Numerical study on the mixing in a barrier …Numerical study on the mixing in a barrier-embedded...

© 2018 The Korean Society of Rheology and Springer 227

Korea-Australia Rheology Journal, 30(3), 227-238 (August 2018)DOI: 10.1007/s13367-018-0022-x

www.springer.com/13367

pISSN 1226-119X eISSN 2093-7660

Numerical study on the mixing in a barrier-embedded partitioned pipe mixer

(BPPM) for non-creeping flow conditions

Hae In Jung1,‡

, Seon Yeop Jung2,‡

, Tae Gon Kang1,* and Kyung Hyun Ahn

2,†

1School of Aerospace and Mechanical Engineering, Korea Aerospace University, Goyang-si, Gyeonggi-do 10540, Republic of Korea

2School of Chemical and Biological Engineering, Institute of Chemical Processes, Seoul National University, Seoul 08826, Republic of Korea

(Received May 20, 2018; final revision received July 16, 2018; accepted July 18, 2018)

In this paper we investigated numerically the flow and mixing characteristics of the barrier-embedded par-titioned pipe mixer (BPPM) in non-creeping flow conditions. Numerical simulations are conducted for threemixing protocols of the BPPM, co-rotational, mirrored co-rotational, and counter-rotational protocols in therange of the Reynolds number (Re), , focusing on the effect of the Reynolds number, the bar-rier height, and the mixing protocols on the mixing in the BPPM. Each mixing protocol creates two cross-sectional flow portraits with crossing streamlines. Poincaré sections were plotted to investigate the flow sys-tem affected by the Reynolds number and the barrier height. Mixing in a specific BPPM is characterizedusing the intensity of segregation in terms of the compactness and the energy consumption. The dependencyof the barrier height and the Reynolds number on the final mixing state of the BPPMs was identified bymixing analyses. The co-rotational protocol results in an efficient mixing in the creeping flow regime.Meanwhile, mirrored co-rotational and counter-rotational protocols, which lead to poor mixing in the creep-ing flow regime, turned out to be efficient protocols in the higher Reynolds number regime.

Keywords: chaotic mixing, static mixer, barrier-embedded partitioned pipe mixer, non-creeping flow,

numerical simulation

1. Introduction

Static mixers are widely used in a variety of applica-

tions, such as polymer blending, food processing, and

miniaturized biomedical or chemical systems (Ghanem et

al., 2014; Hobbs and Muzzio, 1997; Liu et al., 2006;

Nguyen and Wu, 2005; Jayaraj et al., 2007; Suh and

Kang, 2010). In such applications, the typical flow in a

mixing device belongs to the creeping flow regime. If

other means that enhance mixing are not introduced into

the mixing device, mixing in the creeping flow is mainly

governed by molecular diffusion, which is a slow process,

preventing us from achieving a desired mixing state

within the limited length of a static mixer. However, it is

possible to overcome such a limitation by inducing cha-

otic advection as a mean to achieve enhanced mixing

(Aref, 1984; Ottino, 1989; Wiggins and Ottino, 2004).

Mimicking the baker’s transformation – repeated stretch-

ing and folding of fluid elements – chaotic advection is

employed in many mixing devices as a key mechanism to

enhance mixing in low Reynolds number flows (Hwang

and Kwon, 2000; Kang et al., 2007a; 2007b; Kang et al.,

2009; Kim et al., 2004; Meng et al., 2017; Metcalfe et al.,

2006; Stroock et al., 2002). Chaotic trajectories of fluid

particles can be achieved even in a simple laminar flow

field by inducing chaotic advection. According to the the-

ory of the linked twisted map (LTM) (Wiggins and Ottino,

2004), a spatially periodic flow with crossing streamlines

coming from two flow patterns leads to chaotic advection.

Many mixers introduced so far are fitted within the LTM

framework (Jana et al., 1994; Jung et al., 2018; Kang et

al., 2009; Khakhar et al., 1987; Kim et al., 2004; Metcalfe

et al., 2006; Stroock et al., 2002).

To ensure the usefulness of a static mixer in various

applications, it is crucial to understand flow and mixing

characteristics of the mixer in a wide range of Reynolds

number (Re). In a study on the optimization of the Kenics

static mixer (Byrde and Sawley, 1999), mixing showed an

irregular dependency on the Reynolds number. According

to the study, an optimal value of the twist angle of the

blade was found to be close to 180º when Re = 100.

Kumar et al. (2008) presented mixing performance of the

Kenics static mixer in Reynolds numbers ranging from 1

to 25,000 (i.e., from laminar to turbulent flow regime).

Kang et al. (2008) numerically investigated the effect of

the mixing protocol and inertia on the mixing in a barrier-

embedded micromixer. They found that a mixing protocol

showing the best mixing in the creeping flow regime was

not always the optimal design in other Reynolds number

regimes. Later, Kang and Anderson (2014) also studied

0.1 Re 300≤ ≤

‡These authors are equally contributed to this work.*Corresponding author; E-mail: [email protected]†Co-corresponding author; E-mail: [email protected]

Hae In Jung, Seon Yeop Jung, Tae Gon Kang and Kyung Hyun Ahn

228 Korea-Australia Rheology J., 30(3), 2018

the effect of inertia on the flow and mixing characteristics

of a chaotic serpentine mixer (CSM) and proposed an

optimal design for a specific operating condition. Viktorov

et al. (2015) conducted an experimental and numerical

study on the mixing in passive micromixers based on the

split-and-recombine (SAR) principle in a laminar flow

regime, where . Recently, Raza et al. (2018)

presented a three-dimensional SAR micromixer working

in Reynolds numbers ranging from 0.1 to 200.

The present study is a sequel to our previous study (Jung

et al., 2018) on the chaotic mixing in a barrier-embedded

partitioned pipe mixer (BPPM), extending the flow regime

to non-creeping flows where inertia plays an important

role in the flow and mixing. The BPPM is a static mixer

motivated by an inline dynamic mixer, the partitioned-

pipe mixer (PPM) proposed by Khakhar et al. (1987). In

the previous study (Jung et al., 2018), it was shown that,

for a properly chosen set of design parameters, the flow

system in the BPPM is globally chaotic in the creeping

flow regime, showing enhanced mixing performance com-

pared to that of the PPM. In addition, the mixing perfor-

mance of the BPPM is characterized by the intensity of

segregation (Danckwerts, 1952; Meijer et al., 2012). The

best BPPMs in the creeping flow regime are identified

with regard to the compactness of the mixer and the

energy consumption measured by the viscous dissipation

in the flow.

In this study, we attempt to investigate the flow and

mixing of the BPPM for non-creeping flow conditions,

focusing on the influence of the barrier height, mixing

protocols, and inertia on the mixing in the BPPM. The

flow and mixing characteristics in a range of the Reynolds

number ( ) are identified by numerical simu-

lations using a commercial CFD software, ANSYS CFX

18.0 (ANSYS Inc., USA). The mixing in the BPPM influ-

enced by the above-mentioned parameters is studied both

qualitatively and quantitatively using a similar numerical

scheme employed in the previous study (Jung et al., 2018).

2. Problem Formulation

2.1. Mixer geometryIn a BPPM, the mixing elements, consisting of two

orthogonally connected rectangular plates with a slanted

barrier on both sides of the plates, are placed in a station-

ary circular pipe with the diameter D. The slanted barriers

create two rotational flows, either co-rotational or counter-

rotational, depending on the tilting angle of the two bar-

riers. Figure 1 depicts mixing elements of co-rotational,

mirrored co-rotational, and counter-rotational BPPMs, the

three mixing protocols used in simulations. The mirrored

co-rotational BPPM (Fig. 1b) is designed by mirroring the

second half period of the mixing element in the co-rota-

tional protocol with respect to the mid-plane of the plate.

As used in the previous study (Jung et al., 2018), the

pipe diameter (D) is set to 20 mm. The two geometrical

parameters concerned with the flow in the BPPM are the

aspect ratio of the plate (α = Lp/D) and the dimensionless

barrier height (β = H/R), where Lp is the length of the

plate, H the height of the barrier, and R the radius of the

circular pipe. A computational domain consists of six peri-

odic units of a BPPM (see Fig. 2 showing a co-rotational

BPPM as an example). It should be noted that, in this

study, the aspect ratio α is fixed to be 1, but the dimen-

sionless barrier height β varies from 0.35 to 0.65 in incre-

ments of 0.15. The interspace length (Lg), the gap between

two adjacent plates, is fixed to 0.25D.

2.2. Governing equationsWe consider a steady incompressible flow of two New-

tonian fluids that are introduced through the inlet. Gov-

erning equations for the flow and mixing analysis of the

1 Re 100≤ ≤

0.1 Re 300≤ ≤Fig. 1. Periodic units of three designs of the BPPM, (a) co-rotat-

ing BPPM, (b) mirrored co-rotating BPPM, and (c) counter-

rotating BPPM.

Numerical study on the mixing in a barrier-embedded partitioned pipe mixer (BPPM)

Korea-Australia Rheology J., 30(3), 2018 229

BPPMs are the steady Navier-Stokes equation and the

continuity equation for an incompressible flow and the

convection-diffusion equation for the mass transport. The

two fluids introduced through the inlet are assumed to

have the same material properties, enabling us to solve the

same governing equation for the flow problem.

The governing equations for the flow problem are given

by

in Ω, (1)

in Ω (2)

where ρ is the fluid density, μ the fluid viscosity, u the

velocity vector, and p the pressure. At the inlet, the veloc-

ity field for a fully developed laminar flow for a circular

pipe is imposed, while, at the outlet, the pressure is zero.

No-slip and non-penetration conditions are applied at the

wall of the circular pipe and interior walls of the mixing

elements inserted in the pipe. The Reynolds number (Re)

is defined by , where is the average inlet

velocity. To investigate the effect of inertia on the mixing,

flows in a range of Reynolds number, , are

solved.

In the mixing analysis, we solve a steady mass transport

equation, given by,

in Ω (3)

where c is the concentration, the diffusivity (in this

study, m2/s). The boundary conditions for the

inlet, the solid wall, and the outlet are as follows:

on Γi, (4)

on Γw, (5)

on Γo (6)

where cin is the prescribed concentration at the inlet and n

the outward unit normal vector at the boundary. As for the

boundary condition at the inlet (Γi), assuming that only

one of the two fluids contains a solute, cin = 1 for the fluid

introduced through the left semicircle and cin = 0 for the

fluid entering through the other semicircle. The total mass

flux at the wall is zero (Eq. (5)) and the diffusive flux

through the outlet is zero (Eq. (6)). The Péclet number

(Pe), the ratio between the convective transport to the dif-

fusive transport, is defined by .

In simulations, we used approximately 100 million

unstructured tetrahedral and prism elements to discretize a

computational domain, which enables us to obtain a stable

numerical solution for the convection-dominant case in

which the Péclet number is very high (in this study,

). To treat the convection terms in the

two problems, a higher order scheme in ANSY-CFX 18.0

is employed. We used a machine with two octa-core pro-

cessors (Intel(R) Xeon(R) CPUs E5-2680 2.70GHz) and

128 GB memory to perform parallel computations for the

flow and mixing problems. In particle tracking to plot

Poincaré sections, a 4th order Runge-Kutta method is

employed to integrate the velocity obtained as a solution

for the flow problem in a periodic domain.

2.3. Quantitative measure of mixingOne needs a quantitative measure of mixing to assess

the mixing performance of a mixing protocol. To charac-

terize the mixing in the BPPMs, as used in previous stud-

ies (Kang et al., 2008; Kang and Anderson, 2014), the

intensity of segregation (Danckwerts, 1952) is employed

as a measure of mixing. The intensity of segregation (Id)

is calculated using a cross-sectional distribution of the

concentration, defined by

(7)

where is the average concentration in a cross section

Ωc and the variance of the concentration in the cross

section, given by

. (8)

Since we are concerned with equal volume mixing,

in this study. In a completely segregated (i.e.,

unmixed) state, Id = 1. While, in a completely mixed state,

where , Id = 0. As the mixing progresses, the inten-

sity of segregation decreases, that is the deviation of the

concentration from its average value decreases and the

concentration becomes more and more uniform.

3. Results

3.1. Flow characteristicsFigures 3 and 4 depict cross-sectional velocity vectors of

BPPMs with two mixing protocols (co-rotational and

counter-rotational BPPMs) at the four Reynolds numbers,

2( ) pρ μ⋅∇ = −∇ + ∇u u u

0∇⋅ =u

Re = ρuD/μ u

0.1 Re 300≤ ≤

( ) 0c c∇ ⋅ ∇ − ⋅∇ =uD

D11

10−

=D

inc c=

( ) 0c c⋅ − ∇ + =n uD

0c⋅ ∇ =n D

Pe /uD= D

4 710 Pe 3 10≤ ≤ ×

2

(1 )

c

dI

c c

σ

=

−

c

σc

2

σc

2 =

1

Ac

----- Ω

c

∫ c x( ) c–( )2

dA

0.5c =

c c=

Fig. 2. (Color online) The geometry of a co-rotational BPPM

consisting of six periodic units. The black arrow indicates the

direction of the flow.



Re = 1, 10, 100, and 300. In the two cases, the dimen-

sionless height of the barrier (β) is 0.5. The axial location

of the cross section is 0.75Lp from the inlet of the first

periodic unit. Assuming equal volume mixing, two fluids

(red and blue fluids in Figs. 3 and 4) are introduced

through the inlet with the two-fluid interface directed ver-

tically. As the Reynolds number increases, the strength of

the rotational motion also increases in both cases, which

can be identified by the velocity vectors and the defor-

mation of the interface between the two fluids. As such,

the mixing state at a specific cross section will be highly

influenced by the Reynolds number of the flow. It should

be noted that, when only one periodic unit is used with

periodic boundary conditions, back flow is observed at the

outlet of the periodic domain, as the Reynolds number

increases. In such a case, one cannot solve the mass trans-

port equation (Eq. (3)) using the periodic domain, since

the concentration at an inflow boundary, where ,

is unknown. Due to this back flow, we choose a compu-

tational domain composed of six periodic units instead of

using one periodic unit as a computational domain in mix-

ing analysis.

To demonstrate the flow systems in the BPPMs, we plot

Poincaré sections for the three mixing protocols, co-rota-

tional, mirrored co-rational, and counter-rotational BPPMs,

at three Reynolds numbers, Re = 0.1, 10, and 100. Figure

5 depicts the Poincaré sections for the BPPMs with the

two geometrical parameters fixed at α = 1 and β = 0.65.

As for the mixing in the BPPMs composed of the three

mixing protocols, the following conjectures can be made

from the Poincaré sections:

(i) The co-rotational BPPM with β = 0.65 is an effi-

cient mixing protocol in the low Reynolds number,

Re = 0.1, since the chaotic area in the co-rotational

BPPM is the largest among the three protocols.

(ii) As the Reynolds number increases, the co-rota-

tional mixing protocol with β = 0.65 becomes less

efficient due to the increase in the area surrounded

by Kolmogorov–Arnold–Moser (KAM) boundar-

ies, where mixing is regular.

(iii) The mirrored co-rotational protocol with β = 0.65,

the worst mixing protocol at Re=0.1, is expected to

show enhanced mixing in the higher Reynolds num-

ber, Re = 100, since the KAM boundaries observed

in the lower Reynolds number flows are disap-

peared completely.

(iv) For the same reason as the case with the mirrored

co-rotational protocol with β = 0.65, the counter-

rotational protocol with β = 0.65 is also expected to

be an efficient one at the higher Reynolds number

(Re = 100).

The above-mentioned points can be confirmed by con-

ducting in-depth mixing analyses for the BPPMs, which

we will introduce in the following section.

3.2. Mixing analysisThe concentration distribution at a cross section of a

BPPM, obtained as a solution of the convection-diffusion

problem, qualitatively represents a mixing state. In mixing

analysis, the dimensionless height (β) is varied from 0.35

to 0.65 and the Reynolds number (Re) from 0.1 to 300.

Figures 6, 7 and 8 show the evolution of the concentration

for the three mixing protocols, influenced by the three

design parameters, the mixing protocol, β, and Re. A sub-

script in the concentration plots indicates the spatial period

0⋅ <u n

Fig. 3. (Color online) Instantaneous cross-sectional velocity vec-

tors of the co-rotational BPPM at the four Reynolds numbers,

Re=1, 10, 100, and 300. The contour represents the cross-sec-

tional concentration distribution, showing the deformation of the

interface between the two fluids. The white area in the figure

indicates the mixing element inserted in the circular pipe.

Fig. 4. (Color online) Instantaneous cross-sectional velocity vec-

tors of the counter-rotational BPPM at the four Reynolds num-

bers, Re=1, 10, 100, and 300.



where the concentration is plotted (i.e., Ci indicates the

concentration at the ith period). The areas surrounded by

KAM boundaries (depicted in Fig. 5) are well matched

with unmixed zones (red and blue regions in the concen-

tration C6). From Fig. 6, one can find that the co-rotational

BPPM with β = 0.65 shows the best mixing performance

Fig. 5. Poincaré sections of the three mixing protocols for a set of the two geometrical parameters, α = 1 and β = 0.65, when Re=0.1,

10, and 100.

Fig. 6. (Color online) Change of the concentration distribution in the co-rotational BPPMs. Ci represents the concentration at the end

of the ith period.



at Re=0.1, but becomes less efficient as Re increases.

However, inertia has a positive influence on mixing in the

BPPM when β = 0.35. In the case of the mirrored co-rota-

tional BPPM, regardless of the value of β, mixing at

Re = 100 is much better than that in the creeping flow

regime (See Fig. 7). As depicted in Fig. 8, the influence of

Re on mixing in the counter-rotating BPPM seems to be

similar to that observed in the mirrored co-rotational

BPPM.

To quantitatively characterize the mixing performance in

terms of compactness (i.e., the length of a mixer), we cal-

culate the intensity of segregation (Id) at the end of each

Fig. 7. (Color online) Change of the concentration distribution in the mirrored co-rotational BPPMs.

Fig. 8. (Color online) Change of the concentration distribution in the counter-rotational BPPMs.



period. Figures 9, 10, and 11 show Id as a function of the

dimensionless channel length (z* = z/D) for the three mix-

ing protocols at several Reynolds numbers. Each plot

depicts the quantitative evolution of the mixing state in a

BPPM at a specific value of β, affected by the Reynolds

number. Figure 9 shows the change of Id along the z-direc-

tion in the co-rotational BPPMs. When , Id decreases

along the downchannel direction, but the decrease rate is

not significant. One can find that the best mixing in this

mixing protocol is achieved when β = 0.65 and Re = 0.1.

0.5β ≤

Fig. 9. (Color online) The change of the intensity of segregation

(Id) in the co-rotational BPPM along the down-channel direction

affected by the Reynolds number for the three values of the

dimensionless barrier height, (a) β = 0.35, (b) β = 0.5, and (c)

β = 0.65.


(Id) in the mirrored co-rotational BPPM along the down-channel

direction affected by the Reynolds number for the two values of

the dimensionless barrier height, (a) β = 0.35 (b) β = 0.5, and (c)

β = 0.65.



Thus, the co-rotational BPPM is an efficient mixer in the

creeping flow regime. For the co-rotational BPPM with

β = 0.65, mixing in higher Reynolds numbers ( ) is

poorer than that in the creeping flow regime, implying

that, the increase of the Reynolds number in this mixing

protocol does not always lead to an enhanced mixing

within the range of the Reynolds number investigated in

this study.

Interestingly, however, the mirrored co-rotational BPPMs

working at Re = 300 show a significant enhancement in

mixing performance (See Fig. 10). According to the pre-

vious study on the mixing in the BPPM working in the

creeping flow regime, regardless of the geometrical param-

eters, mixing in the mirrored co-rotational BPPM is infe-

rior to that of the co-rotational design (Jung et al., 2018).

Even at the lowest barrier height (β = 0.35), one can

achieve good mixing at the higher Reynolds number

(Re = 300), indicating that the mirrored co-rotational design

can be employed as an efficient mixer at higher Reynolds

number flows. Mixing in counter-rotational BPPMs is

depicted in Fig. 11. When β = 0.35, mixing is not signif-

icant in the investigated range of Re. At each β, the fastest

decrease of Id is observed at the highest Reynolds number

(Re = 300). At higher values of β ( ), increasing Re

leads to a noticeable mixing enhancement. Counter-rota-

tional mixing protocol is a poor mixing protocol in the

creeping flow regime. An efficient mixing at the higher

Reynolds number flow can be achieved with higher bar-

rier height. In low Reynolds number flows of the counter-

rotational BPPMs, increasing the barrier height is not an

option to achieve enhanced mixing.

From the mixing analysis, we found that mixing in the

co-rotational BPPM has an irregular dependency on the

Reynolds number. In this regard, we plot the intensity of

segregation at the end of the 6th period (in this study, the

final mixing state) as a function of Reynolds number (see

Fig. 12). The co-rotational BPPM with β = 0.65 is the best

mixer in the creeping flow regime, a conclusion also

drawn in our previous work (Jung et al., 2018). The mir-

rored co-rotational BPPMs show an efficient mixing only

at Re = 300. The counter-rotational BPPM with β = 0.65

is the best mixer in the higher Reynolds number regime,

. Therefore, the co-rotational design of the

BPPM, which is superior to the other two designs in the

lower Reynolds number regime ( ), is inferior

to its counterparts in the higher Reynolds number regime.

In the mirrored co-rotational and counter-rotational

BPPMs, Id increases slightly with the Reynolds number,

when . Then, it shows a sudden decrease,

when .

We also investigated the influence of the barrier height

on the final mixing state. Figure 13 shows the intensity of

segregation at the final period (6th period) as a function of

the dimensionless barrier height. As for the co-rotational

and mirrored co-rotational BPPMs, there is no regular

dependency of the dimensionless height β on mixing. In

the counter-rotational BPPM, on the other hand, the inten-

sity of segregation is decreasing at all the Reynolds num-

bers, as the dimensionless height increases. A rapid

Re 100≥

0.5β ≥

100 Re 300≤ ≤

0.1 Re 10≤ ≤

0.1 Re 10≤ ≤

100 Re 300≤ ≤


(Id) in the counter-rotational BPPM along the down-channel

direction affected by the Reynolds number for the three values of

the dimensionless barrier height, (a) β = 0.35, (b) = 0.5, and (c)

β = 0.65.



decrease in Id is observed when . Based on the

mixing results presented so far, we can conclude that, in

terms of the compactness of the BPPM, the co-rotational

BPPM is an efficient mixer in the creeping flow regime

and, in the higher Reynolds number regime, the mirrored

co-rotational and the counter-rotational BPPMs are supe-

rior to the co-rotational BPPM.

Finally, we assessed the mixing performance of the

BPPM in terms of energy consumption measured by the

dimensionless pressure drop ΔP*, defined by ,

where ΔP0 is the pressure drop in the empty pipe with the

Re 100≥

ΔP* = ΔP/ΔP0

Fig. 12. (Color online) The intensity of segregation at the end of

the 6th period as a function of the Reynolds numbers. (a) Co-

rotational BPPM, (b) mirrored co-rotational BPPM, and (b)

counter-rotational BPPM.

Fig. 13. (Color online) The intensity of segregation at the end of

the 6th period as a function of the dimensionless barrier height at

six Reynolds numbers, Re=0.1, 1, 10, 100, and 300. (a) Co-rota-

tional BPPM, (b) mirrored co-rotational BPPM, and (c) counter-

rotational BPPM.



same diameter and length as those of the corresponding

BPPM. We plot the intensity of segregation as a function

of the dimensionless pressure drop for the two Reynolds

numbers, Re = 0.1 and 300 (See Figs. 14 and 15). As

depicted in Fig. 14, from the viewpoint of energy con-

sumption, the co-rotational BPPM with β = 0.65 is again

the best mixer in the creeping flow regime. The mirrored

co-rotational protocol is the poorest among the three pro-

tocols, without showing any noticeable change in Id with

β.

When Re = 300, Id shows more significant variation

with β compared to the cases when Re = 0.1. The sensi-

Fig. 14. (Color online) The intensity of segregation in terms of

the pressure loss at Re=0.1 for the three mixing protocols, (a) co-

rotational, (b) mirrored co-rotational, and (c) counter rotational

BPPMs.

Fig. 15. (Color online) The intensity of segregation in terms of

the pressure loss at Re=300 for the three mixing protocols, (a)

co-rotational, (b) mirrored co-rotational, and (c) counter rota-

tional BPPMs.



tivity of Id to the change of β is the highest in the mirrored

co-rotational BPPM (see Fig. 15b). It should be noted that

the decrease rate of Id is the largest in the mirror co-rota-

tional BPPM with β = 0.35. Meanwhile, Id at the final

period is the smallest in the counter-rotational BPPM with

β = 0.65. Extrapolating from the decrease rate of Id, the

mirrored co-rotational BPPM with β = 0.35 is turned out

to be the best mixer in terms of energy consumption. In an

application, where mixing cost is not an issue of the first

importance but the mixing performance is the most critical

issue, the counter-rotational BPPM with β = 0.65 is the

best mixer at this Reynolds number.

4. Conclusion

We investigated the flow and mixing characteristics of a

barrier-embedded partitioned pipe mixer (BPPM) in a

laminar flow regime, where the Reynolds number is in a

range of . Poincaré sections for the three

mixing protocols, co-rotational, mirrored co-rotational,

and counter-rotational BPPMs, are plotted to gain insight

into the flow systems in the three mixing protocols. In

mixing analysis, we focused on the effect of the Reynolds

number, the mixing protocol, and a dimensionless barrier

height on the progress of mixing in the BPPMs. First,

mixing is characterized in terms of the compactness. In a

low Reynolds number regime ( ), co-rotational

BPPMs exhibit a superior mixing performance to that of

the other two BPPMs. As the Reynolds number increases,

however, mirrored co-rotational and counter-rotational

BPPMs show better mixing compared to that of co-ratio-

nal BPPMs. As for the geometrical parameters, we fixed

the aspect ratio of the plate (α) and changed the dimen-

sionless height of the barrier (β) from 0.35 to 0.65 in

increments of 0.15. In the case of co-rational BPPMs

working in the creeping flow regime, mixing is best when

β = 0.65. Meanwhile, in the cases of mirrored co-rota-

tional and counter-rotational BPPMs, the influence of βon mixing is not significant in the creeping flow regime.

In the higher Reynolds number regime, however, the

higher β the faster mixing in the counter-rotational BPPM.

The mirrored co-rotational BPPM, which is the poorest

mixer in the creeping flow regime, turned out to be an

efficient mixer in the higher Reynolds number. From the

viewpoint of energy consumption (measured by the pres-

sure drop), the co-rotational BPPM and the counter-rota-

tional BPPM, both with β = 0.65, are found to be best

mixers in the creeping flow regime and the higher Reyn-

olds number regime, respectively. The application of the

BPPMs to non-Newtonian fluids, a wider range of Reyn-

olds number covering turbulent flow regime, and a more

extensive parameter study will be subjects of our future

work.

Acknowledgement

This work was supported by the National Research

Foundation of Korea (NRF) grant funded by the Korean

government (No. 2015R1D1A1A01057691), and the Korea

Institute of Energy Technology Evaluation and Planning

(KETEP) and the Ministry of Trade, Industry & Energy

(MOTIE) of the Republic of Korea (No. 20141010101880).

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