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A multi-scale flow analysis in hydrogen separationmembranes using a coupled DSMC-SPH method

Jianjun Ye a, Jian Yang a,*, Jinyang Zheng a, Xianting Ding b, Ieong Wong b, Weizhong Li c,Cong Chen c

a Institute of Process Equipment, Zhejiang University, Hangzhou 310027, ChinabDepartment of Mechanical and Aerospace Engineering, University of California, Los Angeles 90095, USAcSchool of Energy and Power Engineering, Dalian University of Technology, Dalian 116024, China

a r t i c l e i n f o

Article history:

Received 16 November 2010

Accepted 24 March 2011

Available online 6 May 2011

Keywords:

Proton exchange membrane fuel cell

(PEMFC)

Membrane separation

Multi-scale flow

Direct simulationMonte Carlo (DSMC)

Smoothed particle hydrodynamics

(SPH)

* Corresponding author. Tel.: þ86 571 879530E-mail address: zdhjkz@zju.edu.cn (J. Yan

0360-3199/$ e see front matter Copyright ªdoi:10.1016/j.ijhydene.2011.03.163

a b s t r a c t

Themembrane separation process has been developed as an effective and efficient method

for obtaining ultra-high purity hydrogen from impure feed streams. A typical membrane

gas flow possesses multi-scale flow characteristics, comprising a macroscopic flow regime

on both sides of the membrane and a microscopic flow regime in the pores within the

membrane. A better understanding of the fundamentals of such flow behaviors and mass

transfer at a multi-scale level is therefore crucial for a better membrane architecture

design, which could lead to better membrane separation efficiency and reliability for

hydrogen productions in fuel cells. In this paper, a novel numerical analysis method

combining the direct simulation Monte Carlo (DSMC) method with the smoothed particle

hydrodynamics (SPH) method is presented for the multi-scale flow prediction in

a membrane. Using the coupled method, the rarefied flow behaviors within a micro-orifice

pore can be predicted by the DSMC method, while the continuum flow behaviors on both

sides of the membrane can be simulated by the SPHmethod simultaneously. To investigate

the various flow behaviors and mass transfer between different components, such as H2

and CO in the membrane, the pressure, velocity, molar concentration, mass flowrate and

rarefaction of the H2 and CO components are compared in details. The influences to the

multi-scale flow from the orifice feature and size are discussed. Some unique phenomena

are observed to be quite different from that observed in either a solely macroscopic or

microscopic flow. The results can be greatly beneficial for the understanding of the

mechanism of membrane separation, and the designing of the membranes for hydrogen

productions in fuel cell applications.

Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights

reserved.

1. Introduction nature [1,2]; it may become the main fuel for all energy-

Due to the scarcity of fossil fuels and fossil fuels’ environ-

mental impacts, hydrogen is regarded as one of the most

important energy carrier for its renewable and non-polluting

98; fax: þ86 571 87953393g).2011, Hydrogen Energy P

related applications in the future. The continuing develop-

ment of a hydrogen economy based on the hydrogen fuel cell

has generated growing interests [3]. Proton exchange

membrane fuel cell (PEMFC) is a type of fuel cell being

.

ublications, LLC. Published by Elsevier Ltd. All rights reserved.

i n t e r n a t i o n a l j o u rn a l o f h y d r o g e n en e r g y 3 7 ( 2 0 1 2 ) 8 9 4e9 0 2 895

developed for portable transportation applications, as well as

for large-scale fuel cell stack applications. The fuel cell is

regarded as one of the most efficient and pollutant-free

technologies for power generation, because it produces only

water as the waste product, with zero discharge [4,5]. Pure

hydrogen is the most preferred fuel for fuel cells. A variety of

technologies have been developed for pure hydrogen

productions, such as steam-methane reforming (SMR), water

electrolyzing, partial oxidation of hydrocarbons and

photovoltaic-electrolysis. At present, the steam-methane

reforming (SMR) method is the most efficient and econom-

ical method to obtain ultra-high purity hydrogen from impure

feed streams [6]. The basic principle of SMR for hydrogen

extraction can be represented as follows

CH4 þH2O/COþ 3H2 (1)

COþH2O/CO2 þH2 (2)

In addition to hydrogen, the resulting reformer gas also

contains a trace amount of CO, which has a devastating effect

on the energy conversion efficiency of the fuel cells via CO-

induced damage of the Pt anode catalyst [7,8]. There are

several technologies to purify hydrogen produced from an

SMR process, such as cryogenic separation, pressure swing

adsorption (PSA), preferential oxidation (PROX) and

membrane separation [9e13].

Cryogenic separation is based on the difference in boiling

temperatures (relative volatility) of the feed components.

Since hydrogen has a relatively higher volatility compared to

hydrocarbons, the hydrogen steam can be separated from

hydrocarbons with a high purity (90%). To further purify the

hydrogen content, the PSA purification process is typically

used where impurities in the feed gas is adsorbed to a fixed

adsorbent bed at a high pressure. This process can eventually

produce a pure hydrogen product with purities in excess of

99.999%. However, the cryogenic separation and the PSA

technologies are energy intensive, and therefore are not

economical for hydrogen production. Their prohibitive cost

would deter the popularization and application of fuel cells.

As for the preferential oxidation (PROX) method, a catalyzer

preferentially oxidizes carbon monoxide (CO) using a hetero-

geneous catalyst placed on a ceramic support. The PROX

process allows the reaction of the CO in a water gas shift

Fig. 1 e SEM photographs of the substrates. (a) surface of

reaction (WGS). Using this technology can reduce CO

concentration from approximately 0.5e1.5% to less than

10 ppm in the feed gas, but it induces undesirable H2 oxidation

and the complexity of having to add precisely-controlled

amounts of gaseous oxygen to the system. Membrane sepa-

ration, which is the production of pure hydrogen using

palladium membranes, is a new method appeared in the

second half of the 1990s. A membrane, which is often fabri-

cated by a Pd film, is a barrier that can selectively permit mass

transfer between the two phases. Based on this technology, an

extremely pure hydrogen product with a purity of 99.9999%

can be achieved. Due to its high efficiency and low power

consumption for hydrogen purification, the membrane sepa-

ration is potentially the most economic and straightforward

method to reduce the CO contamination to the parts per

million level. Furthermore, this separation technology can

also satisfy the growing need for ultra-high-purity gases for

other applied fields [14].

The hydrogen permeability and selectivity are key factors

for the membrane separation. Recently, studies demon-

strated that a hydrogen flux is observed to be inversely

proportional to the membrane thickness, indicating inter-

stitial diffusion as the rate limiting mechanism of hydrogen

permeation. This knowledge, along with the high cost of

palladium, has motivated continuous efforts to decrease the

membrane thickness. Advancements of microfabrication

technology have pushed the defect-free membrane thick-

ness into a sub-micrometer range [15]. However, recent

theoretical and experimental results show that as the

thickness is reduced into the micrometer range, atomic

hydrogen desorption from the permeable surface of the

membrane becomes the dominant mass transfer resistance.

In order to increase mass transfer for a thin Pd membrane,

carrier materials are being studied increasingly both exper-

imentally and numerically, since it is a direct method to

influence flow behavior and improve mass transfer in the

membrane separation technique [16]. The traditional

carriers are mainly porous ceramics, molecular sieves,

porous stainless steel, etc [17]. These carriers work fine in

a macro scale. However, in a micrometer scale, it is

extremely challenging to make pores of a uniform size,

directly abating the efficiency of the membrane. In recent

applications, silicon based carriers have received great

porous TiAl alloy, (b) top view of the porous silicon.

Fig. 2 e The flowchart of a coupled DSMC-SPH method.

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 7 ( 2 0 1 2 ) 8 9 4e9 0 2896

interest. Micro-machining characteristics of silicon are

better than that of ceramic materials and metallic materials.

It is easier and more economical to generate uniform porous

silicon structures. Fig. 1 has a set of scanning electron

microscope (SEM) photographs of the substrates. Fig. 1a is

the porous TiAl alloy and Fig. 1b is the porous silicon. Sizes

of pores on the porous TiAl alloy are in the range of

200 nme2 mm, as measured in the SEM. The pores in the

porous silicon fabricated in a 5%HF solution are uniformly

10um in size [18,19]. The fact that an artificially processed

silicon material possesses uniform pore size permits the

possibility that the hydrogen permeability in a membrane

separation process can be improved by controlling the size

of the pores in a silicon carrier material.

Understanding the performance of flow behaviors through

the microsize or nanosize pores of the substrate is important

in the designing and development of membrane separation

equipment [20,21]. However, measurements in the nano- and

micro- scale are usually very difficult and, sometimes,

imprecise, rendering a scarce documentation of membrane

flow data. On the other hand, a simulation of a gas flow

through nano- and micro- pores is also very complicated:

before entering the substrate, the gaseous flow is in

a continuum regime and the behaviors can be predicted by the

continuum theories; however, upon entering the substrate,

due to the very small characteristic scale of the pores, the flow

becomes rarefied and the behaviors often defy the predictions

of the continuum theories. To the best of our knowledge, there

is little literature discussing such multi-scale substrate flows

and their calculation methods. In the present article, a novel

multi-scale approach is proposed by coupling a rarefied gas

approach, called the direct simulation Monte Carlo (DSMC)

method, with a continuum approach, called the smoothed

particle hydrodynamics (SPH) method. Using this coupled

method, the multi-scale flow behaviors and mass transfer for

reactions that usually occur in membrane separation situa-

tions for a very small orifice can be described. A further

investigation of the different flowbehaviors andmass transfer

between H2 and CO in a membrane is also presented. More-

over, the effects of the orifice size on the multi-scale flow and

mass transfer is investigated in details. The results can be

greatly beneficial to the understanding of the separation

mechanism and the designing of a membrane for hydrogen

productions in fuel cells.

Fig. 3 e Schematic of the coupled DSMC-SPH domain.

2. The coupled numerical method

2.1. DSMC method

The characteristic size of amicro-orifice of amembrane can be

as small as a micrometer or nanometer scale, bringing the

Knudsen number into a rarefied gas flow regime-ranging from

0.01 to 10. In this regime, the fluid motion has to be described

from a molecular point of view and the continuum-based

approach may lead to large errors inflow predictions [22]. The

direct simulation Monte Carlo (DSMC) method, proposed by

Bird, can be an appropriate solution for the flow predictions in

such a micro/nano regime [23,24]. The DSMC method is an

effective numerical method to solve the dynamic equations

for real gases. It is also regarded as the most successful

method for simulating rarefied gas flows [25,26]. The DSMC

method is a probabilistic simulation method that employs

a large number of statistically-selected, simulated particles of

an appropriate physical size. Each simulated particle repre-

sents a large number of real particles. The positions, velocities,

and motion states of these simulated particles are stored and

updated in every time step. During the movement of the

particles, the interactions with boundaries and with other

molecules are characterized by conserving the overall

momentum and energy. During each time interval, which is

muchsmaller than themeancollision time,molecularmotions

and intermolecular collisions are uncoupled. In the DSMC

method, the calculation zone is divided into many computa-

tional cells, and each cell is further divided into sub-cells. The

Table 2 e Parameters of the different cases with Hc.

Case 1 Case 2 Case 3

Hc (mm) 0.6 0.8 1.0

Lc (mm) 2 2 2

Fig. 4 e The geometry of the simulated channel.

i n t e r n a t i o n a l j o u rn a l o f h y d r o g e n en e r g y 3 7 ( 2 0 1 2 ) 8 9 4e9 0 2 897

variable hard sphere (VHS) model and the no time counter

(NTC) method are often used to simulate the molecular

collision kinetics. The time step is set so that each simulated

moleculemoves approximately one-fifth of the cell dimension

at the most probable molecular speed. The microscopic or

nanoscopic flowcharacteristics, suchas pressure, density, and

temperature are obtained statistically by sampling the small

particles’ properties in each cell.

2.2. SPH method

The basic description of the smoothed particle hydrody-

namics (SPH) method follows the review by Monaghan

[27e29]. In the SPH method, the fluid is defined by a finite set

of Lagrangian particles in the computational domain. Strictly

speaking, these are interpolation points used in integrating

the NaviereStokes equations. The equations governing the

evolution of the fluid become the expressions for inter-

particle forces and fluxes when written in the SPH form.

The key in thismethod is the use of a smoothing kernel, i.e.

a function with certain properties that is used to sum up to an

approximate value of the flow field from the surrounding

particles. In the simulation, each particle carries a mass mj,

a velocity vj, and other fluid quantities specific to the given

problem. Themethod is based on the interpolation theory and

the basic formula is

AðraÞ ¼ZD

Aðr0Þ Wðr� r0;hÞ dr0zXNj¼1

mjAj

rjW

�r� rj;h

�(3)

The density of the flows is calculated by the method sug-

gested byMonaghan. Basically, a reference density is set at the

beginning of themodeling, while the increment of the density

is obtained from the continuity equation in the SPH form.

dradt

¼Xb

mbvab$VaWab (4)

Table 1 e Properties of H2 and CO (273 K, 1.01 3 105 Pa).

Species M (kg) zr dref (m) m (Nsm-2)

H2 3.34 � 10�27 2 2.92 � 10�10 0.85 � 10�5

CO 4.65 � 10�26 2 4.2 � 10�10 1.662 � 10�5

Viscous forces are calculated using a formula recently

applied to low-Reynolds-number flows [30]. In SPH form, the

momentum equation can be written as the following

dva

dt¼ �

Xb

mb

�pa þ pb

rarb

�VaWab þ

Xb

mbðma þ mbÞvab

rarb

��

1krabk

dWdra

�þ F (5)

Where F is the body force evaluated at particle a, and ma and mb

are the dynamic viscosity of the fluid corresponding to posi-

tions ra and rb.vab is the relative velocities between a particle

and its neighboring particles.

2.3. Coupled DSMC-SPH method

A detailed description of the coupled DSMC-SPH method for

a flow in channels is shown in Fig. 2. A simulation model of

gaseous flow passing a channel with a constant cross-section

is used in this work. The flow domain is composed of two

overlapping regions based on the alternating Schwarz

method. The expanded region of the channel is described by

the SPH method while the small channel is described by the

DSMC method. To make sure that the two descriptions are

simultaneously valid in the overlapping domain, the char-

acteristic dimension of the channel is chosen to be big

enough so that the continuum theory holds true in both

domains.

In Fig. 3, an example of a hybrid domain used in the work is

shown. The DSMC domain, the SPH domain and the over-

lapping domain are denoted asUD,Us andUo, respectively. The

boundary of the continuum (SPH) domain, Us, is composed of

an inflow boundary and an inner boundary GS that lies within

the DSMC domain while the DSMC domain is bounded by an

outflow boundary and an inner boundary GD that lies within

the SPH domain.

In each iteration, the SPH domain Us is computed with

a given inflow boundary condition and an internal boundary

conditiononGS. ThesolutionUnS atGDand theoutflowcondition

is used as the boundary condition for the DSMC domain. The

nextSPHboundaryconditionGnþ1S is obtained fromthesolution

UnD of the last DSMC calculation. Go is the intermediate layer of

the overlapping domain. The convergence of the multi-scale

method is defined when the updates to the solution U (for

Table 3 e Parameters of the different cases with Lc.

Case 4 Case 1 Case 5

Hc (mm) 0.6 0.6 0.6

Lc (mm) 1 2 3

Fig. 5 e Pressure distributions of the H2 and CO flows in the

multi-scale channel.

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 7 ( 2 0 1 2 ) 8 9 4e9 0 2898

example, pressure, velocity and concentration, etc.) at Go are

less than a specified tolerance value d

jUnþ1GoS

� UnGoS

jUnþ1

GoS

� dks (6)

jUnþ1GoS

� Unþ1GoD

jUnþ1

GoS

� dks (7)

jUnþ1GoD

� UnGoD

jUnþ1

GoD

� dkD (8)

jUnþ1GoD

� Unþ1GoS

jUnþ1

GoD

� dkD (9)

3. Physical and numerical modeling

For a thorough understanding of the fundamentals of multi-

scale flow behaviors and mass transfer, Fig. 4 shows the

geometry of such a simulated 2D multi-scale channel, which

consists of an inlet region, an outlet region and an orifice

region. Lin is the length of the inlet region, Lout is the length of

the outlet region, and Lc is the length of the orifice. Hf is the

height of the inlet region and Hc is the height of the micro or

nano orifice. The multi-scale channel is symmetric relative to

the center point of the channel geometry. pin is the pressure at

the inlet and pe is the pressure at the outlet of the channel. In

the inlet and outlet region, the flow is in a continuum regime,

which is simulated by the SPH method. The flow in the orifice

region is in a slip or transition regime, which is simulated by

the DSMC method. Uo is the overlapping domain, where both

DSMC and SPH methods apply and it is where the two

methods have the minimal discrepancies.

To understand H2 and CO flow behaviors andmass transfer

in themulti-scale channel, properties of H2 and CO are shown

in Table 1. The effects of the orifice size on a multi-scale flow

are also investigated. Numerical details of the cases are shown

in Table 2 and Table 3. In all cases, the length of the inlet

region, Lin, is equal to the length of the outlet region, Lout. The

total length of the channel is 30 mmand the height is 6 mm. The

pressure ratio is set at 1.3 by fixing pin at 0.13 MPa and pe at

0.1 MPa. The temperature of the incoming gas flow and the

wall are both set at 300 K.

Fig. 6 e x-velocity distribution along the centerline of the

H2 and CO flows.

4. Results and discussion

4.1. The flow behaviors of H2 and CO in a multi-scalechannel

Due to the differences in the particle properties, H2 and CO

exhibit different flow behaviors in a multi-scale channel. The

results of the flows are shown in Figs. 5e8. Fig. 5 shows the

pressure distributions along the centerline of the channel. It is

shown that the pressure distribution of H2 flow is consistent

with that of the CO flow. Both of them show very low pressure

drop in the inlet and outlet regions and virtually all the pres-

sure drop occurs at the vicinity of themicro-orifice. Themulti-

scale flow phenomenon is uniquely different than that of its

macro counterparts.

The x-velocity distributions of the centerline are compared

in Fig. 6. For a practical membrane pore, due to the constraints

stemmed from the micro or nano size, the flow velocities in

the inlet region and the outlet region are uniform. However, in

the micro-orifice region, because of the sudden contraction,

the velocity increases rapidly, and peaks near the outlet of the

micro-orifice. At the outlet region of the orifice, because of the

sudden expansion, the flow velocity decreases rapidly. Under

the same pin and pe conditions, the velocity of the H2 is higher

than that of the CO. At the inlet region and the outlet region,

the velocity of the H2 flow is 8 m/s and 11 m/s, respectively,

while that CO flow is only 4m/s and 5m/s, respectively. In the

micro-orifice, themaximum velocity of the H2 flow and that of

the CO flow is 105 m/s and 40 m/s, respectively. The differ-

ences can be explained byH20s lower dynamic viscosity. Under

the same flow conditions, the CO flow will receive more

resistance, so the velocity of CO flow is lower than that of H2.

For mass transfer, Fig. 7 shows the molar concentration

distributions of the H2 flow and the CO flow. At the inlet of the

channel, the molar concentration of the H2 flow and the CO

Fig. 9 e Pressure distributions of the H2 and CO flows at

different Hc.Fig. 7 e Molar concentration distributions of the H2 and

CO flows.

i n t e r n a t i o n a l j o u rn a l o f h y d r o g e n en e r g y 3 7 ( 2 0 1 2 ) 8 9 4e9 0 2 899

flow are both 1.18 mol/L. In themicro-orifice region, themolar

concentrations both drop rapidly; whereas near the outlet, the

molar concentrations both increase, and the molar concen-

tration of the CO is higher than that of the H2. It can be

explained using the ideal gas equation: in the outlet region,

the temperature of the flows decrease, therefore the densities

and themolar concentrations of the flows increase. Moreover,

the temperature drop of the CO is larger than that of the H2, so

the molar concentration of the CO is higher than that of the

H2. It shows that the different mass transfer capacity for

separation in such architecture.

The comparison of the rarefaction between the two in the

multi-scale channel is shown in Fig. 8. In the inlet region of the

multi-scale flow, the Kn numbers are 0.014 and 0.007 for theH2

and CO, respectively. In the outlet region, the Kn numbers of

the H2 and CO are 0.018 and 0.009, respectively. In the micro-

orifice, because of the smaller characteristic length, the Kn

numbers of them increase significantly to 0.17 and 0.08,

respectively. It is shown that the H2 is more rarefied than the

CO. It can be explained that the molecule of the CO is larger

than that of the H2; in accordance with molecular collision

kinetics, the mean free path of the CO is shorter than that of

Fig. 8 e Comparison of the rarefaction of the H2 and

CO flows.

the H2 under the same pressure. Also, the H2 flow spans from

a slip regime to a transition regime with Kn ¼ 0.014 to

Kn ¼ 0.17, and the CO flow spans from a continuum regime to

a slip regime with Kn ¼ 0.007 to Kn ¼ 0.08. These results show

that, the flow regime and its characteristic for a gas can be

changed in a multi-scale channel. It is a quite different from

that of a puremacro flow or micro flow. The results prove that

the coupled DSMC-SPH algorithm can be used for multi-scale

simulations and it also can be used to obtain the distinguished

characteristics for multi-scale flow behaviors and mass

transfer in membrane pores.

4.2. Effects of the size of micro-orifice on the multi-scaleflow behaviors

From the analysis above, in the multi-scale channel, the

pressure drop and the flow regime changemainly occur in the

orifice. It shows that the size of themicro-orifice is a key factor

for the multi-scale flow behaviors and mass transfer in the

membrane pores. Herein, the parameters of the different

cases with varying orifice heights, Hc, and lengths, Lc, are

shown in Table 2 and Table 3, respectively.

Fig. 10 e x-velocity distributions along the centerline at

different Hc.

Fig. 13 e Pressure distributions of the H2 and CO flows at

different Lc.

Fig. 11 e Comparison of the molar concentration of H2 and

CO at different Hc.

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4.2.1. Effects of the Hc on the multi-scale flow behaviorsTo investigate the effects of varying Hc on themulti-scale flow

behaviors, the Hc of the micro-orifice are varied to 0.6 mm,

0.8 mm and 1.0 mm in case 1, case 2 and case 3, respectively.

Fig. 9 shows the pressure distribution with the different Hc.

When Hc ¼ 0.6 mm, the pressure drop in the inlet region and

the orifice are 0.0004 MPa and 0.0292 MPa, respectively. When

Hc ¼ 1.0 mm, the pressure drop in the inlet region and the

orifice are 0.015 MPa and 0.027 MPa, respectively. It shows

that, as Hc increases, the pressure drop in the inlet region

increases, while the pressure drop in the micro-orifice

decreases. It can be explained by the fact that as Hc

increases, the ratio of the characteristic length between the

orifice and the expanded region decreases, and the multi-

scale effects become weaker in the flow. Fig. 10 shows the

x-velocity on the centerline with different Hc. As Hc increases,

the velocity of the flow increases. The reason is the flow

resistance is mainly caused by the sudden contraction in the

channel. When Hc increases, the flow resistance decreases,

thus the flow velocity in the channel increases.

Fig. 12 e Comparison of the flowrates of H2 and CO at

different Hc.

Fig. 11 shows themolar concentrationdistributionsofH2and

CO flows with different Hc. It is shown that the molar concen-

tration increases at the outlet of the channel. As Hc increases,

the increase ofmolar concentration becomesmore remarkable.

The reason is that the pressure gradient in the outlet region is

higher than before. According to literature [31], the higher

temperature dropoccurs at theoutlet under thehigher pressure

gradient. Therefore, the molar concentration increases much

more rapidly in thechannelwithHc increasing. Fig. 12 shows the

mass flowrate of the multi-scale flows with different Hc. The

mass flowrate can always be kept constant for any arbitrary

cross-section in a steady flow; here, the cross-section is set at

x¼ 2.5� 10�5m. For theH2flow, themassflowrates for the three

cases are 2.2 � 10�5 kg/s, 4.17 � 10�5 kg/s, and 6.96 � 10�5 kg/s,

respectively. It is shown that the increasing mass flowrate is

nonlinear with Hc increases. Besides, the mass flowrate of the

CO is higher than that of the H2 flow, and the increase of the

velocity ismore remarkable. It also shows that whenmolecules

in a flow are heavier, the mass flowrate is higher, and the

increase becomes more remarkable with Hc increasing.

Fig. 14 e x-velocity distributions along the centerline at

different Lc.

Fig. 15 e Comparison of the molar concentration of H2 and

CO at different Lc.

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4.2.2. Effects of Lc on the multi-scale flow behaviorsTo investigate the effects of Lc on the multi-scale flow

behaviors, three cases with different Lc are also given. As

shown in Table 3, the Lc of the micro-orifice is varied to 1 mm,

2 mm, and 3 mm in case 4, case 1 and case 5, respectively. Fig. 13

shows the pressure distribution with different Lc. As the Lcincreases, the pressure gradient in the orifice becomes less

significant. According to the Fig. 13, the pressure drop mainly

occurs in the orifice region. It shows that a longer orifice will

lead to a lower pressure drop. As shown in Fig. 14, when

Lc ¼ 1.0 mm, the x-velocity in the inlet region is 17 m/s for the

H2 flow, and the maximum velocity in the orifice is 160 m/s;

when Lc is increased to 3.0 mm, the velocity at the inlet

decreases to 6 m/s, and the maximum velocity in the orifice

also decreases to 75 m/s. This similar flow behavior also

occurs in the CO flow. This result presents that in a multi-

scale flow, the velocity is sensitive to the length of the micro-

orifice: when the length of the orifice increases, the pressure

gradient in the micro-orifice decreases, and then causes

a decrease in the flow velocity.

Fig. 16 e Comparison of the mass flowrate of the H2 and CO

flows at different Lc.

Fig. 15 shows the effect of varying Lc on the molar

concentration distributions. In the inlet region of the channel,

there is little difference of the molar concentration in the

channels with different Lc. In the micro-orifice region, the

molar concentration drops slowly in the longer Lc case. Near

the outlet of the channel, it is shown that the molar concen-

tration increases much more remarkable as Lc increases. The

main reason is that the pressure gradient is steeper than that

of the shorter Lc case in the outlet region, and the temperature

drop is also larger in the longer Lc case. These phenomena

raise the molar concentration with longer Lc.

The effect of varying Lc on the mass flowrate is shown in

Fig. 16. Here, the mass flowrate at the cross-section

x¼ 2.5� 10�5 m is investigated in detail. For the H2 flow, when

Lc¼ 1 mm, 2 mm, and 3 mm, themass flowrates of the H2 flow are

0.73 � 10�5 kg/s, 0.47 � 10�5 kg/s, and 0.35 � 10�5 kg/s,

respectively. For the CO flow, when Lc ¼ 1 mm, 2 mm and 3 mm,

the mass flowrates are 3.7 � 10�5 kg/s, 2.2 � 10�5 kg/s, and

1.54 � 10�5 kg/s, respectively. As the Lc increases, the mass

flowrate decreases: it is caused by the lower velocity in the

multi-scale channel. Furthermore, the relationship between

the mass flow and Lc is nonlinear. The decrease of the mass

flowrate becomes less significant as Lc increases.

5. Conclusions

A novel numerical analysis method for a multi-scale

membrane flow simulation is presented in this paper by

coupling two particle-base algorithms: the DSMC and the SPH

methods. To combine the DSMC and SPH domains, a serial

Schwarz alternating method is employed. The coupled

DSMC-SPH method is used to simulate a multi-scale flow,

which is encountered in the membrane separation process

for hydrogen production. The H2 flow and the CO flow

behaviors and mass transfer are compared in the multi-scale

channel. The results show that, the pressure distributions of

H2 flows and CO flows are consistent; compared with a CO

flow, the velocity of a H2 flow is higher, but the mass flowrate

of the H2 is lower. At the outlet of the channel, the molar

concentration of a CO is higher than that of a H2 flow. In

a multi-scale flow channels, the H2 flow jumps from the slip

regime to the transitional regime and the CO flow jumps

from the continuum regime to the slip regime. Such change

of the flow regime is quite different from that observed in

typical macro flows with conventional numerical methods.

To facilitate future novel membrane designs or membrane

selections, further investigation of the effects of varying

micro-orifice size on the multi-scale flow was conducted:

a few examples with varying orifice height and length (Hc and

Lc) are demonstrated. As Hc increases, the pressure drop

increases in the expanded region but decreases in the orifice,

while the velocity and mass flowrate increase. Also, the

increase of the molar concentration at the outlet becomes

much more remarkable. As Lc increases, the pressure

gradient decreases in the orifice, the velocity and mass

flowrate decrease, and the molar concentration distributions

for both H2 and CO flows increase much more rapidly at the

outlet.

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 7 ( 2 0 1 2 ) 8 9 4e9 0 2902

Acknowledgments

This project is supported by the high-technology research

and development program (863) of China (Number:

2009AA05Z118), the Natural Science Foundation of China

under Grant No. 50475100, the China Postdoctoral Science

Foundation No. 2010047172, the Natural Science Foundation

of Zhejiang Province under Grant No. Z1100221, the Funda-

mental Research Funds for the Central Universities No.

2009QNA4031. We thank Mr Chi K. Lam and Dr Nico van der

Kolk for their useful comments in reviewing the manuscript.

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