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.     

Characteristics of high Reynolds number flow in a critical nozzle

A critical nozzle has been used to measure a mass flow rate of gas. It is well known that the coefficient of discharge of the flow in a critical nozzle is a single function of Reynolds number. The purpose of the present study is to investigate the effect of equation of state (EOS) on the coefficient of discharge and thermodynamics properties through the critical nozzle by using H₂ with the help of a CFD method. In computations of the flow field including the stagnation point upstream of the nozzle, the Redlich–Kwong, Lee–Kesler and Peng–Robinson equations of state were employed to take account of real gas effects. As a result of the present computations, coefficients of discharge using the Redlich–Kwong and Lee–Kesler EOS were in good agreement with experimental results in the range of high Reynolds number and the coefficient of discharge decreased with an increase of Reynolds number in the range of 1.0 × 10⁵ < Re < 2.8 × 10⁶.     

Derivation and validation of a reference data-based real gas model for hydrogen

Hydrogen plays an important role for the decarbonization of the energy sector. In its gaseous form, it is stored at pressures of up to 1000 bar at which real gas effects become relevant. To capture these effects in numerical simulations, accurate real gas models are required. In this work, new correlation equations for relevant hydrogen properties are developed based on the Reference Fluid Thermodynamic and Transport Properties Database (REFPROP). Within the regarded temperature (150–400 K) and pressure (0.1–1000 bar) range, this approach yields a substantially improved accuracy compared to other data-based correlations. Furthermore, the developed equations are validated in a numerical simulation of a critical flow Venturi nozzle. The results are in much better accordance with experimental data compared to a cubic equation of state model. In addition, the simulation is even slightly faster.     

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.     

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.     

Experimental analysis of plasma and heating effect on H2 permeation behavior through Pd–Cu40% membranes in 1mm gap length plate reactor

In this work, experimental analysis of hydrogen permeation behavior under heating only and plasma-heating effect were studied in 15  μm and 20  μm Pd–Cu40% membrane thicknesses. Apure hydrogen gas at feeding pressure of 100 kPa was injected in 1 mm gap length plate micro-channel reactor (PMCR). The permeated hydrogen flux through Pd–Cu40% membranes was measured under heating only experiment at PMCR heating temperature range of 423–573 K and hydrogen flow rates of 0.1–1 L/min. In the plasma-heating experiments, dielectric barrier discharge plasma (DBD) were used at the applied voltage ranges of 10–16 kV, PMCR heating temperatures 423–573 K and hydrogen flow rate 0.1 L/min. The hydrogen permeability was calculated according to the Fick's and Sievert's law equation. It was found that the hydrogen permeability of heating only experiments lower than that obtained from plasma-heating experiments for both Pd–Cu membrane thickness. Further, the hydrogen permeability of the plasma-heating experiments has shown anon-linearity effect which it was presented in the pre-exponential factor and the activation energy pattern. However, it was observed that the hydrogen permeability decreased while the DBD-plasma applied voltage was high, due to the hydrogen gas reverse reaction. A comparison between the hydrogen permeability and the permeation rate% of both experiments has been developed to investigate the dependence on the membrane thickness in both experiments. The analysis shows that the permeability of 15  μm membrane thickness was always higher than 20  μm membrane thickness results and the maximum hydrogen permeability was at PMCR heating temperature of 573 K.     

Effect of non-condensable gas on the performance of steam-water ejector in a trigeneration system for hydrogen production: An experimental and numerical study

An ejector containing phase changing gas-liquid flow process acts as a popular and decisive device in multiple industrial applications, including the hydrogen production, electricity production, fuel cells, refrigeration, petroleum industry and desalination systems. However, non-condensable gas is inevitable for the usual operation of phase-changing gas-liquid ejector in the trigeneration or electrolyzer system for hydrogen production, and rarely research is concerned with this issue. In the present study, the effect of non-condensable gas contained in the condensable gas on the characteristics of gas-centered water ejector is presented, with steam, water and air acting as the gas, liquid and non-condensable gas, respectively. Experimentally, the flow rate of steam is controlled to be 1.45 g/s with an absolute pressure of 120 kPa, the air flow rate varies from 0 to 0.14 g/s, resulting in a non-condensable gas concentration ranging from 0 to 9%, and the resulted water flow rate at 100 kPa and 282.15 K changes from 34.7 to 37.3 g/s. Combined with the numerical methods, the performance of ejector expressed in ejected water flow rate was found to increase firstly with a small amount of non-condensable gas, and decrease when the non-condensable gas reaches a certain amount. In addition, the distributions of multiple local flow parameters including pressure, condensation rate and gas volume fraction, velocity and temperature inside the ejector were shown for different non-condensable concentration, by which the mechanism for the change of ejector performance under varying non-condensable concentration was demonstrated. These findings are initiative and insightful for the ejector design optimization in the trigeneration system for hydrogen production and the proposed numerical models can be utilized in analysis and design of steam ejector with non-condensable gas involved.     

Study for the Gas Flow through a Critical Nozzle

In the present study, computational work using the axisymmetric, compressible, Navier-Stokes equations is carried out to predict the discharge coefficient and critical pressure ratio of gas flow through a critical nozzle. The Reynolds number effects are investigated with several nozzles with different throat diameter. Diffuser angle is varied to investigate the effects on the discharge coefficient and critical pressure ratio. The computational results are compared with the previous experimental ones. It is known that the discharge coefficient and critical pressure ratio are given by functions of the Reynolds number and boundary layer integral properties. It is also found that diffuser angle affects the critical pressure ratio.     

Evaluation of hydrogen concentration effect on the natural gas properties and flow performance

The natural gas flowing through transmission pipeline is impure and has a wide range of non-hydrocarbons components at different concentrations like hydrogen. The presence of hydrogen in the natural gas mixture influences its properties and flow performance. The effect of hydrogen concentration on the natural gas flowing through a transportation pipeline has not been adequately investigated and widely comprehended. In this paper, several mixtures flow through pipeline include typical natural gas and hydrogen at different concentrations up to 10% are evaluated to demonstrate their impact on the flow assurance and the natural gas properties. The string Ruswil – Griespass part from the Transitgas project with 94 km length is simulated applying Aspen Hysys Version 9 and validated using Aspen Plus. The simulation specifications were 1.228 1 10⁶ kg/h mass flowrate, 1200 mm and 1164 mm the outer and inner diameters, and 75 bar and 29.4 °C operating pressure, and temperature. The effect of different hydrogen concentrations has been examined and the differences from the typical mixture are estimated. The results show that the presence of hydrogen in the natural gas mixture reduces its density, 10% hydrogen content records 11.78% reduction in the density of typical natural gas. Interestingly, it has been found that up to 2% of hydrogen concentration turns in elevating the viscosity of the typical natural gas while the viscosity decreases at the point that hydrogen content increases above 2%. In addition, the pressure losses over the transmission pipeline increases due to the presence of hydrogen, 10% hydrogen concentration turns in 5.39% increase in the pressure drop of the natural gas mixture. Also, the temperature drop across the pipeline decreases as the hydrogen concentration increases; 10% hydrogen content can result in a 6.14% reduction in the temperature drop across the pipeline. As well as, the findings prove that the hydrogen strongly impacts the phase envelope by changing from size symmetric to size asymmetric diagram. The effect of pipeline elevations has been investigated by changing the elevation up to 25 m uphill and 25 m downhill. The results state that increase the pipeline elevation turns in increasing the pressure losses over the pipeline length. Along with this, the results illustrate that the presence of hydrogen in the mixture elevates the critical pressure and reduces the critical temperature.     

Effect of heat transfer through the release pipe on simulations of cryogenic hydrogen jet fires and hazard distances

Jet flames originated by cryo-compressed ignited hydrogen releases can cause life-threatening conditions in their surroundings. Validated models are needed to accurately predict thermal hazards from a jet fire. Numerical simulations of cryogenic hydrogen flow in the release pipe are performed to assess the effect of heat transfer through the pipe walls on jet parameters. Notional nozzle exit diameter is calculated based on the simulated real nozzle parameters and used in CFD simulations as a boundary condition to model jet fires. The CFD model was previously validated against experiments with vertical cryogenic hydrogen jet fires with release pressures up to 0.5 MPa (abs), release diameter 1.25 mm and temperatures as low as 50 K. This study validates the CFD model in a wider domain of experimental release conditions - horizontal cryogenic jets at exhaust pipe temperature 80 K, pressure up to 2 MPa ab and release diameters up to 4 mm. Simulation results are compared against such experimentally measured parameters as hydrogen mass flow rate, flame length and radiative heat flux at different locations from the jet fire. The CFD model reproduces experiments with reasonable for engineering applications accuracy. Jet fire hazard distances established using three different criteria - temperature, thermal radiation and thermal dose - are compared and discussed based on CFD simulation results.     

Hydrogen release from a high pressure gaseous hydrogen reservoir in case of a small leak

The dynamic blow-down process of a high pressure gaseous hydrogen (GH₂) reservoir in case of a small leak is a complex process involving a chain of distinct flow regimes and gas states. This paper presents models to predict the hydrogen concentration and velocity field in the vicinity of a postulated small leak. An isentropic expansion model with a real gas equation of state for normal hydrogen is used to calculate the time dependent gas state in the reservoir and at the leak. The subsequent gas expansion to 0.1 MPa is predicted with a zero-dimensional model. The gas conditions after expansion serve as input to a newly developed integral model for a round free turbulent H₂-jet into ambient air. Predictions are made for the blow-down of hydrogen reservoirs with 10, 30 and 100 MPa initial pressure. A normalized hydrogen concentration field in the free jet is presented which allows for a given leak scenario the prediction of the axial and radial range of flammable H₂-air mixtures.     

“Preliminary results of hydrogen production from water vapor decomposition using DBD plasma in a PMCR reactor”

The water decomposition is considered one of the most attractive chemical processes for the production of hydrogen. The present work describes the preliminary results obtained in the experimental study of the water vapor dissociation into hydrogen and oxygen species using Dielectric-Barrier Discharge (DBD) plasma in a plate micro-channel reactor (PMCR). The water vapor molecules are injected without using carrier gas into the PMCR reactor at pressure of 100 kPa and temperature of 573 K. The applied high voltage of the plasma was within range of 14–18 kV and different steam flow rates have been analyzed within range of 100–200 ml/h. The product gases have been separated in ice trap which it was connected directly to the PMCR reactor to prevent the recombination of hydrogen and oxygen species. The concentration of the outlet species has been measured in a gas phase chromatography (GC) instrument. The PMCR reactor heating temperature effect on the water vapor decomposition has been analyzed. It was found that the water vapor is dissociated into their constituent molecular elements of hydrogen and oxygen gas using plasma. The maximum obtained mole fraction, hydrogen flow rate and conversion rate were 2.3%, 9.42 g/h, 42.51% respectively, at steam temperature of 573 K, pressure 100 kPa, PMCR heating temperature 403 K, steam flow rate of 200 ml/h and the plasma discharge high voltage of 18 kV. It was observed that the amount of evolved hydrogen concentration increased with the increase of the PMCR reactor heating temperature. Also, the thermal efficiencies versus the heat supplied have been calculated and the maximum obtained efficiency was 49.32%. Consequently, the evolved hydrogen flow rate appears to depend mainly on the plasma voltage, PMCR reactor heating temperature and the separating temperature of outlet hydrogen and oxygen species. The steam dissociation experiment will be extended to separate hydrogen and oxygen species elements at high temperature conditions.     

Flow rate measurement via isothermal discharge method for hydrogen

The thesis of this study is to investigate that the measurement accuracy of the isothermal discharge method for hydrogen gas with an isothermal tank which is designed for measuring the flow rate characteristics of pneumatic components. Compressed hydrogen in an isothermal tank, which is combined three types of orifice, is discharged from 700 kPa (abs) to atmospheric pressure. The average temperature in the tank during discharge is measured experimentally. In consequence, when the maximum discharge rate is 37 kPa/s during discharge hydrogen, the measurement error is less than 3% in whole discharge time. The temperature response phenomenon in hydrogen is discussed qualitatively in the view point of the internal energy change. The internal energy change immediately after the discharge started was negative because the release enthalpy was larger than the quantity of heat obtained from the stuffing material. After a certain period of time elapsed, the enthalpy change became equal to the heat exchange between the internal hydrogen and the stuffing material.     

Modeling phase equilibrium of hydrogen and natural gas in brines: Application to storage in salt caverns

In this work, the e-PPC-SAFT equation of state has been parameterized to predict phase equilibrium of the system H₂ + CH₄ + H₂O + Na⁺Cl^? in conditions of temperature, pressure and salinities of interest for gas storage in salt caverns. The ions parameters have been adjusted to match salted water properties such as mean ionic coefficient activities, vapor pressures and molar densities. Furthermore, binary interaction parameters between hydrogen, methane, water, Na⁺ and Cl^? have been adjusted to match gas solubility data through Henry constant data. The validity ranges of this model are 0–200 °C for temperatures, 0–300 bar for pressures, and 0 to 8 mol_NaCl/kg_H2O for salinities. The e-PPC-SAFT equation of state has then been used to model gas storage in salt caverns. The performance of a storage of pure methane, pure hydrogen and a mixture methane + hydrogen have been compared. The simulations of the storage cycles show that integrating up to 20% of hydrogen in caverns does not have a major influence on temperature, pressure and water content compared to pure methane storage. They also allowed to estimate the thermodynamic properties of the system during the storage operations, like the water content in the gaseous phase. The developed model constitutes thus an interesting tool to help size surface installations and to operate caverns.     

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.     

High-pressure gaseous hydrogen permeation test method -property of polymeric materials for high-pressure hydrogen devices (1)-

Polymeric materials are widely used in hydrogen energy system such as FCEV and hydrogen refueling stations under high-pressure condition. The permeation property (coefficients of permeation, diffusion and solubility) of polymers under high-pressure hydrogen condition should be discussed as parameters to develop those devices. Also the property should be determined to understand influence of the compression by the pressure on polymer materials. A device which can measure gas permeation property of polymer materials accurately in equilibrium state under high-pressure environment is developed, and the reliability of the measurements is ensured. High-pressure hydrogen gas permeability characteristics up to 100 MPa are measured for high-density polyethylene. An advantage of the method is discussed comparing with the non-equilibrium state method, focusing on the hydrostatic pressure effect. Deterioration of hydrogen permeability is observed along with the decrease of diffusion coefficient, which is supposedly affected by hydrostatic compression effect with the increase of environment pressure.     

Dynamic modeling and characteristic analysis of natural gas network with hydrogen injections

With the transformation of energy structure, the proportion of renewable energy in the power grid continues to increase. However, the power grid's capacity to absorb renewable is limited. In view of this, converting the excess renewable energy into hydrogen and injecting it into natural gas network for transportation can not only increase the absorption capacity of renewable energy but also reduce the transportation cost of hydrogen. While this can lead to the problem that hydrogen injection will make the dynamic characteristics of the pipeline more complicated, and hydrogen embrittlement of pipeline may occur. It is of great significance to simulate the dynamic characteristics of gas pipeline with hydrogen injection, especially the hydrogen mixture ratio. In this paper, the cell segmentation method is used to solve each natural gas pipeline model, the gas components are recalculated in each cell and the parameters of partial differential equation are updated. Additionally, the dynamic simulation model of natural gas network with hydrogen injections is established. Simulation results show that for a single pipeline, when the inlet hydrogen ratio changes, whether or not hydrogen injection has little influence on the pressure and flow. The propagation speed of hydrogen concentration is far less than that of the pressure and flow rate, and it takes about 1.2 × 10⁵ s for the 100 km pipeline hydrogen ratio to reach the steady state again.     

Prediction of state property,flow parameter and jet flame size during transient releases from hydrogen storage systems

The accidental leakage of high-pressure gas storage systems including tank, pipe, etc. can lead to hazardous jet fires resulting in a serious of disastrous events. With the isentropic process assumption on the high-pressure gas leakage or release, the ideal gas equation of state is firstly used to solve the gas transfer problem, and then the Abel-Noble equation of state (AN-EOS) is adopted for the effect of gas molecule volume. Given both the molecule volume and intermolecular attraction should not be ignored for the high-pressure gas, this paper attempts to build the high-pressure gas leakage process model based on the van der Waals equation of state. Together with the available notional nozzle model and the flame size model, the gas leakage process model is used to calculate the gas state property and flow parameter of hydrogen tank leakage and its subsequent jet flame height. The predicted gas mass flow rate, flame height, and gas pressure and temperature are compared to the experimental measurements for validation and the predictions of the model based on ideal gas equation of state and AN-EOS. It is found that the proposed model can give more encouraging results compared to the previous models. The proposed theoretical model shows a great implication for the calculation of other gas tank leakage and can help to predict the thermal radiation field of jet fires.     

Hydrogen permeation under high pressure conditions and the destruction of exposed polyethylene-property of polymeric materials for high-pressure hydrogen devices (2)-

Aiming to elucidate physical property affecting to hydrogen gas permeability of polymer materials used for liner materials of storage tanks or hoses and sealants under high-pressure environment, as model materials with different free volume fraction, five types of polyethylene were evaluated using two methods. A convenient non-steady state measurement of thermal desorption analysis (TDA), and steady-state high-pressure hydrogen gas permeation test (HPHP) were used both under up to 90 MPa of practical pressure. The limit of TDA method of evaluation for the specimens suffering fracture during decompression process after hydrogen exposure was found. Permeability coefficient decreased with the decrease of diffusion coefficient under higher pressure condition. Specific volume and degree of crystallinity under hydrostatic environment were measured. The results showed that the shrinkage in free volume caused by hydrostatic effects of the applied hydrogen gas pressure decreases diffusion coefficient, resulting in the decrease of permeability coefficient with the pressure rise.     

Numerical simulation of high-pressure hydrogen jet flames during bonfire test

Characteristics of high-pressure hydrogen jet flames resulting from ignition of hydrogen discharge during the bonfire test of composite hydrogen storage vessels are studied. Firstly, a 3-D numerical model is established based on the species transfer model and SST k − ω turbulence model to study the high-pressure hydrogen jet flow. It is revealed that under-expanded jets are formed after the high-pressure hydrogen discharging from the vessel. Secondly, the mathematical methods are adopted to study the high-pressure hydrogen jet flames. The effects of pressure, initial temperature and the nozzle diameter on the jet flames are investigated. The results show that the jet flame length increases with the increase of discharge pressure, but decreases with the increase of nozzle diameter and temperature difference between the filling hydrogen temperature and the environment temperature. Finally, the simulation models are established to study the characteristics of hydrogen jet flames in an open space. The effects of barrier walls on the distribution of jet flames are also studied. The results show that the barrier walls can greatly reduce the damage from hydrogen jet flames to testers and properties around.