Theoretical investigation on heat leakage distribution between vapor and liquid in liquid hydrogen tanks

As a key factor affecting thermal behaviors of liquid hydrogen (LH₂) tanks, heat leakage plays an important role in accurate prediction of pressure build-up for safe storage and transportation of LH₂. Uniform heat flux between vapor and liquid in LH₂ tanks is widely adopted as thermal boundary condition in predicting pressure build-up process. However, a distribution of heat flux between vapor and liquid was observed during the self-pressurization process in the experimental test. In light of this, an analytically theoretical model of revealing the energy exchange process among the vapor, liquid and inner wall is proposed to investigate the heat leakage distribution ratio (HDR) between vapor and liquid in LH₂ tanks. The feasibility of the model is validated by the experimental results from NASA. In the whole self-pressurization process of 25,000 s, HDR reduces from 0.803 to 0.235 under a liquid fill ratio of 90% and a total heat leakage of 71.3 W. The results show that the existence of inner wall and different thermal properties between the vapor and liquid make the heat leakage flux non-uniformly distributed into the vapor and liquid. And the geometric structure of tank, thermal properties and initial states of the vapor and liquid have a significant effect on HDR. When coupling the model with thermal multi-zone model, the relative error in pressure prediction is reduced by 61.8% against experimental results. Benefiting from the coupled model, the relative error in pressure prediction caused by the uniform heat flux boundary condition reduces from 90.16% to 8.15%. The present work establishes theoretical foundation on analyzing heat leakage distribution between the vapor and liquid for LH₂ tanks, and provides useful guidance on modifying boundary conditions in accurately predicting thermal behaviors of LH₂ tanks.     

Modeling and thermodynamic analysis of thermal performance in self-pressurized liquid hydrogen tanks

Liquid hydrogen (LH₂) is one of the most economic methods for large-scaled utilization of hydrogen energy. However, safe operation and storage of LH₂ relies on accurate prediction of the pressure rise and adequate investigation on thermal behaviors inside LH₂ tank. In light of this, a modified thermal multi-zone model (TMZM) considering heat and mass transfer between vapor and liquid is developed in this paper. The model has a maximum relative error of 4.67% in predicting pressure rise against the experimental results from NASA. A thermodynamic analysis method is proposed to clarify the influences of key parameters including the temperature, compressibility factor and density of vapor, and working conditions including heat leakage and initial superheated degree on the pressurization rate. The results indicate that temperature of vapor in the ullage and vapor-liquid interfacial mass transfer rate are two main parameters determining the pressurization rate, and the effects of the two parameters are different between different stages. The distinction of stages depends on heat leakage and initial superheated degree. For the working condition with an initial filling rate of 50% and a heat leakage of 10 W, temperature of vapor is the parameter dominates pressurization rate during 96.8% of the whole self-pressurization process. Heat leakage also has a vital impact on the distinction of stages, when heat leakage increases to 80 W, the temperature of vapor dominating stage will reduce to 46.4%. Furthermore, pressurization rate is sensitive to initial superheated degree in the ullage. An increase of 4 K of the initial superheated degree leads to a 53.3% decrease of the pressurization rate. This study provides a useful method for the reliable design and quick optimization of high performance LH₂ tanks.     

Investigation on no-vent filling process of liquid hydrogen tank under microgravity condition

In order to investigate the no-vent filling performance under microgravity, the computational fluid dynamic (CFD) method is introduced to the study, where a model aiming at filling a liquid hydrogen (LH₂) receiver tank is especially established. In this model, the solid and fluid regions are considered together to predict the coupled heat transfer process. The phase change effect during the filling process is also taken into account by embedding a pair of mass and heat transfer models into the CFD software FLUENT, one of which involves liquid flash driven by pressure difference between the fluid saturated pressure and the tank pressure, and the other one indicates and calculates the evaporation–condensation process driven by temperature difference between fluid and its saturated state. This CFD model, verified by experimental data, could accurately simulate the no-vent filling process with good flexibility. Moreover, no-vent filling processes under different gravities are comparatively analyzed and the effects of four factors including inlet configuration, inlet liquid temperature, initial wall temperature and inlet flow rate, are discussed, respectively. Main conclusions could be made as follows: 1) Compared to the situations in normal gravity, the no-vent filling in microgravity experiences a more adequate liquid–vapor mix, which results in a more steady pressure response and better filling performance. 2) Inlet configuration seems to have negligible effect on the no-vent filling performance under microgravity since liquid could easily reach the tank wall and then cause a sufficient fluid-wall contact under any inlet condition. 3) Higher initial tank wall temperature may directly cause a higher pressure rise in the beginning, while this effect on the final pressure is not significant. Sufficient precooling and reasonable inlet liquid subcooled degree are suggested to guarantee the reliability and efficiency of the no-vent fill under microgravity.     

Simulation of boil-off losses during transfer at a LH2 based hydrogen refueling station

Losses along the LH₂ pathway are intrinsic to the utilization of a cryogenic fluid. They occur when the fluid is transferred between 2 vessels (liquefaction plant to trailer, trailer to station storage, station storage to pump or compressor, then possibly onto fuel cell electric vehicles …) and when it is warmed up due to heat transfer with the environment. Those losses can be estimated with good accuracy using thermodynamic models based on the conservation of mass and energy, provided that the thermodynamic states are correctly described. Indeed, the fluid undergoes various changes as it moves along the entire pathway (2 phase transition, sub-cooled liquid phase, super-heated warming, non-uniform temperature distributions across the saturation film) and accurate equations of state and 2 phase behavior implementations are essential. The balances of mass and energy during the various dynamics processes then enable to quantify the boil-off losses. In this work, a MATLAB code previously developed by NASA to simulate rocket loading is used as the basis for a LH₂ transfer model. This code implements complex physical phenomena such as the competition between condensation and evaporation and the convection vs. conduction heat transfer as a function of the relative temperatures on both sides of the saturated film. The original code was modified to consider real gas equations of state, and some semi-empirical relationships, such as between the heat of vaporization and the critical temperature, were replaced by a REFPROP equivalent expression, assumed to be more accurate. Non-constant liquid temperature equations were added to simulate sub-cooled conditions. The model shows that under environmental heat transfer only the liquid phase of a LH₂ vessel would experience cooling, while the boil-off is mainly a result of evaporation from the saturation film onto the vapor phase. Under the conditions assumed for this work, it was also concluded that the actual LH₂ density was lower than the corresponding saturation density given by the working pressure of the vessel. During a bottom fill transfer, for example from a LH₂ trailer to an on-site stationary vessel, it is shown that the boil-off losses are due to the compression of the vapor phase (“pdV” force). The model indicates that the magnitude of those losses is not dependent on the regulated pressure in the receiving vessel but is rather a function of the initial pressure in the vessel, amounting to more than 12% of losses for a vessel initially at 100 psia. At last, the model is used to estimate the amount of vapor H₂ vented when depressurizing a LH₂ trailer following a LH₂ delivery.     

Improved handling of liquid hydrogen at filling stations: Review of six years' experience

Within the industrial-scale solar hydrogen demonstration facility operated by SWB at Neunburg vorm Wald in Germany, a liquid hydrogen (LH₂) filling station has been installed for optimization of the LH₂ transfer process to various vehicle fuel tank systems.New types of vehicle tanks and coupling systems for LH₂ filling lines were realized and tested. Designed for positive self-closing, these coupling systems can be disconnected while containing LH₂.With these coupling systems and vehicle tanks, time needed to refuel LH₂ vehicles is reduced from more than 1 h to less than 3 min, and hydrodynamic losses of liquefaction energy are reduced from approximately 50% of the transferred LH₂ to 0%.An optimized concept for an advanced LH₂ filling station and a vehicle LH₂ tank are described.     

Flashing phenomena of depressurized liquid nitrogen in a pressure vessel. Part 2: Mist formation and behavior of the liquid surface in the early depressurization process

Flashing of liquid nitrogen in a pressure vessel (cryostat) was observed at depressurization rates from 0.01 to 4.0 MPa/s. The explosive boiling behavior was observed by using a video camera. Pressure and temperature changes in the pressure vessel were measured. In the case of high depressurization rates, mist formation was observed in the vapor phase near the vapor—liquid interface in the early stages of the depressurization process. The mist layer became more dense as the depressurization rate increased. Observations of mist formation and the estimated temperature drop of the vapor under an adiabatic expansion process show that mist formation depends on the vapor expansion and boiling near the liquid surface. Mist formation in flashing phenomena plays an important role in the relaxation of thermal nonequilibrium states between the subcooled vapor and the superheated liquid generated by depressurization. © 1998 Scripta Technica, Heat Trans Jpn Res, 27(5): 327–335, 1998     

Operation scenario-based design methodology for large-scale storage systems of liquid hydrogen import terminal

This paper presents an operation scenario-based design methodology to determine the design pressure of the storage system of liquid hydrogen (LH₂) import terminals. The methodology includes operation scenario establishment, thermodynamic analysis, and structural analysis. In a case study conducted, the terminal has a storage capacity of 75,000 m³, imports cargo from a 50,000 m³ LH₂ tanker, and supplies hydrogen in vapor and liquid forms without any loss of boil-off hydrogen (BOH) as a reference case. In the deviation from the reference case, 4.7% of the entire imported LH₂ needs proper treatment as BOH under the application of a non-pressurized storage system. In addition, the vapor pressure of the imported LH₂ is the most influential in determining the design pressure. From the obtained design pressure, the structural analysis is performed in compliance with the Boiler & Pressure Vessel Code of American Society of Mechanical Engineers.     

Numerical study on unsteady heat transfer and fluid flow in a closed cylinder of reciprocating liquid hydrogen pumps

Modeling and optimization of liquid hydrogen (LH₂) pumps require accurate in-cylinder heat transfer correlations. However, the applicability of existing correlations based on gas mediums to LH₂ remains to be verified. In this paper, the unsteady heat transfer and fluid flow in a closed LH₂ pump cylinder are numerically studied by adopting the gas spring model. The phase shifts and temperature distribution in the closed pump cylinder are investigated. LH₂ is less affected by in-cylinder heat transfer and has a more uniform temperature distribution compared to nitrogen gas, while a low-temperature zone appears near the piston face at 120 rpm. Finally, the validity of Lekic's correlation in predicting the heat flux of the LH₂ compression process in the closed pump cylinder is verified, and the efficiency decrement versus rotational speed is analyzed based on the correlation. This work would be useful for selecting a proper in-cylinder heat transfer model for predicting the thermodynamic process in reciprocating LH₂ pumps.     

A liquid hydrogen car with a two-stroke direct injection engine and LH2-pump

Objectives for the practical application of hydrogen cars are (i) engine-output increase (power-up), suppression of abnormal combustion, and NO_x reduction; (ii) the development of a low cost liquid hydrogen-(LH₂) tank having high thermal insulation; and (iii) the development of a method to supply fuel from the LH₂-tank to the engine. We have developed a hydrogen car system consisting of a LH₂-tank-LH₂-pump-injector to inject high pressure and low temperature hydrogen gas into a two-stroke engine that is capable of meeting all the above-mentioned requirements except (ii). The system was then applied to a mini-car equipped with a 0.551, engine. The performance of the car has demonstrated the above-mentioned capabilities from the engine dynamometer and road tests.     

Numerical investigation on chill-down and thermal stress characteristics of a LH2 tank during ground filling

To investigate the thermal and structural characteristics of a flight-scale LH₂ tank during ground fillings, a CFD model and a structural analysis model are established to simulated the chill-down process and the induced thermal stress behavior of the tank, respectively. Results show that, at the early stage of filling, a severe temperature gradient appears at the liquid level, leading to a remarkable local concentration of thermal stress, while the maximal thermal deformation is at the outlet region. After the local wall is chilled down sufficiently, the temperature jump at the interface vanishes as well as the local thermal stress, while the maximal thermal deformation is located at the middle height of tank. The thermal stress is most serious at the beginning stage of filling and the maximum appears at the tank bottom. Moreover, the non-uniformity of the temperature distribution and the average thermal stress level within the tank wall both increase with the filling rate. At a filling rate of 7.5 kg·s⁻¹, the maximal thermal stress and thermal deformation of the target tank are more than 70 MPa and 30 mm.     

Thermal analysis of coupled vapor-cooling-shield insulation for liquid hydrogen-oxygen pair storage

The long-term storage of liquid hydrogen (LH₂)-liquid oxygen (LO₂) pair with extremely low heat leakage is essential for future deep space exploration. Vapor-cooled shield (VCS) is considered an effective insulation structure that can significantly reduce the heat penetration into the LH₂ tanks, however it is relatively ineffective for the LO₂ tanks. Novel coupled VCS insulation schemes for LH₂-LO₂ bundled tanks were proposed to achieve optimal performance not only for the LH₂ but also for the LO₂ tanks. A thermodynamic model had been developed and validated by experiments. The optimal VCS location, the temperature profile within the insulation, the heat leakage reduction contributed by the VCS, and the thermal performance versus scheme structural mass had been parametrically investigated. A comparison indicated that the proposed single integrated shield configuration can reduce the heat flux of the LH₂ and the LO₂ tanks by 64.0% and 54.8%, respectively compared with the non-VCS structure. In addition, the results also confirmed that zero boil-off storage of LO₂ can be achieved by only utilizing the exhausted hydrogen vapor, with no need for an extra cryocooler.     

High-density automotive hydrogen storage with cryogenic capable pressure vessels

LLNL is developing cryogenic capable pressure vessels with thermal endurance 5–10 times greater than conventional liquid hydrogen (LH₂) tanks that can eliminate evaporative losses in routine usage of (L)H₂ automobiles. In a joint effort BMW is working on a proof of concept for a first automotive cryo-compressed hydrogen storage system that can fulfill automotive requirements on system performance, life cycle, safety and cost. Cryogenic pressure vessels can be fueled with ambient temperature compressed gaseous hydrogen (CGH₂), LH₂ or cryogenic hydrogen at elevated supercritical pressure (cryo-compressed hydrogen, CcH₂). When filled with LH₂ or CcH₂, these vessels contain 2–3 times more fuel than conventional ambient temperature compressed H₂ vessels. LLNL has demonstrated fueling with LH₂ onboard two vehicles. The generation 2 vessel, installed onboard an H₂-powered Toyota Prius and fueled with LH₂ demonstrated the longest unrefueled driving distance and the longest cryogenic H₂ hold time without evaporative losses. A third generation vessel will be installed, reducing weight and volume by minimizing insulation thickness while still providing acceptable thermal endurance. Based on its long experience with cryogenic hydrogen storage, BMW has developed its cryo-compressed hydrogen storage concept, which is now undergoing a thorough system and component validation to prove compliance with automotive requirements before it can be demonstrated in a BMW test vehicle.     

Screen channel LAD bubble point tests in liquid hydrogen

This paper presents experimental results for the liquid hydrogen bubble point tests for liquid acquisition devices (LADs) operating in low gravity cryogenic propulsion systems. The purpose of the test was to investigate parameters that affect screen channel LAD performance in a low pressure liquid hydrogen (LH₂) propellant tank and to demonstrate several ways to increase the LH₂ bubble point pressure. Three fine mesh screen channel LAD samples were tested in LH₂ over the range of 16.7 K < T < 21.1 K and 31.5 kPa < P < 155 kPa using gaseous helium and hydrogen as pressurant gases. Results show that bubble point pressure is affected by screen mesh type, liquid temperature and pressure, and type of pressurization gas. Higher bubble points are achieved by using a finer mesh screen and pressurizing and subcooling the liquid with gaseous helium. In addition, there is evidence that the screen pore is itself temperature dependent.     

Two-dimensional thermal analysis of liquid hydrogen tank insulation

Liquid hydrogen (LH₂) storage has the advantage of high volumetric energy density, while boil-off losses constitute a major disadvantage. To minimize the losses, complicated insulation techniques are necessary. In general, Multi Layer Insulation (MLI) and a Vapor-Cooled Shield (VCS) are used together in LH₂ tanks. In the design of an LH₂ tank with VCS, the main goal is to find the optimum location for the VCS in order to minimize heat leakage. In this study, a 2D thermal model is developed by considering the temperature dependencies of the thermal conductivity and heat capacity of hydrogen gas. The developed model is used to analyze the effects of model considerations on heat leakage predictions. Furthermore, heat leakage in insulation of LH₂ tanks with single and double VCS is analyzed for an automobile application, and the optimum locations of the VCS for minimization of heat leakage are determined for both cases.     

Analyses of one-step liquid hydrogen production from methane and landfill gas

Conventional liquid hydrogen (LH₂) production consists of two basic steps: (1) gaseous hydrogen (GH₂) production via steam methane reformation followed by purification by means of pressure swing adsorption (PSA), and (2) GH₂ liquefaction. LH₂ produced by the conventional processes is not carbon neutral because of the carbon dioxide (CO₂) emission from PSA operation. A novel concept is herein presented and flowsheeted for LH₂ production with zero carbon emission using methane (CH₄) or landfill gas as feedstock. A cryogenic process is used for both H₂ separation/purification and liquefaction. This one-step process can substantially increase the efficiency and reduce costs because no PSA step is required. Furthermore, the integrated process results in no CO₂ emissions and minimal H₂ losses. Of the five flowsheets presented, one that combines low and high temperature CO/CH₄ reforming reactions in a single reactor shows the highest overall efficiency with the first and second law efficiencies of 85% and 56%, respectively. The latter figure assumes 10% overall energy loss and 30% efficiency for the cryogenic process.     

CFD simulation of heat transfer and phase change characteristics of the cryogenic liquid hydrogen tank under microgravity conditions

The heat transfer and phase change processes of cryogenic liquid hydrogen (LH₂) in the tank have an important influence on the working performance of the liquid hydrogen-liquid oxygen storage and supply system of rockets and spacecrafts. In this study, we use the RANS method coupled with Lee model and VOF (volume of fraction) method to solve Navier-stokes equations. The Lee model is adopted to describe the phase change process of liquid hydrogen, and the VOF method is utilized to calculate free surface by solving the advection equation of volume fraction. The model is used to simulate the heat transfer and phase change processes of the cryogenic liquid hydrogen in the storage tank with the different gravitational accelerations, initial temperature, and liquid fill ratios of liquid hydrogen. Numerical results indicate greater gravitational acceleration enhances buoyancy and convection, enhancing convective heat transfer and evaporation processes in the tank. When the acceleration of gravity increases from 10^?2 g0 to 10^?5 g0, gaseous hydrogen mass increases from 0.0157 kg to 0.0244 kg at 200s. With the increase of initial liquid hydrogen temperature, the heat required to raise the liquid hydrogen to saturation temperature decreases and causes more liquid hydrogen to evaporate and cools the gas hydrogen temperature. More cryogenic liquid hydrogen (i.e., larger the fill ratio) makes the average fluid temperature in the tank lower. A 12.5% reduction in the fill ratio resulted in a decrease in fluid temperature from 20.35 K to 20.15 K (a reduction of about 0.1%, at 200s).     

Process optimization for large-scale hydrogen liquefaction

The investment in the hydrogen infrastructure for hydrogen mobility has lately seen a significant acceleration. The demand for energy and cost efficient hydrogen liquefaction processes has also increased steadily. A significant scale-up in liquid hydrogen (LH₂) production capacity from today's typical 5–10 metric tons per day (tpd) LH₂ is predicted for the next decade. For hydrogen liquefaction, the future target for the specific energy consumption is set to 6 kWh per kg LH₂ and requires a reduction of up to 40% compared to conventional 5 tpd LH₂ liquefiers. Efficiency improvements, however, are limited by the required plant capital costs, technological risks and process complexity. The aim of this paper is the reduction of the specific costs for hydrogen liquefaction, including plant capital and operating expenses, through process optimization. The paper outlines a novel approach to process development for large-scale hydrogen liquefaction. The presented liquefier simulation and cost estimation model is coupled to a process optimizer with specific energy consumption and specific liquefaction costs as objective functions. A design optimization is undertaken for newly developed hydrogen liquefaction concepts, for plant capacities between 25 tpd and 100 tpd LH₂ with different precooling configurations and a sensitivity in the electricity costs. Compared to a 5 tpd LH₂ plant, the optimized specific liquefaction costs for a 25 tpd LH₂ liquefier are reduced by about 50%. The high-pressure hydrogen cycle with a mixed-refrigerant precooling cycle is selected as preferred liquefaction process for a cost-optimized 100 tpd LH₂ plant design. A specific energy consumption below 6 kWh per kg LH₂ can be achieved while reducing the specific liquefaction costs by 67% compared to 5 tpd LH₂ plants. The cost targets for hydrogen refuelling and mobility can be reached with a liquid hydrogen distribution and the herewith presented cost-optimized large-scale liquefaction plant concepts.     

Liquid hydrogen as a vehicular fuel—a challenge for cryogenic engineering

Present and developing technologies of liquid hydrogen onboard storage and handling are reviewed. Substantial improvement in operating hydrogen fueled internal combustion engines can be made by intense use of the cold hydrogen gas available from the LH₂-fuel tank. Because of the large heat sink capability of liquid hydrogen the volumetric heating value of the cylinder charge can be increased considerably even for external mixture formation. Further success in hydrogen engine development will depend mainly upon the development of suitable internal fuel mixing techniques based on cryogenic liquid fuel injection pumps.     

Studies on Thermal Stratification Phenomenon in LH2 Storage Vessel

A study of convective heat transfer in a cryogenic storage vessel is carried out numerically and experimentally. A scaled down model study is performed using water as the model fluid in a rectangular glass tank heated from the sides. The convective flow and the resulting thermal stratification phenomenon in the rectangular tank are studied through flow visualization, temperature measurement, and corresponding numerical simulations. It is found that a vortex-like flow near the top surface leads to a well-mixed region there, below which the fluid is thermally stratified. In addition, in an attempt to simulate the actual conditions, a numerical study is performed on a cylindrical cavity filled with liquid hydrogen (LH₂) and heated from the sides. The results are compared with our model study with water, and the qualitative agreement is found to be good.     

Fluid thermal stratification in a non-isothermal liquid hydrogen tank under sloshing excitation

To the safe space operation of cryogenic storage tank, it is significant to study fluid thermal stratification under external heat leaks. In the present paper, a numerical model is established to investigate the thermal performance in a cryogenic liquid hydrogen tank under sloshing excitation. The interface phase change and the external convection heat transfer are considered. To realize fluid sloshing, the dynamic mesh coupled the volume of fluid (VOF) method is used to predict the interface fluctuations. A sinusoidal excitation is implemented via customized user-defined function (UDF) and applied on tank wall. The grid sensitivity study and the experimental validation of the numerical mode are made. It turns out that the present numerical model can be used to simulate the unsteady process in a non-isothermal sloshing tank. Variations of tank pressure, liquid and vapor mass, fluid temperature and thermal stratification are numerically investigated respectively. The results show that the sinusoidal excitation has caused large influence on thermal performance in liquid hydrogen tank. Some valuable conclusions are arrived, which is important to the depth understanding of the non-isothermal performance in a sloshing liquid hydrogen tank and may supply some technique reference for the methods of sloshing suppression.