Pedro Magalh˜aes de Oliveira
ON AIR-WATER TWO-PHASE FLOWS IN RETURN BENDS
Florian´opolis 2013
ESCOAMENTO BIF ´ASICO AR- ´AGUA EM CURVAS DE 180◦
Disserta¸c˜ao submetida ao Programa de P´os-Gradua¸c˜ao em Engenharia Mecˆanica para a obten¸c˜ao do t´ıtulo de Mestre em Engenharia Mecˆanica.
Orientador: Prof. Jader Riso Barbosa Jr., Ph.D.
Florian´opolis 2013
de Oliveira, Pedro Magalhães
Escoamento bifásico ar-água em curvas de 180° / Pedro Magalhães de Oliveira ; orientador, Jader Riso Barbosa Jr. - Florianópolis, SC, 2013.
155 p.
Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico. Programa de Pós-Graduação em Engenharia Mecânica.
Inclui referências
1. Engenharia Mecânica. 2. escoamento bifásico. 3. curva de 180° . 4. queda de pressão por atrito. 5. fração de vazio. I. Barbosa Jr., Jader Riso. II. Universidade Federal de Santa Catarina. Programa de Pós-Graduação em Engenharia Mecânica. III. Título.
ESCOAMENTO BIF ´ASICO AR- ´AGUA EM CURVAS DE 180◦
Esta Disserta¸c˜ao foi julgada aprovada para a obten¸c˜ao do t´ıtulo de “Mestre em Engenharia Mecˆanica”, e aprovada em sua forma final pelo Programa de P´os-Gradua¸c˜ao em Engenharia Mecˆanica.
Florian´opolis, 13 de dezembro 2013.
Armando Albertazzi Gon¸calvez Jr., Dr. Eng. Coordenador do Curso
Banca Examinadora:
Prof. Jader Riso Barbosa Jr., Ph.D. Orientador
Prof. J´ulio C´esar Passos, Dr.
Return bends are found in various applications involving two-phase flow, including heat exchangers, transport pipes and separators. Gas-liquid flows in bends are affected by centrifugal forces that tend to separate both phases. If the bend is oriented vertically, the flow is also subjected to gravitational effects. The resulting effect of such forces is a change of the flow configuration as it passes through the bend, which depends on several aspects, such as flow direction (i.e., upward and downward), curvature, flow rates, and physical properties. Thus, the flow shows a distinct behavior in the return bend if compared to a straight tube. The main objective of this study is the characteri-zation of air-water two-phase flows in 180◦ return bends that connect
two 5-m long 26-mm ID horizontal tubes. The bend lies in the vertical position and the two-phase flow can be set as upward or downward. The behavior of the static pressure downstream and upstream of the return bend was measured for a wide range of flow regimes, as was the pressure drop and change in gas holdup associated with the return bend itself. The behavior of the phases in the bend was investigated with a high-speed camera, illustrating several particular features of the two-phase flow in the bend in both directions. The experiments were carried out with bend curvatures 2R/d of 6.1, 8.7, and 12.2 in both upward and downward directions. Superficial velocities varied from 0.2 to 40m/sfor the gas, and were set as 0.05, 0.2 and 1m/sfor the liquid.
The irreversible pressure changes in the bend were determined based on the differential pressure and gas holdup measurements, resulting in an empirical correlation. The gas holdup was measured at 12 different positions, 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 the return bend on the flow and the evaluation of flow parameters along the axis of the tube.
Keywords: two-phase flow, return bend, frictional pressure drop, gas holdup.
Tubula¸c˜oes com curvas de 180◦ s˜ao frequentemente encontradas na
ind´ustria em aplica¸c˜oes envolvendo escoamentos bif´asicos, como tro-cadores de calor e dutos de transporte. Nestes equipamentos, o escoa-mento g´as-l´ıquido sofre um efeito centr´ıfugo devido `a curva, que tende a separar ambas as fases. A influˆencia deste tipo de singularidade ´e ainda mais intensa quando a curva ´e posicionada na vertical, pois o es-coamento ´e sujeito a uma complexa combina¸c˜ao de for¸cas: centr´ıfuga, atrito e gravitacional. Ainda, o efeito resultante depende de parˆametros do escoamento, como sentido (ascendente ou descendente), curvatura, vaz˜oes e propriedades f´ısicas. Devido `a a¸c˜ao combinada das for¸cas, o escoamento apresenta na curva um comportamento distinto daquele observado em tubos retos, sendo a sua investiga¸c˜ao o principal obje-tivo deste estudo. Mais especificamente, este prop˜oe-se a caracterizar o escoamento bif´asico ar–´agua em uma curva de 180◦que conecta dois
tubos retos de 5,5 m e diˆametro de 26,4 mm. A curva ´e posicionada na vertical e o escoamento pode ser imposto nos sentidos ascendente e descendente. Inicialmente, o comportamento da press˜ao est´atica a montante e a jusante da curva foram medidos em in´umeras condi¸c˜oes de escoamento, bem como a queda de press˜ao e a varia¸c˜ao da fra¸c˜ao de vazio entre a entrada e a sa´ıda da curva. O comportamento das fases na curva foram observados com uma cˆamera de alta velocidade, ilustrando aspectos particulares do escoamento bif´asico 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. As velocidades superficiais das fases foram determinadas entre 0,2 e 40m/s
para o ar, e em 0,05, 0,2 e 1m/s para a ´agua. A partir da medi¸c˜ao
de queda de press˜ao total na curva e da varia¸c˜ao da fra¸c˜ao de vazio, avaliou-se somente a parcela irrevers´ıvel da queda de press˜ao na curva, resultando em uma correla¸c˜ao emp´ırica. Em uma segunda parte, a fra¸c˜ao de vazio foi medida em 12 pontos posicionados a montante e a jusante da curva, compreendendo os regimes em tamp˜oes, em golfadas e anular, nas dire¸c˜oes ascendente e descendente, possibilitando uma mel-hor compreens˜ao acerca da influˆencia da curva no escoamento, al´em de permitir avalia¸c˜ao dos parˆametros do escoamento ao longo do eixo da tubula¸c˜ao.
Palavras-chave: escoamento bif´asico, curva de 180◦, queda de press˜ao
Agrade¸co ao Professor Jader R. Barbosa Jr., por manter a porta de sua sala sempre aberta, pelos rascunhos corrigidos do t´ıtulo ao ´ultimo ponto final, por todas as oportunidades e pela amizade nestes trˆes anos de pesquisa e trabalho duro.
Aos que, ao meu lado, desenvolveram este trabalho: os alunos de ini-cia¸c˜ao cient´ıfica Eduardo Strle, Marcos Abe e Rafael Dantas, e os t´ecnicos Marcelo Cardoso, Marcos Esp´ındola e Pedro Cardoso. Aos que trocaram suas noites e fins de semana pelo subsolo do POLO. A todos os colegas de mestrado e de laborat´orio com quem tive o prazer de aprender e trabalhar; em especial a Dalton Bertoldi, Gus-tavo Portella e Mois´es Marcelino, que me guiaram nos meandros da pr´atica experimental e na constru¸c˜ao do aparato.
Ao Prof. Marco da Silva, Nikolas Libert e Leonardo Lipinski, da Uni-versidade Tecnol´ogica Federal do Paran´a, por toda a colabora¸c˜ao e por nos fornecerem os sensores de fra¸c˜ao de vazio, parte fundamental do aparato e que distingue este trabalho.
Ao Prof. Geoffrey F. Hewitt, por gentilmente nos ceder os filmes 16 mm gravados 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 Cient´ıfico e Tecnol´ogico, pelo suporte financeiro.
` A Maria.
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
4.1.1 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
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 map for horizontal flows of air and water at atmospheric pressures in
25.4 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 each other, allowing pressure and temperature measurements. . . 53
Figure 10 Positions of the pressure taps and gas holdup sensors positions. The measurements were taken at symmetric locations between the upper and lower tubes. (Dimensions in meters) . . . 54
Figure 11 Set of valves and tubings, absolute pressure sensor and differential 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 as presented by Libert et al. (2011). . . 59
Figure 15 Superficial velocities of the test conditions shown on the Mandhane 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)
= 0.05m/s, jg= 1m/s. From left to right, images were taken with a
40 ms time interval between consecutive frames. . . 70 Figure 22 Oscillatory flow in upward direction (low liquid flow rate). . . 71 Figure 23 Plug flow in upward direction. . . 71 Figure 24 Phase distribution in upward plug flow (jl = 0.2m/s, jg
= 0.4m/s). The sequence illustrates the nose and body of a rising
bubble. The time interval between frames is 152 ms. . . 73 Figure 25 Phase distribution in downward plug flow (jl= 0.2m/s, jg
= 0.4m/s). The sequence shows the nose and body of a descending
bubble. The time interval between frames is 532 ms. . . 73 Figure 26 Phase distribution in downward plug flow (jl = 0.2m/s,
jg = 0.4m/s). The sequence shows the tail of a descending bubble,
followed by roughening and breakup of the gas-liquid interface. The time interval between frames is 91 ms. . . 74 Figure 27 Phase distribution in upward (left) and downward (right) slug flow in the bend (jl= 0.2m/s, jg = 4m/s). . . 74
Figure 28 Phase distribution for downward annular flow in the bend (jl= 0.2m/s, jg = 20m/s), showing the detachment of disturbances
waves from the film towards the outer part of the curve. Time interval between frames is 30 ms. . . 76 Figure 29 Phase distribution for upward annular flow in the bend (jl= 0.2m/s, jg = 20m/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 low
gas 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 the
low gas flow rate data (plug and slug flow regimes). . . 79 Figure 32 Measured gas holdup values at top and bottom positions of the bend for all flow conditions and curvatures of 6.1, 8.7, and 12.2. . . 81 Figure 33 Liquid level at the position of the lower gas holdup probe. Downward flow, jl= 0.05m/s, jg = 1m/s. From the top, curvatures
of the bend are 6.1, 8.7, and 12.2. . . 82 Figure 34 Average gas holdup values in the bend for (a) upward and (b) downward flow for jl= 0.2m/s. . . 83
Figure 36 Histograms of probability density of the experimental results. . . 86 Figure 37 Frictional pressure drop in the bend for upward and downward 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), Chen et 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 the frictional pressure drop in (a) upward flow and (b) downward flow. 95 Figure 42 Gas holdup distribution in upward and downward flow for the plug, slug, and annular flow regimes. . . 96 Figure 43 Gas holdup distribution for upward and downward plug flow (jl = 0.2m/s, jg = 0.4m/s). . . 97
Figure 44 Gas holdup distribution for upward and downward slug flow (jl = 0.2m/s, jg = 4m/s). . . 97
Figure 45 Gas holdup distribution for upward and downward an-nular flow (jl = 0.2m/s, jg = 20m/s). . . 98
Figure 46 Frictional and accelerational pressure gradients in (a) downward and (b) upward plug flow (jl= 0.2m/s, jg = 0.4m/s). . . 100
Figure 47 Frictional and accelerational pressure gradients in (a) downward and (b) upward slug flow (jl = 0.2m/s, jg = 4m/s).. . . 102
Figure 48 Frictional and accelerational pressure gradients in (a) downward and (b) upward annular flow (jl = 0.2m/s, jg= 20m/s). 103
Figure 49 Velocity distribution of Taylor bubbles in upward and downward plug flow (jl= 0.2m/s, jg = 0.4m/s). . . 104
Figure 50 Velocity distribution of liquid slugs in upward and down-ward slug flow (jl = 0.2m/s, jg = 4m/s). . . 105
Figure 51 Experimental calibration curves of the gas holdup sensors based on the stratified regime. . . 121 Figure 52 Experimental calibration curves of the gas holdup sensors
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 measurement information). . . 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 drop correlations 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 pressure drop 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
NOMENCLATURE Greek α Gas holdup -β Volumetric quality -∆p Pressure difference Pa Absolute roughness m µ Viscosity Ns/m2 ∇p Pressure gradient Pa/m
φ2 Two-phase flow multiplier
-φ2
k Two-phase flow multiplier (k-phase alone)
-φ2
ko Two-phase flow multiplier (total flow assumed k-fluid)
-ρ Density kg/m3
ρ0 Momentum density kg/m3
Roman
d Internal diameter m
f Friction factor
-faq Data acquisition frequency Hz
F r 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
Re Reynolds number
-Sr Slip ratio
-T Temperature K
t Time s
u Velocity m/s
W Mass flow rate kg/s
W e 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
1 INTRODUCTION
Gas-liquid flows are found in the majority of energy-related and cooling applications. The flow of a refrigerant in a heat exchanger and the transport of crude oil or natural gas in a pipe are typical gas-liquid flow problems.
Historically, engineering problems involving two-phase flows have been strongly related to steam generation, dating back to the days of the Industrial Revolution. However, the rigorous study of two-phase flows was initiated in the second half of the twentieth century, after the World War II. At that time, nuclear research started to be used for 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 enormous amounts of thermal energy out of the reactor core and into the steam turbines.
Recently, environmental catastrophes such as the Deepwater Hori-zon oil spill (Gulf of Mexico, 2006) and the Fukushima Daiichi nuclear disaster (Japan, 2011) have encouraged governments to push safety standards to stricter levels.1 These requirements, as well as the
inter-est in the economical value associated with energy production, have stimulated 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 bends are affected by centrifugal forces that tend to separate both phases. If the bend is oriented vertically, the flow is also subjected to gravita-tional effects. The resulting effect of such forces is a change of the flow configuration as it passes through the bend, which depends on several aspects, 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 better assessment of irreversible losses in singularities is required. The objec-1Refer to the following reports: Deepwater Horizon Study Group (2011), Det Norsk Veritas (2011), The Fukushima Nuclear Accident Independent Investigation Comission (2012).
tive of the present study is to characterize air-water two-phase flows in a vertically-oriented 180◦ return bend. To this end, an experimental
apparatus capable of reproducing the majority of flow regimes found in horizontal tubes was designed and constructed, allowing the investiga-tion of the reversible and irreversible pressure changes occurring in the bend and in the straight tube segments – upstream and downstream of it.
This work was carried out at Polo – Research Laboratories for Emerging Technologies in Cooling and Thermophysics, under the aus-pices of a research program on Multiphase Flow in Pipes funded by CENPES/Petrobras.
1.2 OVERVIEW
This thesis is structured as follows. Chapter 2 presents a brief review 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 presented after the literature review, at the end of Chapter 2. Chapter 3 con-tains information about the general features and main components of the experimental apparatus, its measuring devices and techniques, and the 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 frictional pressure drop correlation, and aspects of developing flow in the vicinity of the bend. Chapter 5 presents the conclusions and recommendations for 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.
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-phase flow in 180◦ return bends is carried out, highlighting some unresolved
questions and research gaps that motivated the specific objectives of the 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 modmod-els employed in indus-try are one-dimensional. These models often resort to empirical cor-relations to evaluate frictional losses and phase holdup. Thus, several experimental works have focused on the development of accurate cor-relations for the frictional pressure drop and gas holdup in tubes and singularities for a range of flow conditions.
2.1.1 Pressure drop
In the homogenous model, the two-phase mixture behaves as a pseudo-fluid with average thermophysical properties. The frictional pressure gradient is calculated with the Darcy-Weisbach equation,
dp dz f = f1 d G2 2ρ, (2.1)
where p is the static pressure, z is the axial coordinate of the tube, f is the Darcy friction factor, d is the tube diameter, and G is the total mass flux. The fluid density ρ is taken as the homogeneous mixture density given by (COLLIER; THOME, 1996),
ρh= x ρg +1 − x ρl −1 . (2.2)
where x is dynamic gas mass fraction (quality), x = Gg
and the subscripts g and l denote gas and liquid, respectively. For laminar flow, the Darcy friction factor is given by,
f = 64
Re, (2.4)
while for conditions of turbulent flow, Colebrook (1939) proposed the following implicit expression,
1 √ f = −2log10 3.7d+ 2.51 Re√f (2.5) where Re is the Reynolds number and is the absolute roughness of the tube wall. In order to evaluate both Eqs. 2.4 and 2.5 in the case of homogenous two-phase flow, the Reynolds number must be calculated using a model for the homogeneous viscosity such as the one proposed by McAdams et al. (1942) apud Collier & Thome (1996),
µh= x µg +1 − x µl −1 (2.6) where µ 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, φ2, which
relates the frictional pressure drop of two-phase flow with that of single-phase flow by,
∆pf,tp= φ2k∆pf,k, (2.7)
where ∆pf,k is the pressure drop of the single-phase flow of phase k
with mass flux equal to the mass flux of this phase in the two-phase flow. Other multipliers can be conveniently defined as follows,
∆pf,tp= φ2ko∆pf,ko, (2.8)
where the subscript ko, denotes the single-phase flow of phase k with a mass flux equal to the total mass flux of the two-phase mixture. Following the above definitions, four different two-phase multiplier can be proposed for gas-liquid flows: φ2
l, φ 2 g, φ2lo, φ
2 go.
Lockhart & Martinelli (1949) assumed that the two-phase mul-tipliers are function of the so-called Martinelli parameter, X2, defined
X2= ∆pf,l
∆pf,g. (2.9)
In their work, graphical correlations of two-phase multipliers in terms of this parameter were proposed based on the flow regimes associated with the corresponding single-phase flow of the individual phases (viscous or turbulent). Chisholm (1967, 1983) suggested the following relations for φ2, which have been more extensively used thereafter,
φ2 l = 1 X2 + C X + 1, (2.10) and, φ2 g= X2+ CX + 1. (2.11)
The coefficient C is determined based on the flow conditions shown in Table 1.
Table 1 – Coefficient C of Eqs. 2.10 and 2.11 .
Liquid Gas C
Viscous Viscous 5 Turbulent Viscous 10
Viscous 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 method available (GHIAASIAAN, 2007). The author suggests the following ex-pression to evaluate the liquid-only two-phase multiplier, φ2
lo, φ2 lo= A + 3.24x0.78(1 − x)0.24 ρl ρg 0.91 µ g µl 0.19 1 − µg µl 0.7 F r−0.0454h W e−0.035h , (2.12) where F rhand W ehare the homogeneous-flow Froude and Weber
num-bers. The parameter A is given by,
A = (1 − x)2+ x2ρlfgo
ρgflo
where fko is the Fanning friction factor for single-phase flow of fluid k
with a mass flux equal to the total mass flux of the two-phase flow. M¨uller-Steinhagen & Heck (1986) developed an empirical expres-sion to evaluate the frictional pressure gradient in horizontal tubes given 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 experimental data, and the frictional pressure gradients for single-phase flow are calculated based on the following relation for the Darcy friction factor,
fko= ( 64 Reko, Reko≤ 1187; 0.3164 Re0.25 ko , Reko> 1187. (2.15) 2.1.2 Gas holdup
In the separated flow model, empirical relationships are also used to correlate the gas holdup, α, to the independent parameters of the flow. Using the Lockhart-Martinelli method for pressure drop, an ex-pression for gas holdup was derived by Collier & Thome (1996). It follows that, for the annular flow regime,
φ2
l = (1 − α) −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 are known to provide better results. Smith (1969) proposed the following expression for the gas holdup in horizontal tubes,
α = 1 + ρg ρl 1 − x x 0.4 + 0.6 v u u t ρl ρg + 0.4 1−x x 1 + 0.4 1−x x −1 . (2.17)
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 as
the 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 = β 1 − β (2.19) E1= 1.578Re−0.19lo ρl ρg 0.22 , (2.20) E2= 0.0273W elRe−0.51lo ρl ρg −0.08 . (2.21)
and β is the dynamic volume fraction (volumetric quality),
β = Gg ρg Gg ρg + Gl ρl . (2.22)
Thus, a direct expression for α in terms of Sr is given by substituting
Eq. 2.18 in the following relationship between mass quality and gas holdup (GHIAASIAAN, 2007), x 1 − x = ρg ρl Sr α 1 − α. (2.23)
A very accurate but rather involved method for calculating the gas holdup was proposed by Chexal et al. (1991). The proposed correla-tion covers a wide range flow condicorrela-tions, and yet provides a continuous function. This method is based on the parameters of drift flux two-phase flow models and consists of a large number of implicit equations and over twenty arbitrary constants. Although the Chexal et al. (1991) correlation was used in the present work, its equations were omitted for 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 drop in two-phase flow of refrigerants in small curvature bends focusing on cooling applications (PIERRE, 1964a; TRAVISS; ROHSENOW, 1971; GEARY, 1975; CHEN et al., 2004; SILVA LIMA; THOME, 2010; PADILLA et al., 2011). Others carried out experiments with air-water flows in return bends (USUI et al., 1980;HOANG; DAVIS, 1984;WANG et al., 2008) and discussed in detail the hydrodynamics of two-phase flow in the bend. Among these, different approaches for evaluating the irreversible pressure 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 drop in two different segments: a straight segment upstream of the bend, and another segment that includes the bend and the straight section downstream of it. In this way, it is possible to estimate the frictional component of pressure drop in the bend assuming that the average frictional pressure gradient downstream is equal to the one upstream. Accurate predictions with this method would require a straight section downstream of the bend long enough to allow for flow development (or recovery).
Although the previous methods of pressure drop evaluation seem reasonable for horizontal return bends, they are questionable if the bend is oriented vertically. In this case, the static pressure head, which de-pends on the gas holdup in the bend, must also be accounted for. This was discussed by Usui et al. (1980), who identified that no study had been conducted on the behavior of average gas holdup and pressure drop in the bend at that time. More recently, Chen et al. (2008) and Padilla et al. (2013) evaluated the static pressure change in vertical return 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) used the correlation of Steiner (1997).
The method proposed by Geary (1975) was used extensively in several works that focused on the irreversible losses in bends. Although this method is strongly dependent on the extent of the flow recovery at the pressure tap located downstream of the bend, only a few studies attempted to quantify this effect (TRAVISS; ROHSENOW, 1971;HOANG; DAVIS, 1984; PADILLA et al., 2012; SILVA LIMA; THOME, 2012;DE
KER-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 to Castillo (1957), who carried out a theoretical and experimental inves-tigation of pressure drop in air-water flow. In his work, the two-phase flow in a horizontally-oriented return bend was modeled as the rotation of separated phases in the bend. Thus, predictions with this method only agreed with the experimental data for low gas velocities and the stratified flow regime. Although the phases were assumed to flow at the same velocity, the author argued that the relative motion of the phases played an important role on the pressure drop in the bend.
Pierre (1964a, 1964b), carried out tests with R-12 and R-22 in straight tubes (10.9 mm ID). He proposed an empirical correlation for friction factor based the experimental data (PIERRE, 1964a apud GEARY, 1975). In the same work, the pressure drop of R-12 in hori-zontal return bends was investigated and mathematically expressed in terms of two components: the loss due to turning of the flow, and the loss due to friction. Experiments were conducted with bend curvatures (defined as the ratio of the bend radius to the pipe radius, or 2R/d) of 3.5 and 6.9. According to Geary (1975), the pressure drop correlation proposed by Pierre (1964a) did not take into account the effect of the bend curvature radius, because of the relatively low mass fluxes. Be-cause of that, it could lead to incorrect predictions when used at other flow conditions.
Geary (1975) investigated the two-phase flow of refrigerants in re-turn bends using a test section comprising two horizontal rere-turn bends and three straight-tube segments. Eight return bends of approximately 11.1 mm ID with different curvature radii were used, covering values of bend curvature from 2.3 to 6.5. The mass flux of refrigerant was varied between 100 and 400kg/m2s. The pressure drop was measured between
two taps, one located 40 diameters upstream of the bend and another 40 diameters downstream (Lu = 40d and Ld = 40d). This approach
was used to account for the effect of the bend on the straight sections. The pressure drop in the bend ∆pb was evaluated by the following
expression,
∆pb= ∆pt−Lu+ Ld
where ∆pt is the measured pressure drop between the upstream and
downstream segments, and ∆ps is the pressure drop in a straight
seg-ment of length Ls far upstream of the bend. Although the accuracy
of 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 empirical correlation for the pressure drop in the bend, which took into account the influence of the curvature.
Chisholm (1980) developed a correlation for the pressure drop in horizontal 90◦ bends and compared its predictions with the
steam-water flow data of Fitzsimmons (1964). The method was later extended to cover data for bends other than 90◦ and bend orientations other
than the horizontal (CHISHOLM, 1983). The suggested correlation for the bend pressure drop is,
∆pb= φ2b,l∆pb,l, (2.25)
where the pressure drop for single phase liquid flow in the bend is given by,
∆pb,l= kl
G2
2ρl
, (2.26)
and kl is the loss coefficient for single-phase flow in the bend. In the
present work, this coefficient was evaluated using the method proposed by Idelchik (1992). The two-phase multiplier proposed by Chisholm (1980) is given by, φ2 b,l= 1 + ρl ρg − 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 and water 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 1500kg/m2s, covering
all horizontal flow regimes. Pressure drop was measured in two straight segments and in the bend, similarly to Geary (1975). However, as the return bends were positioned in the vertical plane, Eq. 2.24 must now also account for the static head, and becomes,
∆pb= ∆pt−
Lu+ Ld
Ls
∆ps± [ ¯ρgα + ¯¯ ρl(1 − ¯α)] g2R, (2.29)
where 2R corresponds to the height of the bend, and the sign of the gravitational term is positive for the upward direction and negative for the downward direction. The average values of the phase densities and gas holdup are considered as average values in the bend. Usui et al. (1980, 1981) used a pair of quick-acting solenoid valves at the inlet and outlet of the bend, which were simultaneously closed so the liquid volume could be measured and, from that, an average value of the gas holdup in the bend could be estimated. Although a correlation based on the single-phase frictional pressure drop was proposed, most of their findings were related to the hydrodynamic behavior of the flow, which will 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 test section consisting of consecutive bends (U-type wavy tubes). Chen et al. (2004) carried out experiments with R-410A, using four bends with curvatures ranging from 3.9 to 8.2 and internal diameters between 3.3 and 5.07 mm ID. The mass flux of refrigerant was varied between 100 and 900kg/m2s. The orientation of the bend was not informed, but later
works 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 and
Ld = 140d) of the wavy tubes. The pressure drop of a single bend was
evaluated by dividing the measured pressure drop associated with the entire wavy segment by the number of consecutive bends. The Chen et al. (2004) database was combined with that of Geary (1975) to yield the following correlation for pressure drop in return bends (CHEN et al., 2004), −dp dz b = fρgj 2 g 2d , (2.30)
where jg is the superficial gas velocity, i.e., the average velocity of the
factor, f , was expressed as, f = 10 −2Re0.35 tp W e0.12 g exp(0.1942Rd )x1.26 , (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 lubricating oil on the pressure drop of R-410A and R-134a in the same experimental setup used by Chen et al. (2004). Chen et al. (2008) also conducted experiments in the same experimental setup, but examined the effect of the orientation of the test section (horizontal and vertical) on the flow behavior. In this work, experiments were carried out with R-134a using only the wavy test section of 5.07 mm ID and bend curvature of 5. In the evaluation of the pressure drop in the vertically-oriented wavy section, the contribution due to acceleration of the flow was neglected, and the total frictional loss due to the wavy and the straight segments was expressed as,
∆pf = ∆p ± [ ¯ρgα + ¯¯ ρl(1 − ¯α)] g18R, (2.33)
where ∆p is the measured pressure drop, 18R corresponds to the height of the wavy section consisting of consecutive bends, and the sign of the gravitational term is positive for the upward direction and negative for the downward direction. The phase densities and gas holdup are considered 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 the upward and downward directions. With one equation for each flow direction, and assuming that the frictional component of pressure drop was the same for both directions, it was possible to estimate the gas holdup in the bend,
α = ρ¯l
−h(∆pb)down− (∆pb)up
i 36Rg ( ¯ρl− ¯ρg)
. (2.34)
The pressure drop experimental data of Chen et al. (2008) were inserted 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 author’s knowledge, the assumption of identical frictional pressure drop for both flow directions is incorrect. It is also contradictory because the authors themselves reported higher values of pressure drop in downward flow, particularly at low qualities. As will be seen in the present dissertation, the ac-celeration component of the pressure drop is not always negligible nor can the averaged holdup be assumed always equal to that for straight tubes.
Using the experimental data from Geary (1975) and Chen et al. (2004), Domanski & Hermes (2008) proposed an empirical correlation for predicting the pressure drop in horizontal bends. The pressure drop in a straight segment was correlated to the pressure drop in the bend by a “curvature” multiplier, dp dz b = Λ dp dz s , (2.35)
which was obtained based on the Buckingham-Pi theorem, and is given by the expression, Λ = 6.5 · 10−3 Gxd µg 0.54 1 x− 1 0.21 ρ l ρg 0.34 2R d −0.67 . (2.36) Padilla et al. (2009) used the experimental data from Chen et al. (2004, 2007, 2008) and Traviss & Rohsenow (1971) to propose a new correlation. The pressure gradient was calculated in terms of the pressure gradient in straight tubes plus a local contribution due to the centrifugal 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 M¨uller-Steinhagen & Heck
(1986) correlation and, dp dz sing = 0.047 ρgj 2 g R ! j2 l R 1/3 , (2.38)
which resembles the bend pressure drop due to rotation proposed by Castillo (1957), where jl is the superficial liquid velocity.
Later, Padilla et al. (2011) conducted experiments using R-410A in horizontal bends with curvatures ranging from 3.7 to 4, and internal
diameters between 7.90 and 10.85 mm. The test section used consists of 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 of the bend (Lu= 10d and Ld = 20d). The mass flux ranged between 179
and 1695kg/m2s. A preliminary investigation of the flow development
downstream of the bend was also carried out, which was later discussed in 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 ID and curvature of 9). The total pressure drop was measured between 7 segments, resulting in average values of the pressure gradient in the bend and at positions upstream and downstream of it (at 141, 59 and 6 diameters in both segments). The contribution of the acceleration of the flow to the total pressure drop was neglected. Thus, the frictional pressure drop in the bend was directly associated with the measured values by the following expression,
dp dz b = ( ∆pb−d 2 " dp dz b + dp dz −6d #) 1 πR + ( −d 2 " dp dz b + dp dz +6d #) 1 πR, (2.39) where the measured pressure difference in the bend, ∆pb, includes the
bend 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 bend was subtracted from the total pressure difference by approximating the pressure gradient in the straight segments to the average gradient be-tween the bend and the nearest pressure taps (located at 6d upstream and downstream). Silva Lima & Thome (2010) also investigated the difference between pressure measurements taken at different circumfer-ential positions of the straight tubes (from the inner to the outer part of 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 has received some attention in the literature, being first addressed by Traviss & Rohsenow (1971), who measured the pressure drop and condensation heat transfer coefficient of R-12 along a horizontal segment (4.4-m long, 8-mm ID) immediately downstream of a vertical return bend. They concluded that the effect of a return bend on the downstream pressure drop was negligible when averaged over a length of 90 diameters, and that the pressure gradient did not deviate more than 10% from the fully-developed pressure gradient. In their work, two bends made of glass, 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 “to readjust very rapidly” when disturbed by the presence of the bend; a fact that was verified years later by Silva Lima & Thome (2012) and De 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 demonstrated that disturbance waves are somewhat destroyed as annular flow passes through the bend in upward flow. The high-speed film contains axial viewing sequences of the flow in the outlet of the bend, which help to understand the influence of the bend on the phase distribution in annular flow.
Usui et al. (1980, 1981) carried out air-water flow pressure drop experiments 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 of the static head in the return bend. Usui et al. (1980) used a pair of quick-acting solenoid valves at the inlet and outlet of the bend, which were simultaneously closed so the liquid content in the bend could be measured and, from that, an average value of the gas holdup in the bend could be estimated. They observed that the average gas holdup in the bend was not significantly influenced by the centrifugal force in the upward flow direction and, therefore, presented a good agreement with the Smith (1969) correlation. The opposite was observed for down-ward flow, where the gas holdup values differed significantly from those in straight tubes. The local gas holdup was measured by Usui et al. (1981) at the outlet of the bend and at positions of approximately 66 diameters upstream and downstream of it using an electrolytic probe. Measurements in the plug flow regime showed that the local gas holdup at 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 the downstream position, the cross sectional profile of the gas holdup was very similar to the one upstream of the bend, suggesting the existence of developed state of the flow. Besides measuring pressure drop and gas holdup in the bend, they also conducted visual observations of the flow and presented details on the different phenomena observed, e.g., flow reversal and flooding in the upward direction, and back flow of bubbles and coalescence in the downward flow direction.
Hoang & Davis (1984) conducted experiments with air-water flow in return bends connecting two 25.4-mm ID vertical tubes with curvatures of 4 and 6, in an inverted “U” configuration. Their study was limited to the bubbly flow regime, i.e., only high liquid mass fluxes were used. Static pressure was measured downstream and upstream of the bend, and within the bend itself. For the latter, the pressure taps were 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). High pressure losses were observed – as high as 20 times the pressure loss in single-phase flow – which were attributed to separation and remixing of the phases in the bend. The authors established a developing length of 9 diameters downstream of the bend, where the flow was considered to be well remixed. This value is 10 times lower than the one observed by Traviss & Rohsenow (1971), probably due to the very high liquid flow rates used in the more recent experiments. By comparing the angular pressure profiles with the high-speed film, it was verified that the onset of rotation and stratification (separation) of the flow occurred in and after the first half of the bend, respectively.
Studies focusing on the influence of the bend on the flow regimes of an air-water mixture were carried out by Wang and coauthors in horizontal return bends (WANG et al., 2003, 2004) and vertical return bends (WANG et al., 2005, 2008). In these works, the distribution of the phases was observed via still photography. Return bends of 3 to 6.9-mm ID and curvature of 3, 5 and 7 were used in the horizontal experiments, while a single bend geometry was used in the vertical experiments (6.9 mm ID and 2R/d = 3, where R is the bend radius and d is the pipe diameter). Phenomena such as flow regime transition from stratified to annular flow were observed in horizontal bends, being more 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) conducted experiments of R-134a two-phase flow in return bends in both horizon-tal and vertical orientations. Glass return bends (internal diameters of 8, 11 and 13 mm, and curvatures of approximately 3 and 5) were used to allow visualization of the flow with a high-speed camera. The recovery length downstream of the bend was evaluated qualitatively based on the visual characteristics of the flow, and was found to be larger in the vertical orientation of the bend, specially in upward flow. The authors observed a larger influence of the centrifugal force on the flow rather than the effect gravity, probably due to the small curvatures. Several flow 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 of 7.46) in order to determine the perturbation lengths downstream and upstream of the bend in both upward and downward flows. Addition-ally, the total pressure drop was measured at different pressure taps upstream and downstream of the bends (7.9 and 10.85 mm, curvatures of 3.68 and 4.05), for the above mentioned fluids and R-410A in the downward direction. In their work, the authors evaluate the gravi-tational term of pressure drop by estimating the gas holdup in the bend with the Steiner (1993) correlation. Perturbation lengths of the downward flow were determined as being 5 diameters upstream and 20 diameters downstream of the bend.
Recently, De Kerpel et al. (2013b) developed a method for deter-mining the downstream development length based on the measurement of the flow capacitance by a probe placed on the outer pipe wall. A clustering algorithm was used to group similar signals associated with specific flow regimes for developed flow conditions in straight tubes. Tests were performed with R-134a in a return bend of 8 mm ID and curvature 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 method was able to detect flow disturbances up to 10 diameters downstream of the 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 of the work shown in Tab. 2 (#), the fluids used (fluid ), and if measure-ments of pressure drop (∆p) and gas holdup (α) were carried out. The table also shows if flow visualization was conducted (vis.), and if the issue of flow development (flow dev.) was in some way investigated.
The matter of flow recovery downstream of the bend has been approached by means of flow visualization, total pressure drop mea-surements, and local gas holdup (or capacitance) measurements. The works dealing with vertically-oriented return bends are shown in bold typeface (Tables 2 and 3; except Hoang & Davis (1984) which uses an inverted “U” configuration). Among these, only Usui et al. (1980, 1981) have experimentally evaluated the gas holdup in the bend in order to accurately 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 until the present moment. In order to precisely evaluate the contribution of friction to the pressure drop, is it reasonable to neglect or over simplify the 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 both
8 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 both 12 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.
To what extent the flow parameters are influenced by the bend or, in other 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-liquid flows 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 regimes found in horizontal tubes;
2. Characterize experimentally the main independent parameters of the 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 bend using 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 measurement information).
# fluid ∆p α vis. flow dev.
1 R-12, R-22 X 2 R-12 X X X (∆p) 3 R-22 X 4 air-water X X X X (∆p, α) 5 air-water X X (∆p) 6 R-410A X 7 R-134a X 8 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)
in the straight sections upstream and downstream of the bend; 5. Propose a more accurate method for evaluating the local frictional
pressure 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 a comparison it against existing correlation for straight tubes, ii) the quantification of the magnitude of each component of the
total 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 on flow parameters and bend geometry.
3 EXPERIMENTAL APPARATUS
The present chapter contains information about the experimen-tal apparatus built to investigate the hydrodiynamics of the two-phase flow in return bends. At first, general aspects of the experimental ap-paratus are presented. In the following sections, detailed information is presented on the main components of the apparatus and measuring techniques.
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 individual fluid flow lines equipped with inlet flow mixers where the two phases are introduced. The air-water mixture flows from either of the two mix-ers through 26.4 mm ID horizontal borosilicate glass tubes. The test section 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 the flow. The development length in two-phase flow is not as established as in
single-jg (m/s) jl (m/s) 10-1 100 101 102 10-2 10-1 100 101 bubbly 2 bar 3 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 in 25.4 mm ID tubes.
izontal tubes and return bend are referred as the test section, where absolute pressure, pressure drop, gas holdup, temperature and velocity measurements were taken. The system is an open loop, that is, after the flow exits the test section the air is vented to the ambient, while water flows back to the reservoir.
The experimental apparatus was designed to work in a wide range of flow regimes. The operating range of the flow loop is shown in 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 of the absolute pressure required at the inlet of the flow loop (considering atmospheric pressure at the outlet) in order to overcome the flow losses in 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 with inlet pressures below 2 bar. Experiments were carried out at room tem-perature and low pressure, close to the atmospheric condition, setting the mass fluxes of air and water. Operating conditions are summarized in Table 4.
Table 4 – Test conditions of the experiments Test conditions
Pressure 101 − 400 kPa Temperature 24◦C
Air mass flux 0.15 − 60kg/m2s
Water mass flux 10 − 1400kg/m2s
3.2 COMPONENTS
A schematic representation of the experimental apparatus is shown in Fig. 3. In this figure, the test section is represented by a double line and appears at the top. Other than the test section, the experimental apparatus consists of the following parts, represented by single contin-uous lines: the mixing system (1 and 10), the water line (2-4), and the air line (5-9). The mixing system is formed by two mixers (1), each located 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 of the mixers, and also direct the two-phase flow leaving the test section back to the reservoir.
3.2.1 Air line, water line and mixing system
The water line comprises a thermostatic bath (2), a centrifugal pump (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. The thermostatic bath keeps the temperature of the water at 24oC in a 30 L
reservoir, and allows for particle filtration through a filter attached to its internal circulation system. Water is pumped from the reservoir by the centrifugal pump (3), and the flow rate is set by selecting the rotational speed of the pump in the frequency inverter and adjusting the gate valve and the by-pass. The flow is measured in the Coriolis flow meter and is directed to the top or bottom mixer, depending on the 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 mass flow meter (9) (Fig. 5). Water and particles present in the air are removed in the particle filter, while smaller contaminants such as oil
Air Water R R ∆p P P P T P T ∆p (1) (1) (2) (3) (4) (10) (5)(6) (7) (8) (9) ref.
{
α α α α α T T α ref.*{
Figure 3 – Sc hematic of the exp erimen tal app aratus.2
3 4
9
Figure 4 – Components of the water line.
droplets are removed in the coalescent filter. The air flow is controlled by a pressure regulator and a micrometric valve, and then measured at the flow meter before entering one of the mixers.
The two inlet flow mixers (1) are attached to the ends of the horizontal sections (Fig. 6) through a set of three-way valves, so it is possible to set the air-water mixture to flow upwards or downwards through the return bend. As the flow exits the loop, both fluids are separated in a hydrocyclone; air is released to the atmosphere and water returns to the thermostatic bath.
Although the arbitrary introduction of the phases in a pipe would eventually result in a specific flow regime, a flow mixer located at the inlet of the test section reduces the length required for the flow to develop. In the mixer, this result is accomplished by mixing both phases according to the topology of the expected flow regime. For example, in annular 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 air core.
Two mixers designed and built in the course of this work were placed at the upper and lower ends of the test section. Thus, it is possible to set the air-water mixture to flow upward or downward in the bend (i.e., entering from the bottom or top tube). Figure 7 shows an axial view of one of the mixers, which consist of a cylindrical perspex
5 6
7 8
Figure 5 – Components of the air line.
Figure 7 – Axial view of one of the mixers.
shell with and a porous annular core. Each mixer is equipped with an axial and a radial connection. In this way, one can choose the direction in which each phase will be introduced in the mixer according to the desired flow regime in the test section by setting the position of the three-way valves.
3.2.2 Test section
The test section is a circular channel of 26.4 mm ID, and consists of a 180oreturn bend that connects two horizontal 5-m long tubes. The
return bend, also made of borosilicate glass, comprises a C-shaped sec-tion and two straight secsec-tions of approximately 0.1 m in length, which allow for the mounting of the bend.
The influence of the bend on the behavior of flow parameters (gas holdup, pressure drop) has been investigated using bends with different curvatures (2R/d = 6.1, 8.7, and 12.2)2. Geometric details of the tube
bends are shown in Table 5 and Fig. 8. The manufacturer of the tube bends (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 though this system guarantees a rough alignment of the lower section, a fine alignment was always performed.
of the bends during the fabrication process. The curvature radii of the bends were measured indirectly with image processing software and photographs of the tubes in front of a graph (squared) paper. Since the curvature radius is not perfectly constant along the bend, the distance H was measured with a caliper and does not correspond to the exact value of 2R.
The test section was made fully transparent and therefore suited for optical measurements along its full length. Air and water were selected as working fluids on account of their simple use, thus making calibration procedures easier in Particle Image Velocimetry (PIV) and Laser Doppler Velocimetry (LDV) measurements, which are intended to be used in a later stage of this research.
Table 5 – Geometric details of the tube bends. Bend 2Rd−1 (-) R (mm) L (mm) H (mm)
A 6.1 81 106 155.85
B 8.7 115 113 207.45
C 12.2 161 108 312.50
Each horizontal section has a length of 5.65 m, approximately 214 diameters. The long sections are formed of small borosilicate tubes connected to each other by perspex sleeves (Fig. 9), containing pressure taps and thermocouple wells.
3.2.3 Measuring devices and techniques
a) Pressure
The influence of the bend on the straight segments upstream and downstream of it has been investigated by evaluating the distribution of flow parameters along the axis of the tube. Absolute pressure was measured at taps located 1.85 m upstream and downstream of the re-turn bend. Pressure drop was measured between the inlet and outlet of the bend and between sections of 0.11, 0.22, 0.51, and 1.01 m in length 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 main coordinate system (z = 0) is the position of the pressure taps closest to the bend. Two other auxiliary references, zref and zref∗ , are also
shown in Figure 10. The origin of the auxiliary coordinates is always located upstream of the bend; e.g. in downward flow, zref is located in
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 each other, allowing pressure and temperature measurements.
1.01 0.51 0.22 0.11 p p p p p 0.88 0.61 0.160.05 α α α α α α 0.16 1.04 z 0 zref zref*
Figure 10 – Positions of the pressure taps and gas holdup sensors positions. 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 and no air bubbles were left inside. Each differential transducer measured exclusively the pressure difference between segments of the upper hori-zontal tube, between segments of the lower horihori-zontal tube, or between the inlet and outlet of the bend. Two additional absolute pressure sensors are located at the inlet and outlet mixers.
Total pressure drop in the bend is evaluated by the difference in height between the two pressure taps located at the upper and lower parts of the bend,
∆pb= ∆p + ρlgH, (3.1)
where ∆p is the measured pressure drop, ρlis the density of the liquid
(water) inside the tubings connecting the pressure taps and the sensor manifold, and H is the height difference between the two segments, which is approximately 2R.
The frictional pressure drop was estimated via the conservation of momentum in a control volume between the inlet and outlet of the tube segment. For the return bend, the frictional pressure drop in the bend, ∆pf,b, is given by,
∆pf,b= ∆p + G2 1 ρ0 out − 1 ρ0 in ± ρtpg2R, (3.2)
Figure 11 – Set of valves and tubings, absolute pressure sensor and differential pressure transducers.
Similarly for a straight tube segment, the frictional pressure drop, ∆pf,s, was evaluated as follows,
∆pf,s= ∆p + G 2 1 ρ0 out − 1 ρ0 in . (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 upward flow in the bend, while the negative sign corresponds to downward flow. The subscripts in and out refer to the inlet and outlet sections of the tube, respectively. The momentum density, ρ0, is defined as (
GHIAASI-AAN, 2007), ρ0 = (1 − x) 2 ρl(1 − α) + x 2 ρgα −1 (3.4) and is evaluated using gas holdup values, α, measured at the inlet and outlet 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 of the mixture in the bend, ρtp, is taken as the arithmetic average mixture
is given by,
ρtp= ρgα + ρl(1 − α). (3.5)
From Eq. 3.2 one can also define the pressure drop term con-cerning acceleration of the flow,
∆pa= −G 2 1 ρ0 out − 1 ρ0 in , (3.6)
which also applies for a straight tube section. The gravitational term of pressure drop is given by,
∆pg,b= ±ρtpgH, (3.7)
which is positive for the downward flow direction.
While pressure drop is measured between nine consecutive tube segments (including the bend), absolute pressure is measured only at two positions, as shown in Fig. 3. Nevertheless, the pressure distri-bution along the tube axis can be determined at discrete positions (at pressure taps) as the sum of consecutive pressure drops, given by the following equation, pn= p1+ n X i=2 ∆pi−1,i, (3.8)
where p1 is the measured static pressure, and n is the pressure tap
index, starting at 1 at the farthest upstream position (specified as “ref.” in Fig. 3).
The gradients of the pressure drop components were calculated as follows, ∇pf = ∆pf zout− zin , (3.9) and, ∇pa= ∆pa zout− zin, (3.10)
where zinand zoutare the axial positions of the inlet and outlet sections
of the respective tube segment. For consistency in the presentation of the data, the pressure gradient components calculated according to Eqs. 3.9 and 3.10 are associated with the positions in the middle of the segment.
