Flow characteristics of hydrogen gas through a critical nozzle

Critical nozzles are widely used in the flow measurement and can be used for mass flow-rate measurement of hydrogen gas. The effect of real gas state equation on discharge coefficient of hydrogen gas flow through a critical nozzle was investigated. The real gas critical flow factor was introduced which considers the effect of the real gas on discharge coefficient. An analytic solution of real gas critical flow factor of hydrogen gas calculated from the modern equations of state based on Helmholtz energy, over a wider range of temperature 150–600 K and pressure up to 100 MPa was presented. An accurate empirical equation for real gas critical flow factor was determined by the nonlinear regression analysis. The equation was in good agreement with the high-pressure hydrogen gas experimental data by Morioka and CFD solutions by Nagao and Kim. Using this equation, the discharge coefficient can be directly and accurately calculated. It indicates that the discharge coefficient of hydrogen gas should be comprehensively taken into consideration with stagnation temperature, stagnation pressure and nozzle throat diameter. A lot of detailed results about the effect of real gas state equation were obtained.     

Note on a real gas model for OWC performance

Oscillating water column (OWC) are devices for wave energy extraction equipped with turbines for energy conversion. The purpose of the present work is to study the thermodynamic of a real gas flow through the turbine and its differences with respect to the ideal gas hypothesis, with the final goal to be applied to OWC systems. The effect of moisture in the air chamber of the OWC entails variations on the atmospheric conditions near the turbine, modifying its performance and efficiency. In this work we study the influence of humid air in the performance of the turbine. Experimental work is carried out and a real gas model is asserted, in order to take a first approach to quantify the extent of influence of the air–water vapour mixture in the turbine performance. The application of a real gas model and the experimental study confirmed the deviations of the turbine performance from the expected values depending on flow rate, moisture and temperature.     

Thermodynamic real gas analysis of a tank filling process

A zero-dimensional thermodynamic real gas simulation model for a tank filling process with hydrogen is presented in this paper. Ideal gas and real gas simulations are compared and the entropy balance of the filling process is formulated. Calculated results are validated for a type I tank (steel vessel) with measurements.     

Modelling of gas network transient flows with multiple hydrogen injections and gas composition tracking

Blending hydrogen into the natural gas (NG) network could provide an efficient pathway for decarbonising the NG system through power-to-gas technologies. However, due to the presence of potentially multiple and intermittent hydrogen injection sources, the gas blended throughout the network would be neither homogenous nor at a constant mole fraction. The above features are not captured by the current transient modelling techniques. To bridge this gap, this work presents a transient analysis model that enables the tracking of gas compositions and particularly hydrogen fractions in real-world meshed networks with multiple NG sources, non-pipe elements, and multiple and intermittent hydrogen injection sources. A time-varying compressibility factor is also introduced to account for the variable gas composition across the network. Moreover, numerical techniques are adopted for improving the stability of the Eulerian numerical calculation, and a specific grid size threshold Δx_max is introduced for selecting the stable mesh grid to alleviate convection-dominated oscillations caused by the hydrogen fraction tracking. The case study based on the well-known 20-node Belgian gas network validates the effectiveness of the method in solving practical-scale problems, whereas the unsuitability of steady-state models is also discussed and highlighted. The results clearly demonstrate the effect and importance of introducing variable compressibility factor, hydrogen fraction tracking, and variable gas demand. The impacts of hydrogen blending on pressures and linepack of the network are further investigated.     

Numerical investigation of combustion characteristics for hydrogen mixed fuel in a can-type model of the gas turbine combustor

Numerical simulations are performed to analyze the combustion characteristics of propane fuel mixed with different amounts of hydrogen in a can-type combustor. The volume fraction of the hydrogen fuel varies from 0% to 100% in the fuel mixture. The results indicate that the hydrogen enrichment of the fuel significantly affects the flow structure, mixture fraction, and combustion characteristics. An increase in the volume fraction of hydrogen significantly affects the mean mixture fraction distribution, promotes combustion, and increases the flame temperature and the width of the flammable range within the combustor. Therefore, the degree of temperature uniformity at the outlet of the combustor increases with hydrogen enrichment, corresponding to an increase of 49.64% in the uniformity factor. The hydrogen enriched fuel can also reduce the emissions of CO and CO₂, owing to the reduced amount of carbonaceous fuel.     

Numerical simulation of high pressure hydrogen release through an expanding opening

Computational Fluid Dynamics is an effective tool to develop safety standards related to the sudden release of hydrogen from a high pressure reservoir. In this work, a three-dimensional in-house code is developed to numerically simulate the release of high pressure hydrogen (70 MPa) from a reservoir when the release area into air is expanding with time. Furthermore, high pressure hydrogen flows cannot be accurately simulated by the ideal gas equation; therefore the Abel–Noble real gas equation of state is applied. A transport equation is solved to find the concentration of hydrogen and air in the hydrogen–air mixture generated soon after release. The novelty of this work is to simulate and to study the flow when the release area enlarges rapidly. To obtain this capability, the solid boundaries of the release area are moved and the mesh follows based on a spring method. All the nodes in the mesh are moved at each time step accordingly to have a good quality mesh. Three initial diameters of 1.0 mm, 1.5 mm and 2.0 mm are tested for the release area, and opening wall speeds of 80 m/s and up to 300 m/s are discussed.     

A dynamic two phase flow model for a pilot scale sodium borohydride hydrogen generation reactor

A two-dimensional, non-isothermal and dynamic model was developed to describe a sodium borohydride/hydrogen reactor for stationary use. All relevant transport phenomena were treated in detail and the kinetic model developed previously by the authors was introduced into the algorithm. In this paper the reactive solution was modelled as a two phase flow; with this approach the impact of the hydrogen production on the solution stirring could be observed and quantified.     

A quantitative description on fracture toughness of steels in hydrogen gas

Fracture toughness or critical stress intensity factor of many steels can be reduced by hydrogen gas. In this paper, a simple quantitative model to predict the fracture toughness of steels in gaseous hydrogen is proposed. This model is based on the assumption that fracture of a cracked body occurs when the maximum principal stress ahead of the crack tip reaches the critical cohesive stress for crack initiation. The critical stress is inversely proportional to the accumulated hydrogen concentration. The notion is that the crack will initiate at the elastic-plastic boundary ahead of the crack tip when hydrogen concentration reaches a maximum value after a long-term hydrogen diffusion assisted by the hydrostatic stress. The model describes the dependence of fracture toughness on hydrogen pressure, temperature and yield strength of steels. It can be used to quantitatively predict fracture toughness of steels in hydrogen gas, particularly in high pressure. Some experimental data reported in literature were used to validate the model, and a good agreement was obtained.     

Effect of gas equation of state on CFD predictions for ignition characteristics of hydrogen escaping from a tank

This work involves the investigation of the sensitivity of computational fluid dynamics based models of auto ignition of hydrogen gas escaping into the surroundings to the use of an ideal gas and a real gas Noble–Abel equation of state. Ensuring consistent modeling techniques when the real gas equation of state is implemented, real gas based thermodynamic properties, real gas based property mixture models, and real gas based chemical equilibrium constant formulations are utilized. Within the standard computational fluid dynamics models, a customized chemical kinetic equation integrator is employed. An LES based turbulence model is implemented. For tank pressures of 40, 80, and 120 MPa, differences in the gas conditions, including gas pressures, temperatures, velocities, flow rates, energy, and chemical species mass fractions, are compared. The relationships between the local and time varying gas conditions, chemical reaction indicators, the tank pressure, and the equation of state captured in the simulations are described in detail. The results clearly show the increasing deviation between the ideal gas and Noble–Abel based results as the tank pressure increases, indicating the importance of the use of the proper material model and chemical equilibrium formulation for the conditions of interest.     

A dynamic 1D model of a solid oxide fuel cell for real time simulation

A 1D dynamic solid oxide fuel cell (SOFC) model has been developed for real time applications. The model accounts for all transport and polarization phenomena by developing a system of governing differential equations over 1D control volumes. The 1D model is an improvement over existing 0D real time models in that it can more accurately predict the temperature and pressure variations along the cell while maintaining real time capabilities with regards to computational time. Several simplifications are required to maintain real time capabilities while improving the fidelity of the model.     

A study of the critical nozzle for flow rate measurement of high-pressure hydrogen gas

The mass flow rate measurement using a critical nozzle shows the validity of the inviscid theory,indicating thatthe discharge coefficient increases and approaches unity as the Reynolds number increases under the ideal gas lawHowever,when the critical nozzle measures the mass flow rate of a real gas such as hydrogen at a pressure ofhundreds bar,the discharge coefficient exceeds unity,and the real gas effects should be taken into account.Thepresent study aims at investigating the flow features of the critical nozzle using high-pressured hydrogen gas.Theaxisymmetric,compressible Navier-Stokes computation is employed to simulate the critical nozzle flow,and afully implicit finite volume method is used to discretize the governing equation system.The real gas effects aresimulated to consider the intermolecular forces,which account for the possibility of liquefying hydrogen gas.Thecomputational results are compared with past experimental data.It has been found that the coefficient of dis-charge for real gas can be corrected properly below unity adopting the real gas assumption.     

Development of a novel simulator for modelling underground hydrogen and gas mixture storage

Underground hydrogen storage can store grid-scale energy for balancing both short-term and long-term inter-seasonal supply and demand. However, there is no numerical simulator which is dedicated to the design and optimisation of such energy storage technology at grid scale. This study develops novel simulation capabilities for GPSFLOW (General Purpose Subsurface Flow Simulator) for modelling grid-scale hydrogen and gas mixture (e.g., H₂–CO₂–CH₄–N₂) storage in cavern, deep saline aquifers and depleted gas fields.The accuracy of GPSFLOW is verified by comparisons against the National Institute of Standard and Technology (NIST) online thermophysical database and reported lab experiments, over a range of temperatures from 20 to 200 °C and pressure up to 1000 bar. The simulator is benchmarked against an existing model for modelling pure H₂ storage in a synthetic aquifer. Several underground hydrogen storage scenarios including H₂ storage in a synthetic salt cavern, H₂ injection into a CH₄-saturated aquifer experiment, and hydrogen storage in a depleted gas field using CO₂ as a cushion gas are used to test the GPSFLOW's modelling capability. The results show that GPSFLOW offers a robust numerical tool to model underground hydrogen storage and gas mixture at grid scale on multiple parallel computing platforms.     

Isentropic analysis and numerical investigation on high-pressure hydrogen jets with real gas effects

The present work performs the isentropic analysis and numerical simulation of high-pressure hydrogen jets to study the hydrogen leakage. The exit parameters and the flow characteristics are studied with the ideal gas assumption and real gas effects. The jet exit parameters calculated by the real gas thermodynamic model are different from the results obtained by the ideal gas assumption at high initial pressure based on the isentropic analysis. The ideal gas and the real gas equation of state results in the differences of Mach disk parameters at high initial pressures. The ideal gas assumption underestimates the Mach disk distance by 8% and overestimates the Mach disk diameter by 15% at the initial pressure of 50 MPa. The exit mass flow rates computed from the isentropic expansion assumption agree well with the numerical simulations. The results show that it is reasonable to evaluate mass flow rates of high-pressure hydrogen jets by the isentropic expansion assumption.     

Three dimensional numerical computations on the fast filling of a hydrogen tank under different conditions

Hydrogen-fueled vehicles offer a clean and efficient alternative for transportation. Compressed gas in high pressure tanks is a popular storage mode for hydrogen fuel. Time required for filling a hydrogen tank for vehicular applications should be short. But quick filling of hydrogen tanks at high pressures can result in high gas temperatures which can damage the tank and lead to its rupture. Hence the real time monitoring of gas temperature is essential during filling. This paper reports the findings of numerical simulation of filling process of hydrogen tanks. Real gas effects are considered. Local temperature distribution in the tank is obtained at different durations of the fill. Effect of changes in ambient temperature and initial and inlet gas temperatures is studied. Results of the study can aid in optimizing the filling time and in identifying the most suitable locations for the feedback devices within on-board hydrogen tanks.     

Numerical simulation and validation of flame acceleration and DDT in hydrogen air mixtures

Combustion of hydrogen can take place in different modes such as laminar flames, slow and fast deflagrations and detonations. As these modes have widely varying propagation mechanisms, modeling the transition from one to the other presents a challenging task. This involves implementation of different sub-models and methods for turbulence-chemistry interaction, flame acceleration and shock propagation. In the present work, a unified numerical framework based on OpenFOAM has been evolved to simulate such phenomena with a specific emphasis on the Deflagration to Detonation Transition (DDT) in hydrogen-air mixtures. The approach is primarily based on the transport equation for the reaction progress variable. Different sub-models have been implemented to capture turbulence chemistry interaction and heat release due to autoignition. The choice of sub-models has been decided based on its applicability to lean hydrogen mixtures at high pressures and is relevant in the context of the present study. Simulations have been carried out in a two dimensional rectangular channel based on the GraVent experimental facility. Numerical results obtained from the simulations have been validated with the experimental data. Specific focus has been placed on identifying the flame propagation mechanisms in smooth and obstructed channels with stratified initial distribution. In a smooth channel with stratified distribution, it is observed that the flame surface area increases along the propagation direction, thereby enhancing the energy release rate and is identified to be the key parameter leading to strong flame acceleration. When obstacles are introduced, the increase in burning rate due to turbulence induced by the obstacles is partly negated by the hindrance to the unburned gases feeding the flame. The net effect of these competing factors leads to higher flame acceleration and propagation mechanism is identified to be in the fast deflagration regime. Further analysis shows that several pressure pulses and shock complexes are formed in the obstacle section. The ensuing decoupled shock-flame interaction augments the flame speed until the flame coalesces with a strong shock ahead of it and propagates as a single unit. At this point, a sharp increase in propagation speed is observed thus completing the DDT process. Subsequent propagation takes place at a uniform speed into the unburned mixture.     

Effects of geometry and inconstant mass flow rate on temperatures within a pressurized hydrogen cylinder during refueling

Higher refueling rate leads to higher temperature rise within the cylinder. Excessive temperature should be avoided during the refueling progress. In this paper, we studied the effective methods to control the temperature rise by simulations based on the Computational Fluid Dynamics (CFD). Cylinders of different length to diameter ratios and different inlet diameters were simulated. We found that smaller radio of length to diameter can boost for temperature control and temperature distribution. Larger inlet diameter can restrain temperature rise. Comparing the simulation results with constant, increasing and decreasing mass flow rate, the refueling with increasing flow rate obtains the lowest temperature rise.     

Effects of hydrogen addition on the structure and pollutant emissions of a turbulent unconfined swirling flame

This article aims at investigating the effect of hydrogen addition on the temperature and pollutant emissions of turbulent unconfined swirling methane/air flame. A computational approach utilizing the steady laminar flamelet and the realizable k–ε combustion and turbulence models, respectively, has been used. The turbulence–combustion interaction has been modeled by a β-shaped presumed probability density function. The percentage of hydrogen in the fuel stream is modeled at a wide range from 0% to 50% of the fuel volume flow rate. Results show that with the increase of volumetric hydrogen percentage in the fuel stream the flame structure changes considerably. The size of maximum temperature region decreases significantly to a small region at flame tip and peak temperature rises which leads to increase in NO emission levels. The flame with 10% hydrogen is observed to be slightly of the general trend. This is deemed to be due to the change in flow field as a result of change in fuel density, while the amount of hydrogen is not effective enough to change the combustion characteristics of the flame.     

An MILP model for the reformation of natural gas pipeline networks with hydrogen injection

A mixed integer linear programming (MILP) model is proposed for the reformation of natural gas pipelines. The model is based on the topology of existing pipelines, the load and pressure at each node and the design factors of the region and minimizes the annual substitution depreciation cost of pipelines, the annual construction depreciation cost of compressor stations and the operating cost of existing compressor stations. Considering the nonlinear pressure drop equations, the model is linearized by a piecewise method and solved by the Gurobi optimizer. Two cases of natural gas pipeline networks with hydrogen injection are presented. Several adjustments are applied to the original natural gas pipeline network to ensure that our design scheme can satisfy the safety and economic requirements of gas transportation. Thus, this work is likely to serve as a decision-support tool for the reformation of pipeline networks with hydrogen injection.     

A multi-objective model for optimizing hydrogen injected-high pressure natural gas pipeline networks

The paper develops a statistical model for optimizing the Hydrogen-injected Natural gas (H-NG) high-pressure pipeline network. Gas hydrodynamic principles are utilized to construct the pipeline and compressor station model. The model developed is implemented on a pipeline grid that is supposed to carry Hydrogen as an energy carrier in a natural gas-carrying pipeline. The paper aims to optimize different objectives using ant colony optimization (ACO). The first objective includes a single objective optimization problem that evaluates the maximum permissible hydrogen amounts blended with natural gas (NG) for a set of pipeline constraints. We also evaluated the variations in operational variables on injecting Hydrogen into the natural gas pipeline networks at varying fractions. The study further develops a multi-objective optimization model that includes bi-objective and tri-objective problems and is optimized using ACO. Traditional studies have focused on single-objective optimization with minimal bi-objective issues. In addition, none of the earlier research has shown the effect of introducing Hydrogen to the NG network using tri-objective function evaluations. The bi-objective and tri-objective functions help evaluate the effect of injecting Hydrogen on different operational parameters. The study further attempts to fill the gap by detailing the modelling equations implemented through a bi-objective and tri-objective function for the H-NG pipeline network and optimized through ACO. Pareto fronts that show the tradeoff between the different objectives for the multi-objective problem have been generated. The primary objective of the bi-objective and tri-objective optimization problems is maximizing hydrogen mole percent in natural gas. The other objective chosen is minimizing compressor fuel consumption and maximizing delivery pressure, throughput, and power delivered at the delivery station. The findings will serve as a roadmap for pipeline operators interested in repurposing natural gas pipeline networks to transport hydrogen and natural gas blend (H-NG) and seeking to reduce carbon intensity per unit of energy-delivered fuel.     

A simulation and design tool for hydrogen SI engine systems—Validation of the intake hydrogen flow model

A simulation and design tool applicable to hydrogen powered spark ignition engine systems is introduced in this paper. This software is applicable to single and multi-cylinder engines under steady state or transient operating conditions, and is capable of simulating one-dimensional unsteady chemical species transport through intake and exhaust engine ducting, the induction and combustion of those chemical species, and the engine performance characteristics and emissions which are produced. Results are presented from validation studies carried out on a 1.6 l spark ignition engine converted to operate with manifold-fuelled gaseous hydrogen. These experimental results validate the ability of the simulation to accurately describe the transport of gaseous hydrogen through engine intake ducting, and the displacement of intake air due to hydrogen introduction.