Chemical Engineering Science 202 (2019) 146–156
Contents lists available at ScienceDirect
Chemical Engineering Science
journal homepage: www.elsevier.com/locate/ces
Dynamic analysis of a continuous-flow microwave-assisted screw
propeller system for biodiesel production
Jinghua Ye a,b, Huacheng Zhu a,⇑, Yang Yang a, Kama Huang a, G.S. Vijaya Raghavan b
a
b
College of Electronics and Information Engineering, Sichuan University, Chengdu 610065, China
Department of Bioresource Engineering, Macdonald Campus, McGill University, 21111 Lakeshore Road, Sainte-Anne-De-Bellevue, Quebec H9X 3V9, Canada
h i g h l i g h t s
Biodiesel synthesis is carried out in a microwave-assisted screw propeller system.
Model for biodiesel in the microwave-assisted screw propeller system is developed.
The heating and reaction dynamic inside of the reactor are obtained.
Many factors such as rotation speed, material composition and pitch was analyzed.
The proposed reactor can be used as a large-scale preheater for chemical synthesis.
a r t i c l e
i n f o
Article history:
Received 13 June 2018
Received in revised form 8 March 2019
Accepted 12 March 2019
Available online 15 March 2019
Keywords:
Microwave heating
Heating uniformity
Multi-physics simulation
Screw propeller
Continuous-flow reactor
Biodiesel synthesis
a b s t r a c t
In order to overcome the apparent limitations of large-scale microwave processing, a microwave heating
system with a screw propeller was utilized for biodiesel synthesis. To elucidate the heating dynamics and
reaction process in the reactor, a comprehensive physics-based model was developed. A step-by-step
algorithm based on implicit function, level set methods, and Arbitrary Lagrangian-Eulerian
Formulation (ALE) machinery was proposed to compute the microwave heating process with chemical
reaction and stirring. Material properties applied in the simulation were expressed as bivariate functions
of the reaction solution’s component and temperature. The temperature and reactant concentration of
the microwave reactor outlet were measured and compared to simulation results to validate the simulation model. By using the proposed model, the heating process with different rotating speeds, material
composition (Teflon and metal), pitch, and blade widths of the screw propeller and inlet velocities were
also calculated to determine their effect on the temperature distribution of the reactor.
Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction
As a new renewable energy, biodiesel has been found to possess
numerous advantages, such as high efficiency, ruggedness, and
positive environmental impact, which appears more likely to
replace traditional fuels on a large scale (Leung et al., 2010;
Shahid & Jamal, 2011). Recently, the utilization of microwave heating on biodiesel production has gained increasing attention,
because compared to conventional heating methods, microwave
heating offers the potential to reduce reaction time dramatically,
to increase product yields, and enhance product purities
(Lidström et al., 2001; Motasemi & Ani, 2012). A large number of
studies on microwave-assisted biodiesel production have been
reported (Hernando et al., 2007; Leadbeater & Stencel, 2006;
⇑ Corresponding author.
E-mail address: hczhu@scu.edu.cn (H. Zhu).
https://doi.org/10.1016/j.ces.2019.03.022
0009-2509/Ó 2019 Elsevier Ltd. All rights reserved.
Motasemi & Ani, 2012). However, insufficient depth of penetration
of microwaves is still limiting the large-scale industrial applications of microwave processing biodiesel (Glasnov & Kappe, 2007).
The rapid heating and cooling profiles obtained on a small scale
in high power-density single-mode cavities will disappear when
the materials are processed in a multimode instrument in large
scale (Damm et al., 2009). Meanwhile, thermal runaway (uncontrollable temperature rise due to strong dielectric loss and temperature positive feedback of the material) and hot spot (huge
temperature gradient at a given location) caused by an inhomogeneous electromagnetic field distribution will further constrain
microwave scale-up technology (Horikoshi et al., 2011; Santos
et al., 2011).
In order to overcome the apparent limitations of large-scale
microwave processing, the continuous flow processing approach
has been widely accepted for reinstating the benefits of smallscale microwave heating. (Glasnov & Kappe, 2007; Strauss, 2009).
J. Ye et al. / Chemical Engineering Science 202 (2019) 146–156
147
Nomenclature
C
T
R
E
Cp
C pt
k
kt
k0
p
I
rbp
x
w
r0
ri
rp
l
h
Pd
u
concentration
temperature (°C)
universal gas constant
electric field (V/m)
specific heat capacity of the reaction solution (J/(kg°C))
specific heat capacity of Teflon (J/(kg°C))
thermal conductivity of the reaction solution
(W/(m°C))
thermal conductivity of Teflon (W/(m°C))
wave number in vacuum (rad/m)
pressure (Pa)
unit matrix
rotation axis vector
position vector
rotating speed of the screw propeller (rpm)
outer radius of the screw propeller (mm)
inner radius of the screw propeller (mm)
inner diameter of the pipe
length of X direction of the screw propeller (mm)
thickness of the screw blade (mm)
power dissipated (W)
fluid velocity
Numerous successful examples of microwave-assisted continuous
flow processing have been reported (Barnard et al., 2007;
Choedkiatsakul et al., 2015; Lertsathapornsuk et al., 2008; Tangy
et al., 2017). However, thermal runaway and hot spots still exist
in microwave continuous-flow reactors, especially when the size
of the reactor increases to a certain extent. To get over this problem, some methods have been proposed, including: changing the
electromagnetic field distribution during heating, such as using
the resonance phenomenon, employing various microwave frequencies, and adding a mode stirrer (Antonio & Deam, 2005;
Campañone et al., 2014; Sebera et al., 2012); and redistributing
heat by changing the location of the reactants, such as utilizing a
stirrer in the reactor (Obermayer et al., 2013). Generally, for microwave continuous-flow reactors, the latter method is considered as
the most commonly used and effective method. In our previous
study, a new type of microwave continuous-flow reactor with a
screw propeller was designed for heating a single liquid material,
whose heating uniformity was greatly improved when compared
to the case without stirring (Zhu et al., 2017). Therefore, it can be
expected that synthesizing biodiesel in this reactor should have a
positive outcome. As we know, the heating and reaction dynamics
analysis of the biodiesel synthesis process is critical to control the
reaction conditions and confirm reaction progress. However, the
temperature and reactant concentration inside of the reactor are
difficult to measure under the stirring condition, which necessitates the use of a multi-physical field simulation to elucidate the
heating and reaction dynamics. In our previous study, the heating
process of a single liquid material with stirring in a microwave
continuous-flow reactor was successfully simulated (Zhu et al.,
2017). However, for a chemical reaction, the concentration of the
reactants will be constantly changing, which means the expression
of the reaction mixture parameters and the coupling of different
physical fields during the calculation will be much more complicated than those of a single material. Due to the complexity
described above, a numerical simulation of the biodiesel synthesis
process in microwave continuous-flow reactors with a stirrer has
not been reported yet. Hence, using our designed reactor for biodiesel synthesis and simulating the heating process under such
complex conditions are meaningful.
k1
k1
A1
A1
Eaf
Era
forward reaction rate constant
reverse reaction rate constant
pre-exponential factor of forward reaction
pre-exponential factor of reverse reaction
activation energy of forward reaction
activation energy of reverse reaction
Greek symbols
e0r
real part of the relative effective permittivity
e00r
imaginary part of the relative effective permittivity
q
density of the liquid (kg/m3)
qt
density of Teflon (kg/m3)
l
dynamic viscosity (Pas)
e0
vacuum permittivity, 8.8541878171012 (F/m)
e
complex relative permittivity
lr
relative permeability
x0
angular frequency (rad/s)
r
electrical conductivity (S/m)
x
angular displacement
g
turn number of the screw propeller
In this paper, biodiesel synthesis is carried out in a continuousflow microwave-assisted screw propeller system with oleic acid
and methanol. A step-by-step algorithm based on implicit function,
level set methods, and Arbitrary Lagrangian-Eulerian Formulation
(ALE) machinery will be developed to compute the microwave
heating process with chemical reaction and stirring. The effective
permittivity of the reaction solution will be described as a bivariate
function with the concentration of one reactant and temperature.
The temperature and reactant concentration of the microwave
reactor outlet were measured and compared to simulation results
to validate the simulation model. Moreover, we also calculated the
heating conditions with different rotating speeds, material composition (Teflon and metal), pitch, and blade widths of the screw propeller and inlet velocities, which provides the observation of their
effect on the temperature distribution in the reactor.
2. Methods
2.1. Experimental
Since the dielectric properties of low purity reactants are difficult to characterize, in order to obtain an easier model to simulate,
one can only consider the reaction between a pure fatty acid and
methanol as a method to obtain biodiesel. As a typical fatty acid,
oleic acid is applied to produce biodiesel using methanol with concentrated sulfuric acid as the catalyst. The molar ratio of methanol
to oleic acid is 6:1, and the mass fraction of concentrated sulfuric
acid is 1% of the whole reaction solution (Peng, 2009). The oleic
acid was obtained from the Chengdu Kelong Chemical Reagent Factory. Methanol and concentrated sulfuric acid were provided by
the Chengdu Changlian Chemical Reagent Co., Ltd. All of the chemicals are in analytical reagent grade.
The schematic diagram and the photograph of the experimental
system are shown in Fig. 1, where the manufacturers of the components of the microwave heating system were described in (Zhu
et al., 2017). The microwave frequency is 2.45 GHz, and the effective microwave power (1255 W) is measured by a directional coupler and a microwave power meter before performing the
148
J. Ye et al. / Chemical Engineering Science 202 (2019) 146–156
Fig. 1. (a) Schematic diagram of the experimental system. (b) A photo of experimental system.
experiment. The purpose of the frequency converter is to control
the rotating speed of the motor to stabilize at 5 rpm, which means
the rotating speed of the screw propeller is 5 rpm. The flow velocity at the entrance is 27.8 mL/s, and the initial inlet fluid is a wellmixed chemical reaction solution. The whole heating process lasts
for 240 s. The flow is divided into eight tributaries at the outlet, and
the temperature of the eight tributaries is measured by optical
fibers (FISO FOT-NS-967A, FISO Technologies, Quebec, Canada),
which were recorded at an interval of 10 s by the FISO OSR-4 workstation. Also, we extract the reaction solution from the fluid collection platform of the system of every 60 s, and then cool it down
immediately. Then, phenolphthalein is used as an indicator to perform the acid value titration for the liquid from the oil phase after
the mixture is stratified (Standardization, 2009). According to the
change of acid value before and after the reaction, the mass conversion rate of oleic acid can be calculated.Fig. 2.
2.2. Modelling
The 3D geometry of the above experimental system is developed in commercial finite element software, COMSOL Multiphysics
(5.1, COMSOL Inc., Stockholm, Sweden). The dimension of the calculation model can be found in Fig. 1(a).
The effective permittivity of the reaction solution, as a key
parameter for simulation of microwave heating, is described as a
bivariate function with the concentration of one reactant and temperature in this paper, which was shown in (Zhu et al., 2012):
e0r ðC; TÞ ¼
ðT=T 0 Þa ðCÞ 0T 0 ðCÞ
e
0
eb ðCÞðTT 0 Þ r
ð1Þ
e00r ðC; TÞ ¼
ðT=T 0 Þa ðCÞ 00T 0 ðCÞ
e
00
eb ðCÞðTT 0 Þ r
ð2Þ
0
00
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J. Ye et al. / Chemical Engineering Science 202 (2019) 146–156
Fig. 2. Diagrams of the effective permittivity of biodiesel reaction solutions varying with temperature and concentration: (a) imaginary part, (b) real part.
where e0r ðC; TÞand e0r ðC; TÞare respectively the real and imaginary
part of the relative effective permittivity of the reaction solution
under any temperature, while er 0 and er 0 are under a constant
temperature T0; and a0 ðCÞ, a00 ðCÞ and b0 ðCÞ, b00 ðCÞare functions of
concentration of a reactant, which are determined by experiments.
In this paper, T0, a0 ðCÞ, a00 ðCÞ andb0 ðCÞ, b00 ðCÞ were obtained from our
previous work, and diagrams of the effective permittivity of biodiesel reaction solutions varying with temperature and concentration
are shown as follows (Wu et al., 2013).
For the other properties, specific heat capacity, density,
dynamic viscosity and thermal conductivity also vary with the
solution’s temperature and reaction component in the simulation.
These properties of the mixture are averages of the properties of
different components (as a function of temperature) weighted by
their mass fractions (as a function of concentration) (Wu et al.,
2013). Table 1 summarizes the material properties used for computations (Kaye, 1995; Zhang et al., 2016). The initial temperature
is 20 °C. Liquids used in this work are incompressible Newtonian
fluid. Considering the dimensions of the pipe and the rotating
speed of the screw propeller, the Reynolds Number was found to
be less than 500 indicating the fluid flow inside of the pipe to be
laminar (Batchelor, 2000).
For the multi-physics calculation of the microwave continuous
flow processing of the chemical reactions, Maxwell’s equations,
heat conduction equation, Navier-Stokes equation, and chemical
reaction kinetics equation were inter-coupled. The electromagnetic
field was calculated in the frequency domain as governed by Maxwell’s wave form equation:
0T ðCÞ
00T ðCÞ
2
r l1
r ðr EÞ k0 ðe jr=x0 e0 ÞE ¼ 0
ð3Þ
Referring to (Ye et al., 2017; Zhu et al., 2017), by employing
implicit functions and level set methods, when the screw propeller
is rotating, the position of the reaction solution Ur ðx; y; z; tÞ can be
expressed as:
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi
y 2 þ z2 < r p
!
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð y2 þ z2 < r0 Þ ð y2 þ z2 > r i Þ ðy=z > tanðð2pxg þ w tÞ=lÞ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðy=z < tanðð2pðx þ hÞg þ w tÞ=lÞ þ ð y2 þ z2 < r i Þ
Ur ðx; y; z;tÞ ¼
ð4Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
where
y2 þ z2 < r p represents the space inside of the pipe, and
the remaining item represents the space occupied by the screw propeller at time t. Then, by using the obtained electric field and imaginary part of the relative effective permittivity of the reaction
solution, the local power dissipated inside of the pipe can be
expressed as (Santos et al., 2011):
Pd ¼ 0:5x0 e0 e00r ðC; TÞ Ur ðx; y; z; tÞ jEðx; y; z; tÞj2
ð5Þ
The temperature, velocity and reaction process were calculated
in the time domain. The flow of the reaction solution in the pipe
can be calculated from the Navier-Stokes equation and the mass
conservation equation (continuity equation) (Niu et al., 2016):
q @u=@t þ qðu rÞu ¼ r ½pI þ lðru þ ðruÞT Þ 2=3 lðr uÞI
ð6Þ
@ q=@t þ r ðquÞ ¼ 0
ð7Þ
The liquids stick to the walls of the screw and barrel, requiring a
‘‘no-slip” boundary condition at the walls. The pressure at the outlet of the reactor is set to zero, which means that there is no resistance at the outlet (Yang et al., 2017). The stirring process caused
by the screw propeller is achieved by invoking the Arbitrary
Lagrangian-Eulerian Formulation (ALE) machinery (Zhu et al.,
2017).
dx ¼ dxðrbp ; x; tÞ; dx=dt ¼ w
ð8Þ
Table 1
Summary of material properties applied in the simulation.
Parameter
Methanol
Oleic acid
Methyl oleate
Water
Teflon
Specific heat
capacityðC p ; J=ðkg KÞÞ
486.073 + 4.893 * T
739.852 + 4.147 * T
165.150 + 4.221 * T
5735.929–9.699 * T + 0.0151 * T2
1050
Densityðq; kg=m3 Þ
Thermal
conductivityðk; W=ðm3 KÞ
Dynamic viscosityðl; Pa sÞ
1072.809–0.959 * T
0.2090–0.000353 * T
1100.15–0.698 * T
0.3292–0.000331 * T
1091.736–0.744 * T
0.1314–0.000106 * T
1120.313–0.422 * T
0.2485 + 0.00118 * T
2200
0.24
0.0000724 + 0.0495
* exp(T/64.214)
0.00249 + 1663.122
* exp(T/26.876)
0.00129 + 130.427
* exp(T/28.949)
0.000250 + 17.711
* exp(T/29.205)
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J. Ye et al. / Chemical Engineering Science 202 (2019) 146–156
of the chemical reaction field, ‘‘no-flux” boundary conditions are
applied to all of the species of the reaction solution at the walls of
the screw and reactor. The boundary condition at the outlet is set
as ‘‘outflow”, which means that no solution will flow back from
the outlet (Pan et al., 2019).
A step-by-step algorithm is adopted to simulate the heating
process. The time step is set as 1 s, which means that the permittivity inside of the pipe is updated once the screw propeller rotates
30° (Zhu et al., 2017). In the COMSOL simulation, the calculation of
the electromagnetic field is realized by using the RF Module with
the PARDISO direct solver. Fluid velocity, stirring, heat transfer,
and chemical reaction are solved using the Laminar Flow module,
Moving Mesh module, Heat Transfer in Fluids module, and Transport of Concentrated Species module, respectively, using the Fully
Coupled solving method with a MUMPS direct solver. The procedure followed for solving the coupled problem is schematically
depicted in Fig. 3. A tetrahedral mesh with 285,918 elements is
used (Fig. 4) based on a mesh convergence analysis, which ensures
that any dependent variable did not change by more than 1% of the
total change when the element size was reduced by half (Gulati
et al., 2016).
The temperature distribution of the screw propeller is governed
by heat conduction in the solid (Eq. (9)), while the temperature distribution of the reaction solution is governed by heat conduction
and convection in the fluid (Eq. (10)).
qt C pt @T=@t ¼ kt r2 T
ð9Þ
qC p @T=@t þ qC p u rT ¼ kr2 T þ Pd
ð10Þ
The inlet thermal boundary is set to a constant temperature of
20 °C which is the same as the room temperature. The outlet thermal boundary is set as ‘‘outflow”, and other thermal boundaries are
set as ‘‘thermal insulation”. The chemical reaction of biodiesel synthesis by oleic acid and methanol follows a second-order reversible
kinetics. Using the concentration of water to represent those of
oleic acid, methanol and biodiesel, the kinetics of the biodiesel
reaction can be written as (Wu et al., 2013):
dðC 0RCOOH C H2 O Þ
¼ k1 ðC 0RCOOH C H2 O ÞðC 0CH3 OH C H2 O Þ k1 C 2H2 O
dt
ð11Þ
where C 0RCOOH and C 0CH3 OH are the initial concentrations of oleic acid
and methanol respectively; and C H2 O is the concentration of water.
The forward reaction rate constant k1 and the reverse reaction rate
constant k1 both satisfying the Arrhenius equation:
k1 ¼ A1 expðEaf =RTÞ
ð12Þ
k1 ¼ A1 expðEra =RTÞ
ð13Þ
3. Results and discussion
3.1. Model validation
The temperature of the eight tributaries obtained by simulation
and that obtained by the experiment are compared in Fig. 5. As can
be seen in Fig. 5, the simulated temperatures reach a steady state
earlier than the measured temperatures. This may be due to the
insufficiency of the alternating voltage used for the peristaltic
where the pre-exponential factor A1, A1 and activation energy Eaf ,
Era are provided in Table 2 (Peng, 2009). For the boundary conditions
Table 2
Parameters for the reaction kinetics.
Parameter
Value
C 0RCOOH
1.78 mol/L
C 0CH3 OH
10.73 mol/L
Forward reaction
Reverse reaction
A1
Eaf
A1
Era
743.6
33.8 kJ/mol
0.606
13.9 kJ/mol
Fig. 3. The calculation flow chart.
J. Ye et al. / Chemical Engineering Science 202 (2019) 146–156
151
Fig. 4. Meshed (a) general geometry and (b) the reactor and the screw propeller with tetrahedral mesh elements.
pump and motor, making the pumping speed and the rotating
speed of the screw propeller unable to reach the anticipated value
in the actual heating process. In addition, it can be observed that
the fluctuations with alternations of positive and negative slopes
only appear in the simulated temperatures. This is probably attributable to the fact that the simulated temperatures were obtained
from the outlet, whose temperature will be reduced when the
blade of the screw propeller (which does not absorb microwaves)
passed by. However, the measured temperatures were obtained
from the average temperature of the entire export tributary, and
thus the fluctuation of the temperature will be weakened. By comparing the simulated and experimental data, the average relative
errors of the temperature of the tributary 1–8 are 2.85%, 2.28%,
2.27%, 2.30%, 2.30%, 1.80%, 2.60%, and 2.80%, respectively, as shown
in Fig. 5. In general, the measured temperatures exhibit a good
agreement with the simulated results, which validates the effectiveness of the proposed model.
Fig. 6 shows the mass fraction of oleic acid of the reaction solution from the outlet during the heating process of the simulation
and experiment. In Fig. 6, for the simulation data, the mass fraction
of oleic acid of the reaction solution is obtained from the average
value of eight tributaries. For the experimental data, the reaction
solution that was used to detect the mass fraction of oleic acid is
extracted from the fluid collection platform, which is also a mixture of eight tributaries. One can observe from Fig. 6 that the
experimental result is higher than the simulated result at the
beginning of the heating process, which may be due to the fact that
the temperature of the experiment rises more slowly than that of
the simulation. As the heating process proceeds, however, the measured result gets closer to the simulated one. In addition, when the
Fig. 5. The temperature of the eight outlets obtained by simulation and experiment. (a)–(h) corresponds to 1–8 tributaries, respectively (refer to Fig. 1(a)).
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J. Ye et al. / Chemical Engineering Science 202 (2019) 146–156
Fig. 6. The mass fraction of oleic acid obtained by simulation and experiment.
acid value is measured by titration, due to man-made experimental
error, the dosage of alkali is easy to overdose, resulting in a slightly
higher acid value. Therefore, the mass fraction of oleic acid
obtained by the experiment will be slightly higher than that
obtained by the simulation. Nevertheless, considering the overall
trend, the simulated and experimental results shown in Fig. 6 are
in a fairly good agreement, which further confirms that the proposed model is effective.
3.2. Analysis of temperature, mass fraction, and reaction rate inside of
the reactor
Fig. 7 shows the temperature, mass fraction, and reaction rate
distribution inside of the reactor. As can be seen from Fig. 7, due
to the shortage of microwave penetration depth and the feed position of microwaves, the first position to be heated is the edge of the
central part of the reactor. With the increase of heating time, the
temperature distribution of the longitudinal section of the reactor
(especially the outlet part) gradually becomes increasingly uniform
because of the stirring and propulsion effect of the screw propeller.
Under such conditions, hot spots will not be formed in the reactor,
because the reaction solution is constantly moving vertically and
horizontally, which ensures the safety of the experiment. From
Fig. 7, one can also find that the distribution of reaction rate is similar to that of temperature. This is because the mass fraction of reactants varies little during heating time, and thus according to Eqs.
(12)–(13), the reaction rate (k1 k1) is greatly influenced by temperature. Moreover, in order to quantify the non-uniformity of temperature inside of the reactor, the coefficient of variation (COV),
namely the ratio of the standard deviation to the mean, is adopted
in this paper (Geedipalli et al., 2007). We take 11 cross sections with
different propelling depths in the reactor from inlet to outlet (as
shown in Fig. 8(a)), and calculate the COV of the temperature distribution of these sections at different heating times to quantify the
relationship between temperature uniformity and propelling depth
and heating time. The results plotted in Fig. 9(b) show that the temperature uniformity of the cross section improves with propelling
depth and heating time, which coincides with the conclusion from
Fig. 7. In addition, from Figs. 5, 7, and 9(b), it can be seen that the
outlet temperature of the reactor is stable at approximately 45 °C
with an excellent uniform distribution (with COV < 0.01) after heating for 200 s, and the mass fraction of reactants varies little due to
the relatively short reaction time. This indicates that our microwave reactor can be used as a fast preheater for chemical reactions
that require a specified uniform temperature distribution. Moreover, the outlet of the reactor can be connected to a thermal insulation device to continue the chemical synthesis.
3.3. Effects of rotating speeds of the screw propeller and inlet velocities
on the temperature distribution of the reactor
As a fast microwave preheater, in order to obtain the required
outlet temperature, due to the limited microwave power, it is necessary to adjust the rotating speed of the screw propeller and the
inlet velocity. Here, in order to explore the effect of the rotating
speed of the screw propeller on the temperature distribution of
the reactor, heating processes with rotating speeds of 3.75 rpm,
5 rpm, and 7.5 rpm respectively when the inlet velocity is fixed
Fig. 7. (a–c) The temperature, concentration, and reaction rate distribution inside of the reactor at 0 s, 30 s, 60 s, 120 s, and 240 s.
J. Ye et al. / Chemical Engineering Science 202 (2019) 146–156
153
Fig. 8. (a) Schematic diagram of the cross sections. (b–f) Average temperature evolution of the cross sections inside of the reactor under different conditions.
Fig. 9. COV of the cross section temperature inside of the reactor under different conditions.
to 27.8 mL/s are simulated. Similarly, heating processes with inlet
velocities of 20.85 mL/s, 27.8 mL/s, and 41.7 mL/s, respectively
when the screw propeller rotating speed is fixed to 5 rpm are also
simulated. In order to observe the heating dynamics inside of the
reactor under these cases effectively, the average temperature, as
well as COV, of the longitudinal section during the heating period
from inside to outside of the reactor are calculated and plotted,
as shown in Figs. 8 and 9. As can be seen from Fig. 8(b), (c), and
(e), when the inlet velocity is fixed, the final outlet temperature
of the reactor will not change with the rotating speed of the screw
propeller. However, at a higher rotating speed, the average
temperature will increase more smoothly. This suggests that the
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J. Ye et al. / Chemical Engineering Science 202 (2019) 146–156
Fig. 10. (a) Reflection coefficient (S11) of the case with a metal or Teflon screw propeller. (b) Average temperature difference (TTeflon Tmetal) evolution of the cross sections
inside of the reactor. (c) COV difference (COVmetal COVTeflon) of the cross section temperature inside of the reactor.
temperature uniformity of the sections will improve with the
increase of rotating speed, which is verified by Fig. 9(a)–(c). It
can be also concluded from Fig. 8(d), (e), and (f) that, when the
rotating speed is fixed, the final temperature of reactor and the
time required to reach the final temperature decreases with the
increase of inlet velocity. Moreover, from Fig. 9(b), (d), and (e),
we can clearly find that the temperature uniformity of the sections
also reduces with the increase of inlet velocity. Hence, in practical
applications, a suitable inlet velocity and rotating speed of the
screw propeller can be adopted according to the required outlet
temperature and uniformity.
3.4. Effects of screw propeller material composition and screw
propeller pitch and blade widths on the temperature distribution of the
reactor
Theoretically, when the screw propeller material composition
changes from medium (Teflon) to metal (stainless steel, with a
Fig. 11. (a–c) Average temperature evolution of the cross sections inside of the reactor with different screw propeller pitch. (d–f) COV of the cross section temperature inside
of the reactor with different screw propeller pitch.
J. Ye et al. / Chemical Engineering Science 202 (2019) 146–156
conductivity of 4.032e6 S/m (Kaye, 1995)), the rotation of the
screw propeller will have a greater effect on the electric field.
The increase of the electric field variation in a rotating cycle of a
screw propeller may improve the heating uniformity. To test this
conjecture, we simulate the heating process with a screw propeller
composed of metal and compare the results with those of the case
with a screw propeller composed of Teflon. From Fig. 10(a), it can
be observed that the reflection of microwaves of the metal one is
higher, which may be due to the fact that metals can block the
propagation of microwaves. Meanwhile, the variation of reflection
coefficient caused by the rotation of the metal screw propeller is
just slightly higher than that caused by the rotation of the Teflon
one, which is probably because most of the microwaves have been
absorbed by the reaction solution that surrounds the screw propeller. Due to the increase of microwave reflection, the average
cross section temperature inside of the reactor with a metal screw
propeller is also lower than that with the Teflon one, as shown in
Fig. 10(b). In addition, there is a prominent peak shape near the
central part of the reactor shown in Fig. 10(b), which may be due
to the fact that the incident microwave energy mainly concentrates
on the solution with position opposite the waveguide (i.e. solution
near the central part of the reactor), and thus the reflection caused
by the metal screw propeller near this position will be greater.
Therefore, the average temperature difference (TTeflon Tmetal) of
the cross sections near the central part of the reactor will be much
greater than that in other positions, which makes a ‘‘prominent
peak” in Fig. 10(b). Moreover, as shown in Fig. 10(c), the COV of
155
the cross section temperatures with a metal screw propeller is generally larger than that with the Teflon one. In other words, the temperature uniformity inside of the reactor becomes worse due to the
use of a metal screw propeller, which may be because the temperature growth of the case with a metal screw propeller becomes
smaller while the stirring effect of the screw propeller remains
nearly the same. To sum up, compared with a Teflon screw propeller, the metal screw propeller does not show better results in
this model.
Screw propeller properties including pitch, blade width, and
blade thickness also have effects on the temperature distribution
inside of the reactor. Generally, the blade thickness of the screw
propeller is difficult to adjust in actual machining. Hence, we only
consider the effects of pitch and blade width of the screw propeller
on the temperature distribution inside of the reactor in this paper.
As can be seen in Fig. 11(a)–(c), the temperature evolution with
time of the cases with different screw propeller pitch is nearly
identical. Meanwhile, the maximal temperature rises slightly with
the increase of screw propeller pitch, which may be due to the fact
that the microwave reflection decreases as the volume of the reaction solution inside of the reactor increases (caused by the increase
of screw propeller pitch). In addition, as can be observed in Fig. 11
(d)–(f), COV of the deep cross sections (with the ratio of cross section depth to reactor depth higher than 0.5) is basically reduced
with the increase of the screw propeller pitch, which indicates that
the temperature uniformity near the outlet of the reactor is
reduced by the decrease of the pitch. This may be because when
Fig. 12. (a–c) Average temperature evolution of the cross sections inside of the reactor with different screw propeller blade widths. (d–f) COV of the cross section temperature
inside of the reactor with different screw propeller blade widths.
156
J. Ye et al. / Chemical Engineering Science 202 (2019) 146–156
the pitch is reduced, the blades of the screw propeller become flatter, which will weaken the stirring effect of the screw propeller. In
general, it can be considered that the heating effect is improved
with the increase of the screw propeller pitch in this model. However, the pitch should not be too large because oversized pitch will
lead to a fragile screw propeller structure, making the screw propeller easily damaged when stirring a high viscosity solution.
For the cases with different screw propeller blade widths, the
time required for the outlet temperature to reach stability is
reduced with the decrease of the blade width, as shown in
Fig. 12(a)–(c). This may be attributable to the fact that the heating
rate decreases as the volume of the reaction solution inside of the
reactor increases (caused by the increase of the screw propeller
blade width). However, the maximal temperature rises slightly
with the increase of the screw propeller blade width, which is also
probably due to the decrease of the microwave reflection. Concerning temperature uniformity, in general, it becomes better as the
blade width increases, as shown in Fig. 12(d)–(f). Moreover, as
can be seen from the curl degree of the surfaces in Fig. 12(d)–(f),
the decrease of COV with time is higher at a larger blade width,
which indicates that the stirring effect of the screw propeller is
stronger at a larger blade width. However, similar to the screw propeller pitch, to avoid damages to the screw propeller, the blade
width should also not be too large.
4. Conclusion
The calculation results from the proposed model are in good
agreement with the experimental results, which means this model
can serve as an effective method to deal with the dynamic analysis
of heat and reaction during microwave-assisted continuous flow
production of biodiesel with stirring. The nonuniform heating
caused by the short penetration depth of microwaves as well as
the hot spots and thermal runaway caused by the inhomogeneous
electromagnetic field distribution can be perfectly avoided due to
the stirring effect of the screw propeller. The reaction solution of
more than 20 mL/s can be evenly heated to 35–55 °C within a
few minutes by the proposed reactor, and the inlet velocity and
the rotating speed of the screw propeller can be adjusted according
to practical requirements. In other words, the proposed reactor can
be utilized as a rapid, large-scale preheater for chemical synthesis
that requires a uniform temperature distribution. In addition, the
heating effect of the system can be improved by moderately
increasing the pitch and blade width of the screw propeller. This
work will be of substantial benefit for the design of microwave
reactors for biodiesel continuous flow production and scaled-up
technologies.
Declaration of interests
The authors declared that there is no conflict of interest.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grant No. 61601312, 60151311), Department of
Science and Technology in Sichuan Province (Grant No.
2016FZ0070), and China Scholarship Council (Grant No.
201706240031).
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