Underexpanded Hydrogen Jets Research Articles

Development of a new solver for homogenous mixture based on regularized gas dynamic equation system

AbstractThe paper presents an improved approach for modeling multicomponent gas mixtures based on quasi‐gasdynamic equations. The proposed numerical algorithm is implemented as a reactingQGDFoam solver based on the open‐source OpenFOAM platform. The following problems have been considered for validation: the Riemann problems, the backward facing step problem, the interaction of a shock wave with a heavy and a light gas bubble, the unsteady underexpanded hydrogen jet flow in an air. The stability and convergence parameters of the proposed numerical algorithm are determined. The simulation results are found to be in agreement with analytical solutions and experimental data.

A fast POD prediction method for hydrogen leakage at different pressures

The complexity of hydrogen leakage at different pressures leads to the challenge of developing a prediction method for both low pressure and supercritical pressure hydrogen leakage. In this paper, a reduced-order model (ROM) based on proper orthogonal decomposition (POD) is developed to rapidly predict the hydrogen dispersion caused by leakage in small holes at different pressures. The subsonic and underexpanded hydrogen jets are simulated and verified with experimental data. Numerical results of some pressures are collected as POD snapshots and POD interpolation methods are performed to predict the velocity and hydrogen concentration distributions at desired unsampled pressures. Different sample plans with different sampling intervals and sample numbers are investigated. POD-linear, POD-spline, and POD-RBF (radial basis function) interpolations are compared. The results show that the POD-linear and POD-spline methods can accurately predict the velocity and hydrogen fraction at different pressures, and both are better than the POD-RBF method. The relative errors in predicting the hydrogen mole fraction between the POD-linear and POD-spline methods and the simulation results are 2.26% and 2.37%, respectively. Best of all, the POD interpolation method proposed in this work significantly reduces the time required for prediction, costing only 3.3 ms.

Pressure-based large-eddy simulation of under-expanded hydrogen jets for engine applications

An assessment of Large-Eddy Simulations (LES) of non-reactive under-expanded hydrogen jets by using a pressure-based algorithm is presented. Such jets feature strong compressible discontinuities often considered to be best dealt with by a density-based solver. The crucial contribution of this work is to evaluate the suitability of the pressure-based solver to correctly describe the flow field of gaseous hydrogen jets for engine applications, despite the presence of shock waves in the under-expanded near-orifice region. Inherently, the paper aims at providing guidance on the corresponding numerical aspects to simulate these flows. Hydrogen jets in an argon atmosphere at three different injection pressures are simulated and the results are compared to experiments in literature. Jet tip penetration and cone angle are the main investigated parameters. A good match is found, confirming the solidity of the proposed model. Different LES sub-grid scale models and discretisation schemes are then investigated in order to find the best approach in terms of accuracy and required computational cost. In particular, it is found that the WALE model coupled with a 4th-order cubic scheme for the convective terms yields the most suitable configuration.

Gas-dynamic and mixing analysis of under-expanded hydrogen jets: effect of the cross section shape

Green hydrogen is expected to have a key role in the transition towards a carbon-neutral society, particularly in the transportation sector. Exploration of novel solutions for the direct injection of hydrogen in internal combustion engines (ICEs) is a main topic for both academia and industry. Here, the authors explore the gas-dynamic and mixing features of hydrogen under-expanded jets exiting from non-axisymmetric cross-sections, with the aim to provide guidelines for designing novel generations of ICE hydrogen injectors. Triangular and star shapes have been compared with elliptical and rectangular sections with different aspect ratios. Differences in the shock wave systems are reported, and explanations of the gas-dynamic mechanisms developed by each section are proposed. Non-uniformity in the radial expansion of the jet boundary has been noticed in all of the non-axisymmetric sections, leading to an axis switching of the jet in some cases. Differences in the radial mixing and axial jet penetration have been reported too, and a robust correlation with the vorticity distribution along the jet boundary has been observed.

Numerical study of hydrogen jet in methane / air premixed atmosphere

The work presented a numerical study on the transient characteristics of under-expanded hydrogen jets from a cylindrical nozzle. The finite-volume solution was adopted in the two-dimensional simulation of high-pressure chocked hydrogen jets, by solving the Navier-Stokes equations for gas phase flow. Numerical analyses were respectively performed over the micro level to characterize the fine structures, and over macro levels to explore the key global parameters of the gaseous jets. Parameterization work was conducted in terms of the microscopic characteristics of jets, such as, the length of jet core, the diameter of jet vortex, and the key global parameters, i.e. the penetration and the steady fuel injection rate. The effects of the injection parameters on the micro-structure and macro characteristics were hence quantified.

Numerical investigation of the cryogenic underexpanded hydrogen jets exiting rectangular shaped openings

Cryo-compressed hydrogen shows increasing potentials in hydrogen utilization. The development and revision of safety codes and standards for cryo-compressed hydrogen infrastructure requires studies of accidental leaks for various scenarios. However, the actual leaks are more likely to result in jets through slots rather than round nozzles in most previously studies. In this work, a numerical model of cryogenic hydrogen underexpanded jets was employed to evaluate the effect of jet temperature and aspect ratio of rectangular nozzles on the shock structure and dispersion characteristics. Correlations were proposed to evaluate the effect of jet temperature and aspect ratio of rectangular nozzles on the shock structure and dispersion characteristics. The numerical results revealed that cryogenic hydrogen release caused axial extension of the hazard zone. The aspect ratio of rectangular nozzle shows significant effect on the shock structure and hydrogen dispersion. The shock intensity decreases with aspect ratio and Mach disk disappear when the ratio larger than eight. The effect of nozzle shape on hydrogen diffusion was pronounced at high pressure ratio between nozzle exits and environment. Moreover, the normalized radial volume fraction with various jet temperature collapsed into a Gaussian distribution with low aspect ratio (AR) smaller than 8, and the centerline. The decay rates of centerline normalized volume fraction increased with the aspect ratio. The normalized volume fraction on centerline decay rates increased with the aspect ratio. However, the normalized volume fraction on the minor axis plane did not fit a Gaussian distribution when the aspect ratio was larger than eight due to axis switching, which also produced a wider hazard zone.

CFD simulations of under-expanded hydrogen jets under high-pressure injection conditions

Large-eddy simulations (LES) of hydrogen jets under highly under-expanded conditions are carried out. Computational fluid dynamics (CFD) analysis appears extremely useful to fully understand and optimize the hydrogen injection process, like in internal combustion engines. This work aims to analyze hydrogen high-pressure injection in the near-nozzle region, investigating the formation process and the structure of the Mach disks and the transition to turbulent jets, for nozzle pressure ratios (NPR) of 5.8 and 30. A real fluid model is utilized and compared against the simpler ideal gas model, for injections into an ambient pressure environment. Furthermore, hydrogen-air mixing evolution is investigated in the far-field region. Average quantities obtained from statistical analysis on LES simulations are compared with available data. The near nozzle region, except for the initial transient part, is better captured by accurate spatial discretization methods, while properly predicting far-field effects, like turbulence and acoustic effects, seems to be mostly related to time discretization schemes.

Blast Wave Generated by Delayed Ignition of Under-Expanded Hydrogen Free Jet at Ambient and Cryogenic Temperatures

An under-expanded hydrogen jet from high-pressure equipment or storage tank is a potential incident scenario. Experiments demonstrated that the delayed ignition of a highly turbulent under-expanded hydrogen jet generates a blast wave able to harm people and damage property. There is a need for engineering tools to predict the pressure effects during such incidents to define hazard distances. The similitude analysis is applied to build a correlation using available experimental data. The dimensionless blast wave overpressure generated by delayed ignition and the follow-up deflagration or detonation of hydrogen jets at an any location from the jet, ∆Pexp/P0, is correlated to the original dimensionless parameter composed of the product of the dimensionless ratio of storage pressure to atmospheric pressure, Ps/P0, and the ratio of the jet release nozzle diameter to the distance from the centre of location of the fast-burning near-stoichiometric mixture on the jet axis (30% of hydrogen in the air by volume) to the location of a target (personnel or property), d/Rw. The correlation is built using the analysis of 78 experiments regarding this phenomenon in the wide range of hydrogen storage pressure of 0.5–65.0 MPa and release diameter of 0.5–52.5 mm. The correlation is applicable to hydrogen free jets at ambient and cryogenic temperatures. It is found that the generated blast wave decays inversely proportional to the square of the distance from the fast-burning portion of the jet. The correlation is used to calculate the hazard distances by harm thresholds for five typical hydrogen applications. It is observed that in the case of a vehicle with onboard storage tank at pressure 70 MPa, the “no-harm” distance for humans reduces from 10.5 m to 2.6 m when a thermally activated pressure relief device (TPRD) diameter decreases from 2 mm to a diameter of 0.5 mm.

Experimental study on the effect of fan-shaped water mist on horizontal under-expanded hydrogen jet flames

A series of experiments were performed on the fan-shaped water mist interaction with the horizontal under-expanded hydrogen jet flames. The effects of various water mist pressures and horizontal release positions were focused on flame length, temperature, and radiant heat flux. The results show that, water mist causes the flame to be tilted and the tilt angle of the flame increases with the water mist pressure, and the horizontal length of the flame is shortened. It is also found that water mist may lead to the radiation and temperature enhancement on the axis and downstream of the action position of water mist and flame, which is closely related to the configuration of water mist. However, this situation disappears and the temperature and radiation decrease with the increase of water mist pressure.

Numerical Investigation of the Cryogenic Underexpanded Hydrogen Jets Exiting Rectangular Shaped Openings

Numerical Investigation of the Cryogenic Underexpanded Hydrogen Jets Exiting Rectangular Shaped Openings

The Pressure Peaking Phenomenon for Ignited Under-Expanded Hydrogen Jets in the Storage Enclosure: Experiments and Simulations for Release Rates of up to 11.5 g/s

This work focuses on the experimental and numerical investigation of maximum overpressure and pressure dynamics during ignited hydrogen releases in a storage enclosure, e.g., in marine vessel or rail carriage, with limited vent size area, i.e., the pressure peaking phenomenon (PPP) revealed theoretically at Ulster University in 2010. The CFD model previously validated against small scale experiments in a 1 m3 enclosure is employed here to simulate real-scale tests performed by the University of South-Eastern Norway (USN) in a chamber with a volume of 15 m3. The numerical study compares two approaches on how to model the ignited hydrogen release conditions for under-expanded jets: (1) notional nozzle concept model with inflow boundary condition, and (2) volumetric source model in the governing conservation equations. For the test with storage pressure of 11.78 MPa, both approaches reproduce the experimental pressure dynamics and the pressure peak with a maximum 3% deviation. However, the volumetric source approach reduces significantly the computational time by approximately 3 times (CFL = 0.75). The sensitivity analysis is performed to study the effect of CFL number, the size of the volumetric source and number of iterations per time step. An approach based on the use of a larger size volumetric source and uniform coarser grid with a mesh size of a vent of square size is demonstrated to reduce the duration of simulations by a factor of 7.5 compared to the approach with inflow boundary at the notional nozzle exit. The volumetric source model demonstrates good engineering accuracy in predicting experimental pressure peaks with deviation from −14% to +11% for various release and ventilation scenarios as well as different volumetric source sizes. After validation against experiments, the CFD model is employed to investigate the effect of cryogenic temperature in the storage on the overpressure dynamics in the enclosure. For a storage pressure equal to 11.78 MPa, it is found that a decrease of storage temperature from 277 K to 100 K causes a twice larger pressure peak in the enclosure due to the pressure peaking phenomenon.

Validation of two-layer model for underexpanded hydrogen jets

Previous studies have shown that the two-layer model more accurately predicts hydrogen dispersion than the conventional notional nozzle models without significantly increasing the computational expense. However, the model was only validated for predicting the concentration distribution and has not been adequately validated for predicting the velocity distributions. In the present study, particle imaging velocimetry (PIV) was used to measure the velocity field of an underexpanded hydrogen jet released at 10 bar from a 1.5 mm diameter orifice. The two-layer model was the used to calculate the inlet conditions for a two-dimensional axisymmetric CFD model to simulate the hydrogen jet downstream of the Mach disk. The predicted velocity spreading and centerline decay rates agreed well with the PIV measurements. The predicted concentration distribution was consistent with data from previous planar Rayleigh scattering measurements used to verify the concentration distribution predictions in an earlier study. The jet spreading was also simulated using several widely used notional nozzle models combined with the integral plume model for comparison. These results show that the velocity and concentration distributions are both better predicted by the two-layer model than the notional nozzle models to complement previous studies verifying only the predicted concentration profiles. Thus, this study shows that the two-layer model can accurately predict the jet velocity distributions as well as the concentration distributions as verified earlier. Though more validation studies are needed to improve confidence in the model and increase the range of validity, the present work indicates that the two-layer model is a promising tool for fast, accurate predictions of the flow fields of underexpanded hydrogen jets.

CFD modelling of underexpanded hydrogen jets exiting rectangular shaped openings

Underexpanded jet releases from circular nozzles have been studied extensively both experimentally and numerically. However, jet releases from rectangular openings have received much less attention and information on their dispersion behaviour is not as widely available. In this paper, Computational Fluid Dynamics (CFD) is used to assess the suitability of using a pseudo-source approach to model jet releases from rectangular openings. A comparative study is performed to evaluate the effect of nozzle shape on jet structure and dispersion characteristics for underexpanded hydrogen jet releases. Jet releases issuing from a circular nozzle and rectangular nozzles with aspect ratios ranging from two to eight are modelled, including resolution of the near-field behaviour. The experimental work of Ruggles and Ekoto (2012, 2014) is used as a basis for validating the modelling approach used and an additional case study, in which jets with a stagnation-to-ambient pressure ratio of 300:1 are modelled, is also performed. The CFD results show that for the 10:1 pressure ratio release the hazard volume and hazard distance remain largely unaffected by nozzle shape. For the higher pressure release, the hazard volume is larger for the rectangular nozzle releases than the equivalent release through a circular orifice, though the distance to lower flammability limit is comparable across the range of nozzle shapes considered. For both of the release pressures simulated the CFD results illustrate that a pseudo-source approach produces conservative results for all nozzle shapes considered. This finding has useful practical implications for consequence analysis in industrial applications, such as the assessment of leaks from flanges and connections in pipework.

Effect of shock structure on stabilization and blow-off of hydrogen jet flames

Under-expanded hydrogen jet has characteristic shock structure immediately downstream of the nozzle exit. The shock structure depends on the ratio pEX/pA, i.e. the ratio of nozzle exit to ambient pressure, and the distributions of velocity and concentration in an under-expanded hydrogen jet depend on characteristics of the shock structure. Therefore, the shock structure should affect the blow-off behaviour of under-expanded hydrogen jet flame. Since this issue has not been investigated in detail, this study aims to close this knowledge gap. The effect of changes in shock structure on lift-off length and blow-off conditions for non-premixed turbulent hydrogen free jet flame has been experimentally investigated. The shock structure was varied by using three types of nozzles: convergent, straight and divergent nozzles. Inlet diameters of nozzles change from 0.31 to 1.04 mm and outlet diameters from 0.34 to 1.7 mm. The static pressure and the ratio of cross-section area at the nozzle inlet to that at the outlet were varying parameters in this study. Hydrogen was horizontally spouted through a nozzle to atmosphere. The maximum static pressure in a nozzle was 13.2 MPa. The experiments revealed that when the hydrogen jet had sequential shock cell structures, which occurred in the range of pEX/pA smaller than 2.45, a higher mass flow rate of hydrogen was needed for the stabilization of a jet flame than that for pEX/pA larger than 2.45 and that when closed to the ideal expansion (pEX/pA = 1), the mass flow rate for stable flame became maximum. In addition, it was observed that the lift-off length of stable flames followed with sequential shock cell structures were almost the same when the minimum cross-section area of used nozzles was constant. However, when hydrogen jet had a shock structure with single Mach disk, the lift-off lengths and the minimum mass flow rate required for the stable jet flame were decreasing with the decrease of the cross-sectional area ratio of the nozzle exit to inlet.

LES and RANS modelling of under-expanded jets with application to gaseous fuel direct injection for advanced propulsion systems

A density-based solver with the classical fourth-order accurate Runge-Kutta temporal discretization scheme was developed and applied to study under-expanded jets issued through millimetre-size nozzles for applications in high-pressure direct-injection (DI) gaseous-fuelled propulsion systems. Both large eddy simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) turbulence modelling techniques were used to evaluate the performance of the new code. The computational results were compared both quantitatively and qualitatively against available data from the literature. After initial evaluation of the code, the computational framework was used in conjunction with RANS modelling (k-ω SST) to investigate the effect of nozzle exit geometry on the characteristics of gaseous jets issued from millimetre-size nozzles. Cylindrical nozzles with various length to diameter ratios, namely 5, 10 and 20, in addition to a diverging conical nozzle, were studied. This study is believed to be the first to provide a direct comparison between RANS and LES within the context of nozzle exit profiling for advanced high-pressure injection systems with the formation of under-expanded jets. It was found that reducing the length of the straight section of the nozzle by 50% resulted in a slightly higher level of under-expansion (∼2.6% higher pressure at the nozzle exit) and ∼1% higher mass flow rate. It was also found that a nozzle with 50% shorter length resulted in ∼6% longer jet penetration length. At a constant nozzle pressure ratio (NPR), a lower nozzle length to diameter ratio resulted in a noticeably higher jet penetration. It was found that with a diverging conical nozzle, a fairly higher penetration length could be achieved if an under-expanded jet formed downstream of the nozzle exit compared to a jet issued from a straight nozzle with the same NPR. This was attributed to the radial restriction of the flow and consequently formation of a relatively smaller reflected shock angle. With the conical nozzle used in this study and a 30 bar injection pressure, an under-expanded hydrogen jet exhibited ∼60% higher penetration length compared to an under-expanded nitrogen jet at 100 μs after start of injection. Moreover, the former jet exhibited ∼22% higher penetration compared to a nitrogen jet issued through the conical profile with 150 bar injection pressure.

Modeling of underexpanded hydrogen jets through square and rectangular slot nozzles

The development and revision of safety codes and standards for hydrogen infrastructure requires a solid scientific basis, including studies of unignited releases from high pressure systems for various scenarios. Most hydrogen releases are modeled as axisymmetric jets, but real leaks are more likely to be non-axisymmetric jets issuing from high aspect ratio cracks or slots. In the present study, underexpanded hydrogen jets from square and rectangular nozzles with aspect ratios of 1–16 were numerically modeled for stagnation pressures up to 20 MPa. The near and far flow fields were modeled separately using two sequential computational domains to accurately and efficiently capture the flow characteristics. The numerical models were first validated with experimental data from a previous experimental study and literature data. The mass fraction and velocity distributions show that the centerline decay rates increase as the nozzle aspect ratio increases, but this increase is dependent on the pressure. This means that the canonical decay law of round turbulent jets and plumes no longer applies to the slot nozzle jets for high pressures. The radial profiles collapse onto a Gaussian curve in the major axis plane, but neither collapse, nor are they Gaussian in the minor axis plane with peaks away from the jet centerline. Different shock patterns were identified along the major and minor axes and the axis switching phenomenon seen in the literature was also reproduced. The axis switching resulted in significantly wider flattened concentration distributions compared with the axisymmetric jet which may require consideration during safety analyses for non-circular nozzles. A scaling factor taking both the nozzle shape and pressure effects into account was then developed to better scale the centerline decay rates for jets from both the square and rectangular nozzles. The present study demonstrates that the nozzle shape effects on the jet spreading should not be overlooked and proper scaling factors are required to collapse the data and calculate decay rates.

Simulation of thermal hazards from hydrogen under-expanded jet fire

Thermal hazards from an under-expanded (900 bar) hydrogen jet fire have been numerically investigated. The simulation results have been compared with the flame length and radiative heat flux measured for the horizontal jet fire experiment conducted at INERIS. The release blowdown characteristics have been modelled using the volumetric source as an expanded implementation of the notional nozzle concept. The CFD study employs the realizable k-ε model for turbulence and the Eddy Dissipation Concept for combustion. Radiation has been taken into account through the Discrete Ordinates (DO) model. The results demonstrated good agreement with the experimental flame length. Performance of the model shall be improved to reproduce the radiative properties dynamics during the first stage of the release (time < 10 s), whereas, during the remaining blowdown time, the simulated radiative heat flux at five sensors followed the trend observed in the experiment.

Determination of underexpanded hydrogen jet flame length with a complex nozzle geometry

With the growing number of hydrogen-powered cars and hydrogen filling stations, it is essential to have accurate and reliable engineering models for this infrastructure. The length of a hydrogen jet flame resulting from a high pressure release will have an impact on its consequences. This work examined the effect that nozzle geometry has on hydrogen jet flame length. The geometry was modified by varying the diameter of the spouting nozzle downstream from the choked nozzle upstream. These experimental results were compared with an existing model for estimating jet flame length. Sensors upstream from the complex nozzle geometry measured the temperature, mass flow rate, and pressure for the released hydrogen. A high-speed camera recorded the hydrogen jet flame at a stable pressure and mass flow. Flame lengths were determined with an image processing tool used to analyze the high-speed video for each experiment. By analyzing the dataset with the image processing tool, the jet flame length distribution, minimum and maximum jet flame length, and the jet flame length standard deviation could be computed. Results showed that the nozzle geometry can increase the jet flame length by 62% compared to a single nozzle configuration with equal mass flow rate. With the upstream nozzle as input, the smallest average relative deviation from previously published models was 13%. The discharge coefficients for different nozzles were calculated and presented.

Modeling of large-scale under-expanded hydrogen jet fires

Large-scale hydrogen under-expanded jet flames and lab-scale H2 and CH4 jet flames are simulated by using the standard k-ε model coupled to a hybrid flamelet/transported PDF method and a narrow band correlated-k gas radiation model. The set of flames considered covers a wide range of residence times and optical thicknesses. The notional nozzle concept is adopted to determine injection conditions for the large-scale chocked flames. Model predictions in terms of flame geometry, flame structure, radiant fraction and radiative flux are consistent with the experimental data whatever the scales. Model results show that these flames do not verify the optically-thin approximation since the part of emitted radiant power re-absorbed within the flame ranges from 11% for the smallest H2 flame to about 70% for the largest H2 flame. Neglecting the turbulence-radiation interaction underestimates significantly the radiant fraction whatever the scale and these discrepancies are enhanced with increasing residence time and optical thickness. A simple analysis based on the assumption of homogenous flame is used to correlate the experimental radiant fraction as a function of τGEm(1−Q˙abs/Q˙em) where τG, Em and Q˙abs/Q˙em represent the residence time, an equivalent emission term and the part of emitted radiant power re-absorbed within the flame. Model results are used to provide a proper estimation of the equivalent emission term and self-absorption.

Numerical investigation of a high pressure hydrogen jet of 82 MPa with adaptive mesh refinement: Concentration and velocity distributions

To investigate the safety properties of high-pressure hydrogen discharge or leakage, an under-expanded hydrogen jet flow with a storage pressure of 82 MPa from a small jet orifice with a diameter of 0.2 mm is studied by three-dimensional (3D) numerical calculations. The full 3D compressible Navier-Stokes equations are utilized in a domain with a size of about 3 × 3 × 6 m which is discretized by employing an adaptive mesh refinement (AMR) technology to reduce the number of grid cells. By AMR, the local mesh resolutions can narrowly cover the Taylor microscale lT and direct numerical simulations (DNS) are performed. Both the instantaneous and mean hydrogen concentration distributions in the present jet are discussed. The instantaneous concentrations of hydrogen CH2 on the axis presents significant turbulent pulsating oscillations. The centerline value of the intensity of concentration fluctuation σˆH2 asymptotically comes to 0.23, which is in a good agreement with the existing experimental results. It substantiates the conclusion that the asymptotic centerline value of σˆH2 is independent of jet density ratio. The probability distributions function (PDF) of instantaneous axial CH2 agree approximately with the Gaussian distribution while skewing a little to the higher range. The time averaged hydrogen concentration C¯H2 along the radial directions can also be described as a Gaussian distribution. The axial C¯H2 of 82 MPa hydrogen jet tends to obey the distribution discipline approximated with C¯H2=4200/(z/θ) where z is the axial distance from the nozzle and θ is the effective ejection diameter, which is consistent with the experimental results. In addition, the hydrogen tip penetration Ztip is found to be in a linear relationship with the square root of jet flow time t. Meanwhile, the jet's velocity half-width LVh approximately gains an linear relation with z which can be expressed as LVh=0.09z.