ON AIR-WATER TWO-PHASE FLOWS IN RETURN BENDS

FEDERAL UNIVERSITY OF SANTA CATARINADEPARTMENT OF MECHANICAL ENGINEERING

Pedro Magalhaes de Oliveira

ON AIR-WATER TWO-PHASE FLOWS INRETURN BENDS

Florianopolis

2013


ESCOAMENTO BIFASICO AR-AGUA EMCURVAS DE 180

Dissertacao submetida ao Programade Pos-Graduacao em Engenharia Mecanicapara a obtencao do ttulo de Mestreem Engenharia Mecanica.Orientador: Prof. Jader Riso BarbosaJr., Ph.D.

Florianopolis

2013

atravs do Programa de Gerao Automtica da Biblioteca Universitria da UFSC.

de Oliveira, Pedro Magalhes Escoamento bifsico ar-gua em curvas de 180 / PedroMagalhes de Oliveira ; orientador, Jader Riso Barbosa Jr.- Florianpolis, SC, 2013. 155 p.

Dissertao (mestrado) - Universidade Federal de SantaCatarina, Centro Tecnolgico. Programa de Ps-Graduao emEngenharia Mecnica.

Inclui referncias

1. Engenharia Mecnica. 2. escoamento bifsico. 3. curvade 180 . 4. queda de presso por atrito. 5. frao de vazio.I. Barbosa Jr., Jader Riso. II. Universidade Federal deSanta Catarina. Programa de Ps-Graduao em EngenhariaMecnica. III. Ttulo.


ESCOAMENTO BIFASICO AR-AGUA EMCURVAS DE 180

Esta Dissertacao foi julgada aprovada para a obtencao do ttulode Mestre em Engenharia Mecanica, e aprovada em sua forma finalpelo Programa de Pos-Graduacao em Engenharia Mecanica.

Florianopolis, 13 de dezembro 2013.

Armando Albertazzi Goncalvez Jr., Dr. Eng.Coordenador do Curso

Banca Examinadora:

Prof. Jader Riso Barbosa Jr., Ph.D.Orientador

Prof. Alvaro Toubes Prata, Ph.D.

Prof. Emilio Ernesto Paladino, Dr. Eng.

Prof. Julio Cesar Passos, Dr.

Prof. Marco Jose da Silva, Dr.-Ing.

Somos duplamente prisioneiros: de nosmesmos e do tempo em que vivemos.

Manuel Bandeira

ABSTRACT

Return bends are found in various applications involving two-phaseflow, including heat exchangers, transport pipes and separators. Gas-liquid flows in bends are affected by centrifugal forces that tend toseparate both phases. If the bend is oriented vertically, the flow is alsosubjected to gravitational effects. The resulting effect of such forcesis a change of the flow configuration as it passes through the bend,which depends on several aspects, such as flow direction (i.e., upwardand downward), curvature, flow rates, and physical properties. Thus,the flow shows a distinct behavior in the return bend if compared toa straight tube. The main objective of this study is the characteri-zation of air-water two-phase flows in 180 return bends that connecttwo 5-m long 26-mm ID horizontal tubes. The bend lies in the verticalposition and the two-phase flow can be set as upward or downward.The behavior of the static pressure downstream and upstream of thereturn bend was measured for a wide range of flow regimes, as wasthe pressure drop and change in gas holdup associated with the returnbend itself. The behavior of the phases in the bend was investigatedwith a high-speed camera, illustrating several particular features of thetwo-phase flow in the bend in both directions. The experiments werecarried out with bend curvatures 2R/d of 6.1, 8.7, and 12.2 in bothupward and downward directions. Superficial velocities varied from 0.2to 40 m/s for the gas, and were set as 0.05, 0.2 and 1 m/s for the liquid.The irreversible pressure changes in the bend were determined basedon the differential pressure and gas holdup measurements, resulting inan empirical correlation. The gas holdup was measured at 12 differentpositions, downstream and upstream of the bend, covering the plug,slug and annular flow regimes in both upward and downward flow di-rections. This allowed a better understanding of the influence of thereturn bend on the flow and the evaluation of flow parameters alongthe axis of the tube.Keywords: two-phase flow, return bend, frictional pressure drop, gasholdup.

RESUMO

Tubulacoes com curvas de 180 sao frequentemente encontradas naindustria em aplicacoes envolvendo escoamentos bifasicos, como tro-cadores de calor e dutos de transporte. Nestes equipamentos, o escoa-mento gas-lquido sofre um efeito centrfugo devido a` curva, que tendea separar ambas as fases. A influencia deste tipo de singularidade eainda mais intensa quando a curva e posicionada na vertical, pois o es-coamento e sujeito a uma complexa combinacao de forcas: centrfuga,atrito e gravitacional. Ainda, o efeito resultante depende de parametrosdo escoamento, como sentido (ascendente ou descendente), curvatura,vazoes e propriedades fsicas. Devido a` acao combinada das forcas,o escoamento apresenta na curva um comportamento distinto daqueleobservado em tubos retos, sendo a sua investigacao o principal obje-tivo deste estudo. Mais especificamente, este propoe-se a caracterizaro escoamento bifasico aragua em uma curva de 180 que conecta doistubos retos de 5,5 m e diametro de 26,4 mm. A curva e posicionadana vertical e o escoamento pode ser imposto nos sentidos ascendentee descendente. Inicialmente, o comportamento da pressao estatica amontante e a jusante da curva foram medidos em inumeras condicoesde escoamento, bem como a queda de pressao e a variacao da fracao devazio entre a entrada e a sada da curva. O comportamento das fases nacurva foram observados com uma camera de alta velocidade, ilustrandoaspectos particulares do escoamento bifasico na curva em ambos sen-tidos. Experimentos foram conduzidos para curvaturas 2R/d de 6,1,8,7 e 12,2 nos sentidos de escoamento ascendente e descendente. Asvelocidades superficiais das fases foram determinadas entre 0,2 e 40 m/spara o ar, e em 0,05, 0,2 e 1 m/s para a agua. A partir da medicaode queda de pressao total na curva e da variacao da fracao de vazio,avaliou-se somente a parcela irreversvel da queda de pressao na curva,resultando em uma correlacao emprica. Em uma segunda parte, afracao de vazio foi medida em 12 pontos posicionados a montante e ajusante da curva, compreendendo os regimes em tampoes, em golfadas eanular, nas direcoes ascendente e descendente, possibilitando uma mel-hor compreensao acerca da influencia da curva no escoamento, alem depermitir avaliacao dos parametros do escoamento ao longo do eixo datubulacao.Palavras-chave: escoamento bifasico, curva de 180, queda de pressaopor atrito, fracao de vazio.

AGRADECIMENTOS

Agradeco ao Professor Jader R. Barbosa Jr., por manter a porta desua sala sempre aberta, pelos rascunhos corrigidos do ttulo ao ultimoponto final, por todas as oportunidades e pela amizade nestes tres anosde pesquisa e trabalho duro.

Aos que, ao meu lado, desenvolveram este trabalho: os alunos de ini-ciacao cientfica Eduardo Strle, Marcos Abe e Rafael Dantas, e ostecnicos Marcelo Cardoso, Marcos Espndola e Pedro Cardoso.

Aos que trocaram suas noites e fins de semana pelo subsolo do POLO.

A todos os colegas de mestrado e de laboratorio com quem tive oprazer de aprender e trabalhar; em especial a Dalton Bertoldi, Gus-tavo Portella e Moises Marcelino, que me guiaram nos meandros dapratica experimental e na construcao do aparato.

Ao Prof. Marco da Silva, Nikolas Libert e Leonardo Lipinski, da Uni-versidade Tecnologica Federal do Parana, por toda a colaboracao e pornos fornecerem os sensores de fracao de vazio, parte fundamental doaparato e que distingue este trabalho.

Ao Prof. Geoffrey F. Hewitt, por gentilmente nos ceder os filmes 16 mmgravados em Harwell em 1971, e ao Helder Martinovsky por nos auxil-iar no processo de telecinagem destes.

A` Petrobras e ao Conselho Nacional de Desenvolvimento Cientfico eTecnologico, pelo suporte financeiro.

A` Maria.

A meus pais e minha famlia.

CONTENTS

1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

1.1 MOTIVATION AND OBJECTIVES . . . . . . . . . . . . . . . . . . . . 25

1.2 OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2 LITERATURE REVIEW. . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.1 TWO-PHASE FLOW IN HORIZONTAL TUBES . . . . . . . . . 27

2.1.1 Pressure drop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.1.2 Gas holdup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.2 TWO-PHASE FLOW IN 180 BENDS . . . . . . . . . . . . . . . . . . 32

2.2.1 Pressure drop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.2.2 Flow behavior and gas holdup . . . . . . . . . . . . . . . . . . . . 39

2.3 SUMMARY AND SPECIFIC OBJECTIVES . . . . . . . . . . . . . 42

3 EXPERIMENTAL APPARATUS . . . . . . . . . . . . . . . . . . . 45

3.1 GENERAL ASPECTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.2 COMPONENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.2.1 Air line, water line and mixing system . . . . . . . . . . . . 47

3.2.2 Test section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.2.3 Measuring devices and techniques . . . . . . . . . . . . . . . . 52

3.2.4 Equipment information . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.3 EXPERIMENTAL PROCEDURE . . . . . . . . . . . . . . . . . . . . . . 61

3.4 VALIDATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.5 A FIRST LOOK AT THE FLOW PARAMETERS . . . . . . . . 63

3.6 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

4 RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.1 VISUAL OBSERVATION OF THE FLOW . . . . . . . . . . . . . . 69

4.1.1 Stratified and wavy flow . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.1.2 Plug and slug flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

4.1.3 Annular flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.2 FLOW PARAMETERS IN THE BEND . . . . . . . . . . . . . . . . . 77

4.2.1 Pressure distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

4.2.2 Gas holdup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.2.3 Frictional pressure drop . . . . . . . . . . . . . . . . . . . . . . . . . . 82

4.3 A FRICTIONAL PRESSURE DROP CORRELATION . . . . 93

4.4 DEVELOPING FLOW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

4.4.1 Gas holdup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

4.4.2 Pressure gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

4.4.3 Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

4.5 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

5 CONCLUSIONS AND FUTURE WORK. . . . . . . . . . . . 107

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

APPENDIX A -- Experimental procedures . . . . . . . . . . . . . 119

APPENDIX B -- Uncertainty analysis . . . . . . . . . . . . . . . . . 127

APPENDIX C -- Movie . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

APPENDIX D -- Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

LIST OF FIGURES

Figure 1 Rendered CAD drawing of the experimental apparatus. 45

Figure 2 Operational range of the experimental apparatus (cross-hatched region) on the Mandhane et al. (1974) flow regime mapfor horizontal flows of air and water at atmospheric pressures in25.4 mm ID tubes.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Figure 3 Schematic of the experimental apparatus. . . . . . . . . . . . . . . 48

Figure 4 Components of the water line. . . . . . . . . . . . . . . . . . . . . . . . . . 49

Figure 5 Components of the air line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

Figure 6 Flow mixers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

Figure 7 Axial view of one of the mixers.. . . . . . . . . . . . . . . . . . . . . . . . 51

Figure 8 Geometric parameters of the tube bends. . . . . . . . . . . . . . . 53

Figure 9 Perspex sleeve used to connect borosilicate tubes to eachother, allowing pressure and temperature measurements. . . . . . . . . . 53

Figure 10 Positions of the pressure taps and gas holdup sensorspositions. The measurements were taken at symmetric locationsbetween the upper and lower tubes. (Dimensions in meters) . . . . . . 54

Figure 11 Set of valves and tubings, absolute pressure sensor anddifferential pressure transducers.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Figure 12 Test section and gas holdup capacitive probes. . . . . . . . . . 58

Figure 13 Details of the capacitive probe. . . . . . . . . . . . . . . . . . . . . . . . . 58

Figure 14 Equivalent electric circuit of the capacitance sensor aspresented by Libert et al. (2011). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

Figure 15 Superficial velocities of the test conditions shown on theMandhane et al. (1974) flow regime map. . . . . . . . . . . . . . . . . . . . . . . . . . 63

Figure 16 Frictional pressure drop in a single-phase (water) flow of(a) bend (2R/d = 8.7) and straight sections upstream and down-stream of it (b) single straight section of 1 m. . . . . . . . . . . . . . . . . . . . . . 64

Figure 17 Gas holdup characteristic signal of (a) plug, (b) slug, and(c) annular flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

Figure 18 Pressure characteristic signal of (a) plug, (b) slug, and(c) annular flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

Figure 19 Liquid mass flow rate (relative) characteristic signal of(a) plug, (b) slug, and (c) annular flow.. . . . . . . . . . . . . . . . . . . . . . . . . . . 67

Figure 20 Gas mass flow rate (relative) characteristic signal of (a)

plug, (b) slug, and (c) annular flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

Figure 21 Flow intermittency in the bend for upward flow with jl= 0.05 m/s, jg = 1 m/s. From left to right, images were taken with a40 ms time interval between consecutive frames. . . . . . . . . . . . . . . . . . . 70

Figure 22 Oscillatory flow in upward direction (low liquid flowrate). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

Figure 23 Plug flow in upward direction. . . . . . . . . . . . . . . . . . . . . . . . . . 71

Figure 24 Phase distribution in upward plug flow (jl = 0.2 m/s, jg= 0.4 m/s). The sequence illustrates the nose and body of a risingbubble. The time interval between frames is 152 ms. . . . . . . . . . . . . . . 73

Figure 25 Phase distribution in downward plug flow (jl = 0.2 m/s, jg= 0.4 m/s). The sequence shows the nose and body of a descendingbubble. The time interval between frames is 532 ms. . . . . . . . . . . . . . . 73

Figure 26 Phase distribution in downward plug flow (jl = 0.2 m/s,jg = 0.4 m/s). The sequence shows the tail of a descending bubble,followed by roughening and breakup of the gas-liquid interface. Thetime interval between frames is 91 ms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

Figure 27 Phase distribution in upward (left) and downward (right)slug flow in the bend (jl = 0.2 m/s, jg = 4 m/s). . . . . . . . . . . . . . . . . . . . 74

Figure 28 Phase distribution for downward annular flow in the bend(jl = 0.2 m/s, jg = 20 m/s), showing the detachment of disturbanceswaves from the film towards the outer part of the curve. Timeinterval between frames is 30 ms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

Figure 29 Phase distribution for upward annular flow in the bend(jl = 0.2 m/s, jg = 20 m/s). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

Figure 30 (a) Pressure distribution in upward flow for 2R/d = 8.7,jl = 0.2 m/s and jg = 0.2 - 30 m/s. (b) Detailed view of the lowgas flow rate data (plug and slug flow regimes).. . . . . . . . . . . . . . . . . . . 78

Figure 31 (a) Pressure distribution in downward flow for 2R/d =8.7, jl = 0.2 m/s and jg = 0.2 - 30 m/s. (b) Detailed view of thelow gas flow rate data (plug and slug flow regimes). . . . . . . . . . . . . . . 79

Figure 32 Measured gas holdup values at top and bottom positionsof the bend for all flow conditions and curvatures of 6.1, 8.7, and12.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

Figure 33 Liquid level at the position of the lower gas holdup probe.Downward flow, jl = 0.05 m/s, jg = 1 m/s. From the top, curvaturesof the bend are 6.1, 8.7, and 12.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

Figure 34 Average gas holdup values in the bend for (a) upwardand (b) downward flow for jl = 0.2 m/s. . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

Figure 35 Components of pressure drop; (a) upward flow, 2R/d =6.1, jl = 0.2 m/s, (b) downward flow, 2R/d = 8.7, jl = 1 m/s. . . . . . 84

Figure 36 Histograms of probability density of the experimentalresults. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

Figure 37 Frictional pressure drop in the bend for upward anddownward flow, curvatures of 6.1, 8.1 and 12.2. (continues in Fig.38) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

Figure 38 ...Comparisons with Chisholm (1983), Chen et al. (2004),Domanski & Hermes (2008), and Padilla et al. (2009). . . . . . . . . . . . . 88

Figure 39 Experimental pressure drop data in (a) upflow and (b)downflow compared to the correlations of Chisholm (1983), Chenet al. (2004), Domanski & Hermes (2008), and Padilla et al. (2009). 91

Figure 40 Frictional pressure gradient in the bend. (a) upward flow,(b) downward flow.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

Figure 41 Correlation based on the two-phase multiplier for thefrictional pressure drop in (a) upward flow and (b) downward flow. 95

Figure 42 Gas holdup distribution in upward and downward flowfor the plug, slug, and annular flow regimes. . . . . . . . . . . . . . . . . . . . . . . 96

Figure 43 Gas holdup distribution for upward and downward plugflow (jl = 0.2 m/s, jg = 0.4 m/s). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

Figure 44 Gas holdup distribution for upward and downward slugflow (jl = 0.2 m/s, jg = 4 m/s). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

Figure 45 Gas holdup distribution for upward and downward an-nular flow (jl = 0.2 m/s, jg = 20 m/s). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

Figure 46 Frictional and accelerational pressure gradients in (a)downward and (b) upward plug flow (jl = 0.2 m/s, jg = 0.4 m/s). . . 100

Figure 47 Frictional and accelerational pressure gradients in (a)downward and (b) upward slug flow (jl = 0.2 m/s, jg = 4 m/s). . . . . . 102

Figure 48 Frictional and accelerational pressure gradients in (a)downward and (b) upward annular flow (jl = 0.2 m/s, jg = 20 m/s). 103

Figure 49 Velocity distribution of Taylor bubbles in upward anddownward plug flow (jl = 0.2 m/s, jg = 0.4 m/s). . . . . . . . . . . . . . . . . . . . 104

Figure 50 Velocity distribution of liquid slugs in upward and down-ward slug flow (jl = 0.2 m/s, jg = 4 m/s). . . . . . . . . . . . . . . . . . . . . . . . . . . 105

Figure 51 Experimental calibration curves of the gas holdup sensorsbased on the stratified regime. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

Figure 52 Experimental calibration curves of the gas holdup sensors

based on the stratified regime. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

Figure 53 Probability density plots of expanded uncertainty of se-lected parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

LIST OF TABLES

Table 1 Coefficient C of Eqs. 2.10 and 2.11 . . . . . . . . . . . . . . . . . . . . . 29

Table 2 Summary of experimental works (bend geometries). . . . . . 42

Table 3 Summary of experimental works (fluids and measurementinformation). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Table 4 Test conditions of the experiments . . . . . . . . . . . . . . . . . . . . . . 47

Table 5 Geometric details of the tube bends. . . . . . . . . . . . . . . . . . . . . 52

Table 6 Equipment details. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

Table 7 Uncertainty of measured parameters. . . . . . . . . . . . . . . . . . . . 61

Table 8 Parameters of the statistical analysis for the pressure dropcorrelations based on the presented experimental data. . . . . . . . . . . . 90

Table 9 Empirical parameters of the two-phase multiplier correla-tion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

Table 10 Standard uncertainty of gas holdup sensors using the ex-perimental stratified regime-based calibration. . . . . . . . . . . . . . . . . . . . . 131

Table 11 Main flow parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

Table 12 Total pressure drop measurements and frictional pressuredrop in the bend. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

Table 13 Uncertainty of main flow parameters. . . . . . . . . . . . . . . . . . . . 151

Table 14 Main flow parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

Table 15 Gas holdup measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

Table 16 Total pressure drop measurements. . . . . . . . . . . . . . . . . . . . . . 154

Table 17 Uncertainty of main flow parameters. . . . . . . . . . . . . . . . . . . . 154

Table 18 Uncertainty of gas holdup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

Table 19 Uncertainty of total pressure drop.. . . . . . . . . . . . . . . . . . . . . . 155

Table 20 Uncertainty of accelerational pressure drop. . . . . . . . . . . . . . 155

Table 21 Uncertainty of frictional pressure drop. . . . . . . . . . . . . . . . . . 155

23

NOMENCLATURE

Greek

Gas holdup -

Volumetric quality -

p Pressure difference Pa

Absolute roughness m

Viscosity Ns/m2

p Pressure gradient Pa/m2 Two-phase flow multiplier -

2k Two-phase flow multiplier (k-phase alone) -

2ko Two-phase flow multiplier (total flow assumed k-fluid) -

Density kg/m3

Momentum density kg/m3

Roman

d Internal diameter m

f Friction factor -

faq Data acquisition frequency Hz

Fr Froude number -

G Mass flux kg/m2s

g Gravity m/s2

H Height of the return bend m

j Superficial velocity m/s

L Horizontal tube length m

p Static pressure Pa

R Curvature radius of the bend m

Re Reynolds number -

Sr Slip ratio -

T Temperature K

t Time s

u Velocity m/s

W Mass flow rate kg/s

We Weber number -

x Quality -

X2 Martinelli parameter -

z Axial coordinate m

Subscript

b Return bend

d Downstream

down Downward flow direction

f Frictional

g Gas phase

h Homogenous mixture

in Inlet of return bend

k k-phase

l Liquid phase

n Pressure tap index number

out Outlet of return bend

s Straight segment

tp Two-phase flow

u Upstream

up Upward flow direction

25

1 INTRODUCTION

Gas-liquid flows are found in the majority of energy-related andcooling applications. The flow of a refrigerant in a heat exchanger andthe transport of crude oil or natural gas in a pipe are typical gas-liquidflow problems.

Historically, engineering problems involving two-phase flows havebeen strongly related to steam generation, dating back to the days ofthe Industrial Revolution. However, the rigorous study of two-phaseflows was initiated in the second half of the twentieth century, afterthe World War II. At that time, nuclear research started to be usedfor a noble cause: producing electrical energy. Thus, the consolida-tion of two-phase flow and boiling as research disciplines was associ-ated with the development of the first water-cooled nuclear reactors,as researchers faced challenging design issues in transferring enormousamounts of thermal energy out of the reactor core and into the steamturbines.

Recently, environmental catastrophes such as the Deepwater Hori-zon oil spill (Gulf of Mexico, 2006) and the Fukushima Daiichi nucleardisaster (Japan, 2011) have encouraged governments to push safetystandards to stricter levels.1 These requirements, as well as the inter-est in the economical value associated with energy production, havestimulated the research on Multiphase Flows in the last decade.

1.1 MOTIVATION AND OBJECTIVES

Two-phase flow equipment such as heat exchangers and trans-port pipes often include several return bends. Gas-liquid flows in bendsare affected by centrifugal forces that tend to separate both phases. Ifthe bend is oriented vertically, the flow is also subjected to gravita-tional effects. The resulting effect of such forces is a change of the flowconfiguration as it passes through the bend, which depends on severalaspects, such as flow direction (i.e., upward and downward), flow rates,physical properties and bend curvature.

In order to accurately design two-phase flow equipment, a betterassessment of irreversible losses in singularities is required. The objec-

1Refer to the following reports: Deepwater Horizon Study Group (2011), DetNorsk Veritas (2011), The Fukushima Nuclear Accident Independent InvestigationComission (2012).

26 1 Introduction

tive of the present study is to characterize air-water two-phase flows ina vertically-oriented 180 return bend. To this end, an experimentalapparatus capable of reproducing the majority of flow regimes found inhorizontal tubes was designed and constructed, allowing the investiga-tion of the reversible and irreversible pressure changes occurring in thebend and in the straight tube segments upstream and downstream ofit.

This work was carried out at Polo Research Laboratories forEmerging Technologies in Cooling and Thermophysics, under the aus-pices of a research program on Multiphase Flow in Pipes funded byCENPES/Petrobras.

1.2 OVERVIEW

This thesis is structured as follows. Chapter 2 presents a briefreview of pressure drop and gas holdup calculation methods for hori-zontal tubes, followed by a detailed review of two-phase flow in 180

return bends. The specific objectives of the dissertation are presentedafter the literature review, at the end of Chapter 2. Chapter 3 con-tains information about the general features and main components ofthe experimental apparatus, its measuring devices and techniques, andthe validation procedures. Chapter 4 presents the results of the study,and is divided into four main sections: visual observations of the flow,analysis of the flow parameters in the bend, development of a frictionalpressure drop correlation, and aspects of developing flow in the vicinityof the bend. Chapter 5 presents the conclusions and recommendationsfor future works. Further information on the experimental procedures,uncertainty analysis, edited high-speed image secquences, and tabu-lated experimental data can be found in the appendices.

27

2 LITERATURE REVIEW

Firstly, a review of pressure drop and gas holdup in straight hor-izontal tubes is presented, emphasizing the empirical correlations eval-uated in this work. Next, a detailed review of the works on two-phaseflow in 180 return bends is carried out, highlighting some unresolvedquestions and research gaps that motivated the specific objectives ofthe present work.

2.1 TWO-PHASE FLOW IN HORIZONTAL TUBES

Despite the availability of detailed (i.e., three-dimensional) mod-els for two-phase flows, the majority of the models employed in indus-try are one-dimensional. These models often resort to empirical cor-relations to evaluate frictional losses and phase holdup. Thus, severalexperimental works have focused on the development of accurate cor-relations for the frictional pressure drop and gas holdup in tubes andsingularities for a range of flow conditions.

2.1.1 Pressure drop

In the homogenous model, the two-phase mixture behaves asa pseudo-fluid with average thermophysical properties. The frictionalpressure gradient is calculated with the Darcy-Weisbach equation,(

dp

dz

)f

= f1

d

G2

2, (2.1)

where p is the static pressure, z is the axial coordinate of the tube, fis the Darcy friction factor, d is the tube diameter, and G is the totalmass flux. The fluid density is taken as the homogeneous mixturedensity given by (COLLIER; THOME, 1996),

h =

(x

g+

1 xl

)1. (2.2)

where x is dynamic gas mass fraction (quality),

x =GgG, (2.3)

28 2 Literature review

and the subscripts g and l denote gas and liquid, respectively. Forlaminar flow, the Darcy friction factor is given by,

f =64

Re, (2.4)

while for conditions of turbulent flow, Colebrook (1939) proposed thefollowing implicit expression,

1f

= 2log10(

3.7d+

2.51

Ref

)(2.5)

where Re is the Reynolds number and is the absolute roughness ofthe tube wall. In order to evaluate both Eqs. 2.4 and 2.5 in the case ofhomogenous two-phase flow, the Reynolds number must be calculatedusing a model for the homogeneous viscosity such as the one proposedby McAdams et al. (1942) apud Collier & Thome (1996),

h =

(x

g+

1 xl

)1(2.6)

where represents the fluid dynamic viscosity.In the separated flow model, empirical correlations are used in

order to assess the frictional pressure gradient. Lockhart & Martinelli(1949) introduced the concept of a two-phase flow multiplier, 2, whichrelates the frictional pressure drop of two-phase flow with that of single-phase flow by,

pf,tp = 2kpf,k, (2.7)

where pf,k is the pressure drop of the single-phase flow of phase kwith mass flux equal to the mass flux of this phase in the two-phaseflow. Other multipliers can be conveniently defined as follows,

pf,tp = 2kopf,ko, (2.8)

where the subscript ko, denotes the single-phase flow of phase k witha mass flux equal to the total mass flux of the two-phase mixture.Following the above definitions, four different two-phase multiplier canbe proposed for gas-liquid flows: 2l ,

2g,

2lo,

2go.

Lockhart & Martinelli (1949) assumed that the two-phase mul-tipliers are function of the so-called Martinelli parameter, X2, definedas,

2.1 Two-phase flow in horizontal tubes 29

X2 =pf,lpf,g

. (2.9)

In their work, graphical correlations of two-phase multipliers in terms ofthis parameter were proposed based on the flow regimes associated withthe corresponding single-phase flow of the individual phases (viscous orturbulent). Chisholm (1967, 1983) suggested the following relations for2, which have been more extensively used thereafter,

2l =1

X2+C

X+ 1, (2.10)

and,

2g = X2 + CX + 1. (2.11)

The coefficient C is determined based on the flow conditions shown inTable 1.

Table 1 Coefficient C of Eqs. 2.10 and 2.11 .

Liquid Gas CViscous Viscous 5

Turbulent Viscous 10Viscous Turbulent 12

Turbulent Turbulent 20

One of the most widely used pressure drop correlations was pro-posed by Friedel (1979), and is considered the most accurate methodavailable (GHIAASIAAN, 2007). The author suggests the following ex-pression to evaluate the liquid-only two-phase multiplier, 2lo,

2lo = A+ 3.24x0.78(1 x)0.24

(lg

)0.91(gl

)0.19(

1 gl

)0.7Fr0.0454h We

0.035h , (2.12)

where Frh and Weh are the homogeneous-flow Froude and Weber num-bers. The parameter A is given by,

A = (1 x)2 + x2 lfgogflo

, (2.13)


where fko is the Fanning friction factor for single-phase flow of fluid kwith a mass flux equal to the total mass flux of the two-phase flow.

Muller-Steinhagen & Heck (1986) developed an empirical expres-sion to evaluate the frictional pressure gradient in horizontal tubesgiven by,

(dp

dz

)f,tp

=

{(dp

dz

)f,lo

+ 2x

[(dp

dz

)f,go

(dp

dz

)f,lo

]}(1 x)1/C

+ xC(dp

dz

)f,go

. (2.14)

The value of the constant C was determined as 3 from experimentaldata, and the frictional pressure gradients for single-phase flow arecalculated based on the following relation for the Darcy friction factor,

fko =

{64Reko

, Reko 1187;0.3164Re0.25ko

, Reko > 1187.(2.15)

2.1.2 Gas holdup

In the separated flow model, empirical relationships are also usedto correlate the gas holdup, , to the independent parameters of theflow. Using the Lockhart-Martinelli method for pressure drop, an ex-pression for gas holdup was derived by Collier & Thome (1996). Itfollows that, for the annular flow regime,

2l = (1 )2 . (2.16)Substitution of Eq. 2.16 in 2.10 (with C = 20) provides an

explicit expression for the gas holdup in terms of the Martinelli param-eter. Yet, other empirical correlations available in the literature areknown to provide better results. Smith (1969) proposed the followingexpression for the gas holdup in horizontal tubes,

=

1 +(gl

)(1 xx

)0.4 + 0.6 lg + 0.4 ( 1xx )

1 + 0.4(

1xx

)1

. (2.17)

2.1 Two-phase flow in horizontal tubes 31

According to Ghiaasiaan (2007), one of the most accurate em-pirical methods for calculating the gas holdup is the CISE correlation(PREMOLI et al., 1971). In this method, the slip ratio, Sr, defined asthe ratio of the gas and liquid in-situ velocities can be calculated from,

Sr = 1 + E1

(y

1 + yE2 yE2

)1/2, (2.18)

where

y =

1 (2.19)

E1 = 1.578Re0.19lo

(lg

)0.22, (2.20)

E2 = 0.0273WelRe0.51lo

(lg

)0.08. (2.21)

and is the dynamic volume fraction (volumetric quality),

=

Ggg

Ggg

+ Gll

. (2.22)

Thus, a direct expression for in terms of Sr is given by substitutingEq. 2.18 in the following relationship between mass quality and gasholdup (GHIAASIAAN, 2007),

x

1 x =glSr

1 . (2.23)

A very accurate but rather involved method for calculating thegas holdup was proposed by Chexal et al. (1991). The proposed correla-tion covers a wide range flow conditions, and yet provides a continuousfunction. This method is based on the parameters of drift flux two-phase flow models and consists of a large number of implicit equationsand over twenty arbitrary constants. Although the Chexal et al. (1991)correlation was used in the present work, its equations were omittedfor the sake of simplicity.


2.2 TWO-PHASE FLOW IN 180 BENDS

Substantial experimental research has been conducted on two-phase flow in return bends. Numerous works dealt with pressure dropin two-phase flow of refrigerants in small curvature bends focusingon cooling applications (PIERRE, 1964a; TRAVISS; ROHSENOW, 1971;GEARY, 1975; CHEN et al., 2004; SILVA LIMA; THOME, 2010; PADILLAet al., 2011). Others carried out experiments with air-water flows inreturn bends (USUI et al., 1980; HOANG; DAVIS, 1984; WANG et al., 2008)and discussed in detail the hydrodynamics of two-phase flow in thebend. Among these, different approaches for evaluating the irreversiblepressure change in the bend have been discussed. A first and sim-pler approach is to directly measure the pressure drop in the bend,neglecting any possible reversible pressure change. Another approach,first adopted by Geary (1975), consists of measuring the pressure dropin two different segments: a straight segment upstream of the bend,and another segment that includes the bend and the straight sectiondownstream of it. In this way, it is possible to estimate the frictionalcomponent of pressure drop in the bend assuming that the averagefrictional pressure gradient downstream is equal to the one upstream.Accurate predictions with this method would require a straight sectiondownstream of the bend long enough to allow for flow development (orrecovery).

Although the previous methods of pressure drop evaluation seemreasonable for horizontal return bends, they are questionable if the bendis oriented vertically. In this case, the static pressure head, which de-pends on the gas holdup in the bend, must also be accounted for. Thiswas discussed by Usui et al. (1980), who identified that no study hadbeen conducted on the behavior of average gas holdup and pressuredrop in the bend at that time. More recently, Chen et al. (2008) andPadilla et al. (2013) evaluated the static pressure change in verticalreturn bends by estimating the gas holdup in the bend using the cor-relations of gas holdup for straight tubes. The correlation of Smith(1969) was used by Chen et al. (2008), while Padilla et al. (2013) usedthe correlation of Steiner (1997).

The method proposed by Geary (1975) was used extensively inseveral works that focused on the irreversible losses in bends. Althoughthis method is strongly dependent on the extent of the flow recoveryat the pressure tap located downstream of the bend, only a few studiesattempted to quantify this effect (TRAVISS; ROHSENOW, 1971; HOANG;DAVIS, 1984; PADILLA et al., 2012; SILVA LIMA; THOME, 2012; DE KER-

2.2 Two-phase flow in 180 bends 33

PEL et al., 2013b). Among these, no agreement has been reached re-garding the flow recovery length.

2.2.1 Pressure drop

The first study of two-phase flow in return bends is attributed toCastillo (1957), who carried out a theoretical and experimental inves-tigation of pressure drop in air-water flow. In his work, the two-phaseflow in a horizontally-oriented return bend was modeled as the rotationof separated phases in the bend. Thus, predictions with this methodonly agreed with the experimental data for low gas velocities and thestratified flow regime. Although the phases were assumed to flow atthe same velocity, the author argued that the relative motion of thephases played an important role on the pressure drop in the bend.

Pierre (1964a, 1964b), carried out tests with R-12 and R-22in straight tubes (10.9 mm ID). He proposed an empirical correlationfor friction factor based the experimental data (PIERRE, 1964a apudGEARY, 1975). In the same work, the pressure drop of R-12 in hori-zontal return bends was investigated and mathematically expressed interms of two components: the loss due to turning of the flow, and theloss due to friction. Experiments were conducted with bend curvatures(defined as the ratio of the bend radius to the pipe radius, or 2R/d) of3.5 and 6.9. According to Geary (1975), the pressure drop correlationproposed by Pierre (1964a) did not take into account the effect of thebend curvature radius, because of the relatively low mass fluxes. Be-cause of that, it could lead to incorrect predictions when used at otherflow conditions.

Geary (1975) investigated the two-phase flow of refrigerants in re-turn bends using a test section comprising two horizontal return bendsand three straight-tube segments. Eight return bends of approximately11.1 mm ID with different curvature radii were used, covering values ofbend curvature from 2.3 to 6.5. The mass flux of refrigerant was variedbetween 100 and 400 kg/m2s. The pressure drop was measured betweentwo taps, one located 40 diameters upstream of the bend and another40 diameters downstream (Lu = 40d and Ld = 40d). This approachwas used to account for the effect of the bend on the straight sections.The pressure drop in the bend pb was evaluated by the followingexpression,

pb = pt Lu + LdLs

ps (2.24)


where pt is the measured pressure drop between the upstream anddownstream segments, and ps is the pressure drop in a straight seg-ment of length Ls far upstream of the bend. Although the accuracyof this approach strongly depends on the flow recovery length down-stream of the bend, only a few works1 have dealt with this matter.The upstream and downstream straight-tube measuring lengths are of-ten defined based on subjective criteria and lack of scientific rigor. Still,the work of Geary (1975) revealed a linear relation between the pres-sure gradient in the bend and its curvature, leading to an empiricalcorrelation for the pressure drop in the bend, which took into accountthe influence of the curvature.

Chisholm (1980) developed a correlation for the pressure dropin horizontal 90 bends and compared its predictions with the steam-water flow data of Fitzsimmons (1964). The method was later extendedto cover data for bends other than 90 and bend orientations otherthan the horizontal (CHISHOLM, 1983). The suggested correlation forthe bend pressure drop is,

pb = 2b,lpb,l, (2.25)

where the pressure drop for single phase liquid flow in the bend is givenby,

pb,l = klG2

2l, (2.26)

and kl is the loss coefficient for single-phase flow in the bend. In thepresent work, this coefficient was evaluated using the method proposedby Idelchik (1992). The two-phase multiplier proposed by Chisholm(1980) is given by,

2b,l = 1 +

(lg 1)[

Bx (1 x) + x2] , (2.27)where the coefficient B is,

B = 1 +2.2

kl(2 + Rd

) , (2.28)and R is the curvature radius of the return bend.

Usui et al. (1980, 1981) carried out experiments with air andwater in 24-mm ID vertical return bends with curvatures of 11.3, 16.6,and 22.5. The mass fluxes ranged from 20 to above 1500 kg/m2s, covering

1Refer to Section 2.2.2


all horizontal flow regimes. Pressure drop was measured in two straightsegments and in the bend, similarly to Geary (1975). However, as thereturn bends were positioned in the vertical plane, Eq. 2.24 must nowalso account for the static head, and becomes,

pb = pt Lu + LdLs

ps [g+ l (1 )] g2R, (2.29)

where 2R corresponds to the height of the bend, and the sign of thegravitational term is positive for the upward direction and negative forthe downward direction. The average values of the phase densities andgas holdup are considered as average values in the bend. Usui et al.(1980, 1981) used a pair of quick-acting solenoid valves at the inletand outlet of the bend, which were simultaneously closed so the liquidvolume could be measured and, from that, an average value of the gasholdup in the bend could be estimated. Although a correlation basedon the single-phase frictional pressure drop was proposed, most of theirfindings were related to the hydrodynamic behavior of the flow, whichwill be discussed in the next section.

In a series of papers on pressure drop in return bends, Chen et al.(2004, 2005, 2007, 2008) reported several experiments in a coil-type testsection consisting of consecutive bends (U-type wavy tubes). Chen etal. (2004) carried out experiments with R-410A, using four bends withcurvatures ranging from 3.9 to 8.2 and internal diameters between 3.3and 5.07 mm ID. The mass flux of refrigerant was varied between 100and 900 kg/m2s. The orientation of the bend was not informed, but laterworks indicated that the bends lied in the horizontal plane. The pres-sure drop in the wavy section was evaluated according to Eq. 2.24,with the measuring section between the two pressure taps encompass-ing two straight sections upstream and downstream (Lu = 110d andLd = 140d) of the wavy tubes. The pressure drop of a single bend wasevaluated by dividing the measured pressure drop associated with theentire wavy segment by the number of consecutive bends. The Chen etal. (2004) database was combined with that of Geary (1975) to yieldthe following correlation for pressure drop in return bends (CHEN et al.,2004), (

dpdz

)b

= fgj

2g

2d, (2.30)

where jg is the superficial gas velocity, i.e., the average velocity of thegas phase if it was flowing alone in the channel. The Darcy friction


factor, f , was expressed as,

f =102Re0.35tp

We0.12g exp(0.1942Rd )x

1.26, (2.31)

and Retp is the combined Reynolds number of the flow defined as,

Retp = Rel +Reg. (2.32)

Chen et al. (2005, 2007) investigated the influence of lubricatingoil on the pressure drop of R-410A and R-134a in the same experimentalsetup used by Chen et al. (2004). Chen et al. (2008) also conductedexperiments in the same experimental setup, but examined the effectof the orientation of the test section (horizontal and vertical) on theflow behavior. In this work, experiments were carried out with R-134ausing only the wavy test section of 5.07 mm ID and bend curvature of5. In the evaluation of the pressure drop in the vertically-oriented wavysection, the contribution due to acceleration of the flow was neglected,and the total frictional loss due to the wavy and the straight segmentswas expressed as,

pf = p [g+ l (1 )] g18R, (2.33)where p is the measured pressure drop, 18R corresponds to the heightof the wavy section consisting of consecutive bends, and the sign of thegravitational term is positive for the upward direction and negativefor the downward direction. The phase densities and gas holdup areconsidered as average values in the test section.

As no gas holdup measurements were performed in their work,Chen et al. (2008) estimated the gas holdup usign Eq. 2.33 for theupward and downward directions. With one equation for each flowdirection, and assuming that the frictional component of pressure dropwas the same for both directions, it was possible to estimate the gasholdup in the bend,

=l

[(pb)down (pb)up

]36Rg (l g) . (2.34)

The pressure drop experimental data of Chen et al. (2008) wereinserted in Eq. 2.34 and the results were compared to Smith (1969)correlation. Although a good agreement was reported, the actual com-parison was not shown in the Chen et al. (2008) paper. Nevertheless,the Smith (1969) correlation was used in the calculation of the gravita-


tional contribution in Eq. 2.33. To the present authors knowledge, theassumption of identical frictional pressure drop for both flow directionsis incorrect. It is also contradictory because the authors themselvesreported higher values of pressure drop in downward flow, particularlyat low qualities. As will be seen in the present dissertation, the ac-celeration component of the pressure drop is not always negligible norcan the averaged holdup be assumed always equal to that for straighttubes.

Using the experimental data from Geary (1975) and Chen et al.(2004), Domanski & Hermes (2008) proposed an empirical correlationfor predicting the pressure drop in horizontal bends. The pressure dropin a straight segment was correlated to the pressure drop in the bendby a curvature multiplier,(

dp

dz

)b

=

(dp

dz

)s

, (2.35)

which was obtained based on the Buckingham-Pi theorem, and is givenby the expression,

= 6.5 103(Gxd

g

)0.54(1

x 1)0.21(

lg

)0.34(2R

d

)0.67. (2.36)

Padilla et al. (2009) used the experimental data from Chen etal. (2004, 2007, 2008) and Traviss & Rohsenow (1971) to propose anew correlation. The pressure gradient was calculated in terms of thepressure gradient in straight tubes plus a local contribution due to thecentrifugal effect in the bend (dp/dz)sing, given by,(

dp

dz

)b

=

(dp

dz

)s

+

(dp

dz

)sing

, (2.37)

where (dp/dz)s was calculated using the Muller-Steinhagen & Heck(1986) correlation and,(

dp

dz

)sing

= 0.047

(gj

2g

R

)(j2lR

)1/3, (2.38)

which resembles the bend pressure drop due to rotation proposed byCastillo (1957), where jl is the superficial liquid velocity.

Later, Padilla et al. (2011) conducted experiments using R-410Ain horizontal bends with curvatures ranging from 3.7 to 4, and internal


diameters between 7.90 and 10.85 mm. The test section used consistsof two straight tubes, two return bends and one sudden contraction.The measurement procedure was similar to that of Geary (1975), i.e.,based on two static pressure taps placed upstream and downstream ofthe bend (Lu = 10d and Ld = 20d). The mass flux ranged between 179and 1695 kg/m2s. A preliminary investigation of the flow developmentdownstream of the bend was also carried out, which was later discussedin more details by Padilla et al. (2013).

Pressure drop measurements were carried out by Silva Lima &Thome (2010) using R-134a in horizontal return bends (13.4 mm IDand curvature of 9). The total pressure drop was measured between7 segments, resulting in average values of the pressure gradient in thebend and at positions upstream and downstream of it (at 141, 59 and6 diameters in both segments). The contribution of the acceleration ofthe flow to the total pressure drop was neglected. Thus, the frictionalpressure drop in the bend was directly associated with the measuredvalues by the following expression,

(dp

dz

)b

=

{pb d

2

[(dp

dz

)b

+

(dp

dz

)6d

]}1

piR+{

d2

[(dp

dz

)b

+

(dp

dz

)+6d

]}1

piR, (2.39)

where the measured pressure difference in the bend, pb, includes thebend itself and two straight segments of length 1d at the inlet and out-let of the bend. The pressure drop in the straight segments of the bendwas subtracted from the total pressure difference by approximating thepressure gradient in the straight segments to the average gradient be-tween the bend and the nearest pressure taps (located at 6d upstreamand downstream). Silva Lima & Thome (2010) also investigated thedifference between pressure measurements taken at different circumfer-ential positions of the straight tubes (from the inner to the outer partof the curve), which were considered to be insignificant even very close(at 3.7d) to the bend.


2.2.2 Flow behavior and gas holdup

The issue of flow development downstream of return bends hasreceived some attention in the literature, being first addressed by Traviss& Rohsenow (1971), who measured the pressure drop and condensationheat transfer coefficient of R-12 along a horizontal segment (4.4-m long,8-mm ID) immediately downstream of a vertical return bend. Theyconcluded that the effect of a return bend on the downstream pressuredrop was negligible when averaged over a length of 90 diameters, andthat the pressure gradient did not deviate more than 10% from thefully-developed pressure gradient. In their work, two bends made ofglass, with curvatures of 3.2 and 6.4, were used to allow flow visualiza-tion with a high-frequency light source. The flow regime was found toreadjust very rapidly when disturbed by the presence of the bend; afact that was verified years later by Silva Lima & Thome (2012) andDe Kerpel et al. (2013b) with more sophisticated and precise methods.

A high-speed cine analysis of two-phase air-water flows in verti-cal return bends was presented by George (1971), who demonstratedthat disturbance waves are somewhat destroyed as annular flow passesthrough the bend in upward flow. The high-speed film contains axialviewing sequences of the flow in the outlet of the bend, which helpto understand the influence of the bend on the phase distribution inannular flow.

Usui et al. (1980, 1981) carried out air-water flow pressure dropexperiments in 24-mm vertical return bends with curvatures of 11.3,16.6, and 22.5. In order to evaluate the frictional pressure drop con-tribution, the authors identified the need for a precise assessment ofthe static head in the return bend. Usui et al. (1980) used a pair ofquick-acting solenoid valves at the inlet and outlet of the bend, whichwere simultaneously closed so the liquid content in the bend could bemeasured and, from that, an average value of the gas holdup in thebend could be estimated. They observed that the average gas holdupin the bend was not significantly influenced by the centrifugal force inthe upward flow direction and, therefore, presented a good agreementwith the Smith (1969) correlation. The opposite was observed for down-ward flow, where the gas holdup values differed significantly from thosein straight tubes. The local gas holdup was measured by Usui et al.(1981) at the outlet of the bend and at positions of approximately 66diameters upstream and downstream of it using an electrolytic probe.Measurements in the plug flow regime showed that the local gas holdupat the outlet of the bend was significantly higher than upstream due to


acceleration of the liquid phase at the bottom part of the bend. At thedownstream position, the cross sectional profile of the gas holdup wasvery similar to the one upstream of the bend, suggesting the existenceof developed state of the flow. Besides measuring pressure drop andgas holdup in the bend, they also conducted visual observations of theflow and presented details on the different phenomena observed, e.g.,flow reversal and flooding in the upward direction, and back flow ofbubbles and coalescence in the downward flow direction.

Hoang & Davis (1984) conducted experiments with air-waterflow in return bends connecting two 25.4-mm ID vertical tubes withcurvatures of 4 and 6, in an inverted U configuration. Their studywas limited to the bubbly flow regime, i.e., only high liquid mass fluxeswere used. Static pressure was measured downstream and upstream ofthe bend, and within the bend itself. For the latter, the pressure tapswere distributed every 30 from the inlet to the outlet, both on the in-ner and outer parts of the curve (i.e., concave and convex parts). Highpressure losses were observed as high as 20 times the pressure loss insingle-phase flow which were attributed to separation and remixing ofthe phases in the bend. The authors established a developing length of9 diameters downstream of the bend, where the flow was considered tobe well remixed. This value is 10 times lower than the one observed byTraviss & Rohsenow (1971), probably due to the very high liquid flowrates used in the more recent experiments. By comparing the angularpressure profiles with the high-speed film, it was verified that the onsetof rotation and stratification (separation) of the flow occurred in andafter the first half of the bend, respectively.

Studies focusing on the influence of the bend on the flow regimesof an air-water mixture were carried out by Wang and coauthors inhorizontal return bends (WANG et al., 2003, 2004) and vertical returnbends (WANG et al., 2005, 2008). In these works, the distribution ofthe phases was observed via still photography. Return bends of 3 to6.9-mm ID and curvature of 3, 5 and 7 were used in the horizontalexperiments, while a single bend geometry was used in the verticalexperiments (6.9 mm ID and 2R/d = 3, where R is the bend radiusand d is the pipe diameter). Phenomena such as flow regime transitionfrom stratified to annular flow were observed in horizontal bends, beingmore pronounced in the small curvature radii and large pipe systems.In the vertical bends, flow reversal and frozen slug flow were observed.

In their experiments using R-134a and horizontally oriented re-turn bends (13.4 mm ID and curvature of 9), Silva Lima & Thome(2010) verified differences in pressure gradient as far as 141 diameters


downstream of the bend. Later, Silva Lima & Thome (2012) conductedexperiments of R-134a two-phase flow in return bends in both horizon-tal and vertical orientations. Glass return bends (internal diameters of8, 11 and 13 mm, and curvatures of approximately 3 and 5) were used toallow visualization of the flow with a high-speed camera. The recoverylength downstream of the bend was evaluated qualitatively based onthe visual characteristics of the flow, and was found to be larger in thevertical orientation of the bend, specially in upward flow. The authorsobserved a larger influence of the centrifugal force on the flow ratherthan the effect gravity, probably due to the small curvatures. Severalflow phenomena observed by the authors were in agreement with ob-servations made by Usui et al. (1980, 1981) and Traviss & Rohsenow(1971), such as liquid segregation and droplet deposition in the bend,on the outer part of the curve.

Padilla et al. (2013) conducted a visual observation of HFO-1234yf and R-134a in vertical return bends (6.7 mm ID, curvature of7.46) in order to determine the perturbation lengths downstream andupstream of the bend in both upward and downward flows. Addition-ally, the total pressure drop was measured at different pressure tapsupstream and downstream of the bends (7.9 and 10.85 mm, curvaturesof 3.68 and 4.05), for the above mentioned fluids and R-410A in thedownward direction. In their work, the authors evaluate the gravi-tational term of pressure drop by estimating the gas holdup in thebend with the Steiner (1993) correlation. Perturbation lengths of thedownward flow were determined as being 5 diameters upstream and 20diameters downstream of the bend.

Recently, De Kerpel et al. (2013b) developed a method for deter-mining the downstream development length based on the measurementof the flow capacitance by a probe placed on the outer pipe wall. Aclustering algorithm was used to group similar signals associated withspecific flow regimes for developed flow conditions in straight tubes.Tests were performed with R-134a in a return bend of 8 mm ID andcurvature of 2.75. Measurements of flow capacitance were taken at dif-ferent positions downstream of the bend (from 2.5 to 31.5d), and com-pared with those obtained at developed flow conditions. This methodwas able to detect flow disturbances up to 10 diameters downstream ofthe bend.


2.3 SUMMARY AND SPECIFIC OBJECTIVES

Tables 2 and 3 show a summary of the experimental works re-viewed in this chapter. In Tab. 3, the columns represent the number ofthe work shown in Tab. 2 (#), the fluids used (fluid), and if measure-ments of pressure drop (p) and gas holdup () were carried out. Thetable also shows if flow visualization was conducted (vis.), and if theissue of flow development (flow dev.) was in some way investigated.

The matter of flow recovery downstream of the bend has beenapproached by means of flow visualization, total pressure drop mea-surements, and local gas holdup (or capacitance) measurements. Theworks dealing with vertically-oriented return bends are shown in boldtypeface (Tables 2 and 3; except Hoang & Davis (1984) which uses aninverted U configuration). Among these, only Usui et al. (1980, 1981)have experimentally evaluated the gas holdup in the bend in order toaccurately calculate the static head.

Despite the number of works dealing with two-phase flow in ver-tical return bends, some unresolved questions have remained open untilthe present moment. In order to precisely evaluate the contribution offriction to the pressure drop, is it reasonable to neglect or over simplifythe estimation of the reversible pressure changes occurring in the bend?

Table 2 Summary of experimental works (bend geometries).

# author d 2R/d dir.

1 Pierre (1964) 10.9 3.5, 6.9 hor.2 Traviss et al. (1971) 8 3.2, 6.4 ver.3 Geary (1975) 11.1 2.3 - 6.5 hor.4 Usui et al. (1980,1981) 24 11.3 - 22.5 ver.5 Hoang et al. (1984) 25.4 4 - 6 ver.6 Chen et al. (2004) 3.3 - 5.1 3.9 - 8.2 hor.7 Chen et al. (2005,2007) 5.07 5 both8 Wang et al. (2003,2004) 6.9 3 - 7 hor.9 Wang et al. (2005,2008) 6.9 3 ver.

10 Silva Lima et al. (2010) 13.4 9 hor.11 Silva Lima et al. (2012) 8 - 13 3, 5 both12 Padilla et al. (2011) 7.9 - 10.9 3.7 - 4 hor.13 Padilla et al. (2013) 7.9 - 10.9 3.7 - 4 ver.14 De Kerpel et al. (2013) 8 2.75 ver.

2.3 Summary and specific objectives 43

To what extent the flow parameters are influenced by the bend or, inother words, how does the bend affect the frictional pressure gradient,the gas holdup, and other flow parameters downstream of it?

The present work aims at contributing to answering these ques-tions by presenting a complete set of experimental data on gas-liquidflows in vertical return bends for both upward and downward flow con-ditions. To this end the following specific objectives have been pro-posed:

1. Design and build an experimental apparatus for low-pressure air-water flows, capable of reproducing the majority of flow regimesfound in horizontal tubes;

2. Characterize experimentally the main independent parameters ofthe problem, viz. the gas holdup and the frictional pressure gra-dient as a function of position relative to the bend;

3. Conduct a visual observation of the two-phase flow in the bendusing high-speed imaging to identify the relevant phenomena tak-ing place in the bend;

4. Verify the extent of the influence of the bend on the flow by eval-uating the axial distribution of pressure gradient and gas holdup

Table 3 Summary of experimental works (fluids and measurementinformation).

# fluid p vis. flow dev.

1 R-12, R-22 X2 R-12 X X X (p)3 R-22 X4 air-water X X X X (p, )5 air-water X X (p)6 R-410A X7 R-134a X8 air-water X X (visual)9 air-water X X (visual)

10 R-134a X X (p)11 R-134a X X (visual)12 R-410A X X (p)13 HFO-1234yf, R-134a, R-410A X X X (p)14 R-134a X X ()


in the straight sections upstream and downstream of the bend;

5. Propose a more accurate method for evaluating the local frictionalpressure drop in return bends that quantifies the irreversible pres-sure changes and includes:

i) an evaluation of the average gas holdup in the bend and acomparison it against existing correlation for straight tubes,

ii) the quantification of the magnitude of each component of thetotal pressure drop in the bend,

iii) an investigation of the effect of the bend radius on the fric-tional pressure drop,

iv) development of a simple pressure drop correlation based onflow parameters and bend geometry.

45

3 EXPERIMENTAL APPARATUS

The present chapter contains information about the experimen-tal apparatus built to investigate the hydrodiynamics of the two-phaseflow in return bends. At first, general aspects of the experimental ap-paratus are presented. In the following sections, detailed informationis presented on the main components of the apparatus and measuringtechniques.

Figure 1 Rendered CAD drawing of the experimental apparatus.

3.1 GENERAL ASPECTS

An experimental apparatus was built for the purpose of this re-search and is represented in Fig. 1. The setup consists of two individualfluid flow lines equipped with inlet flow mixers where the two phasesare introduced. The air-water mixture flows from either of the two mix-ers through 26.4 mm ID horizontal borosilicate glass tubes. The testsection consists of a 180 bend connecting the two horizontal tubes,which are approximately 5 m long1. Along the text, the two 5-m hor-

1The horizontal tubes were made long enough to allow the development of theflow. The development length in two-phase flow is not as established as in single-

46 3 Experimental apparatus

j g (m/s)

j l (m

/s)

10-1 100 101 10210-2

10-1

100

101 bubbly

2 bar3 4 5 6 7

slug

stratified wavy

annular

plug

Figure 2 Operational range of the experimental apparatus(cross-hatched region) on the Mandhane et al. (1974) flow regime map

for horizontal flows of air and water at atmospheric pressures in25.4 mm ID tubes.

izontal tubes and return bend are referred as the test section, whereabsolute pressure, pressure drop, gas holdup, temperature and velocitymeasurements were taken. The system is an open loop, that is, afterthe flow exits the test section the air is vented to the ambient, whilewater flows back to the reservoir.

The experimental apparatus was designed to work in a widerange of flow regimes. The operating range of the flow loop is shownin Fig. 2 together with the flow regime map of Mandhane et al. (1974)(dashed lines). The solid lines are the result of a numerical evaluation ofthe absolute pressure required at the inlet of the flow loop (consideringatmospheric pressure at the outlet) in order to overcome the flow lossesin the test section, for a given pair of air and water superficial velocities.As can be seen, the majority of flow conditions can be achieved withinlet pressures below 2 bar. Experiments were carried out at room tem-perature and low pressure, close to the atmospheric condition, settingthe mass fluxes of air and water. Operating conditions are summarizedin Table 4.

phase flow (BRENNEN, 2009), being strongly dependent on the inlet conditions.

3.2 Components 47

Table 4 Test conditions of the experiments

Test conditionsPressure 101 400 kPaTemperature 24 CAir mass flux 0.15 60 kg/m2sWater mass flux 10 1400 kg/m2s

3.2 COMPONENTS

A schematic representation of the experimental apparatus is shownin Fig. 3. In this figure, the test section is represented by a double lineand appears at the top. Other than the test section, the experimentalapparatus consists of the following parts, represented by single contin-uous lines: the mixing system (1 and 10), the water line (2-4), and theair line (5-9). The mixing system is formed by two mixers (1), eachlocated at the ends of the test section, and a set of three-way valves.These valves direct the flow from the air and the water lines into one ofthe mixers, and also direct the two-phase flow leaving the test sectionback to the reservoir.

3.2.1 Air line, water line and mixing system

The water line comprises a thermostatic bath (2), a centrifugalpump (3) controlled by a frequency inverter, a gate valve and a by-pass line, and a Coriolis mass flow meter (4), also shown in Fig. 4. Thethermostatic bath keeps the temperature of the water at 24 oC in a 30 Lreservoir, and allows for particle filtration through a filter attached toits internal circulation system. Water is pumped from the reservoirby the centrifugal pump (3), and the flow rate is set by selecting therotational speed of the pump in the frequency inverter and adjustingthe gate valve and the by-pass. The flow is measured in the Coriolisflow meter and is directed to the top or bottom mixer, depending onthe position of the three-way valves.

The air line is attached to a main compressed air line, and con-sists of a particulate filter (5), a coalescent filter (6), a pressure regulator(7), a micrometric valve (8), and a hot wire anemometer-based massflow meter (9) (Fig. 5). Water and particles present in the air areremoved in the particle filter, while smaller contaminants such as oil


Air

Water

R

R

p

PP

PT

PT

p

(1)

(1)

(2)(3)

(4)

(10)

(5)(6)

(7)(8)

(9)

ref.{

TT

ref.*{

Figu

re3

S

chem

aticof

the

exp

erimen

talap

paratu

s.

3.2 Components 49

2

3

4

9

Figure 4 Components of the water line.

droplets are removed in the coalescent filter. The air flow is controlledby a pressure regulator and a micrometric valve, and then measured atthe flow meter before entering one of the mixers.

The two inlet flow mixers (1) are attached to the ends of thehorizontal sections (Fig. 6) through a set of three-way valves, so it ispossible to set the air-water mixture to flow upwards or downwardsthrough the return bend. As the flow exits the loop, both fluids areseparated in a hydrocyclone; air is released to the atmosphere and waterreturns to the thermostatic bath.

Although the arbitrary introduction of the phases in a pipe wouldeventually result in a specific flow regime, a flow mixer located at theinlet of the test section reduces the length required for the flow todevelop. In the mixer, this result is accomplished by mixing both phasesaccording to the topology of the expected flow regime. For example, inannular flow, air was injected axially, and water was injected radially.In this way, a film is formed close to the wall and dragged by the aircore.

Two mixers designed and built in the course of this work wereplaced at the upper and lower ends of the test section. Thus, it ispossible to set the air-water mixture to flow upward or downward inthe bend (i.e., entering from the bottom or top tube). Figure 7 showsan axial view of one of the mixers, which consist of a cylindrical perspex


56

78

Figure 5 Components of the air line.

Figure 6 Flow mixers.

3.2 Components 51

Figure 7 Axial view of one of the mixers.

shell with and a porous annular core. Each mixer is equipped with anaxial and a radial connection. In this way, one can choose the directionin which each phase will be introduced in the mixer according to thedesired flow regime in the test section by setting the position of thethree-way valves.

3.2.2 Test section

The test section is a circular channel of 26.4 mm ID, and consistsof a 180 o return bend that connects two horizontal 5-m long tubes. Thereturn bend, also made of borosilicate glass, comprises a C-shaped sec-tion and two straight sections of approximately 0.1 m in length, whichallow for the mounting of the bend.

The influence of the bend on the behavior of flow parameters (gasholdup, pressure drop) has been investigated using bends with differentcurvatures (2R/d = 6.1, 8.7, and 12.2)2. Geometric details of the tubebends are shown in Table 5 and Fig. 8. The manufacturer of the tubebends (Schott) ensured minimal distortion of the circular cross-section

2In order to replace the return bends, the lower horizontal section moves verti-cally by means of a lifting system, while the upper section is kept fixed. Even thoughthis system guarantees a rough alignment of the lower section, a fine alignment wasalways performed.


of the bends during the fabrication process. The curvature radii ofthe bends were measured indirectly with image processing software andphotographs of the tubes in front of a graph (squared) paper. Since thecurvature radius is not perfectly constant along the bend, the distanceH was measured with a caliper and does not correspond to the exactvalue of 2R.

The test section was made fully transparent and therefore suitedfor optical measurements along its full length. Air and water wereselected as working fluids on account of their simple use, thus makingcalibration procedures easier in Particle Image Velocimetry (PIV) andLaser Doppler Velocimetry (LDV) measurements, which are intendedto be used in a later stage of this research.

Table 5 Geometric details of the tube bends.

Bend 2Rd1 (-) R (mm) L (mm) H (mm)A 6.1 81 106 155.85B 8.7 115 113 207.45C 12.2 161 108 312.50

Each horizontal section has a length of 5.65 m, approximately214 diameters. The long sections are formed of small borosilicate tubesconnected to each other by perspex sleeves (Fig. 9), containing pressuretaps and thermocouple wells.

3.2.3 Measuring devices and techniques

a) Pressure

The influence of the bend on the straight segments upstream anddownstream of it has been investigated by evaluating the distributionof flow parameters along the axis of the tube. Absolute pressure wasmeasured at taps located 1.85 m upstream and downstream of the re-turn bend. Pressure drop was measured between the inlet and outletof the bend and between sections of 0.11, 0.22, 0.51, and 1.01 m inlength along the 1.85-m long segments in the upper and lower tubes(Fig. 10). It should be noted from Fig. 10 that the origin of the maincoordinate system (z = 0) is the position of the pressure taps closestto the bend. Two other auxiliary references, zref and z

ref , are also

shown in Figure 10. The origin of the auxiliary coordinates is alwayslocated upstream of the bend; e.g. in downward flow, zref is located in

3.2 Components 53

H

R

L

L

1

2

Figure 8 Geometric parameters of the tube bends.

27.3

1/4" NPT 50 50

26.

4

64.6

10

32.

25

Figure 9 Perspex sleeve used to connect borosilicate tubes to eachother, allowing pressure and temperature measurements.


1.01 0.51 0.22 0.11

p p p p p

0.88 0.610.16

0.05

0.161.04

z0

zrefzref*

Figure 10 Positions of the pressure taps and gas holdup sensorspositions. The measurements were taken at symmetric locations

between the upper and lower tubes. (Dimensions in meters)

the upper horizontal section (at the most upstream pressure tap).A set of valves and tubings connect three differential pressure

transducers and an absolute pressure sensor to the pressure taps, as il-lustrated in Fig. 11. This system was completely filled with water andno air bubbles were left inside. Each differential transducer measuredexclusively the pressure difference between segments of the upper hori-zontal tube, between segments of the lower horizontal tube, or betweenthe inlet and outlet of the bend. Two additional absolute pressuresensors are located at the inlet and outlet mixers.

Total pressure drop in the bend is evaluated by the difference inheight between the two pressure taps located at the upper and lowerparts of the bend,

pb = p+ lgH, (3.1)

where p is the measured pressure drop, l is the density of the liquid(water) inside the tubings connecting the pressure taps and the sensormanifold, and H is the height difference between the two segments,which is approximately 2R.

The frictional pressure drop was estimated via the conservationof momentum in a control volume between the inlet and outlet of thetube segment. For the return bend, the frictional pressure drop in thebend, pf,b, is given by,

pf,b = p+G2

(1

out 1in

) tpg2R, (3.2)

3.2 Components 55

Figure 11 Set of valves and tubings, absolute pressure sensor anddifferential pressure transducers.

Similarly for a straight tube segment, the frictional pressure drop,pf,s, was evaluated as follows,

pf,s = p+G2

(1

out 1in

). (3.3)

In the above equations, p is the total measured pressure drop (p =pout pin), G is the total mass flux and g is the gravitational accelera-tion. The positive sign of the gravitational term corresponds to upwardflow in the bend, while the negative sign corresponds to downward flow.The subscripts in and out refer to the inlet and outlet sections of thetube, respectively. The momentum density, , is defined as (GHIAASI-AAN, 2007),

=[

(1 x)2l(1 ) +

x2

g

]1(3.4)

and is evaluated using gas holdup values, , measured at the inlet andoutlet of the tube. In Eq. 3.4, x is the dynamic vapor mass fraction, i.e.,the ratio of the air and the total mass flow rates. The average density ofthe mixture in the bend, tp, is taken as the arithmetic average mixturedensity between the inlet and outlet of the bend. The mixture density


is given by,

tp = g+ l(1 ). (3.5)From Eq. 3.2 one can also define the pressure drop term con-

cerning acceleration of the flow,

pa = G2(

1

out 1 in

), (3.6)

which also applies for a straight tube section. The gravitational termof pressure drop is given by,

pg,b = tpgH, (3.7)which is positive for the downward flow direction.

While pressure drop is measured between nine consecutive tubesegments (including the bend), absolute pressure is measured only attwo positions, as shown in Fig. 3. Nevertheless, the pressure distri-bution along the tube axis can be determined at discrete positions (atpressure taps) as the sum of consecutive pressure drops, given by thefollowing equation,

pn = p1 +

ni=2

pi1,i, (3.8)

where p1 is the measured static pressure, and n is the pressure tapindex, starting at 1 at the farthest upstream position (specified as ref.in Fig. 3).

The gradients of the pressure drop components were calculatedas follows,

pf = pfzout zin , (3.9)

and,

pa = pazout zin , (3.10)

where zin and zout are the axial positions of the inlet and outlet sectionsof the respective tube segment. For consistency in the presentation ofthe data, the pressure gradient components calculated according toEqs. 3.9 and 3.10 are associated with the positions in the middle of thesegment.

3.2 Components 57

b) Gas holdup

During the experiments on pressure drop in the bend, gas holdupwas evaluated by two non-intrusive capacitance sensors positioned atthe straight portions of the tube bend segment, as seen in Fig. 12. Forthe experiments focusing on the influence of the bend on the straightsegments upstream and downstream of it, gas holdup was measuredwith the capacitance sensors positioned at different locations of thetest section at each run. The gas holdup variation along each horizontaltube was determined from measurements taken at 6 positions as shownFig. 10. During each run, the probes were positioned in pairs accordingto 3.

The technique consists in measuring the electrical capacitance ofthe mixture, which is known to vary according to the gas holdup. Theelectronics and sensors were designed and built according to Libertet al. (2011) and Libert (2013). Each sensor probe was made up oftwo electrodes (Fig 13) mounted flushed on the outer wall of the tube,thus constituting a capacitor in which the dielectric is formed by theair-water flow and the tube wall.

An equivalent electric circuit of the capacitance sensor is shownin Fig. 14. A high frequency (MHz) signal is applied in the transmit-ting electrode and read at the receiving electrode. The signal is thenamplified in the electronics, filtered, and read in the acquisition sys-tem. The calibration details and accuracy of the sensors are presentedin Appendices A.2 and B.2.5.

c) Velocity

The velocity of the characteristic flow structures of the flowregimes, such as Taylor bubbles in plug flow and liquid slugs in slugflow, was calculated based on the normalized capacitance signal (V )of the two gas holdup sensors. During each run, the probes were po-sitioned at a known distance, zs, from each other. Two simultaneousdiscrete signals were acquired by the same acquisition system, in a syn-chronous manner and with a frequency of 1000 Hz. These two signals(consisting of a relatively long time interval) were compared by meansof a normalized cross-correlation (ORFANIDIS, 1996),


Figure 12 Test section and gas holdup capacitive probes.

Figure 13 Details of the capacitive probe.

3.2 Components 59

Ctp

Rtp

C w C w

Figure 14 Equivalent electric circuit of the capacitance sensor aspresented by Libert et al. (2011).

RV 1 V 2 (m) =1

N

Nm1n=0

V 1,n+mV2,n, 0 m N 1 (3.11)

where V 1 and V2 are vectors of the measured flow capacitance of probes

1 and 2, each of which with N elements.The time lag between the signals, t, was estimated based on

the value of m that gives the maximum value of RV 1 V 2 (m),

t = mmax1

faq, (3.12)

where faq is the data acquisition frequency. Thus, the velocity of theflow structures3 is given by,

u =t

zs. (3.13)

d) Temperature

Water temperature and room temperature were kept at 24 C.

3It should be noted that this method allows for an evaluation of the averagevelocity of the flow structures using the entire signal (e.g., in plug flow the signalconsists of a time interval covering several bubbles), as opposed to evaluating thevelocity of each structure individually and than averaging the results.


Nonetheless, flow temperature was evaluated by four T-type thermo-couples measuring temperature right at the inner wall of the channel.Two are located at the flow mixers, and the other two at the inlet andoutlet of the pressure measurement segment (Fig. 3).

e) Visualization

A Phantom V310 high-speed camera was used to record the fastphenomena related to the motion of the phases. The flow was recordedat a rate of 3287 frames per second (at resolution of 1024800 pixels).Three light-emitting diode sources were used to illuminate the flow,and were synced with the exposure time interval of the camera.

3.2.4 Equipment information

Table 6 shows the specification of sensors and other relevantequipment used in this work. Table 7 presents the expanded uncertaintyand range of sensors (for a confidence interval C.I.) according to themanufacturers. A detailed uncertainty analysis has been conductedand is presented in Appendix B.

Table 6 Equipment details.

Sensors Manufacturer ModelAbsolute pressure HBM P3MBDifferential pressure Rosemount 3051SAir mass flow rate Kurz 504FTBWater mass flow rate Micromotion CMF050Gas holdup UTFPR SICEMTemperature Omega Type T

Others Manufacturer ModelAcquisition system NI SCXIGlass tubes Schott DuranThermostatic bath Marconi MA184Pump KSB P1000Frequency inverter Weg CFW08Pressure regulator Parker 06R

3.3 Experimental procedure 61

Table 7 Uncertainty of measured parameters.

Sensor U C.I. RangeAbsolute pressure 0.72 kPa 0.99 0 1000 kPaDifferential pressure 2.6 Pa 0.99 4000 PaAir mass flow rate 2.125% of rate 0.95 0 120 kg/hWater mass flow rate 0.163rate % of rate 0.99 < 163 kg/hWater mass flow rate 0.1% of rate 0.99 163 6800 kg/hGas holdup 17.32% (max.) 0.95 0 1Temperature 1 C 0.95 40 125 C

3.3 EXPERIMENTAL PROCEDURE

The experimental procedure is described as follows. The test rigis initialized by turning the thermostatic bath on and setting the valvesystem so only air enters the test section. The pressure regulator andthe micrometric valve are set to generate a flow of air inside the testsection. After the test section is completely free of liquid water, voltagesignals of both gas holdup sensors are read and stored for calibration(signal normalization4) purposes. The valves are then set to a positionwhere only water enters the test section and the pump is turned on.A shut-off valve (10) located downstream the test section is partiallyclosed, thus generating an increase of pressure inside the test section.Following that, any air bubbles inside the tubing connecting the pres-sure transducers to the test section are purged from the system. Then,the shut-off is opened after the system has been purged, and voltagesignals of both gas holdup sensors are again read and stored.

After performing the previous procedure, experiments can becarried out. As the pump is turned on and the pressure regulator isopened, mass fluxes of air and water are set by adjusting the valves andpump speed. Mass fluxes of each phase are measured individually up-stream of the inlet mixer. Only a few minutes are required for the flowrates to stabilize in the test section at each condition. Figure 15 showsthe superficial velocities (depicted on the flow regime map of Madhaneet al., 1974) used in the tests to evaluate the pressure drop in the bend.In this case, 174 experimental runs were performed. Superficial gasvelocities at the inlet of the measuring section (marked as ref. in Fig.3) were varied between 0.2 and 40 m/s for three nominal values of super-ficial liquid velocity (0.05, 0.2 and 1 m/s) covering the stratified, plug,

4Refer to Section A.2


slug and annular flow regimes. The flow regimes observed upstream ofthe bend for all experimental conditions agreed with the flow regimemap.

In the experiments dedicated to evaluating the influence of thebend on the straight segments upstream and downstream, tests werecarried out for three flow regimes in both upward and downward direc-tions, accounting for six distinct flow conditions. For each condition,the superficial liquid velocity was set as 0.2 m/s, and the superficial gasvelocity was varied between the nominal values of 0.4, 4 and 20 m/s,corresponding to the plug, slug and annular flow regimes, respectively.Measurements were taken at 12 positions of the gas holdup probes. Intotal, 36 experimental runs were performed (six flow conditions), withthe pair of gas holdup probes placed at six different positions along thetest section (Fig. 3).

As the majority of the flow conditions involve intermittent flowregimes, the sampling interval needed to be significantly larger thanthe characteristic time scales of the flow structures (e.g. slug and waveperiods), as suggested by Coleman & Steele (2009) for timewise exper-iments. The sampling interval used in the present study varied froma few seconds (single-phase flow and annular flow) to several minutes(plug and slug flows) depending on the condition. The sampling rateused was 1 kHz. While data were saved, one had to select the horizontaltube segments where the differential pressure measurements were beingtaken, by adjusting the 5-way valves (seen in Fig. 11).5

3.4 VALIDATION

The validation of the experimental apparatus was carried out bymeasuring pressure drop at the test section for single-phase water flow,and comparing it with values obtained from the Darcy-Weisbach equa-tion and correlations proposed by Idelchik (1992) and Kitto & Stultz(2005). A single bend with curvature of 8.7 was used. Figure 16(a)shows the frictional pressure drop of the two horizontal sections and thebend, measured at different flow conditions represented by the Reynoldsnumber. At high Reynolds numbers, experimental results slightly di-verge from the proposed correlations. However, the frictional pressuredrop of the 1 m straight tube segment upstream of the bend agrees withthe values obtained from the Darcy-Weisbach equation (Fig. 16(b)),

5Details of the experimental procedures are presented as an itemized list insection A.1.

3.5 A first look at the flow parameters 63

j g (m/s)

j l (m

/s)

10-1 100 101 10210-2

10-1

100

101 bubbly

slug

stratified wavy

annular

plug

Figure 15 Superficial velocities of the test conditions shown on theMandhane et al. (1974) flow regime map.

suggesting that the discrepancy in Fig. 16(a) is due to a minor devia-tion of both Idelchik (1992) and Kitto & Stultz (2005) bend correlationsat those specific test conditions.

3.5 A FIRST LOOK AT THE FLOW PARAMETERS

The dynamics of gas-liquid flows is very complex due to inter-facial phenomena and compressibility of the gas phase. In such flows,the concept of fully developed

Documents

ON AIR-WATER TWO-PHASE FLOWS IN RETURN BENDS