Fluid Flow and Heat Transfer Simulations for Complex Industrial Applications 2018 Isbn 978-91-7485-415-2 Issn 1651-4238 P.O

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Mälardalen University Doctoral Dissertation282 Doctoral University Mälardalen Fluid flow heat and transfer simulations flow Fluid industrial complex for applications smoothed particle Navier-Stokes towards hydrodynamics averaged Reynolds From Hosain Lokman Md

Md Lokman Hosain FLUID FLOW AND HEAT TRANSFER SIMULATIONS FOR COMPLEX INDUSTRIAL APPLICATIONS 2018 ISBN 978-91-7485-415-2 ISSN 1651-4238 P.O. Box 883, SE-721 23 Västerås. Sweden 883, SE-721 23 Västerås. Box Address: P.O. Sweden 325, SE-631 05 Eskilstuna. Box Address: P.O. www.mdh.se E-mail: [email protected] Web: 1

Mälardalen University Press Dissertations No. 282

FLUID FLOW AND HEAT TRANSFER SIMULATIONS FOR COMPLEX INDUSTRIAL APPLICATIONS

FROM REYNOLDS AVERAGED NAVIER-STOKES TOWARDS SMOOTHED PARTICLE HYDRODYNAMICS

Md Lokman Hosain

2018

School of Business, Society and Engineering 2

Mälardalen University Press Dissertations No. 282

FLUID FLOW AND HEAT TRANSFER SIMULATIONS FOR COMPLEX INDUSTRIAL APPLICATIONS FROM REYNOLDS AVERAGED NAVIER-STOKES TOWARDS SMOOTHED PARTICLE HYDRODYNAMICS

Md Lokman Hosain

Akademisk avhandling som för avläggande av teknologie doktorsexamen i energi- och miljöteknik vid Akademin för ekonomi, samhälle och teknik kommer att offentligen försvaras fredagen den 14 december 2018, 13.00 i Delta, Mälardalens högskola, Västerås.

Fakultetsopponent: Professor Moncho Gomez Gesteira, University of Vigo

Akademin för ekonomi, samhälle och teknik 4

Abstract Optimal process control can significantly enhance energy efficiency of heating and cooling processes in many industries. Process control systems typically rely on measurements and so called grey or black box models that are based mainly on empirical correlations, in which the transient characteristics and their influence on the control parameters are often ignored. A robust and reliable numerical technique, to solve fluid flow and heat transfer problems, such as computational fluid dynamics (CFD), which is capable of providing a detailed understanding of the multiple underlying physical phenomena, is a necessity for optimization, decision support and diagnostics of complex industrial systems. The thesis focuses on performing high-fidelity CFD simulations of a wide range of industrial applications to highlight and understand the complex nonlinear coupling between the fluid flow and heat transfer. The industrial applications studied in this thesis include cooling and heating processes in a hot rolling steel plant, electric motors, heat exchangers and sloshing inside a ship carrying liquefied natural gas. The goal is to identify the difficulties and challenges to be met when simulating these applications using different CFD tools and methods and to discuss the strengths and limitations of the different tools. The mesh-based finite volume CFD solver ANSYS Fluent is employed to acquire detailed and accurate solutions of each application and to highlight challenges and limitations. The limitations of conventional mesh-based CFD tools are exposed when attempting to resolve the multiple space and time scales involved in large industrial processes. Therefore, a mesh-free particle method, smoothed particle hydrodynamics (SPH) is identified in this thesis as an alternative to overcome some of the observed limitations of the mesh-based solvers. SPH is introduced to simulate some of the selected cases to understand the challenges and highlight the limitations. The thesis also contributes to the development of SPH by implementing the energy equation into an open-source SPH flow solver to solve thermal problems. The thesis highlights the current state of different CFD approaches towards complex industrial applications and discusses the future development possibilities. The overall observations, based on the industrial problems addressed in this thesis, can serve as decision tool for industries to select an appropriate numerical method or tool for solving problems within the presented context. The analysis and discussions also serve as a basis for further development and research to shed light on the use of CFD simulations for improved process control, optimization and diagnostics.

ISBN 978-91-7485-415-2 ISSN 1651-4238 5

Dedicated to my family 6

“Essentially, all models are wrong, but some are useful” – George E. P. Box 7

Acknowledgements

The research in this PhD thesis was conducted at the Future Energy Center, Mälardalen University, Västerås, Sweden, with financial support from The Knowledge Foundation, SSAB, ABB, Mälarenergi and Eskilstuna Energi & Miljö. My first and foremost thanks go to my main supervisor Prof. Rebei Bel- Fdhila for his continuous and invaluable guidance, support, suggestions and inspiration throughout this thesis work. I would like to acknowledge my co-supervisor Prof. Konstantinos Kyprian- idis, Prof. Erik Dahlquist and Dr. Hailong Li for their guidance and support during my thesis work. Many thanks to Prof. Emeritus Dan Loyd and Dr. Jan Sandberg for reviewing this PhD thesis and providing valuable comments and suggestions. I am very thankful to Alex J. C. Crespo and Jose M. Domínguez from the University of Vigo, Spain for hosting me and supporting me during the implementation of the thermal models in the open-source SPH code DualSPHysics. My special thanks go to my colleagues and friends at my department for many fruitful discussions. Finally, I would like to show my deepest gratitude to my beloved wife Nupur Akther; without her support this PhD would have been impossible. I would also like to thank my sister-in-law Fahima Akther for all the mental support and inspiration from the first day I arrived in Sweden. I would also like to show gratitude towards my parents for all the inspiration I received from them during my studies.

Md Lokman Hosain October, 2018. Västerås, Sweden. 8

Summary

The energy demand and environmental impacts from the industrial sector are growing concerns within the European Union (EU) due to the need to comply with the strict energy and environmental policy. Optimal process control can significantly enhance energy efficiency of heating and cooling processes in many industries. Process control systems typically rely on measurements and so called grey or black box models that are based mainly on empirical correlations, in which the transient characteristics and their influence on the control parameters are often ignored. A robust and reliable high-fidelity numerical technique, to solve fluid flow and heat transfer problems, such as computational fluid dynamics (CFD), which is capable of providing a detailed understanding of the multiple underlying physical phenomena, is a necessity for optimization, decision support and diagnostics of complex industrial systems. There are several different options within CFD methods and tools, however, choosing the right numerical tool to solve advanced engineering problems, and particularly in industrial research and development (R&D) is often difficult, and the consequences of choosing the wrong tool can be very costly. This thesis deals with several energy-intensive complex industrial applications. The goal is to identify the difficulties and challenges to be met when simulating these applications using different CFD tools and methods and to discuss the strengths and limitations of the different tools. The thesis focuses on performing high-fidelity CFD simulations of a wide range of industrial applications to highlight and understand the complex nonlinear coupling between the fluid flow, heat transfer and other phenomena inherent to the investigated processes, e.g. combustion or induced transients. The industrial applications studied in this thesis include the runout table (ROT) cooling process and slab reheating furnace in a hot rolling steel plant, rotating machines such as electric motors and generators, heat exchangers and sloshing inside a ship carrying liquefied natural gas (LNG). The mesh-based finite volume CFD solver ANSYS Fluent is employed to acquire detailed and accurate solutions of each application and to highlight challenges and limitations. The limitations of conventional mesh-based CFD tools are exposed when attempting to resolve the multiple space and time scales involved in large industrial processes. They are not capable of addressing the multiple jet impingement on a fast-moving strip that we encounter in the ROT cooling process, and are often only partly successful, as in the slab reheating furnace. Therefore, a mesh-free particle method, smoothed 9

particle hydrodynamics (SPH) is identified in this thesis as an alternative to overcome some of the observed limitations of the mesh-based solvers. SPH is introduced to simulate some of the selected cases to understand the challenges and highlight the limitations. The thesis also contributes to the development of SPH by implementing the energy equation into an open-source SPH flow solver to solve thermal problems. The comparison between the solutions from finite volume and SPH methods presented in this thesis clearly indicates their strengths and limitations for different types of problems. The thesis highlights the current state of different CFD approaches towards complex industrial applications and discusses the future development possibilities. The overall observations and the hypothesis, based on the industrial problems addressed in this thesis, can serve as decision tool for industries to select an appropriate numerical method or tool for solving problems within the presented context. The analysis and discussions also serve as a basis for further development and research to shed light on the use of real-time CFD simulations for improved process control, optimization and diagnostics. 10

Sammanfattning

Energibehovet och miljöpåverkan från industrisektorn är växande problem inom Europeiska unionen (EU) på grund av behovet av att följa den stränga energi- och miljöpolitiken. Optimal processstyrning kan avsevärt förbättra energieffektiviteten hos uppvärmnings- och kylprocesser i många industrier. Styrsystem för processer baserar sig vanligtvis på mätningar och så kallade gray- eller black-box modeller som huvudsakligen bygger på empiriska ko- rrelationer, där de tillfälliga egenskaperna och deras påverkan på kontroll- parametrarna ofta ignoreras. En robust och tillförlitlig numerisk teknik, för att lösa fluidflöde och värmeöverföringsproblem, så som Computational Fluid Dynamics (CFD), som kan ge en detaljerad förståelse för de olika underlig- gande fysikaliska fenomenen, är en nödvändighet för optimering, beslutsstöd och diagnostik av komplexa industriella system. Det finns flera olika alternativ inom CFD-metoder och verktyg, men det är ofta svårt att välja rätt nu- meriska verktyg för att lösa avancerade tekniska problem, särskilt inom indus- triell forskning och utveckling, och konsekvenserna av att välja fel verktyg kan vara mycket kostsamma. Avhandlingen behandlar flera energiintensiva komplexa industriella applikationer. Målet är att identifiera de svårigheter och utmaningar som behöver överkommas när man simulerar dessa applikationer med hjälp av olika CFD-verktyg och -metoder och att diskutera styrkor och begränsningar hos de olika verktygen. Avhandlingen fokuserar på att utföra CFD-simuleringar för ett brett spektrum av industriella applikationer för att belysa och förstå den komplexa olinjära kopplingen mellan fluidflöde, värmeöverföring och andra inneboende fenomen för de undersökta processerna, t.ex. förbränning eller inducerade transienter. De industriella applikationer som studeras i denna avhandling inkluderar kylning av tunna stålplåtar och uppvärmning av stålskivor vid varmvalsning inom stålindustrin, roterande maskiner som elmotorer och generatorer, värmeväxlare och skvalpning i tankar inuti transportfartyg för flytande naturgas. Den nätbaserade CFD-lösaren ANSYS Fluent har använts för att få detaljerade och noggranna lösningar för varje applikation och för att identifiera utmaningarna och begränsningarna. Begränsningarna hos konventionella nätbaserade CFD-verktyg avslöjas när lösningar söks för multipla rums- och tidsskalor som ingår i stora industriella processer. De är inte kapabla att hantera de multipla jetstrålar på en rörlig stålplåt som vi stöter på i kylprocessen av stålplåtar och ofta är de endast delvis framgångsrika, till exempel för industriella värmeugnar. Därför identifieras 11

en nätfri partikelmetod, Smoothed Particle Hydrodynamics (SPH) i denna avhandling som ett alternativ för att övervinna några av de observerade begränsningarna hos nätbaserade lösare. SPH används i denna avhandling för att simulera några av de utvalda fallen för att förstå utmaningarna och belysa begränsningarna. Avhandlingen bidrar också till utvecklingen av SPH genom att implementera energiekvationen i en SPH-ﬂödeslösare, med öppen källkod, för att kunna lösa termiska problem. Jämförelsen mellan lösningarna från nätbaserade och SPH metoder som presenteras i denna avhandling visar tydligt på metodernas styrka och begränsningar för olika typer av problem. Avhandlingen belyser nuvarande CFD-metoder för komplexa industriella applikationer och diskuterar framtida utvecklingsmöjligheter. De övergripande observationerna och hypotesen, baserad på de industriella problem som behandlas i denna avhandling, kan fungera som beslutsverktyg för industrier i att välja en lämplig numeriskt metod eller verktyg för att lösa problem inom den presenterade kontexten. Analysen och diskussionerna utgör också grunden för vidareutveckling och forskning för att belysa användningen av CFD-simuleringar i realtid för förbättrad processkontroll, optimering och diagnostik. 12

List of Papers

This thesis is based on the following papers, which are referred to in the text by their Roman numerals:

I Hosain, M. L., Bel Fdhila, R., Daneryd, A., 2015. Heat transfer by liquid jets impinging on a hot flat surface. Appl. Energy 164, 934-943. II Hosain, M. L., Bel Fdhila, R., Sand, U., Engdahl, J., Dahlquist, E., Li, H., 2016. CFD Modeling of Real Scale Slab Reheating Furnace, in: 12th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, HEFAT2016. III Hosain, M. L., Fdhila, R.B., 2015. Literature Review of Accelerated CFD Simulation Methods towards Online Application. Energy Procedia 75, 3307-3314. IV Hosain, M. L., Bel Fdhila, R., Rönnberg, K., 2017a. Taylor-Couette flow and transient heat transfer inside the annulus air-gap of rotating electrical machines. Appl. Energy 207, 624-633. V Hosain, M. L., Fdhila, R.B., 2017. Air-Gap Heat Transfer in Rotating Electrical Machines: A Parametric Study. Energy Procedia 142, 4176- 4181. VI Hosain, M. L., Rönnberg, K., Bel Fdhila, R., 2017b. Air Flow inside Rotating Electrical Machines: A Comparison between Finite Volume and SPH Method. NAFEMS World Congress, NWC17. VII Hosain, M. L., Sand, U., Fdhila, R.B., 2018. Numerical Investigation of Liquid Sloshing in Carrier Ship Fuel Tanks. IFAC-PapersOnLine 51-2, 583-588. VIII Hosain, M. L., Bel-Fdhila, R., Kyprianidis, K., 2018. Simulation and validation of flow and heat transfer in an infinite mini-channel using Smoothed Particle Hydrodynamics. Energy Procedia 00, 00-00. (Ac- cepted for publication) IX Hosain, M.L., Domínguez, J.M., Crespo, A.J.C., Bel-Fdhila, R., Kypri- anidis, K., 2018. Smoothed Particle Hydrodynamics modeling of transient conduction and convection heat transfer. (Journal Manuscript)

Reprints were made with permission from the publishers. 13

Part of this thesis (Paper I, II and III) was previously included in the Licentiate thesis “Towards Accelerated Simulations for Fluid Flow and Heat Transfer of Large Industrial Processes” (Hosain, 2016). 14

Contents

Page 1 Introduction ...... 1 1.1 Background...... 1 1.2 Research challenges...... 3 1.3 Research framework...... 5 1.4 Objective of the thesis...... 6 1.5 Contributions to knowledge...... 7 1.6 Thesis outline...... 8 2 Literature Review...... 10 3 Methodology ...... 15 3.1 Modelling approach...... 15 3.2 Different approaches in CFD...... 16 3.2.1 Governing equations...... 17 3.2.2 Energy transport equation...... 18 3.2.3 Mixture fraction transport equation...... 18 3.3 Mathematical Models for RANS...... 18 3.3.1 RANS transport equations...... 18 3.3.2 Turbulence transport equations...... 19 3.3.3 Energy transport equation...... 20 3.3.4 Volume of Fluid (RANS-VOF)...... 21 3.4 Mathematical Models for SPH...... 21 3.4.1 SPH form of the governing equations...... 22 3.4.2 Pressure formulation...... 23 3.4.3 Boundary conditions...... 23 3.4.4 SPH thermal implementation...... 24 3.5 Industrial applications addressed using RANS...... 24 3.5.1 Hot rolling process...... 25 3.5.2 Rotating machines...... 30 3.5.3 LNG vessels in carrier ships...... 32 3.6 Industrial applications addressed using SPH...... 33 3.6.1 Rotating machine...... 34 3.6.2 LNG vessel in carrier ship...... 34 3.6.3 Transient heat conduction...... 34 3.6.4 Transient heat convection...... 36 4 Results and discussion ...... 39 4.1 Reynold Averaged Navier-Stokes...... 39 15

4.1.1 Hot rolling process...... 39 4.1.2 Rotating machines...... 45 4.2 Smoothed Particle Hydrodynamics...... 48 4.2.1 Rotating machines...... 48 4.2.2 LNG vessel in carrier ships...... 49 4.2.3 Heat conduction...... 52 4.2.4 Heat convection...... 54 4.3 Discussion...... 56 5 Summary of appended papers...... 62 6 Conclusions ...... 67 7 Future work ...... 69 References...... 71 Appendix...... 79 Papers ...... 81 16

List of Tables

Page

1.1 Relation between the papers and the research questions.....5

3.1 Mesh information for the FVM models...... 33 3.2 Tank sloshing case speciﬁcations...... 35 3.3 Thermal properties of Aluminium and Water...... 36 17

List of Figures

Page

Figure 1.1: Schematic showing the relationship between the research topics and the papers ...... 5

Figure 2.1: Hierarchical classiﬁcation of methods in CFD ...... 11

Figure 3.1: Methodological approach for CFD simulations ...... 16 Figure 3.2: Different approaches of discretization for CFD simulations .. 16 Figure 3.3: Hot rolling process in steel industries ...... 25 Figure 3.4: Single impinging jet 3D model ...... 26 Figure 3.5: Multiple impinging jet 3D model ...... 27 Figure 3.6: Mesh for impinging jet cooling model ...... 27 Figure 3.7: Slab re-heating furnace in 2D ...... 28 Figure 3.8: Furnace model with boundary conditions ...... 29 Figure 3.9: Mesh for the furnace model ...... 29 Figure 3.10: Rotating machine model with boundary conditions ...... 30 Figure 3.11: Mesh for the rotating machine model ...... 31 Figure 3.12: LNG Tank model with dimensions ...... 32 Figure 3.13: SPH models for the rotating machine ...... 34 Figure 3.14: Heat conduction model with discretization ...... 35 Figure 3.15: Mini-channel with boundary conditions ...... 36 Figure 3.16: Numerical discretization for the mini-channel ...... 37 Figure 3.17: Tube bank heat exchanger ...... 38 Figure 3.18: Numerical discretization for the tube bank heat exchanger model ...... 38

Figure 4.1: Schematic of impinging jet cooling ...... 39 Figure 4.2: Interface of water jet for different inlet velocities ...... 40 Figure 4.3: Heat transfer coefﬁcient for different inlet velocities ...... 41 Figure 4.4: Comparison of simulated jet diameter with correlation ..... 41 Figure 4.5: Temperature ﬁeld for single and multiple jets ...... 42 Figure 4.6: Water splashing due to the interaction between jets ...... 42 Figure 4.7: Path lines of velocity inside the furnace ...... 43 Figure 4.8: Iso-surfaces of mass fraction and temperature ...... 44 Figure 4.9: Volume average temperature of the steel slab ...... 44 Figure 4.10: Velocity vectors on cross-section planes inside the motor ... 45 18

Figure 4.11: Average velocity profile in the air-gap of the motor ...... 46 Figure 4.12: Flow and temperature distribution in the air-gap of the motor 46 Figure 4.13: Temperature contour on internal surface of the stator ...... 46 Figure 4.14: Heat transfer coefficient on the rotor surface ...... 47 Figure 4.15: Air velocity profile inside the motor from FVM and SPH model 48 Figure 4.16: Air velocity contours close to the motor wafters ...... 48 Figure 4.17: Velocity profile inside the air-gap of the motor: FVM vs. SPH 49 Figure 4.18: Visualization of tank sloshing at different time instances .... 50 Figure 4.19: Simulated and measured Pressure on the tank wall ...... 50 Figure 4.20: Simulated forces on the tank wall: FVM vs. SPH ...... 51 Figure 4.21: Simulated and Froude-scaled forces on the tank wall ...... 51 Figure 4.22: Temperature contour of heat conduction in aluminium ..... 52 Figure 4.23: Temperature profiles of heat conduction in aluminium ..... 52 Figure 4.24: Temperature contour of heat conduction in water ...... 53 Figure 4.25: Temperature profiles of heat conduction in water ...... 53 Figure 4.26: Velocity and temperature contour in the mini-channel ...... 54 Figure 4.27: Temperature profiles in the mini-channel ...... 54 Figure 4.28: Velocity and temperature field in the tube bank heat exchanger 55 Figure 4.29: Temperature profiles in the tube bank heat exchanger ...... 56 19

Nomenclature

Abbreviations

2D Two dimensions

3D Three dimensions

BC Boundary Condition

CFD Computational Fluid Dynamics

CPU Central Processing Unit

CUDA Compute Uniﬁed Device Architecture

DBC Dynamic Boundary Condition

DNS Direct Numerical Simulation

EU European Union

FDM Finite Difference Method

FEM Finite Element Method

FFD Fast Fluid Dynamics

FMM Fast Multipole Methods

FVM Finite Volume Method

GHG Greenhouse Gas

GPGPU General Purpose Graphic Processing Unit

HPC High Performance Computing

LBM Lattice Boltzmann Method

LES Large Eddie Simulation

LNG Liqueﬁed Natural Gas

LPG Liqueﬁed Petroleum Gas (Propane) 20

MAC Marker And Cell MPI Message Passing Interface OpenCL Open Computing Language OpenMP Open Multi Processing POD Proper Orthogonal Decomposition R&D Research and Development RANS Reynolds Averaged Navier Stokes equations ROM Reduced Order Modelling ROT Runout Table RQ Research Question SPH Smoothed Particle Hydrodynamics SVD Singular Value Decomposition TC Thermocouple VOF Volume of Fluid Symbols C Constant [-] c Speed of sound [m/s]

cp Speciﬁc heat capacity [J/(Kg.K)] Cr Courant number [-] d Nozzle diameter [m] D(Z) Jet diameter [m]

Dh = 2gp, Hydraulic diameter [m]

Dmin Minimum D(Z) [m] dp Particle spacing [m] E Total energy [J] F Force [N] f Mixture fraction [-] 21

f r Frequency [1/s] g Gravitation acceleration [m/s2]

Gk Generation of turbulence kinetic energy due to the mean velocity gradients [-] gp Air-gap width between the rotor and the stator [m] H Height of tank [m] h Smoothing radius [m] h(r) Liquid ﬁlm thickness [m]

H1 Height of initial water level [m]

2 ht Heat transfer coefﬁcient [W/m K] k Turbulence kinetic energy [m2/s2]

L Characteristic length [m]

Nu Nusselt number [-]

Nu0 Nusselt number at stagnation point [-]

ht.d Nu = , Nusselt number based on d [-] d κ

ht.Dh NuD = , Nusselt number based on hydraulic diameter [-] h κ p Pressure [Pa]

Pr Prandtl number [-] q00 Heat ﬂux [W/m2] r Radial position [m] r1 Radius of region I [m] r2 Radius of region II [m] r3 Radius of region III [m] ra Vector position of particle a [m] rb Vector position of particle b [m] rp Distance between two particles [m] 22

uL Re = , Reynolds number [-] ν S Source term [J]

S1,S2 Sensor [-] T Temperature [◦C] t Time [s]

T1 Time for a full roll motion [s] u Velocity [m/s]

u∗ Friction velocity at the nearest wall [m/s]

u0 Fluctuating velocity [m/s]

Uf Fluid velocity at inlet [m/s] W Smoothing kernel function [-]

w Width of tank [m]

x Cartesian axis direction [m]

x1 Distance of S1 from bottom wall of the tank [m]

x2 Distance of S2 from left wall of the tank [m] y Distance to the nearest wall [m] u∗y y+ = , Non-dimensional wall distance [-] ν

YM Contribution of the ﬂuctuating dilatation in compressible turbulence to the overall dissipation rate [-]

Z Distance downward from the nozzle [m]

z0 Distance between nozzle and strip [m]

Zi Elemental mass fraction for element i [-] Special characters

δ Hydrodynamic boundary layer thickness [m]

δT Thermal boundary layer thickness [m]

δi j Kronecker delta [-] 23

ε Turbulence dissipation rate [m2/s3] γ Isotropic constant [-] κ Thermal conductivity [W/m.K] λ Scaling factor [-] µ Dynamic viscosity [kg/m.s] ν Kinematic viscosity [m2/s] ω Speciﬁc rate of dissipation [1/s] φ Viscous dissipation [-] ρ Density [kg/m3] 3 ρ0 Reference density [kg/m ]

τi j Stress tensor [-] θ Rolling angle [degree] Subscripts ε Turbulence dissipation rate ∞ Free stream ﬂuid µ Dynamic viscosity a Particle a b Particle b e f f Effective f Fluid f uel Fuel stream inlet g Gas h Heat k Turbulence kinetic energy m Mass min Minimum ox Oxidizer stream inlet t Turbulent 24 25

1. Introduction

This chapter presents the research background, research questions formulated based on the research gaps, the research framework, objective of the thesis and the contributions to knowledge. The relationship between the research topics and the papers are also presented. This chapter includes the thesis outline and the limitations of the thesis.

1.1 Background Industrial processes and products, e.g. the runout table (ROT) cooling process in hot rolling steel industries (Cho et al., 2008; Mishra et al., 2015; Vakili, 2011), industrial furnaces and boilers (Dong, 2000; Stopford, 2002; Zhang et al., 2010), microchips and power electronics in high voltage products (Soon & Ghazali, 2008; Subramanyam & Crowe, 2000; Winder, 2004), motors and generators (de Almeida et al., 2012; Mecrow & Jack, 2008; Saidur, 2010), and marine applications (Johnson & Andersson, 2016; Vergara et al., 2012; Winebrake et al., 2007) are recognized as some of the major intensive energy consumers in these industries. Many of these processes often rely heavily on non-renewable energy resources. For instance, in hot rolling steel industries, large steel slabs are typically heated in furnaces in which fossil fuels like liquefied petroleum gas (LPG) are used as a primary source for combustion. The steel sector is an important and leading business area in many European Union (EU) countries and has been identified as critical owing to the large amount of greenhouse gas (GHG) emissions (Pardo et al., 2012). Another rapidly growing sector contributing significantly to high energy consumption is electric motors. Electric motors consume half of all electricity in industrialized countries (de Almeida et al., 2012). Within the EU, they consume about 60-80% of energy used in the industrial sector and about 35% in the commercial sector. EU regulations and policies on energy and environment (“EU Commission Regulation (EC) No 640/2009”, 2009) are targeting a strong reduction in the impact of GHG emissions on the environment (Patyk, 2013; Saidur, 2010). Optimizing existing products and improving process control for industries has a necessity to reduce energy consumption and GHG emissions. Energy- intensive processes or products often involve a wide range of complex multi- physical phenomena that a control system tends to govern towards optimum operations. The physical phenomena in the industrial processes and products

1 26

discussed in this thesis involve turbulent flow and heat transfer. The detailed dynamic behavior of complex fluid flow and heat transfer and their influence on the control parameters are generally not taken into account in control systems that rely on measurements, black box models or empirical correlations. For example, in the re-heating furnace in a steel plant (Hosain et al., 2016), large slabs inside the furnace are heated to about 1250 ◦C by following a predetermined temperature profile. The heating profile must be adhered to in order to achieve a specified quality of steel. The pre-heating zone in the furnace is roughly 20 m long, 11 m wide and 10 m high, and between 6 and 10 thermocouples are placed very close to the roof and the side walls to measure the gas temperature. The measurements are then used in the control system to estimate the surface and average temperature of the slabs. The question is, how reliable and efficient can the control system be, given that it mostly relies on a data-fitting approach based on a few measurement points? The best choice would be to directly measure the surface temperature of the slab; however, this is currently impossible owing to the limitations of the available thermocouple technologies. Process control, such as the system described above, can be improved by employing more advanced models and methods such as computational fluid dynamics (CFD), which are capable of providing all the necessary input details and features. CFD is a very robust tool for analyzing the flow and heat transfer accurately. It can provide detailed insight into processes in which complex and fully non-linear phenomena may be present. High fidelity simulations based on CFD can be used to evaluate the current performance, improve online control and help optimize operation of industrial processes. How- ever, it is often very challenging to perform CFD simulations for large industrial processes and complex products. This is due to the existence of multiple space and time scales in the industrial processes and the limitations of the numerical techniques. In conventional CFD methods, the numerical domain is discretized using mesh elements, and the accuracy of the model is completely dependent on the quality of the mesh and the physical, chemical and mechanical phenomena involved. The mesh generation is often the most important and time-consuming pre-processing step for the mesh-based CFD solver. Moreover, the mesh needs to be locally refined in order to resolve interesting local features. The presence of microscale features (e.g. boiling, combustion) and macroscale features (e.g. burners in the furnace or water jets at the ROT cooling process in industrial processes make it very challenging to generate a suitable mesh and perform simulation within a useful timeframe for the results to be used in the design steps or in online control. In many cases, a very coarse mesh is applied to simulate the whole process to obtain an overall flow pattern; however, this approach sacrifices accuracy by neglecting small-scale features (Huang et al., 2008; J. G. Kim et al., 2000; Morgado et al., 2015). Despite several limitations, CFD simulations are still commonly used to model, analyze and improve industrial flow and heat transfer applications. CFD simulations

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can also be used in the online control tool by running the simulations in real time, considering coarse discretization, where the relative effect of different control parameters on the process performance, rather than absolute accuracy, is the main concern. Another possibility may be to create a lookup table from a series of offline CFD simulations, and use the lookup table to control the process. A further option is to simplify the process geometry by applying appropriate boundary conditions when possible, and simulate a small section of the process to get an accurate solution (Hosain et al., 2016). Recent technological development of parallel computing devices has significantly improved the numerical performance of conventional mesh-based CFD solvers. Despite this improved performance, simulating the whole process in detail by resolving the local flows using mesh-based commercial CFD solvers remains beyond reach. Mesh-free CFD methods based on simplified physics can be an alternative for overcoming some of the limitations of conventional mesh-based solvers. Smoothed Particle Hydrodynamics (SPH) has been identified as a potential mesh-free particle-based method in this thesis, mainly due to its mesh-free feature, flexibility, fast-solving capability and good support for visualization. The attraction of SPH is that it provides the opportunity for easy balancing of the speed and accuracy of the simulation, which is a very big advantage from the online control perspective. However, the main idea in this thesis is not to replace mesh-based methods with mesh- free particle-based methods, but to complement them, or choose the best methods to fit the purpose. The theories behind the mesh-based and the mesh-free methods employed in this thesis are explained in detail in chapter3.

1.2 Research challenges The most popular methodology used to address industrial applications using CFD simulations uses the mesh-based finite volume method (FVM), where the Reynolds Averaged Navier–Stokes (RANS) equations are discretized and solved in commercial or open-source packages. This is mainly because of the well-established knowledge of the approach and its applicability to a wide range of engineering fields. FVM-based CFD solvers are very robust for solving complex problems related to multiphase flows and heat transfer. They are mesh-based solvers and have been widely used to solve very complex problems for several decades. However, solving industrial problems involving high deformation, multiple solid movements with strong and complex fluid–solid or fluid–fluid interactions remains a big challenge for such solvers and the overall approach. Industrial problems with fluid–fluid or fluid–solid interactions require extra care during the mesh generation phase. The limitations, difficulties and challenges in solving complex industrial problems have not been rigorously discussed in the literature.

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Mesh-based methods are used successfully to simulate large processes such as full 3D furnaces (Huang et al., 2008; Marino et al., 2002; Morgado et al., 2015). However, in these cases the detailed combustion chemistry and the local geometrical details are ignored. To date, no 3D simulations have been published for industrial processes based on FVM that cover both microscale and macroscale features. Particle-based methods such as SPH (Auer, 2008; Krog & Elster, 2012) are gradually emerging and gaining popularity in the CFD community because of their fast solving capability, flexibility and simplicity. The SPH approach is currently being widely used for visual fluid and thermal effects in films and video games, where accuracy is not very important. Recent developments in SPH towards engineering applications, the level of accuracy achieved and the diversity of its applicability (J. Monaghan, 2012) have opened doors for new types of industrial applications (Shadloo et al., 2016). The SPH user community is small and growing, thus the propagation and development of this method towards industrial applications has been slow compared to other, conventional methods. The types of industrial applications of interest in this thesis have not been previously addressed by the SPH user community. Therefore, the limitations and challenges of SPH for many industrial applications are still unknown due to lack of study. As mentioned earlier, the learning curve is one of the limiting factors for use of emerging methods such as SPH for industry. Recently, in their SPH studies, Shadloo et al. (Shadloo et al., 2016) demonstrated that its diverse applicability (J. Mon- aghan, 2012) has a lot to offer for industrial applications. Special attention and substantial efforts are required from scientists and R&D engineers to enlarge the capability of SPH for new types of applications. Furthermore, comparisons between different methods aimed at selecting the right method for a particular application needs to be addressed. Based on the research challenges and the knowledge gap discussed above, three research questions (RQ) are formulated in this thesis:

• RQ1 What are the limitations of RANS when used to simulate complex industrial applications?

• RQ2 Under what circumstances can SPH replace or complement RANS?

• RQ3 What is the potential of using SPH in on-line control tools?

The research questions are formulated in a general manner, however, the conclusions are based on selected applications within the research framework (section 1.3). The research questions are discussed in detail together with con- cluding remarks in section 4.3.

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Table 1.1: Relation between the papers and the research questions

Research question Papers RQ1 I,II,III,IV,V RQ2 VI,VII,VIII,IX RQ3 VII

Fluid Flow and Heat Transfer Simulations for Complex Industrial Applications

Eulerian Vs. Lagrangian

FVM SPH Paper I Cooling at ROT

Slab reheating Paper II furnace

Literature review Paper III

Rotating machines: Paper IV Taylor-couette flow Rotating machines: Paper V Parametric analysis

Rotating machines: FVM vs. SPH Paper VI

Liquid sloshing in Tank Paper VII

Heat transfer in mini-channels Paper VIII

SPH Thermal model Paper IX

Figure 1.1: Schematic showing the relationship between the research topics and the papers

1.3 Research framework The work in this thesis mainly aims to use CFD to solve energy-intensive complex industrial processes, where ﬂow and heat transfer problems are critical. The work is performed in tight collaboration with several industries to deﬁne the current challenging cases that need to be studied. The industrial applica-

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tions studied in this thesis are the ROT cooling process, presented in Paper I, the slab reheating furnace in hot rolling steel plant, investigated in Paper II, the electric motor, studied in Papers IV, V and VI, and the tank sloshing in a LNG carrier ship, presented in Paper VII. The studied problems cover both single and multi-phase flows. The cases also cover heat transfer in the form of conduction, convection and radiation, as well as combustion. In the first stage of this work, the industrial applications are solved using the Eulerian mesh-based finite volume RANS CFD solver ANSYS Fluent. This task was performed to underline the limitations of RANS and highlight the challenges of simulating large and complex industrial applications. To overcome some of the observed limitations of RANS, the search is directed towards finding alternative methods that are more flexible and faster compared to RANS methods (Paper III). In the later stage of this work, the Lagrangian particle method SPH is identified as a potential alternative to compensate for some of the weaknesses of RANS methods. To evaluate the applicability and the performance of the SPH solver for industrial problems, the rotating machine (Paper VI) and tank sloshing (Paper VII) cases are simulated to benchmark the SPH solutions with the solutions from the finite volume solver. Finally, the research work is directed towards SPH development, where the energy equation is implemented in the open-source SPH code DualSPHysics to simulate thermal problems. To validate the thermal implementation in Du- alSPHysics and to illustrate its accuracy, several laminar heat transfer cases, heat transfer in infinite mini-channel (Paper VIII) and heat transfer in heat exchangers (Paper IX) are simulated. The included scientific papers (Paper I - Paper IX) are briefly summarized in chapter5. The appended papers can be linked to the research questions presented in section 1.2 and to the research topic as illustrated in Table 1.1 and Figure 1.1, respectively. The analysis presented in this thesis is limited to the studied cases presented in the included papers. The research questions are answered in this thesis mainly based on the observations and hypotheses made in the appended papers. The answers to the research questions are presented in section 4.3 in the form of a discussion, which is limited to the studied cases. However, the observations illustrated in this thesis may serve as a decision tool to select a suitable CFD approach to deal with the type of industrial problems analyzed within this framework.

1.4 Objective of the thesis The overall objective of the thesis is to perform high fidelity fluid flow and heat transfer simulations for several industrial processes and products to better understand the underlying physical phenomena, to identify a few energy-intensive processes and products to numerically investigate in detail

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using the most popular CFD methods in commercial packages, and highlight the challenges and their limitations. Another key objective of this thesis is to identify alternative CFD methods that are suitable and sufficiently flexible for use in different industrial applications, to overcome some of the limitations of conventional CFD methods. Furthermore, the thesis aims to discuss the potential use of CFD simulation from a real-time application perspective and shed light on online process control using high fidelity simulations.

The goals of the thesis can be explicitly described by the following points:

• To build CFD models for selected energy-intensive processes and products related to multiphase ﬂow, free-surface ﬂow and heat transfer. Moreover, to validate the results using analytical solutions or available data from published literature (RQ1).

• To discuss the usefulness and limitations of the methods commonly used in commercial CFD packages (RQ1).

• To ﬁnd alternative methods that can overcome the underlying limitations of RANS methods for industrial applications (RQ1).

• To introduce SPH for industrial ﬂow and heat transfer simulations and discuss the current limitations (RQ2).

• To discuss the type of applications where SPH can be used for online process control purposes (RQ3).

1.5 Contributions to knowledge The main contribution of this doctoral research is towards the industrial applications. The thesis also contributes to scientific knowledge from both the fundamental and applied perspective. Selected energy intensive industrial processes are investigated using high fidelity CFD simulations, the difficulties and challenges are highlighted and possible ways to overcome these are discussed.

The overall contribution of the thesis can be brieﬂy summarized as follows:

• Performing high fidelity simulations of selected energy-intensive processes and products to provide detailed insight to enhance the understanding of the underlying complex fluid flow and heat transfer phenomena. The simulated applications involve ROT cooling in hot rolling

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steel industries, slab re-heating furnace, sloshing dynamics in carrier ships fuel tanks, rotating machines, and heat exchangers.

• Discovering unknown phenomena involved in the studied industrial applications and presenting hypotheses. Discussing and highlighting the difﬁculties and challenges involved in simulating such industrial processes using different CFD approaches.

• Performing sensitivity analysis to evaluate the impact of different control parameters on thermal performance.

• Providing the state of the art by reviewing literature relevant to the studied topics in this thesis. Performing a literature survey and classifying available CFD methods applicable to different types of industrial and engineering applications from a real-time simulation perspective.

• Introducing and using SPH for industrial ﬂow and heat transfer applications and evaluating its potential usefulness to thermal problems. Discussing the challenges and limitations of SPH for industrial thermal simulations and indicating future directions based on these observations.

• Implementing SPH thermal equations in an open-source SPH-based CFD solver, DualSPHysics, using C++. Using and validating the SPH thermal implementation by solving thermal problems related to heat conduction and convection. Discussing the limitations of SPH for thermal problems. Highlighting the future challenges to simulating complex industrial ﬂow and heat transfer.

1.6 Thesis outline This thesis is written based on the appended papers and contains the following chapters:

Chapter 1 Introduction This chapter presents the research background, research questions formulated based on the research gaps, the research framework, objective of the thesis and the contributions to knowledge. The relationship between the research topics and the papers are also presented. This chapter includes the thesis outline and the limitations of the thesis.

Chapter 2 Literature review This chapter presents a literature review in the ﬁeld of multiphase ﬂows and heat transfer to illuminate the state of the art of the selected in-

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dustrial applications. It also presents a literature review on available advanced CFD methods. Chapter 3 Methodology This chapter presents a detailed explanation of the overall methodology to address an industrial application using the CFD approach. All the numerical models for the simulated cases and the governing equations are presented. Chapter 4 Results and discussion This chapter presents the key results from the performed simulations and provides a detailed discussion of the studied topic while answering the research questions. Chapter 5 Summary of appended papers This chapter summarizes the included papers and the author’s contribution to the papers. Chapter 6 Conclusions This chapter presents the major conclusions of the thesis. Chapter 7 Future work This chapter suggests the potential future direction of the research topic presented in this thesis.

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2. Literature Review

This chapter presents a literature review in the ﬁeld of multiphase ﬂows and heat transfer to illuminate the state of the art of the selected industrial applications. It also presents a literature review on available advanced CFD methods.

CFD simulation techniques have been used to solve a variety of industrial fluid flow and heat transfer problems for several decades. The area of interest of the research presented in this thesis is to solve engineering problems related to single-phase and multiphase flows and heat transfer. The literature review presented in this chapter mainly covers literature in this context, while providing a broad perspective on applicability of different CFD methods to industrial applications. The extent of applicability of CFD simulations to industrial applications is completely dependent on the physical phenomena and the time scale associated with the application. Industrial processes and products are often so large and complex that it becomes too difficult to solve them numerically using CFD techniques. The recent developments of high-performance computing (HPC) resources have revolutionized the usage of CFD simulation for large and complex problems. Today, the use of HPC with supercomputers is the most common approach for CFD engineers. The algorithms involved in the methods are usually parallelized so that simulations can be run in parallel using supercomputers with multicore architecture. Nevertheless, simulating entire processes such as ROT cooling or the furnace using CFD while resolving microscopic features like boiling and combustion, remains unapproachable with currently available computing capabilities. The only way to overcome this limitation at present is to simplify the models and use methods with simplified physics. This thesis explores the applicability, capability and efficiency of different CFD methods for complex engineering problems from a perspective of increasing the speed of simulation. There are two classes of CFD methods; these are the Eulerian approach and Lagrangian approach. In the Lagrangian approach, fluid is represented by a set containing a large number of particles that possess properties such as mass, velocity and temperature. All the particles are then traced along the flow and the time evolution of different properties is calculated based on the interactions between the particles. In the Eulerian approach, the fluid is represented by using control volumes as mesh elements whose coordinates are fixed. The fluid

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flowing through these control volumes is observed and fluxes are calculated to measure the rate of change of properties such as velocity and temperature. Methods developed based on the Eulerian approach are called mesh-based methods, and methods developed based on the Lagrangian approach are called mesh-free particle methods. Both classes of methods have pros and cons. The mesh-free characteristic is one of the biggest advantages of Lagrangian CFD methods for R&D engineers, as meshing is the most time-consuming and challenging pre-processing phase for Eulerian CFD solvers. In recent decades, researchers have developed methods that combine Lagrangian and Eulerian frameworks to complement the weaknesses of both classes. These methods are classified as hybrid methods (Figure 2.1).

● Finite Volume Method (FVM) Conventional ● Finite Difference Method (FDM) Methods ● Finite Element Method (FEM) ● Spectral Methods

● Reduced Order Modeling (ROM) Mesh ▪Proper Orthogonal Decomposition(POD) Based Methods ▪ Singular value Decomposition (SVD) ● Marker & Cell (MAC)

CFD ● Smoothed Particle Hydrodynamics(SPH) Advanced ● Fast Multipole Method (FMM) Mesh free Numerical ● Method of Fundamental Solutions (MFS) Methods methods ● Finite Pointset Method (FPM) ● Moving Particle Semi-Implicit Method(MPS)

● Fast Fluid Dynamics (FFD) Hybrid ● Particle in Cell Method (PIC) Accelerated Methods methods ● Vortex in Cell Method (VIC) ● Lattice Boltzmann Method (LBM)

● MPI CPU ● OpenMP ● Cloud Computing ● CUDA Hardware Parallel Techniques programming GPGPU ● OpenCL ● Cloud Computing

CPU+GPGPU

Figure 2.1: Hierarchical classiﬁcation of methods in CFD (Hosain & Fdhila, 2015)

Mesh-based conventional methods are the most well-established and popular methods, and are mature enough to handle complex problems with high accuracy. These methods are extremely reliable, however they come at a very high numerical cost, which limits their use in ﬂuid ﬂow and heat transfer simulations for large industrial processes. Therefore, simulations using these methods are only used for small-scale problems (Mazumder & Lu, 2013).

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Large industrial processes have also been addressed using FVM in Huang et al.(Huang et al., 2008) and Morgado et al.(Morgado et al., 2015); however, these have performed poorly from a speed perspective. Mathematically simplified mesh-based methods like reduced order modelling (ROM) (Lappo & Habashi, 2009; Lieu et al., 2006) can, in many cases, provide enhanced numerical performance, and enable simulations to be performed in real time. How- ever, the accuracy is usually reduced in such applications. Therefore, when using mesh-based methods, one needs to balance the speed and accuracy of the simulations. The main drawback, however, is that the entire workflow, including mesh generation, needs to be repeated to tune the accuracy and speed, making this a less user-friendly option for R&D engineers. On the other hand, mesh-free particle-based CFD methods have several advantages over mesh-based solvers. Due to the inherent Lagrangian properties, the convection of the particles happens due to the interaction forces, therefore the equations involved in this approach are simpler than those in mesh-based solvers. The most popular method in this class is the SPH method, mainly due to its simplicity, flexibility and promising performance. The SPH method produces satisfactory results for problems involving disruptive free surfaces, multiple fluids, elastic fracture, thermal matter diffusion and chemical precip- itation (J. Monaghan, 2012). It can also be applied to physiological problems such as soft tissue and blood flows. SPH is known to be robust for free-surface and multiphase flows (J. Monaghan, 2012; Randles et al., 2016). This is because, for free-surface flow, such as the impinging jet problem and sloshing in a tank, there is no need to solve the two phases (air and water) to identify the interface between them. The surface tension of the water itself creates the air– water interface. SPH has recently been used to solve a wide range of industrial applications (Shadloo et al., 2016). The recent diverse applications (Shadloo et al., 2016) of SPH include mainly aerospace (Ortiz et al., 2004; Siemann & Groenenboom, 2014), car and automotive (Barcarolo et al., 2014; Oger et al., 2009), energy production, e.g. marine (Baeten, 2009; Hosain et al., 2018), oil and gas (Violeau et al., 2007), hydropower (Manenti & Ruol, 2008; Tomas- icchio et al., 2012) and industrial processing, for example, casting, grinding, high speed cutting, mixing and separation, friction stir welding, solidifica- tion, oxidation, droplet breakup and spray coating (Shadloo et al., 2016). The SPH method is not a suitable choice for problems with high Reynolds number turbulent flows, steady flows, slow dynamic flows and flow without complex interfaces (Shadloo et al., 2016). This is because the SPH method still requires development in several modules, e.g. robust boundary conditions and turbulence. The SPH method is still far from being well-established enough to replace the mesh-based FVM solver. However, in its current state, the flexibility of SPH has a lot to offer the industrial applications. Hybrid methods are also of interest for free-surface flows, multiphase flows and heat transfer simulations. In recent developments, researchers have been trying to combine different methods to develop new methods that combine

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benefits from both Eulerian and Lagrangian frames of reference. An example of these is fast fluid dynamics (FFD), as used by Zuo and Chen (Zuo & Chen, 2009, 2010) to simulate air flow inside buildings in real time. Another method, Lattice Boltzmann Method (LBM), solves the Boltzmann equation instead of the Navier Stokes equations and is popular for thermal problems. Geveler et al.(Geveler, Ribbrock, Mallach, & Göddeke, 2011) implemented LBM to solve various complex fluid flow cases, achieving real-time performance. This literature review demonstrates that there is no unique recipe or method that can work for all types of industrial flow simulations. Mesh-based solvers are reliable, robust and have a well-known degree of accuracy; however, they are numerically too demanding to be used for large industrial processes. On the other hand, the mesh-free and hybrid methods are very flexible and easy to use. However, the knowledge gap on applicability, accuracy, stability and convergence rate limits their extensive use in industrial R&D. Therefore, the application of mesh-free and mesh-based methods for large industrial applications remains a dilemma. In this thesis, the conventional mesh-based FVM solver is used to analyze flow and heat transfer for selected industrial applications. The results presented in this thesis provide detailed insight into each simulated application. The difficulties and challenges involved in simulating industrial processes are highlighted based on the experiences gathered from the performed simulations. Hypotheses are formulated, based on the results of the simulations, on how to use the simulation results to improve the processes. The promising flexibility of the SPH method and its diverse applications inspires its usage for industrial heat transfer simulations. One of the goals of the thesis is to introduce and use SPH for industrial heat transfer simulations; however, no commercial or open-source SPH thermal solver is currently available. A small number of thermal simulations (Cleary, 1998; Rook et al., 2007; Sigalotti et al., 2003; Szewc et al., 2011) based on SPH have been performed; however, these do not comprehensively cover the knowledge of applicability of SPH for industrial heat transfer applications. Within the framework of this thesis, in Pa- per IX, as a first step towards using SPH for industrial heat transfer simulation, the energy conservation equations are implemented into an open-source SPH flow solver called DualSPHysics (Crespo et al., 2015). The SPH thermal implementation is used to solve a few classical CFD problems, and the solutions are validated using analytical solutions. The solutions from the SPH thermal solver are also compared with the solution from the FVM solver to benchmark the solutions. The challenges faced and the limitations observed while using the SPH thermal solver are discussed. Moreover, method comparison is also one of the key focuses of this thesis for evaluating the efficiency of different methods for industrial applications. The SPH thermal solver will be released in future as an open-source package for the SPH user community to open up the area of thermal simulations using SPH. The main idea behind this development is to have a flexible thermal solver, the accuracy and speed of which can

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be adjusted easily to fit the demand of a specific industrial process. In future, the results from both the SPH and FVM thermal solvers could be combined to synthesize the knowledge of a process from both overall and detailed solution perspectives. The SPH thermal solver and the FVM thermal solver can both be used where they fit best, in complementary fashion. For example, some parts of the process can be simulated using the SPH thermal solver, and other parts of the same process can be simulated using the FVM thermal solver. The results can then be combined for a full picture of the process. This development is a small step towards the future goal of this work, which is to direct research towards real-time simulations for industrial processes. The ultimate goal will be to use CFD simulation in online control tools for decision support and to operate the processes in an energy-efficient way.

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3. Methodology

In this chapter, the approach to performing the CFD simulations for industrial processes is illustrated. The theories and models are also presented in detail.

3.1 Modelling approach A methodological approach is followed in this thesis to simulate and analyze the industrial applications. The approach can be divided into the following four main steps (Figure 3.1).

Step 1. A background review is performed to understand the research area and to gather information on related works published by other researchers before proceeding. The process is then analyzed in detail and the scope and the expected outcome from the numerical study are defined based on the formulated hypothesis. To reach the defined goal, sufficient information is generated about the process to be able to build the numerical domain and to select the most realistic boundary conditions.

Step 2. The numerical domain is developed based on the information col- lected in the previous step; the domain is then discretized using mesh or particles depending on the chosen CFD approach. Suitable mathematical models are then employed to solve a well-deﬁned problem.

Step 3. After obtaining the ﬁrst solution, post-processing is performed. A mesh grid-sensitivity analysis is also performed to ensure that the solution is grid-independent in the case of mesh-based solvers. The ﬁnal solution is then validated using available theories, experiments or measurements. If the results are not valid, then the model is revisited to make possible adjustments and step 2 is repeated.

Step 4. The valid results are then analyzed and hypotheses are made based on the simulation results. Detailed insight regarding the process is provided and possible improvements are suggested based on the phenomena re- vealed by the simulations.

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Background review Model Development Solve & Post-process Analyse CAD Process analysis Validate results Hypotheses Make hypotheses

Discretise

Boundary & Physics

Figure 3.1: Methodological approach for CFD simulations

3.2 Different approaches in CFD

Particle i Influence domain

Ω Ω

(a) (b) Figure 3.2: Different approaches of discretization for CFD simulations (a) Mesh (b) particles

Two different approaches, based on Eulerian and Lagrangian reference frames, respectively, are used in this thesis to perform high fidelity CFD simulations for industrial applications. The CFD methods developed based on the Eulerian reference frame are called mesh-based methods. In this approach, the numerical domain Ω is discretized using mesh elements (Figure 3.2a) and a set of highly nonlinear equations, the Navier–Stokes equations (section 3.2.1), are solved over all the mesh elements. In this thesis, the time-averaged versions of the original Navier–Stokes equations, RANS equations are solved. This idea, where the Reynolds decomposition is applied to separate the flow variables into mean (time-averaged) and fluctuating

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components to derive the RANS equations, was proposed by Reynolds Osborne (Reynolds, 1895). The RANS equations are principally used to describe turbulent flows, this is the most common way to model turbulent flows in most commercial CFD packages. There are other approaches, such as DNS (direct numerical simulations) and LES (large eddie simulation), to solve the Navier–Stokes equations. However, both of these approaches are numerically much more demanding than the RANS approach, and are therefore not a preferred option for large problems in industrial R&D. The equations involved in the RANS modelling approach are presented in detail in section 3.3. The most popular mesh-based FVM method is employed in this thesis. CFD methods developed based on the Lagrangian reference frame are called mesh-free particle-based methods. In this approach, the fluid is represented by a set of fluid particles (Figure 3.2b) that have properties like mass, position, velocity and temperature. The original set of Navier–Stokes equations is solved in this approach; however, the convection of the particles occurs automatically due to the interaction forces between the particles. Thus, the nonlinear convective terms in the original Navier–Stokes momentum equations (section 3.2.1) are neglected. The most popular Lagrangian mesh-free particle method, SPH, is employed in this thesis. The Navier–Stokes equations are approximated using SPH kernel approximation operators, thus the SPH form of the equations are solved. The equations involved in the SPH modelling approach are presented in detail in section 3.4.

3.2.1 Governing equations A system of transport equations employed to model any ﬂuid ﬂow mainly involve the conservation of mass and momentum. Additional equations must also be solved; for example, the energy conservation equation, to model the heat transfer, turbulence equations, to model the turbulence, and species transport equations, for combustion. The mass and momentum equations are presented below. The mass conservation equation can be written as follows:

∂ρ ∂ + (ρui) = 0 (3.1) ∂t ∂xi

The momentum conservation, in the original Navier–Stokes equation, is described by the following equation: ∂ ∂ ∂ p ∂ ∂ui (ρui) + (ρu jui) = − + µ +Fi (3.2) ∂t ∂x j ∂xi ∂x j ∂x j | {z } | {z } convective term diffusive term

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where, ρ is density, ui is velocity in tensor notation, p is pressure, µ is dynamic viscosity and Fi is external force.

3.2.2 Energy transport equation The energy conservation equation can be expressed as follows:   ∂T ∂T  ∂ ∂T ρcp  + ui  = κ + φ (3.3)  ∂t ∂xi  ∂xi ∂xi | {z } convective term

where, T is thermal energy, cp is speciﬁc heat capacity, κ is thermal conductivity and φ is the viscous dissipation or the rate of internal heat generation per unit volume.

3.2.3 Mixture fraction transport equation The mixture fraction concept is applied in Paper II to model the combustion, under the assumption of equal mass diffusivities of the species involved in the system. The individual species transport equation is then reduced to a single Zi − Zi,ox transport equation for the mixture fraction f = as follows: Zi, f uel − Zi,ox ∂ ∂ ∂ µ ∂ f (ρ f ) + (ρui f ) = + Sm + Suser (3.4) ∂t ∂xi ∂xi σ ∂xi

where, µ is viscosity and σ is a constant.

3.3 Mathematical Models for RANS The computational transport equation systems, the RANS equations, employed to model the ROT cooling (Paper I), the slab re-heating furnace (Paper II), the rotating machines (Paper IV - Paper V) and sloshing in tank (Paper VII) are presented in this section.

3.3.1 RANS transport equations RANS is a time averaged version of the original Navier–Stokes equations presented in section 3.2.1. Reynolds decomposition (Reynolds, 1895) is applied to decompose the flow variables into mean (time-averaged) and fluctuating components to derive the RANS form of the governing equations. The decom- 0 0 position of flow variables gives rise to a special nonlinear term (−ρui u j ) in the momentum conservation equation, called the Reynolds stress term, which

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requires additional modelling to close the RANS equations. This Reynolds stress term is mainly responsible for the modelling of turbulent quantities, which gives rise to many turbulence models, for example, two equation models, like k − ε or k − ω turbulence models. The model equations for k − ε and k − ω turbulence models are presented in section 3.3.2. The RANS version of the momentum conservation equations can be written as follows:

∂ ∂ ∂ 0 0 ∂ p ∂ (ρui) + (ρu jui) + ρui u j = − + τi j + Fi (3.5) ∂t ∂x j ∂x j ∂xi ∂x j

where, u and u0 represents the time-averaged and the ﬂuctuating velocity, respectively. The diffusion term is rewritten using the Newtonian ﬂuid stress tensor τi j, where τi j is modelled as follows: ∂ui ∂u j 2 ∂uk τi j = µ + − δi j (3.6) ∂x j ∂xi 3 ∂xk

0 0 The Reynolds stress term (−ρui u j ) is deﬁned as, 0 0 ∂ui ∂u j 2 ∂uk −ρui u j = µt + − ρk + µt δi j (3.7) ∂x j ∂xi 3 ∂xk

where, µ and µt are laminar and turbulent viscosity, respectively.

3.3.2 Turbulence transport equations 0 0 The Reynolds stress term (−ρui u j ) can be modelled in various ways. In this thesis, two different turbulence models, the k − ε and the k − ω models are employed.

3.3.2.1 k − ε turbulence model Industrial ﬂow problems are most often turbulent and thus require the turbulence to be modelled by modelling the Reynolds stress term in the momentum equation. There are several options of turbulence models available in the sci- entiﬁc literature. The k − ε model (Launder & Spalding, 1974) is the most robust and economic turbulence model for industrial processes (Li et al., 2017). The k−ε turbulence models are employed to model the turbulence in the simulations of the ROT cooling process (Paper I), the furnace (Paper II) and the rotating machines (Paper IV - Paper VI). The equations describing the turbulence kinetic energy (k) and the turbulence dissipation rate (ε) are as follows:

∂ ∂ ∂ µt ∂k (ρk) + (ρku j) = µ + + Gk − ρε −YM (3.8) ∂t ∂x j ∂x j σk ∂x j

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2 ∂ ∂ ∂ µt ∂ε ε (ρε) + (ρεu j) = µ + + ρC1Sε − ρC2 √ ∂t ∂x j ∂x j σε ∂x j k + νε (3.9)  k p  2 2Si jSi j k ε where turbulence viscosity µt = ρCµ , C1 = max0.43, , ε  k p  2Si jSi j + 5 ε C2 = 1.9, σk = 1.0 and σε = 1.2 (ANSYS Inc., 2018).

3.3.2.2 k − ω turbulence model The SST k − ω turbulence model developed by (Menter, 1994) is used for the simulation of liquid sloshing in a rectangular tank (Paper VII). This turbulence model provides both robustness and stability in this type of process. The following equations represent the transport of the turbulent kinetic energy (k) and the vorticity (ω), respectively.

∂ ∂ ∂ ∂k (ρk) + (ρku j) = Γk + Gk −Yk (3.10) ∂t ∂x j ∂x j ∂x j

∂ ∂ ∂ ∂ω (ρω) + (ρωu j) = Γω + Gω −Yω + Dω (3.11) ∂t ∂x j ∂x j ∂x j

µt The effective diffusivity terms for k and ω are given by: Γk = µ + and σk µt ∗ ρk Γω = µ + , respectively. The turbulent viscosity is given by: µt = α , σω ω ∗ where α is a low Reynolds number region correction dampening factor. Gk, represents the generation of turbulence kinetic energy due to mean velocity gradients. Yk, represent the dissipation rate of k. Gω , represents the generation of ω. Yω , represent the dissipation rate of ω. Dω , is the cross-diffusion term related to Γk and Γω .

3.3.3 Energy transport equation The energy transport equation (3.3) is usually written in the form of total energy as follows (ANSYS Inc., 2018):

∂ ∂ ∂ ∂T (ρE) + [ui (ρE + p)] = κe f f + ui (τi j)e f f + Sh (3.12) ∂t ∂xi ∂x j ∂x j

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µt where E is the total energy, κe f f = κ + cp is the effective thermal con- Prt ductivity, Sh is heat of the chemical reaction and (τi j)e f f is the deviatoric stress tensor, deﬁned as ∂ui ∂u j 2 ∂uk (τi j)e f f = µe f f + − µe f f δi j (3.13) ∂x j ∂xi 3 ∂xk

3.3.4 Volume of Fluid (RANS-VOF) The volume of fluid (VOF) model is in principle an interface-tracking method integrated into the RANS model as it is formulated in the CFD commercial code ANSYS Fluent (ANSYS Inc., 2018). This is a very robust approach for simulating multiphase flows. This approach is employed in this thesis to simulate the multiphase flow simulations, the ROT cooling (Paper I) and the liquid sloshing in tank (Paper VII). In this formulation, each phase has its individual continuity equation, however both phases share the same set of momentum equations. For RANS–VOF, the continuity transport equation, also called the volume fraction equation, for the gas phase is given by (ANSYS Inc., 2018): 1 ∂ ∂ (αgρg) + αgρguig = 0 (3.14) ρg ∂t ∂xi

where αg, ρg and uig are the volume fraction, the density and the velocity of the gas phase in tensor notation, respectively. The interpolation near the liquid–gas interface surface is calculated by using the geometric reconstruct method developed by Youngs (Youngs, 1982). The method assumes that the interface between two ﬂuids has a linear slope within each cell, and uses this linear shape to calculate the advection of ﬂuid through the cell faces. This method is the most accurate method currently available in ANSYS Fluent. In the RANS–VOF approach, the momentum equation presented in section 3.3.1 is solved, and the same equation is solved for both phases.

3.4 Mathematical Models for SPH SPH is simply an interpolation method where any function can be evaluated by using the values of different properties of a set of particles. This section presents the SPH form of the governing equations presented in section 3.2.1, together with the necessary fundamentals to illustrate the SPH methodology.

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3.4.1 SPH form of the governing equations The basic principle of SPH is to approximate any function A(r) by the discrete integral interpolants using smoothing kernel function W(r,h) as follows:

Ab A(ra) = ∑mb W(ra − rb,h) (3.15) b ρb

where, the summation is calculated over all the particles b within the smoothing radius h. Equation (3.15) is then used to calculate gradient, divergence and vorticity of different physical properties. The SPH form of the mass conservation equation presented in section 3.2.1 can be expressed as follows:

∂ρa ∂Wab = −∑mb(ub − ua) (3.16) ∂t b ∂xi

The convective term in equation (3.2) is excluded in the SPH version of the momentum conservation equation, since the convection happens automatically due to the interaction forces between the particles. Thus the momentum conservation equation in the SPH form can be written as follows:

∂ua pb pa ∂ ∂ ∂ui = −∑mb 2 + 2 W(ra − rb,h) + ν +g (3.17) ∂t b ρb ρa ∂xi ∂x j ∂x j | {z } diffusion term

There are two different ways to model the viscous diffusion term available in the DualSPHysics software (Crespo et al., 2015), artificial viscosity scheme, and laminar and sub-particle scale (SPS) turbulence model. The artificial viscosity scheme (J. J. Monaghan, 1992) is the most common in the SPH community due to its simplicity and robustness. In this approach, the viscosity is chosen as an artificial parameter, generally much higher than the real viscosity of the fluid. In this scheme, the viscosity needs to be tuned for a specific type of problem to capture the correct physical dynamic behavior of the fluid. On the other hand, the laminar and SPS model decomposes the diffusion term into laminar and turbulent components. The turbulence can then be modelled by following the stress tensor modelling approach used by Go- toh et al. (Gotoh et al., 2004) in their moving particle semi-implicit model. For the detail of both the artificial and laminar and SPS turbulence viscosity treatment, see the DualSPHysics user guide (Crespo et al., 2016).

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3.4.2 Pressure formulation In the DualSPHysics, the pressure is formulated using the equation of state. This SPH formulation of pressure is based on density in a weakly compressible approach where the ﬂuid is considered slightly compressible, and a density variation within less than 1% is allowed (Crespo et al., 2016). This approach adjusts the compressibility to artiﬁcially lower the speed of sound in order to maintain a reasonable time-step size. A variable time step is calculated based on the instantaneous courant number which is calculated based on the speed of sound of all the particles in the domain. The courant number (Cr) is a non-dimensional number that correlates the velocity (ui), the small- est particle distance (∆xi ) and the time-step size (∆t) according to the stability ∆t condition, the Courant–Friedrichs–Lewy (CFL) condition, as Cr = ui . The ∆xi relationship between the pressure and the density in weakly compressible SPH (WCSPH) can be expressed as follows (J. Monaghan, 1994):

ρ γ p = b − 1 (3.18) ρ0

2 where, γ is the isotropic constant, b = c0 ρ0/γ, ρ0 is the reference density p and c0 = c(ρ0) = (∂ p/∂ρ)|ρ0 is the speed of sound at the reference density.

3.4.3 Boundary conditions Modelling wall boundaries is one of the great challenges in SPH because the kernel support for the ﬂuid particles near the wall is truncated. The imperme- ability condition needs to be ensured to keep the mass balanced, while correctly representing any dynamic behavior of the ﬂuid particles that is induced by the viscous effect at the solid surfaces. Several techniques to model solid boundaries are available in the SPH literature, for example, dynamic boundary condition (DBC) (Crespo & Gomez-Gesteira, 2007), virtual particles (Ferrari et al., 2009; Jin et al., 2015; Vacondio et al., 2012), Lennard–Jones repulsive force (Rapaport, 2004) and boundary integral approach (Cercos-pita, 2012). However, there is no general boundary treatment available that can be used for all types of problems (Filho et al., 2016). A general and robust boundary condition development remains one of the big challenges for SPH.

Dynamic boundary condition (DBC) The dynamic boundary particle approach (Crespo & Gomez-Gesteira, 2007) is used to model wall surfaces in DualSPHysics. In this approach, the solid surfaces are represented by a separate set of fluid particles for which the same set of fluid flow equations are solved, however these solid particles do not move in response to the forces exerted on them. The DBC treatment available in DualSPHysics represents the wall surfaces reasonably well for a wide range

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of fluid flow problems. However, DBC has been reported to produce a small gap at the wall, which restricts the fluid particles from remaining attached to the wall surface. The gap can be reduced by increasing particle resolution, however, it cannot be completely eliminated.

Open boundary condition DualSPHysics currently supports open boundary condition for periodic boundaries. In this boundary treatment, the particles near one open lateral boundary are allowed to interact with the particles near the complementary open lateral boundary on the other side of the domain (Crespo et al., 2015).

3.4.4 SPH thermal implementation DualSPHysics (Crespo et al., 2015) is an open-source fluid flow solver based on the WCSPH approach, in which the mass conservation equation (3.16) and the momentum conservation equation (3.17) have already been implemented. DualSPHysics is the most user friendly and popular SPH code in the SPH community, and is robust for SPH-based fluid flow simulations. However, the solver does not provide the functionality to solve thermal problems in its current official version. To be able to solve thermal problems, we therefore implement the energy conservation equations (3.3) in the DualSPHysics code, which is presented in detail in Paper IX. The convective term is excluded from the energy equation, since the convection occurs automatically due to the interaction between the particles. The energy conservation equation (3.3) can be presented in its SPH form as follows (J. J. Monaghan, 2005):

∂T mb 4κaκb cp,a = ∑ (Ta − Tb)Fab (3.19) ∂t b ρaρb κa + κb

where, cp, κ and T are speciﬁc heat capacity, thermal conductivity and 1 ∂Wab temperature, respectively. Fab = , where rab is the distance between rab ∂xi particles a and b.

3.5 Industrial applications addressed using RANS RANS models are employed in this thesis to perform simulations for several industrial applications using the mesh based ﬁnite volume CFD solver AN- SYS Fluent. The industrial applications simulated in this thesis involve ROT cooling in hot rolling steel industries (Paper I), the re-heating furnace (Paper II), rotating machines (Paper IV - Paper VI), the liquid sloshing in LNG tanks (Paper VII), Poiseuille ﬂow heat transfer (Paper VIII) and the heat exchanger

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(Paper IX). The numerical models for all the applications are presented and the model development techniques are explained in this section.

Furnace Mechanical treatment Runout table(ROT)

Figure 3.3: Hot rolling process in steel industries (Picture: SSAB)

3.5.1 Hot rolling process The hot rolling process (Figure 3.3) is a very long process in hot rolling steel industries, in which large steel slabs are rolled into thin steel sheets. At the beginning of the process, the steel slabs are heated up to 1250 ◦C in several phases in the furnace. The heated slabs are then mechanically treated to make thin sheets. Finally, the steel sheets are cooled down to 200 ◦C at the ROT cooling section, where hundreds of water jets impinge on the steel sheet to cool it rapidly. The cooling section is a very important phase of the process as it is directly related to the crystallization of the steel atoms. The quality of the steel sheet is completely dependent on how it is heated up in the furnace and how it is cooled at the ROT cooling section. Hot rolling steel industries are one of the largest energy consumers, and often rely on non-renewable energy resources such as LPG. The consumption of fossil fuels during combustion has a high environmental impact in the form of 3 emissions such as CO2 and NOx. For instance, about 1000 m LPG per hour is combusted to heat the steel slabs in the furnace studied in this thesis. More- over, about 15 million litres of clean water are used per hour to cool the steel sheets in the ROT cooling section, according to the steel plant. As a result, the waste water from the plant contains traces of various materials which directly contribute to water pollution and affect the environment adversely. It is often very difﬁcult to conduct measurements while running the process due to the

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high temperatures involved. Advanced CFD simulations are therefore used to provide significant and useful information about the process and to discover unknown factors that influence the process. In this thesis, the first step of the hot rolling process, the slab re-heating furnace (Paper II) and the last step of the process, the impinging jet cooling at the ROT (Paper I) are simulated using CFD to gain detailed insight into the process.

3.5.1.1 Impinging jet cooling The ROT cooling problem is basically a liquid jet impingement cooling problem, where the liquid jets hit the hot flat surface perpendicularly to cool the steel sheet as the steel sheet is moving at a certain speed. Impingement jets are used in the hot rolling steel industries to cool the hot metal because of their good heat transfer performance. The temperature is usually very high, and the water therefore boils at the ROT cooling section. However, in this study, the steel sheet is assumed to be stationary and the temperature is considered below 100 ◦C to avoid the boiling phenomena in order to simplify the problem. After the jet impinges on the steel sheet, a very thin liquid film spreads over the whole sheet. The thickness of the film can be as small as one millimeter, which makes it very challenging to model using CFD simulations. The liquid film must be completely resolved by maintaining at least a few layers of mesh cells to be able to calculate the thermal gradients in the liquid film correctly. In Paper I, the heat transfer from the hot steel sheet to the liquid jets is simulated by developing three different models. Two 3D models are developed to analyze the heat transfer due to a single jet and double jets. The double-jet model is mainly developed to investigate the jet–jet interaction and its influence on the global heat transfer. In addition, a 2D axisymmetric model is developed to accurately calculate the liquid film thickness, to capture the dynamics of the jet interface and to perform a parametric analysis to evaluate the thermal performance at different flow rates.

Inlet Pipe radius (0.015 m) Pressure outlet Cylinder radius (0.05 m) Pipe height (0.05 m) Pressure outlet Cylinder height (0.15 m)

Y XY- symmetry

1.2 m Steel sheet Z X

0.6 m Pressure outlet

(a) (b) 0.05 m Figure 3.4: Single impinging jet 3D model (a) Full domain (b) Simulated domain with dimensions and boundary conditions

At the ROT cooling section, there is usually a large number of water jets impinging on the steel sheet (Figure 3.3) to achieve a uniform cooling over

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Inlet Pipe radius (0.015 m) Cylinder radius (0.05 m) Pipe height (0.05 m) Pressure outlet YZ- symmetry Cylinder height (0.15 m)

Pressure outlet Y XY- symmetry

Z X 0.6 m 0.6 m

Steel sheet Pressure outlet

0.05 m (a) (b) Figure 3.5: Multiple impinging jet 3D model (a) Full domain (b) Simulated domain with dimensions and boundary conditions

(a) (b) Figure 3.6: Mesh for impinging jet cooling model (a) 2D-axisymmetric model (b) 3D model the entire sheet. Using the mesh-based CFD approach, simulating such a large process is unapproachable due to need for a very large mesh to cover the entire ROT. Therefore, the problem needs to be simplified by reducing it to a smaller problem to be solved using CFD. It can be assumed that every water jet has an identical cooling effect; however, there are significant interactions between the jets since they are very close to each other. Therefore, it is crucial to analyze the cooling performance of a single water jet as well as the influence on the cooling performance due to the interaction from the surrounding jets. To do this, a single-jet 3D model (Figure 3.4) is developed to analyze the cooling performance of a single-jet, and a double-jet 3D model (Figure 3.5) is developed to analyze the influence of the jet–jet interaction on the thermal performance. The numerical domain is created in such a way that the domain size is small enough to reduce the number of mesh cells, but large enough to avoid possible influences of boundary conditions on the solution. For the 3D models (Figure 3.4 and Figure 3.5), a rectangular domain on the steel surface and a

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circular beam connecting the water pipe and the steel surface are chosen. The dimensions of the rectangular domain and the circular beam are chosen in such a way that the pressure outlet boundary conditions do not affect the air– water interface. For the single-jet model, a symmetry boundary condition is used on one side and half of this domain is simulated (Figure 3.4). However, for the double-jet model, symmetry is applied on two sides, thus one fourth of the original domain is simulated (Figure 3.5). The meshes for the 2D and the 3D single jet are presented in Figure 3.6. Rectangular cells and hexahedral cells are used to generate the mesh for the 2D and the 3D models, respectively. Impinging water jet is a free-surface flow problem and the location of the air–water interface is not known. It is crucial to capture the air–water interface accurately to obtain correct overall flow dynamics of the jet, and to be able to accurately predict the cooling performance. Therefore, the mesh is refined in the vicinity of the expected interface. To resolve the boundary layer, the cells close to the steel sheet are also refined to maintain a non-dimensional wall distance (y+) value around 30. A y+ value in this range guarantees the turbulence wall law functionality (Salim & Cheah, 2009). The mesh quality for the models is presented in Table 3.1.

TC 3&4 TC 5&6 TC 1&2 Burner Burner Burner Zone 1 Zone 3 Zone 5+6

Slab Zone 2 Zone 4 Zone 7+8 Burner Burner 16 m Figure 3.7: Slab re-heating furnace (side view) in 2D showing different zones, burners and thermocouples (TC) in Zone1

3.5.1.2 Re-heating furnace The slab re-heating furnace in the hot rolling steel industry is very large, and is divided into several zones. The 11 m × 1.6 m × 0.22 m (weight ∼30 ton) slabs are heated to about 1250 ◦C following a heating curve called the ideal curve, which is a unique recipe to achieve a speciﬁc quality of steel sheet. The main challenge in simulating this large furnace is the large number of burners together with the combustion; it is beyond the capability of mesh-based CFD solvers to simulate the whole process with the available computational resources. Therefore, a reduced model was developed to understand the ﬂow pattern inside the furnace and to observe the impact of having multiple burners operating next to each other by using the periodicity assumption, in Paper II. The furnace at the studied hot rolling steel plant consists of 8 zones in total, where Zone 1 and Zone 2 are the preheating zones (Figure 3.7). In this study, the main focus is to analyze the heat transfer in the preheating zone, Zone

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Outlet BC: Periodic BC: Wall (a)

(b) Zone 1 BC: Symmetry 19m

Steel slab Air inlet

LPG(C3H8) (c) (d)

Figure 3.8: Furnace model with boundary conditions (BC) (a) Burner conﬁguration in 3D (b) Numerical domain with single burner (c) Zone 1 and 2 in 3D (d) Burner conﬁguration in 2D

(a)

X Z (b)

Figure 3.9: Mesh for the furnace model (3.4 million cells) (a) burner (b) the whole domain

1. Zone 1 has 8 burners in a row, each with approximately 3500 kW capacity (Figure 3.8c). The burners in Zone 1 are conﬁgured in a periodic manner. Therefore, to reduce the numerical domain, a slice of Zone 1 is simulated together with the real burner conﬁguration in full size. Periodic boundary conditions are used on both sides of the cross-section surfaces of the numerical

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domain to represent the whole of Zone 1 (Figure 3.8b). Zone 2 has a similar power capacity to Zone 1. Therefore, we consider Zone 2 to be identical to Zone 1 and we use symmetry boundary condition to represent Zone 2 (Figure 3.8b). In this way, the numerical domain is greatly reduced in comparison to the original size of Zone 1 and Zone 2, but still represents them numerically. The movements of the steel slabs are introduced by considering a constant speed of 3.84 mm/sec. The mesh for the pre-heating zone of the furnace is presented in Figure 3.9. The mesh cells are reﬁned to capture all the small-scale effects of the burners, combustion and the heat transfer to the steel slabs. The non-dimensional wall distance at the steel slab surface, y+, is maintained at 30 which is sufﬁcient to ensure the turbulence wall law functionality (Salim & Cheah, 2009).

Surfaces of housing A B Stator internal surface 0.22m C 0.005m 0.2m Wafters Y Y

X 0.15m Z 0.05m Z

0.3m Rotor (Grey) 0.4m C 0 Rotor Wafters Air 0.4 Rotor shaft B A (a) (b) Figure 3.10: Rotating machine model (a) Domain together with boundary conditions (b) 2D cross-section illustrating the dimensions (AA, BB and CC are the XY cross-section plane used for post-processing)

3.5.2 Rotating machines Rotating machines like motors, generators and turbomachinery are another example of an energy-intensive sector, with an engineering apparatus that is widely used in residential, commercial and industrial sectors. A large amount of energy is consumed by rotating machines, and the use of such devices is continuously increasing. This sector is identified as one of the key sectors with large energy savings potential by the European commission (“EU Commis- sion Regulation (EC) No 640/2009”, 2009). There are two major aspects of energy savings from rotating machines, energy efficient machinery and energy efficient control systems (Abdelaziz et al., 2011). Around 5–25% of the energy consumed by electric motors is lost during the energy conversion process (Andreas, 1992). An increase in efficiency of 2% in existing standard motors will reduce losses by 25% (Saidur, 2010). On the other hand, replacing exist-

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ing standard motors with motors with energy-efficient control systems, such as a variable speed controller based on the load, output and demand, could reduce the energy consumption by 15–30% (Mecrow & Jack, 2008). About 15% of the consumed electrical energy is converted into heat due to various losses in the machine (Pyrhönen et al., 2008). The temperature increase inside the machine is caused by the waste energy and friction during machine operation. The maximum temperature inside the machine is a limiting factor for the efficiency and performance of the machine. Overheating has a long-term impact on the lifetime of a machine. Detailed knowledge of the heat transfer inside the machine is required in order to design an efficient thermal management system. The majority of the heat transfer from the rotor occurs in the thin air-gap (∼1 mm) between the rotor and the stator. This air-gap width has a significant impact on the friction losses and the heat transferred between the rotor and the stator. Another key parameter that influences the heat transfer in the air-gap is the rotation speed of the rotor, which is the most important parameter in motors with a variable speed controller.

Figure 3.11: Mesh for the rotating machine model

The complex windings, fins of the rotor and the very thin air-gap (less than 1 mm) between the rotor and the stator make it very challenging to simulate the motor using CFD. The air-gap needs to be completely resolved in the numerical models, since the heat transfer primarily takes place in this narrow region. To address this important application, several models addressing different aspects are developed in this thesis (Paper IV – Paper VI). In paper IV, a numerical model to simulate the fluid flow and heat transfer inside the machine is developed, employing the mesh-based FVM method. The developed model is a simplified motor in which the motor windings are modelled virtually. The air-gap thickness, for the present analysis, is considered larger than is usually found in motors to avoid a large number of mesh cells. Con- stant wall temperature of 150 ◦C is applied to the rotor surface in the air-gap,

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where the rotor is rotating at a constant speed of 1500 rpm. The details and dimensions of the model are illustrated in Figure 3.10. The same model (Fig- ure 3.10a) is also used in Paper VI, where the SPH method is used for the first time to simulate the air flow inside this type of machine. The SPH model in Paper VI does not include heat transfer analysis due to the unavailability of a commercial or open-source SPH thermal solver. In Paper V, a parametric study is performed to analyze the flow and heat transfer inside the machine by varying the air-gap width and the rotation speed of the rotor. Nine different simulations, considering 3 different air-gap widths (1 mm, 3 mm, 5 mm) and 3 different rotation speeds (1500 rpm, 5000 rpm, 10000 rpm), are performed to obtain a full spectrum of the thermal performance of the machine in different scenarios. A FVM model is employed for the parametric study. Figure 3.11 presents the mesh for the FVM models used in Paper IV and Paper V. The mesh does not include the solid rotor, because the rotor is modelled by its surfaces. The mesh elements in the air-gap and surrounding the wafters are refined to capture the aerodynamics and the heat transfer accurately. The mesh quality for the rotating machine models is presented in Table 3.1.

H z -ϴ +ϴ S1 H1 x1 Center x w

Figure 3.12: LNG Tank model with dimensions

3.5.3 LNG vessels in carrier ships Transport of LNG in cargo vessels is increasingly used to transport fuel across the globe. The stability of these large carrier ships is severely affected by the LNG sloshing inside the tanks. The dynamic liquid movement inside the tank, the result of the different types of movements of the ship (rolling, yawing and pitching), is termed sloshing. Sloshing phenomena in LNG containers can damage the internal coating of the tank. Very strong impacts can sometimes occur on the tank walls, potentially causing hazardous damage. The sloshing must be avoided as much as possible to achieve better control of the ship and to avoid any accidents. Several studies have highlighted the challenges

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encountered as a result of the sloshing, and have proposed anti-sloshing tank structures (Ha, 2007). The forces on the walls due to the sloshing are predicted by a control system to control the ship. Measuring the forces acting on the internal walls of the tank by placing sensors is prohibited because such equipment can ignite the fuel, and is therefore highly dangerous. Two different approaches, RANS–VOF and SPH, are employed in Paper VII to simulate the sloshing inside a rectangular tank under periodical rolling motion, in 2D. RANS–VOF is a robust mesh-based solver for simulating multiphase flows. SPH is also known to be very efficient for such types of flows (J. Monaghan, 2012). Tracking the free surface of the liquid efficiently is key to predicting the sloshing impact and the various forces acting on the walls inside the tank. A small-scale tank with two different filling levels is simulated, and the results from both RANS–VOF and SPH models are validated using available experimental data. Water is considered as the working fluid due to the availability of experimental data. The scaling laws are evaluated for this problem and a large-scale tank is also simulated using SPH to validate the concept in Paper VII. The numerical model is presented in Figure 3.12. The tank is subject to a sinusoidal roll motion with rolling angle ± θ, centered at z-axis with a frequency f r = 1/T1, where T1 is the time for a full roll motion. In Figure 3.12, x and z are axes, w is width of the tank, H is the height of the tank, x1 is distance of sensor S1 from the bottom of the tank, x2 is distance of sensor S2 from the left wall of the tank, θ is rolling angle and H1 is initial height of water level. The simulated cases are illustrated in Table 3.2.

Table 3.1: Mesh information for the FVM models presented in section 3.5. For details of the mesh quality measure, see (ANSYS Inc., 2018) Model Number Cell type Max. aspect Min. orthogonal Max. Y+ value of cells ratio quality skewness at wall 2D-axisymmetric(ROT) 27,000 Quad 37 1 None 2 ∼ 15 3D 1-jet (ROT) 1.4 million Hex 44 0.74 0.55 4 ∼ 30 3D 2-jet (ROT) 1.6 million Hex 51 0.70 0.57 4 ∼ 33 Furnace 3.4 million Mixed 34 0.23 0.85 30 ∼ 300 Rotating machines 1.4 million Hex 35 0.99 0.05 1 ∼ 18 Tank sloshing 18,000 Hex 1.4 1 1 47 ∼ 128

3.6 Industrial applications addressed using SPH SPH models are employed in this thesis to perform simulations for rotating machines (Paper VI), liquid sloshing in LNG tanks (Paper VII), Poiseuille ﬂow heat transfer (Paper VIII) and the heat exchanger (Paper IX). This section presents the numerical models and the techniques used to develop the models for these applications.

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3.6.1 Rotating machine The SPH method is used to simulate the air ﬂow inside the rotating machine presented in 3D in Figure 3.10 in Paper VI. A cross section of the rotating machine is also simulated in 2D (Figure 3.13b). The air is represented considering uniform particle resolution, with about 2.8 million particles and 70000 particles used to represent the 3D and 2D models, respectively. The heat transfer is not simulated for this case because of unavailability of a commercial or open-source SPH thermal solver. The air-ﬂow simulation results from the 3D and 2D SPH models are compared with the results from FVM models in Paper VI.

Stator (Transparent) Stator

Rotor Fluid particles Rotor(Grey) (Blue) (a) (b) Figure 3.13: SPH models for the rotating machine presented in Figure 3.10 (a) 3D model (2.8 million particles) (b) 2D cross section model (70000 particles)

3.6.2 LNG vessel in carrier ship Several SPH models are developed to simulate the sloshing in a rectangular tank in Paper VII, using the model presented in Figure 3.12. Four different cases are developed, consisting of two different ﬁlling levels (18% and 70%). The simulated cases with all the details are presented in Table 3.2. Case 1 and Case 2 present the model-scale tank, whereas Case3 and Case 4 present the full-scale tank. SPH is employed to simulate all the cases, but RANS–VOF is employed to simulate Case1 only. The large-scale tank is simulated using SPH to validate the downscaling approach for the tank sloshing problem.

3.6.3 Transient heat conduction Transient heat conduction in solid and liquid are simulated to validate the SPH thermal implementation presented in Paper IX. The energy conservation equation is implemented in the open source SPH ﬂuid ﬂow solver DualSPHysics.

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Table 3.2: Tank sloshing case speciﬁcations

Cases Case 1 Case 2 Case 3 Case 4 w (m) 0.9 0.9 20 20 H (m) 0.508 0.508 11.29 11.29

H1 (m) 0.093 0.3553 2.07 7.89 θ (degree) ±4 ±4 ±4 ±4

T1 (sec) 1.67 1.22 7.87 5.75 x1 (m) 0.093 2.07 x2 (m) 0.025 0.56 dp (m) 0.002 0.002 0.0444 0.0444 Approach SPH yes yes yes yes VOF yes no no No

A square aluminium block, with 0.1 m sides, is initialized to 20 ◦C. A constant temperature of 90 ◦C is applied from one side of the block and the other sides are kept at 20 ◦C. Similarly, for conduction in liquid, a square alunimium cavity of size 0.1 m × 0.1 m is ﬁlled with water. A constant temperature of 90 ◦C is applied from one side, while keeping the other sides at 20 ◦C. Both cases are simulated using FVM and SPH. The model, boundary conditions, the mesh for the FVM model and the particles for SPH model are presented in Figure 3.14. The material properties used for the simulations are presented in Table 3.3.

(a) (b) (c) Figure 3.14: Heat conduction model with discretization (a) domain together with thermal boundary conditions (b) FVM mesh (∼ 40000 cells) (c) SPH particles (∼ 40000 particles)

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Table 3.3: Thermal properties of Aluminium and Water

Properties Aluminium Water Density (Kg/m3) 2719 1000 Thermal conductivity (W/m.K) 202.4 0.6 Heat capacity (J/kg.K) 871 4182 Kinematic viscosity (m2/s) 0.000001

3.6.4 Transient heat convection Transient heat convection for two different cases, (i) flow and heat transfer in an infinitely long mini-channel and (ii) flow and heat transfer in a tube bank heat exchanger, are simulated using the SPH thermal implementation. Both cases are simulated in 2D under laminar conditions using FVM and SPH. For the SPH approach, the laminar viscosity modelling approach (Crespo et al., 2015) is used. The material properties used for water and aluminium are presented in Table 3.3.

3.6.4.1 Inﬁnite mini channel

Entry flow profile Fully developed flow profile 20°C

δT δ

Periodic 2mm Periodic In out

40°C Water Solid wall Velocity profile

Hydrodynamic boundary layer (δ) Thermal boundary layer (δT)

Figure 3.15: Mini-channel with boundary conditions

Mini- and micro-channel flow heat transfer occurs in many important engineering and industrial applications, such as heat exchangers, chemical re- actors, motors and generators, and district heating. Poiseuille flow and heat transfer can be applied to the laminar flow and heat transfer in an infinitely long channel. The flow field in Poiseuille flow is divided into two regions, the hydrodynamic entrance region and the fully developed region. In the entrance region, the laminar hydrodynamic boundary layer grows rapidly due to the viscous force at the walls. The boundary layers from top and bottom walls grow until they merge and the flow field reaches a state where the velocity profile no longer changes. The same also applies to the thermal development, however, the thermal boundary layer is thinner than the hydrodynamic bound-

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ary layer for water, and it therefore takes longer to reach a thermally steady state. To model the Poiseuille flow, a 2D horizontal channel of width 2 mm is chosen, and a periodic boundary condition is applied in the direction of the flow. The configuration of the simulated micro-channel is illustrated in Figure 3.15. The top wall is set to a constant temperature of 20 ◦C and the bottom wall is set to a constant temperature of 40 ◦C. The water temperature is initialized to 20 ◦C and adherence boundary condition is applied to the solid walls of the channel. This case is simulated under laminar conditions. Gravitational acceleration is neglected since the channel is very thin. Figure 3.16 shows the numerical discretization of the domain (Figure 3.15) for FVM and SPH.

(a) (b) Figure 3.16: Numerical discretization for the mini-channel (a) FVM mesh (∼ 50000 cells) (b) SPH particles (∼ 50000 particles)

3.6.4.2 Tube bank heat exchanger The tube bank in cross flow has been subject to many studies, mainly due to its presence in a wide range of heat exchangers (Khan et al., 2006; Safwat Wilson & Khalil Bassiouny, 2000; Wang et al., 2016). A tube bank heat exchanger is a bank of tubes, containing flowing liquid at one temperature, immersed in a cross flow of liquid at a different temperature. Heat is exchanged between the tube bank and the cross-flow liquid. The tube bank heat exchanger is simulated in Paper IX as a 2D cross section of a tube bank, immersed in a cross-flow liquid, presented in Figure 3.17a. It consists of equally spaced (0.01 m) tubes arranged in a staggered manner. The tubes are 0.01 m in diameter, and contain liquid at 100 ◦C. The cross-flow water is initialized at 10 ◦C and a periodic boundary condition is applied to model the cross flow over the tube bank. The tubes are numerically modelled by applying a constant temperature boundary condition. The detailed configuration of the simulated heat exchanger in 2D is shown in Figure 3.17b. This case is also simulated under laminar conditions, where an acceleration of 0.001 ms-2 is applied in the direction of the cross flow. Gravitational acceleration is neglected for this case. Figure 3.18 shows the numerical discretization of the domain (Figure 3.17b) for FVM and SPH.

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X=0.01 X=0.02 X=0.03

0.01m 0.08m 0.01m

Y=0.05 Cross flow Periodic Periodic Y=0.04 In Out

Y=0.03

Y Z

X 0.04m X Y Solid wall (10°C) Cold water channel (10°C) Water Hot tubes Hot water tubes (100°C) (a) (b) Figure 3.17: Tube bank heat exchanger (a) 3D schematic (b) 2D cross section with dimensions (dashed lines inside the domain are used for post-processing)

Mesh Particles (a) (b) Figure 3.18: Numerical discretization for the tube bank heat exchanger model (a) FVM mesh (∼300000 cells) (b) SPH particles (∼300000 particles)

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4. Results and discussion

This chapter presents the results of numerical simulations for the engineering and industrial applications presented in section 3.5 and section 3.6, obtained from both mesh-based FVM and mesh-free particle-based SPH solver. The results presented in this chapter illustrate the accuracy and reliability of the solutions from each solver. This chapter highlights the difﬁculties and challenges of simulating industrial applications by employing mesh-based and mesh-free solvers, and outlines the future of such approaches. This chapter also provides a detailed discussion of the studied topic while answering the research questions.

4.1 Reynold Averaged Navier-Stokes 4.1.1 Hot rolling process The hot rolling process is addressed in this thesis by employing mesh-based FVM solvers based on the RANS approach. The hot rolling process involves very complex physical phenomena, both in the ROT cooling process and the re-heating furnace. Emerging methods, such as SPH, are not mature enough to handle such complex industrial problems. Thus, RANS methods are currently the appropriate choice.

d Pipe

Uf Axis of rotation

Free surface

δ – Momentum boundary layer δT – Thermal boundary layer h(r) Hydraulic jump Stagnation point I r1 II r2 III r3 Steel surface Radial flow Stagnation zone Radial flow zone zone Figure 4.1: Schematic of impinging jet cooling, I: the stagnation zone, II: the laminar boundary layer, III: the momentum boundary layer reaches the ﬁlm surface

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4.1.1.1 Impinging jet cooling The jet impingement cooling at the ROT cooling process is a free-surface multiphase flow with highly deforming interfaces and a high pressure gradient. After impinging the steel surface, the liquid jet becomes stagnant in the stagnation zone and then spreads over the whole steel sheet as a thin liquid film due to the high pressure gradient (Figure 4.1). Capturing the dynamic air–water interface and resolving the thermal and pressure gradients taking place in the thin liquid film are a big challenge for any numerical method. Therefore, to understand the flow and thermodynamics of the impinging jet, an accurate modelling technique must be employed. The RANS–VOF multiphase model equations, presented in section 3.3.4, are solved in Paper I, to simulate the numerical models presented in section 3.5.1.1 under steady-state conditions. The liquid is considered incompressible, and the turbulence is accounted for by employing the k − ε turbulence models presented in section 3.3.2.1. Moreover, the heat transfer is modelled by solving the energy conservation equation presented in section 3.3.3.

Figure 4.2: Interface of water jet for different inlet velocities

The numerical results presented in Paper I are analyzed and validated ana- lytically and using experimental data, mainly focusing on the location of the air–water interface (Figure 4.2), the liquid ﬁlm thickness and the heat transfer coefﬁcient (Figure 4.3). At the ROT, an array of jets is used to cool the steel sheet. Each jet is responsible for cooling a small zone locally, called the stagnation zone, since the maximum cooling occurs within the stagnation zone of an impinging jet (Figure 4.3). The combined cooling effect from all the water jets result in a uniform cooling over the steel sheet. The size of the stagnation

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Figure 4.3: Non-dimensional heat transfer coefﬁcient (Nusselt number, Nu) for different inlet velocities

Figure 4.4: Comparison between simulation and correlation (4.1) of the minimum jet diameter (Dmin)

zone is influenced by the inlet flow rate. The parametric study presented in Paper I shows a linear relationship between the inlet water flow rate and the maximum heat transfer coefficient.

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Figure 4.5: Temperature ﬁeld showing the cooling effect when using single and multiple jets

Figure 4.6: Water splashing due to the interaction between jets

The inlet velocity (Uf ) and the gravitational effect (g) on the interface of the water jet can be described using the continuity equation and the Bernoulli’s equation as follows (for detail, see, Appendix): q 4 2 D(Z) = d/ 1 + 2g(z0 − Z)/Uf (4.1)

The analytical correlation (4.1) presented in Paper I can be used to estimate the minimum water jet diameter, Dmin (Figure 4.2). The minimum jet diameter can then be used to estimate the diameter of the zone with maximum cooling effect by using the correlation (4.2) given in Paper I based on the simulation results.

rNumax = 0.825Dmin (4.2)

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Thus, the uniformity of the cooling effect over the steel sheet can be estimated by using the correlation (4.2). The cooling effect when using single and multiple jets is illustrated in Figure 4.5. The double-jet 3D case simulated in transient shows a lot of splashing due to the interaction between the radial flows from the jets. This splashing phenomenon makes it extremely challenging to simulate due to the instability and divergence issues during the simulations (Li et al., 2017). To obtain a stable solution, the distance between jets is considered much larger than the original configuration of a typical ROT. Therefore, the simulated double jets behave like isolated jets in terms of fluid flow and thermal characteristics. The results presented in Paper I show the degree of accuracy of the models. They indicate that the mesh-based solver was unable to handle the complex interaction between the two jets that are close to each other. Therefore, simulating the entire ROT, consisting of hundreds water jets, employing such a numerical method appears unfeasible.

4.1.1.2 Re-heating furnace The re-heating furnace model presented in Figure 3.8 is simulated under steady-state condition by solving the RANS equations presented in section 3.3.1 in Paper II. The turbulence is accounted for by employing the k − ε turbulence model presented in section 3.3.2.1. To model the heat transfer and the combustion, the energy conservation equation and the mixture fraction transport equations presented in section 3.3.3 and section 3.2.3, respectively, are solved. The combustion is modelled by considering infinitely fast chemistry, where the gas density is modelled using the probability density function concept incorporated in the non-premixed combustion method (ANSYS Inc., 2018). A single burner in a real furnace configuration is 3 simulated, in which air (21% O2 and 79% N2) flow at 75200 m /hour at 560 ◦ 3 ◦ C and LPG (C3H8) flow at 1000 m /hour at 20 C are introduced. To imitate the real scenario, a constant speed is applied to move the slabs inside the furnace, and temperature-dependent thermal properties were considered for the slabs.

Figure 4.7: Path lines of velocity illustrating recirculation inside the furnace

Several difﬁculties and challenges were faced during the modelling of the furnace. Firstly, it is very large and extremely complex in terms of geometry;

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Figure 4.8: Iso-surfaces (a) mass fraction of O2 (b) temperature on the iso-surfaces of mass fraction of O2

Figure 4.9: Volume average temperature of the steel slab

thus, to identify an optimal numerical domain, which is numerically solv- able but also sufﬁcient to represent the pre-heating zone of the furnace, was challenging, and the ﬁnal model presented in Paper II was reached by trial and error. Generating a good mesh (Figure 3.9) was another challenging task which took a major effort. Secondly, the multiple physical phenomena and

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time scales, for example, slab movements and fast combustion chemistry together with conduction, convection and radiation heat transfer, make it challenging to simulate and reproduce the events in the furnace. The numerical results presented in Paper II reveal high degrees of recirculation (Figure 4.7) inside the furnace, which result in incomplete combustion in the system. The uncombusted oxygen reaches the steel slab surface due to the recirculation (Figure 4.8), and forms an iron oxide layer, which is one of the common problems faced in the studied steel plant. The calculated average temperature of the steel slab is compared to the estimated slab temperature in the online control system in the steel plant, which clearly shows a deviation from the goal to reach the ideal curve (Figure 4.9).

4.1.2 Rotating machines The rotating machine model geometry presented in Figure 3.10 is simulated by solving the RANS equations presented in section 3.3.1. The model is developed considering multiple reference frames, a rotating and a stationary frame, and the sliding-mesh technique (ANSYS Inc., 2018) is used to model the rotating system efﬁciently. The turbulence and heat transfer are modelled by employing the k − ε turbulence model and solving the energy conservation equations, which are presented in section 3.3.2.1 and section 3.3.3, respectively. Several studies are performed for rotating machines, employing both FVM and SPH methods. This section presents the results from FVM models, and the results from the SPH model are presented in section 4.2.1.

(a) (b) Figure 4.10: Velocity vectors on cross-section planes inside the motor (a) Taylor vortices ap-pears in pairs (b) Boundary layer ﬂow pattern in the air-gap surrounding the rotor)

Paper IV presents a vigorous analysis of the rotating machines covering the details of the interesting flow field and their effect on local and global thermal performance. A high emphasis was given to resolving the flow and heat transfer phenomena in the thin air-gap between the rotor and the stator. The simula-

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Figure 4.11: Simulated average velocity proﬁle in the air-gap of the motor together with analytical solution and experimental data (Reichardt, 1956)

(a) (b) Figure 4.12: Taylor vortex ﬂow and temperature distribution inside the air-gap of the motor (a) velocity contour (b) temperature contour

Figure 4.13: Temperature contour on internal surface of the stator for rotor speed of 10000rpm (a) 5mm air-gap (b) 3mm air-gap (c) 1mm air-gap

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(a)

(b)

tions presented in this paper are performed under transient conditions to investigate the transient effects due to the turbulence created by the rotor wafters. The velocity profile in the air-gap Figure 4.11 and the non-dimensional heat transfer coefficient from the simulation are validated by using analytical solutions and experimental data (Reichardt, 1956). The complex Taylor vortices appears in pairs, presented in Figure 4.10, and are captured well by the simulations, clearly illustrating the level of accuracy of the solver. The Taylor vortices appear in the velocity field in the air-gap (Figure 4.12a), resulting in similar vortices to the temperature field (Figure 4.12b), which consequently introduce an oscillating pattern to the heat transfer coefficient (Figure 4.14). A parametric study carried out by varying the air-gap width and the rotation speed of the rotor is performed in Paper V. The results show that for a thin air-gap like those encountered in a real electric motor, the Taylor vortices disappear (Figure 4.13). The presence of Taylor vortices significantly increases the heat transfer capability (Figure 4.14). The observations presented in Paper V indicate that both the air-gap width and the rotation speed have significant influence on the heat transfer. The heat transfer increases with increasing air- gap width and increasing rotation speed of the rotor (Figure 4.14). Thus, the design of a rotating machine can be influenced by varying the air-gap width to take advantage of the Taylor vortices, and the machine can be operated at higher speed to enhance the thermal performance. However, further justifica- tion of these observations is required from an electromagnetic perspective.

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Figure 4.15: Air velocity proﬁle on the YZ cross-section plane (Figure 3.10b) at time t=2 sec (a) FVM 3D model (b) SPH 3D model

Figure 4.16: Air velocity contour on XY cross-section planes close to the motor wafters at time t=2 sec (FVM 3D model (top) and the SPH 3D model (bottom)), where the rotor is rotating counter clockwise (a) Velocity profile on plane AA (Figure 3.10b) (b) Velocity profile on plane BB (Figure 3.10b) (c) Velocity profile on plane CC (Figure 3.10b)

4.2 Smoothed Particle Hydrodynamics 4.2.1 Rotating machines The SPH method is employed to model the air-flow inside the rotating machine in Paper VI. To model the rotating machine presented in Figure 3.13, the SPH forms of the continuity and the momentum equations presented in section 3.4.1 are solved under the transient condition. The turbulence is modelled by employing laminar and SPS turbulence modelling approaches (Crespo et al., 2015). The results obtained from the SPH models are compared to the simulation results presented in Paper IV. The velocity field inside the machine illustrated in Figure 4.15 and Figure 4.16 show an overall agreement; however, the velocity field inside the air-gap was unresolved in the SPH model

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Figure 4.17: Velocity profile inside the air-gap between the rotor and the stator for the SPH 2D, SPH 3D and FVM 3D models due to the low particle resolution in the air-gap. The velocity profiles from 2D and 3D SPH models presented in Figure 4.17 show that the results from the 3D model could be improved by considering higher particle resolutions. The fluid particles near the boundary inside the air-gap show unphysical oscillating behavior, which mainly arises from the boundary wall treatment used to model the solid wall surfaces (Crespo et al., 2015). To improve the results in the air-gap, this issue first needs to be addressed by developing a new type of boundary condition to properly resolve the shear stresses.

4.2.2 LNG vessel in carrier ships Sloshing in the tank is a multiphase problem. Tracing the air–liquid phase is very important to obtain the correct dynamics of the liquid and the forces acting on the walls due to the movements. This problem is solved by employing both FVM and SPH. For the FVM model, the RANS–VOF equations presented in section 3.3.4 and the k − ω turbulence model presented in section 3.3.2.2 are employed. In the SPH approach, the SPH version of the Navier– Stokes equations presented in section 3.4.1 is applied. The artiﬁcial viscosity modelling approach (Crespo et al., 2015) is used to model the viscous diffusion. Using the SPH approach, only the liquid phase is solved, whereas both the liquid and air phases are simulated in the RANS–VOF approach. Thus, the SPH model produces quicker results than the FVM model. The free surface and the pressure forces presented in Figure 4.18 and Fig- ure 4.19, respectively, from both models are compared and validated using experimental data (Souto-Iglesias et al., 2011), showing good accuracy. The forces presented in Figure 4.20 from both models are also in very good agreement. One of the main ideas in this work is to evaluate the scaling laws, so that

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Figure 4.18: Snapshots of sloshing from the experiment (Souto-Iglesias et al., 2011), SPH simulation and VOF simulation for Case 1 at time t = 2.15 sec, 2.55 sec, 3.12 sec and 6.04 sec.

Figure 4.19: Comparison of Pressure (Pa) values from sensor S1 from the experiment (Souto-Iglesias et al., 2011), SPH simulation and VOF simulation for Case 1 (Table 3.2) the forces acting on the walls in a large-scale tank can be estimated from the simulation result using a small-scale tank. To evaluate this, a large-scale tank is also simulated using SPH, and the results are used to validate the scaling approach. The Froude number scaling laws are applied to evaluate the geometric, kinematic and dynamic similarities between the small and large-scale tanks. The Froude number scaling laws are presented in Table 3.2, where λ

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Figure 4.20: Comparison of the Force on the left wall of the tank between SPH and VOF simulations for Case 1 (Table 3.2)

Figure 4.21: Forces on the left wall of the full tank for Case 3 (Table 3.2) SPH simulation Vs. Froude-number-scaled forces on the left wall of the model tank for Case 1 (Table 3.2) SPH simulation

is the scaling factor, the ratio between the characteristic lengths of the tanks. The upscaled forces from the small tank are compared with the calculated forces from the large-scale tank simulations in Figure 4.21. This shows that the upscaling laws are applicable to the tank sloshing problem; thus simulating a small-scale tank will be sufﬁcient to predict the forces for the large-scale tank.

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Temperature (°C)

SPH

FVM

Figure 4.22: Comparison of temperature contour between SPH and FVM for conduction in aluminium

Figure 4.23: Temperature proﬁles on Line 1 (Figure 3.14) at different time instances from FVM and SPH

4.2.3 Heat conduction 4.2.3.1 Conduction in solid The model presented in Figure 3.14 is simulated to model the conduction in an aluminium block by solving the energy conservation equations using both FVM and SPH. The temperature solution at different time instances obtained from the models are illustrated and compared in Figure 4.22 and Figure 4.23.

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The temperature contours (Figure 4.22) and the proﬁles (Figure 4.23) from both models are in full agreement.

Temperature (°C)

SPH

FVM

200 sec 500 sec 1000 sec Figure 4.24: Comparison of temperature contour between SPH and FVM for conduction in water

Figure 4.25: Temperature proﬁles on Line 1 (Figure 3.14) at different time instances from FVM and SPH

4.2.3.2 Conduction in liquid Heat conduction is simulated for still water in a cavity to evaluate the heat propagation from the solid boundary to the liquid. The natural convection is not considered; therefore, the liquid does not move as a result of the temperature change in the water. This case is simulated mainly to evaluate the thermal

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diffusivity of water. The thermal diffusivity of water is much lower compared to aluminium; therefore, the heat propagation in the water is slower than that of aluminium. The conduction in still water is simulated up to 1000 sec. The temperature contours and temperature proﬁles on Line 1 (Figure 3.14) at different time instances are presented in Figure 4.24 and Figure 4.25, respectively. The temperature solutions from both solvers are in good agreement.

Figure 4.26: The velocity and temperature contours in the mini-channel from SPH and FVM models (a) Velocity contours (b) Temperature contours

Figure 4.27: Temperature proﬁles in the mini-channel from SPH and FVM models

4.2.4 Heat convection 4.2.4.1 Inﬁnite mini channel The Poiseuille ﬂow heat transfer is simulated under laminar conditions by employing FVM and SPH in Paper VIII. The velocity and the temperature con-

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tours, at different time instances, from SPH and FVM models are presented in Figure 4.26; they are nearly indistinguishable. The velocity and temperature proﬁles are compared and validated using the analytical solution. The temperature proﬁles along the width of the channel from both SPH and FVM, presented in Figure 4.27, are in full agreement.

4.2.4.2 Tube bank heat exchanger The fluid flow and heat transfer in the tube bank heat exchanger are simulated under laminar conditions using FVM and SPH in Paper IX. Figure 4.28 shows the velocity and temperature contours after 30 sec. The velocity fields from both solvers are similar; however, SPH predicts slightly higher velocity compared to FVM (Figure 4.28a). The temperature fields from both solvers are almost identical (Figure 4.28b). The temperature profiles on Y lines (Fig- ure 3.17b) from the SPH model are in good agreement with the profiles from the FVM model (Figure 4.29). However, there are slight disagreements in the temperature profiles just behind the tubes on the Y lines. This is mainly due to the gap produced by the dynamic boundary condition in DualSPHysics.

(a) (b) Figure 4.28: Velocity and temperature field in the tube bank heat exchanger from SPH and FVM models at t=30sec (a) Velocity field (b) Temperature field

The thermal results presented in section 4.2.3 and section 4.2.4 show that SPH has a great potential for solving thermal problems. The accuracy achieved by the SPH thermal solver indicates the usefulness of SPH for conductive and convective heat transfer problems. The current use of the SPH thermal solver is limited to laminar ﬂow and heat transfer. Additional

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Figure 4.29: Temperature proﬁles in the tube bank heat exchanger from SPH and FVM models at different time instances (a) On line Y=0.03m (Figure 3.17b) (b) On line Y=0.04m (Figure 3.17b) (c) On line Y=0.05m (Figure 3.17b) investigations on different turbulent ﬂow problems are needed to further evaluate the stability, accuracy and reliability of the SPH thermal solver.

4.3 Discussion The results presented in section 4.1 and 4.2 provide an overview of the accuracy, reliability and capability of the two employed CFD approaches, RANS and SPH, to model and predict engineering fluid flow and heat transfer processes. This section discusses the observations from the studied cases and the potential of such CFD approaches to satisfy future demands of the industrial sector. The research questions formulated in section 1.2 are also discussed. To improve or optimize any industrial process or product, it is necessary to have a clear understanding of the underlying physical phenomena. Such understanding can be attained by employing a high fidelity method such as CFD. Before addressing an industrial application using CFD simulations, the purpose of employing this method and the expected outcome from the simulations need to be defined. Many factors need to be considered before choosing a suitable CFD method. For example, whether the flow can be considered steady or transient and whether it is possible to apply geometric simplification using, for instance, symmetry or periodicity aspects. At present, the available functionality in FVM and SPH solvers has a large influence on this choice. SPH is a highly flexible method, however, steady-state approach, symmetric boundary conditions, inlet-outlet boundary conditions, robust treatment for boundary walls, local refinement of particles and heat transfer are some of the necessary functionalities that are currently not supported by the majority of available SPH codes. On the other hand, mesh-based FVM CFD programs provide much wider flexibility and accurate results while supporting the aforementioned functionalities. However, FVM CFD programs are limited by their

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numerical performance and the complex workflow, including mesh generation. The idea of this thesis is to use the positive features from both FVM and SPH to mitigate the weaknesses of both solvers. The FVM results presented in section 4.1 can readily be used in the respective industrial applications to improve the processes and products. For example, the heat transfer coefficient and the uniformity of the cooling performance over the steel sheet can be estimated by using the results presented and the correlation provided in Paper I. The results presented in Paper II for the re-heating furnace show that this kind of simulation can be used to diagnose problems like avoiding the formation of iron oxide on the slab surface by changing the alignment of the burners. The results in Paper II also provide an idea of the accuracy of the interpolation method used in the control tool to control the steel slabs. The results presented in Paper IV and Paper V can be used to improve the design and enhance the heat transfer in an electrical motor. However, all these models need to be extended in order to approach reality, for example, considering multiple jets in the ROT, multiple burners in the reheating furnace and including the electromagnetics in the rotating machine model, to have realistic output. The results from the SPH thermal solver presented in section 4.2 illustrate the accuracy level and clearly show the potential of using SPH for more realistic engineering thermal problems. However, functionalities such as efficient particle refinement techniques, robust solid wall treatment, inlet-outlet open boundary conditions and turbulence models are needed before the SPH can be applied to model and simulate engineering and industrial problems, like the ROT, reheating furnace and rotating machines.

Discussion towards the research questions

RQ 1 What are the limitations of RANS when used to simulate complex industrial applications?

Industrial flow simulations are mostly turbulent. Thus, employing a suitable turbulence model is a necessity to model the turbulence properly. Among several options of turbulence models in CFD simulations (DNS, LES, RANS), the standard RANS approach is the most economical and robust to numerically investigate an industrial application (Spalart, 2000). The RANS modelling approach is applicable to a wide range of turbulent flows and has been validated by many experimental results over decades. The RANS models are supported by several models and closure laws, among which many are empirical or semi-empirical. The direct numerical simulation (DNS) approach provides instantaneous results without any averaging or filtration. However, DNS is extremely expensive due to its mesh and the requirement for large computational power; thus, it is mainly used for simple cases and for fundamental research purposes. In terms of numerical performance, large eddy

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simulation (LES) rests in between RANS and DNS – some approximation is involved, but the approach is still very expensive for industrial large simulations. LES is also gradually emerging for industrial applications; however, it is mainly affordable for some internal flows in industrial applications. The recent development of HPC technologies has shifted the general trend from RANS towards LES, giving rise to new hybrid models like RANS–LES. Thus, the choice between different approaches mainly depends on the level of accuracy that is required for a specific simulation and the available computational resources. The cost estimation for simulation by RANS, LES and DNS, reported by Spalart (Spalart, 2000), shows that LES and DNS are generally still too expansive to be used for large industrial simulations. The results from RANS models presented in section 4.1 show the accuracy level and reliability of the employed approach for simulating a very simplified portion of the ROT, a small slice of the reheating furnace and the rotating machine. It is a huge challenge for RANS methods to simulate full complex industrial applications, which involve, for example, microscopic heat transfer phenomena such as in boiling and film cooling, and also interaction between complex secondary flows and mixing (Li et al., 2017). In many cases, the limitations of RANS models are exposed when trying to predict such thermal flows in industrial applications, where they suffer from severe instability and divergence issues. By using RANS models in this thesis, it has been possible to produce results with acceptable accuracy; however, only a small portion of each process is simulated, mainly due to the poor computational performance. For instance, the model shows unstable behavior when simulating interactions between multiple nearby jets at the ROT. Another limitation is the requirement for a large number of mesh elements to resolve thin liquid film, combustion chemistry and the very thin gap between the rotor and stator, for the ROT, reheating furnace and rotating machine, respectively. The complexity involved in the mesh generation pre-processing phase also requires a large amount of knowledge of the flow and the physics occurring in the process. For example, refining all the local regions, like boundary layers, to resolve the shear forces and the thermal gradients, or resolving the regions where interfaces appear in multiple phases or where interactions may take place. All this makes it cumbersome to generate a good mesh while maintaining a time-efficient workflow in industrial R&D. The accuracy and speed are always important factors that need to be balanced for industrial flow simulations. The flexibility to balance the accuracy and the speed of a RANS-based solver is severely restricted due to the required time and effort during re-meshing. Performing a large-scale simulation in a reasonable time is only possible by considering very coarse mesh, when the reliability of the results may be questionable. In summary, covering small details while simulating large-scale processes like the ROT and furnace are beyond the capability of RANS solvers with currently available computational resources. If the numerical results are to be used to control a process, a fast and flexible

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method other than mesh-based RANS methods must be used to produce large-scale simulation results in a reasonable time scale. To overcome these limitations, the general trend is to use mesh-free particle methods, hybrid methods or model-reduction approaches. However, most of the mesh-free and hybrid methods listed in Figure 2.1 are still under development, and thus a complete knowledge of their applicability to all the engineering fluid flow simulations is not available. Other emerging approaches to address large simulations are a multizonal approach or coupled methods. In a multi-zonal approach, large processes are usually divided into different zones, each zone is solved independently, and the results from different zones are then shared (Hu et al., 2018). In coupled methods, different sections of the same process are solved using different methods based on their capabilities, and the solution is shared or transferred between different zones (Kumar et al., 2015). To overcome some of the aforementioned limitations of RANS, SPH was selected as an alternative in this thesis. Thus, within the framework of this thesis, SPH thermal equations are implemented in the open-source SPH code DualSPHysics. This allows to SPH or a hybrid SPH–FVM approach to be used for industrial thermal simulations in future. The main idea is to overcome the limitations and benefit from both SPH and FVM methods.

RQ 2 Under what circumstances can SPH replace or complement RANS?

The growing use of SPH in different engineering CFD applications in the last two decades clearly indicates its potential in the field of CFD (Shadloo et al., 2016). The main motivation to use SPH in this thesis is its mesh- free feature, flexibility, robustness for different flow simulations, including free-surface flows, visualization, ease of use and straightforward possibility of adaptation by adding new multiphysics functionality. SPH is an emerging method, and thus many functionalities are currently missing in available SPH codes; for example, steady-state, symmetry condition, inlet-outlet boundary conditions, robust general wall boundary conditions and multi-resolution particle, which are necessary for many industrial flow and thermal simulations. From a theoretical perspective, SPH provides comparable accuracy to RANS- based FVM for a wide range of problems. However, the current development status and the support for the aforementioned missing functionalities in SPH will have a large role in the choice between SPH and FVM (Shadloo et al., 2016). Turbulence is another factor that requires special care and effort when modelling turbulent flows. Although methods like RANS based k − ε models are easy to implement in SPH, it is preferable to develop a turbulence model within the SPH framework to preserve the general principles (J. Monaghan, 2017, 2011). In many cases, the theory is available in the literature, however the development is slow because of the small user community. SPH is commonly used for coastal engineering problems, mainly due to the numerical efficiency and robustness when solving free-surface flows (J. Mon-

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aghan, 1994). Therefore, the majority of SPH developments are centered on coastal engineering problems. For free-surface flows, solving only the liquid phase provides sufficiently accurate results without any complex surface tracking algorithms, like those used in the RANS–VOF approach. This is a big advantage for flow problems such as those in the ROT or tank sloshing. Tank sloshing is one of the type of problems where SPH is the best fit and provides higher efficiency than FVM. The diverse applications of SPH include free- surface flows, multiphase flows, flows with floating bodies, fluid–structure interactions, blood flow, etc. (J. Monaghan, 2012; Shadloo et al., 2016). In this thesis, the main focus is on solving thermal problems. For heat transfer applications, it is very important to resolve the hydrodynamic and thermal boundary layers to efficiently calculate the viscous stress and thermal gradient, respectively. For thermal problems, it is a common approach for mesh-based methods to locally refine the mesh close to the wall where heat transfer takes place. By contrast, a uniform particle resolution is the most common choice for SPH developers; this is very inefficient for many industrial applications. This is because, all the available adaptive particle refinement algorithms based on splitting and coalescing are very sensitive due to strict stability and accuracy criteria, which makes the SPH algorithm very complex and numerically expensive (Shadloo et al., 2016). The rotating machine application simulated using SPH in Paper VI illustrates the need for such local refinement of particles in the air-gap between the rotor and the stator. Therefore, multi-resolution is one of the most important issues that must be addressed in order to use SPH in new industrial applications. The SPH thermal solver presented in this thesis illustrates the accuracy of SPH when solving laminar heat transfer problems. To use the SPH thermal solver for industrial problems with turbulent flows, it is necessary to use the multi-resolution particle feature to resolve the boundary layers. Therefore, SPH can be efficient for flows where boundary layers are less important, and for flows where the necessity of the multi-resolution particle feature can be avoided. Currently, replacing RANS-based FVM with SPH is not an easy choice, other than for free-surface flows. SPH can be used to complement FVM for solving flows with complex fluid–structure interactions, high deformation and interaction between complex secondary flows. SPH can also complement RANS using a coupled FVM–SPH approach.

RQ 3 What is the potential of using SPH in on-line control tools?

The accuracy of SPH for industrial fluid flow simulations and its flexibility inspire its use for industrial process control purposes. The use of SPH for online applications is decided by number of factors; for example, the computational cost, accuracy, efficiency and knowledge of applicability. The accuracy and speed of a SPH solver can easily be controlled by adjusting particle resolution, the influence radius and the number of neighboring particles for the

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interactions. SPH solvers in general perform slower than FVM solvers due to the requirement for a large number of neighboring particles to achieve similar accuracy and the Courant–Friedrichs–Lewy (CFL) condition (Courant et al., 1967), which applies to the small time steps (Shadloo et al., 2016). Moreover, the accuracy of the solver is tightly linked to the reliability and the computational cost of the simulation. However, because of the simplicity of the SPH algorithms, it is easy to parallelize the code to achieve significant speed-up by using HPC facilities like GPGPU (general purpose graphic processing unit) architecture-based parallel clusters, which often allow the simulation to run in real time (S. Kim & Park, 2014; Ji et al., 2012; Du & Kanai, 2014; Nie et al., 2015; He Yan et al., 2009). This is why SPH is heavily used in computer graphics industries for visualization of special fluid flow and thermal effects in films and games. SPH has a great potential to be used for a number of industrial processes if the simulation can be performed quickly enough to meet the time-scale of an online control tool. Real-time simulation can be achieved for flow problems involving free surfaces, such as sloshing in a tank. The simulation results for the sloshing tank presented in Paper VII shows good potential for use in online control tool in ships. The tanks can be simulated in small scale in real time, and then Froude number scaling laws can be applied to predict the forces on the wall for a large tank. Among the weaknesses of this approach, there are several SPH parameters, such as the influence radius, the viscosity and speed of sound, which need to be tuned for every application to reach a certain accuracy. This is a major bottleneck when using SPH. This kind of parameter tuning for new applications leaves uncertainties which need to be resolved in the future development of SPH by developing best practice guidelines. Developments like local particle refinement and best practice guidelines are needed to make SPH truly useful for complex industrial processes and to use the results in online control tools in appropriate cases.

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5. Summary of appended papers

The included papers are brieﬂy summarized in this chapter. The author’s contributions to the appended papers are also clearly stated here.

• Paper I: Heat transfer by liquid jets impinging on a hot flat surface (Hosain, Bel Fdhila, & Daneryd, 2015) Several CFD models to simulate impinging water jet cooling at ROT cooling process in hot rolling steel industries are developed in this paper. The analysis presented in this paper contributes to impinging jet cooling technology from both fundamental and applied perspectives. The thermal performance of the liquid impinging jet is analyzed in terms of single and multiple water jets impinging on a hot steel surface. A 3D model is developed to analyze the cooling effectiveness of the impinging water jet for hot rolling industries. A 2D axisymmetric model is also used to perform a parametric analysis to analyze the influence of the flow rate on the heat transfer. A correlation to predict the radial position of the maximum heat transfer co-efficient is also given based on the numerical results. Furthermore, a high fidelity 3D model of a double jet is developed to simulate jet–jet interaction in terms of flow and heat transfer. The presented results are validated using available theoretical and experimental results from published literature. The 2D parametric analysis shows a linear relationship between the flow rate and the average surface heat flux. A significant influence of flow rates on the diameter of the stagnation zone is also observed from the simulation results, which may greatly influence the uniformity of the cooling performance when the steel sheet is cooled using an array of jets.

• Paper II: CFD Modeling of Real Scale Slab Reheating Furnace (Hosain et al., 2016) In this paper, a 3D full-scale CFD model is developed to simulate the complex ﬂow and combustion inside an industrial slab re-heating furnace for hot rolling steel industries. The real operating conditions from the steel plant are used to simulate the temperature distribution inside the steel slabs. The conduction, convection and radiation heat transfer are simulated by resolving the detailed combustion from the

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liquefied natural gas burners. The simulated gas temperature inside the furnace is validated using measured data from the steel plant. The simulated heating profile of the steel slab is also compared to the predicted heating profile from the online control tool. Numerical results show a high degree of recirculation inside the furnace, which is consequently responsible for forming iron oxide layers on the steel slabs, one of the common problems encountered in the hot rolling steel plant.

• Paper III: Literature Review of Accelerated CFD Simulation Methods towards Online Application.(Hosain & Fdhila, 2015) In this paper, a literature survey is performed to identify the available CFD methods for solving industrial problems related to multi-phase flow, free-surface flow and heat transfer. The main purpose of the survey is to identify CFD methods that can be used to perform simulations in real time or near real time to be used in the online control system for decision support during the ongoing process operation. The reviewed methods are presented by classification into different families together with a brief overview of each method.

• Paper IV: Taylor-Couette flow and transient heat transfer inside the annulus air-gap of rotating electrical machines. (Hosain, Bel Fdhila, & Rönnberg, 2017) In this paper, a simplified 3D model of a rotating machine (motor) consisting of a rotor and a stator is developed to analyze the transient fluid flow and heat transfer inside the machine. The main focus of the article is evaluation of the Taylor–Couette flow heat transfer in the air-gap between the rotor and the stator. The complex flow patterns due to the aerodynamic friction and the turbulence generated by the rotor wafters are discussed and their influence on the heat transfer is also highlighted. The transient effects induced by the rotor wafters introduces oscillations to the Taylor–Couette vortices, which result in oscillations of the hotspots. However, the observed oscillations do not influence the global thermal performance.

• Paper V: Air-Gap Heat Transfer in Rotating Electrical Machines: A Parametric Study. (Hosain & Fdhila, 2017) This paper is a continuation of work based on Paper IV, in which a parametric analysis is performed by varying the air-gap width between the rotor and the stator and the rotation speed. The heat transfer in the air-gap of a rotating machine is analyzed in detail by performing 9 simulations combining 3 different air-gap widths

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and 3 different rotation speeds. The results from all 9 models are compared, and the efficiency of heat transfer is discussed. The heat transfer coefficients from all the models are validated successfully by available correlations from experimental data. The results show that the heat transfer coefficient increases with increase in rotation speed and the air-gap width. The heat transfer is enhanced when Taylor vortices are present. The Taylor vortices disappear with an air- gap of 1 mm or less, thus the heat transfer coefficient drops significantly.

• Paper VI: Air Flow inside Rotating Electrical Machines: A Comparison between Finite Volume and SPH Method. (Hosain, Rönnberg, & Bel Fdhila, 2017) In this paper, the SPH method is introduced for the first time to simulate the air-flow inside the rotating machine. A simplified model geometry representing a fully enclosed motor consisting of a rotor and a stator is used to model the airflow using both the mesh-based finite volume method (FVM) and the mesh-free particle-based SPH. The results from both methods are compared and their limitations are discussed. The results presented in this paper show the ability of SPH to capture the complex aerodynamics with an accuracy comparable to the results from the FVM model.

• Paper VII: Numerical Investigation of Liquid Sloshing in Carrier Ship Fuel Tanks. (Hosain et al., 2018) This paper presents and compares simulations of liquid sloshing in a carrier ship fuel tank using SPH and the VOF method. A downscaled 2D geometry of a partially filled tank is considered to investigate the sloshing under sinusoidal roll motion. The main purpose of this study is to assess the accuracy and efficiency of the two numerical methods. The application of scaling laws, which are often used to reduce the size of a large complicated system, is also evaluated. The pressure and forces acting on the walls of the tank are numerically calculated and validated using available experimental data. Due to its relatively short simulation time, SPH is also used for the full-scale geometry, to validate the downscaling approach. The SPH method shows higher efficiency when capturing the sloshing dynamics, while producing the results much more quickly than the RANS–VOF model. Moreover, the results from the SPH model indicate that the Froude number scaling law can be applied to the tank sloshing problem.

• Paper VIII: Simulation and validation of ﬂow and heat transfer in an inﬁnite mini-channel using Smoothed Particle Hydrodynamics. (M. L.

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Hosain, Fdhila & Kyprianidis) (Accepted for publication in Energy procedia) In this paper, laminar Poiseuille flow heat transfer in an infinitely long mini-channel is simulated. The main purpose of this study is to investigate the usability of the mesh-free particle-based SPH method for convective heat transfer problems. To evaluate this capability, we chose to solve a simple well-established problem: the laminar flow and heat transfer through an infinitely long mini-channel. The same case is also solved using FVM. The simulated flow and heat transfer by the SPH model is compared to the solution from FVM and the analytical solution. The results show that the SPH thermal solver achieves a highly satisfactory accuracy level.

• Paper IX: Smoothed Particle Hydrodynamics modeling of transient conduction and convection heat transfer. (M. L. Hosain, Dominguez, Crespo, Fdhila & Kyprianidis) (Journal Manuscript) This paper implements the thermal equations in the open-source SPH code DualSPHysics. DualSPHysics is the most user-friendly and popular open-source code written in C++ based on the weakly compressible SPH (WCSPH). However, DualSPHysics is currently capable of solving only fluid flow, which limits its use for problems related to heat transfer. The main contribution of this article is the implementation of the energy conservation equation in DualSPHysics, which extends its functionality to solving heat transfer problems. The work was performed in tight collaboration with the main developers of DualSPHysics, from the University of Vigo, Spain. In this article, several classical 2D laminar heat transfer problems are solved to verify the accuracy of the SPH thermal model. The cases are chosen for the ability to test our code for both conduction and convection heat transfer. The cases involve conduction in an aluminium block and in still water in a cavity, laminar water flow between two infinite parallel plates and a tube bank heat exchanger. The same cases are solved using FVM to benchmark the solutions from both solvers. The thermal solution achieved with the SPH thermal solver are in good agreement with the solution from the FVM solver, demonstrating the efficiency of SPH for solving laminar heat conduction and convection heat transfer problems.

Author’s Contributions to the appended papers: The author developed all the numerical models used for the simulations, performed all the simulations and analyzed the results presented in Paper I – Paper VI, Paper VIII and Paper IX. The author also developed the SPH

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model, performed the SPH simulations and analyzed the results in Paper VII, while, the RANS–VOF simulations in Paper VII were performed by co-author Ulf Sand from ABB corporate research. The author reviewed relevant literature reported in all the appended papers and wrote the majority of all the appended papers, serving as ﬁrst author. Valuable inputs, comments and suggestions to improve the papers were received from the co-authors of the respective papers. All the work presented in the appended papers was performed under the supervision of the main supervisor and the co-supervisors.

Limitations of the studies The thesis presents CFD simulations of several industrial ﬂow and heat transfer. The limitations of the work are as follows:

• The jet–jet distance considered in the double-jet model in Paper I is much larger than usually encountered in the ROT cooling process in a steel plant. This is because the RANS–VOF solver suffered from severe instability and divergence issues with smaller jet–jet distances. Further- more, boiling is a typical phenomenon at the ROT cooling process due to the high temperature conditions and the steel sheet usually moves at a certain speed. In this study, the steel sheet is considered as stationary and a temperature below 100 ◦C is considered to avoid boiling phenomena in order to simplify the problem.

• The model geometry for the rotating machine application in Paper IV is a design used for model assessment and veriﬁcation purposes, and is intended to resemble a low voltage motor. The air-gap between the rotor and the stator is considered at 5 mm, whereas it is typically about 1 mm. However, to mitigate this limitation, a 1mm gap was considered in the parametric study presented in Paper V. The reason for using a larger air-gap was to be able to use the same model for SPH in order to make comparison with FVM. Resolving a 1 mm air-gap in the SPH model was impractical due to the limitation of uniform resolution for the whole rotating machine.

• The SPH thermal model presented in Paper IX is used to solve laminar ﬂow and heat transfer cases only. To model turbulent ﬂows, more robust boundary conditions and turbulence models have to be implemented.

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6. Conclusions

This chapter presents the major conclusions of the thesis.

The main focus in this thesis is the analysis of complex fluid flow and heat transfer in selected industrial processes to be able to improve, diagnose and control them. To improve or optimize any industrial process or product, it is essential to have a clear understanding of the underlying physical phenomena. The most reliable approaches, such as experiments and measurements to analyze a process or product, are not always preferable, due to the uncer- tainty and associated cost. It is often extremely difficult to reproduce the real phenomena with experiments. Furthermore, it is often not possible to perform detailed measurements to describe a large-scale process like the slab re-heating furnace, due to the unavailability of suitable measurement technologies. Therefore, the fluid flow and heat transfer in the selected industrial applications have been simulated in this thesis by employing two different CFD approaches, RANS and SPH. The thesis provides detailed insight into different processes and products, from both fundamental and applied physics perspectives. The strengths and limitations of the introduced CFD approaches are highlighted and the future of such approaches for industrial applications is discussed. One of the main goals of this thesis is to introduce and use SPH for industrial flow and thermal simulations. To evaluate the capability and efficiency of SPH to solve thermal problems, SPH thermal equations are implemented into the open-source code DualSPHysics. The SPH thermal solver is used to solve heat conduction and convection problems to illustrate and compare the accuracy with the RANS-based FVM method. The four industrial applications and the theoretical cases simulated in this thesis are jet impingement cooling in the ROT cooling process, slab re-heating furnace, rotating machines, sloshing in a moving tank, tube bank heat exchanger and Poiseuille flow heat transfer. The rotating machine, sloshing in tank, Poiseuille flow heat transfer and the heat exchanger are solved using both FVM and SPH. The impinging jet cooling and the re-heating furnace are simulated using FVM. The idea in this thesis is to use the positive features from both FVM and SPH, combining their strengths and mitigating their limitations, to simulate large industrial processes. The simulation results from ROT cooling and the furnace exhibit multiphysics phenomena with interactions between secondary flows. The multiple space and time scales present in large industrial processes like the ROT and the furnace make it extremely

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challenging to simulate such flows. In some cases, such as in the case of ROT, FVM failed to resolve the interactions between multiple streams from water jets impinging very close to each other. The FVM solver suffers from severe instability and divergence issues due to the splashing in the ROT and high degrees of re-circulations in the furnace. The mesh-based RANS solvers are limited in such industrial applications. Therefore, an alternative approach, SPH, is implemented in this thesis to shed some light on the potential of using SPH for complex industrial flows and thermal simulations. However, the SPH thermal solver needs to be complemented by developing more general and robust boundary conditions and suitable turbulence models to solve industrial turbulent flow and thermal problems. Several other functionalities, such as inlet-outlet boundary conditions and multiresolution particles, need to be implemented before the SPH method can be considered as an established method for the type of industrial applications analyzed here. To complement the capabilities and mitigate the limitations of both SPH and FVM, a coupled FVM–SPH solver could be an interesting solution for large industrial simulations in the future. However, targeting such an approach requires further justifications. The SPH thermal development in this thesis is an important step towards a coupled FVM–SPH fast thermal solver for industrial flow and thermal simulations.

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7. Future work

This chapter suggests some possible potential future work based on the discussion, described research challenges, limitations of the work and the identiﬁed research need.

• The impinging jet model presented in Paper I can be extended by considering multiple jets with a smaller separation than the one considered. Parametric studies could be performed by varying the nozzle diameter and the distance between the nozzle and the steel surface to investigate their inﬂuence on the cooling efﬁciency.

• The reheating furnace simulated in paper II consists of several zones. In this paper only the preheating zone (Zone1) is simulated. The model can be extended by including more zones of the furnace.

• The sloshing in a partially ﬁlled tank in Paper VII is simulated under sinusoidal rolling motion. However, in reality the sloshing is a result of combined forces from rolling, yawing and pitching motions of a ship. The presented model could be extended in future by considering yawing and pitching motion to simulate a more realistic case scenario. To do this the model needs to be extended to a 3D domain.

• The SPH thermal development in Paper IX is limited to laminar flow cases due to the unavailability of a suitable boundary condition in Dual- SPHysics that can resolve a thin boundary layer. The thermal development needs to be complemented by adding new features such as robust wall boundary condition, local particle refinement and suitable turbulence models to enhance the applicability to industrial turbulent flows and thermal problems.

• A coupled FVM–SPH solver can be developed to simulate large industrial processes to overcome the highlighted limitations of both methods.

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Appendix

Velocity and gravitation effect on the interface of the water jet The gravitational effect on the interface of a free surface impinging jet can be described using the Continuity equation and the Bernoulli’s equation. The following assumptions are made for the derivation: • The water jet remains circular after it leaves the nozzle. • The total energy of the jet is conserved.

Gravitation and velocity effect on the free surface

Let, Uf , U are the jet velocities, d, D are the jet diameters, A1,A2 are the cross section areas of the jet, z0,Z are the distances from the plate and P1,P2 are pressures at h1 and h2 respectively. The gravitational constant is g and the ﬂuid density is ρ. Then, the continuity equation can be written as:

A1u1 = A2u2 2 2 ⇒ (πd /4)Uf = (πD /4)U 2 2 ⇒ d Uf = D U 2 2 ⇒ d /D = U/Uf

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Now, the Bernoulli’s equation can be written as follows:

2 2 Uf /2 + gz0 + P1/ρ = U /2 + gZ + P2/ρ 2 2 ⇒ Uf /2 + gz0 = U /2 + gZ (Let,P1 = P2 = 1atm) 2 2 ⇒ U = Uf + 2g(z0 − Z) 2 2 2 ⇒ U /UF = 1 + 2g(z0 − Z)/Uf 4 4 2 2 2 ⇒ d /D = 1 + 2g(z0 − Z)/Uf (substituting,U/Uf = d /D ) 2 1/4 ⇒ d/D = (1 + 2g(z0 − Z)/Uf ) 2 −1/4 ⇒ D = d(1 + 2g(z0 − Z)/Uf )