The hydrogen flow characteristics of the multistage hydrogen Knudsen compressor based on the thermal transpiration effect

Multistage hydrogen Knudsen compressor based on the thermal transpiration effect has very exciting prospect for the hydrogen transmission in the micro devices. Understanding of the hydrogen flow characteristic is the key issue for the designs and applications of the hydrogen energy systems. Firstly, the numerical models of the multistage hydrogen Knudsen compressor are established. The distributions of the rarefaction, velocity and temperature at different stages of the hydrogen flow are calculated and presented. Moreover, the dimensional pressure increases of the hydrogen gas flow are analyzed, and the flow behaviors in the microchannel and the connection channel are discussed. Secondly, the numerical simulation at different connection channel height is implemented, and the hydrogen gas flow characteristics in the connection are analyzed. Especially, the performances of the pressure drop in the connection channel under different channel heights are studied, and the hydrogen gas compression characteristics of different cases are compared and discussed. Also, the effect of the connection channel height on the hydrogen gas pressure increase in the microchannel is investigated. The studies presented in this paper could be greatly beneficial for the hydrogen detection and transmission.     

Flow and transmission characteristics of the multistage hydrogen Knudsen pump in the micro-power system

The multistage hydrogen Knudsen pump based on the thermal transpiration effect has exciting application prospects for hydrogen transport in the micro-power system. The multistage hydrogen Knudsen pump with the silica microchannel is beneficial to its temperature control, which can accurately provide hydrogen transport and storage for the micro-power system. In this paper, the model of the multistage hydrogen Knudsen pump with the silica microchannel is established. The effects of the microchannel height, width and parallel number on the flow and transmission characteristics of the multistage hydrogen Knudsen pump are studied by using the method of N–S equations with the slip boundary. The temperature difference, Knudsen number, thermal transpiration effect, maximum mass flow rate, maximum pressure difference and performance curve under different microchannel parameters are analyzed in detail. The results show that the thermal transpiration effect increases with the microchannel height and decreases with the microchannel width. As the number of parallel microchannels increases, the microchannel is closer to the silicon cantilever, and the thermal transpiration effect becomes stronger. The pumping performance increases with the microchannel height, width and parallel number. The pressurization performance increases with the microchannel height and parallel number. The research results have important guiding significance for the application and design of the multistage hydrogen Knudsen pump in the micro-power system.     

Characteristics of thermal transpiration effect and the hydrogen flow behaviors in the microchannel with semicircular obstacle

The thermal transpiration effect has great potential applications for the hydrogen energy. In this paper, the thermal transpiration effect and the hydrogen flow behaviors are studied in the microchannel with the semicircular obstacles. Firstly, the slip boundary model is used in the simulation of the flow performance in the microchannel. The validity of the model at different Kn is verified by comparing with some previous work. Then, the hydrogen flow characteristics of the thermal transpiration effect with the semicircular obstacle are investigated. The result shows that as the size of the semicircular obstacle increases, the hydrogen flow path of the thermal transpiration effect becomes longer, and the temperature gradient decreases. As the characteristic length of the hydrogen flow decreases, there is an obviously negative influence on the thermal transpiration flow. A deeper analysis shows that the thermal driven flow and the pressure driven flow will produce y-component velocity, which leads to a backflow under the effect of semicircles, and the semicircular obstacles make the Knudsen layer spread to the channel center.     

Effect of the microchannel obstacles on the pressure performance and flow behaviors of the hydrogen Knudsen compressor

The hydrogen Knudsen compressor has potential applications on the hydrogen transmission for the microdevices and systems. In this paper, the numerical model of the hydrogen Knudsen compressor was established, combining the NS continuity equations with the slip boundary conditions. The effect of structures on the performance of the hydrogen Knudsen compressor is studied by generating different obstacles in the microchannels. This paper is mainly concerned on the rectangular and the triangular obstacles, and the influence of the obstacles length and height are investigated, respectively. The Knudsen number distribution and the rarefaction of the hydrogen gas flow are analyzed. Also, the characteristic of the pressure increase for the compressor under different parameters are investigated and discussed. The effect of the structure parameters on the flow velocity distributions are detailed described, as well as the velocity contour and the vortex distributions. Moreover, the variation of the Knudsen layers of the hydrogen gas flow in the hydrogen Knudsen compressor is presented, and the key factor of the Knudsen layers is analyzed and discussed. The results is significantly beneficial for the applications and designs of hydrogen Knudsen compressor.     

Three dimensional channel effect on the flow characteristics and the performance of hydrogen Knudsen compressors

As a new type of the micro fluidic device, Knudsen compressor can provide the potential utilizations on the hydrogen transport in the micro systems. Considering actual structure of the compressor is three-dimensional, flow characteristic studies are the key issue for the performance predictions. Firstly, the model of three-dimensional Knudsen compressor is built, and the validity of the model is proved by comparison with the experimental result. Secondly, the flow behaviors in the three-dimensional model is investigated, and the distributions of pressure and velocity are investigated. Also, the performance of the hydrogen Knudsen compressor in two-dimensional structure and three-dimensional structure are compared and discussed. Thirdly, the three-dimensional hydrogen Knudsen compressors with different width are analyzed, and the pressure increase in different cases of the hydrogen Knudsen compressors are studied.     

Thermal transpiration effect on the mass transfer and flow behaviors of the pressure-driven hydrogen gas flow

Thermal transpiration is a rarefied gas effect that drives the gas flow creeping in a microchannel due only to an imposed temperature gradient, which is often encountered in the hydrogen-transportation microfluidic applications such as proton exchange membrane fuel cell (PEMFC). Because of its impact on the pressure-driven flow behavior in the microchannel, this pumping phenomenon needs to be studied in designing and improving microfluidic devices for hydrogen transportation. However, so far little literature has discussed the thermal transpiration effects on the flow behaviors under normal boundary conditions. In this paper, a DSMC-SPH coupled multiscale approach is proposed on the study of the thermal transpiration effect on hydrogen gas multiscale flow behaviors. Various wall temperature distributions are used under a pressure-driven condition. The remarkable influence of thermal transpiration on the multiscale hydrogen gas flow are investigated and discussed. Since the thermal transpiration effect is often occurred in hydrogen transportation, the present simulation results can provide significant insights for designing and improving proton exchange membrane fuel cell (PEMFC).     

The effect of creep flow on two-dimensional isoflux microchannels

Microchannel convective heat transfer and friction loss characteristics are numerically evaluated for gaseous, two-dimensional, steady state, laminar, constant wall heat flux flows. The effects of Knudsen number, accommodation coefficients, second-order slip boundary conditions, creep flow, and hydrodynamically/thermally developing flow are considered. These effects are compared through the Poiseuille number and the Nusselt number. Numerical values for the Poiseuille and Nusselt numbers are obtained using a continuum based three-dimensional, unsteady, compressible computational fluid dynamics algorithm that has been modified with slip boundary conditions. To verify the numerical results, analytic solutions of the hydrodynamically and thermally fully developed momentum and energy equations have been derived subject to both first- and second-order slip velocity and temperature jump boundary conditions. The resulting velocity and temperature profiles are then utilized to obtain the microchannel Poiseuille and Nusselt numbers as a function of Knudsen number, first- and second-order velocity slip and temperature jump coefficients, Brinkman number, and the ratio of the thermal creep velocity to the mean velocity. Excellent agreement between the numerical and analytical data is demonstrated. Second-order slip terms and creep velocity are shown to have significant effects on microchannel Poiseuille and Nusselt numbers within the slip flow regime.     

Effect of inclined and low magnetic field in gaseous slip flow in two‐dimensional rectangular microchannel using first‐order boundary conditions

In the present work, the effect of an oriented low magnetic field on near‐continuum gaseous slip flow inside a two‐dimensional rectangular microchannel has been studied using first‐order boundary conditions. The flow was assumed to be compressible, laminar, and steady. The governing equations were solved analytically to obtain the solutions of velocity, temperature, and the pressure of the flow. The influence of different parameters such as Knudsen number, aspect ratio, Hartmann number, and pressure ratio were studied and analyzed. It was found that the electric and magnetic field with an inclined angle had significant effects on the flow properties. The results showed that the velocity increases and the temperature decreases as the inclination angle of the magnetic field decreases. The velocity increases as the Knudsen number, pressure ratio, and aspect ratio increase, while it decreases with increasing of the Hartmann number. The temperature decreases with increasing of the Knudsen number, pressure ratio, and aspect ratio, while the temperature increases as the Hartmann number increases. The results of the present study were validated with published results in the literature.     

Calibration of low-pressure MEMS gas sensor for detection of hydrogen gas

Detection of hydrogen by sensors are significant for improvement and safe usage of hydrogen gas as an energy source. In this paper, the application of the MEMS gas sensor for detection of hydrogen gas is numerically studied to develop the application of this device in different industrial applications. The flow feature and force generation mechanism inside a rectangular enclosure with heat and cold arms as the non-isothermal walls are inclusively discussed. In this study, the pressure of hydrogen is varied from 62 to 1500 pa correspond to Knudsen number from 0.1 to 4.5 to investigate all characteristics of the thermal-driven force inside the MEMS sensor. In order to simulate a rarefied gas inside the micro gas detector, Boltzmann equations are applied to obtain high precision results. To solve these equations, Direct Simulation Monte Carlo (DSMC) approach is used as a robust method for the non-equilibrium flow field. The effects of length, thickness and temperature of arms are comprehensively investigated in different ambient pressures. In addition, the effect of various hydrogen concentrations on the Knudsen force is studied. Our findings show that maximum Knudsen force occurs at P = 387 pressure and intensifies when the length of the arms is increased from 50 μm to 150 μm. In addition, the obtained results demonstrate that the generated force is highly sensitive to hydrogen gas species and this enables device for detection of hydrogen gas.     

Compressibility and Rarefaction Effects on Pressure Drop in Rough Microchannels

A numerical analysis of the flow field in rough microchannel is carried out with a finite volume compressible solver, including generalized Maxwell slip flow boundary conditions suitable for arbitrary geometries. Roughness geometry is modeled as a series of triangular obstructions. The relative roughness from 0% to 2.65% was considered. Because for truly compressible flow we have no fully developed flow condition, the simulation is performed over the whole length of the channel. A wide range of Mach numbers is considered, from nearly incompressible to chocked flow conditions. Flow conditions with a Reynolds number up to around 200 were computed. The outlet Knudsen number corresponding to the chosen range of Mach and Reynolds number ranges from a very low value to 0.0249. Performance charts are presented in terms of both average and local Poiseuille number as a function of local Knudsen, Mach, and Reynolds numbers. In particular, it appears that roughness strongly decreases the reduction in pressure loss due to rarefaction. Thus, the roughness effect is stronger at a high Knudsen. Furthermore, the compressibility effect has a major effect on pressure drop when the local Mach number exceeds 0.3.     

Burnett simulation of gas flow and heat transfer in micro Poiseuille flow

The Burnett equations with slip boundary conditions are used to simulate the compressible gas flow and heat transfer in micro Poiseuille flow in the slip and transition flow regime. A relaxation method on Burnett terms is proposed in the present study and the thermal creep effect is considered. Convergent results at Knudsen number up to 0.4 are achieved and the results agree very well with experimental data. It is found that with the increase of Knudsen number, the Poiseuille number decreases while Nusselt number increases. The local Poiseuille number decreases along the whole channel while the local Nusselt number decreases rapidly first and then increases slowly afterwards.     

Similarity solutions for flows and heat transfer in microchannels between two parallel plates

In this paper we give analytical similarity solutions of the Navier–Stokes equations coupled with energy equation of Newtonian fluid in a microchannel between two parallel plates taking into account the effects of viscous dissipation, the velocity slip and the temperature jump at the wall. Two different thermal boundary conditions are considered: the constant heat flux (CHF) and the constant wall temperature (CWT). We provide new similarity transformations for the governing equations and derive the expressions of Poiseuille number (Po) and Nusselt number (Nu). Then, the homotopy analysis method (HAM) is employed to solve the nonlinear differential equations with related boundary conditions. Both the dimensionless analytical expressions of velocity and temperature are obtained. The rarefaction effects on velocity distribution and flow friction are exhibited. The interactive effects of the Brinkman number (Br) and the Knudsen number (Kn) on Nu are analytically studied for both the CHF and CWT cases.     

3D study of temperature drop behavior of subsonic rarefied gas flow in microchannel

3D Numerical study of temperature variation for subsonic rarefied gas flow in a microchannel is carried out using an in-house MPI-based parallelized DSMC code. The temperature drop in the microchannel decreases with an increase in the aspect ratio whereas it increases with an increase in the pressure ratio, the cross-aspect ratio (CAR), and the Knudsen number. 3D and 2D simulations results are compared and effect of the CAR and Knudsen number are brought out. Finally, a correlation that predicts the temperature drop is formulated along with a list of conditions that ensures a near isothermal flow.     

Constructal design and thermal analysis of microchannel heat sinks with multistage bifurcations in single-phase liquid flow

Based on constructal theory, five different cases with multistage bifurcations are designed as well as one case without bifurcations, and the corresponding laminar fluid flow and thermal performance have been investigated numerically. All laminar fluid flow and heat transfer results are obtained using computation fluid dynamics, and a uniform wall heat flux thermal boundary condition is applied all heated surfaces. The inlet velocity ranges from 0.66 m/s to 1.6 m/s with the corresponding Reynolds number ranging from 230 to 560. The pressure, velocity, temperature distributions and averaged Nusselt number are presented. The overall thermal resistances versus inlet Reynolds number or pumping power are evaluated and compared for the six microchannel heat sinks. Numerical results show that the thermal performance of the microchannel heat sink with multistage bifurcation flow is better than that of the corresponding straight microchannel heat sink. The heat sink with a long bifurcation length in the first stage (Case 1A) is superior. The usage of multistage bifurcated plates in microchannel heat sink can reduce the overall thermal resistance and make the temperature of the heated surface more uniform (Case 3). It is suggested that proper design of the multistage bifurcations could be employed to improve the overall thermal performance of microchannel heat sinks and the maximum number of stages of bifurcations is recommended to be two. The study complements and extends previous works.     

Numerical simulation of roughness effects on flow and heat transfer in microchannels at slip flow regime

A numerical simulation for studying fluid flow and heat transfer characteristics in microchannels at slip flow regime with consideration of slip and temperature jump is studied. The wall roughness is simulated in two cases with periodically distributed triangular microelements and random shaped micro peaks distributed on the wall surfaces. Various Knudsen numbers have used to investigate the effects of rarefaction. The numerical results have also checked with available theoretical and experimental relations and good agreements has achieved. It has been found that rarefaction has more significant effect on flow field in microchannels with higher relative roughness. The negative influence of roughness on fluid flow and heat transfer found to be the friction factor increment and Nusselt number reduction. In addition high influence of roughness distribution and shape has been shown by a comparison of Poiseuille and Nusselt numbers for tow different cases.     

Stability of thermal transpiration flows in rectangular enclosures – Axisymmetric disturbances

Occurrence of instabilities for thermal transpiration flow of rarefied gases has been discussed in two-dimensions. Only axisymmetric disturbances have been considered due to symmetry of the basic flow. Effect of four second-order slip models (Cercignani, Deissler, Schamberg, and Beskok) and a first-order slip model (Maxwell) on the limits of the proposed instability have been examined. We have found that Beskok model is always stable to axisymmetric disturbances and Maxwell model is more stable compared with the other second order models. Variation of critical Reynolds number for different rarefaction levels (Knudsen numbers) has also been studied. Increase in Knudsen number leads to monotonic decrease in critical Re numbers.     

Pressure- and Temperature-Driven Flow Through Triangular and Trapezoidal Microchannels

A detailed study of pressure- and temperature-driven flows through long channels of triangular and trapezoidal cross sections is carried out. Due to the imposed pressure and temperature gradients there is a combined gas flow consisting of a thermal creep flow from the cold toward the hot reservoir and a Poiseuille flow from the high- toward the low-pressure reservoir. The formulation is based on the linearized Shakhov model subject to Maxwell boundary conditions, and it is solved numerically using a finite-difference scheme in the physical space and the discrete velocity method in the molecular velocity space. The results are valid in the whole range of the Knudsen number. In addition to the dimensionless flow rates, a methodology is presented to estimate for a certain set of input data the mass flow rates and the pressure distribution along the channel. Finally, special attention is given to the case of zero net mass flow and to the computation of the coefficient of the thermomolecular pressure difference.     

Investigation of irreversibilities in a microchannel by differing viscosity,including buoyancy forces and suction/injection

Single-phase Poiseuille flow considering oxides of copper-water nanoliquid in the upright microchannel with uneven viscosity causes the production of inbuilt irreversibility in the system. This is reported in the present investigation involving the buoyancy force with suction/injection at the walls by taking into account different shapes of nanoparticles. The equations so obtained being highly nonlinear is attempted to solve via Runge–Kutta–Fehlberg shooting scheme. Flow and heat transmission characteristics are explored by considering the nanoparticle's shape. The result exemplifies that the viscosity variation parameter escalates the flow profile as well as temperature profile. The thermal radiation and Biot number boost the let go of thermal energy, which leads to system cooling. The temperature profile for nanoparticle shape factor upholds the fact that temperature is high for lamina-shaped nanoparticles and least for spherical-shaped nanoparticles. Also, the Biot number, radiation parameter, and nanoparticle volume fraction serve in lowering the entropy, which augments the exergetic effectiveness of the system.     

Effect of Non-Equilibrium Condensation of Moist Air on Unsteady Behaviour of Shock Waves around a Circular Arc Blade

The unsteady phenomena in the transonic flow around airfoils are observed in the flow field of fan,compressorblades and butterfly valves,and this often causes serious problems such as the aeroacoustic noise,the vibration.In the transonic or supersonic flow where vapour is contained in the main flow,the rapid expansion of the flowmay give rise to a non-equilibrium condensation.However,the effect of non-equilibrium condensation on thetransonic internal flows around the airfoil has not yet been clarified satisfactorily.In the present study,the effectof non-equilibrium condensation of moist air on the self-excited shock wave oscillation on a circular arc bladewas investigated numerically.The results showed that in the case with non-equilibrium condensation,frequenciesof the flow oscillation became smaller than those without the non-equilibrium condensation.     

间隙变化对轴流压气机转子近失速工况叶顶流场的影响研究

为研究间隙变化对轴流压气机转子近失速工况下叶顶流场结构的影响,以轴流压气机转子Rotor37为研究对象,对其叶顶流场进行定常和非定常的数值模拟。计算结果表明：随着叶顶间隙的减小,压气机的总压比和等熵效率均有所提高,稳定运行范围扩大;2倍设计间隙下,叶尖泄漏涡经激波作用后发生膨胀破碎,堵塞来流通道,诱发压气机堵塞失速;0.5倍设计间隙下,吸力面流动分离加剧,发生回流,部分回流与来流在压力面前缘上游发生干涉,进口堵塞加剧,致使部分来流从前缘溢出,导致压气机叶尖失速;不同间隙下压气机失速过程的主导因素不同,大间隙下失速由叶尖泄漏涡破碎的非定常波动引起,小间隙下失速主要由流动分离引发的周期性前缘溢流所主导。