The applicability of CFD codes for two-phase flows has always been limited to special cases due to the very complex nature of its interface. Due to its tremendous computational cost, methods based on direct resolution of the interface are not applicable to most problems of practical relevance. Instead, averaging procedures are commonly used for these applications, such as the Eulerian-Eulerian approach, which necessarily means losing detailed information on the interfacial structure. In order to allow widespread application of the two-fluid approach, closure models are required to reintroduce in the simulations the correct interfacial mass, momentum, and heat transfer. It is evident that such closure models will strongly depend on the specific flow pattern. When considering vertical pipe flow with low gas volume flow rates, bubbly flow occurs. With increasing gas volume flow rates larger bubbles are generated by bubble coalescence, which further leads to transition to slug, churn-turbulent, and annular flow. Considering, as an example, a heated tube producing steam by evaporation, as in the case of a vertical steam generator, all these flow patterns including transitions are expected to occur in the system. Despite extensive attempts, robust and accurate simulations approaches for such conditions are still lacking. The purpose of this dissertation is the development, testing, and validation of a multifield model for adiabatic gas-liquid flows at high gas volume fractions, for which a multiple-size bubble approach has been implemented by separating the gas structures into a specified number of groups, each of which represents a prescribed range of sizes. A fully-resolved continuous gas phase is also computed, and represents all the gas structures which are large enough to be resolved within the computational mesh. The concept, known as GENeralized TwO Phase flow or GENTOP, is formulated as an extension to the bubble population balance approach known as the inhomogeneous MUltiple SIze Group (iMUSIG). Within the polydispersed gas, bubble coalescence and breakup allow the transfer between different size structures, while the modeling of mass transfer between the polydispersed and continuous gas allows including transitions between different gas morphologies depending on the flow situations. The calculations were performed using the computational fluid dynamic code from ANSYS, CFX 14.5, with the support of STAR-CCM+ v8.06 and v9.02. A complete three-field and four-field model, including a continuous liquid field and two to three gas fields representing bubbles of different sizes, were first tested for numerical convergence and then validated against experimental data from the TOPFLOW and MT-Loop facilities.

The applicability of CFD codes for two-phase flows has always been limited to special cases due to the very complex nature of its interface. Due to its tremendous computational cost, methods based on direct resolution of the interface are not applicable to most problems of practical relevance. Instead, averaging procedures are commonly used for these applications, such as the Eulerian-Eulerian approach, which necessarily means losing detailed information on the interfacial structure. In order to allow widespread application of the two-fluid approach, closure models are required to reintroduce in the simulations the correct interfacial mass, momentum, and heat transfer. It is evident that such closure models will strongly depend on the specific flow pattern. When considering vertical pipe flow with low gas volume flow rates, bubbly flow occurs. With increasing gas volume flow rates larger bubbles are generated by bubble coalescence, which further leads to transition to slug, churn-turbulent, and annular flow. Considering, as an example, a heated tube producing steam by evaporation, as in the case of a vertical steam generator, all these flow patterns including transitions are expected to occur in the system. Despite extensive attempts, robust and accurate simulations approaches for such conditions are still lacking. The purpose of this dissertation is the development, testing, and validation of a multifield model for adiabatic gas-liquid flows at high gas volume fractions, for which a multiple-size bubble approach has been implemented by separating the gas structures into a specified number of groups, each of which represents a prescribed range of sizes. A fully-resolved continuous gas phase is also computed, and represents all the gas structures which are large enough to be resolved within the computational mesh. The concept, known as GENeralized TwO Phase flow or GENTOP, is formulated as an extension to the bubble population balance approach known as the inhomogeneous MUltiple SIze Group (iMUSIG). Within the polydispersed gas, bubble coalescence and breakup allow the transfer between different size structures, while the modeling of mass transfer between the polydispersed and continuous gas allows including transitions between different gas morphologies depending on the flow situations. The calculations were performed using the computational fluid dynamic code from ANSYS, CFX 14.5, with the support of STAR-CCM+ v8.06 and v9.02. A complete three-field and four-field model, including a continuous liquid field and two to three gas fields representing bubbles of different sizes, were first tested for numerical convergence and then validated against experimental data from the TOPFLOW and MT-Loop facilities.

Safe and reliable operation of nuclear power plants is the basic requirement for the utilization of nuclear energy since accidents can release radioactivity and with that cause irreversible damage to human beings. Reliability and safety of nuclear reactors are highly dependent on the stability of thermal hydraulic processes occurring in them. Nucleate boiling occurs in Pressurized Water Reactors (PWRs) and Boiling Water Reactors (BWRs) as well as in their passive safety systems during an accident. Passive safety systems are solely driven by thermal gradients and gravitational force removing residual heat from the reactor core independent of any external power supply in the case of accidents. Instability of flow boiling in these passive circuits can cause flow oscillations. These oscillations may induce insufficient local cooling and mechanical loads, which threatens the reactors’ safety. Analysis of boiling two-phase flow and associated heat and mass transfer requires an accurate modeling of flow regime transitions and prediction of boiling parameters such as void fraction, steam bubble sizes, heat transfer coefficient, etc. Flow boiling has been intensively investigated through experiments, one-dimensional codes, and Computational Fluid Dynamics (CFD) methods. Costly hardware and no accessibility to all locations in complex geometries restrict the experimental investigation of flow boiling. Since one-dimensional codes such as ATHLET, RELAP and TRACE are ”lumped parameter” codes, they are unable to simulate complex flow boiling transition patterns. In the last decades, with the development of supercomputers, CFD has been considered as a useful tool to model heat and mass transfer occurring in flow boiling regimes. In many industrial applications and system designs, CFD codes and particularly the Eulerian-Eulerian (E-E) two-fluid model are quickly replacing the experimental and analytical methods. However, the application of this approach for flow boiling modelling poses a challenge for the development of bubble dynamics and wall boiling models to predict heat and mass transfer at the heating wall as well as phase-change mechanism. Many empirical and mechanistic models have been proposed for bubble dynamics modelling. Nevertheless, the validity of these models for only a narrow range of operating conditions and their uncertainties limit their applicability and consequently presently necessitate us to calibrate them for a given boundary condition via calibration factors. For that reason, the first aim of this thesis is the development of a bubble dynamics model for subcooled boiling flow, which needs no calibration factor to predict the bubble growth and detachment. This mechanistic model is formulated based on the force balance approach, physics of a single nucleated bubble and several well-developed models to cover the whole bubble life cycle including formation, growth and departure. This model considers dynamic inclination angle and contact angles between the bubble and the heating wall as well as the contribution of microlayer evaporation, thermal diffusion and condensation around the bubble cap. Validation against four experimental flow boiling data sets was conducted with no case-dependent recalibration and yielded good agreement. The second goal is the implementation of the developed bubble dynamics model in the E-E two-fluid model as a sub-model to improve the accuracy of boiling flow simulation and reduce the case dependency. This implementation requires an extension of the nucleation site activation and wall heat-partitioning models. The bubble dynamics and heat-partitioning models were coupled with the Population Balance Model (PBM) to handle bubble interactions and predict the Bubble Size Distribution (BSD). In addition, the contribution of bubble sliding to wall heat transfer, which has been rarely considered in other modelling approaches, is considered. Validation for model implementation in the E-E two-fluid model was made with ten experimental cases including R12 and R134a flow boiling in a pipe and an annulus. These test cases cover a wide range of operating parameters such as wall heat flux, fluid velocity, subcooling temperature and pressure. The validated parameters were the bubble diameter, void fraction, bubble velocity, Interfacial Area Density (IAD), bubble passing frequency, liquid and wall temperatures. Two-phase flow morphologies for an upward flow in a vertical heating pipe may change from bubbly to slug, plug, and annular flow. Since these flow patterns have a great impact on the heat and mass transfer rates, an accurate prediction of them is critical. The aim of this thesis is the implementation of the developed bubble dynamics and heat-partitioning models in the recently developed GENeralized TwO-Phase flow (GENTOP) framework for the modelling of these flow patterns transition as well. An adopted wall heat-partitioning model for high void fractions is presented and for a generic test case, flow boiling regimes of water in a vertical heating pipe were modelled using ANSYS CFX 18.2. Moreover, the impacts of wall superheat, subcooling temperature and fluid velocity on the flow boiling transition patterns and the effects of these patterns on the wall heat transfer coefficient were evaluated.:Nomenclature xi 1 Introduction 1 1.1 Background and motivation . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2 State-of-the-art in modelling of subcooled flow boiling 11 2.1 Physics of boiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2 Bubble growth modelling . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 CFD simulation of boiling flows . . . . . . . . . . . . . . . . . . . . . 21 2.3.1 The Eulerian-Eulerian two-fluid model . . . . . . . . . . . . . 21 2.3.2 The Population Balance Model (PBM) . . . . . . . . . . . . . 22 2.3.3 Governing equations of the two-fluid model . . . . . . . . . . 25 2.3.4 Closure models for adiabatic bubbly flow . . . . . . . . . . . . 28 2.3.5 Phase transfer models . . . . . . . . . . . . . . . . . . . . . . 37 2.3.6 The Rensselaer Polytechnic Institute (RPI) wall boiling model 37 2.4 Flow boiling transition patterns in vertical pipes . . . . . . . . . . . . 42 2.5 The GENeralized TwO-Phase flow (GENTOP) concept . . . . . . . . . 45 2.5.1 Treatment of the continuous gas . . . . . . . . . . . . . . . . 46 2.5.2 The Algebraic Interfacial Area Density (AIAD) model . . . . . 46 2.6 Interfacial transfers of continuous gas . . . . . . . . . . . . . . . . . 47 2.6.1 Drag and lift forces . . . . . . . . . . . . . . . . . . . . . . . . 48 2.6.2 Cluster and surface tension forces . . . . . . . . . . . . . . . . 49 2.6.3 Complete coalescence . . . . . . . . . . . . . . . . . . . . . . 50 2.6.4 Entrainment modelling . . . . . . . . . . . . . . . . . . . . . . 51 2.6.5 Turbulence modelling . . . . . . . . . . . . . . . . . . . . . . 51 2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3 An improved bubble dynamics model for flow boiling 55 3.1 Modelling of the bubble formation . . . . . . . . . . . . . . . . . . . 55 3.1.1 Bubble growth rate . . . . . . . . . . . . . . . . . . . . . . . . 57 3.1.2 Force balance . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 ix 3.1.3 Detachment criteria . . . . . . . . . . . . . . . . . . . . . . . 63 3.1.4 Wall heat flux model . . . . . . . . . . . . . . . . . . . . . . . 69 3.1.5 Heat transfer in the heating wall . . . . . . . . . . . . . . . . 70 3.2 Results and discussions . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.2.1 Discretization dependency study . . . . . . . . . . . . . . . . 72 3.2.2 Model validation . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.2.3 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . 79 3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4 An improved wall heat-partitioning model 85 4.1 The cavity group activation model . . . . . . . . . . . . . . . . . . . . 85 4.1.1 Bubble sliding length and influence area . . . . . . . . . . . . 88 4.1.2 Model implementation in the Eulerian-Eulerian framework . . 89 4.2 Results and discussions . . . . . . . . . . . . . . . . . . . . . . . . . . 90 4.2.1 DEBORA experiments . . . . . . . . . . . . . . . . . . . . . . 90 4.2.2 Subcooled flow boiling of R134a in an annulus . . . . . . . . 102 4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 5 Modelling of flow boiling patterns in vertical pipes 115 5.1 Adopted wall heat-partitioning model for high void fractions . . . . . 115 5.2 Results and discussions . . . . . . . . . . . . . . . . . . . . . . . . . . 118 5.2.1 Effect of wall superheat on the flow boiling transition patterns 118 5.2.2 Effect of flow morphologies on the wall heat transfer coefficient124 5.2.3 Comparison of GENTOP and Eulerian-Eulerian two-fluid models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 5.2.4 Effect of subcooling on the flow boiling transition patterns . . 129 5.2.5 Effect of inlet fluid velocity on the flow boiling transition patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 6 Conclusions and outlook 133 6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 6.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 References 137 Declaration 155