Estimation of final hydrogen temperature from refueling parameters

Compressed hydrogen storage is currently widely used in fuel cell vehicles due to its simplicity in tank structure and refueling process. For safety reason, the final gas temperature in the hydrogen tank during vehicle refueling must be maintained under a certain limit, e.g., 85 °C. Many experiments have been performed to find the relations between the final gas temperature in the hydrogen tank and refueling conditions. The analytical solution of the hydrogen temperature in the tank can be obtained from the simplified thermodynamic model of a compressed hydrogen storage tank, and it serves as function formula to fit experimental temperatures. From the analytical solution, the final hydrogen temperature can be expressed as a weighted average form of initial temperature, inflow temperature and ambient temperature inspired by the rule of mixtures. The weighted factors are related to other refueling parameters, such as initial mass, initial pressure, refueling time, refueling mass rate, average pressure ramp rate (APRR), final mass, final pressure, etc. The function formula coming from the analytical solution of the thermodynamic model is more meaningful physically and more efficient mathematically in fitting experimental temperatures. The simple uniform formula, inspired by the concept of the rule of mixture and its weighted factors obtained from the analytical solution of lumped parameter thermodynamics model, is representatively used to fit the experimental and simulated results in publication. Estimation of final hydrogen temperature from refueling parameters based on the rule of mixtures is simple and practical for controlling the maximum temperature and for ensuring hydrogen safety during fast filling process.     

Final hydrogen temperature and mass estimated from refueling parameters

The final temperature and mass of compressed hydrogen in a tank after a refueling process can be estimated using the analytical solutions of a lumped parameter thermodynamic model of high pressure compressed hydrogen storage system. The effects of three single refueling parameters (ambient temperature, initial pressure and mass flow rate) and three pairs of the refueling parameters on the final hydrogen temperature are studied, for both 35 MPa and 70 MPa tanks. Overall expressions for the final hydrogen temperature, expressed as a function of the three factors, are obtained. The formulae for the final hydrogen temperature provide an excellent representation of the reference data. The effects of the refueling parameters (mass flow rate, initial pressure and inflow temperature) on the final hydrogen mass are determined from the physical model. An overall expression of the final hydrogen mass is also obtained. The final hydrogen temperature can be controlled by reducing the ambient temperature or the mass flow rate, or increasing the initial pressure. The final hydrogen mass can be maximized by reducing the mass flow rate or the inflow temperature, or increasing the initial pressure. This study provides simple engineering formulae to assist in establishing refueling protocols for gaseous hydrogen vehicles.     

Determining correlations between final hydrogen temperature and refueling parameters from experimental and numerical data

During the hydrogen filling process, the excessive temperature rise may cause the hydrogen storage tank to fail. Therefore, preventing the temperature from rising too high is an important guarantee for the safety of the hydrogen storage cylinder. The analytical solution of a single-zone thermodynamic model for hydrogen refueling is obtained. Based on the analytical solution of the final hydrogen temperature derived from the hydrogen filling theoretical model, the relationship among the final hydrogen temperature and the initial temperature and the inlet temperature and the ambient temperature is obtained. The model is used to achieve correlations coefficients among the above parameters. Data of Type III 40L tank and Type IV 29L tank used in the model are from the experiment, and data of Type III 25L tank and Type IV 174L tank are from the simulation. The results show that our analytical solution is applicable for determining correlations between final hydrogen temperature and refueling parameters from experimental and numerical data. Our analytical solution is more accurate than the reduced model reported in reference. At the same time, the effects of the initial temperature and the inlet temperature on the final temperature are stronger in Type IV tank than in the Type III tank. This study may provide guides for improving hydrogen refueling standards.     

Single-tank storage versus multi-tank cascade system in hydrogen refueling stations for fuel cell buses

Many countries in Europe are investing in fuel cell bus technology with the expected mobilization of more than 1200 buses across Europe in the following years. The scaling-up will make indispensable a more effective design and management of hydrogen refueling stations to improve the refueling phase in terms of refueling time and dispensed quantity while containing the investment and operation costs. In the present study, a previously developed dynamic lumped model of a hydrogen refueling process, developed in MATLAB, is used to analyze tank-to-tank fuel cell buses (30–40 kg_H2 at 350 bar) refueling operations comparing a single-tank storage with a multi-tank cascade system. The new-built Aalborg (DK) hydrogen refueling station serves as a case study for the cascade design. In general, a cascading refueling approach from multiple storage tanks at different pressure levels provides the opportunity for a more optimized management of the station storage, reducing the pressure differential between the refueling and refueled tanks throughout the whole refueling process, thus reducing compression energy. This study demonstrates the validity of these aspects for heavy-duty applications through the technical evaluation of the refueling time, gas heating, compression energy consumption and hydrogen utilization, filling the literature gap on cascade versus single tank refueling comparison. Furthermore, a simplified calculation of the capital and operating expenditures is conducted, denoting the cost-effectiveness of the cascade configuration under study. Finally, the effect of different pressure switching points between the storage tanks is investigated, showing that a lower medium pressure usage reduces the compression energy consumption and increases the station flexibility.     

Impact of refueling parameters on storage density of compressed hydrogen storage Tank

Hydrogen fuel cell vehicle (HFCV) is one of the key contributors to sustainable development of the society. For commercial deployment and market acceptability of fuel cell vehicles, efficient storage of hydrogen with an optimum refueling is one of the important challenge. Compressed hydrogen storage in Type IV tanks is a mature and promising technology for on-board application. The fast refueling of the storage tank without overheating and overfilling is an essential requirement defined by SAE J2601. In this regard, station parameters such as hydrogen supply temperature, filling rate and vehicle tank parameters such as filling time strongly influences the storage capacity of the tank, affecting driving range of the fuel cell vehicle. This paper investigates the impact of these parameters on storage density of the tank defined in terms of state of charge. For this, refueling simulation based on SAE J2601 protocol has been performed using computational fluid dynamic approach to investigate the influence of station parameters on storage density of the tank. Further, the root cause analysis was carried out to investigate the contribution of station and vehicle tank parameters for enhancing the storage density of the tank. Finally, the regression model based on these refueling parameters was developed to predict the density attained at different filling conditions. The results confirmed the strong contribution of pressure, filling time, supply temperature and least contribution of temperature, filling rates in enhancing the storage density of the tank. The results can provide new insight into refueling behavior of the Type IV tank for fuel cell vehicle.     

Neural network based optimization for cascade filling process of on-board hydrogen tank

Compressed hydrogen storage is widely used in hydrogen fuel cell vehicles (HFCVs). Cascade filling systems can provide different pressure levels associated with various source tanks allowing for a variable mass flow rate. To meet refueling performance objectives, safe and fast filling processes must be available to HFCVs. The main objective of this paper is to establish an optimization methodology to determine the initial thermodynamic conditions of the filling system that leads to the lowest final temperature of hydrogen in the on-board storage tank with minimal energy consumption. First, a zero-dimensional lumped parameter model is established. This simplified model, implemented in Matlab/Simulink, is then used to simulate the flow of hydrogen from cascade pressure tanks to an on-board hydrogen storage tank. A neural network is then trained with model calculation results and experimental data for multi-objective optimization. It is found to have good prediction, allowing the determination of optimal filling parameters. The study shows that a cascade filling system can well refuel the on-board storage tank with constant average pressure ramp rate (APRR). Furthermore, a strong pre-cooling system can effectively lower the final temperature at a cost of larger energy consumption. By using the proposed neural network, for charging times less than 183s, the optimization procedure predicts that the inlet temperature is 259.99–266.58 K, which can effectively reduce energy consumption by about 2.5%.     

Generalized model development for a cryo-adsorber and 1-D results for the isobaric refueling period

We have developed 3-D model equations for a cryo-adsorption hydrogen storage tank, where the energy balance accommodates the temperature and pressure variation of all the thermodynamic properties. We then reduce the 3-D model to the 1-D isobaric system and study the isobaric refueling period, for simplified geometry and charging conditions. The hydrogen capacity evolution predicted by the 1-D axial bed model is significantly different than that predicted by the lumped-parameter model because of the presence of sharp temperature gradients during refueling. The 1-D model predicts a higher hydrogen capacity than the lumped-parameter model. This observation can be rationalized by the fact that a bed with temperature gradients on equilibration should desorb gas, whenever the adsorbed phase entropy is lower than the gas phase entropy. The 1-D analysis of the isobaric refueling period does not show any significant difference in hydrogen capacity evolution among the axial, single and multicartridge annular bed designs. Hence, a multicartridge annular design, though giving a slightly lower pressure drop, does not offer any heat and mass transfer enhancement over the single cartridge design. And, the single cartridge annular design appears to be optimal.     

A thermodynamic analysis of refueling of a hydrogen tank

A thermodynamic analysis of refueling of a gaseous hydrogen fuel tank is described. This study may lend itself to the applications of refueling a hydrogen storage tank onboard a hydrogen fuel-cell vehicle. The gaseous hydrogen is treated as an ideal or a non-ideal gas. The refueling process is analyzed based on adiabatic, isothermal, or diathermal condition of the tank. A constant feed-rate is assumed in the analysis. The thermodynamic state of the feed stream also remains constant during refueling. Ideal-gas assumption results in simple closed-form expressions for tank temperature, pressure, and other parameters. The non-ideal behavior of high-pressure gaseous hydrogen is addressed using the newly developed equation of state for normal hydrogen, which is based on the reduced Helmholtz free energy formulation. Sample calculations are presented using initial tank and feed stream conditions commensurate to practical vehicular applications. Comparing to the non-ideal analysis, the ideal-gas assumption always results in under-prediction of the tank temperature and pressure irrespective of the filling condition. For a given target tank pressure, the refueling time is the shortest under adiabatic condition and is the longest under isothermal condition with the tank being maintained at the initial tank temperature. The adiabatic and isothermal conditions can be viewed, respectively, as the lower and upper bounds of the refueling time for a given final target tank pressure.     

Experimental analysis of solar thermal storage in a water tank with open side inlets

This paper investigates thermal mixing caused by the inflow from one or two round, horizontal, buoyant jets in a water storage tank, which is part of a thermal solar installation. A set of experiments was carried out in a rectangular tank with a capacity of 0.3 m³, with one or two constant temperature inflows. As a result, two correlations based on temperature measurements have been developed. One of the correlations predicts the size of a zone of homogenous temperature, referred to herein as the mixing zone, which develops when a single hot inflow impinges on the opposite wall of the tank. The other identifies the degree of mixing resulting from the interaction between a hot inflow and a cold inflow located below the hot one. The correlations are combined with energy balances to predict the amount of hot water available in a tank with open side inlets and the corresponding temperatures of the outflows. Outdoor measurements were also performed in a solar installation, in which a commercial water storage tank with a 1.5 m³ capacity, heated by a solar collector array with a useful surface area of 42.2 m², drives a LiBr-H₂O absorption chiller. Comparison of the predicted and measured outflow temperatures under a variety of weather conditions shows a maximum difference of 3 °C.     

Thermodynamic analysis of hydrogen tank filling. Effects of heat losses and filling rate optimization

A thermodynamic analysis of the refueling of a gaseous fuel tank and a thermal analysis of heat losses through tank walls is presented. The objective of the thermodynamic analysis is to compare the temperature and pressure evolutions coming from different equations of state and from thermodynamic tables. This comparison is performed with nitrogen and hydrogen and the compression is assumed adiabatic. It is shown that the ideal-gas assumption results in under-prediction of the tank temperature and pressure for hydrogen but in over-prediction for nitrogen. An approximate analytical expression of the Redlich–Kwong equation of state is given which is in very good agreement with thermodynamic tables. To handle heat losses, different approaches are used and compared. First, a global thermal conductance is introduced which allows deriving analytical expressions. Then, a thermal nodal modeling of tank walls is proposed to take into account thermal capacity effects. Finally a 1D semi-infinite modeling of the tank walls is presented. Finally, this model is used to optimize mass flow rate in order to limit the temperature rise during the filling process.     

Improvement of heat transfer model for adsorptive hydrogen storage system

Hydrogen adsorption on high surface area activated carbon is an effective solution of hydrogen storage. Improvement is necessary for the heat transfer model of adsorptive hydrogen storage system. Distributed and lumped parameter models are implemented by the Comsol software and Matlab/Simulink software respectively. The evolution of pressure and temperature during charge and discharge processes is investigated. We adopted following measures for a further improvement on the model: (1) Wall temperature is improved by varying heat transfer coefficient; (2) A more realistic geometry with insert tube improves near inlet temperature; (3) Lumped parameter model is improved by considering thermal conductivity; (4) Distributed and lumped parameter models are well validated by experiments; (5) Heat transfer is modeled under conditions of air cooling and water cooling. The water cooling condition is better than air cooling condition in decreasing the temperature of the storage tank and improving the storage capacity.     

CFD analysis of fast filling scenarios for 70 MPa hydrogen type IV tanks

High injection pressure is combined with high refueling rate for vehicles storing pressurized gaseous hydrogen onboard. As a drawback, high temperatures are developed inside the tank, which can jeopardize the structural integrity of the storage system. Computational Fluid Dynamics (CFD) codes already proved to be a valuable tool for predicting the temperature distribution within the tank during fast refueling. Results of hydrogen fast filling CFD simulations for a type IV tank, filled to 70 MPa at different working conditions are presented as follow up of the CFD model validation performed against experimental data. Alternative rates of pressure rise, adiabatic and cold filling are investigated to evaluate the effect on maximum hydrogen temperatures inside the tank. Results confirmed that the developed CFD model could be a suitable tool for investigating fast filling scenarios when experimental data are not yet available or of difficult realization.     

Dual solutions in a thermal diffusive flow over a stretching sheet with variable thickness

The development of thermal diffusive flow over a stretching sheet with variable thickness has been investigated. The non-linear coupled partial differential equations governing the flow and thermal fields are first transformed into a set of non-linear coupled ordinary differential equations by a set of suitable similarity transformations. The resulting system of coupled non-linear differential equations is solved using the Shooting method by converting into an initial value problem. In this method, the system of equations is converted into the set of first order system which is solved by fourth-order Runge–Kutta method. It is interesting to note that multiple solutions are observed for certain wall thickness parameter (β) and velocity power index (m). Velocity overshoot near the wall is observed for certain solution branches. The significant impacts on the boundary layer development along the wall on the velocity profiles and on the shear stress distribution in the fluid have been found by the non-flatness of the stretching surface. The mass suction effect is introduced by the non-flatness, when the velocity power index is less than one. The mass injection effect is lead to non-flatness when the velocity power index is greater than one. It is found that dual solution exists only for negative value of velocity power index (m). The presence of dual solutions in velocity and temperature fields for certain values of wall thickness parameter (β) and velocity power index (m) are revealed by this study.     

Hybrid formulation and solution for transient conjugated conduction–external convection

This work presents a hybrid numerical–analytical solution for transient laminar forced convection over flat plates of non-negligible thickness, subjected to arbitrary time variations of applied wall heat flux at the fluid–solid interface. This conjugated conduction–convection problem is first reformulated through the employment of the coupled integral equations approach (CIEA) to simplify the heat conduction problem on the plate by averaging the related energy equation in the transversal direction. As a result, an improved lumped partial differential formulation for the transversally averaged wall temperature is obtained, while a third kind boundary condition is achieved for the fluid from the heat balance at the solid–fluid interface. From the available steady velocity distributions, a hybrid numerical–analytical solution based on the generalized integral transform technique (GITT), under its partial transformation mode, is then proposed, combined with the method of lines implemented in the Mathematica 5.2 routine NDSolve. The interface heat flux partitions and heat transfer coefficients are readily determined from the wall temperature distributions, as well as the temperature values at any desired point within the fluid. A few test cases for different materials and wall thicknesses are defined to allow for a physical interpretation of the wall participation effect in contrast with the simplified model without conjugation.     

Finite element simulation of heat and mass transfer in activated carbon hydrogen storage tank

A mathematical model of heat and mass transfer in activated carbon (AC) tank for hydrogen storage is proposed based on a set of partial differential equations (PDEs) controlling the balances or conservations of mass, momentum and energy in the tank. These PDEs are numerically solved by means of the finite element method using Comsol Multiphysics^TM. The objective of this paper is to establish a correct set of PDEs describing the physical system and appropriate parameters for simulating the hydrogen storage process. In this paper, we establish an axisymmetric model of hydrogen storage by adsorption on activated carbon, considering heat and mass transfer of hydrogen in storage tank during the charging process at room temperature (295 K) and the pressure of 10 MPa. To simulate the hydrogen storage process accurately, the heat capacity of adsorbed phase, the contact thermal resistance between the AC bed and the steel wall and the inertial resistance of high speed charging hydrogen gas are all taken into account in the model. The governing equations describing the hydrogen storage process by adsorption are solved to obtain the pressure changes, temperature distributions and adsorption dynamics in the storage tank. The pressure reaches a maximum value of 10 MPa at about 240 s. A small downward trend appears in the later stage of the charging process, which lasts 700 s. The temperature distribution is highest in the center of the tank. The temperature history exhibits a rapid increase initially, followed by a steady decline. A modified Dubinin–Astakhov (D–A) model is used to represent the hydrogen adsorption isotherms. The highest hydrogen uptake is 10 mol H₂/kg AC, at the entrance of hydrogen storage tank, where the temperature is lowest. The adsorption distribution at a given time is mainly determined by the temperature distribution, because the pressure is almost uniform in the tank. The adsorption history, however, is dominated by the pressure history because the pressure change is much larger than temperature change during the charging process of hydrogen storage.     

A review of: “World Energy Supply: Resource,Technologies” Perspectives MANFRED GRATHWOHL

A theoretical model for unsteady one-dimensional temperature field inside the hot-water storage tank of a thermosyphonic solar system is carried out. Hot water flows into a vertical storage tank via its top central line at low constant rates. The measured temperature profiles along the central axis inside the storage tank of a V-trough thermosyphonic solar heater are observed to be in line with the analytical predictions. The linearity of the temperature profiles as checked experimentally is distinctly observed for high inflow velocities of the hot water into the storage tank.     

Investigation of thermal performance of a ground coupled heat pump system with a cylindrical energy storage tank

An analytical and computational model for a solar assisted heat pump heating system with an underground seasonal cylindrical storage tank is developed. The heating system consists of flat plate solar collectors, an underground cylindrical storage tank, a heat pump and a house to be heated during winter season. Analytical solution of transient field problem outside the storage tank is obtained by the application of complex finite Fourier transform and finite integral transform techniques. Three expressions for the heat pump, space heat requirement during the winter season and available solar energy are coupled with the solution of the transient temperature field problem. The analytical solution presented can be utilized to determine the annual variation of water temperature in the cylindrical store, transient earth temperature field surrounding the store and annual periodic performance of the heating system. A computer simulation program is developed to evaluate the annual periodic water and earth temperatures and system performance parameters based on the analytical solution. Copyright © 2003 John Wiley & Sons, Ltd.     

The design and optimization of a cryogenic compressed hydrogen refueling process

Cryo-compressed hydrogen storage has excellent volume and mass hydrogen storage density, which is the most likely way to meet the storage requirements proposed by United States Department of Energy（DOE）. This paper contributes to propose and analyze a new cryogenic compressed hydrogen refueling station. The new type of low temperature and high-pressure hydrogenation station system can effectively reduce the problems such as too high liquefaction work when using liquid hydrogen as the gas source, the need to heat and regenerate to release hydrogen, and the damage of thermal stress on the storage tank during the filling process, so as to reduce the release of hydrogen and ensure the non-destructive filling of hydrogen. This paper focuses on the study of precooling process in filling. By establishing a heat transfer model, the dynamic trend of tank temperature with time in the precooling process of low-temperature and high-pressure hydrogen storage tank under constant pressure is studied. Two analysis methods are used to provide theoretical basis for the selection of inlet diameter of hydrogen storage tank. Through comparative analysis of the advantages and disadvantages of the two analysis methods, it is concluded that the analysis method of constant mass flow is more suitable for the selection in practical applications. According to it, the recommended diameter of the storage tank at the initial temperature of 300 K, 200 K and 100 K is selected, which are all 15 mm. It is further proved that the calculation method can meet the different storage tank states of hydrogen fuel cell vehicles when selecting the pipe diameter.