Estimating leaked hydrogen gas flow in confined space through coupling zone model and point source buoyancy plume theory

A semi-analytical model combining zone model and virtual point source buoyancy plume theory is proposed to predict the gas flow and dispersion behaviors of leaked hydrogen in confined space with an opening. The height of interface between the upper and lower layers, outflow velocity and hydrogen molar fraction in outflow at steady stage are quantitively analyzed to study the effects of leakage mass flux and opening geometry. A computational fluid dynamics (CFD) tool, FLACS, is employed to simulate the interested scenarios and validate the reliability of the developed model. The results show that the interface height declines as the leakage mass flux increases, but the outflow velocity and hydrogen molar fraction exhibit inverse tendencies. The interface height is positively proportional to both opening width and height, but the opening height plays a more important role. At steady stage, the simulated interface height fluctuates within 0.1 m uncertainty range, which is identical to the grid size, and it well fits the analytical estimations. The opening width affects the outflow velocity more greatly than that of opening height. The fluctuation of the simulated interface height enhances the inaccuracy of the predicted outflow velocity in the acceptable range. Meanwhile, it is found that with fixed opening geometry the ratio of outflow velocity with higher leakage mass flux to that with lower leakage mass flux remains at 1.28 when the leakage mass flux is doubled. The variations of opening width and height have little and significant effects on outflow hydrogen molar fraction, respectively. Similarly, for given opening geometry the ratio of hydrogen molar fraction with higher leakage mass flux to that with lower leakage mass flux is about 1.58 when the leakage mass flux is doubled.     

Affecting mechanism of partition boards on hydrogen dispersion in confined space with symmetrical lateral openings

Dispersion and natural ventilation of hydrogen leaked at the floor center of a confined space are analytically and numerically studied in this contribution. Two symmetrical openings located atop two opposite walls and several sets of partition boards with varying heights, 0–1.0 m with 0.2 m increment, mounted under the ceiling were designed to examine their effects on ventilation efficiency. Without partition boards, a semi-analytical model combining a modified buoyancy ceiling jet theory and zone model was established to predict the key parameters at steady stage. The analytical predictions were compared with numerical results. 15 monitors were predesigned at an opening and the channels separated by the partition boards to collect the velocity and hydrogen concentration evolutions. The results show that the existence of the partition boards significantly promotes the ventilation efficiency by decreasing the hydrogen concentration in the confined space, constraining the flammable regime into a smaller volume, and increasing both the inflow and outflow velocities. Better ventilation efficiency is achieved by higher partition boards until a critical height after which no appreciable improvement can be gained. Applying the partition boards considerably shortens the developing stage of the dispersion process and intensifies the turbulence of outflow. Conclusions obtained in current work may benefit the natural ventilation system and building structure design for hydrogen safety in practical applications.     

An analytical solution for thermally fully developed combined pressure – electroosmotically driven flow in microchannels

An analytical solution is presented to study the heat transfer characteristics of the combined pressure – electroosmotically driven flow in planar microchannels. The physical model includes the Joule heating effect to predict the convective heat transfer coefficient in two dimensional microchannels. The velocity field, which is a function of external electrical field, electroosmotic mobility, fluid viscosity and the pressure gradient, is obtained by solving the hydrodynamically fully-developed laminar Navier–Stokes equations considering the electrokinetic body force for low wall zeta potentials. Then, assuming a thermally fully-developed flow, the temperature distribution and the Nusselt number is obtained for a constant wall heat flux boundary condition. The fully-developed temperature profile and the Nusselt number depend on velocity field, channel height, solid/liquid interface properties and the imposed wall heat flux. A parametric study is presented to evaluate the significance of various parameters and in each case, the maximum heat transfer rate is obtained.     

Boundary layer theory approach to the concentration layer adjacent to a ceiling wall of a hydrogen leakage: Far region

The field of the hydrogen leakage in partially open space can be divided into two main regions according to the importance of the hydrogen concentration distribution and the flow behavior. These two regions are the jet region and the boundary layer region which are adjacent to the ceiling wall of the space, resulting from impinging the hydrogen jet to the wall. The boundary layer region in turn can be divided into two regions, according to the modeling of the flow. These regions are the stagnation-point boundary layer region and the far boundary layer region. Previously, we studied the region of stagnation-point flow (Hiemenz flow) [El-Amin MF, Kanayama H. Boundary layer theory approach to the concentration layer adjacent to a ceiling wall at impinging region of a hydrogen leakage. Int J Hydrogen Energy, in press.]. The current paper is devoted to analyze the far region of the boundary layer adjacent to the ceiling wall using the boundary layer theory. Also, an experiment has been conducted on the hydrogen leakage in partially open space to estimate the concentration distribution vertically at the center of the domain under the ceiling wall. In order to verify the boundary layer theory approach, a comparison between the measurements and the boundary layer theory approximations is investigated and the results showed a good agreement. The wall shear stress, the local friction factor, the friction drag and the non-dimensional drag coefficient of the ceiling wall are calculated. Also, both momentum and concentration boundary layer thicknesses are estimated.     

Simulation of methane steam reforming in a catalytic micro-reactor using a combined analytical approach and response surface methodology

In this study, a steady-state analytical model for heat and mass transfer in a 2D micro-reactor coated with a Nickel-based catalyst is developed to investigate microscale hydrogen production. Appropriate correlations for each species’ net rate of production or consumption, mass diffusivity, and the heat of reactions are developed using a detailed reaction mechanism of methane steam reforming. The energy and species conservation equations are then solved for the reactive mixture coupled with the wall energy equation. Finally, the response surface methodology (RSM) is employed to study the effects of channel height, inlet velocity and temperature, wall thickness and conductivity, and external heat flux on CH4 conversion. It is found that the inlet gas temperature, among different parameters, has the most influence on the overall performance of the microchannel hydrogen production. Also, the maximum necessary heat of reforming reaction increases by 84% and 26% if the CH₄ conversion changes from 50% to 60% and 60% to 70%, respectively. The developed analytical simulation can be a useful tool for designing experiments in micro-scale hydrogen production.     

Profiles of hydrogen molar fraction and temperature in ZrV1.9Fe0.1 alloy bed for hydrogen absorption

Profiles of hydrogen molar fraction and temperature in a long ZrV_1.9Fe_0.1 alloy particle bed with a small diameter were determined experimentally and analytically as a basic study of chemical heat pumps operated at higher temperature. Since the alloy bed absorbed hydrogen even at $\text{873}\text{K}$ and generated heat, the alloy was considered a suitable material for heat pump or hydrogen storage at higher temperature. Experimental profiles of both hydrogen molar fraction at the bed outlet and temperature inside the bed agreed with analytical solutions to heat and mass transfer equations. The analytical solutions were obtained under the conditions where constant-pattern approximation could be applied to the temperature and concentration profiles propagating in a bed with the same velocity. Properties relating with heat transfer such as a heat capacity, enthalpy change of hydrogen absorption and a heat-transfer coefficient between a wall and particles were correlated to two dimensionless parameters, α and β.     

Numerical studies of dispersion and flammable volume of hydrogen in enclosures

This paper presents a numerical study of dispersion and flammable volume of hydrogen in enclosures using a simple analytical method and a computational fluid dynamics (CFD) code. In the analytical method, the interface height and hydrogen volume fraction of the upper layer are obtained based on mass and buoyancy conservation while the centreline hydrogen volume fraction is derived from similarity solutions for buoyant jets. The two methods (CFD and analytical) are used to simulate an experiment conducted by INERIS, consisting of a 1 g/s hydrogen release for 240 s through a 20 mm diameter orifice into an enclosure. It is found that the predicted centreline hydrogen concentration by both methods agrees with each other and is also in good agreement with the experiment. There are however differences in the calculated total flammable volume because the analytical method does not consider local mixing and diffusion in the upper layer which is assumed uniformly well mixed. The CFD model, in comparison, incorporates the diffusion and stratification phenomena in the upper layer during the mixing stage.     

Boundary layer theory approach to the concentration layer adjacent to the ceiling wall of a hydrogen leakage: Axisymmetric impinging and far regions

As hydrogen leaks into a partially open space with a ceiling wall, a boundary layer of hydrogen can be constructed under that wall due to the impingement on the wall and the buoyancy force. The resulting boundary layer can be divided into two regions, namely the stagnation-point region and the far region. When the geometry of the source of the hydrogen leak is circular, such as a pinhole or an o-ring, the behavior of leakage flow will be axisymmetric due to the resulting radial jet. In contrast, when the geometry of the source of the hydrogen leak is planar, such as a crack, the behavior of leakage flow will be planar due to the resulting planar jet. Previously, we studied the planar case in the context of both the stagnation-point flow region [El-Amin MF, Kanayama H. Boundary layer theory approach to the concentration layer adjacent to a ceiling wall at impinging region of a hydrogen leakage. Int J Hydrogen Energy 2008; 33(21): 6393–00] and the far region [El-Amin MF, Inoue M, Kanayama H. Boundary layer theory approach to the concentration layer adjacent to a ceiling wall of a hydrogen leakage: far region. Int J Hydrogen Energy 2008; 33(24):7642–7]. This paper is concerned with both the stagnation-point flow region and the far region of the axisymmetric concentration boundary layer adjacent to a ceiling wall. Flow in the stagnation-point region is treated as Hiemenz flow, while it is treated as Blasius flow in the far region. The current results are compared with the planar cases [El-Amin MF, Kanayama H. Boundary layer theory approach to the concentration layer adjacent to a ceiling wall at impinging region of a hydrogen leakage. Int J Hydrogen Energy 2008; 33(21): 6393–00; El-Amin MF, Inoue M, Kanayama H. Boundary layer theory approach to the concentration layer adjacent to a ceiling wall of a hydrogen leakage: far region. Int J Hydrogen Energy 2008; 33(24):7642–7] for both stagnation-point flow and far regions. Both momentum and concentration boundary layer thicknesses are estimated, as well as the local friction factor.     

Motion trajectory prediction model of hydrogen leak and diffusion in a stable thermally-stratified environment

The motion trajectory of hydrogen leakage is an essential safe issue for the application of hydrogen energy. A dimensionless fast-running motion trajectory prediction model is proposed to predict the dispersion characteristics of the buoyant jet of hydrogen leakage for the accident. The impact of different leakage angles, leakage velocity and thermal stratification of ambient air on hydrogen leakage behavior was analyzed. The new developed model was verified by experimental results in literatures. Leakage hydrogen can flow upwards freely in a uniform environment. However, it shows an oscillating trajectory at a certain height in a thermally stratified environment, which is so called “locking phenomenon”. The trajectory of hydrogen leakage is upward and hydrogen gathers at the top of the space to form stratification in a uniform environment, while the hydrogen leakage shows an oscillating trajectory at a certain height in a thermal stratification environment. With the increase of Froude number Fr, it shows that the stable height and maximum height of the leakage airflow have a trend of rising first and then falling in a thermally stratified environment. The findings are expected to give guidance in real-world situations, for example, a larger Fr value and a larger temperature gradient can lead to a decrease in the stable height in the thermally stratified environment. It is found that the fitting of the stable height with different temperature gradients satisfies the power function relationship. This work is expected to be helpful for reducing hydrogen leakage accumulation and explosion risk.     

A theoretical framework for calculating full-scale jet fires induced by high-pressure hydrogen/natural gas transient leakage

Previous experimental results on full-scale jet fires induced by high-pressure hydrogen/natural gas transient leakage can only be suitable for solving practical engineering problems, or testing the limitation of previous models. Thus, this paper presents a theoretical framework for the high-pressure hydrogen/natural gas leakage and the subsequent jet fire. The proposed framework consists of a transient leakage model, a notional nozzle model, a jet flame size model, a radiative fraction correlation and a line source radiation model. The framework is validated by comparing the model predictions and experimental measurements of mass flow rate, total flame height and thermal radiation field of hydrogen, natural gas, hydrogen/natural gas mixture jet fires with a flame height up to 100 m. The comparison shows that the theoretical framework can give considerable predictions to properties of full-scale jet fires induced by high-pressure hydrogen/natural gas transient leakage.     

Numerical heat transfer analyses of a wavy-laminar falling film using moving curvilinear coordinates

In most processes using water film, surface instabilities can be found at the free surface. This work focuses on analyzing their influence on wall heat flux. This is a coupled phenomenon whose full solution would be computationally intensive, so a simplified method is developed. The interface of the film is predicted using an algorithm based on statistical data measurements and the velocity profile is supposed auto-similar to that of Nusselt. The problem is solved numerically using a moving mesh fitted to the shape of the interface. The subsequent statistical analysis highlighted the relative importance of height fluctuations on wall heat flux.     

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.     

Numerical and analytical study of laminar film condensation in upward and downward vapor flows

Abstract

Laminar film condensation in upward and downward vapor flows is numerically investigated by using a sharp-interface level-set method to track the condensate film surface and accurately calculating the phase-change mass flux under the saturation temperature condition at the interface. An analytical model for steady laminar film condensation in upward as well as downward vapor flows is developed to validate the present numerical results. As the vapor velocity increases, the condensation rate is observed to decrease in upward vapor flows whereas it increases in downward vapor flows. The effects of vapor velocity and wall temperature on laminar film condensation in upward and downward vapor flows are investigated.     

An analytical model for the velocity and gas fraction profiles near gas-evolving electrodes

Understanding multiphase flow close to the electrode surface is crucial to the design of electrolyzers, such as alkaline water electrolyzers for the production of green hydrogen. Vertical electrodes develop a narrow gas plume near their surface. We apply the integral method to the mixture model. Considering both exponentially varying and step-function gas fraction profiles, we derive analytical relations for plume thickness, velocity profile, and gas fraction near the electrode as a function of height and current density. We verify these analytical relations with the numerical solutions obtained using two-dimensional mixture model simulations. We find that for low gas fractions, the plume thickness decreases with an increase in current density for an exponentially varying gas fraction profile. In contrast, the plume thickness increases with increasing current density at high gas fractions for an approximately step-function-shaped gas fraction profile, in agreement with experiments from the literature.     

Planar momentum-dominated regime of small-scale hydrogen leakage

The geometry of the source of hydrogen leakage is essential in forming hydrogen flow and distribution in air. For example, if the geometry of the source is circular, the behavior of leakage flow becomes axisymmetric and a radial jet is constructed. On the other hand, if the geometry of the source is planar, the behavior of hydrogen leakage becomes planar and a planar jet is constructed. Throughout this article, the problem of momentum-dominated regime of a planar slow-leak hydrogen–air jet resulting from a hydrogen leakage from a planar source is considered. We derive a set of analytical expressions for selected physical turbulent properties. Several quantities of interest are obtained, including the cross-stream velocity, the Reynolds stresses, the velocity-concentration correlation, the dominant turbulent kinetic energy production term, the turbulent eddy viscosity, the turbulent eddy diffusivity, and the turbulent Schmidt number. Moreover, the normalized jet-feed material density and the normalized momentum flux density are correlated.     

Solar thermochemical hydrogen: The heat source-process interface

A discussion of issues and considerations related to the interface between a solar heat source and a thermochemical hydrogen process and some details of a tubular heat exchanger operating as such an interface in a cavity-type receiver are presented. The issues include the temperature and heat input requirements for the endothermic reaction, type of receiver, heat storage, transient operations, and control. A thermal performance analysis of a tubular reactor/heat exchanger operating in a cavity-type solar receiver is applied to SO₃ decomposition. The analysis produces axial distributions of temperature tube wall and process fluid, reaction rate, conversion, velocity, density, pressure and residence time. Process fluid conditions at the inlet, tube characteristics, reaction kinetics and cavity operating temperature are inputs. The cavity temperature affects average heat flux and, therefore, heat-exchanger cost and receiver efficiency and, therefore, mirror field cost. A design which minimizes the combined cost may be found and examples are shown.     

Effects of structural parameters on the performance of a micro-reactor with micro-pin-fin arrays (MPFAR) for hydrogen production

To enhance the energy conversion efficiency of the micro-reactor with micro-pin-fin arrays (MPFAR) for hydrogen production, the effect of structural parameters (the height of the micro-pin-fin, the transverse and longitudinal center distance between two adjacent micro-pin-fins) on the performance of the MPFAR for hydrogen production is investigated. Based on the geometrical parameters, a theoretical model of material balance for hydrogen production in the MPFAR is established. The calculated results show that with the increase of the micro-pin-fin height or the decrease of the distance between two adjacent micro-pin-fins, the methanol conversion rate and the CO molar fraction increase. The methanol conversion rate increases by about 10% when the height of micro-pin-fin increases from 0.2 to 1 mm or the center distance between the two adjacent micro-pin-fins increases from 1.2 to 2.6 mm. The comparisons between the experimental and calculated results validate the theoretical model of material balance utilized in this study. Finally, a better geometrical structure of micro-pin-fin arrays is obtained, in which the height of the micro-pin-fin, the transverse and longitudinal center distances between two adjacent micro-pin-fins are 1.0 mm, 1.2 mm and 1.2 mm, respectively. The hydrogen yield in the MPFAR can reach about 8.3 ml/min under the condition that the methanol conversion rate is above 90%.     

Analysis of magnetohydrodynamics peristaltic transport of hydrogen bubble in water

This paper established the theoretical and analytical analysis of a unidirectional laminar bubbly two-phase flow in a symmetric channel with flexible wall. The two-phase model uses water as base fluid with hydrogen bubble suspended in it. Rayleigh-Plesset equation in term of volume fraction is used to model void produce due to presence of hydrogen. The flow is driven by symmetric peristaltic movement of the wall. A uniform magnetic field in the transverse direction to peristaltic motion is applied. Homotopy perturbation Method (HPM) is utilized to formulate the series solution, after simplifying the differential governing equations under the influence of long wave length and low Reynolds number. The volume of the void and radius of the bubble is analyzed graphically. The consequence demonstrates that the void fraction bubbles rapidly approaches to unity, which is due to quasi-statically unstable. Due to Lorentz force fluid velocity suppresses by increasing the transverse magnetic field while reverse performance is noted for Weber number and power law index.     

烟气传播的近壁效应实验研究

在全尺寸受限空间内火灾发展过程中，测量顶棚不同径向距离的一氧化碳气体浓度随时间的变化，发现在热烟气层尚未形成的早期阶段墙壁能够起到类似输送管道的作用促进气体沿壁面的传播，使得一氧化碳等气体产物较快到达顶棚位置．随着热烟气层形成，进入准稳态阶段后，开始时间、平均浓度与标准差三个稳态特征之间的相互关系通过引入“稳态系数”得以量化，墙角火因为受到近壁自然对流的较大影响，稳态系数低于墙壁火．此外，通过均值浓度比给出了“卷吸效率因子”的估计值，虽然均大于镜像模型的计算结果，但是考虑到阴燃的低耗氧量，结果被认为是合理的．