two-phase flow modelling of the pressure gradient of the delivery...

UNIVERSIDAD POLITÉCNICA DE MADRID

ESCUELA TÉCNICA SUPERIOR DE INGENIEROS DE MINAS Y ENERGÍA

Titulación: GRADUADO EN INGENIERÍA DE LA ENERGÍA

Itinerario: TECNOLOGÍAS ENERGÉTICAS

Two-phase flow modelling of the pressure gradient of the delivery pipe of a

spiral pump.

TRABAJO FIN DE GRADO

Elisa Anderson Vázquez

2018

UNIVERSIDAD POLITÉCNICA DE MADRID

ESCUELA TÉCNICA SUPERIOR DE INGENIEROS DE MINAS Y ENERGÍA

Titulación: GRADUADO EN INGENIERÍA DE LA ENERGÍA

Itinerario: TECNOLOGÍAS ENERGÉTICAS

Título del Proyecto:

Two-phase flow modelling of the pressure gradient of the delivery

pipe of a spiral pump.

Realizado por:

Elisa Anderson Vázquez

Supervisor UPM:

Arturo Hidalgo López del Departamento Ingeniería Geológica y

Minera

Supervisor en empresa aQysta:

Jaime Michavila

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Acknowledgements

Firstly, I would like to express my gratitude to all the members of the team that form aQysta

for the great learning opportunity, patience and positivity. To Jaime for trusting me, letting me

lead the project and always being available and willing to help.

I would also like to say thank you to Prof. Portela for always knowing how to answer all my

questions and to Prof. Mudde for introducing me to him. To Arturo for having confidence in

me and letting me make the pertinent decisions about the project. To Prof. Michavila for the

academic and specially a life guidance and having such a positive spirit. Thank you for noticing

my hard work and valuing it.

Finally, thank you to all my friends and family. For their unconditional support, acceptance and

love.

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Index Acknowledgements ................................................................................................................................ iii

Index ......................................................................................................................................................... i

List of Figures ........................................................................................................................................ iii

List of Tables ......................................................................................................................................... iv

List of Illustrations ................................................................................................................................ iv

Abstract ................................................................................................................................................... v

1. Introduction ................................................................................................................................... 2

2. Company and Pump Description ................................................................................................. 4

2.1 About aQysta ................................................................................................................................. 4

2.2 About the Barsha Pump ........................................................................................................... 5

3. Research objective, questions and procedure ............................................................................. 8

3.1 Research objective/main question ........................................................................................... 8

3.2 Secondary questions ................................................................................................................ 8

3.3 Relevance of the project .......................................................................................................... 9

3.4 Approach and structure ........................................................................................................... 9

4. Multiphase Flow Theory: ........................................................................................................... 12

4.1 Multiphase Flow Models: ...................................................................................................... 12

4.2 Multiphase Flow Patterns: ..................................................................................................... 13

4.2.1 Vertical Flow Patterns: .................................................................................................. 13

4.2.2 Horizontal Flow Patterns: .............................................................................................. 15

4.2.3 Inclined Flow: ............................................................................................................... 17

4.3 Two-phase Flow Maps ................................................................................................................ 17

5. Theoretical Two- Phase Flow Models ........................................................................................ 22

5.1 Single Phase Flow ................................................................................................................. 22

5.2 Homogeneous Flow model .................................................................................................... 23

5.2.1 Theoretical model .......................................................................................................... 24

5.2.2 Computational results of the Homogeneous Flow Model ............................................. 26

5.3 Drift Flux model .......................................................................................................................... 30

5.3.1 Theoretical model .......................................................................................................... 30

5.3.2 Computational results .................................................................................................... 32

5.4 Separated Flow ...................................................................................................................... 33

5.4.1 Theoretical Model ......................................................................................................... 33

5.4.2 Computational results .................................................................................................... 36

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5.5 Evaluation of effect of the different parameters based on the models .................................. 38

6. Adapted Slug flow model ............................................................................................................ 40

6.1 Theoretical model .................................................................................................................. 40

6.2 Computational results ............................................................................................................ 47

7. Experiments: calculating the pressure gradient, slug dimensions, volumetric air and water

flow and the void fraction. .................................................................................................................. 50

7.1 Experiment objectives and limitations .................................................................................. 50

7.2 Preparation: equipment and setup ......................................................................................... 50

7.3 Experiment design: ................................................................................................................ 53

7.4 Experiment set ups: ............................................................................................................... 53

7.5 Layout of the experiment ...................................................................................................... 54

7.6 Experiment protocol .............................................................................................................. 56

7.7 Important considerations ....................................................................................................... 57

7.8 Measurements........................................................................................................................ 60

8. Comparison of the models and the experiments ....................................................................... 62

8.1 Inclined pipe: effect of internal diameter and volumetric flow ............................................. 62

8.2 Horizontal pipe: effect of internal diameter and volumetric flow ......................................... 66

8.3 Effect of inclination ............................................................................................................... 68

9. Application to real pumping scenarios: Dolakha (Nepal)........................................................ 70

9.1 Computational results ............................................................................................................ 70

9.2 Effect of the different parameters on the pressure drop for Hijar (Valencia) ........................ 71

10. Recommendations ................................................................................................................... 74

10.1 Recommendations for the company aQysta .......................................................................... 74

10.2 Recommendations for future research ................................................................................... 75

11. Conclusions .............................................................................................................................. 76

Bibliography ........................................................................................................................................ 77

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List of Figures

Figure 1. Barsha pump in operation. (aQysta: Innovating for Impact, 2018) ......................................... 5

Figure 2. Flow regimes for two-phase flow in vertical pipes. ............................................................... 15

Figure 3. Main flow regimes for two-phase flow in horizontal pipe. .................................................... 16

Figure 4. Flow patterns for inclined pipes. ............................................................................................ 17

Figure 5. Flow map for 2.5 cm horizontal tube. - Experiment, -- Theory. (Barnea, Shoham, Taitel, &

Dukler, 1979) ......................................................................................................................................... 19

Figure 6. Flow map for 2.5 cm tube for an inclination of 10 degrees with respect to the horizontal. -

Experiment, -- Theory. (Barnea, Shoham, Taitel, & Dukler, 1979) ........................................................ 20

Figure 7. Effect of pipe inclination on flow pattern transition boundaries. (Bhagwat & Ghajar, 2016) 21

Figure 8. Slug flow (left) and wavy slug flow (right). (Bhagwat & Ghajar, 2016) .................................. 21

Figure 9. Measurement of the inclination angle used for experiments. .............................................. 27

Figure 10. Homogeneous model pressure gradient with internal diameter, Di, for ϴ=9º (left) and ϴ=

0º (right) for a volumetric flow of ṁ=0.35 L/s. ..................................................................................... 28

Figure 11. Homogeneous model pressure gradient with volumetric flow, ṁ, for ϴ=10º (left) and 𝜃= 0º

(right) for an internal diameter of 38 mm. ........................................................................................... 29

Figure 12. Homogeneous model pressure gradient with inclination angle, Theta, for ṁ=0.5 L/s and an

internal diameter of 38 mm for ϴ [0º, 90º] (left) and [0º, 10º] (right). ................................................ 29

Figure 13. Separated model pressure gradient with internal diameter, Di, for ϴ=10º (left) and ϴ = 0º

for a volumetric flow of ṁ=0.35 L/s. ..................................................................................................... 37

Figure 14. Separated model pressure gradient with volumetric flow, ṁ, for Theta=10º (left) and Theta

= 0º (right) for an internal diameter of 38 mm. .................................................................................... 37

Figure 15. Separated model pressure gradient with inclination angle, Theta, for ṁ=0.5 L/s and an

internal diameter of 38 mm for Theta [0º, 90º] (left) and [0º, 10º] (right). ......................................... 38

Figure 16. Slug unit geometry. (Crowe, Multiphase Flow Handbook, 2006) ........................................ 40

Figure 17. Pressure gradient with internal diameter, Di, for an inclination angle of ϴ=9º (left) and

horizontal pipe (right) for volumetric flows of ṁ=0.35 L/s. .................................................................. 47

Figure 18. Pressure gradient with volumetric flow rate, ṁ, for internal diameters Di= 0.038 m and an

inclination angle of ϴ=9º (left) and ϴ=0º (right). .................................................................................. 48

Figure 19. Pressure gradient with inclination angle, ϴ, for an internal diameter Di= 38 mm and a

volumetric flow of ṁ= 0.5 L/s. ϴ ranges from [0,90] (left) and [0,10] (right). ...................................... 48

Figure 20. Spiral pump in water basin that was used as water input. The start of the delivery pipe can

also be depicted. ................................................................................................................................... 51

Figure 21. Spiral from the back. The portable control can be seen, as well as part of the motor that

turns the pump. ..................................................................................................................................... 52

Figure 22. Analogue glycerine manometer [1-1.6 bar]. ........................................................................ 52

Figure 23. National Instruments data logger used for the digital pressure sensor. ............................. 52

Figure 24. Geka-coupling used to connect pipes of different diameters. Similar hose pillars are used in

case the diameter is the same. ............................................................................................................. 53

Figure 25. View of the location of the experiments. ............................................................................. 54

Figure 26. Picture of a slug made during the experiments. .................................................................. 57

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Figure 27. Inclination of 10º in the output of the delivery pipe. The bucket with the inclined side can

also be spotted on the left, next to the green container. The graduated bucket used to measure the

volumetric mass flow rate can also be seen on the left. ...................................................................... 58

Figure 28. Curve in the pipe with more than 1-meter radius. .............................................................. 59

Figure 29. Linear pipes, with a neglectable misalignment of 2 cm. ...................................................... 59

Figure 30. Pressure gradient with internal diameter, Di, for an inclination angle of 9º and 0.36 L/s. . 63

Figure 31. Pressure gradient with internal diameter Di for an inclination angle of 9º and 0.6 L/s. ..... 64

Figure 32. Pressure gradient with volumetric flow for inclination angles of 9º and internal diameters

of 25 mm. .............................................................................................................................................. 64

Figure 33. Pressure gradient with volumetric flow for an inclination angle of 9º and an internal

diameter of 38 mm. .............................................................................................................................. 65

Figure 34. Pressure gradient with internal diameter for horizontal pipes and 0.41 L/s. ...................... 66

Figure 35. Pressure gradient with internal diameter, Di, for horizontal pipes with 0.55 L/s. .............. 67

Figure 36. Pressure gradient with volumetric flow for horizontal pipes with 25mm of internal

diameter. ............................................................................................................................................... 68

Figure 37. Pressure difference with inclination angle for 0.36 L/s and 25mm for inclination angles that

go from 0 to 9º. ..................................................................................................................................... 68

Figure 38. Zoom out of the pressure gradient with inclination angle for 0.36 L/s and 25mm of internal

diameter for inclination angles that go from 0 to 90º. ......................................................................... 69

Figure 39. Pressure gradient with the internal diameter, Di, for an inclination angle of 9.65º and a

volumetric flow of 0.4 L/s. .................................................................................................................... 72

Figure 40. Pressure gradient against volumetric flow for an inclination angle of 9.65º and an internal

diameter of 40mm. ............................................................................................................................... 73

Figure 41. Pressure gradient against the inclination angle, for a volumetric flow of 0.4 L/s and an

internal diameter of 40 mm. ................................................................................................................. 73

Figure 42. Steps followed during the development of the project. ...................................................... 88

List of Tables

Table 1. Inputs to calculate the single-phase flow pressure gradient. (Pipe roughness, 2018) ........... 23

Table 2. Results for single-phase flow for three different pipe diameters. .......................................... 23

Table 3. Different diameters, rotational speeds, delivery pipe length and possible inclinations. ........ 53

Table 4. Set ups for inclined pipe, 10º. ................................................................................................. 54

Table 5. Set ups for horizontal pipe. ..................................................................................................... 54

Table 6. Measurements for horizontal pipe with three different diameters and three different

rotational velocities of the pump. ......................................................................................................... 60

Table 7. Measurements for inclined pipe, 10º, with three different diameters and three different

rotational velocities of the pump. ......................................................................................................... 61

Table 8. Computational results of the theoretical models with the inputs given for Dolakha (Nepal). 71

List of Illustrations

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Illustration 1. Spiral hose. The delivery pipe will come out from the axel perpendicularly. Source:

(Post, 2015) ............................................................................................................................................. 6

Illustration 2. Inclined pipe layout for experiment. .............................................................................. 55

Abstract

This project has been carried out in collaboration with the company aQysta, with the aim of

developing a model to predict the pressure gradient of the two-phase flow fluid that runs

through the delivery pipe of a spiral pump. To do so, theoretical models have been studied,

computed and adapted using the software tool MATLAB. Experiments were carried out to

validate the results of the models and the results were plotted and analysed to later proceed to

draw conclusions and make recommendations. The result of this project is a program with

which the company can determine the viability of positioning the spiral pump in a certain

location and would continue to be useful for pumps of a larger size that the company is currently

developing.

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1. Introduction

This project was undertaken in collaboration with the company from Yes!Delft aQysta that

develops hydraulic pumps, mainly for irrigation purposes. These pumps function with the

hydraulic energy from the rivers and canals where they are placed, so they do not consume

electricity nor fossil fuels. This makes the pumps totally sustainable and nearly maintenance

free. (aQysta: Innovating for Impact, 2018)

The fluid that is delivered by the majority of aQysta’s pumps through the delivery pipe is a two-

phase flow consisting of a liquid phase and a gaseous phase. The study of multi-phase flow is

still a major challenge up to today due to the unpredictability of the motion of the various

turbulent phases that makes it difficult to obtain experimental results and simulaions, in many

cases, cannot be done because of the limited computational power and speed. (Brennen,

Fundamentals of Multiphase Flow, 2005)

This project aims to provide the company aQysta with a tool that can be used to precisely

estimate the pressure drop that the delivery pipe of the pumps will undergo in different possible

sites. Moreover, to explain how the different parameters, such as the inclination angle of the

delivery pipe, the pipe diameter or the pipe volumetric flow affect this pressure drop.

To do so, different mathematical models have been analysed and programmed using the

software tool MATLAB and computed with the characteristic parameters of one of aQysta’s

pumps, the Barsha pump. In addition, experiments will be conducted to corroborate the results

and the mathematical models will be adjusted and corrected to give more precise results for the

pressure drop of this hydraulic pump.

Chapter 2 will focus on a description of the company aQysta and the Barsha pump, to have a

clearer understanding of the importance and background of the project. Chapter 3 illustrates the

main objectives of the project, relevance and methodology. In Chapter 4, a theoretical analysis

of multi-phase flow and other important concepts of fluid dynamics can be found. Different

flow patterns and flow maps will be analysed.

Chapter 5 and 6 will detail the different mathematical models, their limitations and results.

Furthermore, in Chapter 7, the experimental procedures and results will be developed to later

compare them with the theoretical results in Chapter 8. Finally, some real scenarios are covered

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in Chapter 9, recommendations are given for aQysta and for further research in Chapter 9 the

main conclusions and are discussed in Chapter 10.

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2. Company and Pump Description

2.1 About aQysta

The company aQysta was founded in 2013 by three young, former TU-Delft students. They

were and are aware of the urgency to find new ways to pressurise and pump water up from

rivers and canals to irrigate locations in rural areas that are at a height, in developing countries

such as Nepal. There is a need for a reliable, cost-effective and robust system that can provide

irrigation water all throughout the year, at a stable cost. Nowadays, in the rare case that property

owners can afford it, diesel pumps or electrical pumps are being used. If this is not the case,

farmers are forced to carry water buckets to irrigate their crops, a method with which crops do

not get enough water. (aQysta: Innovating for Impact, 2018)

These alternatives, despite having lower investment costs, have a series of other

inconveniences. Firstly, for many locations in developing countries, it is of great difficulty to

have a regular supply of fuel and the electrical grid is intermittent and unreliable. Solar power

for electrical pumps is normally not a possibility, due to the high investment and the

maintenance. Moreover, if a diesel or electrical pump gets damaged or fails, it is nearly

impossible to get the necessary new parts to fix it. Regarding costs, operating with one of these

pumps requires paying the operation expenses of the electricity or fuel, costs that may vary over

time. Finally, diesel pumps are highly contaminating and both type of pumps, when no longer

in use, should be recycled. In these countries, this is normally not a possibility, causing further

environmental problems.

For giving an alternative to these types of pumps, aQysta was rewarded awarded in 2016 for

the development of the Barsha pump by the Siemens Stiftung Foundation, for being one of the

best technological innovations that make use of clean energy in Europe. (Carrasco, 2017)

Currently, aQysta is already developing new technologies, that have renovated and improved

designs. The new water pumps will deliver more power and need an even more precise

prediction of the pressure drop in the delivery pipe as they are designed to work with larger

pipe diameters and larger volumetric flows.

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2.2 About the Barsha Pump

The Barsha pump (Barsha meaning rain in Nepalese) has been the first pump developed and

commercialized by aQysta. This pump, nowadays, can supply up to 25 meters vertically. It can

pump up to 43 000 litres per day that make the irrigation of up to three hectares of fields possible

(aQysta: Innovating for Impact, 2018). Making use of this technology, it is possible to save

70% of the costs that would be spent if a fossil fuel pump was used instead. As a result, the

investment costs are repaid in only two years. (Carrasco, 2017)

Figure 1. Barsha pump in operation. (aQysta: Innovating for Impact, 2018)

Barsha pump design

The Barsha pump has a very simple construction and operation mechanism. It consists of a pipe

made of PVC, forming a spiral attached to a fixing structure that positions it perpendicular to

the water as can be seen in Illustration 1. Making use of the hydraulic force of the water flow

from the river or canal, the spiral rotates at an approximately constant rotational velocity.

(Mortimer & Annable, 2010)

One side of the pipe is left open and serves as an inlet of alternate plugs of water and air. The

length of these alternate plugs is dependent on the immersion of the spiral that is set with a

floating mechanism. Each plug of water transmits the pressure through the air to the next water

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section, providing a pressure head. Consecutive and cumulative pressure heads build up in the

inner coils, resulting in a pressure gradient that serves to pump up the water. (Tailer, 2018)

The more internal part of the spiral is attached to the non-rotating delivery pipe that transports

the two-phase flow to the location of choice. This project focuses on this delivery pipe.

Illustration 1. Spiral hose. The delivery pipe will come out from the axel perpendicularly. Source: (Post, 2015)

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3. Research objective, questions and procedure

In this chapter, the objective, questions and how these will be answered is explained. There are

primary and secondary questions, as well as experimental and theoretical procedures that have

been followed.

3.1 Research objective/main question

The main objective of this project is to develop a tool that can be used by the company aQysta

to predict the pressure gradient of the delivery pipe of a spiral pump installed for different

locations, each one with specific characteristics.

3.2 Secondary questions

Two secondary questions will be answered in this project. The first one is how the pressure

gradient of the delivery pipe of the spiral pump varies when changing the different parameters

of the pump, these parameters being:

- Diameter of the pipe (Di)

- Longitudinal angle of the pipe (ϴ)

- Volumetric water and air flow (ṁ)

When doing so, the following intermediate results will be obtained theoretically and/or

experimentally:

- The flow regime (in which the mix behaves). The types of flows (stratified, slug, etc)

are explained in chapter 4.1.

- Length of water and air slugs (if slug flow).

- Position of water and air slugs (if slug flow).

- Water and volumetric distribution (if stratified flow).

- Velocity of water and air slugs.

In addition, the second question aims to determine if there is airlift effect and if there is, when

it occurs and if it can be used reduce the pressure gradient so that the water can be pumped to

larger heights.

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3.3 Relevance of the project

After reading the objectives it is important to comprehend why are those objectives relevant.

Having a model that can determine the pressure drop in the delivery pipe is vital to determine

if a location is suitable or not for the placement of a spiral pump.

In many countries the volumetric flow of rivers varies depending on seasonal rains or droughts.

With this tool, the effect that this change would have on the operation of the pump and the

difference in the height to which a pump can deliver water in a certain location can be evaluated.

Moreover, the decision of whicht is the most appropriate diameter of the delivery pipe is also

determined using the information from the model, because it helps to evaluate the effect that

having a different diameter would have in the pressure drop. This design variable, not only

influences the operation of the pump, but also the cost of the whole system, as the price is

directly proportional to the diameter of the pipe.

This tool can also help evaluate which locations are suitable and which are not, depending on

the distance that the water must travel as well as the height. It can also help to determine the

sensitivity that is an important aspect when modelling physical phenomena, in order to have an

idea of the most relevant parameters to consider.

This project will also intend to determine if there is a possibility of taking advantage of the

airlift effect and if there is, how and when this could be done. This effect is explained in detail

in chapter 5.5.

3.4 Approach and structure

The method followed to answer these questions is, firstly, to do an in-depth literature review

on multiphase flow and more specifically on two-phase flow models, maps and experiments.

This way, there is a clear view of the necessity of the project, its limitations and the state of the

art of this technology. Chapter 4 gives a theoretical overview of the most important concepts

that must be understood for the correct understanding of the models and the project in general.

Moreover, different models suggested in the literature are studied and their suitability and

relevance has been considered. The most relevant models are programmed and computed using

the software MATLAB, using as inputs the characteristics of aQysta’s pumps.

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The inputs used for the models are:

- Liquid and gas flow rates (ṁ)

- Diameter of the pipe (D)

- Length of the pipe (L)

- Liquid holdup (α)

- Longitudinal angle of the pipe (ϴ)

Possible intermediate outputs of the models are:

- Flow regime

- Length of the water and air slugs (if slug flow)

- The position of these slugs (if slug flow)

- The velocity of the mixture

The final output of the models is:

- Pressure gradient

Experiments have been conducted to validate the models and to compare the results. These will

be further explained in chapter 6. Finally, recommendations for aQysta are developed and

possible ways to continue with this study are suggested.

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4. Multiphase Flow Theory:

In this chapter, theoretical concepts will be introduced in order to facilitate the understanding

of the whole project. Chapter 4.1 focuses on a brief introduction on the multiphase flow model’s

objectives, methods and limitations. In addition, chapter 4.2 explains what a flow pattern is and

describes which ones can be found for vertical, horizontal and inclined pipes. Finally, in chapter

4.3 different flow maps are analysed to predict which flow patterns would be found when

operating aQysta’s pumps and therefore which theoretical models are the ones that should be

chosen for a more in-depth study.

4.1 Multiphase Flow Models:

An important part of studying multiphase flow is trying to predict and model the

behaviour of the flows in detail. There are three ways in which this can be done (Brennen,

Multiphase flow models, 2005):

- Experimentally, extrapolating and doing calculations with calibrated measurements that

have been taken from a prototype.

- Theoretically, using mathematical equations that form models to describe the

characteristics of a certain flow.

- Computationally, using the power and speed of modern technology and software to

develop the calculations.

In this project, two-phase flow has been studied from the three perspectives, experimentally,

theoretically and computationally, to fulfil the aim of going an in-depth study of two-phase

flow. The two-phase flow will be formed by a liquid phase and a gaseous phase.

There are some applications for which a prototype cannot be made or would have to be made

with very different dimensions that would result in unreliable results (Brennen, Multiphase flow

models, 2005). An example of this would be the experiments in which the superficial tension

plays a role, as the results would depend on the size of the prototype and if they were to be

extrapolated for another scale, they would be invalid.

Consequently, for these applications, the calculations rely on theoretical and computational

models. In the far future, the Navier-Stokes equations for each of the phases could possibly be

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coded. However, the computer power and speed that would be needed is far from being a reality

for most flows, and the computing of multiphase flow is still a major hurdle (Brennen,

Multiphase flow models, 2005).

4.2 Multiphase Flow Patterns:

One of the main difficulties in predicting the behaviour of multiphase flow is that the mass,

momentum and energy transfer can be very sensitive to the geometric distribution that may

have a considerable effect in the surface available for mass, momentum and energy exchange

between phases (Brennen, Multiphase flow models, 2005).

The first step to understanding multiphase flow is analysing and describing the distinctive

geometric distributions that commonly occur in these types of flows called flow patterns or

flow regimes. This subsection will focus on the flow patterns that most commonly appear in

horizontal and vertical pipes and define several instabilities that cause one flow pattern to

transition to another. The transitions in multiphase flow are comparable to the transitions

between laminar and turbulent flow in single phase flow.

Flow patterns are normally defined by visual inspection. Nonetheless, some other methods such

as analysing the pressure fluctuations of a control volume can be also used if information is

difficult to obtain visually (Brennen, Multiphase flow models, 2005).

4.2.1 Vertical Flow Patterns:

The flow patterns are going to be described in a logical order, starting with the pattern with the

lowest void fraction and finishing with the one that in contrast, has the largest, or in other words,

relatively more air per section of pipe. Figure 2 shows the different regimes and looking at it

while reading each description can be useful for a better visualisation.

- Bubbly flow: Numerous small air bubbles that vary in shape and size traveling through

a continuous liquid phase. The bubbles are commonly spherical or elongated and are

considerably smaller compared with the diameter of the pipe (Thome, Two-Phase Flow

Patterns and Flow Pattern Maps , 2014). For vertical pipes or inclined pipes with high

liquid flow rates, the bubble size is tiny and are distributed symmetrically (Swanand M.

Bhagwat, 2016).

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- Slug flow: Sections of water and air are interspersed. The bubbles dimensions are of

similar size as the pipes diameter and are bullet shaped. The large bubbles get close to

each other and collapse to form even larger bubbles, called Taylor bubbles (Barnea,

1980). These bubbles normally have a thin film of liquid between them and the pipe

wall that may flow slowly in the opposite direction of the main flow due to gravity. The

liquid slug may include some small bubbles that slip away from the main bubble

(Thome, Two-Phase Flow Patterns and Flow Pattern Maps , 2014). (Barnea, Shoham, & Taite,

Flow pattern characterization in two phase by electrical conductance probe, 1980)

- Churn flow: This is a flow pattern that appears in the transition between slug flow and

annular flow. It occurs when the flow becomes very unstable, with both phases traveling

intermittently upwards and downwards through the pipe, however having net upward

flow. The instability is caused because the shear forces that push the flow are nearly

equivalent to the force of gravity. This type of flow should be avoided for most of the

applications, as it creates stresses and can damage the pipes (Thome, Two-Phase Flow

Patterns and Flow Pattern Maps , 2014).

- Annular flow: In this flow, gas travels at high speed through the centre of the pipe,

while the liquid phase is pushed towards the pipe wall, forming an annular film. This

flow happens when the void fraction becomes relatively large and the dominant force is

the shear force over gravity. In the interface between the two phases, normally small

waves appear that lead to small droplets of the liquid phase being dragged by the

gaseous phase (Thome, 2014). This type of flow is difficult to analyse through visual

inspection as the walls are wet and it may seem as single-phase flow. (Thome, Two-

Phase Flow Patterns and Flow Pattern Maps , 2014).

- Misty flow: This flow pattern can be seen at high void fractions and flow rates. It can

be visualised as the opposite as bubbly flow. In other words, as a continuous gas phase

with very small droplets that can make the tube misty. There may be a need for

magnification of special lighting to spot this type of flow (Thome, 2014). (Thome, Two-

Phase Flow Patterns and Flow Pattern Maps , 2014).

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Figure 2. Flow regimes for two-phase flow in vertical pipes. (Thome, Two-Phase Flow Patterns and Flow Pattern Maps , 2014)

4.2.2 Horizontal Flow Patterns:

Some horizontal flow regimes are similar to those in vertical flow but have several differences

that are worth mentioning. In many cases, gravity plays an important role in the geometric

structure of the flow. Horizontal regimes are going to be explained from smaller to larger void

fractions as it has also been done for vertical flows. Once again, looking at the drawings found

in Figure 3 can be good for a better understanding and visualisation of the regimes.

- Bubbly flow: this flow is characterized by relatively small bubbles that travel through

the upper part of the pipe due to their buoyancy. It occurs at low flow rates and high

liquid flow rates (Swanand M. Bhagwat, 2016). These bubbles can appear uniformly

throughout the pipe or not, depending on the mass flow rate of the fluids. If the shear

forces are dominant, the bubbles will be dispersed in a uniformly (Thome, 2014).

(Thome, Two-Phase Flow Patterns and Flow Pattern Maps , 2014).

- Stratified flow: This type of flow is defined by having the two phases flowing in two

separate parallel layers. The gaseous phase moves through the upper part of the pipe

while the liquid phase, as it has a larger density, travels through the lower part of the

pipe. At low flow rates, the interface between phases is horizontal and stable. However,

with increasing liquid and gas flow rates waves are formed, their size depending on the

relative velocity between the two phases and resulting in a very dynamic interface

(Swanand M. Bhagwat, 2016).

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- Plug flow: This flow is characterised by the long bubbles that flow though the upper

part of the tube, separated by liquid plugs. That is why this regime can also be called

the elongated bubble regime. The diameter of the slugs is relatively smaller than the

tube diameter and continuous liquid phase flows though the lower section of the pipe.

This flow is considered an intermittent flow, as well as the slug flow that is similar and

will be explained below (Thome, 2014). (Thome, Two-Phase Flow Patterns and Flow

Pattern Maps , 2014).

- Slug flow: In this regime there are also bubbles flowing separated by section of water.

However, in this case the diameter of these bubbles is much larger, getting to a similar

size as the pipe diameter (Thome, 2014). At a fixed pipe diameter, the void fraction,

size of the bubbles, their shape and frequency are dependent on the phase flow rates and

pipe orientation (Swanand M. Bhagwat, 2016). (Thome, Two-Phase Flow Patterns and

Flow Pattern Maps , 2014)

- Annular flow: The main difference between the annular flow for vertical and horizontal

flows is that in horizontal regimes, the lower part of the water annulus is much thicker

than the upper part. Once again, there may be drops dispersed in the gaseous phase that

travels through the centre of the pipe (Thome, 2014). (Thome, Two-Phase Flow Patterns

and Flow Pattern Maps , 2014).

Figure 3. Main flow regimes for two-phase flow in horizontal pipe. (Thome, Two-Phase Flow Patterns and Flow Pattern Maps , 2014)

All these flow models can be classified depending on the separation of the different phases, as

well as intermittency. The flow regimes position themselves in a spectrum with the extremes

17

being dispersed and separated regimes. Dispersed flows have a main phase and a secondary

phase in the form of drops, bubbles or particles. However, in separated flows, there are two

distinct phases that flow without mixing. Examples of dispersed flows may be misty of bubbly

flow and of separated flows may be stratified flow (Crowe, 2006). (Crowe, Multiphase Flow

Handbook, 2006)

4.2.3 Inclined Flow:

Figure 4 illustrates the different flow patterns explained above por inclined pipes. As it can be

seen, gravity also plays an important role in this case.

Figure 4. Flow patterns for inclined pipes.

4.3 Two-phase Flow Maps

To develop a model for the output of the Barsha pump, there is a need to predict the flow pattern

of the delivery pipe. The most effective way to determine this is by using flow maps. The

pressure drop, heat and mass transfer are highly dependent on the geometric distribution of the

different phases and consequently, on the flow pattern. Therefore, an effort has been made to

accurately predict which flow patterns will occur in both horizontal and vertical pipes. In

addition, the flow pattern for inclined pipe is also predicted, even though there is noticeably

less literature published on the effect of having an inclined pipe (Barnea, Shoham, Taitel, &

Dukler, 1979).

The transitions between flow patterns can be unpredictable, as they are dependent on many

factors that should be taken into consideration such as the entrance conditions or the roughness

18

of the walls. Therefore, the transition between flow patterns in the maps is not a well-defined

line, but a transition area (Brennen, Multiphase flow models, 2005).

Another difficulty when analysing flow maps, is that in most cases they are dimensional and

each one only applies to specific dimensions and flow characteristics. There have been attempts

to develop dimensionless flow maps, such as the one developed by Weisman and Kang in 1981.

However, these maps are not as reliable as the transition areas are defined by the fluid

properties. (Brennen, Fundamentals of Multiphase Flow, 2005)

To determine the flow pattern of the delivery pipe of Barsha pump in operation, several flow

maps are going to be studied and analysed with the parameters of the pump. In the first place,

a study will be analysed that was conducted to determine the flow map for a pipe with an

internal diameter (Di) of 2.5 cm, which are exactly the dimensions of the pipe used in the

experiments. This research was compared to a previous study made by A.E. Dukler in the

University of Houston, U.S.A, that had very similar results (Barnea, Shoham, Taitel, & Dukler,

1979).

Flow maps identify the patterns occurring in a range of a certain parameter. This parameter can

be volume fluxes, mass fluxes or other depending on the author. Many maps, including the one

just mentioned, are defined using the liquid and gas superficial velocities, Usg and Ulg. These

parameters can be defined using the following formulas:

𝑈𝑠𝑙 =

𝐺 ∗ (1 − 𝑥)

𝜌𝑙

(1)

𝑈𝑠𝑔 =

𝐺 ∗ 𝑥

𝜌𝑔

(2)

For the Barsha pump, the parameters used in these two formulas are (Bhagwat & Ghajar, 2016):

- x (gas quality) = 0.0012 [-]

- A (cross-section) = 0.00049087 [𝑚2]

- 𝜌𝑙 (liquid water density) = 997.784736 [kg/m3]

- 𝜌𝑔 (air density) = 1.188 [kg/m3]

- 𝑚𝑑𝑜𝑡𝑙 (liquid flow rate) = 0.35/1000 [m3/s]

19

- 𝑚𝑑𝑜𝑡𝑔 (gas flow rate) =0.35/1000 [m3/s]

G (two-phase mixture gas flux) =𝜌𝑙 ∗ 𝑚𝑑𝑜𝑡𝑙+𝜌𝑙 ∗ 𝑚_𝑑𝑜𝑡𝑙

𝐴

=712,28 [kg/m2s]

(3)

Using these parameters, the value for 𝑈𝑠𝑔 equals 0.713 and we consider the 𝑈𝑠𝑙 to be the same

value assuming that no overtaking takes place between water and air. Figure 1. shows a flow

map that reflects the comparison between the experimental data with transitions between

regimes showed with solid lines and the Taitel-Dukler theoretical results with transitions

highlighted with a dashed line. The orange arrows show the exact point where the Barsha pump

will operate.

There is no doubt from Figure 5 that the pump will operate in an intermittent regime. This

regime is composed of slug flow pattern and elongated bubble flow pattern which are very

much alike. Slugs of liquid are distributed through the pipe, separated by air sections that flow

through the top section of the tube. In this case, it has been considered that the only difference

between these patterns is that in the case of elongated bubbles, the liquid slugs are free of small

gas bubbles. (Barnea, Shoham, Taitel, & Dukler, 1979).

Figure 5. Flow map for 2.5 cm horizontal tube. - Experiment, -- Theory. (Barnea, Shoham, Taitel, & Dukler, 1979)

This study also researched the effect the inclination of the pipe would have in the flow patterns.

Figure 2. shows the results for a tube with a diameter of 2.5 cm and an upward inclination with

20

respect to the horizontal of 10 degrees. Once again, the Barsha pump will operate in an

intermittent regime. It can also be noted that there is intermittent flow for a much wider range

of superficial velocities. For inclination angles larger or equal to 10 degrees, there will be no

stratified region, and even for inclination angles of 3 degrees, the conditions for stratified flow

are very limited. The comparison between the experimental data and theoretical results can also

be depicted in the figure.

Figure 6. Flow map for 2.5 cm tube for an inclination of 10 degrees with respect to the horizontal. - Experiment, -- Theory. (Barnea, Shoham, Taitel, & Dukler, 1979)

A more recent research shows a similar study, but this time for a much larger range of

inclination angles, going from 0 degrees to the vertical 90 degrees, as their main goal was to

study the effect of different inclinations of the two-phase flow air-water phenomenon (Bhagwat

& Ghajar, 2016). Experiments were carried out with pipes that had a 1.27 cm internal diameter,

so results are comparable with the 2.5 cm diameter delivery pipe of the Barsha pump.

Figure 7 shows the different possible flow patterns for inclination angles of 0, 30, 60, and 90

degrees. Once again, the orange lines show where the Barsha pump would operate. For nearly

all inclination angles, the flow would be characterized by slug flow. However, for inclination

angles of approximately 90 degrees, there would be an intermittent regime. In this study, the

slug flow is described as being a regime where alternative slugs or air and water appear, whereas

the intermittent flow is illustrated as being more chaotic and pulsating. This regime is

considered to have subcategories such as slug wavy and churn.

21

Figure 7. Effect of pipe inclination on flow pattern transition boundaries. (Bhagwat & Ghajar, 2016)

Figure 8 shows slug flow (left) and wavy slug flow (right) in an inclined glass tube. As it has

just been demonstrated by the analysis of two reliable studies, these types of flow regimes are

the ones that will appear in the Barsha pump delivery pipe.

Figure 8. Slug flow (left) and wavy slug flow (right). (Bhagwat & Ghajar, 2016)

To conclude, low regimes are very sensitive to the angle of inclination of the pipe. Inclining the

pipe causes the intermittent and more precisely, the slug flow to appear at a much larger range

of flow conditions, causing the stratified flow to not be seen unless the inclination angles are

very small. The Barsha pump will most likely operate in an intermittent regime, more accurately

in slug flow. For this reason, slug flow models will be further researched.

22

5. Theoretical Two- Phase Flow Models

This chapter will focus on giving a detailed description of various theoretical models that have

been computed in MATLAB to calculate both the gravimetrical as well as the frictional pressure

gradient in the delivery pipe, as well as other parameters such as the dimensions of the slugs.

The slug flow that appears in the delivery pipe, consists in water and air slugs. To calculate the

pressure drop, various theoretical models will be analysed and computed. Firstly, the

homogeneous model, followed by the drift flux model and the separated flow model.

Secondly, the slug model proposed in the book `Multiphase flow handbook´ by Clayton T.

Crowe will be developed and adapted to later conduct experiments to validate the results, using

a pipe with a study length of 50 m with different diameters and volumetric flow rates.

The results obtained with these methods will be compared in chapter 7 and aQysta will have a

tool with which they can calculate the pressure gradient of the delivery pipe depending on the

inclination angle, the pipe diameter and length, as well as the liquid hold up and the volumetric

flow rate.

The models studied in this chapter go from the simplest ones to the most precise, complicated

and complete model. This logical order has been decided in order to explain first the simplest

models to later fully understand the procedure and equations of the most complicated ones.

Regarding the structure of the chapter, single-phase flow will be analysed, to get an idea of the

upper boundary and order of magnitude of the values that are going to be dealt with. Then, the

homogeneous flow model will be detailed, to continue explaining and analysing the drift flux

model. In addition, the separated flow model will be explained to finally develop the slug flow

model to later compare and analyse all the results in chapter 7.

5.1 Single Phase Flow

Having a rough idea of what the upper frictional pressure drop boundary and what are the order

of magnitude of the values that are going to be dealt with in this project is of vital importance

to asses if all the values obtained during this project are within the limits and are reasonable.

Therefore, some calculations making use of the pressure drop online calculator (Pressure Drop

Calculator, 2018) for horizontal pipes are going to be done.

23

Table 1 illustrates the input values that the program asked for and that have been used and Table

2 shows the results obtained for three different diameters of pipe.

Table 1. Inputs to calculate the single-phase flow pressure gradient. (Pipe roughness, 2018)

Parameter Value [units]

Flow medium/temperature Water / 20 [ºC]

Length of the pipe 50 [m]

Pipe roughness (PVC) 0.0015 [mm]

Volumetric flow 0.5 [L/s]

Dynamic Viscosity 1001.61 10-6 [kg/ms]

Table 2. Results for single-phase flow for three different pipe diameters.

D1=25mm D2=32mm D3=38mm

Pressure drop [bar] 0.25 0.08 0.03

Velocity of the flow [m/s] 1.02 0.62 0.44

Reynolds number [-] / flow

type

25 379 /

turbulent

19 827 /

turbulent

16 696 /

turbulent

With the help of Table 2, the values of the pressure gradient, velocity of the flow and Reynolds

number can be consulted to see the range of the values and the upper limits, always taking into

consideration the inputs illustrated in Table 1.

From the results obtained it can already be clearly seen that for the intermediate volumetric

flow of 0.5 L/s, the frictional pressure gradient will be in the order of millibars, being nearly

negligible for pipe diameters of 38 mm. Even for a maximum volumetric flow of 0.8 L/s it

would still be relatively small with a value of 0.08 bar. The flow in all cases will be turbulent

and the flow velocity will be in the order of magnitude of less or around 1 m/s.

5.2 Homogeneous Flow model

This chapter focuses on the analysis of the homogeneous flow model. Firstly, the approach

followed to develop this model is described. Then the formulas are explained and organised in

the order in which they appear when the model is computed. Finally, the different computational

results are plotted and analysed.

24

5.2.1 Theoretical model

To develop the homogeneous model for the two-phase flow for air and water, a single-phase

flow with a homogeneous density is considered. In other words, the continuous and dispersed

phases are modelled as one unique continuous phase (Homogeneous flow models, 2018). This

homogeneous density will be proportional to the homogeneous void fraction and the densities

of both phases (Thome, 2018). (Thome, Two-Phase Pressure Drops inside Tubes, Chapter 13, (in Databook III), 2018).

The total pressure gradient (∆𝑃𝑡𝑜𝑡𝑎𝑙) is the sum of the static or gravimetric pressure drop

(∆𝑃𝑔𝑟𝑎𝑣), the momentum pressure drop (∆𝑃𝑚𝑜𝑚) and the frictional pressure drop (∆𝑃𝑓𝑟𝑖𝑐). To

calculate it, the following fixed as well as variable inputs need to de defined. The code used to

compute this model can be found in appendix 1.

Fixed inputs:

- ρ: Densities [kg/m3]

- µ: Viscosities [Pa/s]

- x: Quality [-]

- g: Gravity [m/s2]

- λL: Liquid hold up (-)

Inputs that vary for the different locations:

- L: Length of the pipe [m]

- D: Diameter of the pipe [m]

- ṁ: Flow rate [m3/s]

- ϴ: Inclination angle [º]

The whole model evolves around the fact that there is a fluid of homogeneous density, therefore,

the first step to develop this model is to calculate the section of the pipe and the quality, to

calculate homogeneous void fraction and finally this fundamental parameter.

A = π (

𝐷

2)

2

(4)

25

x =

𝑚𝑔

𝑚𝑔 + 𝑚𝐿=

(1 − λ𝐿)𝐴 𝐿 𝜌𝐺

((1 − λ𝐿)𝐴 𝐿 𝜌𝐺) + (λ𝐿𝐴 𝐿 𝜌𝐿)

(5)

Assuming that there is no relative velocity and there is no slip between phases ug/uL is equal to

one and the homogeneous void fraction is:

𝛼ℎ =

1

1 + ((𝑢𝐺

𝑢𝐿)

(1 − 𝑥)𝑥

𝜌𝑔

𝜌𝐿)

(6)

So, the homogeneous density:

𝜌𝐻 = 𝜌𝐿(1 − 𝛼ℎ) + 𝜌𝑔𝛼ℎ (7)

With this parameter, the static or gravimetric pressure gradient can be determined with the

following equation:

∆𝑃𝑔𝑟𝑎𝑣 = 𝜌𝐻 𝑔 𝐿 sin 𝜃 (8)

For horizontal flows, where ϴ = 0, this parameter will be equal to zero, as there is no

gravimetrical pull against the fluid.

In addition, to calculate the frictional pressure gradient, the mass velocity [kg/m2s] has to be

taken into consideration:

mass_vel =

m_dot 𝜌𝐻

𝐴

(9)

The frictional pressure gradient is dependent on the two-phase friction factor, 𝑓𝑡𝑝, expressed in

terms of the Blasius equation:

𝑓𝑡𝑝 =

0.079

𝑅𝑒0.25

(10)

This equation depends on the Reynolds number, that in turn depends on the mass velocity and

the two-phase dynamic viscosity, computed with the quality averaged viscosity, as is shown

with the following formulas:

26

𝜇𝑡𝑝 = 𝑥 𝜇𝑔 + (1 − 𝑥) 𝜇𝐿 (11)

Re =

𝑚𝑎𝑠𝑠_𝑣𝑒𝑙 𝐷𝑖

𝜇𝑡𝑝

(12)

The frictional pressure gradient:

∆𝑃𝑓𝑟𝑖𝑐 =

2 𝑓𝑡𝑝 𝐿 𝑚𝑎𝑠𝑠_𝑣𝑒𝑙2

𝐷 𝜌𝐻

(13)

The momentum pressure gradient per unit length of the tube, for adiabatic flow where the

quality x is a constant, is equal to zero and is expressed with the following formula:

∆𝑃𝑚𝑜𝑚 =𝑑 (

𝑚𝑑𝑜𝑡𝜌𝐻

)

𝑑𝑧

(14)

Finally, the total pressure gradient, as anticipated before, is the sum the static, gravimetric and

momentum pressure gradient, that can be multiplied by 10-5 to convert it from [Pa] to [bars].

∆𝑃𝑡𝑜𝑡𝑎𝑙 = ∆𝑃𝑔𝑟𝑎𝑣 + ∆𝑃𝑓𝑟𝑖𝑐 + ∆𝑃𝑚𝑜𝑚

(15)

5.2.2 Computational results of the Homogeneous Flow Model

The most relevant plots for inclined and horizontal pipes, obtained with the code that can be

found in appendix 1, have been plotted below. All the graphs have been plotted considering a

constant pipe length of 50 meters and a volume fraction of 60% of water inside the pipe.

Figure 10 and Figure 11 focus on the effect of the diameter and the volumetric flow on the

pressure gradient, for both inclined (left) and horizontal (right) pipe. Despite having the same

shape, it is interesting to see the values in the y-axis, as the graph for the horizontal pipe shows

how much of the pressure drop in the inclined pipe is caused by friction.

For the study of the effect of the diameter, a volumetric flow rate of 0.35 L/s was chosen, and

to study the effect of the volumetric flow rate, a constant diameter of 38mm. Figure 12 (left)

illustrates the effect of the inclination angle, for pipes with a diameter of 38 mm and a

volumetric flow rate of 0.5 L/s. This graph has been zoomed in (on the right) to highlight the

27

linear trend that is followed at first for the range of angles that aQysta´s water pumps normally

work with. The values have been chosen so that the pressure gradient development can be

shown as clearly as possible.

The angle chosen to analyse the results of the models was 9 degrees. This angle was chosen so

that the results could be easily compared with the measurements obtained with the experiments.

To know exactly with what angle the experiments had been carried out, the distances were

measured, and simple trigonometric equations were used. However, as measuring long

distances can give considerable errors, on top of that, the software MB-Ruler was used for a

more accurate measurement.

As it can see in Figure 9, 9.1 degrees were measured with the software. Nonetheless, a slight

deformation can be seen in the picture due to the angle from it was taken: the more in the centre

of the picture you measure, the less the deformation is. That is why, after taking into

consideration both approaches, the final decision was to consider 9 degrees of inclination of the

ramp. The whole layout of the experiment can be consulted in section 6.2. For the rest of the

models, these parameters are going to be kept constant, so that in chapter 7 all the results can

be compared with the values obtained with the experiments.

Figure 9. Measurement of the inclination angle used for experiments.

It is also interesting to note how in Figure 12, from 0º to 45º, the pressure follows a linear trend,

whereas from 45º to 90º, it tuns into a parabolic shape. This is because in the first angles, the

pressure is dominated mostly by the friction pressure gradient and as the inclination gets more

28

pronounced, the static pressure gradient is dominant with the airlift effect playing a significant

role that flattens the curve.

Figure 10 depicts the pressure gradient against the internal diameter for a volumetric flow of

0.35 L/s and an inclination of 9º (left) and 0º (right). Both graphs have been plotted one next to

the other to facilitate the comparison between them. The focus should be in the magnitude, as

the one on the right represents the frictional component of the one on the right. These plots

cannot be plotted on the same graph as the difference between magnitudes makes it difficult to

read the pressures.

Figure 10. Homogeneous model pressure gradient with internal diameter, Di, for ϴ=9º (left) and ϴ= 0º (right) for a volumetric flow of ṁ=0.35 L/s.

Figure 11 illustrates the effect of the volumetric flow on the pressure gradient for an inclined

pipe (left) and a horizontal pipe (right) with a 38 mm diameter. Once again, the figure on the

right illustrates the frictional component of the one on the right, that also includes the static or

gravimetrical component.

29

Figure 11. Homogeneous model pressure gradient with volumetric flow, ṁ, for ϴ=10º (left) and 𝜃= 0º (right) for an internal diameter of 38 mm.

Figure 12 plots how the pressure gradient varies with the inclination angle for a pipe that has a

volumetric flow rate of 0.5 L/s and a 38 mm diameter. The figure on the left illustrates this for

angles that go from 0 to 90 degrees, whereas the figure on the right zooms into the first 10

degrees, that are the operational regime of most of aQysta’s pumps.

Figure 12. Homogeneous model pressure gradient with inclination angle, Theta, for ṁ=0.5 L/s and an internal diameter of 38 mm for ϴ [0º, 90º] (left) and [0º, 10º] (right).

30

5.3 Drift Flux model

The study of the drift flux model is relevant because of its applicability to a wide range of two-

phase flow problems and its relative simplicity. The mixture is considered as one, instead of

two different phases and the relative motion between phases is taken into account (Takashi

Hibiki, 2003).

With this model it is not possible to analyse the pipe as a whole, as it only gives precise results

for flows that have a bubbly flow pattern. However, its analysis is particularly necessary

because the final slug flow model follows a similar approach in order to analyse the liquid slugs.

Evaluating the drift flux model is a vital step for the understanding of the slug flow model,

described and analysed in chapter 6.

5.3.1 Theoretical model

To compute the drift flux model (Crowe, Dispersed bubble flow, 2006), the following constant

input parameters have to be defined:



- g: Gravity [m/s2]

- σ: surface tension [N/m]

- k: Roughness [m]

As well as the inputs that vary for the different locations:





The first step to compute this model is to calculate the gas velocity to later calculate the void

fraction and finally the total pressure drop formed by the frictional and static pressure gradients.

The momentum pressure gradient is not considered as the pipe is assumed to be adiabatic. The

code used to compute this model can be found in appendix 2.

31

To calculate the gas velocity, two components must be taken into consideration: the velocity of

the bubbles and the buoyancy. Bubbles travel at a higher pace than the liquid phase. In case of

turbulent flow, this velocity of the bubbles, 𝑢𝑐 , is 25% larger than the centreline velocity of the

pipe, 𝑢𝑚.

𝑢𝑐 = 𝐶𝑜 𝑢𝑚 (16)

Where the constant 𝐶𝑜 is the distribution parameter that equals 1.25.

To calculate the mixture velocity, 𝑢𝑚, first the section of the pipe has to be determined:

A = π (𝐷𝑖

2)

2

(17)

And then it can be calculated with the following equation:

𝑢𝑚 =𝑚𝑑𝑜𝑡_𝑣𝑜𝑙

𝐴

(18)

Furthermore, the buoyancy of the bubbles is also taken into consideration with the rise velocity

𝑢𝑏, that is calculated with the following expression.

𝑢𝑏 = 1.53 [𝜎𝑔∆𝜌

𝜌𝐿2 ]

14

(19)

Taking these two components into consideration, the gas velocity is expressed as:

𝑢𝑔 = 𝑢𝑐 + 𝑢𝑏 (20)

To calculate the frictional pressure gradient, the friction factor has to be computed with a

MATLAB function that uses a Colebrook iteration method (Appendix 5). The inputs of this

function are the mixture Reynolds number for which the void fractions and the mixture density

has to be calculated and the roughness of the pipe that was given as input.

32

So, the void fractions are:

𝛼𝐺 =𝑢𝑆𝐺

𝑢𝐺 𝑎𝑛𝑑 𝛼𝐿 = 1 − 𝛼𝐺

(21)

The mixture density:

𝜌𝑚 = 𝛼𝐿 𝜌𝐿 + 𝛼𝐺𝜌𝐺 (22)

And with these parameters the mixture Reynolds number can be calculated:

𝑅𝑒𝑚 =𝐷𝑖 𝜌𝑚𝑢𝑚

𝜇𝐿

(23)

The friction factor is computed with the function that can be found in appendix 5.

With these parameters, the frictional pressure gradient is calculated with the equation:

∆𝑃𝑓𝑟𝑖𝑐𝑡 = − (𝑑𝑝

𝑑𝑥)

𝐹= 2𝑓𝑚𝜌𝑚

𝑢𝑚2

𝐷

(24)

Furthermore, the gravimetrical pressure gradient can also be calculated:

∆𝑃𝑠𝑡𝑎𝑡 = (𝛼𝐺𝜌𝐺 + 𝛼𝐿 𝜌𝐿 ) 𝑔 𝐿 sin 𝜃 (25)

Finally, the total pressure gradient would be the sum of both frictional and static pressure drop:

∆𝑃𝑡𝑜𝑡 = ∆𝑃𝑓𝑟𝑖𝑐𝑡 + ∆𝑃𝑠𝑡𝑎𝑡 (26)

5.3.2 Computational results

This model cannot be used to analyse the flow of the whole pipe, as it is only accurate for the

sections of water slugs that have a bubbly flow pattern. To get meaningful results, this model

should be combined with the separated flow model. The drift flux model would be used to

analyse the liquid slugs making use of the code in appendix 2 whereas the separated flow model,

33

explained in the next subchapter, would be used to evaluate the gaseous slugs (code in appendix

3).

Using this method, only data points could be plotted, and the results would be less precise than

the ones obtained using the separated flow model, homogeneous flow model and adapted slug

flow model for the whole of the pipe. For this reason, we consider this analysis to be irrelevant

and out of the scope of this project.

5.4 Separated Flow

In the separated model, two different pipes are supposed, one with the liquid phase, water, and

another with the gaseous phase, air, which have a diameter proportional to the void fraction.

No mixing between phases is considered. The code for this model can be found in appendix 3.

5.4.1 Theoretical Model

The input data that has to be determined to compute the model is:



- g: Gravity [m/s2]

- σ: surface tension [N/m]

- x: quality [-]

As well as the inputs that vary for the different locations:



- Mass_ vel: Flow rate [kg/m2s]


- λL: Liquid hold up (-)

The two inputs that may need clarification are the mass velocity and the quality of the two-

phase flow. The mass velocity is determined by multiplying the volumetric flow rate by the

density and divided by the section of the pipe. The quality is the ratio between the mass of gas

and the total mass of the mixture. With the liquid hold up and section of the pipe the ratio

between gaseous volume and total volume can be calculated and with the value of the density,

the quality can be quantified.

34

Like in the drift flux model, the total pressure drop is the sum of the frictional and static pressure

gradient, as the momentum pressure gradient is neglected due to the assumption that the pipe is

adiabatic, and the input is the same as the output. To calculate the frictional pressure gradient,

in this occasion, the Friedel correlation is going to be applied, as it gives the most accurate

results.

In order to calculate the static of gravimetric pressure gradient, the void fraction needs to be

computed with the following formula developed by Steiner in 1993 (Thome, 2018):

α =

𝑥

𝜌𝐺[(1 + 0.12(1 − 𝑥)) (

𝑥

𝜌𝐺+

1 − 𝑥

𝜌𝐿) +

1.18(1 − 𝑥)[𝑔𝜎(𝜌𝐿 − 𝜌𝐺)]0.25

𝑚𝑚𝑣𝑒𝑙 𝑡𝑜𝑡2 𝜌𝐿

0.5 ]

−1

(27)

The company aQysta very rarely needs to work with vertical flow, however, if this was the

case, the void fraction is more precisely determined with the Rouhani and Axelsson expression:

α =𝑥

𝜌𝐺[[1 + 0.2(1 − 𝑥) (

𝑔𝐷𝜌𝐿2

𝑚𝑣𝑒𝑙 𝑡𝑜𝑡2 )

14⁄

] (𝑥

𝜌𝐺+

1 − 𝑥

𝜌𝐿)

+1.18 (1 − 𝑥)[𝑔𝜎(𝜌𝐿 − 𝜌𝐺)]0.25

𝑚𝑣𝑒𝑙 𝑡𝑜𝑡2 𝜌𝐿

0.5 ]

−1

(28)

With the void fraction, the two-phase density can be computed:

𝜌𝑡𝑝 = 𝜌𝐿(1 − α) + 𝜌𝐺 α (29)

So, the static pressure gradient is:

∆𝑃𝑠𝑡𝑎𝑡 = 𝜌𝑡𝑝 𝑔 𝐿 sin 𝜃 (30)

As it has already been mentioned, for the frictional pressure gradient, the Friedel correlation is

applied. Both liquid and gas friction factors are obtained from the Reynolds number as follows:

35

𝑅𝑒𝐿 =

𝑚𝑣𝑒𝑙 𝑡𝑜𝑡𝐷⁄

𝜇𝐿

(31)

𝑓𝐿 =

0.079

𝑅𝑒𝑙0.25

(32)

𝑅𝑒𝐺 =

𝑚𝑣𝑒𝑙 𝑡𝑜𝑡𝐷⁄

𝜇𝐺

(33)

𝑓𝐺 =

0.079

𝑅𝑒𝐺0.25

(34)

To obtain the friction pressure gradient, the Friedel correlation utilizes a two-phase multiplier,

Φ𝑓𝑟2 , that will be multiplied by the pressure gradient for the liquid-phase flow, ∆𝑃L.

∆𝑃𝑓𝑟𝑖𝑐 = ∆𝑃𝑙 Φ𝑓𝑟2

(35)

Where the two parameters are,

∆𝑃𝐿 = 4 𝑓𝑙

𝐿

𝐷𝑚𝑣𝑒𝑙 𝑡𝑜𝑡

21

2 𝜌𝐿

(36)

And

Φ𝑓𝑟2 = 𝐸 +

3.24 𝐹 𝐻

𝐹𝑟𝐻0.045𝑊𝑒𝐿

0.035 (37)

However, to determine the two-phase multiplier, dimensionless factors E, F, H, FrH and WeL

have to be computed with the following equations:

E = (1 − 𝑥)2 + (

𝑥2𝜌𝐿𝑓𝑔

𝜌𝑔𝑓𝑙)

(38)

36

F = 𝑥0.78(1 − 𝑥)0.224

(39)

H = (

𝜌𝐿

𝜌𝐺)

0.91

(𝜇𝐺

𝜇𝐿)

0.19

(1 −𝜇𝐺

𝜇𝐿)

0.7

(40)

𝐹𝑟𝐻 =

𝑚𝑣𝑒𝑙 𝑡𝑜𝑡2

𝑔 𝐷 𝜌𝐻2

(41)

𝑊𝑒𝐿 =

𝑚𝑡𝑜𝑡𝑎𝑙2 𝐷

𝜎 𝜌𝐻

(42)

To calculate 𝐹𝑟𝐻, the two-phase homogeneous density with the quality is needed:

𝜌𝐻 = (𝑥

𝜌𝐺+

1 − 𝑥

𝜌𝐿)

−1

(43)

Finally, the total pressure drop can be obtained:

∆𝑃𝑡𝑜𝑡 = ∆𝑃𝑠𝑡𝑎𝑡 + ∆𝑃𝑓𝑟𝑖𝑐 (44)

5.4.2 Computational results

In this subchapter the computational results for the separated flow model are plotted. Figure 13

(left) illustrates the pressure gradient against the internal diameter for a 9º inclined pipe with a

volumetric flow of 0.35 L/s. On the right, a similar plot is shown for horizontal pipes, so that

the frictional component of the pressure difference can be compared with the total pressure

gradient.

37

Figure 13. Separated model pressure gradient with internal diameter, Di, for ϴ=10º (left) and ϴ = 0º for a volumetric flow of

ṁ=0.35 L/s.

Figure 14 illustrates the pressure gradient against the volumetric flow for a pipe with a 38 mm

diameter and an inclination angle of 9º on the left and horizontal pipe on the right. It is worth

highlighting the y-axis of both graphs that should be compared in order to see the difference in

magnitude.

Figure 14. Separated model pressure gradient with volumetric flow, ṁ, for Theta=10º (left) and Theta = 0º (right) for an internal diameter of 38 mm.

Figure 15 shows the increasing trend of the pressure gradient due to the increase on the static

pressure component. On the left, this increase is plotted from 0 to 90 degrees to show that the

trend is not always linear. On the right, this plot is zoomed in to see the first 10 degrees, which

is the inclination in which the majority of aQysta’s pumps will operate.

38

Figure 15. Separated model pressure gradient with inclination angle, Theta, for ṁ=0.5 L/s and an internal diameter of 38 mm for Theta [0º, 90º] (left) and [0º, 10º] (right).

5.5 Evaluation of effect of the different parameters based on the models

In the two models that have been used to analyse the whole length of the pipe, the homogeneous

flow model and the separated flow model, similar trends can be seen. In this subchapter, what

these are and why these trends are followed will be briefly explained.

Firstly, as the diameter increases, the pressure drop decreases relatively steeply. This is due to

the fact that as the diameter increases, the frictional effects become less relevant, as there is less

shear stress between the fluids and the walls of the pipe.

However, the opposite happens with the volumetric flow: as it is increased, there is more shear

stress against the pipe walls and the frictional component of the pressure is reduced. Both trends

can be seen in both horizontal as well as inclined pipes.

Despite having a slightly curved trendline, the flow rate can be considered to linearly grow with

the rotational speed of the pump (Post, 2015). This is not exactly what happens because as the

rotational speed increases, the pump intake goes more times into the water but collects less

water each time. This is due to the higher intake speed that creates more turbulence in the water

basin and leaves less time to evacuate the air that makes room for the water.

Finally, as the inclination angle of the delivery pipe increases, the gravimetrical or static

component of the pressure gradient becomes more and more relevant, causing the pressure drop

to increase. This relation may not be intuitive for the different flow patterns, as for each one

there are complex effects that affect how the water is pushed upwards (Post, 2015).

39

It can be seen in both models that the relation between the pressure drop and the inclination

angle is not linear. This is due to the airlift effect, that becomes relevant as the inclination of

the pipe, volumetric flow and internal diameter increase.

The air lift effect happens when the air bubble has a similar diameter as the pipe and does not

let the water slip around it. Instead the compressed air pushes the water slugs causing the

pressure drop to go down for higher inclinations as can be seen in Figure 12 and Figure 15.

These plots demonstrate that this effect is not only present for the pumps developed by aQysta,

but also relevant and should be taken into consideration.

40

6. Adapted Slug flow model

This subchapter will focus on the implementation and adaptation of the of model for slug flow

suggested in the book ``Multiphase Flow Handbook´´ by Clayton T. Crowe, that further

develops the model of Dukler and Hubbard (1975). For the model to be valid for inclined pipes,

as well as for high pressure application, the gas flow is not neglected and taken into

consideration in a similar way to the liquid flow.

This model is considered to be an adaptation because the formulas that were originally obtained

experimentally to determine the lengths of the liquid and gaseous slugs have been adapted to

better predict the pressure drop for the parameters in the range used by aQysta’ s water pumps.

The adaptations that have been made are described below.

6.1 Theoretical model

Figure 16 illustrates the slug unit geometry, composed by a liquid slug with dispersed bubbles

and a gas slug with a water film beneath it when the pipe is nearly horizontal and surrounding

it when it gets closer to being vertical. This model is a hybrid between the separated model that

is used to account for the gas and film section and the drift flux model for the dispersed flow

section.

Figure 16. Slug unit geometry. (Crowe, Multiphase Flow Handbook, 2006)

The explanation of the equations of this model will be done in a logical order, starting with the

inputs and the secondary equations to get to the primary ones that will give us the pressure

gradient which will be the final result.

41

The fixed inputs that stay the same and are not dependent on the site or setup up are:

- ε: Roughness [m]



- σ: Surface tension [N/m]

- g: Gravity [m/s2]

The variable parameters that affect the pressure gradient and that their effect on the pressure

gradient is being studied is:




- λ: Liquid/total proportion [-]


Subindices:

- m: mixture

- L: liquid

- b: bubble

- Ls: liquid slug with dispersed bubbles

- u: unit length slug (gas + liquid)

The first equation is the mixture Reynolds number, which will tell us if the flow is laminar or

turbulent.

𝑅𝑒𝑚 =

𝐷𝜌𝐿𝑢𝑚

𝜇𝐿

(45)

Being the velocity of the mixture,

𝑢𝑚 = ṁ/𝑃𝑖𝑝𝑒 𝑐𝑟𝑜𝑠𝑠 𝑠𝑒𝑐𝑡𝑖𝑜𝑛 (46)

42

The Reynolds number is used to compute Zuber´s distribution parameter, that was also used in

the drift flux model. For the characteristics of aQysta´s pumps, the flow will always be

turbulent. In the most unprobable case, that it turned to be laminar, C0 would equal 2.

𝐶0 =

𝑙𝑜𝑔𝑅𝑒𝑚 + 0.089

𝑙𝑜𝑔𝑅𝑒𝑚 − 0.74

(47)

The bubble rise velocity, also calculated in the drift flux model, uses the constant C1 that is a

function of the pipe size and surface tension.

𝑢𝑏 = 𝐶1√∆𝜌𝑔𝐷

𝜌𝐿

(48)

The constant C1 is a function of pipe size and surface tension. Its value was only determined

for vertical flows, 0.35 and in literature, for inclined flow, various possible numbers have been

considered. The one used in the calculations for aQysta’s pumps with inclined pipe is 0.2

(Omgba-Essama, 2014).

Then, the shedding parameter C is calculated, that is used to take into consideration how much

water from the liquid slug slips into the film.

C = (𝐶0 − 1) +

𝑢𝑏

𝑢𝑚 (49)

A precise method to determine the holdup of the liquid section with dispersed bubbles, αLs, is

still under investigation. Currently, if the mixture velocity um is higher than the bubble

dispersion velocity um1, the holdup of this section is calculated as follows:

𝛼𝐿𝑠 =

𝑢𝑚0 + 𝑢𝑚1

𝑢𝑚0 + 𝑢𝑚

(50)

If not, αLs would equal 1. The parameter um1 is the disperse bubble velocity which gives a value

under no bubbles will be produced, is fixed and equals 1m/s. um0 is the velocity proportional to

fraction of dispersed bubbles that join the Taylor bubble and is represented by the equation:

43

𝑢𝑚0 =240

𝐶0 − 1𝐸0

(−1/2)(1 −

1

3sin 𝜃) [

𝑔𝜎∆𝜌

𝜌𝐿2 ]

14⁄

+𝑢𝑏

𝐶0 − 1

(51)

For this equation the Etövös number is needed,

𝐸0 =

𝑔∆𝜌𝐷2

4𝜎

(52)

Furthermore, the liquid holdup of the whole slug unit αL:

𝛼𝐿 =

𝐶𝛼𝐿𝑠 + λ𝐿

1 + 𝐶

(53)

A simplified approach to determine the ratio between the length of the liquid slug length and

the total unit slug length is the equation:

𝑟𝑎𝑡𝑖𝑜 =

𝑙𝑠

𝑙𝑢= λ𝐿 − 0.1 (54)

To compute the average liquid holdup in the air slug with the film, αavg_lf, the length of both gas

and liquid slugs must be determined. In this section of the model, adaptations have been made

to the formulas that have been obtained experimentally so that the results obtained with this

model can better predict the pressure drop for aQysta´s pumps.

To determine the total unit slug length, the slug frequency, vs, is introduced using the following

correlation,

𝑣𝑠 = [𝐹𝑚𝑖𝑛 + 𝐴(𝐹𝑚

0.1 − 𝐹𝑚𝑖𝑛0.1 )2] (

𝑔

𝐷)

0.5

(55)

where,

𝐹𝑚 = √𝑢𝑚

2

𝑔𝐷

(56)

𝐹𝑆𝐿 = λ𝐿𝐹𝑚

(57)

44

A = 0.6𝐹𝑆𝐿1

(58)

𝐹𝑠,𝑚𝑖𝑛 = 3.7𝐹𝑆𝐿0.66

(59)

𝐹𝑚𝑖𝑛 = 0.0695𝐹𝑆𝐿0.9

(60)

with which the total unit length slug length will be determined.

𝑙𝑢 =

𝑢𝑡

𝑣𝑠

(61)

ut is the translational velocity at which the slug propagates.

𝑢𝑡 = (1 + 𝐶)𝑢𝑚

(62)

Finally, the average liquid holdup in the air slug with the film, αavg_lf, can be calculated,

𝛼𝑎𝑣𝑔_𝑙𝑓 =𝛼𝐿𝑙𝑢−𝛼𝐿𝑆𝑙𝑆

𝑙𝑓

(63)

where ls is the length of the liquid slug,

𝑙𝑠 = 𝑟𝑎𝑡𝑖𝑜𝑙𝑢 (64)

and the length of the air slug with the thin liquid film below it is,

𝑙𝑓 = 𝑙𝑢 − 𝑙𝑠 (65)

Once the holdup of the unit slug and the air and liquid slug have been computed, as well as their

lengths, the precise gas and liquid velocity of the film region can be calculated. A higher value

for air velocity is expected.

𝑢𝐿𝑓 = (1 − 𝐶

𝛼𝐿𝑠 − 𝛼𝐿𝑓

𝛼𝐿𝑓) 𝑢𝑚

(66)

𝑢𝐺𝑓 = (1 + 𝐶

𝛼𝐿𝑠 − 𝛼𝐿𝑓

1 − 𝛼𝐿𝑓) 𝑢𝑚

(67)

45

To calculate the shear stress of the film of water and air slug against the walls of the pipe, there

is a need to calculate the friction factors. There are several possible ways in which this can be

done, as there are many valid correlations and diagrams, such as the Moody diagram, that can

be used.

As this model has been computed in MATLAB with the goal to analyse the effects of different

parameters such as the internal diameter, the friction factor could not be left as a constant. An

iterative method making use of the Colebrook correlation was computed as a function in

MATLAB (Clamond D. , 2008). The Colebrook correlation being:

1

√λ= −2 log10 (

𝑘

3.7+

2.51

𝑅

1

√λ )

(68)

The expression of the shear stress of the gas and liquid against the wall are the following.

𝜏𝑊𝐺 = 𝑓𝐺

𝜌𝐺𝑢𝐺2

2

(69)

𝜏𝑊𝐿 = 𝑓𝐿

𝜌𝐿𝑢𝐿2

2

(70)

PG and PL are the perimeters of gas and liquid against the pipe wall.

𝑃𝑓 = 𝛼𝑎𝑣𝑔_𝑙𝑓 𝜋𝐷𝑖

(71)

𝑃𝑏 = (1 − 𝛼𝑎𝑣𝑔_𝑙𝑓) 𝜋𝐷𝑖

(72)

To finally compute the pressure gradient due to friction, the friction factor of the water slug

against the pipe wall needs to be calculated. It is done by using the same method as before, with

a function in MATLAB, using an iterative method with the Colebrook relation.

The frictional pressure gradient per unit length slug in [Pa] is:

∆𝑃𝑓𝑟𝑖𝑐 = (𝜏𝑊𝑓

𝑃𝑓

𝐴+ 𝜏𝑊𝑏

𝑃𝑏

𝐴)

𝑙𝑓

𝑙𝑢+ 2𝑓𝑠𝜌𝑠

𝑢𝑚2

𝐷

𝑙𝑠

𝑙𝑢

(73)

46

To convert it into bars and have it for a pipe of length L:

∆𝑃𝑓𝑟𝑖𝑐_𝑡𝑜𝑡 = ∆𝑃𝑓𝑟𝑖𝑐10−5

𝐿

𝑙𝑢

(74)

To finally compute the total pressure gradient the gravimetrical pressure drop needs to be

computed.

∆Pgrav = (𝛼𝐺𝜌𝐺 + 𝛼𝐿𝜌𝐿)𝑔 sin 𝜃

(75)

with

𝛼𝐺 = 1 − 𝛼𝐿 (76)

To have the total gravimetrical pressure loss in a pipe with length L converted into bars,

∆Pgrav_tot = ∆Pgrav10−5

𝐿

𝑙𝑢

(77)

Finally, the total pressure gradient [bars] of a pipe with length L and diameter D, inclined ϴ

degrees equals,

∆𝑃𝑡𝑜𝑡 = ∆𝑃𝑓𝑟𝑖𝑐_𝑡𝑜𝑡 + ∆Pgrav_tot (78)

Step by step summary of the calculations for the adapted slug flow model:

Calculate:

1. Distribution parameter Co

2. Bubble rise velocity ub

3. Shedding parameter C

4. Liquid holdup in slug cylinder λLs

5. Liquid holdup for slug unit λL

6. Ratio between slug length and total unit length

7. Average liquid holdup in film

8. Gas and liquid velocities for the film regions uG and uL

9. Perimeters and shear stresses in the film region

10. Frictional pressure gradient

11. Total pressure gradient

47

6.2 Computational results

The most relevant plots for inclined pipes have been plotted below. All the graphs, once again,

have been plotted considering a constant pipe length of 50 meters and a volume fraction of 60%

of water inside the pipe.

Figure 17 presents the effect of the internal diameter on the pressure gradient for inclination

angles of 9º (left) and horizontal pipes (right) for volumetric flow rates of ṁ = 0.35 L/s. Once

again, there should be a focus on the y-axis as the magnitudes of the different plots can be

compared.

Figure 17. Pressure gradient with internal diameter, Di, for an inclination angle of ϴ=9º (left) and horizontal pipe (right) for volumetric flows of ṁ=0.35 L/s.

Figure 18 illustrates the pressure gradient against the volumetric flow for pipes 38 mm internal

diameter and inclination angles of ϴ = 9º (left) and ϴ = 0º (right). The adapted slug flow model

is the only model that takes into consideration the airlift effect, as it can be clearly seen in the

plots below. As the volumetric flow of the inclined pipe increases, the pressure drop decreases

due to the fact that the compressed air bubbles push the liquid slugs causing the pressure drop

to go down.

48

Figure 18. Pressure gradient with volumetric flow rate, ṁ, for internal diameters Di= 0.038 m and an inclination angle of ϴ=9º (left) and ϴ=0º (right).

Figure 19 illustrates the effect of the inclination angle against the pressure gradient for

volumetric flows of 0.5 L/s and internal diameters of 38 mm. On the left, the inclination angles

range from 0º to 90º, whereas on the left, the plot is zoomed in so that angles up to 10º are

shown. These angles are the ones in which aQysta’s pumps operate.

Figure 19. Pressure gradient with inclination angle, ϴ, for an internal diameter Di= 38 mm and a volumetric flow of ṁ= 0.5 L/s. ϴ ranges from [0,90] (left) and [0,10] (right).

With the adapted slug flow model, the analysis of theoretical two-phase model finished. The

next chapter will focus on explaining the experiments procedures and results that will be later

used to validate the theoretical models.

50

7. Experiments: calculating the pressure gradient, slug dimensions,

volumetric air and water flow and the void fraction.

In this chapter, the experiment´s equipment will be listed and the different setups followed,

described. Furthermore, the experiment´s protocol is analysed in detail and the results showed

in tables and briefly commented, as a more in-depth analysis and comparison with the results

obtained with the theoretical model will be developed in chapter 7.

7.1 Experiment objectives and limitations

The objective of the experiments is to validate and test the theoretical model computed with

MATLAB. Different experiments have been carried out to measure the pressure drop, length

and morphology of the air and water slugs, their velocity, the liquid holdup and the volumetric

flow rate of air and water.

There are some limitations and constraints that had to be overcome. Firstly, in the Netherlands

it is very complicated to find possible locations where there is a height difference and that is

appropriate for an experiment of these characteristics. For this reason, horizontal and 9º

inclination has been tested.

There was also the time and budget constraint: setting every experimental layout correctly was

very time consuming, as there was more than 100 m of pipe that had to be correctly set for each

one and a lot of measurements had to be done. Due to the time constraint, in the original

experiment design, three pipe diameters were going to be tested. Nonetheless, experiments with

two of them, 25 mm and 38mm, were finally carried out.

7.2 Preparation: equipment and setup

To carry out the experiments, firstly, all the necessary equipment had to be ordered and

delivered and the time that this takes must be taken into consideration when designing the

experiments.

The equipment is listed below, as well as pictures of the most important apparatus that are also

briefly described.

51

- Spiral pump (Figure 20 and Figure 21)

- Delivery pipe x3 with different diameters

- Glycerine manometers [0 - 1.6 bars] (Figure 22)

- Pressure sensor with data logger (Figure 23)

- Motor with enough power to turn the spiral

- Big container with an input hole at the lower side for the hose

- Graduated bucket x2

- Cameras x2 at least

- Ball valve with quick geka coupling

- Geka couplings for the three different diameter sizes (Figure 24)

- Hose pillars for the three different diameter sizes

- Protection for pipes (if needed)

- Adaptor from bucket

- Hose clamps

- Scale

- Measuring tape

- Chronometer

Figure 20. Spiral pump in water basin that was used as water input. The start of the delivery pipe can also be depicted.

52

Figure 21. Spiral from the back. The portable control can be seen, as well as part of the motor that turns the pump.

Figure 22. Analogue glycerine manometer [1-1.6 bar].

Figure 23. National Instruments data logger used for the digital pressure sensor.

53

Figure 24. Geka-coupling used to connect pipes of different diameters. Similar hose pillars are used in case the diameter is the same.

7.3 Experiment design:

Three rotational velocities were intended to be tested for every diameter of pipe, for both

inclined and horizontal setups, which would make a total of 18 experiments and 6 different

setups. Due to time constraints, 12 experiments were carried out with 4 different layouts.

Nonetheless, the set ups and tables with the three diameters are going to be presented, as it

would be very interesting if someone would develop this study further and wanted to carry out

the experiments that are left.

Table 3. Different diameters, rotational speeds, delivery pipe length and possible inclinations.

Diameters (cm) Rotational speeds (rpm)

Delivery pipe length (m)

Inclination (degrees)

1 2.5 5 50 meters Inclined and Horizontal

2 3.2 7.5 50 meters Inclined and Horizontal

3 3.8 10 50 meters Inclined and Horizontal

7.4 Experiment set ups:

In this subsection, the 9 different set ups and the 18 different experiments can be clearly seen.

The numbers 1, 2 and 3 in the charts, correspond to specific diameters and rotational speeds

that can be checked in the table above.

54

Table 4. Set ups for inclined pipe, 10º.

Inclined set up: 10 º with respect to the horizontal

Diameter/rotational speed Diameter/rotational speed Diameter/rotational speed

1 / 1 2 / 1 3 / 1

1 / 2 2 / 2 3 / 2

1 / 3 2 / 3 3 / 3

Table 5. Set ups for horizontal pipe.

horizontal set up

Diameter/rotational speed Diameter/rotational speed Diameter/rotational speed

1 / 1 2 / 1 3 / 1

1 / 2 2 / 2 3 / 2

1 / 3 2 / 3 3 / 3

7.5 Layout of the experiment

Figure 25 shows the location where the experiments took place. The building shown in the

picture is one of the two buildings that form Yes!Delft, the start-up incubator. Several aspects

had to be taken into consideration before starting the set-up.

Firstly, as you can see in the picture, the ramp that was used is intended for cars to go to the car

park. Moreover, there are large sliding cargo doors for trucks to deliver goods and large objects

to the different start-ups. If cars or trucks passed over the water, they would most certainly get

deformed and this would affect the experiment.

Figure 25. View of the location of the experiments.

55

The first solution that was thought for this was to use protections like the ones that can see in

Illustration 2. However, many of these would be needed and they are normally intended to

protect cables and not pipes, so there was a possibility that they would not be suitable for the

pipes of a larger diameter. The final decision was to carry out the experiments in the weekend

and in a vacation period, so that the least number of cars and trucks would be there. This strategy

worked, however, in the few cases that a car wanted to pass, the pipes had to be disconnected

and reconnected afterwards.

Illustration 2. Inclined pipe layout for experiment.

On the left the key for Illustration 2 can be found, where the main

components and apparatus used in the experiments are illustrated.

Neither the pump or the delivery bucket is depicted on the key, as they

are so easily recognisable in the diagram.

At the top of the ramp, there is an extra valve, geka-coupling and a hose

pillar that in the end were not needed, as the pipe was sufficiently long

to get to the delivery bucket and this way there was less components that

could affect the exit of the delivery pipe. Moreover, as well as the

glycerine manometer, pressure sensor was used to make more precise

measurements.

56

The horizontal section of the pipe that transported the flow from the pump to the inclined section

of study, was thought so that the flow had a section in which it could develop before getting to

the study section. It was 26 meters long, in other words, more than 100 diameters long, which

is more than enough length for that purpose.

7.6 Experiment protocol

1. Evaluate if the setup is correctly ensembled.

2. Start the pump with the convenient rotational speed.

3. Let the flow stabilize and reach steady state.

4. Measure the liquid volumetric flow rate. This is done by measuring in a certain amount

of time, how many kilograms of water are delivered. For 5 rpm, the delivered mass in

60 seconds was measured, in 7.5 rpm in 45 seconds and in 10 rpm in 30 seconds.

5. Repeat step nº 4 three times and average the result. Calculate the volumetric liquid flow

rates.

6. Change the delivery hose from the upper connection of the container to the lower one.

7. Put the graduated bucket inside the container until it can be totally submerged.

8. Invert the bucket and measure how much time it takes to fill itself with 15 L of air.

9. Repeat step 8 three times and average the result. Calculate the volumetric gas flow rate.

10. Change the delivery hose again to the upper connection of the container.

11. Wait for the flow to stabilise again.

12. Start the pressure sensor.

13. Film the slug from the top, 30 meters away from the delivery of the hose, for later seeing

the morphology of the slugs and measure their length.

14. Film the slug laterally, 30 meters away from the delivery of the hose.

15. Film the slug from the top, 10 meters away from the delivery of the hose, for later seeing

the morphology of the slugs and measure their length.

16. Film the slug laterally, 10 meters away from the delivery of the hose.

17. Time how much time it takes for a slug to move 3.2 meters.

18. Repeat step 15 three times to have an average mixture velocity.

19. Note down the pressure shown in the analogue manometer.

20. Stop the measurements of the pressure sensor.

21. Close valves simultaneously.

57

22. Measure the % of water there is in the pipe to calculate the liquid holdup.

Next experiment

23. Change the rotational speed to the one that corresponds to the next experiment.

24. Repeat steps 1 to 22 from previous experiments.

25. Repeat the procedure for the last rotational speed and the rest of the pipe diameters and

inclinations.

Figure 26 shows a picture of an air bubble traveling through a 38 mm pipe taken during the

experiments. These were filmed as indicated in steps from 13 to 15.

Figure 26. Picture of a slug made during the experiments.

7.7 Important considerations

Before presenting the measurements, some essential comments must be done about the

experiments for a better analysis and understanding of the importance and difficulties that were

encountered during these experiments and that should be taken into consideration if repeated

or even if a similar layout is intended to be used for different purposes.

Firstly, when measuring the volumetric flow rate, how to collect the water without adding

height to the last section of the pipe is an issue. For horizontal flow it was solved by positioning

the pipe next to a step, so that the water could be delivered without adding extra height.

However, for the inclined flow a new concept had to be thought of. The end of the slope used

had slightly less inclination than the 9º, so if we attached the pipe to a rigid metal structure and

made it continue with 9º inclination, as it can be seen in Figure 27, there was enough height to

collect the water. Moreover, to measure the volumetric liquid flowrate, a bucket with an

inclined side was used, to make the measuring easier and the splashing less. It can be seen on

the left of Figure 27.

58

Figure 27. Inclination of 10º in the output of the delivery pipe. The bucket with the inclined side can also be spotted on the left, next to the green container. The graduated bucket used to measure the volumetric mass flow rate can also be seen on

the left.

It should also be highlighted that to measure the volumetric liquid flow rate, the mass of water

was measured and not the volume. This was because the mass measurement has much less error

and it is easily converted to volume dividing by the density. Furthermore, to measure the

volumetric air flow rate, once again the volume was not measured, but the time it took to deliver

15 L of air was measured instead. The compressibility of air was thought to possibly make a

difference in the measurements, but it was shown that the effect it had was minimum and that

it could be not taken into consideration.

The correct layout of the pipes also can give some food for thought. The pipe needed to transport

the water from the spiral pump to the study straight section of pipe, another pipe with a 25 mm

diameter was used. There was a concern because there was going to be a curved section, but

after doing some calculations and after questioning Transport Phenomena TU-Delft Professor

Luis Portela, it was decided that if the curve had more than 1-meter radius, the effect could be

neglected. As it can see in the Figure 28 below, the radius was much more than 1 meter.

59

Figure 28. Curve in the pipe with more than 1-meter radius.

Moreover, the study section of straight pipe was intended to be as linear as possible. As it can

be seen in Figure 29, concrete low pillars were used as a reference and a 2 cm misalignment is

estimated, that compared to 50 meters of pipe is considered neglectable.

Furthermore, in the middle of the slope there was a 6º bend that it was thought that had to be

made, but in the end, it was possible to continue in a straight line. It is worth mentioning that

in the case that the 6 º bent had been impossible to avoid, its effect, because of such a small

angle, would have also been unnoticeable.

Figure 29. Linear pipes, with a neglectable misalignment of 2 cm.

60

The cross-section of the pipe should also be taken into consideration. In the case of the pipe

with a 25 mm diameter, the pipe cross-section did stay circular. However, because of the way

that it had been packaged, the cross-section of the pipe with a 38 mm diameter was more oval

shaped. This, in terms of the pressure gradient, did not make that much difference. Nonetheless,

when measuring the liquid holdup, in other words, the distance of pipe that after the valves are

closed is full of water, this effect should be taken into consideration.

A way to solve this is to measure the volume of water in the pipe after the circular valves have

been simultaneously closed and divided it by the total volume of water that can fit in the same

section pipe. This way, a correct relation between the volume of water in the pipe and the total

volume of the pipe can be done.

Finally, measuring the gas velocity and the water velocity separately, instead of the mixture

velocity was considered. However, as these values would be very similar, it was decided not to.

Nonetheless, a way to measure the liquid velocity would have been to inject a small amount of

dye into the water flow and measure the amount of time it takes to travel a certain length. This

method would only work with flows with very regular slugs and nearly no slippage of the water

slug to the film under the air slug.

7.8 Measurements

In this chapter, the different measurements taken during the experiments are presented. These

values are used in the next chapter to validate the theoretical models. Table 6 shows the average

liquid flow rate, average gas flow rate, pressure, mixture velocity and liquid hold up for

horizontal pipes whereas Table 7 illustrates the measurements for inclined pipes.

Table 6. Measurements for horizontal pipe with three different diameters and three different rotational velocities of the pump.

HORIZONTAL Averaged liquid flow rate [L/s]

Averaged gas flow rate [L/s]

Pressure [bars]

Mixture velocity

[m/s]

Liquid holdup [%]

D1, w1 0.21 0.2 0.1 0.93 0.55

D1, w2 0.26 0.29 0.22 0.96 0.55

D1, w3 0.36 0.38 0.3 0.99 0.57

D2, w1 0.24 0.18 0.024 Stratified 0.6

D2, w2 0.29 0.27 0.08 Stratified 0.67

D2, w3 0.38 0.36 oscillating Stratified 0.61

61

Table 7. Measurements for inclined pipe, 10º, with three different diameters and three different rotational velocities of the pump.

INCLINED 10º

Averaged liquid flow rate [L/s]

Averaged gas flow rate [L/s]

Pressure [bars]

Mixture velocity

[m/s]

Liquid holdup [%]

D1, w1 0.2 0.18 0.61 0.93 0.67

D1, w2 0.25 0.26 0.63 1.69 0.65

D1, w3 0.34 0.31 0.7 1.32 0.61

D2, w1 0.19 0.17 0.56 0.54 0.74

D2, w2 0.28 0.27 0.53 0.69 0.64

D2, w3 0.35 0.35 0.52 0.79 0.66

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8. Comparison of the models and the experiments

In this chapter, the theoretical models will be compared with the experiments carried out for

three different flow rates and two different diameters. The inputs chosen for the simulations

have been decided so that they match the experiment parameters and have already been

discussed in chapter 5.2. This way, the comparisons and results give a clear view of how each

parameter affects the pressure drop and to what extent.

Firstly, the effect on inclined pipes is analysed in chapter 8.1, as the pressure drop is larger due

to the gravimetrical pressure gradient, that has to be taken into consideration as well as the

frictional pressure gradient. In chapter 8.2, comparisons for horizontal theoretical models and

experiments are analysed. In this chapter, the role that friction plays can be clearly seen. Finally,

in chapter 8.3 the effect of inclination will be discussed.

8.1 Inclined pipe: effect of internal diameter and volumetric flow

Figure 30 illustrates the evolution of the pressure drop with the internal diameter. The

theoretical adapted slug flow model has been adjusted so that it follows the tendency shown in

the experiments very accurately. The error at 38 mm is approximately of 3%.

Adjusting the model so that it would predict the pressure drop as precisely as possible when

varying the pipe diameter was done because it is one of the most important design choices, as

the volumetric flow and the inclination angle are normally imposed by the river flow and

velocity of water and the inclination of the landscape where the pump will possibly be situated.

The larger the internal diameter, the less pressure drop there is. If the inclination angle remains

the same, as the diameter gets larger, friction between the fluids and the pipe walls becomes

less meaningful.

63

Figure 30. Pressure gradient with internal diameter, Di, for an inclination angle of 9º and 0.36 L/s.

Figure 31 is added so it can be compared with Figure 30, as it shows the evolution of the

pressure gradient when varying the internal diameter for a larger volumetric flow of 0.6 L/s.

When the volumetric flow is increased, the pressure drop also increases in nearly 0.1 bars. Once

again, the adapted slug flow model is the one that gives the better estimation, with a maximum

error for pipes with 33 mm diameter of 20 % that will quickly become much smaller as the

diameters get larger.

64

Figure 31. Pressure gradient with internal diameter Di for an inclination angle of 9º and 0.6 L/s.

Figure 32 shows how the pressure drops develops when the volumetric flow rate increases for

pipes with a 25 mm internal diameter. It is important to notice that both the theoretical models

as well as the experiments that have been carried out show an increase in the pressure drop as

the volumetric flow increases. This is expected as when the volumetric flow increases, the

Reynolds number increases as well as the friction factor.

This study shows that to predict the effect of the volumetric flow on the pressure gradient, the

separated model is the one that gives the most precise values, with a maximum error at 0.36 L/s

that decreases as the volumetric flow increases. The separated flow model will give a slight

underestimation if the volumetric flow is lower than 0.7 L/s and a slight overestimation if it is

higher, being the value most precise then the flow rate is around 0.7 L/s.

Figure 32. Pressure gradient with volumetric flow for inclination angles of 9º and internal diameters of 25 mm.

Figure 33 has been added as a comparison with the previous figure and is of great importance.

It shows the evolution of the pressure gradient with the volumetric flow for a larger internal

diameter of 38mm. For this larger diameter, the separated and the homogeneous flow model

follow an upward trend, whereas the adapted slug flow model as well as the results obtained

with the experiments show that as the volumetric flow increases, the pressure drop decreases.

65

As explained for the pipe with an internal diameter of 25 mm, the expected result would be to

have an increase of the pressure drop as the volumetric flow increases, however the experiments

and adapted slug flow model show otherwise. This is due to the airlift effect explained below.

The model that best predicts the pressure gradient for volumetric flows until 0.62 L/s is the

adapted slug flow model, as it follows the downward inclination. Nonetheless, from that value

onwards, the separated flow model in the one that predicts best, as the results get more precise

as the volumetric flow increases.

Figure 33. Pressure gradient with volumetric flow for an inclination angle of 9º and an internal diameter of 38 mm.

Airlift effect

As already mentioned in chapter 5.5 the airlift effect is most dominant at higher inclination

angles and large flows and quick flow velocities (Post, 2015). It happens when the compressed

air bubble is the same size as the pipe diameter because the water cannot slip downwards and

the air flow that goes at a higher pace due to its smaller density can push the water slugs, causing

pressure drop to decrease.

When the pipe diameter is smaller, there is more turbulence and friction, causing more

interaction between phases (Post, 2015) and when the liquid velocity is low it is easier for the

gaseous bubbles to overtake than to push the liquid slug.

66

8.2 Horizontal pipe: effect of internal diameter and volumetric flow

Analysing the pressure gradient for horizontal pipe is of great relevance as it shows the effect

of the friction for different pipe diameters and volumetric flows. These results can be compared

with the figures above, however, the fact that different inputs have been used has to be taken

into consideration. This was done so that the theoretical results could be compared with the

results obtained with the experiments.

Figure 34 shows the downward trend of the pressure gradient with the internal diameter. With

smaller internal diameters, when conducting the experiments, a very irregular flow was seen.

However, for larger diameters, a stratified pattern was easy to identify. This is why, for smaller

diameters the theoretical models are not as precise as for larger diameters, being the

homogeneous flow model the most precise results.

The adapted slug flow model does not give precise results due to the fact that for horizontal

flows, the flow pattern was not slug flow. It was unsteady and fluctuating between stratified,

slug and wavy flow patterns for small internal diameters and stratified flow for larger ones.

Figure 34. Pressure gradient with internal diameter for horizontal pipes and 0.41 L/s.

Figure 35 has been added to show the downward trend of the pressure gradient with the internal

diameter for a larger volumetric flow of 0.55 L/s. The theoretical models only predict precisely

67

for diameters close to 26 mm. This is because the model was adjusted so that it would predict

better for flows with some inclination as aQysta´s pumps nearly always need to pump water to

a certain height. Knowing that for larger diameters the models give a very accentuated

underestimation is very relevant.

Figure 35. Pressure gradient with internal diameter, Di, for horizontal pipes with 0.55 L/s.

Figure 36 illustrates the upward trend of the pressure gradient with increasing volumetric flow

rates. For horizontal pipes, flow patterns are closer to stratified flow than slug flow, and that is

why the homogeneous and separated flow patterns give more precise results, having the larger

error for 0.41 L/s.

The evolution of the pressure gradient with the volumetric flow for a larger diameter is not

plotted, as the pressure sensor gave very irregular results, so the plot obtained did not give any

relevant information. The reason for this is that the pressure was too small, as some water was

simply flowing slowly through the lower part of the pipe.

68

Figure 36. Pressure gradient with volumetric flow for horizontal pipes with 25mm of internal diameter.

8.3 Effect of inclination

The inclination angle is one of the most important parameters of study that highly affects the

pressure drop as can be seen in Figure 37. The adapted slug flow model is the one that gives

the most precise results with a maximum error of approximately 6%. The other models give an

underestimation.

Figure 37. Pressure difference with inclination angle for 0.36 L/s and 25mm for inclination angles that go from 0 to 9º.

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Figure 37 illustrates the pressure drop for inclination angles that go from 0 to 90 degrees. This

graph is of great relevance, as it shows that the pressure drop stops following a linear trend for

angles higher that 25º. As it was already introduced at the end of chapter 8.3, this is due to the

airlift effect. This effect, as can be seen in the figure below, increases with the inclination angles

and decreases the pressure gradient, as the gaseous bubbles push the liquid slugs instead of

overtaking them.

Figure 38. Zoom out of the pressure gradient with inclination angle for 0.36 L/s and 25mm of internal diameter for inclination angles that go from 0 to 90º.

70

9. Application to real pumping scenarios: Dolakha (Nepal)

In this chapter, the models will be used to calculate the pressure drop of the delivery pipe of a

pump that has been installed in Dolakha (Nepal), in a small area called Lamatar. Firstly, the

inputs that were provided and how the rest were calculated is shown. Then the results obtained

are discussed and shown in a table. Finally, how the pressure drop would develop if small

changes in the inputs parameters happen is analysed.

9.1 Computational results ṁ

The values available from this installation are the internal diameter, volumetric flow rate, height

and horizontal distance of the specific location in Hijar:

- Di (Internal diameter) = 40 [mm]

- ṁ (Volumetric flow rate) = 0.4 [L/s]

- h (height) = 17 [m]

- l (horizontal length) = 100 [m]

- liquid hold up = 51%

However, to use as inputs in the model the inclination angle and the exact distance between the

input and output of the delivery pipe are needed. To calculate them, simple trigonometry is

used:

L [m]

h=17 [m]

l = 100 [m]

To calculate the inclination angle (ϴ):

tan 𝜃 =17

100

θ = 9.65 degrees

To calculate the length between the input and output of the delivery pipe (L):

ϴ [º]

71

sin 𝜃 =17

L

L = 101.4 [m]

Knowing all the inputs, the pressure drop can be computed for the different theoretical models,

the results being showed in Table 8. The total pressure drop has been divided into frictional

pressure drop and gravimetrical pressure drop to see the contribution of each component.

Table 8. Computational results of the theoretical models with the inputs given for Dolakha (Nepal).

Theoretical model Frictional Pressure

Drop [bar]

Gravimetrical

Pressure Drop [bar]

Total Pressure Drop

[bar]

Adapted Slug Flow

Model

0.156 1.01 1.03

Separated Flow

Model

0.0357 0.9401 0.976

Homogeneous Flow

Model

0.024 0.899 0.924

As the pump in this location has already been installed, the value of the actual pressure drop

has been measured and is 1.1 bar. As can be seen in Table 8, the model that most precisely

estimates the pressure drop is the adapted slug flow model, whereas the homogeneous slug flow

model and the separated flow model give a slight underestimation.

This could have been predicted by looking at Figure 30 and Figure 31 which represent the

pressure gradient against two volumetric flow rates, one above and one below the one in

Dolakha for a 9º inclined pipe. Figure 34 and Figure 35 may also be illustrative, as the same

parameters are plotted for horizontal pipes.

9.2 Effect of the different parameters on the pressure drop for Hijar (Valencia)

In this subchapter the effect that a small change in the input parameters will have in the pressure

drop in analysed. The results given by the different models are plotted so that the trends can be

seen and evaluated.

72

Figure 39 illustrates the pressure gradient against the internal diameter. As the internal diameter

is a design variable, this plot is of great relevance as the effect of decreasing the diameter up to

5mm can be seen. As the diameter increases, the pressure drop decreases as the effect of the

friction becomes less relevant. As it has been mentioned in the subchapter before, the adapted

slug flow model shows the best estimation.

Figure 39. Pressure gradient with the internal diameter, Di, for an inclination angle of 9.65º and a volumetric flow of 0.4 L/s.

Figure 40 shows the pressure gradient against the volumetric flow rate. With this figure the

upward trend is depicted. The adapted slug flow model is the only model that takes the air-lift

effect into consideration. For the characteristics of this pump and location, it is not only present

but very relevant. It occurs because of the pronounced inclination of the delivery pipe of 9.65º.

73

Figure 40. Pressure gradient against volumetric flow for an inclination angle of 9.65º and an internal diameter of 40mm.

Figure 41 illustrates the pressure gradient against the inclination angle for a volumetric flow of

0.4 L/s and an internal diameter of 40 millimetres. The larger the inclination angle, the larger

the pressure gradient due to the increase of the gravimetrical component of the pressure. This

plot shows how small changes in the inclination can cause significant changes in the pressure

gradient.

Figure 41. Pressure gradient against the inclination angle, for a volumetric flow of 0.4 L/s and an internal diameter of 40 mm.

74

10. Recommendations

In this section, recommendations for the company as well as for future students wanting to

continue doing research in this area of fluid dynamics are presented. The company aQysta has

to start using the tool that has been provided and there are many areas in which students can

develop, improve and analyse multiphase flow models.

10.1 Recommendations for the company aQysta

The models have been designed and organised to be as more user friendly as possible. This has

been done so that anyone in the company can learn how to use the model and evaluate a location

for a water pump.

The first recommendation should be to incentivise the use of this new tool and try it out for

more real locations where spiral pumps are intended to be installed. If there are some objective

parameters, for example, the pump has to be able to deliver water at this height, and this

distance, the models can be used to see which the best way would be to fulfil them.

Moreover, the models can be tested comparing the results that are obtained with measurements

taken from pumps that have already been installed. To do so, the fact that there are many

uncertainties in the results given by those measurements should be taken into account.

However, having data to contrast the models with would be of great help to further develop the

models and make them more precise.

Another way to have a better validation of the models would be to conduct more experiments

for example for a different inclination angle or for an intermediate diameter between the 25 mm

and 38 mm.

Finally, taking into consideration the airlift is highly recommended. Specially for the Hy-

pump, as the volumetric flow rates and diameter of the pipe will be larger. As the velocity of

the flow is not going to be proportionally high, there is a need to evaluate if airlift will be

present or not for the parameters of the pumps of this new design.

75

10.2 Recommendations for future research

This project focuses mainly on the delivery pipe of the spiral pump for a certain range of internal

pipe diameters and volumetric flow rates. Specially for the future development of the Hy-pump,

a study focusing on larger values for these parameters would be appropriate.

Furthermore, there are many other components of the pump that are also worth studying such

as the main spiral, the scoop or the entrance of the spiral of the flow merger that unites the flows

coming from the different spirals into one unique pipe.

When conducting experiments like the ones described in this project or of similar

characteristics, I would highly advise to read over chapter 6.7 that describes important factors

that have to be taken into consideration when conducting an experiment of those characteristics.

In this project it is proven that the air lift effect is present. However, it does not go in depth on

how the company could take advantage of it or how it could be used. A study focusing on this

would also be very relevant.

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11. Conclusions

To conclude, there should be a reference to the objectives of this project. The main objective of

developing a tool with which the company aQysta can analyse the pressure gradient of the

delivery pipe of the spiral pumps has been accomplished. This analysis has been done in a

theoretical manner at first, analysing models that are present in the literature to later conduct

experiments to validate their results.

A real case scenario has also been evaluated to demonstrate how this tool could be used by the

company. The pressure drop of a pump that will be installed in Dolakha (Nepal) has been

evaluated. Moreover, the effect that small changes in the input parameters such as internal

diameter, volumetric flow rate or inclination angle can have on the pressure drop is evaluated.

Moreover, the effect of the internal diameter, inclination angle and volumetric liquid and

gaseous flow on the pressure gradient is understood and explained and the different results are

plotted, analysed and compared.

The airlift has been proven to be present in aQysta’s pumps, can be relevant for some locations

and clearly should be taken into consideration when doing the relevant calculations that have

to be done to determine the installation of the pumps.

The adapted slug model has been adapted so that the pressure drop is very precisely determined

then evaluating the effect of the internal diameter. It has been intended to have a model that

will give as good or better results as the diameters and volumetric flow rates become larger.

This is because, already mentioned at the start of the project, aQysta is developing and

designing a new pump that will operate with larger flows and would need larger pipe diameters.

The limitations of the models have to be taken into consideration. For diameters smaller than

25 mm the results are not accurate and with some inputs the model can give results that may

have an error margin close to 15%. However, these can be easily found, and the results can be

revaluated.

77

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80

ECONOMIC ANALYSIS

AND

SCHEDULE

82

Economic analysis

Index

1. Economic analysis and budget…………………………………………… 84

1.1 Resources analysis ............................................................................................... 84

1.2 Equipment ............................................................................................................ 84

1.3 Components ......................................................................................................... 85

1.4 Hoses ................................................................................................................... 85

1.5 Workforce ............................................................................................................ 86

1.6 Total costs ............................................................................................................ 86

2. Methodology .......................................................................................................... 88

3. Schedule for the thesis .......................................................................................... 90

References: .................................................................................................................... 92

Tables:

Table 1. Water and Electricity Resource price [1] [2]. ................................................... 84

Table 2. Equipment price [3] [4] [5] [6] [7]. .................................................................. 84

Table 3. Components used in the experiment price [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]

[18] [19] [20] [21] [22]. .................................................................................................. 85

Table 4. Hose Price [23] [24] [25] [26]. ......................................................................... 85

Table 5. Budget for the workforce. ................................................................................ 86

Table 6. Total cost of the project. ................................................................................... 86

Table 7. Gantt chart of the project. ................................................................................. 90

84

1. Economic analysis and budget

In this chapter the budget needed for this project has calculated and structured in tables that

show cost of resources (Table 9), equipment (Table 10), components (Table 11), hoses (Table

12) and workforce (Table 13). Every element shown in the tables has been referenced to refer

to it for future experiments and budgeting. Finally, the total cost of the project can be seen in

Table 14.

1.1 Resources analysis The resources needed for this project were water and electricity. Water was used when testing

and has been calculated with the flow rate, time and market price. Electricity has also been

taken into consideration using the power consumed by the laptop and the hours spent carrying

out the project.

Table 9. Water and Electricity Resource price [1] [2].

[1] [2]

1.2 Equipment

To calculate the cost of the equipment, an operation lifetime of 10 years with an availability

of 10 hours a day has been taken into consideration. The hours in which the equipment was

used are used to estimate the cost, that can be seen in Table 10.

Table 10. Equipment price [3] [4] [5] [6] [7].

[3] [4] [5] [6] [7]

Quantity Unit ConceptPrice per unit

(€/unit)

Total cost

(€)Ref.

18 m^3 Water 1.76 31.68 [1]

24 kWh Electricity 0.16 3.84 [2]

35.52TOTAL Resources


(€)

Total cost

(€)Ref.

40 h Test pump 0.03 1.20 [3]

1.06 h Scale 0.04 0.04 [4]

0.50 h Pallet truck 0.01 0.01 [5]

1 u MATLAB 35.00 35.00 [6]

1 u Office Packet 32.95 32.95 [7]

69.20TOTAL Equipment

85

1.3 Components

In Table 11 the price of the different components of the set-up of the experiments are shown.

When choosing the manometer, the range has to be taken into consideration. In this case, the

chosen range has been from 0-1.6 bars.

Table 11. Components used in the experiment price [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22].

• [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]

1.4 Hoses

Hoses from three different sizes where bought to carry out the experiments. The ones used in

the study section had to be transparent for a good visualization.

Table 12. Hose Price [23] [24] [25] [26].

[23] [24] [25] [26]


(€)

Total cost

(€)Ref.

10 u Hose pillar 2-sided 25 mm 2.21 22.10 [8]



4 u Geka coupling hose pillar 25 mm 2.27 9.08 [11]

2 u Geka coupling hose pillar 32 mm 3.26 6.52 [12]

2 u hose pillar 38 mm and 1-1/4 male thread 4.21 8.42 [13]

2 u Geka female theard 1-1/4 female thread 3.22 6.44 [14]

2 u Adaptor from bucket to return pipe 3.65 7.30 [15]

1 u 0-1.6 bar glycerine Manometer 12.40 12.40 [16]

1 u Ball valve with geka coupling 1 inch 10.80 10.80 [17]

10 u Hose clamps 25 mm x 40 mm 0.24 2.40 [18]

2 u Measuring tape 11.95 23.90 [19]

2 u Buckets 7.99 15.98 [20]

1 u Stopwatch 6.99 13.98 [21]

2 u Go-pro Camaras 219.00 219.00 [22]

383.44TOTAL Components


(€/m)

Total cost

(€)Ref.

50 m 25 mm Non-Transparent Hose 1.91 95.50 [23]

100 m 25 mm ID Transparent hose 2.37 237.00 [24]

75 m 32 mm ID Transparent hose 2.83 212.25 [25]75 m 38 mm ID Transparent hose 4.21 315.75 [26]

860.50TOTAL Hoses

86

1.5 Workforce

Mainly four people where involved in the project: the student, a supervisor in Spain, a

supervisor in the Netherlands and the lead fluid dynamic engineer for aQysta.

Table 13. Budget for the workforce.

1.6 Total costs

Finally, the total cost of the project will be TEN THOUSAND AND NINTY SIX EUROS WITH SIXTY-SIX

CENTS, as can be depicted in Table 14.

Table 14. Total cost of the project.


(€)

Total cost

(€)5 h Numerical Analysis and Modeling Proffesor, Arturo Hidalgo 50 250

5 h Fluid Dynamics Proffesor, Luis Portela 50 250

15 h Lead aQysta Fluid Engineer, Jaime Michavila 50 750

300 h Energy Engineering student, Elisa Anderson 25 7,500.00

8,750.00TOTAL Workforce

Section Concept Total cost (€)

1.1 Resources 35.52

1.2 Equipment 69.20

1.3 Components 383.441.4 Hoses 860.5

1.5 Workforce 8,750.00

TOTAL cost 10,098.66

88

2. Methodology

There were six main stages during this project, that were the following. Firstly, an in-depth

literature review was done, to get familiar with the state of the art and the prior work done in

this field. After that, a thorough study the theoretical models was done to understand all the

variables and equations, to later compute the models that were found most interesting and

relevant, using the software MATLAB.

Later, experiments were conducted to validate the model and to give enough information to

develop and adapt the model to the characteristics of aQysta´s pumps. Finally, all the results

were analysed, and the document was written.

Figure 42. Steps followed during the development of the project.

Literature Review

Study Theoretical

Models

Computing the models

with MATLAB

Conduct experiments

Analyseresults

Ellaboration of report

90

3. Schedule for the thesis

This project was carried out during the second semester of 2018. It was organised this way since

most the classes were scheduled for the first semester and I could be dedicated to the project

nearly full time. Table 15 illustrates how much the different stages of the project lasted and

when they were carried out. Moreover, the objective schedule can be compared with the actual

moment when each stage was finished.

Table 15. Gantt chart of the project.

05-mar 12-mar 19-mar 26-mar 02-abr 09-abr 16-abr 23-abr 30-abr 07-may 14-may 21-may 28-may 05-jun 12-jun 19-jun

Literature Study

Company, objectives, etc

State of the art

1D models -> homog, separated

taking slug into consideration

Developing the model

matlab homogeneous

matlab separated model

matlab drift flux model

slug flow model

graphs and study of these models

Preparing testing + developing model

Defining test requirement

Prepare testing

Write detailed procedure

Testing

Experiment

Develop de results

Compare with model + 1 st draft

Comparisson

draft

Final report

Progress update

Final report

Corrections

Key

Objective

Done

92

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93

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two-phase flow modelling of the pressure gradient of the delivery...

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