Numerical simulation of hydrogen filling process in novel high-pressure microtube storage device

Novel high-pressure microtube hydrogen storage device has higher hydrogen storage density and safety than conventional hydrogen tanks. A one-dimensional numerical model for hydrogen filling process in microtubes is established, with reasonable calculation methods and accurate physical properties adopted. Based on the analysis of flow parameters variations, three stages of the filling process are summarized. At the beginning of the filling process, the maximum temperature appears at the inlet, but the average temperature does not rise significantly during the whole process. The effects of microtube length, filling pressure and environmental temperature are investigated and discussed. The results show that excessively long microtubes greatly increase the filling time and higher filling pressure reduces the filling time and improves the filling efficiency. The microtube hydrogen storage device achieves higher hydrogen storage density and filling efficiency in lower temperature mediums. It reveals that high filling pressure, low temperature encapsulation and reasonable microtube size design are the future development directions of microtube hydrogen storage for better application.     

Forced convective heat transfer in a microtube including rarefaction,viscous dissipation and axial conduction effects

Subsonic gas convective heat transfer in a microtube with a constant cross-sectional area and uniform wall temperature is investigated both analytically and numerically. First, the effect of rarefaction on heat transfer characteristics, at a distance from the inlet where Nu becomes constant, is analytically investigated for two cases: (i) including and (ii) neglecting the viscous dissipation effect. An exact solution for Nu in fully developed flow is presented for the case without viscous dissipation, while a closed-form solution for the asymptotic Nu is also provided for the case with viscous dissipation. Next, a numerical model is employed to investigate the simultaneous effects of rarefaction, viscous dissipation, and axial conduction for developing hydrodynamic and temperature conditions. The Nusselt number is substantially affected by viscous dissipation, rarefaction and axial conduction.     

Experimental Study on Subcooled Flow Boiling in Horizontal Microtubes and Effect of Heated Length

ABSTRACT

In this study, subcooled flow boiling was investigated in horizontal microtubes. Experiments were conducted using deionized water as the working fluid over a mass flux range of 4000–7000 kg m^?2s^?1 in microtubes with inner and outer diameters of ～600 and ～900 μm, respectively. Microtubes with lengths of 3, 6, and 12 cm were tested to clarify the effect of heated length on flow boiling heat transfer and pressure drop characteristics. A force analysis related to two-phase flow was conducted to understand the effect of forces on bubble dynamics. Pressure drop and heat transfer data in flow boiling were acquired. Experimental heat flux data were compared with partial boiling heat flux correlations, and good agreements were obtained. Pressure drop was larger in longer microtubes in comparison to shorter ones, while higher heat fluxes were obtained in shorter microtubes at the same wall superheat. Two-phase heat transfer coefficient increased with the microtube length due to lower temperature difference between wall temperature and bulk fluid temperature in longer microtubes. Higher heat fluxes achieved in shorter microtubes at the same wall superheat imply higher critical heat fluxes in shorter microtubes.     

Heat transfer characteristics of gaseous flows in microtube with constant heat flux

Heat transfer characteristics of gaseous flows in a microtube with constant heat flux whose value is positive or negative are investigated on two-dimensional compressible laminar flow for no-slip regime. The numerical methodology is based on the Arbitrary–Lagrangian–Eulerian (ALE) method. The computations are performed for tubes with constant heat flux ranging from −10⁴ to 10⁴ W m⁻². The tube diameter ranges from 10 to 100 μm and the aspect ratio of the length and diameter is 200. The stagnation pressure, p_stg is chosen in such away that the Mach number at the exit ranges from 0.1 to 0.7. The outlet pressure is fixed at the atmosphere. The wall and bulk temperatures in microtubes with positive heat flux are compared with those of negative heat flux case and also compared with those of the incompressible flow in a conventional sized tube. In the case of fast flow, temperature profiles normalized by heat flux have different trends whether heat flux is positive or negative. A correlation for the prediction of the wall temperature of the gaseous flow in the microtube is proposed. Supplementary runs with slip boundary conditions for the case of D = 10 μm conducted and rarefaction effect is discussed. With increasing Ma number, the compressibility effect is more dominant and the rarefaction effect is relative insignificant where Kn number is less than Kn = 0.0096. And, the magnitudes of viscous dissipation term and compressibility term are investigated along the tube length.     

Thermally Developing Electro-osmotic Convection in Microchannels with Finite Debye-Layer Thickness

ABSTRACT

Thermally developing electro-osmotically generated flow with in circular microtubes with finite Debye-layer thickness has been analyzed. This study focuses on finite Debye-layer effects, a scenario for which the velocity distribution across the tube cross section varies with the ratio of tube radius and Debye length (termed here the relative microtube radius). Numerical solution of the hydrodynamically developed, thermally developing transport for such a flow is presented in this article. The effect of variations in the relative microtube radius and strength of the Joule and viscous heating on the thermal transport are explored over the possible ranges of the governing parameters.     

Experimental and numerical studies of liquid flow and heat transfer in microtubes

Experimental and numerical studies were conducted to reveal the flow and heat transfer characteristics of liquid laminar flow in microtubes. Both the smooth fused silica and rough stainless steel microtubes were used with the hydraulic diameters of 50–100 μm and 373–1570 μm, respectively. For the stainless steel tubes, the corresponding surface relative roughness was 2.4%, 1.4%, 0.95%. The experiment was conducted with deionized water at the Reynolds number from 20 to 2400. The experimental data revealed that the friction factor was well predicted with conventional theory for the smooth fused silica tubes. For the rough stainless steel tubes, the friction factor was higher than the prediction of the conventional theory, and increased as the surface relative roughness increased. The results also confirmed that the conventional friction prediction was valid for water flow through microtube with a relative surface roughness less than about 1.5%. The experimental results of local Nusselt number distribution along the axial direction of the stainless steel tubes do not accord with the conventional results when Reynolds number is low and the relative thickness of the tube wall is high. The numerical study reveals that the large ratio of wall thickness over tube diameter in low Reynolds number region causes significant axial heat conduction in the tube wall, leading to a non-linear distribution of the fluid temperature along the axial direction. The axial heat conduction effect is gradually weakened with the increase of Reynolds number and the decrease of the relative tube wall thickness and thus the local Nusselt number approaches the conventional theory prediction.     

A LOCALLY IMPLICIT SCHEME FOR TURBULENT FLOWS ON DYNAMIC MESHES

A locally implicit scheme with an anisotropic dissipation model is developed on dynamic quadrilateral-triangular meshes. The unsteady Favre-averaged Navier-Stokes equations with moving domain effects and a low-Reynolds-number k  ? ε turbulence model are solved to study turbulent flows over vibrating blades with negative interblade phase angle. A treatment of viscous flux on quadrilateral-triangular mesh is also presented. To assess the accuracy of the locally implicit scheme with anisotropic dissipation model on quadrilateral-triangular mesh, the turbulent flow around an NACA 0012 airfoil is investigated. Based on the comparison with the experimental data, the accuracy of the present approach is confirmed. From the distributions of magnitude of the first harmonic dynamic pressure difference coefficient which includes the present solution and the related experimental and numerical results, it is found that the present solution approach is reliable and acceptable. The unsteady flow behaviors for turbulent flows over vibrating blades with negative interblade phase angle are demonstrated.     

The effect of viscous dissipation in thermally fully-developed electro-osmotic heat transfer in microchannels

The influence of viscous dissipation on thermally fully-developed, electro-osmotically generated flow has been analyzed for a parallel plate microchannel and circular microtube under imposed constant wall heat flux and constant wall temperature boundary conditions. Such a flow is established not by an imposed pressure gradient, but by a voltage potential gradient along the length of the tube. The result is a combination of unique electro-osmotic velocity profiles and volumetric heating in the fluid due to the imposed voltage gradient. For large ratio of the microtube radius (or microchannel half-width) to Debye length, the wall-normal fluid velocity gradients can be extremely high, which has the potential for significant viscous heating. The solution for the fully-developed, dimensionless temperature profile and corresponding Nusselt number have been determined for both geometries and for both thermal boundary conditions. It is shown that three dimensionless parameters govern the thermal transport: the relative duct radius (ratio of the duct radius or plate gap half-width to Debye length), the dimensionless volumetric source (ratio of Joule heating to wall heat flux), and a dimensionless parameter that relates the magnitude of the viscous heating to the Joule heating. Surprisingly, it is shown that the influence of viscous dissipation is only important at low values of the relative duct radius. For magnitudes of the dimensionless parameters which characterize most practical electro-osmotic flow applications, the effect of viscous dissipation is negligible.     

Experimental and Numerical Investigation of Inlet Temperature Effect on Convective Heat Transfer of γ-Al2O3/Water Nanofluid Flows in Microtubes

ABSTRACT

Nanofluids are the combination of a base fluid with nanoparticles with sizes of 1–100 nm. In order to increase the heat transfer performance, nanoparticles with higher thermal conductivity compared to that of base fluid are introduced into the base fluid. Main parameters affecting single-phase and two-phase heat transfer of nanofluids are shape, material type and average diameter of nanoparticles, mass fraction and stability of nanoparticles, surface roughness, and fluid inlet temperature. In this study, the effect of inlet temperature of deionized water/alumina (Al₂O₃) nanoparticle nanofluids was both experimentally and numerically investigated. Nanofluids with a mass fraction of 0.1% were tested inside a microtube having inner and outer diameters of 889 and 1,067 µm, respectively, for hydrodynamically developed and thermally developing laminar flows at Reynolds numbers of 650, 1,000, and 1,300. According to the obtained numerical and experimental results, the inlet temperature effect was more pronounced for the thermally developing region. The performance enhancement with nanoparticles was obtained at rather higher Reynolds numbers and near the inlet of the microtube. There was a good agreement between the experimental and numerical results so that the numerical approach could be further implemented in future studies on nanofluid flows.     

Combined influences of viscous dissipation,non-uniform Joule heating and variable thermophysical properties on convective heat transfer in microtubes

This study presents a comprehensive investigation on hydrodynamic and thermal transport properties of mixed electroosmotically and pressure driven flow in microtubes. Particular emphasis is given to investigating the combined consequences of viscous dissipation, non-uniform Joule heating, and variable thermophysical properties. Analytical solutions are obtained using the Debye–Hückel linearization and constant fluid properties assumption, while a numerical solution is presented for variable fluid properties and non-uniform distribution of Joule heating. The results indicate that, viscous heating effect is pronounced significantly when a favorable pressure gradient exists and cannot be neglected at low values of the dimensionless Debye–Hückel parameter. Moreover, uniform Joule heating assumption, even at low zeta potentials, may reduce the accuracy of the predicted thermal features considerably. The wall shear stress is found to be strongly dependent upon the zeta potential, which is underestimated by the Debye–Hückel linearization. Compared with the constant fluid properties case, decreasing electrical resistivity of the fluid by increasing temperature, amplifies the total energy generation due to the Joule heating and reduces the Nusselt number.     

湍流场协同模型构建及减阻应用

在稳态、无体积力流动场协同模型的基础上,将场协同原理与湍流流动有效结合,引入Favre平均和RANS,根据Navier-Stokes方程建立了不可压湍流场协同模型。基于最小机械能耗散原理,在约束条件下推导使黏性耗散函数满足极小值的数值解,将不可压缩湍流模型与流动减阻相关联,构建了湍流场协同减阻模型。以后台阶流动验证模型的有效性,结果显示:改变结构后,黏性耗散值从0.633 0 W减小到0.245 0 W,优化了61.3%。     

Boiling incipience in microchannels

The available data dealing with boiling incipience of water in microtubes (tubes with diameters in the 0.1-1 mm range) are analyzed. Macroscale models and correlations appear to under predict the heat fluxes that lead to the boiling incipience in microtubes. It is suggested that boiling incipience in microchannels may be controlled by the thermocapillary force that tends to suppress the microbubbles that form on wall cavities. Accordingly, a semi-empirical method is proposed for predicting the boiling incipience in microtubes. The effect of the turbulence characteristics of the microtube on the proposed method is also examined.     

Slip-flow and heat transfer of gaseous flows in the entrance of a wavy microchannel

The present work investigates the developing fluid flow and heat transfer through a wavy microchannel with numerical methods. Governing equations including continuity, momentum and energy with the velocity slip and temperature jump conditions at the solid walls are discretized using the finite-volume method and solved by SIMPLE algorithm in curvilinear coordinate. The effects of creep flow and viscous dissipation are assumed. The numerical results are obtained for various Knudsen numbers. The results show that Knudsen number has declining effect on both the C_f.Re and Nusselt number on the undeveloped fluid flow. Significant viscous dissipation effects have been observed for large Knudsen number. Also, viscous dissipation causes a singular point in Nusselt profiles.     

Laminar,transitional and turbulent friction factors for gas flows in smooth and rough microtubes

Theoretical and experimental works on microscale transport phenomena have been carried out in the past decade in the attempt to analyze possible new effects and to assess the influence of downscaling on the classical correlations which are used in macro-scale heat and fluid flow, following the need to supply engineers with reliable tools to be used in the design of micro-scale devices. These results were sometimes in mutual contrast, as is the case for the determination of the friction factor, which has been found to be lower, higher or comparable to that for macroscopic channels, depending on the researchers. In this work the compressible flow of nitrogen inside circular microchannels from 26 μm to 508 μm in diameter and with different surface roughness is investigated for the whole range of flow conditions: laminar, transitional and turbulent. Over 5000 experimental data have been collected and analysed. The data confirmed that in the laminar regime the agreement with the conventional theory is very good in terms of friction factors both for rough and smooth microtubes. For the smaller microchannels (<100 μm) when Re is greater than 1300 the friction factor tends to deviate from the Poiseuille law because the flow acceleration due to compressibility effects gains in importance. The transitional regime was found to start no earlier than at values of the Reynolds number around 1800. Both smooth and sudden changes in the flow regime have been found, as reported for conventional tubes. Fully developed turbulent flow was attained with both smooth and rough tubes, and the results for smooth tubes seem to confirm Blasius' relation, while for rough tubes the Colebrook–White correlation is found to be only partially in agreement with the experimental friction factors. In the turbulent regime the dependence of the friction factor on the Reynolds number is less pronounced for microtubes than the prediction of the Colebrook–White correlation and the friction factor depends only on the microtube “relative roughness”.     

Simulation of Convective Heat Transfer of Gas–Liquid Bubble Train Flow in Wet Microtube

In this paper, a direct numerical simulation of a two‐phase incompressible gas–liquid flow for simulation of bubble motion and convective heat transfer in a microtube is presented. The microtube radius is 10 μm. The interface between the two phases is tracked by the volume of fluid method with the continuous surface force model. Newtonian flows are solved using a finite volume scheme based on the PISO algorithm. Numerical simulation is done on an axisymmetric domain with a periodic boundary condition for different values of pressure gradient, void fraction, and bubble period. Mean pressure gradient is fixed for each simulation. The superficial Reynolds numbers of gas and liquid phases studied are 0.3 to 7 and 5 to 210, respectively. Numerical results are coincident with the Serizawa regime map, and there is a linear relation between the void fraction and gas flow ratio. Simulation shows local Nusselt number increases in the presence of a gas bubble.     

Fluid flow in microtubes with axial conduction including rarefaction and viscous dissipation

Graetz problem inside the microtube is revisited considering rarefaction effect, viscous dissipation term and axial conduction in the fluid for uniform wall temperature boundary condition in the slip flow regime. The flow is assumed to be hydrodynamically fully developed, thermally developing, and the velocity profile is solved analytically. The temperature field is determined by the numerical solution of the energy equation. The rarefaction effect is imposed to the problem via velocity-slip and temperature jump boundary conditions. The local and fully developed Nu numbers are obtained in terms of dimensionless parameters; Pe, Kn, Br, κ. Fully developed Nu numbers and the thermal entrance length are found to increase by the presence of the finite axial conduction.     

Numerical simulation of laminar flow of water-based magneto-rheological fluids in microtubes with wall roughness effect

Fully developed laminar flows of water-based magneto-rheological (MR) fluids in microtubes at various Reynolds and Hedsrom numbers have been numerically simulated using finite difference method. The Bingham plastic constitutive model has been used to represent the flow behavior of MR fluids. The combined effects of wall roughness and shear yield stress on the flow characteristics of MR fluids, which are considered to be homogeneous by assuming the small particles with low concentration in the water, through microtubes have been numerically investigated. The effect of wall roughness on the flow behavior has been taken into account by incorporating a roughness–viscosity model based on the variation of the MR fluid apparent viscosity across the tube. Significant departures from the conventional laminar flow theory have been acquired for the microtube flows considered.     

NUMERICAL STUDY OF COMPRESSIBLE TURBULENT FLOW IN MICROTUBES

Micro- and conventional compressible, turbulent tube flows were solved numerically in this study. The numerical procedure solves the compressible, turbulent boundary-layer equations using an implicit finite-difference scheme. The parabolic character of the boundary-layer equations renders the numerical procedure a very efficient, accurate, and robust tool for studying compressible microtube flows. The Baldwin–Lomax two-layer turbulence model is adopted in the numerical procedure. The numerically calculated friction factors are compared with the Blasius correlation, the Fanno line flow prediction, and the experimental data. The comparison shows that the numerically calculated friction factors for conventional tube flows agree quite well with the Blasius correlation. The numerical friction factors for microtube flows are larger than the Blasius correlation due to the compressibility effects. They also are greater than the Fanno line flow prediction and the experimental data. This is because the Fanno line flow and the experimental data assume that the flow is adiabatic, but in reality, compressible, turbulent microtube flows are neither adiabatic nor isothermal, as demonstrated by the numerical results in this study.     

Hydrodynamics and heat transfer in two-dimensional minichannels

This work presents measurements of the friction and heat transfer coefficients in 2D minichannels of 1.12 mm to 300 μm in thickness. The friction factor is estimated from the measured pressure drop along the whole channel. The heat transfer coefficient is determined from a local and direct measurement of both temperature and heat flux at the wall using a specific transducer. The experimental results are in good agreement with classical correlations relative to channels of conventional size. The observed deviations are explained either by macroscopic effects (mainly entry and viscous dissipation effects) or by imperfections of the experimental apparatus.     

Investigation of mixing mechanisms and energy balance in reactive extrusion using three-dimensional numerical simulation method

The polymerization of ε-caprolactone in fully-filled conveying elements of co-rotating twin-screw extruders was analyzed with three-dimensional numerical simulation method. The effects of screw rotational speed, geometry of screw element, and initial conversion at the channel inlet on polymerization progression were studied. The simulation results show that polymerization is accelerated with increasing screw pitch, due to the increase in mixing intensity. With increasing screw rotational speed, the reaction could either slow down or speed up, depending on the viscosity of the reaction system. It is found that the advancement of polymerization depends on the competition among heat from reaction, viscous dissipation and heat loss through the wall surfaces.