Mathematical Modelling of Fluid Flows in Pipe Networks

The mathematical description of splitting and merging of flows is an important part of a detailed heat exchanger simulation model suitable for studying dynamic and static flow instabilities. This thesis considers one such description, the network models for fluid flow in junctions. Briefly described, these models consist of a one dimensional hyperbolic conservation law, the corresponding equation of state, coupling conditions and wave equations. In the present work, the generalized Riemann problem has been considered and thus each pipe section has a constant initial condition. The set of coupling conditions enables the construction of boundary conditions at the pipe-junction interface of each pipe section connected at a junction. They are defined such that the boundary condition of each section is related to the initial conditions of all the connected pipe sections. The wave equations relate the constructed boundary condition and the initial condition of a pipe section under the restriction that the constructed state must propagate into the section. This thesis mainly considers network models derived for the isothermal and isentropic Euler equations. A mandatory coupling condition is thus that mass is conserved at the junction. However, as the conservation laws consist of two equations, a second condition is needed. The choice of a momentum related coupling constant, H(, v), is common in the literature and has therefore been applied in this thesis as well. In particular, the proper selection of the coupling constant expression has been the main focus of the work. Both pressure and momentum flux have been commonly applied as momentum related coupling constant in network models presented in the literature. In this thesis, existence and uniqueness of solutions to the generalized Riemann problem have been proved for network models that apply the two different constants. The proof is restricted to sets of initial conditions that belong to the subsonic region. That is, the region where both the initial conditions and the solutions are subsonic. An investigation of the physical soundness of the solutions for a junction connecting three pipe sections revealed that none of the proposed coupling constants yield physical solutions for all subsonic flows at the pipe-junction interfaces. In particular, a duality was observed for isothermal flows. In the flow-ranges where pressure as coupling constant yields physical solutions, momentum flux yields unphysical solutions, and opposite. Unphysical solutions are characterised by the presence of energy production in a junction. The lack of physically sound solutions within the entire subsonic region lead to a search for an alternative coupling constant. As a result, the Bernoulli invariant has been suggested and existence and uniqueness of solutions to the corresponding generalized Riemann problem have been proved for sets of initial data that belong to the subsonic region. It has also been proved that the constant yields physically sound solutions for all subsonic solutions. A numerical implementation of three network models based on the isothermal Euler equations have been performed in addition to the theoretical investigation. The three different models applied pressure, momentum flux and Bernoulli invariant as momentum related coupling constant, respectively. Test cases for three different network layouts were derived, and corresponding numerical results presented. Each set of simulation results has been analysed with respect to physical soundness. All cases are seen to support the analytically based conclusion; only Bernoulli invariant as momentum related coupling constant yields physical solutions for all sets of initial conditions that belong to the subsonic region.PhD i energi- og prosessteknikkPhD in Energy and Process Engineerin

Applying endogenous learning models in energy system optimization

Conventional energy production based on fossil fuels causes emissions which contribute to global warming. Accurate energy system models are required for a cost-optimal transition to a zero-emission energy system, an endeavor that requires an accurate modeling of cost reductions due to technological learning effects. In this review, we summarize common methodologies for modeling technological learning and associated cost reductions. The focus is on learning effects in hydrogen production technologies due to their importance in a low-carbon energy system, as well as the application of endogenous learning in energy system models. Finally, we present an overview of the learning rates of relevant low-carbon technologies required to model future energy systems.Comment: review paper: main article (11 pages), appendices (8 pages), references (4 pages

Theories and Mechanism of Rapid Phase Transition

Light hydrocarbons and hydrogen can replace high-alkane fuels with the benefit of reduced CO2 emissions. Their liquefaction to a cryogenic state is one of the most suitable solutions for storage and transport. An unexpected release of these fuels might lead to a rapid phase transition (RPT). RPT is a physical explosion well-known for liquefied natural gas (LNG), and may occur when this substance is spilled onto water. The heat provided by the water to the cryogenic fuel might lead to a sudden evaporation of the liquid, resulting in an explosion. The generated blast wave has the potential to damage equipment and personnel. The RPT phenomenon can also occur in different types of industrial applications when molten metals accidentally come in contact with water. In these cases, the water is the cold fluid which expands violently. In this study, the RPT phenomenon is investigated for cryogenic fluids (liquefied hydrocarbons, nitrogen and hydrogen) as well as for smelts (molten inorganic salts) and molten metals (aluminum). The contribution has a twofold purpose as it addresses relevant past accidents and lay the foundation for future modelling activities to simulate the cryogenic-pool formation on water, triggering of an RPT event and the RPT explosion consequences. Furthermore, the RPT theories and mechanisms comprehension is critical to qualitatively evaluate the probability for a liquid hydrogen (LH2) RPT. In particular, a comparison between liquid nitrogen (LN2) and LH2 is conducted to understand under which conditions an LH2 RPT might occur. The results of this study are to be validated through the Safe Hydrogen Fuel Handling and Use for Efficient Implementation (SH2IFT) project, in which a series of LH2 spill tests onto water will be conducted.publishedVersionThis journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge. Our policy is to permit Authors to reuse part of their CET articles or to self-archive the published version of their work in Institutional Repository, provided that AIDIC/CET is acknowledged as the source. The version to be used is the Publisher’s PDF. No embargo period is required

A combined fluid-dynamic and thermodynamic model to predict the onset of rapid phase transitions in LNG spills

Transport of liquefied natural gas (LNG) by ship occurs globally on a massive scale. The large temperature difference between LNG and water means LNG will boil violently if spilled onto water. This may cause a physical explosion known as rapid phase transition (RPT). Since RPT results from a complex interplay between physical phenomena on several scales, the risk of its occurrence is difficult to estimate. In this work, we present a combined fluid-dynamic and thermodynamic model to predict the onset of delayed RPT. On the basis of the full coupled model, we derive analytical solutions for the location and time of delayed RPT in an axisymmetric steady-state spill of LNG onto water. These equations are shown to be accurate when compared to simulation results for a range of relevant parameters. The relative discrepancy between the analytic solutions and predictions from the full coupled model is within 2% for the RPT position and within 8% for the time of RPT. This provides a simple procedure to quantify the risk of occurrence for delayed RPT for LNG on water. Due to its modular formulation, the full coupled model can straightforwardly be extended to study RPT in other systems.Comment: 22 pages, 11 figure

Moving toward the low-carbon hydrogen economy: experiences and key learnings from national case studies

The urgency to achieve net-zero carbon dioxide (CO2) emissions by 2050, as first presented by the IPCC special report on 1.5 °C Global Warming, has spurred renewed interest in hydrogen, to complement electrification, for widespread decarbonization of the economy. We present reflections on estimates of future hydrogen demand, optimization of infrastructure for hydrogen production, transport and storage, development of viable business cases, and environmental impact evaluations using life cycle assessments. We highlight challenges and opportunities that are common across studies of the business cases for hydrogen in Germany, the UK, the Netherlands, Switzerland and Norway. The use of hydrogen in the industrial sector is an important driver and could incentivise large-scale hydrogen value chains. In the long-term hydrogen becomes important also for the transport sector. Hydrogen production from natural gas with capture and permanent storage of the produced CO2 (CCS) enables large-scale hydrogen production in the intermediate future and is complementary to hydrogen from renewable power. Furthermore, timely establishment of hydrogen and CO2 infrastructures serves as an anchor to support the deployment of carbon dioxide removal technologies, such as direct air carbon capture and storage (DACCS) and biohydrogen production with CCS. Significant public support is needed to ensure coordinated planning, governance, and the establishment of supportive regulatory frameworks which foster the growth of hydrogen markets

Mathematical Modelling of Fluid Flows in Pipe Networks

The mathematical description of splitting and merging of flows is an important part of a detailed heat exchanger simulation model suitable for studying dynamic and static flow instabilities. This thesis considers one such description, the network models for fluid flow in junctions. Briefly described, these models consist of a one dimensional hyperbolic conservation law, the corresponding equation of state, coupling conditions and wave equations. In the present work, the generalized Riemann problem has been considered and thus each pipe section has a constant initial condition. The set of coupling conditions enables the construction of boundary conditions at the pipe-junction interface of each pipe section connected at a junction. They are defined such that the boundary condition of each section is related to the initial conditions of all the connected pipe sections. The wave equations relate the constructed boundary condition and the initial condition of a pipe section under the restriction that the constructed state must propagate into the section. This thesis mainly considers network models derived for the isothermal and isentropic Euler equations. A mandatory coupling condition is thus that mass is conserved at the junction. However, as the conservation laws consist of two equations, a second condition is needed. The choice of a momentum related coupling constant, H(, v), is common in the literature and has therefore been applied in this thesis as well. In particular, the proper selection of the coupling constant expression has been the main focus of the work. Both pressure and momentum flux have been commonly applied as momentum related coupling constant in network models presented in the literature. In this thesis, existence and uniqueness of solutions to the generalized Riemann problem have been proved for network models that apply the two different constants. The proof is restricted to sets of initial conditions that belong to the subsonic region. That is, the region where both the initial conditions and the solutions are subsonic. An investigation of the physical soundness of the solutions for a junction connecting three pipe sections revealed that none of the proposed coupling constants yield physical solutions for all subsonic flows at the pipe-junction interfaces. In particular, a duality was observed for isothermal flows. In the flow-ranges where pressure as coupling constant yields physical solutions, momentum flux yields unphysical solutions, and opposite. Unphysical solutions are characterised by the presence of energy production in a junction. The lack of physically sound solutions within the entire subsonic region lead to a search for an alternative coupling constant. As a result, the Bernoulli invariant has been suggested and existence and uniqueness of solutions to the corresponding generalized Riemann problem have been proved for sets of initial data that belong to the subsonic region. It has also been proved that the constant yields physically sound solutions for all subsonic solutions. A numerical implementation of three network models based on the isothermal Euler equations have been performed in addition to the theoretical investigation. The three different models applied pressure, momentum flux and Bernoulli invariant as momentum related coupling constant, respectively. Test cases for three different network layouts were derived, and corresponding numerical results presented. Each set of simulation results has been analysed with respect to physical soundness. All cases are seen to support the analytically based conclusion; only Bernoulli invariant as momentum related coupling constant yields physical solutions for all sets of initial conditions that belong to the subsonic region

Numerical network models and entropy principles for isothermal junction flow

<p>Post print included in PhD has been published OA doi:10.3934/nhm.2014.9.65 </p

The risk for rapid phase transition in LNG spilled on water : an overview of the Predict-RPT project

publishedVersio

Pipe Networks: Coupling Constants in a Junction for the Isentropic Euler Equations

AbstractThe modelling of junctions in pipe networks with subsonic flows is discussed, where pipes are described by one-dimensional, single-phase isentropic flow models. We first study the Riemann problem in a pipe to understand what information is needed to couple two pipes in a flat junction. Using this insight, we generalise the Riemann problem to an arbitrary number of pipes meeting together at a junction. Three coupling strategies found in the literature are presented, where only one leads to physically sound solutions for all the selected test cases. The theoretical derivation is performed in previously published literature.The junction is considered to be a point with no volume. The three coupling strategies are, first, to impose all the pipe sections to be at the same pressure at the junction. The second is to impose equal momentum fluxes at the inlet of all the pipes coupled to the junction. The third is to impose all the pipe sections to reach the junction at a unique stagnation enthalpy, that is, equal for all of them. Only the latter satisfies the second law of thermodynamics, expressed through an entropy condition, in all the test cases run in the study. For the two former coupling strategies, test cases where the entropy condition is violated could be found and are presented.The different coupling strategies are implemented in a numerical model. The one-dimensional models for the pipe sections are solved using a Roe scheme. We illustrate with numerical cases that we can find initial conditions for which the entropy condition is violated for the two first coupling strategies, while the third verifies it in all the cases