o n t r o l l i n g or preventing the violent i n s t a b i l i t y described in this study: (a) - operate at flowrates which avoid the up-down tr a n s i t i o n region ( i e . , avoid Froude numbers from 0.25 to 0.65) using flowrate control (refer to Figures 28, 29 and 30). (b) - raise the value of subcooling in the l i q u i d by lowering i t s temperature or rai s i n g i t s pressure, thus moving the OCB curve to a higher flowrates and shrinking the CPD and "violent" regions (not feasible in evaporator and boiler i n s t a l l a t i o n s where saturation i s a requirement). (c) - use pool depths much greater than the downcomer diameter through l e v e l c o n t r o l . (d) - i f possible provide some means of v i s u a l i z a t i o n of the pool interface or the downcomer entrance. The performance of the downcomer can then be e a s i l y evaluated and modifications made i f necessary. 66 7.2 Further Work 7.2.1 Modifications To The Apparatus And Instrumentation As in any experimental study of a preliminary nature, suggestions for ways to improve the apparatus and instrumentation became obvious upon completion of the work. A smaller c i r c u i t , perhaps using a 1.9 cm diameter test section, and smaller c i r c u l a t i o n pump and piping, would lessen the volumetric requirements of Freon used. Use of a shorter test section, perhaps 1.0 m long, would lessen the vacuum requirements, decreasing the severity of crazing problems in the vacuum chamber. This would be accomplished without compromising s i g n i f i c a n t l y the length-to-diameter r a t i o of the test section. A water-cooled condensor could be placed at the discharge to the vacuum pump to recover part of the Freon vapour losses. This should be attempted only i f i t can be achieved without a large increase in the complexity of the apparatus. Pressure and displacement transducers should be purchased for the accurate and r e l i a b l e measurement of chamber pressure and pool depth using the data ac q u i s i t i o n system, synchronous with the measurement of chamber temperature and siphon flowrate. The f l o a t -67 operated displacement transducer would be mounted inside the vacuum chamber, leaving the experimenter free to make q u a l i t a t i v e observations and to control the regimes. Both of these instruments would probably be very expensive due to the i r stringent s p e c i f i c a t i o n s (Pch ± 100 Pa in 0-101 kPa range and H ± 0.5 mm with a 0-10 cm range). Greater v e r t i c a l difference in elevation (say 1.5 m) should be allowed for between the lower vessel and the pump to lessen cavitation problems at the pump suction. S i m i l a r l y a "U-shaped" loop could be placed in the siphon loop where the l i q u i d leaves the overflow vessel, with the flosensor near the bottom of the loop. This would provide greater subcooling at the flosensor, completely ensuring no ca v i t a t i o n occurred on the paddlewheel. A large, e a s i l y regulated needle valve should be used to control flow in the siphon loop. As small changes in flowrate are s i g n i f i c a n t , i t i s important that the eff e c t s of a small change in valve position be predictable, and adjustments e a s i l y made. A temperature compensated probe should be used for flowrate fluctuation measurement, thereby eliminating the e f f e c t of changes in l i q u i d temperature on the indicated v e l o c i t y . 68 7.2.2 Further Areas Of Study The results presented here should be independently v e r i f i e d , preferably using a d i f f e r e n t f l u i d and di f f e r e n t diameter of downcomer. Further topics that should be investigated i f the i n s t a b i l i t i e s are to be completely understood are: (a) - further measurement of flowrate fluctuation (in the various regimes) for each entrance (b) - the effect of a large uncontrolled whirlpool on the observed regimes (c) - the effect of a horizontal entrance leading to a downcomer (d) - minimizing the effect of the i n s t a b i l i t y with s p e c i a l l y designed entrances (e) - the interaction and feedback between the downcomer flowrate and pressure fluctuations, and the two-phase regimes present at the entrance (f) - the effect of the size, shape and location of the large bridged vapour space parameter on any observed regimes (g) - using potential flow techniques [10], solve for the velo c i t y f i e l d s for several entrance geometries. Using t h i s information, predictions can be made for the flowrate at incipient c a v i t a t i o n and the 69 f l o w r a t e s a t w h i c h t h e u p - d o w n t r a n s i t i o n o c c u r s . 70 I ENTRANCE INSTABILITY -DOWNCOMER VACUUM PUMP -SATURATED VAPOUR SATURATED LIQUID AND VAPOUR FROM PROCESS SATURATED LIQUID -CONDENSATE TANK •** cH— - C O N D E N S A T E RETURN TO PROCESS F i g u r e 1 - I n d u s t r i a l Example Of The I n s t a b i l i t y (Steam and C o n d e n s a t e ) . 71 Pch ft i H/D -LIQUID LEVEL AT F r • O 0-25 REGION WHERE F r DEPENDS ON H/D AND Pch INACCESSIBLE REGION  F r Figure 2 - Incipient Drawdown With Liquid Level At Downcomer Entrance (Air-Water). 72 Figure 3 - Incipient Drawdown With Liquid Level Below Downcomer Entrance (Air-Water [9]). VCR 4 16 mm PHOTOGRAPHIC EQUIPMENT KJ38 II11 loo www SIPHON-LOOP V4 3 ^ TEST SECTION H (2-54 cm 0x|83cmLG.) -VACUUM CHAMBER 0 V7 V8 VACUUM PUMP TO ATM. I r TO MANOMETER VACUUM ACCUMULATOR V6 PRESS. TRANSD H I TEMP. PROBE h-f FLOSENSOR I NEFF PDP-11 D.A.S. MINI. HOT FILM PROBER CONSTANT TEMPERATURE ANEMOMETER LOWER VESSEL LINE ARI2ER FFT ANALYZER M CIRCULATION LOOP PLOTTER CIRCULATION PUMP F igure 4 - Experimental Schematic. Figure 75 PLAN rPOLYCARBONATE BELL JAR gure 6 -ELEVATION D e t a i l s Of Vacuum Chamber. ALL DIMENSIONS IN cm 13 0 (TYP.) V 2-54 I. D. x 183 LONG GLASS TUBE (TYP.) 45° (TYP.) -2-54 1—1-3 2-54R CTi 7a SHARP-EDGED 7b RE-ENTRANT 7C ROUNDED MAT'L : ALUMINUM t ALL DIMENSIONS IN cm Figure 7 - Downcomer Entrance Geometries. ( 7 a - sharp-edged, 7b - re-entrant, 7c - rounded) r 77 Figure 8 - Constant Temperature Anemometer Schematic. 78 r PROMPT FOR: DATE. Patm. CONTROL CHARACTER ( C O SCAN •' - SAMPLE Pch. Tch, Fr g> 1 0 Hz FOR 50 SECONDS PROMPT FOR: H, Pch (MANOMETER) I SCAN:-SAMPLE Tch. Fr g l O H 2 FOR 5 SECONDS I TIME AVERAGE I CONVERT TO REAL UNITS I PROMPT FOR DESCRIPTIVE CODE I NOTE CC * O USED FOR ALL FINAL DATA ACQUISITION OUTPUT DATA AT TERMINAL £ IN OUTPUT FILE • t Figure 9 - Data Acquisition System Schematic. 79 1.6 — air — water • low SC o high SC 1.2 H / D 0.8 0.4 0 0.4 0.8 Froude Number = V/\[QD 1.2 Figure 10 - The E f f e c t Of Subcooling On Incipient Drawdown For The Re-entrant Geometry, (air-water drawdown data from [9], Low SC i s SC £ 9.0, N = 32, SCAVG = 3.9, SD = 2.6, High SC i s SC £ 9.0, N = 8, SCAVG = 16.8, SD = 10.3) 80 1.6 — air — water • shp " V " 1.2 A H / D 0 . 8 Figure 11 - Incipient Drawdown For Rounded And Sharp-edged Geometries. (air-water drawdown data from [9], Rounded (rd) - N = 30, SCAVG = 12.5, SD = 5.6, Sharp-edged (shp) - N = 24, SCAVG = 21.9, SD = 14.5) 81 3.0 2.4 H/D 1.6 0.8 — a ir -water a low SC o high SC 0 1 m. » '///////. 0.4 0.8 Froude Number = v / /gD" 1.2 F i g u r e 12 - The E f f e c t Of Subcooling On The Onset Of C a v i t a t i o n Bubbles (OCB) For The Re-entrant Geometry, ( a i r - w a t e r drawdown data from [ 9 ] , Low SC i s SC <> 9.0, N = 37, SCAVG = 4.8, SD • 2.4, High SC i s SC £ 9.0, N = 13, SCAVG = 18.8, SD = 7.2) 82 3.0 — air - water ° low SC o high SC 2.4 H/D 1.6 0.8 • co 0.4 0.8 Froude Number = V//gD F i g u r e 13 - The E f f e c t Of Subcooling On The Onset Of C a v i t a t i o n Bubbles (OCB) For The Sharp-edged Geometry. ( a i r - w a t e r drawdown data from [ 9 ] , Low SC i s SC £ 9.0, N • 10, SCAVG • 6.2, SD = 2.6, High SC i s SC £ 9.0, N = 4, SCAVG = 12.4, SD - 2.2) 83 1.6 Froude Number = V//gD F i g u r e 14 - V i o l e n t Region For The Re-entrant ( r e ) , Rounded (rd) And Sharp-edged (shp) Geometries. ( a i r - w a t e r drawdown data from [ 9 ] , re - N = 5, SCAVG = 13.0, SD = 15.8, rd - N = 3, SCAVG = 15.5, SD = 3.7, shp - N = 5, SCAVG = 9.3, SD =1.9) 84 2.4 H / D 1.6 0.8 o — air-water o o o o o o o o 0 0.4 0.8 Froude Number = V//gD gure 15 - C r i t i c a l Pool Depth (CPD) For The Re-entrant Geometry. (air-water drawdown data from [9], N = 9, SCAVG = 21.2, SD = 6.4) 85 1.6 air-water Figure 16 - C r i t i c a l Pool Depth (CPD) For The Rounded Geometry. (air-water drawdown data from [9], N = 23, SCAVG = 10.1, SD = 2.1) 86 3.0 2.4 H / D 1.6 0.8 — air - water • low SC o high SC o a o o o o o D • • ( • o ° D D D 0.4 0.8 Froude Number = V/\[QD 1.2 F i g u r e 17 - The E f f e c t Of Subcooling On CPD For The Sharp-edged Geometry. ( a i r - w a t e r drawdown data from [ 9 ] , Low SC i s SC <, 9.0, N = 9, SCAVG = 6.0, SD = 1.2, High SC i s SC * 9.0, N = 9, SCAVG = 19.0, SD = 7.6) 18a 18b 18c 18e 18f Figure 18 - Pictures Of Incipient Drawdown, Spouting And OCB In The Re-entrant Geometry. (18a - drawdown cone and ca v i t a t i o n bubble, 18b - drawdown cone during violent regime, 18c - spouting from above, I8d, I8e, and 18f - OCB at 0, 1.8 and 2.5 sees.) 18d 88 WVrV>rVy^  0 2.0 4.0 6.0 8.0 TIME (SECONDS) 0.0100 0.0075 tr iii o Q. cn 0.0050 0.0025 25 50 75 FREQUENCY (Hz) 100 F i g u r e 19 - Froude Number F l u c t u a t i o n And Frequency A n a l y s i s For The Re-entrant Geometry. (AFr* = 10% (approximately)) 89 0 1.0 2.0 3.0 4.0 TIME (SECONDS) 0.0250 0.0175 tr. Ixi £ 0.0125 co 5 rr 0.0063 1 V 50 100 FREQUENCY (Hz) 150 200 F i g u r e 20 - F r o u d e Number F l u c t u a t i o n A n d F r e q u e n c y A n a l y s i s F o r The Rounded G e o m e t r y . ( A F r * = 2 7 % ( a p p r o x i m a t e l y ) , n o t e - s m a l l b u b b l e s t r a v e r s i n g by p r o b e ) 90 4.8 3.2 o w 1.6 O > 1.0 2.0 3.0 TIME (SEC) 4.0 te. UJ o 0. tn S 0.020 0.015 0.010 0.005 * L 50 100 FREQUENCY (Hz) 150 200 Figure 21 - Froude Number Fluctuation And Frequency Analysis For The Sharp-edged Geometry. (AFr* = 15% (approximately)) 91 '//////A 2 2 b Figure 22 -777777, 77777} 2 2 c 777777A Froude Number Fluctuation In The Re-entrant Geometry During Bridging. (22a - fluctuation (AFr* = 80% (approximately)), 22b - bridging with vapour annulus, 22c - bridging with vapour core) 23a 23b 23c Figure 23 - Miscellaneous Pictures Of The Re-entrant Geometry. (23a - asymmetric spouting occuring with straightening cross, 23b - vapour region attached at vena contracta, 23c - spouting occurring from large bridged vapour space) Figure 24 - Streamline Pattern In Liquid-Only Flow. (24a - re-entrant geometry, 24b - sharp-edged geometry, 24c - rounded geometry) 25a FROUDE NUMBER • V//gTT 25b FROUDE NUMBER « V/VgD~ Figure 25 - Theoretical OCB Curves. Note scale change. (25a - without entrainment, 25b - with entrainment, derived from; H/D = Fr 2/2 - SC with Pch of 76000 Pa (nominal), giving H/D = -118.9 + 7.56Tch + Fr 2/2) 0 o 0 o 0 o o°o 2 6 a 26b Figure 26 - Violent Spouting In The Re-entrant Geometry. (26a - bubble at position near entrance with evolved vapour spouting upwards, 26b - bubble at position below entrance with evolved vapour swept downwards) 0 0.4 0.8 1.2 Froude Number = V/JgD Figure 27 - Expected Behaviour (Three-dimensional Incipient Drawdown At Different Values Of Subcooling. volume bounded by OCB and surfaces) 97 3.2 2.4 0.8 LIQUID PHASE ONLY VAPOUR , VAPOUR BUBBLES/ BUBBLES • " ° ' DOWN • C P D . OCB VAPOUR AND LIQUID PHASE INSTABILITY* ID FLOW IMPOSSIBLE IN THIS REGION 0.4 0.8 Froude Number = V/^gD 1.2 gure 28 - Idealized CPD For The Re-entrant Geometry At SC=9. (the OCB curve i s the location of cav i t a t i o n from pure l i q u i d phase, and CPD i s the depth that must be exceeded to expel any previously entrained or generated vapour) 98 3.2 LIQUID P H A S E ONLY 2.4 H/D 1.6 0.8 0 FLOW IMPOSSIBLE IN THIS REGION 0.4 0.8 Froude Number = V//gD 1.2 F i g u r e 29 - I d e a l i z e d CPD For The Rounded Geometry At SC=9. (CPD i s the depth that must be exceeded t o ex p e l any p r e v i o u s l y e n t r a i n e d or generated vapour) 99 3.2 2.4 H / D 1.6 0.8 LIQUID PHASE ONLY • I / • VIOLENT » INSTABILITY / C P D VAPOUR / VAPOUR BUBBLES • BUBBLES UP / DOWN / / VAPOUR AND LIQUID PHASE ID FLOW IMPOSSIBLE IN THIS REGION 0.4 0.8 Froude Number = V//gD~ 1.2 F i g u r e 30 - I d e a l i z e d CPD For The Sharp-edged Geometry At SC=9. (the OCB curve i s the l o c a t i o n of c a v i t a t i o n from pure l i q u i d phase, and CPD i s the depth t h a t must be exceeded t o expe l any p r e v i o u s l y e n t r a i n e d or generated vapour) 100 BIBLIOGRAPHY 1. Simpson, L. "Sizing Piping For Process Plants", Chemical Engineering, June, 1968, p. 192 - 214. 2. Bergles, A.E., C o l l i e r , J.G., Delhaye, J.M., Hewitt, G.F. and Mayinger, F. Two-Phase Flow And  Heat Transfer In The Power And Process Industries. McGraw-Hill, New York, 1981. 3. Knapp, D. and Hammit, F.G. Cavitation. Engineering Societies Monographs, McGraw-Hill, Toronto, 1970. 4. Souders, M., Corneil, H.G., Emert, F.L. and Huntington, R.L. "Performance Of Bubble-Plate Columns", Industrial and Engineering Chemistry, Vol. 30, 1938, p. 86 - 91 . 5. Oba, R., Ikohagi, T. and Kim, K.T. "Cavitation In An Extremely Limited Flow Through Very Small O r i f i c e s " , International Symposium on Cavitation Inception, ASME Polyphase Flow Committee of Fluids Engineering Divi s i o n , New York, 1979, p. 147 -152. 6. Lienhard, J.H. and Goss, CD. "Influences Of Size And Configuration On Cavitation In Submerged O r i f i c e Flows", ASME Paper 71-FE-39, 1971. 7. Davidian, J. and Glover, J.E. "Development Of The Non-Circulatory Waterspout", Proceedings, ASCE, Journal of the Hydraulics D i v i s i o n , Vol. 82, Paper No. 1038-3, August, 1956, p. 1038-3 -1038-7. 8. Harleman D., Morgan R. and Purple R. "Selective Withdrawal From A V e r t i c a l l y S t r a t i f i e d F l u i d " , 8th Congress International Association For Hydraulic Research, August, 1959, p. 10-C-1 - 10-C-16. 9. Kalinske, A.A. "Hydraulics Of V e r t i c a l Drain And Overflow Pipes", B u l l e t i n 26, University of Iowa Studies, 1939-1940, p. 26 - 40. 10. Vallentine, H. R. Applied Hydrodynamics. Butterworths, London, 1967. 101 11. Kelly, A.G. "Hydraulic Design Of Siphons", Proceeds Institute of Mechanical Engineers, Vol. 180, 1965-1966, p. 981 - 1011. 12. Bharathan, D. "Air-Water CounterCurrent Annular Flow", E l e c t r i c Power Research In s t i t u t e , NP-1165, September, 1979. 13. Wallis, G.B., deSieyes, D.C., R o s s e l l i , R.J. and Lacombe, J . "CounterCurrent Annular Flow Regimes For Steam And Subcooled Water In A V e r t i c a l Tube", EPRI NP-1336, January, 1980. 14. Handbook Of Air Conditioning System Design. Carrier Air Conditioning Company, McGraw-Hill, Toronto, 1965. 15. Kline, S.J., and McClintock, F.A. "The Description Of Uncertainties In Single Sample Experiments", Mechanical Engineering, January, 1953, p. 3. 16. T a i t e l , Y., Bornea, D. and Dukler, A.E. "Modelling Flow Patterns For Steady Upward Gas-Liquid Flow In V e r t i c a l Tubes", AIChE Journal, Vol. 26, May, 1980, p. 345 - 354. 102 APPENDIX A - DIMENSIONAL ANALYSIS Two methods of dimensional analysis are used; (A1) a derivation from a simple model using Bernoulli's equation and (A2) a c l a s s i c a l Buckingham ir analysis AJ_ Bernoulli ' s Equation Note: Po and Vo are the pressure and v e l o c i t y at point "o" Assumptions: (a) - no v e l o c i t y or pressure gradient across the tube (b) - no temperature gradient in the pool or downcomer (c) - no vapour phase i n t i t i a l l y present (d) - no surface tension e f f e c t s (e) - no flow separation or entrainment (f) - no f r i c t i o n a l d i s s i p a t i o n in the pool (g) - thermodynamic equilibrium exists at a l l times (h) - uniform nucleation s i t e spacing Pch 103 Using Bernoulli's equation between the pool interface and point "o" and subtracting Psat Po - Psat = Pch - Psat + pgH - pVo2/2 Dividing by pgD (Po - Psat)/pgD = (Pch - Psat)/pgD + H/D - Vo2/2gD But since Vo2/2gD = Fr 2/2 (Po - Psat)/pgD = (Pch - Psat)/pgD + H/D - Fr 2/2 From t h i s equation we observe: Po - Psat = 0 at incipient c a v i t a t i o n (OCB) (Pch - Psat)/pgD = dimensionless subcooling (SC) H/D = dimensionless pool depth Fr = dimensionless flowrate Therefore, when inc i p i e n t c a v i t a t i o n occurs at the tube entrance SC + H/D - Fr 2/2 = 0 104 A2 Buckingham TT Analysis The relevant independent variables are: Pch - Psat(Tch), p, g, D, H, V, n, a These variables are comprised of the fundamental dimensions [M], [ L ], and [T], Using p, g, and D as the recurring set of variables, the following f i v e dimensionless groups are obtained: TT1 = (Pch - Psat (Tch) )/pgD, TT2 = H/D, TT3 = V(gD)" l / 2, TT4 = ^/(pg^D 3^) , TT5 = a/(pgD 2) Making the same assumptions as in (A1) with the viscous and surface tension forces having no effect on the flow regimes ( i e . the bubbles are large and their r i s e v e l o c i t y i s determined by the tube diameter) the following three dimensionless groups remain: TT1 = SC = (Pch - Psat (Tch) )/pgD, TT2 = H/D, TT3 = Fr = V(gD) - 1 / 2 Note that 7r3/7r4 = Reynolds number and ir3/'(^5)^ = Weber number 1 05 APPENDIX B - SAMPLE CALCULATIONS AND ERROR ANALYSIS Sample C a l c u l a t i o n s NOTE: - f o r e a c h measurement a v a l u e o f H/D, F r a n d SC was c a l c u l a t e d . H a n d AZ (manometer) were r e c o r d e d m a n u a l l y a n d T c h and Q were r e c o r d e d by t h e d a t a a c q u i s i t i o n s y s t e m U n i t s : H, D, AZ (m) P s a t , P c h , Patm ( P a ) V ( m / s ) , Q ( l i t r e s / s ) C o n s t a n t s : p = p ( F r e o n - 1 1 ) = 1500 kg/m 3 a t 15°C ( f r o m [ 1 4 ] ) pw = p ( w a t e r ) = 1000 kg/m 3 D = 0.0254 m, g = 9.8 m/s 2 1 06 Therefore: Fr = V(gD)- 1 / 2 = 4Q/( 1 000TT( 0 . 0254) 2-5 ( 9 . 8 ) ^  ) = 3.96Q H/D = H/0.0254 SC = (Pch - Psat)/pgD With Psat = 2823Tch + 31650 (lin e a r i z e d for small ATch from [14]) Pch = Patm - pwgAZ (AZ from manometer) Error Analysis As stated in [15], i f Y i s the dependent variable and Y = Y(x1,x2...xn), then the uncertainty of the result i s Y ± y with y = [(e19Y/9xl) 2 + (e29Y/9x2) 2 + ...(en9Y/9xn) 2]** where e1 to en are the uncertainties or probable errors of the variables x1 to xn respectively. 1 07 The uncertainty estimates (e's) are: Psat ± 300 Pa (as Tch ± 0.1°C) Pch ± 300 Pa (as AZ ± 0.02 m and Patm ± 100 Pa) Q ± 0.003 l i t r e s / s H ± 0.001 m D ± 0.0005 m Placing these uncertainties into the above equation using p a r t i a l derivatives from the equations defining H/D, Fr and SC, error estimates (y's) are obtained of: AH/D = ± 0.04 AFr = ± 0.01 ASC = ± 1.17 Notes: - fluctuations in chamber pressure prevented reading the manometer with greater than the above mentioned accuracy - t h i s analysis has neglected both time lapse and judgement errors which may be quite large 108 APPENDIX C - INDEX TO VIDEO CASSETTE REGIME NUMBER and PAGE NUMBER (refer to text) ENTRANCE GEOMETRY, REGIME AND COMMENTS #1 - p. 6,7,8 RE-ENTRANT NOTE: - air-water th i s regime only - incipient drawdown in two-component flow - entrainment of a i r bubbles with small spherical bubbles r i s i n g up into the chamber - small vortices v i s i b l e p e r i o d i c a l l y - trapped a i r bubbles r i s i n g through the false f l o o r around the entrance - annular flow (with necking) when the l i q u i d l e v e l i s lowered below the entrance #2 - p. 36,39 RE-ENTRANT NOTE: - Freon-11 i s shown in the following regimes - OCB from a liquid-o n l y regime - triggering of cav i t a t i o n by bubble passing through the vena contracta - violent spouting of r i s i n g bubbles #3 - p. 8 RE-ENTRANT NOTE: - annular flow in a l i q u i d l e v e l well below the downcomer entrance - the lower v i s c o s i t y of Freon-11 w i l l cause a higher flowrate (and more necking) at a given pool depth than in air-water flow - nominal H/D = 0.20, Fr = 0.20 and SC = 11.1 109 REGIME NUMBER and PAGE NUMBER (refer to text) ENTRANCE GEOMETRY, REGIME AND COMMENTS #4 - p. 38,53 RE-ENTRANT NOTE: - a violent i n s t a b i l i t y - flowrate in the up-down tr a n s i t i o n , therefore bubbles accumulate i n , but cannot escape from the entrance region - cavitation occurring throughout the entrance region - nominal H/D = 0.28, Fr = 0.43 and SC = 7.7 #5 - p. 39,45 RE-ENTRANT NOTE: #5a - bubbles formed in OCB cleared by CPD (CPD curve above OCB) - nominal H/D = 1.42, Fr = 0.39 and SC = 4.5 #5b - OCB at high Froude number showing a vapour cavity attached to the tube wall with a l l generated bubbles (small) swept down the tube #6 - p. 38,45 RE-ENTRANT NOTE: - violent regime - an annular cavity (similar to regime #5b forms, and with increasing flowrate the vapour moves to the core of the tube, giving r i s e to spouting at high Froude number - nominal H/D = 1.02, Fr =0.76 and SC = 9.3 1 10 REGIME NUMBER and PAGE NUMBER (refer to text) ENTRANCE GEOMETRY,, REGIME AND COMMENTS #7 - p. 45,38 RE-ENTRANT NOTE: - the annular cavity (#5b) w i l l detach as the flowrate i s decreased into the up-down t r a n s i t i o n area - violent spouting then occurs - the large bubbles (slugs) tend to be bullet-shaped - nominal H/D = 0.71, Fr = 0.39 and SC = 4.1 #8 - p. 53 RE-ENTRANT NOTE: - small bubbles in high frequency o s c i l l a t i o n at verge of cavitation inception - interaction and coalescence of bubbles downstream - the i n s t a b i l i t y becomes more violent with increasing flowrate as the bubbles become larger - eventually a vapour cavity attaches at the entrance - nominal H/D = 0.32, Fr = 0.25 and SC = 3.7 #9 - p. 53,40 RE-ENTRANT NOTE: #9a - OCB with small bubbles swept down the tube - a stationary cavity forms and grows in size u n t i l large bubbles break loose and r i s e (segregation of bubbles due to shape and size) #9b - CPD at "constant" flowrate (the pool depth must be changed very slowly i f the flowrate at the flosensor i s to be equal to that in the downcomer) - OCB returns af t e r the bubbles have cleared (OCB curve above CPD) 111 REGIME NUMBER and PAGE NUMBER (refer to text) ENTRANCE GEOMETRY, REGIME AND COMMENTS #10 - p. 8 RE-ENTRANT NOTE: - necking chokes off the flow as bridging occurs with increasing flowrate - necking i s enhanced by the presence of a cavi t a t i o n bubble at the entrance #11 - p. 53 RE-ENTRANT NOTE: - high frequency o s c i l l a t i o n of small bubbles at low pool depths and flowrates - interaction between o s c i l l a t i n g bubbles and cavi t a t i o n at the entrance - nominal H/D = 0.59, Fr = 0.29 and SC = 5.8 #12 - p. 56,46 ROUNDED NOTE: - violent i n s t a b i l i t y with spouting - similar to "churn" flow [16] - large bubbles remain "mobile" and detached from the wall - vapour generation at periphery of bubble - nominal H/D =1.3, Fr = 0.34 and SC = 22.3 1 1 2 REGIME NUMBER and PAGE NUMBER (refer to text) ENTRANCE GEOMETRY, REGIME AND COMMENTS #13 - p. 49 ROUNDED NOTE: - inc i p i e n t drawdown showing large drawdown cone that follows the curvature of the entrance #14 - p. 38 ROUNDED NOTE: - a large slug of vapour moves between a position at the entrance and a position downstream - a l l generated vapour i s swept down the tube except when the bubble i s at the tube entrance - violent spouting against the chamber roof - penetration of vapour down the tube - nominal H/D = 1.46, Fr = 0.48 and SC = 27.3 #15 - p. 39,45 SHARP-EDGED NOTE: #l5a - violent regime passing through CPD (with "constant" flowrate) - nominal H/D = 0.51, Fr = 0.33 and SC = 11.1 #15b - cavitation triggered by a r i s i n g bubble - the size and shape of a "large" bubble becomes an extra parameter necessary to describe the flow - nominal H/D = 0.91, Fr = 0.61 and SC = 24.8 #15c - incipient drawdown - nominal H/D = 0.35, Fr = 0.36 and SC = 25.6 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0095668/manifest

Comment

Related Items