the effects of viscosity on core-annular flow

Challenge the future

THE EFFECTS OF VISCOSITY ONCORE-ANNULAR FLOWNumerical Simulations and Experiments for Core-AnnularFlow

RHOHETH RADHAKRISHNAN

Supervisors : Prof. dr. ir. R.A.W.M. Henkes: Prof. dr. ir. G. Ooms: Dr. ir. M.J.B.M. Pourquie

THE EFFECTS OF VISCOSITY

ON CORE-ANNULAR FLOWNumerical Simulations and Experiments for Core-Annular Flow

MASTER OF SCIENCE THESIS

Rhoheth Radhakrishnan

16th November 2016

To obtain the degree of Master of Science in Mechanical Engineering at theDelft University of Technology

Student number: 4419073

Supervisor: Prof. dr. ir. R.A.W.M. Henkes, TU DelftProf. dr. ir. G. Ooms, TU DelftDr. ir. M.J.B.M. Pourquie, TU Delft

Thesis committee: Dr. ir. B.W. van Oudheusden, TU Delft

An electronic version of this thesis is available at http://repository.tudelft.nl/.Process and Energy report number: 2794

http://repository.tudelft.nl/

Preface

I would like to take this opportunity to thank everyone who has been a part of thisproject. Core-annular flow has interested me ever since I was introduced to it by Prof. dr.ir. Gijs Ooms and Dr. ir. Mathieu Pourquie who have guided me through this projectwith their vast experience on this topic. I thank Prof. dr. ir. Ruud Henkes for his criticalcomments on the work and his eye for detail which have certainly helped me in writingthis report. I would also like to thank Dr. ir. Bas van Oudheusden for participating in mygraduation committee.

I would like to thank the students before me at TU Delft who have studied this topic.This work has been built upon their contributions to this area of research.

This project was unique for me because it has involved numerical work and a consider-able amount of time was spent on the experiments. Experiments are always hard and thesupport from the staff of Process and Energy, TU Delft has helped a lot in this regard. Theflow visualizations were performed with the support of Edwin Overmars, Carsten Sandersand Erik van Duin. I think we all learnt a lot from that experience. A special thanks toCarsten Sanders for all his help and for sharing his philosophy on experiments in general.

My fellow students in the Master’s room have made the last year very entertaining forme. Small talk, Dutch lessons and football have been welcome breaks during this period.

I would like to say that the duration spent in Delft with my roommates and my fellowstudents in the SFM track have been some of my best yet. I cannot figure out how the lasttwo years would have gone by without you guys.

Most importantly, I would like to thank my family for all their support. Our everydaytalks about my life here and news about what is happening back at home have helped mepower through.

Abstract

A study has been performed on the effects of the viscosity of the liquid in the core of coreannular flow. This is a multiphase flow regime for two immiscible liquids in a pipe wherethe high-viscosity liquid forms a core and the other low-viscosity liquid forms a lubricatingannulus around the core and along the wall. This is a very efficient method to transportoil. Another method is to heat the oil to reduce its viscosity prior to use in single phasetransport. The advantage of combining these two methods is discussed in this thesis.

First, two dimensional, axisymmetric numerical simulations using the OpenFOAM VoFsolver have been performed based on previously performed experiments in vertical pipes.Periodic boundary conditions have been imposed in all the simulations under laminar con-ditions. The choice of the oil-water viscosity ratio is shown to influence the interfacialwave profile and the oil throughput. The highest throughput is achieved at an intermediateviscosity ratio. Simulations are also performed with a temperature gradient between thepipe wall and the oil which now has a temperature dependent viscosity. Multiple solutionsare observed in some of the simulations when the conductivity is increased, which gives arelatively fast evolution to the final isothermal state. The causes for these multiple stateshave been investigated. It is concluded that the domain length and the initialization of thevelocity profile influence the results.

Next, the study has been extended to core annular flow in horizontal pipes. Experimentshave been performed in which the oil has been heated to temperatures as high as 50 C toreduce its viscosity. The pressure drop that was measured along a 1 m section of the pipeshows a small dependence on the oil viscosity, for fixed oil and water flow rates. Images fromthe footage recorded for these experiments show how the interface waves and the levitationmechanism are affected when the oil viscosity is decreased. Three dimensional numericalsimulations based on the experiments have been performed employing the Launder Sharmak-ε turbulence model. Periodic boundaries are used to study the development of the flow.The pressure drop measured in the experiments is imposed in these simulations to study theeffect of changing the viscosity. The oil holdup fraction is also imposed in the simulations.At high viscosity, deviations are found between the simulation results and the experiments interms of the wave profiles and the resulting oil and water flow rates. For the lowest viscosity,the simulations show that the oil core will foul the upper wall of the pipe whereas theexperiments show core annular flow with oil droplets. Simulations in which the experimentalflow rate is imposed do not improve the results. The main conclusion from this study isthat in horizontal pipes, core annular flows are more stable when the oil-water viscosityratios are high.

Contents

List of Figures

List of Tables

1 Introduction 1

2 Characterization of Core Annular Flow 52.1 Flow regimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.1 Vertical flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1.2 Horizontal flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Dimensionless numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2.1 VCAF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2.2 HCAF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3 PCAF equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.4 Other quantities of interest . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3 Isothermal VCAF simulations 93.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.1.1 Case 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.2 Simulation details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.2.1 interFoam solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2.2 Geometry and mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.2.3 Initial conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.2.4 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.2.5 Time-step restrictions . . . . . . . . . . . . . . . . . . . . . . . . . . 133.2.6 Discretization schemes . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.3 Isothermal simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.3.1 Case 2: n=66 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.3.2 Case 3: n=10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.4 Discussion of results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.4.1 Wave amplitudes and profiles . . . . . . . . . . . . . . . . . . . . . . 173.4.2 Domain length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.4.3 Velocity profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4 Heat transfer in VCAF 214.1 Energy equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.2.1 Case 4: Temperature = 310 K, conductivity k = 0.145 W/mK . . . 224.2.2 Case 5: Temperature = 330 K, k = 0.145 W/mK . . . . . . . . . . . 244.2.3 Case 6: Temperature = 310 K, k = 2 W/mK . . . . . . . . . . . . . 24

4.3 Verification of the results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.3.1 Wave initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.3.2 Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.3.3 Changing the domain length . . . . . . . . . . . . . . . . . . . . . . 26

4.4 Multiple solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

5 Experiments on HCAF 355.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

5.1.1 Low viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355.1.2 High viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355.1.3 A new dimensionless number . . . . . . . . . . . . . . . . . . . . . . 36

5.2 Experimental set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375.2.1 Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.3 Physical properties of the oil . . . . . . . . . . . . . . . . . . . . . . . . . . 395.4 Experimental parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

6 HCAF simulations 456.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

6.1.1 Turbulence in the annulus . . . . . . . . . . . . . . . . . . . . . . . . 466.2 Numerical solution procedure . . . . . . . . . . . . . . . . . . . . . . . . . . 47

6.2.1 Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476.2.2 Geometry and mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . 476.2.3 Turbulence modelling . . . . . . . . . . . . . . . . . . . . . . . . . . 486.2.4 Schemes and boundary conditions: . . . . . . . . . . . . . . . . . . . 486.2.5 Simulation details . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

6.3 Results: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506.3.1 Case A: T=23 C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506.3.2 Case B: T=30 C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536.3.3 Case C: T=40 C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556.3.4 Case D: T=50 C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

6.4 Comparisons with experiments . . . . . . . . . . . . . . . . . . . . . . . . . 596.5 Simulations with constant total mass flow rate . . . . . . . . . . . . . . . . 61

6.5.1 Formulation of the new solver . . . . . . . . . . . . . . . . . . . . . . 616.5.2 Results with the new solver . . . . . . . . . . . . . . . . . . . . . . . 626.5.3 Pressure drop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

7 Conclusions and recommendations 697.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 697.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

A 78

Nomenclature

Symbol Definition Unit

V ∗o (0) Centreline velocity m/sCo Courant number -D Diameter mρ Density kg/m3

η Density ratio -µ Dynamic viscosity kg/(ms)Fr Froude number -h Hold-up ratio -ν Kinematic viscosity m2/sumv Mixture velocity m/sf∗ Pressure gradient N/m2

R Radius ma Radius ratio -K Ratio of driving forces -Re Reynolds number -ω Specific dissipation rate 1/sCp Specific heat J/kg-Kus Superficial velocity m/sσ Surface tension kg/s2

J Surface tension parameter -k Thermal conductivity W/m-Kk Turbulent kinetic energy m2/s2

ε Turbulent dissipation rate m2/s3

V Velocity m/sn Viscosity ratio of oil and water -m Viscosity ratio of water and oil -Q Volumetric flow rate m3/sT Temperature Kεw Water addition ratio -We Weber number -

List of Figures

1.1 Core annular flow of oil lubricated by water in an 8” diameter pipe at SanTome, Venezuela. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Cartoons of the lubrication model and the flying core model. . . . . . . . . 2

2.1 Cartoon of flow regimes taken from Bai et al.[5]. . . . . . . . . . . . . . . . 52.2 Cartoon of the cross section of the pipe with core annular flow taken from [24]. 7

3.1 (a) Wave shapes at different times (b) Amplitude vs time; these figures arebased on simulations taken from [24]. . . . . . . . . . . . . . . . . . . . . . . 10

3.2 (a) Final volume fraction (b) Streamlines in a frame of reference where theoil core is stationary. The figures are taken from [24]. . . . . . . . . . . . . . 11

3.3 Left and Middle: 3D geometry, Right: axisymmetric geometry. . . . . . . . 123.4 (a) Wave amplitude growth rate (b) Profile of interface at different times. . 153.5 (a) Final volume fraction (red-oil, blue-water) (b) Velocity along pipe radius. 153.6 (a) Wave amplitude growth rate (b) Profile of interface at different times. . 163.7 (a) Final volume fraction (b) Velocity along pipe radius. . . . . . . . . . . . 163.8 (a) Comparison of final interface profiles for all cases (b) Comparison of wave

amplitude for all cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.9 (a) Change in wave amplitude (b) Profile of interface at different times. . . 173.10 Comparison of velocity profiles for all cases. . . . . . . . . . . . . . . . . . . 183.11 Reduced pressure isolines and contours for all cases. . . . . . . . . . . . . . 193.12 (a) Streamlines in a frame of reference in which the wall is moving for case

3 (red-oil, blue-water) (b) Initial velocity profiles for all cases. . . . . . . . . 19

4.1 Test case with the energy equation using a temperature of 285 K: (a) Finalresult of bamboo waves after 5 sec (b) Change in wave amplitude with time. 22

4.2 (a) Final volume fraction for case 4 (b) Comparison of amplitude growth (c)Comparison of final interface profiles. . . . . . . . . . . . . . . . . . . . . . . 23

4.3 Case 4: (a) Comparison of the final velocity profiles for both cases (b) Tem-peratures at different time instances. . . . . . . . . . . . . . . . . . . . . . . 23

4.4 Case 5: (a) Final volume fraction (b) Comparison of the wave amplitude (c)Comparison of the interface profiles. . . . . . . . . . . . . . . . . . . . . . . 24

4.5 Case 6: (a) Final volume fraction (b) Wave profiles at different times (c)Wave amplitude against time . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.6 Case 6: (a) Temperature profile (b) Velocity profiles at different times. . . . 254.7 Case 7: (a) Final volume fraction, (b) and (c) Wave profiles at different times. 274.8 Case 7: (a) Comparison of wave amplitude for case 6 and 7, (b) Temperature

profiles, (c) Velocity profiles at different times. . . . . . . . . . . . . . . . . 284.9 (a) Final wave profile (b) Wave profiles at different times for Case 8. . . . . 294.10 Case 8 versus case 4: (a) Wave amplitude vs time (b) Comparison of velocity

profiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.11 Case 9: (a) Final volume fraction (b) Wave profiles at different times. . . . 30

4.12 Comparison of case 5 and case 9: (a) Wave amplitude vs time (b) Velocityprofiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.13 (a) and (b) Initial and final comparisons of velocity profiles (c) Comparisonof interfacial wave growth for cases 7, 10 and 11. . . . . . . . . . . . . . . . 32

4.14 Final volume fraction (a) Case 10 (b) Case 11. . . . . . . . . . . . . . . . . 32

5.1 Schematic overview of the front side of the setup. . . . . . . . . . . . . . . . 375.2 Schematic overview of the back side of the setup. . . . . . . . . . . . . . . . 385.3 Comparison of the old and new viscosity measurements. . . . . . . . . . . . 405.4 Footage of core annular flow at different temperatures of 23, 30 and 40 C. . 415.5 Footage of core annular flow at an oil temperature of 50 C. . . . . . . . . . 425.6 Oil fouling (marked within red) near both the pressure ports at temperature

50 C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.7 Comparison of the measured pressure drop. . . . . . . . . . . . . . . . . . . 43

6.1 (a) and (b) Dye injection at consecutive time instances for εw=20% andUmv= 1 m/s (c) Dye injection at a higher location. . . . . . . . . . . . . . . 46

6.2 (a)-(d): Dye injection at consecutive time instances for εw = 30% and Umv=0.7m/s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

6.3 Case A: Volume fraction at different times. . . . . . . . . . . . . . . . . . . 506.4 Case A: Momenta against time. . . . . . . . . . . . . . . . . . . . . . . . . . 506.5 Case A: Velocity profiles at different times for T=23 C. . . . . . . . . . . . 516.6 Case A: (a) Volume fraction and (b) Axial velocity after 2.62 sec. . . . . . . 516.7 Case A:- Top: Pressure contours on the interface, Bottom: Pressure isolines

and pressure on the walls. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526.8 Case A: Turbulent viscosity contours. . . . . . . . . . . . . . . . . . . . . . 526.9 Case B: At t = 2.8 sec (a) and (b) Volume fraction (c) Velocity. . . . . . . . 536.10 Case B: Momenta against time. . . . . . . . . . . . . . . . . . . . . . . . . . 536.11 Case B: Velocity profiles at different times. . . . . . . . . . . . . . . . . . . 546.12 Case B: (a) Pressure and (b) Pressure isolines at t=2.8 sec. . . . . . . . . . 546.13 Case B:- (a) Pressure on the walls (b) Turbulent viscosity contours. . . . . . 546.14 Case C: At t = 2.62 sec (a) and (b) Volume fraction (c) Velocity. . . . . . . 556.15 Case C: Momenta plotted against time. . . . . . . . . . . . . . . . . . . . . 556.16 Case C: velocity profiles at different times. . . . . . . . . . . . . . . . . . . . 566.17 Case C at 2.62 sec: (a) Pressure contours on the interface and (b) Pressure

on the pipe wall at t=2.62 sec. . . . . . . . . . . . . . . . . . . . . . . . . . 566.18 Case C at 2.62 sec: (a) Pressure isolines and (b) Turbulent viscosity. . . . . 566.19 Case D: Volume fraction at different times. . . . . . . . . . . . . . . . . . . 576.20 Case D: Volume fractions at time 2 sec (left) and 2.5 sec (right). . . . . . . 576.21 Case D: Axial velocity at time 2 sec (left) and 2.5 sec (right). . . . . . . . . 586.22 Case D: Velocity profiles at different times . . . . . . . . . . . . . . . . . . . 586.23 Case D: Pressure contours at interface. . . . . . . . . . . . . . . . . . . . . . 586.24 Comparison of velocity profiles for all cases . . . . . . . . . . . . . . . . . . 596.25 Comparison of experimental footage and simulations at 2.2 sec for case D. . 616.26 Comparison of experimental footage and simulations at 2.35 sec and 2.5 sec

for case D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 616.27 Case A1: (a) and (b) Final volume fraction (c) Turbulent viscosity at 4.36 sec. 626.28 Case A1: (a) Oil and water flow rates. (b) Hold-up h. . . . . . . . . . . . . 636.29 Case A1: Comparison of velocity profiles for different times. . . . . . . . . . 636.30 Case B1: (a) and (b) Final volume fraction (c) Turbulent viscosity at 5 sec. 646.31 Case B1: Comparison of velocity profiles for different times. . . . . . . . . . 646.32 Case B1: (a) Oil and water flow rates. (b) Hold-up, h. . . . . . . . . . . . . 65

6.33 Case C1: (a) and (b) Final volume fraction (c) Turbulent viscosity at 3.9 sec. 656.34 Case C1: (a) Oil and water flow rates (b) Hold-up, h. . . . . . . . . . . . . 656.35 Case C1: Comparison of velocity profiles for different times. . . . . . . . . . 666.36 Comparison of the pressure drop for cases A1, B1 and C1. . . . . . . . . . . 66

A.1 Summary of experiments taken from Shi et al. [29] . . . . . . . . . . . . . . 78

List of Tables

3.1 Properties of oil and water for case 1. . . . . . . . . . . . . . . . . . . . . . 14

4.1 Thermodynamic properties of oil and water used in the energy equation. . . 214.2 Comparison of velocity and amplitudes for different growth phases in case 7. 31

5.1 G/V ratios and kinematic viscosity at different temperatures. . . . . . . . . 405.2 Oil-water flow rates and mixture velocities for different water addition ratios. 41

6.1 Comparison of oil-water flow rates and pressure drops for all simulations. . 596.2 Comparison of oil-water flow rates and pressure drops for all the experiments

at 17.5% εw. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596.3 Comparison of experiment and simulation for pressure drop. . . . . . . . . . 67

Chapter 1

Introduction

Core annular flow is a multiphase flow regime for two immiscible liquids in a pipe whereone liquid forms a core and the other liquid forms a lubricating annulus around the corealong the wall. Much attention has been given to this flow in the literature because of theinteresting underlying physics and its practical importance.

The potential for these flows has been extensively used in the area of oil transport.Today, this flow also gains popularity in emerging areas like microfluidics where it is in-vestigated in the context of the controlled formation and manipulation of tiny volumes ofliquids or in drug delivery with encapsulation. Coming back to oil transport, with the de-pletion of world wide reserves of low viscosity oil, it is becoming more important to be ableto extract and transport higher viscosity oil from these reserves. Pumping high viscosity oilbecomes increasingly difficult due to the friction at the walls. From the Poiseuille equationfor laminar flows in pipes we see that the pressure gradient required to drive the flow isproportional to the viscosity:

4P =128µLQ

πD4(1.1)

where Q is the flow rate, µ is the dynamic viscosity, D is the diameter of the pipe and 4Pis the pressure gradient

Heating the oil is a common practice in the industry to reduce its viscosity and to makeits transport easier. An even better method is to use Core Annular Flow (CAF), whereby athin lubricating film of a less viscous fluid surrounds the more viscous oil. This drasticallyreduces the pressure gradient required to achieve the same throughput of oil. Experimentshave shown that the pressure drop reduces to that of flow of only water through the samepipe. Ingen Housz [28] was able to show that for some oil-water mixture ratios, there is areduction by almost 300% in the pressure drop. In the past, this method has been used suc-cessfully in field operations. One example is a 6 inch diameter, 24 mile long Shell pipelinefrom the North midway sunset reservoir in California. The pipe was operated for nearly12 years for flow rates of upto 24,000 barrels per day. Figure 1.1 shows a visualization ofcore-annular flow.

The first comprehensive classification of CAF was made by Charles et al.[31] for densitymatched CAF, using experiments and theory. The density difference (with the density ofthe liquid in the core being lower than the density of the liquid in the annulus) causes itto levitate upwards. A surprising observation is that the core does not foul the pipe wall.Ooms [1] and Oliemans and Ooms [3] proposed a model to explain this phenomenon basedon lubrication forces between the waves on the core, the upper annulus and the wall thatwill balance the buoyancy. Feng et al. [7] concluded that inertia is important. They haveproposed a flying core model; see Fig. 1.2. For both theories the interfacial waves are very

1

Introduction 2

crucial. Bannwart et al. [15] have proposed a model based on the analogy of the core as abubble rising in a column.

Figure 1.1: Core annular flow of oil lubricated by water in an 8” diameter pipe at San Tome,Venezuela.

Joseph et al.[9] were successful in performing and comparing experiments and stabilityanalysis of vertical up and down core annular flows. Li and Renardy[10] carried out un-steady numerical simulations based on the experiments of Bai et al. [11] and they founda good agreement with the experiments. Several other researchers have performed theo-retical analyses, detailed experiments and numerical simulations to study various aspectssuch as the nonlinear wave generation, the levitation mechanism and hold-up and pressurecorrelations. Review articles by Joseph et al.[8], Ghosh et al.[21] and Shi et al.[29] very wellsummarize the work done in this domain. The third article is a comprehensive summaryof the most important experiments on core annular flow and stratified flows.

Figure 1.2: Cartoons of the lubrication model and the flying core model.

Beerens[24] successfully performed numerical simulations for the vertical pipe experi-ments of Bai et al.[5] with the OpenFOAM VoF solver interFoam. Important conclusionswere made by Ooms et al.[26] on the levitation forces in horizontal core annular flows. In-gen Housz [28] performed experiments for core annular flow in a horizontal pipe in the labfacility of Process and Energy at Delft University of Technology. One of the conclusionsfrom his study was that core annular flows thrive on highly viscous cores and that the lowestpressure drops were achieved for such configurations. He also compared his experimentalresults with numerical simulations using the interFoam solver achieving considerable suc-cess in the comparison of wavelengths and amplitudes.

The effect of heating the oil in the context of CAF has not been investigated yet. IngenHousz[28] made the first steps in his horizontal CAF experiments, and he has suggestedthat oils with lower viscosity require a higher pressure gradient for the same throughput.

Master of Science Thesis R. Radhakrishnan

Introduction 3

In this thesis, the effect of heating the oil in vertical and horizontal CAF has been stud-ied. For the vertical CAF, experiments of Bai et al.[5] have been numerically simulated,now with a temperature gradient between the oil and the wall. Experiments on horizontalCAF have been conducted in the TU Delft setup by adding a heating element to study theeffects of heating the oil. Simulations are presented for these experiments to confirm theexperimental results and to gain a better understanding of the flow.

The objective of this Master Project is: to investigate the effect of the oil viscosity onthe core annular flow properties (such as the interfacial waves, hold-up and pressure drop),through changing the temperature of the oil.

In Chapter 2, an introduction is given to multiphase flows and the non-dimensionalnumbers that are used to characterize them. These non-dimensional numbers are laterused in this thesis in the context of CAF. In chapter 3, a description is given of the numer-ical technique with the volume of fluid approach that was used in the simulations. Twocases are discussed in which the oil viscosity has been changed from a base case. The ef-fects of heat transfer and a temperature dependent viscosity in vertical core annular flowsis studied in Chapter 4.

Chapters 5 and 6 are dedicated to core annular flow in horizontal pipes. Pressure dropmeasurements and pictures of the film footage from the experiments will be shown. Inchapter 6, numerical simulations of the performed experiments are discussed. In the finalchapter, conclusions and recommendations for further research are presented.


Chapter 2

Characterization of Core AnnularFlow

Multiphase flows are in general more complicated to analyze than single phase flows dueto the density and viscosity jumps and the interfacial tension. In order to characterizemultiphase flows, dimensionless numbers are used. In this chapter, an overview is given ofthe dimensionless numbers that are used throughout this study. Consequently, the basicequations are described for perfect core annular flow which are required for the initializationof the numerical simulations.

2.1 Flow regimes

2.1.1 Vertical flows

Bai et al.[5] found a number of flow regimes in their experiments for vertical core annularflow (VCAF). Cartoons of these flow regimes are shown in Fig. 2.1. The most importantregimes they identified were Perfect Core Annular Flow (PCAF), oil drops in water, oilslugs in water, Bamboo waves, Disturbed Core Annular Flow (DCAF), Corkscrew waves,oil sticking to the wall and oil/water dispersion. Moreover, they created flow regime mapsfor oil versus water superficial velocities.

Figure 2.1: Cartoon of flow regimes taken from Bai et al.[5].

The Bamboo Wave (BW) and the Disturbed Core Annular Flow (DCAF) regimes which

5

Characterization of Core Annular Flow 6

are usually found at high superficial oil velocities characterize core annular flow.

2.1.2 Horizontal flows

A good summary of experiments in HCAF has been presented by Shi et al.[29]. Theydescribe the different flow regimes as reported by several authors for horizontal multiphaseflows. They highlight that core annular flows are preferred in configurations with highviscosity oil cores and high oil and water superficial velocities. An additional complexityin HCAF is that the density difference between the two liquids causes the core to levitateupwards.

2.2 Dimensionless numbers

Multiphase flows can be difficult to analyze because of the number of forces which act oneach phase and the interface between them. Dimensionless numbers can help us here. Fiveforces can be distinguished to, which are most influential:Inertial force: ρU2L2

Pressure force: 4PL2

Gravitational force: ρgL3

Viscous force: µULSurface tension: σLDimensionless numbers are based on these forces, such as:

Reynolds number = Re =Inertial force

Viscous force=ρLU

µ(2.1)

Froude number = Fr =

√Inertial force

Gravitational force=

√U2

gL(2.2)

Weber number = We =Inertial force

Surface tension force=ρLU2

σ(2.3)

where L and U are characteristic length and velocity scales.

2.2.1 VCAF

Bai et al.[5] used other dimensionless numbers to characterize the flow in their own exper-iments:

Viscosity ratio = m =Water viscosity

Oil viscosity=µwµo

(2.4)

Radius ratio = a =Pipe radius

Oil radius=R2

R1(2.5)

Density ratio = η =water density

oil density=ρwρo

(2.6)

Ratio of driving forces = K =Oil driving force

Water driving force=f∗ + ρog

f∗ + ρwg(2.7)

where f∗ is the pressure drop across the pipe.

Surface tension parameter = J =σR1ρoµ2o

(2.8)


Characterization of Core Annular Flow 7

σ is the surface tension between the two liquids.The Reynolds number for each phase is:

Rei =ρiV

∗0 (0)R1

µi(2.9)

where i represents the phase and V ∗0 (0) is the centerline velocity of the core.

Figure 2.2: Cartoon of the cross section of the pipe with core annular flow taken from [24].

2.2.2 HCAF

In HCAF, the buoyancy induced by the density difference causes the core to become ec-centric. It is thus important to select a dimensionless parameter that accounts for thegravitational force. Ingen Housz [28] suggested a modified definition of the Froude number:

Fr =

√Inertial force

Gravitational force=

√ρou2mv

(ρw − ρo)gD(2.10)

where ρ is the density, D is the diameter, umv is the mixture velocity which is the sum ofthe superficial velocities of the oil and water. Subscripts o and w represent the oil and waterphase, respectively. The Froude number is important as it represents the balance betweenthe downward inertial force of the moving core and the gravitational force responsible forthe levitation phenomenon.

For the Reynolds number in the water annulus for PCAF, we use the relation:

Rew =ρumv(R2 −R1)

µw(2.11)

2.3 PCAF equations

The Perfect Core Annular Flow is defined as the case where the oil forms a perfect concentriccylindrical core inside the water annulus. Experimentally, this flow is very difficult to obtain.Using the Navier-Stokes equations, Li and Renardy [12] derived the dimensionless velocitiesin the core and annulus:

Core:V (r) = 1− (mr2K

A) (2.12)

Annulus:V (r) = (a2 − r2 − 2(K − 1)ln(r

a)]/A (2.13)

V(r) has been made dimensionless by dividing the velocity profile by the centreline velocityV∗0(0). The coefficient A is given by:

A = mK + a2 − 1 + 2(K − 1) ∗ ln(a) (2.14)


Isothermal VCAF simulations 8

All dimensionless parameters used in the above equations are mentioned in section 2.2.1.The equations (2.12)-(2.14) are used to initialize the velocity profile at the beginning of thesimulations that will be discussed in the next chapters.

For HCAF, gravity acts perpendicularly to the pressure gradient. Thus the term, K, isequal to 1. The velocity field can be reformulated as:

Core:V (r) = 1− (mr2

m+ a2 − 1) (2.15)

Annulus:V (r) = (a2 − r2)/(m+ a2 − 1) (2.16)

2.4 Other quantities of interest

1. The superficial velocity is the ratio of the flow rate of a phase and the cross sectionalarea of the pipe.

us, i =QiπR2

(2.17)

where i represents the phase.

2. The water addition ratio or the water-cut is the ratio of input water flow rate to thethe total oil+water flow rate

εw =Qw

Qw +Qo(2.18)

where Qw and Qo represent the water and oil flow rate respectively.

3. The hold-up ratio is defined as the ratio of the input oil-water flow rate ratio (= Qo/Qw)to the in-situ oil-water volume ratio (= Vo/Vw).

h =QoVo

VwQw

=(1− εw)(1− αw)

εwαw(2.19)

where εw is the water addition ratio or the water-cut. αw is the oil volume fraction or oilhold up fraction: this is the fraction of pipe cross section area covered by oil. Equation(2.19) can be slightly modified to obtain the radius ratio for a PCAF:

h =

QoQw

πR21L

π(R22−R2

1)L

=QoQw

(R2

2

R21

− 1)

a =R2

R1=

√1 + h

QwQo

=

√1 + h

us,wus,o

(2.20)

Bai et al.[5] found in their experiments that the hold-up ratio h always remained con-stant at a value of 1.39 for upward core annular flows. This value is used in this thesis toinitialise the core radius R1 in the simulations.


Chapter 3

Isothermal VCAF simulations

3.1 Introduction

Bai et al.[5] conducted experiments for upward and downward core annular flow in verticalplastic pipes with an inner diameter of 9.6 mm. The oil used was SAE30 and the annulusconsisted of a mixture of glycerin-water. Their experiments showed different flow patternsdepending on the oil and water superficial velocities (Fig. 2.1). In the CAF regime, theyobserved axisymmetric bamboo waves and corkscrew shaped waves for upward and down-ward flows, respectively. At low Reynolds number, these waves were more pronounced.The bamboo waves form a regular train of waves with a nearly constant wavelength andamplitude. At higher Re, the wave amplitudes reduce, and the flow regime is the one withdisturbed bamboo waves. Now there is little distinction between upward and downwardflows.

Li and Renardy[12] performed direct numerical simulations for the above mentionedexperiments using a Volume of Fluid (VoF) code. They used a constant pressure gradientto drive the flow with periodic boundary conditions. The domain length was set as anintegral number of the most unstable wavelength measured from either the experiments orfrom the linear stability calculation of Joseph et al. [25]. Their simulations predicted wavesthat are very similar to the ones found in the experiments.

Kouris and Tsamopoulous [17] also performed numerical simulations of the experimentsof Bai et al.[5] with periodic boundary conditions using a VoF code. The main differencein their approach and that of Li and Renardy is that instead of driving the flow with aconstant pressure gradient, they chose to impose a constant total mass flow rate which ishow the experiments were also performed. Their simulations showed a better agreementwith experiments than the simulations by Li and Renardy, in terms of wavelength, wavespeed and holdup ratios. They have put some emphasis in their paper on the nonlineardynamics that influence these flows.

Beerens [24] simulated some of these experiments for upward flows using the Open-FOAM VoF solver interFoam. Like Li and Renardy [12], he imposed a constant pressuregradient to drive the flow with periodic boundary conditions. The simulations were per-formed on domain lengths equal to the most unstable wavelength and 30 times the mostunstable wavelength. His results showed good agreement with the simulation results in [12]in terms of wave shapes and the holdup. For the long pipe simulations, he has reportedthat a range of different wavelengths exist in the pipe with most wavelengths showing adistribution around the wavelength of the most unstable wave reported in the experiments.

9


3.1.1 Case 1

A short summary is presented for case 1 from Beerens’ thesis. This case has also beensimulated by [12] and [17]. The summary serves as an introduction to the main findings inthe literature for VCAF. The simulations were performed on an axisymmetric pipe domainof diameter of 9.6 mm and an axial length 1.16 cm (corresponding to most unstable wave).The dimensionless parameters from the experiments are the following:

m = 0.0015, a = 1.28, ζ = 1.10,K = −0.93, J = 7.96e−2, Re1 = 0.95.

The ratio m=0.0015 corresponds to an oil viscosity that is 663 times larger than thewater viscosity. Fig. 3.1 show the wave profile and growth in wave amplitude, as taken fromthe study of Beerens [24]. Fig. 3.1a shows that, initially, a small sinusoidal perturbationon the interface grows linearly until the wave almost touches the wall. Beyond this lineargrowth regime, the wave at the interface evolves into a single bamboo wave with a constantamplitude. Fig. 3.2a shows the final profile after the flow has developed from one of thelong pipe simulations. Red contours represent the oil phase and blue is water.

(a)

0 5 10 15 20

time (sec)

0

1

2

3

4

5

6

Am

plitu

de(m

)

×10-4

(b)

Figure 3.1: (a) Wave shapes at different times (b) Amplitude vs time; these figures are based onsimulations taken from [24].

The pressure gradient forces the oil and water to move upwards and it is just sufficientto counteract the effects of gravity and wall shear stress. Furthermore, since the density ofoil is less than water, the pressure force on the core is supplemented by an upward buoyantforce. As the oil is pushed through the water, there is a higher pressure in front of theinterfacial wave than behind the wave. This difference causes a lubrication-like effect, dueto which there is flow of water from the high to the low pressure regions, further stretchingthe wave.

Streamlines [24] are plotted in Fig. 3.2b in a frame of reference where the oil core isstationary and the wall moves downwards. There are two types of water flow. One is adownward flow near the wall (owing to a low pressure gradient), and the other one is anup-flow because water is trapped in the wave trough and is lifted by the oil. Increasing thepressure gradient causes the wavelength and amplitude to decrease, resulting in a higheroil flow rate and a lower water flow rate.



(a) (b)

Figure 3.2: (a) Final volume fraction (b) Streamlines in a frame of reference where the oil core isstationary. The figures are taken from [24].

The crests are sharper than the troughs implying a force from the more viscous oil tothe less viscous water. The fact that such waves are observed in low Re flows shows thatthese waves are not driven by inertia, but are an effect of viscosity and density stratification.

3.2 Simulation details

3.2.1 interFoam solver

The simulations in the present study were carried out with interFoam. It uses the Volume ofFluid (VoF) method which considers both fluids as a single homogeneous fluid. To identifythe phase, the solver solves for an indicator function representing the fluid fraction. A scalarvalue is assigned to the indicator function α such that α = 1 when the control volume isfilled with the primary fluid (oil) and 0 when filled with the other phase (water). Sincethe solver uses an Eulerian approach, an advection equation is required for the indicator asrepresented by equation (3.1). The density and viscosity at each cell are weighted functionsof the indicator function represented by equations (3.2) and (3.3).

∂α1

∂t+∇.(uα1) = 0 (3.1)

ρ = α1ρ1 + (1− α1)ρ2 (3.2)

µ = α1µ1 + (1− α1)µ2 (3.3)

The continuity and momentum equations are are represented by equations (3.4) and(3.5):

∂ui∂xi

= 0 (3.4)

∂ui∂t

+ uj∂ui∂xj

= −1

ρ

∂p

∂xi+ ν

∂2ui∂x2j

+ gi +1

ρf∗i (3.5)

f∗i is the interfacial tension term which following Brackbill et al.[6] is

f∗i = −σκ∂αi∂xi

(3.6)



where κ is the local interfacial curvatureGenerally, VoF codes employ a geometric reconstruction of the interface. interFoam

however, uses a compressive flux modelling called interfaceCompression which limits thediffusion of the indicator function. More information can be obtained from the studies onthe interFoam solver by Deshpande et al.[23] and Santiago[30].

3.2.2 Geometry and mesh

The flow in the vertical pipe simulations is assumed to be axisymmetric. Therefore a 2Dwedge geometry is used as shown in Fig. 3.3:

Figure 3.3: Left and Middle: 3D geometry, Right: axisymmetric geometry.

Generally a sufficiently fine mesh is required so that the interface is not smeared overtoo many cells. For the axisymmetric case, 128 x 128 grid cells have been defined. Thisnumber of grid cells is suggested by Beerens [24]. The grid is equidistant and not stretched.Since the flow is assumed to be laminar, the mesh near the walls is not refined.

3.2.3 Initial conditions

The analytical solution for Perfect Core Annular Flow (PCAF) mentioned in section 2.3 isused to initialize the velocity and the volume fraction. Bai et al. [5] found in their exper-iments for upward flows that the hold up ratio was always 1.39. Experimental oil, watersuperficial velocities and h=1.39 is substituted in eq. (2.20) to determine the oil-waterradius ratio, a.

The pressure gradient f∗ is determined from the experimental value of K and is imposedbetween the periodic faces to drive the flow. The pressure gradient is formulated as a bodyforce on each cell.

K =f∗ + ρo ∗ gf∗ + ρw ∗ g

(3.7)

Kouris et al. [17] showed that if no initial perturbation is given to the flow, numer-ical disturbances develop in the transient simulations after a long time (approx.15 sec)which develop into bamboo waves. To reduce this time for wave development, an initialperturbation in the form of a sinusoidal wave of amplitude 10−5 m is applied at the interface.

3.2.4 Boundary conditions

At the wall, the no-slip boundary condition is specified. On the left and right faces of thewedge, symmetry boundary conditions are used which ensures that the flow in the radial



direction (adjacent to these faces) is symmetric. At the front and back faces, periodicboundary conditions are specified. Therefore the flow that exits at the back face is reintro-duced at the front face.

For periodic boundary conditions, all properties at the inlet and the outlet are matched.The result is that the pressure gradient term ( ∂p

∂xi) will be zero. An additional pressure is

therefore applied as a body force, f∗, measured from eqn (3.7). The momentum equationsare now:

∂ui∂t

+ uj∂ui∂xj

= −1

ρ

∂p

∂xi+ ν

∂2ui∂x2j

+ gi +1

ρf∗i +

1

ρf∗ (3.8)

Periodic boundary conditions are used as they have the advantage that by using a lim-ited domain length, the temporal development of the flow can be studied. A drawback isthat the length of the domain has to represent at least an integer number of wavelengths.If the domain is smaller, it can result into no waves at all at the interface or into breakupof the larger interfacial wave to smaller waves.

3.2.5 Time-step restrictions

The interFoam solver uses an adjustable time step which is based on the Courant number,Co in the domain. Beerens [24] has suggested that the Co should be restricted to 0.02 forthe simulations. This is due to the large viscosity of the oil. This criterion imposes a severerestriction on the largest time step. The Courant number is defined as:

Co = u4t4x

(3.9)

where u is the velocity, 4t is the maximum time step and 4x is the size of the cell. Toovercome this restriction, the wall is moved for all the simulations in the opposite directionto the pressure gradient. In this way, the local magnitude of the velocity at a grid cell islower. Larger time steps can then be made by the solver.

3.2.6 Discretization schemes

Discretization schemes that were used in interFoam are: backward Euler in time, limitedlinear for the advection terms of the velocity components, and van Leer for the advectionof the scalar. Interface compression (Rusche (2002)) has been used to get a sharp interface.The pressure-velocity coupling was applied using the PIMPLE scheme, with two correctorloops. The following linear solvers have been used: Preconditioned Conjugate Gradient forthe pressure and Preconditioned Bi-Conjugate Gradient for the velocity components.



3.3 Isothermal simulations

In this chapter, two isothermal simulations are discussed, based on Case 1. The oil usedby Bai et al.[5] was 663 times more viscous than water. The oil viscosity has been reducedto two conditions such that it is 66 times and 10 times higher than the water viscosity. Asthese cases will be compared with case 1, the radius ratio, pipe radius, density ratio andpressure gradient will remain the same. Since experimental data were not available, thelength of the most unstable wave which is required to set the domain length is unknown.Nevertheless, simulations were performed maintaining the same domain length as in Case1, which is 1.16 cm. The properties of oil and water used in case 1 are given in Table 3.1.

Table 3.1: Properties of oil and water for case 1.

Physical property Value

Oil kinematic viscosity, νo 663 cSt

Oil density, ρo 905 kg/m3

Water kinematic viscosity, νw 1 cSt

Water density, ρw 995 kg/m3

Surface tension, σ 8.54 x 10−3 N/m

The simulations are considered stationary when the wave amplitude does not change withtime anymore. The wave amplitude is calculated by the following relation:

Amplitude =(Maximum position of crest)-(Minimum position of trough)

2(3.10)

A new dimensionless number, n, is used in this section:

n =1

m=

Oil viscosity

Water viscosity(3.11)



3.3.1 Case 2: n=66

The parameters for PCAF are:m = 0.015, a = 1.28, ζ = 1.10,K = −0.93, J = 7.98.

Fig. 3.4, shows the change in amplitude and wave shapes at different times. The initialperturbation grows linearly until about 0.6 sec, developing into a bamboo shaped profile,after which the amplitude decays until it reaches a constant value of 2.5 x 10−4 m at 8 sec.There is no change in the final wave amplitude until 22 sec. The final wave profile is shownin Fig. 3.5a. The wave at the interface is not as steep as the bamboo waves in case 1.

0 5 10 15 20 25

time (sec)

0

1

2

3

4

5

6

Am

plit

ud

e(m

)

×10-4

(a)

0 0.002 0.004 0.006 0.008 0.01 0.012

Pipe Length (m)

3.2

3.4

3.6

3.8

4

4.2

4.4

Am

plit

ud

e (

m)

×10-3

time=0 s

time=0.5 s

time=3.5 s

time=11.5 s

time=21.5 s

(b)

Figure 3.4: (a) Wave amplitude growth rate (b) Profile of interface at different times.

Fig. 3.5b shows the velocity profile. The core velocity is nearly constant at the corecenter and the interface, implying that the viscosity ratio is still high enough so that oilbehaves as a solid body. The final axial velocity is 0.4 m/s (0.23+0.17) relative to the pipewall.

(a)

0 1 2 3 4

Pipe radius (m) ×10-3

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

Ve

locity (

m/s

ec)

time=0 s

time=0.5 s

time=3.15 s

time=11.05 s

time=23 s

(b)

Figure 3.5: (a) Final volume fraction (red-oil, blue-water) (b) Velocity along pipe radius.

The fact that the waves are not very pointed can be attributed to the effect of surfacetension. The surface tension parameter, J, has increased by a factor of 100 compared to case



1. This is because this parameter is inversely proportional to the square of the viscosity.An increased effect of surface tension causes the wave to be more rounded at the crests. Itis also possible that the increased surface tension is responsible for the decay in the waveamplitude after the initial growth phase.

3.3.2 Case 3: n=10

The parameters for PCAF are:m = 0.1, a = 1.28,K = −0.93, ζ = 1.10, J = 317.82.

0 1 2 3 4 5

time (sec)

0

1

2

3

4

5

6

7

8

Am

plit

ude(m

)

×10-4

(a)

0 0.002 0.004 0.006 0.008 0.01 0.012

Pipe Length (m)

3

3.2

3.4

3.6

3.8

4

4.2

4.4

Am

plit

ude (

m)

×10-3

time=0 s

time=0.4 s

time=0.8 s

time=5 s

(b)

Figure 3.6: (a) Wave amplitude growth rate (b) Profile of interface at different times.

Unlike cases 1 and 2, where the wave quickly develops into a sinusoidal profile, the wavedevelopment for this case is very erratic. After about 0.8 sec, there are no changes in theprofile. The final profile after 5 sec is shown in Fig. 3.7a and it is different from the bamboowaves. The velocity profiles indicate that the oil core does not behave like a solid body. Atthe pipe centre and interface, the core velocity is 0.38 m/s and 0.16 m/s, respectively.

(a)

0 1 2 3 4


-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Ve

locity (

m/s

ec)

time=0 s

time=0.5 s

time=1 s

time=5 s

(b)

Figure 3.7: (a) Final volume fraction (b) Velocity along pipe radius.



3.4 Discussion of results

3.4.1 Wave amplitudes and profiles

A comparison of the wave profiles and amplitudes for all 3 cases is made in Fig. 3.8. Al-though the amplitudes are similar for cases 1 and 3, their profiles are very different. Thewaves in case 2 look like bamboo waves except that the waves are not very steep.

0 0.002 0.004 0.006 0.008 0.01 0.012

Pipe Length (m)

3

3.2

3.4

3.6

3.8

4

4.2

4.4

Am

plitu

de (

m)

×10-3

Case 1

Case 2

Case 3

(a)

0 5 10 15 20 25

time (sec)

0

1

2

3

4

5

6

7

8

Am

plit

ude(m

)

×10-4

Case 1

Case 2

Case 3

(b)

Figure 3.8: (a) Comparison of final interface profiles for all cases (b) Comparison of wave amplitudefor all cases.

Bamboo waves are characterized by sharp crests and wide troughs. Kouris et al.[17]have discussed that these waves are a result of the more viscous fluid (oil) penetrating theless viscous fluid (water) as a result of viscous stratification. For case 1, since the viscosityratio is larger, bamboo waves form at the interface. When reducing the viscosity ratio incase 2, the resulting bamboo waves at the interface have a less steep crest and trough.

0 1 2 3 4 5

time (sec)

0

1

2

3

4

5

6

7

Am

plitu

de

(m)

×10-4

(a)

0 0.002 0.004 0.006 0.008 0.01 0.012

Pipe radius (m)

3

3.5

4

4.5

Am

plitu

de

(m

)

×10-3

time=0 s

time=0.04 s

time=1.5 s

(b)

Figure 3.9: (a) Change in wave amplitude (b) Profile of interface at different times.

The wave profile for case 3 has not been reported before for vertical core annular flow,to the best of the author’s knowledge. To confirm whether these wave profiles are onlycharacteristic for low viscosity ratios, the final profile from case 3 was substituted in asimulation where the oil viscosity is 663 times larger than the water viscosity (Case 1).



Interestingly, the wave profile quickly changes to the bamboo wave profile after 1 sec. Thechange in wave amplitude and wave profile are shown in Fig. 3.9.

3.4.2 Domain length

For all the simulations, at least one wave is visible at the interface. This indicates thatchanging the viscosity ratio, does not dampen waves with a length imposed by the lengthof the chosen computational domain.

3.4.3 Velocity profiles

0 1 2 3 4

Pipe Radius (m) ×10-3

-0.2

-0.1

0

0.1

0.2

Ve

locity (

m/s

)

Case 1

Case 2

Case 3

Figure 3.10: Comparison of velocity profiles for all cases.

The velocity profiles for all cases are compared in Fig. 3.10. For Cases 1 and 2, where theoil cores are quite viscous, the velocity profiles show that the oil moves like a solid core withconstant velocity. When going from Case 1 to Case 2, decreasing the oil viscosity increasesthe core velocity by nearly a factor 3. When further reducing the viscosity (Case 3), thewave profile changes from the bamboo wave shape to a profile where the core no longerbehaves like a solid body. The core moves now fastest at the centre.

The lowest amplitudes are predicted for Case 2. Due to this, the velocities are also thehighest. To understand why, the reduced pressure contours with isovalues are shown in Fig.3.11. The reduced pressure is equal to the total pressure minus the pressure contributiondue to gravity. The reduced pressure signifies the contribution to the pressure due to theflow and surface tension. In all 3 cases, since the oil is moving upwards, the pressure in frontof the wave is higher than behind the wave. This causes water to flow from the region ofhigher to lower pressure causing a lubrication-like effect. For large amplitude waves, watertrapped in the wave troughs drags the oil core, which makes its transport more difficult.For cases 1 and 3, the wave amplitudes are quite large. This results in a higher drag on theoil core as compared to case 2.



Figure 3.11: Reduced pressure isolines and contours for all cases.

When considering the streamlines in Fig. 3.12a, a large recirculation zone is observedextending from the wave trough up to the core. The colours red and blue represent theoil and water phases, respectively. The formation of these structures in the oil core canexplain the rather steep dip in the core velocity profile for case 3.

(a)

0 0.5 1

Radius ratio, a

0

0.2

0.4

0.6

0.8

1

Ve

loci

ty (

m/s

)

Case 1

Case 2

Case 3

(b)

Figure 3.12: (a) Streamlines in a frame of reference in which the wall is moving for case 3 (red-oil,blue-water) (b) Initial velocity profiles for all cases.

An interesting question is whether it is possible to find the optimum viscosity ratio suchthat the core not only behaves like a solid body, but the viscosity is also low enough tomaximize transport. Interestingly, equation 2.12 and 2.13 which are used for the initializa-tion of the velocity profile for PCAF, give us an indication. A parametric study for theseequations by varying the viscosity ratio m showed that when the value of m was reduced(i.e. when the oil viscosity is increased), the oil always behaved more like a solid core.Increasing this value (i.e reducing the oil viscosity) introduces more curvature to the corevelocity profile. In Fig. 3.12b, the initial velocity profiles are shown for the cases 1-3. Forcases 1 and 2, the core profile behaves like a solid body. Increasing m, causes a dip in theprofile as is seen for case 3.


Chapter 4

Heat transfer in VCAF

In the previous chapter, three simulations were discussed for different viscosity ratios. Prac-tically, this is achieved by heating the oil prior to transporting it through a pipe. It wouldbe interesting to investigate how the flow will be affected in transient conditions where thewall is at a lower temperature than the oil and the water. Heat transfer through the pipewall to the oil will result in a change in the oil-water viscosity ratio. In this chapter, westudy how core annular flow will be affected for such conditions.

4.1 Energy equation

InterFoam does not by default solve for the energy equation. In order to take heat transferinto account, the solver had been modified by adding the following equation:

ρCp(∂T

∂t+ ui

∂T

∂xi) = k

∂2T

∂x2i+ S + µφv (4.1)

where ρ,Cp, T, and k are the density, specific heat, temperature and conductivity, respec-tively. S and µφv are zero since there is no source term and the contribution of the viscousdissipation is neglected. Cp and k are constants which do not depend on the temperatureand their values are specified in Table 4.1.

Table 4.1: Thermodynamic properties of oil and water used in the energy equation.

Phase Cp (J/Kg-K) k (W/m-K)

Oil 1900 0.145

Water 4000 1

To couple the energy and momentum equations, a relation needs to be defined betweenthe fluid properties and the temperature. We know that the density, viscosity and surfacetension are dependent on the temperature. Among them the viscosity shows the strongestvariation. In the solver, it is assumed that only the oil viscosity is a function of thetemperature by using the following relation:

ν = a ∗ e−bT (4.2)

where ν and T are the kinematic viscosity and the temperature respectively. a and b areconstants. The oil viscosity is made a function of temperature such that at a temperatureof 310 K, the oil viscosity is 66 times higher than the water viscosity (corresponding to case2). This is realized by using the values: a = 166376596.8, b= 0.0921.

21

Heat transfer in VCAF 22

According to these relations:n=663 at 285 K (corresponding to case 1) and,n=10 at 330 K (corresponding to case 3).

The simulations are performed with the intention to observe how the wave dynamicschange when the oil viscosity is changed from one thermal state to another. For instance, inCase 2, the wave crest is not very steep/pointed. The simulations can show how the waveprofile will change when the oil becomes colder, or in other words, when the oil viscosityincreases.

In all the simulations the computational domain, solution procedures and mesh remainthe same as described in the previous chapter.

Test case

Since interFoam had to be adjusted to take into account the energy equation, an isothermalsimulation was run where the oil-water and wall are maintained at a temperature of 285K. The oil and water viscosity ratio n is 663, which is the same as used in case 1. Allnon-dimensional parameters mentioned in section 2.2.1 remain the same for case 1 and thetest case.

0 1 2 3 4 5

time (sec)

0

1

2

3

4

5

6

Am

plitu

de(m

)

×10-4

Figure 4.1: Test case with the energy equation using a temperature of 285 K: (a) Final result ofbamboo waves after 5 sec (b) Change in wave amplitude with time.

The simulations were continued until 5 sec. The results for the wave profiles and forthe amplitude growth are exactly the same as for case 1, confirming that with the additionof the energy equation, for an isothermal simulation, when the mesh, domain length andnon-dimensional parameters remain the same, there is no change in the results with thenew solver.

4.2 Results

Since the simulations in this section are based on the conditions described in the previouschapter, comparisons will be made with cases 1, 2 and 3.

4.2.1 Case 4: Temperature = 310 K, conductivity k = 0.145 W/mK

The oil and water temperature is 310 K and the wall temperature is 285 K. At steady statewith a temperature of 285 K this case is similar to case 2.



(a)

0 10 20 30 40

time (sec)

0

1

2

3

4

5

6

Am

plitu

de(m

)

×10-4

Case 2

Case 4

(b)

0 0.002 0.004 0.006 0.008 0.01 0.012

Pipe Length (m)

3.4

3.5

3.6

3.7

3.8

3.9

4

Am

plitu

de (

m)

×10-3

Case 2

Case 4

(c)

Figure 4.2: (a) Final volume fraction for case 4 (b) Comparison of amplitude growth (c) Compar-ison of final interface profiles.

The simulation was terminated at 40 sec. Fig 4.2 shows the comparisons between cases2 and 4 for the wave amplitudes and wave profiles. For this case, the wave developmentshows a growth, decay and a saturation phase, similar to case 2. The onset of the wavesaturation with heat transfer is slightly delayed. The difference in the final amplitude ofboth cases is 0.5 x 10−4m.

0 1 2 3 4 5

Pipe Radius (m) ×10-3

-0.2

-0.1

0

0.1

0.2

0.3

Velo

city (

m/s

)

Case 4

Case 2

(a)

0 1 2 3 4


280

285

290

295

300

305

310

315

Tem

pera

ture

(K

)

time=0 s

time=0.5 s

time=3.15 s

time=11.05 s

time=23 s

(b)

Figure 4.3: Case 4: (a) Comparison of the final velocity profiles for both cases (b) Temperaturesat different time instances.

The temperature and velocity profiles are shown in Fig 4.3 (a) and (b). The temperaturechange over the 23 sec time period is slow which is because the oil conductivity is very small.The initial change in temperature is larger because water has a higher conductivity. Thecentre line velocity is 0.42 m/s (0.25+0.17) relative to the wall. The core behaves like asolid body.



4.2.2 Case 5: Temperature = 330 K, k = 0.145 W/mK

Similar to case 4, but due to the low oil conductivity, the temperature penetration is veryslow. The final wave profile, amplitude and velocity are the same as for case 3. The resultsare shown in Fig. 4.4. Similar as found for the results for case 3, the core for case 5 doesnot behave like a solid body. For this simulation, the centre line velocity is 0.16 m/s.

(a)

0 5 10 15 20

time (sec)

0

1

2

3

4

5

6

7

8

Am

plitu

de

(m)

×10-4

Case 3

Case 5

(b)

0 0.002 0.004 0.006 0.008 0.01 0.012

Pipe Length (m)

3

3.2

3.4

3.6

3.8

4

4.2

4.4

Am

plitu

de

(m

)

×10-3

Case 3

Case 5

(c)

Figure 4.4: Case 5: (a) Final volume fraction (b) Comparison of the wave amplitude (c) Compar-ison of the interface profiles.

4.2.3 Case 6: Temperature = 310 K, k = 2 W/mK

So far due to the low conductivity the heat transfer from the wall to the oil core is slow.To increase the heat transfer rate, the thermal conductivity has been increased from 0.145to 2 W/mK for this simulation. This is of course not possible in an experiment.

Similar to Case 4, the initial perturbation develops into a single large amplitude bamboowave at about 0.5 sec. The amplitude then decreases until the interface is nearly flat at 6sec. After this decay, two waves appear with an amplitude that increases to 2 x 10−4 mafter 10 sec. These bamboo waves maintain this amplitude even after 30 sec.

The temperature profiles are shown in Fig. 4.6(a). At 25 sec, the temperature through-out the domain is 285 K. The centre line velocity relative to the wall is 0.40 m/s (0.23+0.17)and this is higher than in case 1 which has a velocity of 0.14 m/s (0.17-0.03). These resultsare quite surprising because although the non-dimensional parameters (except the Reynoldsnumber) are the same for both flows, the number of waves, core velocity, wave amplitudeand wavelength are different. In other words, there is a possibility of multiple solutions forthe same set of dimensionless numbers.



(a)

0 0.002 0.004 0.006 0.008 0.01 0.012

Pipe Length (m)

3.2

3.4

3.6

3.8

4

4.2

4.4

Am

plitu

de (

m)

×10 -3

time=0 s

time=0.5 s

time=6 s

time=8.5 s

time=25 s

(b)

0 5 10 15 20 25 30

time (sec)

0

1

2

3

4

5

6

Am

plitu

de(m

)

×10-4

(c)

Figure 4.5: Case 6: (a) Final volume fraction (b) Wave profiles at different times (c) Waveamplitude against time

0 1 2 3 4


280

285

290

295

300

305

310

315

Tem

pera

ture

(K

)

time=0 s

time=0.5 s

time=6 s

time=8.5 s

time=25 s

(a)

0 1 2 3 4


-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Velo

city (

m/s

)

time=0.5 s

time=6 s

time=8.5 s

time=25 s

(b)

Figure 4.6: Case 6: (a) Temperature profile (b) Velocity profiles at different times.



4.3 Verification of the results

In the previous section, simulations were presented without changing the domain length,mesh density and wave initialization procedures. In this section we will look at the effects ofchanging these conditions. This is even more important because the possibility of multiplesolutions in vertical core annular flows has not been reported before. In this section, resultsare discussed for simulations in which the above mentioned conditions have been varied.

4.3.1 Wave initialization

The interface is initially perturbed to speed up the wave development. For all simulations,a perturbation in the form of a single sinusoidal wave has been used. Beerens[24] reportedthat when initializing with a double wave, the growth rate changed in his simulations. Thischange, however, did not seem to affect the final solution since he always reported a singlebamboo wave.

For case 6, when two and later, four waves with amplitude 10−5m were initialized atthe interface, the final solution showed two interfacial waves.

4.3.2 Mesh

All simulations presented so far had a mesh of 128x128 cells in the axial and radial direc-tions. This mesh resolution was suggested by Li and Renardy [12], Kouris et al. [17] andBeerens[24].

Mesh convergence studies have been performed for case 6, as multiple solutions wereobserved for that case. For sake of brevity, only the number of waves at the interface isreported when the simulation has reached steady state, i.e. when the temperature of theoil core is equal to the wall temperature.1. Mesh density 96 x 96: The final profile is a single bamboo wave similar to case 1.2. Mesh density 128 (axial) x 96 (radial): 2 waves are observed. This shows that atleast 128 cells are required in the axial direction for the occurrence of two waves.3. Mesh density 128 (axial) x 128 (radial): two waves are observed.4. Mesh density 256 x 256: No waves are observed.

A possible reason for the absence of waves on the finest mesh is that any unstable wavein this case is longer than the computational domain length.

4.3.3 Changing the domain length

Perhaps, the increase in the number of waves is a consequence of a shorter/longer domain.To check this, the pipe length was increased by a factor of 2. The mesh was adapted suchthat it has 256 x 128 (axial x radial) cells.

Case 7: Temperature = 310 K, k = 2 W/mK, domain length increased by afactor 2

The wave profiles are shown in Fig. 4.7(b) and (c).The initial perturbation develops into twolarge amplitude waves during the growth phase. This is followed by a decay in amplitudeuntil 5 sec. Four waves are observed at the interface at this time. During the subsequentgrowth phase, the number of waves changes from 4 to 3. Finally after 40 sec, three wavesare visible at the interface as shown in Fig. 4.7(a).



(a)

0 0.005 0.01 0.015 0.02 0.025

Pipe radius (m)

3.2

3.4

3.6

3.8

4

4.2

Am

plit

ude (

m)

×10-3

time=0 s

time=2 s

time=5 s

(b)

0 0.005 0.01 0.015 0.02 0.025

Pipe radius (m)

3.4

3.6

3.8

4

4.2

Am

plit

ude (

m)

×10-3

time=12 s

time=18 s

time=40 s

(c)

Figure 4.7: Case 7: (a) Final volume fraction, (b) and (c) Wave profiles at different times.

Fig. 4.8 (a) compares the wave amplitude for case 7 with case 6. Increasing the domainlength has the following effects:1. The decay and subsequent growth of the waves occur at different times for the cases 6and 7.2. Both cases have different final amplitudes. Unlike case 6, where the amplitude is con-stant after 10 sec, for case 7 the amplitude fluctuates at around 3.4 x 10−4 m, even after 40sec. The most likely explanation for this fluctuation is that more than three waves can existin this domain length. Since the simulations allow for only an integer number of waves,three waves are forced as a solution. It is also possible that after running the simulationfor longer times, the amplitude will stabilize.

For case 7 the final amplitude and wavelength of the interfacial waves are a factor of1.5 times larger than for case 6. As a result, the core moves with a velocity of 0.29 m/s(0.12+0.17), which is slower than for case 6 where the core centre line velocity is 0.40 m/s.Fig 4.8 (c) shows the velocity profiles at different times. The green line represents thevelocity profile for case 6.



0 10 20 30 40

time (sec)

0

1

2

3

4

5

6

Am

plit

ude(m

)

×10-4

Case 6

Case 7

(a)

0 1 2 3 4

Pipe radius (m)×10

-3

280

285

290

295

300

305

310

315

Tem

pera

ture

(K

)

time=0 s

time=0.45 s

time=6 s

time=12 s

time=25 s

(b)

0 1 2 3 4

Pipe radius (m)×10

-3

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Ve

locity (

m/s

)

time=0.48 s

time=6 s

time=12 s

time=25 s

Case 6, 30 sec

(c)

Figure 4.8: Case 7: (a) Comparison of wave amplitude for case 6 and 7, (b) Temperature profiles,(c) Velocity profiles at different times.

It is quite clear from these simulations that choosing the correct domain length is impor-tant. Case 7 and case 6 do not vary very much in terms of the wave shapes. However, thedomain length has a significant effect on the final flow characteristics, such as the numberof waves, the wave amplitude and the final core velocity. It is important to note that, forthe above simulation, the exact domain length is still unknown. Therefore it would help toperform simulations taking a longer length of the pipe.



Case 8: Temperature = 310 K, k=0.145 W/mK, domain length increased by afactor 2

0 0.005 0.01 0.015 0.02 0.025

Pipe length (m)

3.2

3.4

3.6

3.8

4

4.2

Am

plit

ud

e (

m)

×10-3

time=0

time=2

time=12

time=28.5

Figure 4.9: (a) Final wave profile (b) Wave profiles at different times for Case 8.

The final wave profile for case 8 is shown in Fig. 4.9 (a). There are two interfacial waveswhich are not as steep as the waves in case 7. These two waves also do not show the sameamplitude. After the decay and the subsequent growth phase, the final amplitude fluctuatesbetween 3 to 4.5 x 10−4 m even after 28 sec. This value is nearly twice as high as for case4.

Since the wave amplitude is larger, the final centre line velocity (0.35 m/s) is lower thanfor case 4 (0.42 m/s). The comparison has been made in Fig. 4.10(b).

0 5 10 15 20 25 30 35

time (sec)

0

1

2

3

4

5

6

7

Am

plitu

de(m

)

×10-4

Case 4

Case 8

(a)

0 1 2 3 4


-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Velo

city (

m/s

)

Case 4

Case 8

(b)

Figure 4.10: Case 8 versus case 4: (a) Wave amplitude vs time (b) Comparison of velocity profiles.



Case 9: Temperature = 330 K, k = 0.145 W/mK, domain length increased bya factor 2

0 0.005 0.01 0.015 0.02 0.025

Pipe length (m)

2.5

3

3.5

4

4.5

Am

plit

ud

e (

m)

×10-3

time=0 sec

time=2 sec

time=5 sec

time=23.5 sec

Figure 4.11: Case 9: (a) Final volume fraction (b) Wave profiles at different times.

The initial wave development is erratic. After 5 sec, the interface reaches a constant profile.Two waves are observed on the interface. Comparison with case 3 shows that the finalamplitude for both cases is the same. The comparison of the velocity profile also showsvery small differences.

0 5 10 15 20

time (sec)

0

0.2

0.4

0.6

0.8

1

Am

plitu

de(m

)

×10-3

Case 5

Case 9

(a)

0 1 2 3 4


-0.2

-0.1

0

0.1

0.2

Velo

city (

m/s

)

Case 5

Case 9

(b)

Figure 4.12: Comparison of case 5 and case 9: (a) Wave amplitude vs time (b) Velocity profiles.

4.4 Multiple solutions

From the previous section, we learn that the correct domain length is required to accu-rately predict the waves at the interface. However, the cause of the occurrence of multiplesolutions is still unknown.



We will take a closer look at case 7. The instability development consists of the growth,decay and a final growth phase before the amplitude saturates at a mean value. In table4.1, the wave amplitudes and core velocities have been reported at the end of each of thesephases.

Table 4.2: Comparison of velocity and amplitudes for different growth phases in case 7.

Phase Time (sec) Amplitude (m) Velocity (m/s)

Growth 0-0.5 5.8e−4 0.22

Decay 0.5-5 1.2e−4 0.38

Growth 5-32 3.4e−4 0.29

At the start of the simulation, the core velocity is initialised so that it moves at 0.17 m/srelative to the wall. The pressure gradient applied to the flow accelerates the oil core. Dueto the viscosity and density jumps, instabilities are amplified which result in two bambooshaped waves. The presence of these waves causes the core velocity to drop to 0.22 m/srelative to the wall.

The finite surface tension most likely causes the wave amplitude to decrease. Duringthe decay phase, since the amplitude decreases, the core velocity now increases to 0.38 m/srelative to the wall. Before the next growth phase, which starts at approximately 5 sec,the core already moves at a higher velocity than at the start of the simulation. Due to thislarger velocity, it is possible that the next stable solution has three waves.

To verify this, two simulations were performed, without heat transfer, with the sameviscosity ratios but with a different initialization for the velocities. The viscosity ratio isn=663. This value has been chosen because for case 1 there is only a growth and saturationin amplitude. The domain length is 2.32 cm. These two simulations are referred to as cases10 and 11.Case 10: The core moves with a velocity of 0.17 m/s relative to the wall. The dimension-less parameters are:m = 0.00166, a = 1.28, ζ = 1.10,K = −0.93, J = 7.96e−2, Re1 = 0.95.Case 11: The core moves moves with a velocity of 0.87 m/s relative to the wall. Thedimensionless parameters are:m = 0.00166, a = 1.28, ζ = 1.10,K = −0.93, J = 7.96e−2, Re1 = 4.86.

The initial and final velocity profiles are shown in Fig. 4.13 (a) and (b). In Fig 4.13(c)the wave amplitude versus time has been compared for cases 7, 10 and 11. The final pro-files for case 10 and 11 have been shown in Fig 4.14. For case 10, due to the smaller corevelocity, the wave amplitude quite quickly saturates at 5.5 x 10−4 m after 5 sec. The finalprofile has two bamboo waves. For case 11, the wave development is rather erratic. Afterapproximately 28 sec, three bamboo waves are observed with an average amplitude of 3.4 x10−4m. The core velocity for case 11 is about 0.29 m/s, which is also higher than for case10. It is interesting to note that this value is the same as found for case 7.



0 1 2 3 4


-0.2

0

0.2

0.4

0.6

0.8

Ve

locity (

m/s

)

Case 10

Case 11

(a)

0 1 2 3 4


-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

Velo

city (

m/s

)

Case 10

Case 11

Case 7

(b)

0 10 20 30 40

time (sec)

0

1

2

3

4

5

6

Am

plitu

de

(m)

×10-4

Case 11

Case 10

Case 7

(c)

Figure 4.13: (a) and (b) Initial and final comparisons of velocity profiles (c) Comparison ofinterfacial wave growth for cases 7, 10 and 11.

(a)

(b)

Figure 4.14: Final volume fraction (a) Case 10 (b) Case 11.

We now know that multiple solutions can occur for the same domain length, when pe-riodic boundary conditions are used, depending on the initialization of the core velocity atthe start of the simulations. It is not just a consequence of applying heat transfer.



A summary of all the simulations that were presented in chapters 3 and 4 is given inTable 4.3.

Table 4.3: Summary of VCAF simulations.


Chapter 5

Experiments on HCAF

HCAF has been studied in an experimental setup at TU Delft, in the laboratory of Processand Energy. In this chapter this setup will be introduced, followed by a description of someimportant properties of the oil (Shell Morlina S4 B 680) which was used for the experiments.Finally the measured pressure drops and footages of the flow are shown.

5.1 Introduction

In the past, several researchers have reported experiments on immiscible two phase flows inhorizontal pipes. Shi and Yeung [29] have given a detailed review of liquid-liquid flow sys-tems and they report how flow patterns can be grouped into the following main categories:1) Stratified flows (ST) (smooth or wavy interface) 2) Dispersed flows (D) 3) Intermittentflows (I) (slugs/plugs/ large bubbles) 4) Core Annular Flows (CAF). Other configurationswhich are reported are transitional regimes between the above mentioned regimes.

Multiphase flows are particularly difficult to characterize due to the number of forceswhich influence them. In the experiments, we will primarily change the viscosity by heatingthe oil to different temperatures. In this section, we can start by distinguishing the previousliterature according to two phase oil and water experiments with high and low oil viscosities.Results are discussed for experiments where the pipe diameter is more than 1 inch.

5.1.1 Low viscosity

For low viscosity oils, the most dominant flow patterns are ST, D and transitional regimesbetween them. Examples are the experiments of Trallero et al.[9], Vielma et al.[20] andAngeli et al.[13]. Increasing the oil viscosity (Sridhar et al.[22] ,Grassi et al.[18]) increasesthe possibility for the formation of I and CAF.

Stratified flows tend to form only when there is a density difference between the twophases. This is known from the experiments of Charles et al.[31] who studied flow patternsin density matched fluids and reported CAF, I and D regimes. At high mixture velocities,I and D regimes are observed. The reason for this could be that, in low viscosity oil- waterflows, increasing the mixture velocity increases the turbulence in both phases. When theturbulence is high, the oil phase breaks up, resulting in dispersed flows. When the turbulentkinetic energy of the flow is not high enough, the oil can flow continuously (CAF if viscosityis sufficiently high) or discontinuously (I or D).

5.1.2 High viscosity

Several experiments have been reported with high viscosity oils due to its potential forapplication in lubricated pipelines. The patterns which are usually reported are S, CAF

35

Experiments on HCAF 36

and oil dispersed (lumps, slugs, plugs) in water. S is observed under limited conditionswhen the density difference is large and the mixture velocity is low.

When increasing the mixture velocities, CAF is a dominant flow pattern which hasbeen reported by several authors including Ooms et al.[2], Oliemans et al.[4], and Sotgia etal. [19]. Very eccentric CAF is reported when the density difference is large, the mixturevelocity is low and the water addition ratio εw is high. CAF is more concentric and wavywhen the mixture velocity is increased and εw is decreased. Oil fouling is commonly reportedin this regime.

5.1.3 A new dimensionless number

In section 2.2, a modified Froude number, as used by Eduard [28] was introduced. TheFroude number is the ratio between the buoyancy related forces and the inertial forces. Heshowed in his experiments that for water addition ratios between 8% and 20%, the pressuredrop has a linear relation with Fr. This result is important because it shows that Fr can beused to characterize CAF. The only issue is that there is no consideration of the viscosityin that formulation. Since the CAF is usually reported for high viscosity ratios, the use ofonly Fr seems to be an incomplete characterization.

Brauner et al. [10] consider the Eotvos number Eo’ as a strong candidate to characterizetwo phase flows. Eo is the ratio of the gravitational force and the surface tension force:

Eo′ =4ρgD2

8σ(5.1)

Furthermore, Bannwart [16] has proposed that for CAF to develop, the criterion of Eo’< 2.55 must be satisfied. Although some authors do report CAF satisfying this criterion,Ooms et al. [2], Mckibben et al. [14] and Sridhar et al. [22] report CAF at higher Eo’ of50, 13.5 and 12.8, respectively. Again, the Eotvos number does not account for the velocity(inertia) or viscosity which are important for CAF.

Shi et al. [29] have proposed a new dimensionless number which accounts for the effectsof density difference, inertia (velocity) and viscosity:

G

V=

Gravitational Forces

Viscous Forces=4ρgD2

µU=Re

Fr(5.2)

where 4ρ is the density difference, D is the pipe diameter, U is the mixture velocity and µis the dynamic viscosity of the oil. A low G/V ratio (< 1) means that the viscous force dom-inates the gravitational force. The latter force dominates when G/V > 40. This criterionwas used by Shi et al. [29] to check if this correlation holds for the experiments of other au-thors. Their table of the comparison has been included as an appendix in the present report.

For low viscosity flows at G/V ratios of 400-4000, stratified flows are usually reported.When this ratio is reduced to 40-400, usually by an increase of the mixture velocity, dis-persed flows are reported. For low viscosity oils, when the mixture velocity is increased,turbulence in one or both of the phases causes immediate breakup of the stratified flow.

For high viscosity oils, when the G/V ratio is less than 1, CAF is almost always re-ported. This is because the core has a high viscosity and flows as a continuous phase.Further increase in the mixture velocity causes oil lumps in water. This is because al-though there is no turbulence in the oil phase (owing to high viscosity), turbulence in the



water might be significant enough to break up the oil into lumps.

Based on the above mentioned literature, we know that core annular flows are thepreferred flow regime at high viscosity ratios and at relatively high mixture velocities. Forthe experiments, a heating element has been added to the setup to reduce the oil viscosity.Use will be made of the G/V ratio to check if the experimental parameters satisfy the CAFregime.

5.2 Experimental set-up

Figure 5.1: Schematic overview of the front side of the setup.

The main components in the setup have been numbered in figures 5.1 and 5.2.1. Pipe: The setup consists of horizontal PVC pipes with an inner diameter of 21 mmalong a total length of 7.5 m (including bends and straight sections). The sections are: a2 meter straight section starting from the oil-water divider. This is followed by a curvedsection with a 0.25 m radius of curvature, a straight section of 3 m length and finally acurved section which leads via hoses to a separation tank. Two holes, 1 m apart, have beendrilled along the 3 m section. Spouts have been attached to measure the pressure differencealong this section.

2. Divider: The divider consists of an inner and outer pipe through which oil and waterenter, respectively. This configuration separates the flow at the inlet as an inner oil coreand an outer annulus of water.

3. Oil pump: A powerful oil pump is placed between the reservoir and the divider toensure a smooth step-less flow of the very viscous oil into the setup. The flow rate of thepump is adjusted before the experiment is started. The pump is also used to recirculatethe oil during the heating to ensure a faster heat transfer.



Figure 5.2: Schematic overview of the back side of the setup.

4. Oil reservoir: The oil reservoir is a 60 liter container used to store the oil. The reser-voir is connected to the oil pump via a hose.

5. Separation tank: The pipe ends in a separation tank where the oil-water mixtureis collected. Oil and water, with their relatively large density difference, are separated bygravity in about 22 hours[28].When the oil and water have separated, the oil stays on top. This oil is pumped back tothe oil reservoir using a pump once the separation is complete. Water at the bottom isregularly removed.

6. Heating setup: The heating setup is used to heat up the oil to desired temperatures bypumping hot water into copper coiled tubes in the oil reservoir. The internal temperatureof the water in the heating setup can be adjusted. There is a temperature sensor placed inthe reservoir by which the external local temperature (oil in reservoir) can be checked onthe setup display.

7. LabVIEW: LabVIEW is used via a computer interface to collect data related to theexperiment. A pressure sensor and water flow meter were connected to the setup and areused to confirm the oil and water flow rates. The accuracy of the water flow meter was ver-ified by Ingen Housz[28] and was found to be within 4%. The temperature of the oil is alsorecorded during the experiment by a temperature sensor connected to the Labview software.

8. U-tube manometer: A U-tube manometer is inverted and connected via spouts to1 mm holes in the pipe and is used to measure the pressure drop. The connection to thespouts and the manometer is made via flexible transparent pipes. The spouts are turneddownwards to increase the probability of the holes being in the water annulus when due tothe levitation, the oil core is lifted up. The working fluid in the U-tube is water.



5.2.1 Procedure

The oil and water flow rates are adjusted before the experiment is started. First only wateris allowed to flow through the setup. When the water flow is continuous, i.e. there areno air bubbles anymore, the oil is pumped from the oil reservoir, via the oil pump andthe divider, into the pipe. The oil-water mixture passes through the pipe sections and isdumped into the separation tank where the mixture is allowed to separate by gravity in 22hours. When the oil separates, it is recirculated back into the storage tank.

At the test section, pressure measurements are recorded with a U-tube manometer. Themanometer did not react quickly to the flow. Measurements are thus recorded when theyare steady or do not change over 5-6 sec. Visualization via pictures or video can be madeusing a LaVision camera that is setup approximately 5 m from the inlet. At this location,a transparent box filled with water has been placed on the pipe to reduce optical distortioncaused by refraction. Footage were recorded at 1000 fps. Some pictures have been takenwith a black background since this contrasts very well with the oil which has a white/yellowcolour.

If the oil is heated, this is done prior to the start of the experiment. Heating the oiltakes considerable time due to its low thermal conductivity. Moreover, heating by the cop-per coils is local. To improve the heat transfer, the oil is recirculated between the pumpand the reservoir. Although this speeds up the heating process, achieving temperatures ashigh as 50 C usually takes 1.5 - 2 hours.

More information on the setup can be obtained in the study by Ingen Housz [28].

5.3 Physical properties of the oil

Shell Morlina S4 B 680 has been used in the experiments. It is pale yellow in colour. Sincethe same oil was used by Ingen Housz, it has been recirculated in the system for more thana year. During this time, the colour of the oil has changed from off-white to yellow and ithas also developed a smell similar to hydrogen sulphide. This we learnt is because of anaer-obic bacteria which develop between the oil- water interface (mostly in the separation tank).

The density of the oil has increased due to the presence of small water droplets whichcould not fully be separated. The oil density is:

ρo = 857 kg/m3 (5.3)

The interfacial tension between oil and water was measured by Ingen Housz [28] usinga ring tensiometer at 21 C. In this thesis, the same value has been used:

σ = 1.6 ∗ 10−2N/m (5.4)

Viscosity

When the oil was new, measurements had been made for the dependence of the viscosityon the temperature for temperatures between 15 and 30 C. In our experiments, the oil hasbeen heated to higher temperatures. To measure the viscosity at different temperatures, arheometer was used, which measures the viscosity at various shear rates for different tem-peratures in a Couette geometry. The measurements between 20 and 60 C in Fig. 5.3 showa strong dependence of the viscosity on the temperature.



We have also verified whether the oil properties changed over time. Comparison withthe old measurements do indeed show that there is a change in the oil viscosity. This ismost likely due to the presence of some fine water dispersion in the oil after use.

20 30 40 50 60 70

Temp (oC)

0

500

1000

1500

2000

2500

3000vi

scos

ity (

cSt)

Shell Morlina S4 B 680

New measurement

Old measurement

Figure 5.3: Comparison of the old and new viscosity measurements.

5.4 Experimental parameters

From the description in the previous sections, we know that CAF is preferred when theoil viscosity and mixture velocity are sufficiently high. Keeping this in mind, the mixturevelocity is set to 1.28 m/s for all experiments. The experiments were performed at wateraddition ratios of 17.5% and 12.5%. The experiments will be reported for temperatures of23 C, 30 C, 40 C and 50 C.

Use was made of the G/V ratio to ensure that the experiments were performed in theCAF regime. In Table 5.1, values of the G/V ratio at different temperatures are reported.

Table 5.1: G/V ratios and kinematic viscosity at different temperatures.

Temperature (C) Viscosity (cSt) G/V ratio

23 2100 0.27

30 1435 0.39

40 805 0.70

50 480 1.17

The criterion of G/V < 1, which is required for stable CAF, is satisfied for all consideredtemperatures with the exception of 50 C. But also for 50 C the value of G/V is much lowerthan the criterion for the transition to dispersed/stratified flows which is reported at G/V> 40. Hence CAF was expected for all considered temperatures.

5.5 Results

The experimental conditions are given in Table 5.2.



Table 5.2: Oil-water flow rates and mixture velocities for different water addition ratios.

εw Oil flow Water flow Mixture Velocityrate (Qo ) rate (Qw ) (Umv )

12.5 % 0.36 l/s 0.052 l/s 1.2 m/s

17.5 % 0.36 l/s 0.076 l/s 1.26 m/s

In all pictures, the flow is from left to right. Images of the footage are shown for experi-ments at a 17.5% water addition ratio. At 23 C in Fig. 5.4 (a), wavy CAF is observed withprominent waves on both the upper and lower interface. The waves on the upper interfaceshow steeper slopes in the flow direction. In some parts of the footage, it is also clear thatthe amplitude of the waves in the lower annulus are higher than in the upper annulus.

At 30 C, in Fig. 5.4 (b), waves can be clearly seen for both the upper and lower annu-lus. The waves for both the upper and lower annulus are also not very much out of phasewith each other and we find more waves than in the previous case implying a decrease inwavelength. The amplitude of the waves for the lower annulus is larger than for the upperannulus. Moreover, the slope of the wave crests in the flow direction is not as steep as forthe 23 C footage. This could mean that although waves form on the interface, they aredeformed by water, which indicates that the core behaves less as a rigid body as comparedto the behaviour at 23 C.

At 40 C the viscosity ratio reduces to about one-third of the 23 C case. Two picturesfor this temperature are shown in Fig. 5.4 (c) and (d). The initial footage (Fig. 5.4 (c))shows well defined wave trains with quite a large amplitude for both the lower and upperinterface. After about 2 sec (Fig. 5.4 (d)), the core is very eccentric and the waves at theupper interface are seen to be considerably smaller than at the lower interface. Foulingdoes not occur although bubbles were observed at some instances. Unlike the pictures for23 and 30 C, the wave crests are clearly deformed. An interesting observation is that thenumber of waves in the lower annulus has been increasing with higher temperatures. Theflow is still CAF.

(a) T=23 C (b) T=30 C

(c) T=40 C (d) T=40 C

Figure 5.4: Footage of core annular flow at different temperatures of 23, 30 and 40 C.



At 50 C, the viscosity is nearly one-fifth of the viscosity at 23 C. Fig. 5.5 (a) and(b) have been taken without and with the contrasting backgrounds, respectively. In bothcases, it is quite clear that the oil has started to break up. Although at some instances,waves characteristic of core annular flow are visible, small bubbles are seen at all timesbeing convected with the flow. The flow is probably at a transitional regime between CAFand intermittent flow. Compared to the previous cases, the core is also very eccentric.This is seen in Fig. 5.5 (b), where the lower annulus is seen to be thicker than the upperannulus. Fouling was observed near the pressure ports as shown in Fig. 5.6 (a) and (b).At such low viscosities, the oil no longer behaves as a continuous solid core and will breakup to form bubbles/lumps of oil in the water. It is difficult to maintain CAF at these hightemperatures/low viscosities.

(a) Picture with contrasting background. (b) Picture without contrasting background

Figure 5.5: Footage of core annular flow at an oil temperature of 50 C.

(a) (b)

Figure 5.6: Oil fouling (marked within red) near both the pressure ports at temperature 50 C.

The measured pressure drop per meter length is shown in Fig. 5.7 for 12.5 and 17.5% εw. For both the ratios, the measurements are reported at 23, 30, 35, 40, 45 and 50 C.Note that the vertical axis goes from 110 to 130 mm H2O. Between 23 and 30 C at 12.5%εw, the pressure drop increases, after which slightly lower pressure drops were measured.The lowest pressure drops were measured for 50 C. A similar trend is observed at the wateraddition ratio of 17.5 %. The experiments show that core annular flow can still be observedat low viscosities and they also require a slightly lower pressure drop to achieve the samethroughput.



Figure 5.7: Comparison of the measured pressure drop.

5.6 Discussion

The advantage of CAF is that by adding a little water to the oil, viscous oil can be trans-ported through a pipe at a pressure gradient that is almost as low as the case that onlywater is present in the pipe at the same velocity. In the experiments, since the mixturevelocity is the same for all temperatures, one can argue that it is not very surprising thatthe pressure measurements are quite similar to each other. This is especially supported bythe fact that the pictures show CAF at a temperature of 23 C, 30 C and 40 C.

It is still hard to reconcile why the lowest pressure drop was measured for 50 C eventhough the flow was very eccentric and oil breakup was visible. Repeating the experi-ments did not always show reproducible readings. Large deviations were observed for thesame experimental conditions especially at temperatures higher than 30 C. To improve themeasurements, the pipe was cleaned several times and the pressure port connections werechanged. These changes did not improve the reproducibility.

A possible explanation is that at 50 C, owing to the large eccentricity and oil breakup,the 1 mm hole connected to the manometer might be fouled, resulting in wrong/incompletemeasurements. Fouling is most prominently observed at these locations as shown in Fig. 5.6.

Keeping this in mind, numerical simulations based on the experiments are discussed inthe next chapter to gain a better insight into the experiments and on how CAF behaves atlower viscosities.


Chapter 6

HCAF simulations

This chapter is meant to obtain a better understanding of the experimental results. Theexperiments did give us an insight into the flow regimes and pressure drops for differentviscosity ratios. In this chapter, results are presented for simulations based on the fourexperiments discussed in the previous chapter.

6.1 Background

Beerens [24] performed laminar, horizontal flow simulations with the interFoam solver. Hissimulations were based on the experiments of Bai et al.[5]. However, Beerens assumed thepipe to be horizontal instead of vertical. He reported that the levitation of the core wasbalanced by a net downward force caused by a positive pressure which develops betweenthe waves, the upper annulus and the wall. Ooms et al. [26] studied the levitation forcesin HCAF for small density ratios and high viscosity ratios. They have shown that viscousas well as inertial forces are important. Their simulations were for low Re flows.

Ingen Housz[28] performed numerical simulations based on some of his experiments. Hefirst performed laminar flow simulations for mixture velocities of 1.18 m/s. The velocityprofiles showed an unphysical spike at the interface for the lower annulus. He reasoned thatthis error could be attributed to a transition to turbulence. Simulations with the Launder-Sharma k-ε turbulence model did not show this spike. The simulations also predicted aconsiderable amount of turbulence developing in the water. As the core levitated upwards,the turbulence in the upper annulus reduces while in the lower annulus it will increase.Overall, there was a discrepancy of around 22% in the mixture velocity when comparedwith experiments. Moreover, when comparing different turbulence models, he found thatthe k-ω SST model showed the best agreement with experiments.

Although the k-ω SST has performed better, k-ε has been employed in this thesis be-cause in the current version of OpenFOAM, there is still no turbulence damping for theSST model. This is important since the k-ω-SST is a combination of k-ω near the wall andk-ε away from the wall. In the current version of OpenFOAM, the model does not switchback to k-ω at the interface. A damping coefficient is required at the interface to dampthe turbulence. CFD tools such as Fluent have a damping function that switches on at theinterface to damp the turbulent viscosity. Shi [27] has used such a damped k-ω SST modeland he has reported good agreement with his own experiments.

45

HCAF simulations 46

6.1.1 Turbulence in the annulus

Since the numerical simulations by Ingen Housz [28] predicted turbulence, we were inter-ested to see if the turbulence could also be observed in the experiments. Therefore, weinjected a solution of black ecoline dye into the flow at the lower annulus. Based on theidea of Reynolds, who injected a thin filament of dye in the flow, an erratic dispersion of thedye would indicate turbulence while an undisturbed filament means that the flow is laminar.

To ensure that the waves do not not disturb the dye, use was made of the core eccen-tricity when injecting the dye into the lower annulus. The first experiment was performedfor a flow with 20% water addition ratio and 1 m/s mixture velocity. Pictures from thefootage are shown in Fig. 6.1. The dye is disturbed by the large amplitude waves in thelower annulus. Although dispersion of the dye is visible, it is still difficult to conclude if thedispersion is an effect of the waves disturbing the dye or of the turbulence. Interestingly inone configuration as shown in Fig. 6.1 (c), when the injection was accidentally made at ahigher location, we observed the dye being convected along with the waves, possibly evenfollowing the wave shape at that location of the interface.

(a) (b)

(c)

Figure 6.1: (a) and (b) Dye injection at consecutive time instances for εw=20% and Umv= 1 m/s(c) Dye injection at a higher location.

Since at εw = 20% the waves are quite large, the dye injection was done for a flow withεw = 30% and Umv=0.7 m/s. At such high water addition ratios, the flow is very eccentric.Although the mixture velocities are quite low, photographs in Fig. 6.2 show the dye beingdispersed.


HCAF simulations 47

(a) (b)

(c) (d)

Figure 6.2: (a)-(d): Dye injection at consecutive time instances for εw = 30% and Umv= 0.7m/s.

6.2 Numerical solution procedure

Details of the solver have already been discussed in chapter 3. interFoam is used withoutthe energy equation. Simulations are performed for εw = 17.5% since footages have beenrecorded for these experiments.

6.2.1 Initialization

The flow is initialized by using the equations for PCAF. Since we do not know what theundisturbed oil radius is, similar as for the vertical flow simulations, the following equationis used with the holdup ratio as 1.39:

a =

√1 + h.

us,wus,o

(6.1)

The oil and water superficial velocities that are required for eq. 6.1 are calculated from theexperimental flow rates. Since it takes some time for the flow to develop from rest, the corevelocity is initialized as 1.28 m/s for all the simulations.

6.2.2 Geometry and mesh

For HCAF, the assumption of axisymmetry cannot be made because the core will eventu-ally become eccentric. The diameter of the domain is equal to the pipe diameter and thelength is 2.56 cm. Periodic boundary conditions are used to study the temporal flow devel-opment. The simulations for the vertical pipe with the temperature gradient have shownthat using the correct axial length is very important. The experimental footage show thatthe wave length of the most unstable wave at T = 23 C in the upper and lower annulus isless than the pipe diameter of 2.1 cm. Moreover, the experiments show that decreasing theoil viscosity decreases the wave amplitude and the wavelength. Hence the present domainlength of 2.56 cm is a reasonable choice.


HCAF simulations 48

The mesh is block structured with 125 x 80 x 60 points in the radial, circumferentialand axial directions. This corresponds to 600,000 grid points. Since a turbulence model willbe used, it will be useful to know if the mesh spacing is sufficient for the model. This canbe verified in terms of y+ values. Assuming a single phase flow through a plane channel,the wall friction velocity is given by:

uτ =

√dp

dz

R2

2ρw(6.2)

wheredpdz is the pressure gradient, ρw is density of water and R2 is the pipe radius. For apipe diameter of 2.1 cm, 125 equidistant grid points means that the size of each cell in theradial direction is δr = 8.4 x 10−5. y+ is calculated as:

y+ =δr ∗ uτνw

(6.3)

For a pressure gradient of 1200 Pa/m and a water kinematic viscosity of 10−6 m2/s, y+ isapproximately 9. Generally for low Re turbulence models, the minimum y+ values shouldbe 1.

6.2.3 Turbulence modelling

Typically k-ε models are good for high Re flows where wall functions are used to accountfor the log layer in this region. For low Re flows, a correction has to be introduced to thek and ε equations. Changes are made by introducing damping functions in the original k-εequations and by solving for a new modified dissipation equation.

∂ρk

∂t+∇.(ρkU) = ∇(µ+

µtσk∇k) + 2µtSijSij − ρε (6.4)

∂ρε

∂t+∇.(ρεU) = ∇(

µ+ µtσk

∇ε) + C1εf1ε

k2µtSijSij − C2εf2ρ

ε2

k+ E (6.5)

fµ = e− 3.4

(1+Reτ 50)2 f1 = 1 f2 = 1− 0.3e( −Reτ )2,

ε0 = 2ν(∂√k

∂y) E = 2ννt(

∂2U

∂y2)2 Cε1 = 1.44

Cε2 = 1.92 Cµ = 0.09 σk = 1 σε = 1.3

6.2.4 Schemes and boundary conditions:

The no slip boundary condition is applied at the wall. Periodic boundary conditions areused at the pipe entrance and exit.

For the temporal discretization, Backward Euler is used. The TVD scheme is used forthe spatial discretization of the advection terms. Gauss Interface compression is used tolimit the interface diffusion. The pressure velocity coupling is applied with the PIMPLEscheme (combination of PISO and SIMPLE). The following linear solvers are employed: Pre-conditioned Conjugate Gradient and Preconditioned Bi-Conjugate Gradient for the pressureand velocity components, respectively. For the discretization of the divergence terms forturbulence, first order Gauss upwind is used. The Courant number is limited to 0.01.


HCAF simulations 49

6.2.5 Simulation details

All simulations have been made for a water addition ratio of 17.5%. The following param-eters are maintained constant during the simulation:

ρo 857 kg/m3

ρw 998 kg/m3

νw 1e−6 m2/s

R1 9.23 ∗ 10−2 m

R2 10.5 ∗ 10−2 m

σ 1.6 ∗ 10−2 N/m

f∗ 1200 Pa/m

εw 17.5%

kint 0.2 m2/s2

kwall 1.0 ∗ 10−15 m2/s2

εint 200 m2/s3

εwall 1.0 ∗ 10−15 m2/s3

kint, εint are uniform internal turbulent fields applied to the flow to expedite the develop-ment of turbulence. kwall, and εwall are boundary conditions at the wall as suggested inWilcox [11].

The velocity of the core in all the simulations is initialized to 1.28 m/s. The wall isstationary. The pressure gradient imposed in all simulations is 1200 Pa/m. This valueis used because in all the experiments, the measured pressure gradients was in the rangeof 1100-1300 Pa/m. This thus means that the pressure gradient and the oil holdup areprescribed in the simulations, whereas the oil and water flow rates are following as outputquantities from the simulations.


HCAF simulations 50

6.3 Results:

6.3.1 Case A: T=23 C

(a) t = 0.5 sec (b) t = 1 sec (c) t = 1.5 sec

(d) t = 2 sec (e) t = 2.5 sec (f) t = 2.62 sec

Figure 6.3: Case A: Volume fraction at different times.

The volume fraction on a centered slice of the pipe is shown in Fig. 6.3 (a)-(f). FromPCAF the flow quickly becomes eccentric and the waves develop on the upper and lowerinterface. With an increase in the core eccentricity, the amplitude of the waves at the upperand the lower interface decrease and increase, respectively. Results for the variation in yand z momenta of the core against time are shown in Fig. 6.4 (a) and (b). Fluctuationsare still observed in the y momentum, but mostly around 0. Since the momenta changelittle with time, the flow is considered to be converged. At 2.62 sec, waves on the upperand lower interface have amplitudes of 0.16 mm and 0.9 mm, respectively.

0 0.5 1 1.5 2 2.5

Time (sec)

-5

-4

-3

-2

-1

0

1

2

p y

(N

.s)

×10-6

(a) y-momentum

0 0.5 1 1.5 2 2.5

Time (sec)

0

0.005

0.01

0.015

0.02

p z

(N

.s)

(b) z-momentum

Figure 6.4: Case A: Momenta against time.

The axial velocity is shown in Fig. 6.5. As mentioned before, the solution is initializedso that the oil core velocity is approximately 1.28 m/s. The flow accelerates and the velocityof the core is 1.58 m/s at 2 sec. Between 2 and 2.62 sec, the oil core velocity is constant.


HCAF simulations 51

Small changes can be observed in the velocity at the lower water annulus due to turbulenceand the waves. No deviation is observed in the velocity in the upper water annulus between2 - 2.62 sec. Fig. 6.6 shows a front view of the flow and the corresponding axial velocity.The mixture velocity is 1.4 m/s and is higher than the experimental mixture velocity whichwas 1.26 m/s.

-0.01 -0.005 0 0.005 0.01

Pipe radius (m)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2A

xia

l V

elo

city (

m/s

)

time=0

time=1

time=2

time=2.5

time=2.62

Figure 6.5: Case A: Velocity profiles at different times for T=23 C.

(a) (b)

Figure 6.6: Case A: (a) Volume fraction and (b) Axial velocity after 2.62 sec.

The pressure is shown on the interface in Fig. 6.7 (a)-(b). The red locations on theinterface indicate the presence of bulges/waves on the core. At these locations, higher pres-sures develop, which balance the buoyancy and prevent the core from fouling the top wall.The pressure at 0.25 sec shows the presence of corkscrew waves. As the flow becomes moreeccentric, these corkscrew waves change to intermittent bulges. The flow in the horizontalpipes has a complex three dimensional behaviour which is very different from the axisym-metric bamboo waves in vertical upward CAF. Isolines of the pressure are shown in in Fig.6.7 (c). The lines on the upper annulus are straight and perpendicular to the direction ofthe water flow. This means that the pressure is almost constant between the pipe wall andthe interface. Fig. 6.7(d) shows the pressure on the upper and lower walls. Comparingthe pressures shows that there is a net downward force exerted on the core due to higherpressures on the top wall.


HCAF simulations 52

(a) t = 0.25 sec. (b) t = 2.62 sec.

(c) Pressure isolines at 2.62 sec.

0 0.005 0.01 0.015 0.02 0.025

Pipe length (m)

-50

-40

-30

-20

-10

0

10

20

30

40

50

Reduced p

ressure

(P

a)

upper wall

lower wall

(d) Pressure plotted on pipe walls.

Figure 6.7: Case A:- Top: Pressure contours on the interface, Bottom: Pressure isolines andpressure on the walls.

Turbulent viscosity contours are shown in Fig. 6.8. νt is zero in the oil due to itshigh molecular viscosity. As the core becomes eccentric, turbulence in the upper annulusreduces. The maximum turbulent viscosity after 2.62 seconds in the lower water annulus isnearly 21 times the viscosity of water.

(a) t=0.5 sec. (b) t=2.62 sec.

Figure 6.8: Case A: Turbulent viscosity contours.


HCAF simulations 53

6.3.2 Case B: T=30 C

(a) (b) (c)

Figure 6.9: Case B: At t = 2.8 sec (a) and (b) Volume fraction (c) Velocity.

The final volume fractions at t=2.8 sec are shown in Fig. 6.9 (a) and (b). At 2.8 sec, waveson the upper and lower annulus have an amplitude of 0.2 mm and 0.4 mm, respectively.Since the momentum of the core in the z direction is constant after 1.5 sec, the flow isconsidered to be stationary.

0 1 2 3

Time (sec)

-5

-4

-3

-2

-1

0

1

2

p y

(N

.s)

×10-6

(a) y-momentum

0 0.5 1 1.5 2 2.5

Time (sec)

0

0.005

0.01

0.015

0.02

p z

(N

.s)

(b) z-momentum

Figure 6.10: Case B: Momenta against time.

The axial velocity is shown in Fig. 6.11. From the initial velocity of 1.28 m/s, thecore accelerates and reaches a constant value of 1.49 m/s after 2 sec. Thereafter there isnot much change in the velocity or eccentricity anymore. At 2.8 sec, the core velocity is1.49 m/s as seen in Fig. 6.9. The mixture velocity is 1.37 m/s which is lower than for case A.

The pressure on the interface is shown in Fig. 6.12 (a) at 2.8 sec. Waves can be seenall over the interface. Isolines of the pressure are shown in Fig. 6.12 (b). Due to the wavesand the core eccentricity, higher pressures are observed at the top wall. Turbulent viscositycontours show that the turbulence is highest at the lower annulus where the maximumturbulent viscosity is nearly 22 times the water viscosity.


HCAF simulations 54

-0.01 -0.005 0 0.005 0.01

Pipe radius (m)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Axia

l V

elo

city (

m/s

)

time=0 s

time=1 s

time=2 s

time=2.5 s

time=2.8 s

Figure 6.11: Case B: Velocity profiles at different times.

(a) (b)

Figure 6.12: Case B: (a) Pressure and (b) Pressure isolines at t=2.8 sec.

0 0.005 0.01 0.015 0.02 0.025

Pipe length (m)

-50

-40

-30

-20

-10

0

10

20

30

40

50

Pre

ssure

(P

a)

upper wall

lower wall

(a) (b)

Figure 6.13: Case B:- (a) Pressure on the walls (b) Turbulent viscosity contours.


HCAF simulations 55

6.3.3 Case C: T=40 C

(a) (b) (c)

Figure 6.14: Case C: At t = 2.62 sec (a) and (b) Volume fraction (c) Velocity.

The simulation has been performed until 2.62 sec. Initially as the waves develop and thecore becomes eccentric, waves are seen on both the upper and lower interface. After 1.5sec, the flow becomes very eccentric and the upper interface is almost flat. Waves are stillvisible on the lower annulus. The final volume fraction can be seen in Fig. 6.14 (a) and(b). The amplitude of the waves at the lower interface is 0.39 mm.

0 0.5 1 1.5 2 2.5

Time (sec)

-5

-4

-3

-2

-1

0

1

p y

(N

.s)

×10-6

(a) y-momentum

0 0.5 1 1.5 2 2.5

Time (sec)

0

0.005

0.01

0.015

0.02

p z

(N

.s)

(b) z-momentum

Figure 6.15: Case C: Momenta plotted against time.

After 2.62 sec, the y momentum still fluctuates around zero. In Fig. 6.15(b), the z-momentum reduces between 2 and 2.62 sec. Since no waves appear on the upper interface,the core will most likely foul the pipe wall after some time. The axial velocity at differenttimes is shown in Fig. 6.16. The velocity profiles show that the core initially acceleratesto about 1.4 m/s at 2 sec, after which it reduces to 1.38 m/s at 2.62 sec. This, however,is the velocity at the lower annulus. Due to the absence of waves, the core faces moreresistance closer to the upper interface, resulting in a slightly lower velocity. Compared tothe previous cases, the oil core no longer behaves like a solid body at 40 C.

The pressure on the interface at 2.62 sec shows a smooth profile near the upper annulus.The pressure is higher in the upper annulus owing to the large core eccentricity. Wavescan be seen on the sides. Turbulence is quite high in the lower annulus and the maximumturbulent viscosity is about 28 times the molecular viscosity of water.


HCAF simulations 56

-0.01 -0.005 0 0.005 0.01

Pipe radius (m)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Axia

l V

elo

city (

m/s

)

time=0

time=1

time=2

time=2.5

time=2.62

Figure 6.16: Case C: velocity profiles at different times.

(a)

0 0.005 0.01 0.015 0.02 0.025

Pipe length (m)

-50

-40

-30

-20

-10

0

10

20

30

40

50

Pre

ssure

(P

a)

upper wall

lower wall

(b)

Figure 6.17: Case C at 2.62 sec: (a) Pressure contours on the interface and (b) Pressure on thepipe wall at t=2.62 sec.

(a) (b)

Figure 6.18: Case C at 2.62 sec: (a) Pressure isolines and (b) Turbulent viscosity.


HCAF simulations 57

6.3.4 Case D: T=50 C

In the experiments, the largest eccentricity and core breakup among all the footages wereobserved at 50 C. The time development of the flow is shown in Fig 6.19 in a plane per-pendicular to the flow direction. Starting from the concentric position, the core quicklybecomes eccentric. Unlike the previous cases which showed waves at 2 sec, for this case nowaves are observed on the upper or lower annulus. After about 2.35 sec, the core fouls thepipe wall.

(a) t = 2 sec. (b) t = 2.35 sec. (c) t = 2.5 sec.

Figure 6.19: Case D: Volume fraction at different times.

Fig. 6.20 and 6.21, show contours for the volume fraction and axial velocities at 2 and2.5 sec. At 2 sec, similar as found for the 40 C case, the velocity at the lower interface ishigher than at the upper interface. Once fouling occurs, this effect is more pronounced.

The velocity profiles are shown in Fig. 6.22. After 1 sec, the interface is flat. Due tothe core eccentricity, higher pressures at the upper interface slow down the core. This effectcan be observed from the velocity profiles at 1 and 2 sec. Finally at 2.5 sec, the effect offouling on the velocity profile becomes apparent.

Figure 6.20: Case D: Volume fractions at time 2 sec (left) and 2.5 sec (right).


HCAF simulations 58

Figure 6.21: Case D: Axial velocity at time 2 sec (left) and 2.5 sec (right).

-0.01 -0.005 0 0.005 0.01

Pipe radius (m)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Axi

al V

elo

city

(m

/s)

time=0 s

time=1 s

time=2 s

time=2.5 s

Figure 6.22: Case D: Velocity profiles at different times

The pressure contours on the interface show the presence of waves at 0.5 sec. With thedevelopment of the flow, these waves reduce in amplitude. At 2 sec, no waves can be seen onthe interface in a 3D view. Higher pressures are still observed in the upper annulus owing tothe eccentricity. Due to the absence of waves, there is not enough downward force to balancethe buoyancy and this eventually leads to fouling. The maximum turbulent viscosity be-fore the fouling is highest for this case and it is about 30 times the water molecular viscosity.

(a) t = 0.5 sec. (b) t = 2 sec.

Figure 6.23: Case D: Pressure contours at interface.


HCAF simulations 59

6.4 Comparisons with experiments

The results in the experiments and simulations are quite different. While the experimentsshow reducing pressure gradients for lower viscosities (while keeping the oil and waterthroughput the same), the simulations indicate that the CAF is more difficult to maintainat lower viscosities. Moreover, waves were visible on the upper interface for the 40 C ex-periments, while they were absent in the simulations. In Fig. 6.24, the velocity profiles arecompared for all the cases. Comparing cases A and B, the velocity profiles are almost thesame except near the upper wall, where there is a small dip in Case B. In Cases C and D,this dip is more prominent at the upper interface.

-0.01 -0.005 0 0.005 0.01

Pipe radius (m)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Axia

l V

elo

city (

m/s

)

23 C

30 C

40 C

50 C

Figure 6.24: Comparison of velocity profiles for all cases

In tables 6.1 and 6.2, the oil and water flow rates and the pressure drops are reportedfor all the cases for the simulations and experiments.

Table 6.1: Comparison of oil-water flow rates and pressure drops for all simulations.

Case Qo (l/s) Qw (l/s) Pressure drop (Pa/m) Oil hold up fraction

Case A(23 C) at 2.61 sec 0.4 0.084 1200 0.77

Case B(30 C) at 2.8 sec 0.4 0.072 1200 0.77

Case C(40 C) at 2.62 sec 0.36 0.072 1200 0.77

Case D(50 C) at 2.35 sec Fouling Fouling 1200 0.77

Table 6.2: Comparison of oil-water flow rates and pressure drops for all the experiments at 17.5%εw.

Case Qo (l/s) Qw (l/s) Pressure drop (Pa/m) Oil hold up fraction

23 C 0.36 0.076 1225 0.75

30 C 0.36 0.076 1235 0.75

40 C 0.36 0.076 1157 0.8

50 C 0.36 0.076 1117 0.69


HCAF simulations 60

The tables also give the oil hold-up fraction, which is the fraction of the pipe vol-ume that is occupied with oil. In the simulations the oil hold-up fraction is imposed. Asmentioned in section 6.2.5, the oil hold-up fraction in the simulations is equal to (R1

R2)2=0.77.

The oil hold-up fraction in the experiments is estimated from the footage. The pic-tures show the thickness of the upper and lower annulus in the mid-plane. Assuming thatthe oil core is fully cylindrical, we can determine the oil hold-up fraction. The 2D areaof the oil in the pipe has been estimated and this value is divided by the length of thepipe in the footage to determine an effective oil core diameter, Deff . The oil hold-up

fraction in the experiments is determined as (Deff2∗R2

)2. Note that the oil hold-up fraction inthe experiments and the simulations are in very good agreement except for the case at 50 C.

As mentioned before, the major difference between the experiments and the simulationsis that while in the experiments a certain oil flow rate and water flow rate are chosen, inthe simulations a constant pressure gradient in the form of a body force is imposed. Fur-thermore a certain oil holdup fraction is imposed in the simulations. These differences inimposed conditions in the experiments versus the simulations could be responsible for thedifferences observed in the simulations and experimental footage.

Before changing the solver to impose a constant mass flow rate in the simulations,experiments were performed to check if the phenomenon of fouling as predicted by the sim-ulations at 50 C can also be observed in the experiments. This is crucial because it mighttell us how well the solver can predict the physics of the actual flow.

Most notably, in case D (T=50 C), fouling occurs at the top wall at 2.35 sec in thesimulations. The oil and water flow rates at one of the periodic boundaries can be calculatedbefore and at the onset of fouling. By performing experiments at these conditions, acomparison can be made between the experiments and simulations. For this, the followingconditions are considered from the simulations:1. When the core is very eccentric and has not yet fouled the wall (2.2 sec) and2. At the onset of fouling (2.35 sec).

Comparison at 2.2 sec

The calculated oil and water flow rates in the simulations at 2.2 sec are 0.269 l/s and 0.066l/s, respectively. This corresponds to a mixture velocity of about 0.97 m/s. The oil washeated to 50 C and experiments were performed at the above mentioned flow rates. Thefootage of the experiments shows that the upper interface is very smooth while the lowerinterface shows some waves. The core did not foul the pipe in the experiments. The resultsfrom the simulations have been added for comparison in Fig. 6.25. The simulations showno waves at the lower interface whereas the experiments do show waves. The experimentsshow a clear water annulus near the top wall whereas in the simulations the annulus is verythin.


HCAF simulations 61

Figure 6.25: Comparison of experimental footage and simulations at 2.2 sec for case D.

Comparison at 2.35 seconds

Oil and water flow rates in the simulation are 0.146 l/s and 0.056 l/s, respectively. Thiscorresponds to a mixture velocity of 0.6 m/s. A comparison between the footage andsimulations is made in Fig. 6.26. Initially, CAF with a nearly flat upper interface isobserved in the experiments. Small waves can be seen on the lower annulus and the oildoes not foul the pipe. After 1-2 sec, fouling can be seen in the pipe for the experiments.The experimental footages are quite similar to the pictures of the simulations shown at2.5 sec in Fig. 6.26 (d). These experimental footage and simulations show a fairly goodagreement.

(a) Initial experimental footage (b) Simulation volume fraction at 2.35 sec.

(c) Fouling in the experiments. (d) Simulation volume fraction at 2.5 sec.

Figure 6.26: Comparison of experimental footage and simulations at 2.35 sec and 2.5 sec for caseD.

6.5 Simulations with constant total mass flow rate

6.5.1 Formulation of the new solver

For a constant total mass flow rate, the pressure body forces representative of the pressuregradient are replaced by a body force which acts towards equalizing the total flow rate(measured at a periodic boundary) and the desired flow rate. In the new solver, the following


HCAF simulations 62

steps are performed:1. Input the desired total volumetric flow rate Qdesired to the solver.2. Calculate the actual volumetric flow rate Qactual at any of the two periodic boundaries.3. Find the difference in the flow rates in step 1 and 2 and translate it as an incrementalvelocity dU and an acceleration term da in the following manner:

dU =Qdesired −QactualArea of boundary

(6.6)

da =dU

dt(6.7)

where dt is the time step.4. The acceleration term da multiplied by the density is added to the momentum equationsas a body force as shown in equation 6.8. This added force slowly adapts the flow to thedesired flow rate.

ρ∂ui∂t

+ ρuj∂ui∂xj

= − ∂p

∂xi+ µ

∂2u

∂x2i+ ρgi + f∗i + ρ ∗ da (6.8)

The comparison of the forcing term for all the cases can be used to determine the case forwhich the maximum pressure gradient is required when the desired flow rate is achieved.The desired flow rate is 0.436 l/s (0.36 l/s (oil) + 0.076 l/s (water)). Simulations for caseA and B have been restarted from the last time step mentioned in the previous section.This has been done because the simulations generally require a long computer time, namelyabout one week to calculate for 2.5 seconds. Case C has been started from 0 sec.

6.5.2 Results with the new solver

Case A1: T=23 C

(a) (b) (c)

Figure 6.27: Case A1: (a) and (b) Final volume fraction (c) Turbulent viscosity at 4.36 sec.

Starting from 2.62 sec, the simulation has been continued until 4.36 sec. The volumefraction in Fig. 6.27 when compared with case A does not show significant differences.Large amplitude and small amplitude waves are observed on the upper and the lowerinterface, respectively. The velocity profiles are shown in Fig. 6.29. Starting from 2.62 sec,where the centre line velocity is 1.58 m/s, the velocity has quickly reduced to 1.34 m/s at2.65 sec. Until 4.36 sec, there are no changes in the velocity profile. The oil and water flowrates and hold-up, h are measured at one of the periodic faces and are shown in Fig. 6.28.The flow rates fluctuate around 0.36 l/s and 0.076 l/s (experimental flow rates are shownin Fig. 6.28 (a) as dashed lines) for the oil and water, respectively. The flow rates fluctuate


HCAF simulations 63

because the cross sectional area of oil and water at the periodic boundaries are differentat every time step. Large fluctuations around the input value of 1.39 are observed for thehold-up.

(a) (b)

Figure 6.28: Case A1: (a) Oil and water flow rates. (b) Hold-up h.

-0.01 -0.008 -0.006 -0.004 -0.002 0 0.002 0.004 0.006 0.008 0.01

Pipe radius (m)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Axia

l V

elo

city (

m/s

ec)

time = 2.6 s

time = 3 s

time = 3.5 s

time = 4 s

time = 4.36 s

Figure 6.29: Case A1: Comparison of velocity profiles for different times.


HCAF simulations 64

Case B1: 30 C

(a) (b) (c)

Figure 6.30: Case B1: (a) and (b) Final volume fraction (c) Turbulent viscosity at 5 sec.

Case B has been restarted from 2.78 sec and has been run until 5 sec. Compared withcase B, the flow has changed only slightly. The most notable difference is in the turbulentviscosity in the water layer which has reduced to 17.5 times the water molecular viscosity.The velocity of the core has quickly changed from 1.49 m/s at 2.78 sec to 1.34 m/s at 2.8sec. Until 5 sec, the velocity does not change. The flow rates of oil and water and thehold-up are shown in Fig. 6.32. Similar to case A1, large fluctuations are observed in thehold-up around 1.39. The flow rates fluctuate around the experimental values of 0.36 l/sand 0.076 l/s for oil and water, respectively.

-0.01 -0.005 0 0.005 0.01

Pipe radius (m)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Axia

l V

elo

city (

m/s

ec)

time = 2.78 s

time = 3 s

time = 4 s

time = 5 s

Figure 6.31: Case B1: Comparison of velocity profiles for different times.


HCAF simulations 65

(a) (b)

Figure 6.32: Case B1: (a) Oil and water flow rates. (b) Hold-up, h.

Case C1: 40 C

(a) (b) (c)

Figure 6.33: Case C1: (a) and (b) Final volume fraction (c) Turbulent viscosity at 3.9 sec.

The simulation has been performed until 3.9 sec. From the final volume fractions, we seethat there is not much difference between cases C and C1. There are again no waves on theupper interface, the core is very eccentric and the turbulent viscosity at the lower annulusis almost 27 times the molecular viscosity of water.

(a) (b)

Figure 6.34: Case C1: (a) Oil and water flow rates (b) Hold-up, h.

From the velocity profiles, see Fig. 6.35, the velocity of the core is almost constant atthe lower interface, but deviates more with time at the upper interface. The core is still


HCAF simulations 66

levitating upwards and will eventually foul the pipe. From all the cases, it is quite clearthat there is not much difference in the final solution whether a constant pressure gradientor mass flux is imposed to drive the flow. The oil and water flow rates for case C1 areshown in Fig.6.34 (a). Due to the large eccentricity of the core and the absence of wavesat the interface, the core experiences a large resistance at the top wall. Due to this, theoil flow rate decreases while the water flow rates is increased to ensure that the total massflux imposed at the beginning of the simulation remains constant. The hold-up value willcontinue to decrease until the core fouls the wall.

-0.01 -0.005 0 0.005 0.01

Pipe radius (m)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Axia

l V

elo

city (

m/s

)

time = 0 s

time = 2 s

time = 3 s

time = 3.9 s

Figure 6.35: Case C1: Comparison of velocity profiles for different times.

6.5.3 Pressure drop

The pressure drop to ensure a constant flow rate for all the simulations A1, B1 and C1are shown in Fig. 6.36. The maximum pressure drop is required for case C1 in which theoil viscosity is the lowest. In the absence of waves, when the core eccentricity increases,the pressure drop used by the solver increases as it becomes more difficult to maintain theinput flow rate. Comparing cases A1 and B1 shows that the pressure drops are almost thesame although the viscosity is reduced.

2.5 3 3.5 4 4.5 5

Time (sec)

-1000

-500

0

500

1000

1500

Pre

ssu

re d

rop

(P

a/m

)

Case A1

Case B1

Case C1

Figure 6.36: Comparison of the pressure drop for cases A1, B1 and C1.


HCAF simulations 67

To properly compare the pressure drops for the experiments and simulations, it is impor-tant to ensure that the comparisons are made at the same time instants. The first pressurespout in the experimental setup is located approximately 4.08 m from the inlet. Since themeasurement section is 1 m, the oil-water mixture has travelled 5.08 m when the pressuredrop is recorded. For a mixture velocity of 1.26 m/s, we can say that the measurementshould have been taken after approx. 4 sec. Table 6.3 shows the comparison.

Table 6.3: Comparison of experiment and simulation for pressure drop.

Temperature Viscosity (cSt) Experiment (Pa/m) Simulation (Pa/m) Error

23 C at 4 sec 2100 1225 847 31%

30 C at 4 sec 1435 1235 852 31%

40 C at 3.9 sec 805 1157 1660 43%

Variations in the experiments and simulations are quite large. The pressure drop in thesimulation is higher than in the experiment at 40 C, because the interFoam solver does notpredict waves at the upper interface, while in the experiments they are visible.

The difference in pressure drop for the experiments and the simulations at 23 and 30 Cis about 30%. For the experiments at 23 C and 30 C, the footage showed well defined waveshapes. Moreover, the waves at the upper and lower interface are seen to be not very muchout of phase. The same can not be said for the waves in the simulations. This could be aninability of the interFoam solver to accurately predict the flow with the current assumptionsof the domain length. This was observed in chapter 4 for case 8, where the wave amplitudefluctuated around a mean amplitude even after 28 sec. The simulations were not continuedfor a longer duration as it took two weeks to solve for 5 sec. The k-ε turbulence model usedfor the simulations could also be inaccurately predicting the turbulence in the annulus andnear the interface which is contributing to the error. Modelling assumptions, such as notconsidering the wall roughness of the pipe in the simulations could for example be anotherreason for the lower pressure drop.

For both the methods used, i.e. imposing a constant pressure drop and a total massflow rate, the numerical simulations show that when the viscosity of the oil is reduced tothe value measured at 40 C, no waves are observed on the upper interface. Due to thelevitation of the core flow, the core will experience an increased resistance near the topwall. Therefore at lower viscosities, a higher pressure drop will be required to obtain thesame throughput. At high viscosity ratios (T = 30 C or lower), the simulations indicatethat there are no advantages in increasing the oil viscosity any higher. The oil viscositymust be high enough for waves to develop at the upper interface. The simulations thuspredict that the benefits of using core annular flow to reduce the pressure drop for a giventhroughput are clearer for more viscous oils. This seems to be in contrast, however, to whatis found in the experiments.

The simulations from this chapter have been summarized in Table 6.4.


HCAF simulations 68

Table 6.4: Summary of simulations for HCAF.


Chapter 7

Conclusions and recommendations

7.1 Conclusions

In this thesis a study has been performed on the influence of the viscosity of the liquidin the core on the characteristics of core annular flow in vertical and horizontal pipes.These characteristics include the pressure drop, interfacial wave profiles and the throughput.Core annular flow is of practical relevance for the transport of heavy oil (viscous oil) inthe oil industry because this is a very efficient method. In particular, this method ofwater lubrication is more efficient than heating up the oil to reduce its viscosity in singlephase transport. In a broader sense, the aim of this master project was also to study theadvantages of combining these two methods, i.e. heating up the oil and creating waterlubrication.

Vertical core annular flow

For the vertical pipe, 2D axisymmetric simulations are performed using the OpenFOAMsolver interFoam. The flow is laminar and no turbulence model is used. All simulations areperformed using periodic boundary conditions. The simulations were performed based onthe recommendations made by Beerens in his Master’s thesis. One of the simulations madeby Beerens which has an oil-water viscosity ratio of n=663 is also used as a base case inthe present study. Two cases were studied at lower oil-water viscosity ratios of n=66 andn=10. In all the simulations, the oil-water radius ratio, density ratio, surface tension andimposed pressure gradients are maintained the same. One would expect that decreasingthe oil viscosity would give a higher throughput (i.e. an increasing velocity at the corecentre). This is true for the viscosity ratio of 66, but not for 10, as the latter gives a lowerthroughput than for the viscosity ratio of 66. This is because of changes that occur in theinterfacial behaviour: for the two cases with the highest viscosity ratios, the oil core almostmoves as a solid body and the waves look like bamboo waves. For the lowest viscosity thevelocity profile is gradual, the wave amplitude is large and the wave shape is not like of thebamboo type.

In order to study how the flow is affected by transient conditions, in which the oiland the water are initially at a higher temperature than the pipe wall, simulations for thevertical pipe were also performed with a temperature dependent viscosity and with heattransfer. A relation was defined between the oil viscosity and the temperature such thatthe oil viscosity ratio is 663 when the oil temperature is equal to the pipe wall temperatureof 285 K. At temperatures of 310 K and 330 K, the viscosity ratio is 66 and 10, respectively.Results of these simulations were compared with the isothermal simulations. The resultswithout and with heat transfer for the case with the intermediate viscosity ratio of n=66showed only small differences in the core velocity and the wave amplitude. For the cases

69

Conclusions and Recommendations 70

with n=10, no differences were observed in the wave amplitude and the core velocity. Theoil viscosity did not change much after a long simulation time of 40 sec for the case withn=66. This is because the oil takes a long time to cool down to a different temperature dueto its low thermal conductivity of k=0.145 W/mK.

The thermal conductivity was then increased to k=2 W/mK for the case with the vis-cosity ratio n=66 so that the oil quickly cools down to the condition where the viscosityratio is n=663. The solution at stationary state (no more heat transfer) was expected toshow a single bamboo wave as was observed for the isothermal case with n=663. However,the final solution showed two bamboo waves. The bamboo waves for the latter case also hasa lower amplitude and the core moves faster than in the solution with the single bamboowave. We have found that multiple solutions are possible for the same oil-water viscosityratio when all other parameters are maintained the same. To investigate this phenomenonfurther, changes were made to the mesh density and the number of waves at the interfaceduring the initialization. Increasing the mesh density to 256 x 256 grid cells showed nowaves. This shows that the most unstable wave for n=66 is longer than the prescribeddomain length.

Next, a simulation was performed for n=66 and k=2 W/mK in a domain length whichwas increased by a factor 2. At steady state (n=663), the final solution showed 3 waves.The wave amplitudes are larger and the core velocity is also smaller than for the simula-tion in the smaller domain length which gives only two waves. This shows that changingthe domain length affects the final wave characteristics. Simulations for the larger domainlength for the case with n=66 and n=0.145 W/m-K showed that the final wave amplitudeat the stationary state oscillates with a high frequency around a mean value. For n=10and k = 0.145 W/m-K with the double length domain, no differences are found in thewave amplitude and in the velocity profile when compared with the results for the smallerdomain. This means that for n=663 and n=10, the most unstable waves have almost thesame length while for a viscosity ratio of n=66, the most unstable wave is longer.

Multiple solutions were further investigated for the viscosity ratios of n=663 on thedouble length domain by performing simulations for two cases in which the core movedwith initial velocities of 0.87 m/s and 0.17 m/s relative to the wall. It is seen that for thecase with the higher initial velocity, the final solution shows three waves as compared tothe latter case where the final solution shows two waves. From these results we learn thatthe simulations for core annular flow with periodic boundary conditions are sensitive to theinitialization of the velocity profile.

Horizontal core annular flow

Experiments were performed for core annular flow in a horizontal pipe. The diameter ofthe pipe is 2.1 cm. The oil viscosity was reduced by heating the oil to different tempera-tures of 30, 40 and 50 C. From the literature, it was understood that core annular flow isa dominant flow regime when the mixture velocity and the oil viscosity are high. Use wasmade of the G/V ratio as suggested by Shi to ensure that the experiments were in the coreannular flow regime. In all the experiments performed, the oil and water flow rates werethe same and the mixture velocity is 1.2 m/s and 1.26 m/s when the water addition ratiois 12.5% and 17.5%, respectively. The pressure drop was measured along a 1 m section andfootages were obtained for these measurements. The measured pressure drop for a certainoil and water flow rate is almost independent of the oil viscosity. For all the experiments,core annular flow is observed.



At 23 C and 30 C, the experimental footages show regular wave trains with large ampli-tude waves in the upper and lower annulus. The waves at 30 C are slightly deformed whencompared to the waves at the temperature of 23 C. Decreasing the viscosity shows morewaves at the oil-water interface. At temperatures higher than 40 C which gives a viscosityratio of 805, the core levitation is quite pronounced and the waves at the upper interfacehave a low amplitude. When increasing the oil temperature to 50 C, although core annularflow is still observed, oil bubbles can also be seen in the water annulus. This means thatthe core breaks up at such a low viscosity of 480 cSt. The repeatability of the experimentsat a temperature of 40 C and higher was difficult. This is due to partial fouling of the oilat the pipe walls.

The experimental conditions for the 17.5 % water addition ratio were simulated with3D conditions using the Launder Sharma k-ε turbulence model in OpenFOAM. Periodicboundary conditions are used for these simulations. The domain length is 2.56 cm and islarger than the length of the most unstable wave which is observed in the experiments. Theoil radius is initialized from the experimental oil and water flow rates and the value for thehold up ratio h is 1.39.

In the first set of simulations corresponding to the experimental viscosities, a pressuregradient of 1200 Pa/m is imposed between the periodic boundaries. This means that whilein the experiments, the flow rates of oil and water are imposed, in the simulations the pres-sure gradient and the hold up are imposed. The simulation is considered as stationary whenthe momentum in the y and z direction are steady. In contrast to the experiments whichshowed a small reduction in the pressure drop when the viscosity is reduced, the simula-tions show that at temperatures higher than 40 C, the pressure drop required to maintaina constant total mass flow rate increases. Furthermore, at these higher temperatures thereare no waves on the upper interface in the simulations, whereas such waves are presentin the experiments. Simulations at 50 C show that the core fouls the pipe while in theexperiments little fouling is observed (more fouling near the 1 mm holes in the pipe whichare connected to the pressure ports). Moreover, the simulations at 50 C did not predictthe oil breakup which is observed in the experiments. At the viscosities corresponding to23 and 30 C, the simulations did not predict the wave shapes which were observed in theexperiments. The final mixture velocity in the simulations is higher than the experimentalmixture velocities.

Simulations were also performed by imposing a constant total mass flow rate corre-sponding to the total experimental oil and water flow rates. Simulations for 23 C and 30 Cwere restarted from the previously mentioned steady state results. For these simulations,we see that the flow rate quickly reduces to the experimental flow rates. No changes wereobserved in the wave shapes. Comparison of the pressure drops show no advantage in coreannular flow when the oil-water viscosity ratio is higher than 1435 (measured at 30 C). For40 C, the simulations were started from 0 sec. For these simulations, again, no waves arepredicted at the upper interface. Comparisons of the experimental and simulation pressuredrops at 4 sec for 23, 30 and 40 C show deviations. The reasons for this could be an insuf-ficient domain length, an inability of the interFoam solver to predict breakup or also thatthe applied turbulence model which was originally developed for single phase flows is notoptimized for the accurate prediction of the turbulence and waves near the interface.

The research objective set forth at the beginning of this thesis was to understand theeffects of the core viscosity in core annular flow. In vertical pipes, the highest throughputwill be achieved at intermediate viscosities where the oil will behave like a solid body i.e.



when the velocity at the pipe center and the wave interface are the same. In horizontalpipes, due to the levitation mechanism, at low viscosities, waves at the upper interface havelow amplitudes. This flow is not stable and will lead to the core fouling or break-up. Trans-port of oil with core annular flow in horizontal pipes is most efficient when the oil-waterviscosity ratio is high.

In the context of combining heating of the oil prior to use in core annular flow, thismethod is best suited for applications with oil transport through vertical pipes. However,one must consider that due to the low conductivity of oil, considerable time and energy hasto be spent for heating the oil to the desired viscosity.

7.2 Recommendations

In the simulations for horizontal core annular flow, although the y and z momentum lookconverged, the waves are still changing over time. Simulations need to be performed fora longer domain length and over a longer time period. The need for this became clear inthe vertical pipe simulations, where the amplitude is not constant even not after a longsimulation time of over 40 sec.

The turbulence models which are generally available were originally developed for sin-gle phase turbulent flows. Although these models have also been used in the literature formultiphase flows, it is rare to find a good justification for these models. RANS will stillbe the preferred method over LES due to the strict Courant number requirement of 0.02in interFoam. A finer grid (which is required for LES computations) will only lead to evensmaller time steps.

CFD tools like Fluent include a damping for the turbulence near the interface. It wouldbe interesting to perform simulations in Fluent and compare them with the OpenFOAMresults shown in this thesis. Perhaps these simulations can predict the breaking up of theoil core into droplets as seen in the experiments for 50 C.

In OpenFOAM it is easiest to prescribe the oil hold-up fraction and the pressure dropas boundary conditions and to obtain the oil and water flow rates as results from the sim-ulations. It is also possible to prescribe the total flow rate and the oil holdup fraction andto obtain the pressure drop as a result. Preferably we would like to prescribe the oil andwater flow rates, and obtain the pressure drop and oil holdup fraction as results, like whatis done in the experiments. It is recommended to develop a computer script or methodsuch that the latter is possible in OpenFOAM.

In the vertical pipe simulations, for the case with intermediate viscosity ratios, it makessense to perform simulations in a long pipe to find the exact length of the most unstablewave. Previously much success has been achieved by various authors in the simulations ofBai’s experiments when the oil viscosity is high. The results for the new simulations withlower viscosity are very interesting and need to be confirmed with experiments.

An error analysis of the experiments is also recommended. This was especially realizedduring the experiments when the pressure drop measurements were difficult to reproduce.The U tube manometer in general is slow to react and gets fouled by the oil if not cleanedregularly. A more advanced pressure measurement device like a differential transducermight help in this regard. At low viscosities, the chances of the oil breaking up and fouling



the pipe are higher. Using a PVC pipe which is hydrophobic is not recommended as ittends to be fouled more easily. Another problem is that the pipe walls tend to get stickyover a long usage period to the extent where even repeated cleaning with detergents doesnot help anymore. Using glass or Perspex tubes can help in this regard.

It is also recommended to use high speed cameras to make movies in colour of theexperiments. In this way, the interfacial waves can be more easily studied and comparedwith the numerical simulations.


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Appendix A

Figure A.1: Summary of experiments taken from Shi et al. [29]

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the effects of viscosity on core-annular flow

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