sustainability

Article
Investigation of Mixing Behavior of Hydrogen Blended to
Natural Gas in Gas Network
Mingmin Kong , Shuaiming Feng, Qi Xia, Chen Chen *, Zhouxin Pan and Zengliang Gao

Institute of Process Equipment and Control Engineering, Zhejiang University of Technology,

Hangzhou 310032, China; kmmzjut@163.com (M.K.); fsm9704@163.com (S.F.); xq23238@163.com (Q.X.);
zhouxinpan@zjut.edu.cn (Z.P.); zlgao@zjut.edu.cn (Z.G.)
* Correspondence: chen89@zjut.edu.cn

Abstract: Hydrogen is of great significance for replacing fossil fuels and reducing carbon dioxide
emissions. The application of hydrogen mixing with natural gas in gas network transportation
not only improves the utilization rate of hydrogen energy, but also reduces the cost of large-scale
updating household or commercial appliance. This paper investigates the necessity of a gas mixing
device for adding hydrogen to existing natural gas pipelines in the industrial gas network. A
three-dimensional helical static mixer model is developed to simulate the mixing behavior of the
gas mixture. In addition, the model is validated with experimental results. Parametric studies are
performed to investigate the effect of mixer on the mixing performance including the coefficient
of variation (COV) and pressure loss. The research results show that, based on the, the optimum
number of mixing units is three. The arrangement of the torsion angle of the mixing unit has a
greater impact on the COV. When the torsion angle θ = 120◦ , the COV has a minimum value of 0.66%,



and when the torsion angle θ = 60◦ , the COV has a maximum value of 8.54%. The distance of the

 mixing unit has little effect on the pressure loss of the mixed gas but has a greater impact on the COV.
Citation: Kong, M.; Feng, S.; Xia, Q.; Consecutive arrangement of the mixing units (Case A) is the best solution. Increasing the distance of
Chen, C.; Pan, Z.; Gao, Z. the mixing unit is not effective for the gas mixing effect. Last but not least, the gas mixer is optimized
Investigation of Mixing Behavior of to improve the mixing performance.
Hydrogen Blended to Natural Gas in
Gas Network. Sustainability 2021, 13, Keywords: natural gas; hydrogen; helical static mixer; CFD; pressure loss of helical static mixer;
4255. https://doi.org/10.3390/ coefficient of variation (COV)
su13084255

Academic Editor: Wenye Lin

1. Introduction
Received: 22 February 2021
Accepted: 8 April 2021
As one of the most promising clean energy sources, hydrogen is of great significance
Published: 12 April 2021
for replacing fossil fuel and reducing pollutants and greenhouse gas emissions [1]. Adding
hydrogen to the natural gas network for the utilization of factories, gas stations, and
Publisher’s Note: MDPI stays neutral
urban communities does not only help to relieve the greenhouse gas emission, but also
with regard to jurisdictional claims in
facilitates the market’s ability to consume hydrogen [2]. In the recent twenty years, hy-
published maps and institutional affil- drogen mixed with compressed natural gas (HCNG) has been studied for combustion
iations. of internal combustion engines [3]. Adding hydrogen to CNG as a fuel can improve en-
gine combustion performances [4], including increasing thermal efficiency [5], decreasing
combustion duration [6], extending lean burn limit, and reducing pollutants and carbon
dioxide emissions [5–7]. So far, much research has shown that adding a certain amount
Copyright: © 2021 by the authors.
of hydrogen to the natural gas can increase the combustion heat efficiency and reduce
Licensee MDPI, Basel, Switzerland.
the emission of pollutants [8,9]. At present, the PREMIX code of the CHEMKIN program
This article is an open access article
based on the GRI-Mech 3.0 mechanism is a commonly used numerical simulation method
distributed under the terms and for studying the characteristics of the laminar premixed combustion of natural gas mixed
conditions of the Creative Commons with hydrogen [10,11]. Gimeno-Escobedo et al. [12] have explored a more computationally
Attribution (CC BY) license (https:// economical alternative to the methane-hydrogen combustion kinetic model. Based on the
creativecommons.org/licenses/by/ GRI-Mech 3.0 mechanism, the new mechanism gnf-26 of 26 substances and 143 reactions
4.0/). of methane-hydrogen flame has been reduced and verified. However, this mechanism

Sustainability 2021, 13, 4255. https://doi.org/10.3390/su13084255 https://www.mdpi.com/journal/sustainability

Sustainability 2021, 13, 4255 2 of 17

is only applicable for the case with the mixing ratio of methane and hydrogen less than
one: 1. De Vries et al. [13] redefines the range of blending hydrogen ratio to ensure that
the mixture has a lower Wobbe Index. When the proportion of hydrogen added to the gas
pipeline is 20%, the thermal comfort loss on the end users is only 4.7%, and the gas network
management at this time is not complicated. Wojtowicz et al. [14] proposed that 15%
hydrogen blending in natural gas can ensure the safe combustion of fuel in domestic and
commercial appliances without changing the structure of gas appliances. Zhao et al. [15]
proposed that the addition of hydrogen is unfeasible due to the flashback problem al-
though the proportion of hydrogen less than 15% will not have a significant impact on the
performance of the residents’ stove in domestic natural gas appliances.
For the complex gas network, there are mainly gas supply stations, gas transmission
pipes, pressure regulating equipment, central gas distribution control system, solenoid
valves, and residential end users [16]. Under the premise of ensuring the safe transportation
of feeding hydrogen into the natural gas pipeline network, the maximum safe transport
distance, inlet pressure, gas flow velocity, ambient temperature, and the geometric char-
acteristics of the pipeline must be considered. Witkowski et al. [17] and Ogden et al. [18]
believe that mixing hydrogen in natural gas pipeline requires consideration of many factors,
such as market, economy, technology, and pipeline network design. Under appropriate
conditions and a relatively low hydrogen concentrations (5–15%), this scheme is feasible
and may require minor changes to the operation and maintenance of the pipeline network.
Quarton et al. [19] studied that it is feasible to inject a certain proportion of hydrogen into
the natural gas network, and the Feed in Tariffs (FITs) is €20–50/MWh. From a long-term
development perspective, whether this solution is more desirable than electrification will
depend on the flexibility of the gas grid linepack and the cost of expanding the power
infrastructure. When hydrogen is added to natural gas pipeline, there are two main
limiting factors in the mixing ratio of hydrogen, namely, supply chain conditions and
end-use tolerance. In addition, the gas flow rate, velocity of hydrogen injection and the
mixing device are major factors which determine the mixing performance of large-scale
and long-distance transportation of hydrogen blended to natural gas network. In the
case of slow laminar flow, initially the stratified mixture will be uniform at a distance
of 4000 times of the nominal diameter [20]. Therefore, we believe that within a certain
range, the short-distance transportation of hydrogen and natural gas mixtures may have
the possibility of stratification, and there is a certain basis for the need for mixing device.
However, there is rare research conducted to investigate the feasibility of hydrogen and
natural gas mixture via helical static mixer (mixing device) in gas network. The mixture of
hydrogen and natural gas has been homogenized in the end-user device, it can not only as
a direct fuel combustion, and also provides the use of a hydrogen fuel cell vehicles [18].
In addition, the hydrogen may be separated by pressure swing adsorption (PSA) tech-
nology [21]. Therefore, the gas mixing device should be inside the gas station, a distance
less than 4000 times of the nominal diameter. Conventionally, a relatively large mixing
container is always used to increase the mixing contact area and time [22,23]. Although the
container is more suitable for internal combustion engines with relatively small storage
usage, it is not suitable for gas supply with much larger usage and fluctuations due to the
size and the risk of hydrogen leakage. Basically, the application of static mixers is expected
to greatly improves safety.
Static mixers have been widely used for the mixing of two-phase fluids including
gas–liquid and liquid–liquid [24–29]. Zidouni et al. [24] simulated the gas–liquid flow
phenomenon in the helical static mixer by CFD (Computational Fluid Dynamic) method,
and analyzed the gas volume fraction, velocity, and bubble diameter on different sections.
Their model can simulate the gas–liquid mixing performance of the helical static mixer
including the gas phase dispersion and bubble size distribution. There are many parameters
for evaluating the mixing characteristics of static mixers, including turbulent kinetic energy,
shear force, and coefficient of variation (COV) [30]. In order to further improve the static
mixer, some scholars have carried out further research on structural parameters and
Sustainability 2021, 13, 4255 3 of 17

configurations. Based on the CFD simulation of RANS (Reynolds-averaged Navier–Stokes

equations) method, Montante et al. [31] studied the mixing effect of two liquids with
different densities and viscosities in a pipe equipped with a corrugated SMV static mixer.
Compared with the simple coefficient of variation estimation, the calculation method and
parameters can be easily extended to any combination of mixing elements, distributor
geometry, and pipe scale, which helps to determine the best combination of geometric
arrangement and physical variables. Zhuang et al. [30] studied the application of a new
type of double vortex static mixer in the field of nitrogen oxide removal technology. The
experimental results obtained by using particle image velocimetry (PIV) are in good
agreement with their model-predicted results. Compared with other SV static mixers, the
new static mixer is more efficient.
Although the gas–liquid and liquid–liquid two-phase flow in the static mixer have
been studied, the analysis of the mixing effect of the gas–gas mixing in the static mixer is
still rare, especially from the mixer structure to evaluate the influence of related parameters
on the mixing effect. The number of mixing units, the torsion angle of the mixing units,
and the distance of the mixing units are important structural parameters of the helical
static mixer. It is particularly important to study its influence on the mixing process of
natural gas and hydrogen in the industrial gas network system. Related research shows
that the flame structure of combustion after gas premixing is stable, it is less susceptible
to changes in hydrogen/air mass flow rate and equivalence ratio. When the stoichiom-
etry is small, the pre-mixed gas combustion has better thermal performance. The use of
static mixers can improve the uniformity of the gas real-time mixing and the combustion
effect [32]. Furthermore, it ensures the safety of large-scale mixed hydrogen and natural
gas transportation and provides a solid foundation for the sustainable development of
clean energy technologies.
In this paper, a three-dimensional model is developed to simulate the mixing of natural
gas and hydrogen in helical static mixer, the model is validated by comparing the model
generated data with the established experimental data. Based on the model, a parametric
study is performed to investigate the effects of the number of mixing units, e.g., the torsion
angle of the mixing units, the distance of the mixing units on the mixing effect (coefficient
of variation, COV), and pressure loss. Last but not least, we obtain the optimal structural
dimensions of the helical static mixer and the operating conditions to improve the mixing
effect of natural gas and hydrogen for in gas network transportation.

2. Modeling
The internal mixing units of the helical static mixer are placed vertically and staggered
at 90◦ . The length of a single mixing unit L3 is 94 mm, the diameter D1 (D1 = D2 ) is 50 mm,
and the thickness is 2 mm. Figure 1 takes the structure of a 7 units static mixer as an
example for further introduction. The static mixer has a length of L1 which is equal to 1 m,
an inner diameter of 50 mm, and a wall thickness of 1 mm. The two inlets are methane and
hydrogen inlets, and the outlet is the pressure outlet condition. The horizontal distance
between the hydrogen inlet and the methane inlet L2 is 200 mm, and the distance from
the mixing unit is 100 mm. Figure 2 shows the cross section of the given position of the
outlet of the mixing unit. Four points of the outlet section: a, b, c, d are selected to obtain
the mixed gas concentration value, where the horizontal distance between a point and the
center position is l1 (l1 = 6 mm), the vertical distance between b point and the center is
l2 (l2 = 12 mm), the horizontal distance between point c and the center is l3 (l3 = 18 mm),
and the vertical distance between point d and the center is l4 (l4 = 24 mm). According to
the gas-phase component concentration values ci (i = 1, 2, 3, 4) at four points, the COV
is calculated.
Sustainability 2021, 13, 4255 4 of 17

Figure 1. Schematic diagram of helical static mixer with 7 mixing units.

Figure 2. Schematic diagram of points a, b, c, d at different positions of the section.

Among the main components of natural gas, the highest volume fraction of methane
is 91.5% [33]. For purposes of this work, the natural gas can be simplified as pure methane.
The mixture of natural gas with hydrogen can be regarded as a mixture of methane and
hydrogen. Table 1 lists the physical parameters of the helical static mixer and mixed gas of
different mixing units.

Table 1. Properties parameters of helical static mixer with different units and mixed gas (25 ◦ C,
1.01 × 105 Pa).

Symbols Helical Static Mixer

Units, N N=1 N=3 N=5 N=7
Diameter, D (m) 0.05 0.05 0.05 0.05
Length, L (m) 1.00 1.00 1.00 1.00
Wall thickness, w (m) 1.0 × 10−3 1.0 × 10−3 1.0 × 10−3 1.0 × 10−3
Unit thickness, s (m) 3.0 × 10−3 3.0 × 10−3 3.0 × 10−3 3.0 × 10−3
Diameter of unit, dmix (m) 0.05 0.05 0.05 0.05
Unit length, Lmix (m) 0.094 0.282 0.47 0.658
Unit arrangement angle, θ (◦ ) 90
Gas properties CH4 H2
Density (kg/m3 ) 0.65 0.08
Dynamic viscosity (Pa·s) 1.11 × 10−5 8.92 × 10−6
Sustainability 2021, 13, 4255 5 of 17

2.1. Governing Equations

The mixed gas flow studied in this paper is in a turbulent state, and its Reynolds
number calculation expression is [34]:

ρvD
Re = (1)
µ

where
ρ—Fluid density (kg/m3 )
v—Fluid velocity (m/s)
D—Equivalent diameter (m)
µ—Dynamic viscosity of fluid (Pa·s).
Adding a certain volume fraction of hydrogen to the natural gas to mix, we define the
hydrogen mixing ratio XH2 of the mixed gas as

VH2
XH2 = (2)
VCH4 + VH2

where
V CH4 —The volume of methane (%)
V H2 —The volume of hydrogen (%)
As one of the important parameters for evaluating the gas mixing effect, the coefficient
of variation (COV) is expressed as [30]:
q
1 2
σ M ∑ ( ci − c )
COV = = 1
(3)
M ∑ ci
c

where
ci —The discrete phase concentration of the i-region at the outlet (mol/m3 )
σ—The standard deviation
M—Total number of i regions (i = 1, 2, 3, 4)
c—The volume average concentration of the discrete phase in the entire section (mol/m3 ).
It can be seen from Equation (3) that the COV value is between 0 and 1, and the smaller
the value, the more uniform the mixing is. Based on the industrial production application,
the mixing can be considered effective if the value of the coefficient of variation (COV) is
less than 5% [30]. This paper studies the gas–gas mixture state. Considering the low fluid
density, strong diffusivity, and small intermolecular force, the COV value is further strictly
required to be below 2%.
The continuity and momentum equations are solved by a finite volume method (FVM).
In the process of mixed gas flow, the mass conservation equation is satisfied:

∂ρm →
+ ∇ · ( ρ m · v m ) = Sm (4)
∂t
where Sm is a user-defined generalized source term.
The momentum conservation equation is expressed as follows:
→ → →
∂t ( ρm · v m ) 
+ ∇ · (ρm · v m · v m ) =
∂
→

→ →T → n → → (5)
−∇ P + ∇ · µm · (∇ v m + ∇ v m ) + ρm g + F + ∇ · ( ∑ αk · ρk · v dr,k · v dr,k )
k =1

n
µm = ∑ αk · µk (6)
i =1
→ → →
v dr,k = v k − v m (7)
Sustainability 2021, 13, 4255 6 of 17

where
ρm —The mixed phase density (kg/m3 )
vm —The mixed phase velocity (m/s)
P—The pressure loss at inlet and outlet of mixed phase (Pa)
g—Acceleration of gravity (m/s2 )
F—Drag force between mixed phases (N)
αk —The volume fraction of the k-phase
µm —The mixed phase dynamic viscosity (Pa·s)
vdr,k —The k-phase drift velocity [m/s] (k is 1 or 2, k = 1 indicates that the first phase is
methane, and k = 2 indicates that the second phase is hydrogen) [35].

2.2. Boundary Conditions

For the numerical simulation of the mixing process of methane and hydrogen, Fluent
19.0 software is used for calculation, and the pressure-based steady-state solution method
is adopted. The inlets are all velocity boundary conditions, the methane inlet is set as the
main phase, the hydrogen inlet is the secondary phase, and the outlet boundary is set as the
pressure outlet. Due to the density of the gas is smaller, the mixed phase is turbulent flow
in helical static mixer, and gravity factors have little effect on it, so it will not be considered
in this paper.
The current simulation is achieved in steady-state conditions. The convection terms in
the governing equations are discretized by a second order upwind scheme. The SIMPLE
(Semi-Implicit Method for Pressure-Linked Equations) algorithm is used for pressure-
velocity coupling. The gradients of solution variable at the cell center is determined by
least square cell based. The convergence limit is set to a scaled residual lower than 10−6 for
all mentioned equations.

2.3. Numerical Simulation

In order to improve the accuracy of the numerical simulation analysis of the model,
taking the helical static mixer with three mixing units as an example, the cell unit sizes are
1.5 mm, 2 mm, 3 mm, 4 mm, 5 mm, and 6 mm, respectively. Table 2 records the number of
cells for different cell sizes.

Table 2. Number of cells divided by different cell sizes.

Cell Size (mm) 1.5 2 3 4 5 6

Number of cells 2,451,630 1,247,508 491,830 250,487 150,781 96,775

Furthermore, the volume fraction ratio of methane and hydrogen blending is selected
to be 4:1 (methane accounts for 80%, hydrogen accounts for 20%), the mixing model adopts
the mixture multiphase flow mixing solution model, and the turbulence model chooses the
Realizable k-ε model to solve. Table 3 records the average outlet velocity and pressure loss
between the inlet and outlet of helical static mixer under different cell numbers. Through
the cell independence analysis, when the cell size is 2 mm, the calculation results meet
the requirements.

Table 3. The average outlet velocity and pressure loss under different cell numbers.

Cell Size (mm) 1.5 2 3 4 5 6

Number of cells 2,451,630 1,247,508 491,830 250,487 150,781 96,775
Average outlet
3.903 3.9 3.89 3.88 3.88 3.87
velocity, v (m/s)
Pressure loss, ∆P (Pa) 26.88 26.92 26.44 26.65 26.93 27.73

Given that the inlet velocity of methane is 3 m/s, the inlet velocity of hydrogen gas is
calculated according to the mixing ratio of hydrogen added 20%. Table 4 records the value
Sustainability 2021, 13, 4255 7 of 17

of hydrogen inlet velocity under 20% hydrogen ratio conditions. In addition, the settings
of the number of other mixing units are the same as above.

Table 4. Calculation parameters.

Hydrogen Inlet Velocity,

Hydrogen Ratio, X H2 (%) Number of Mixing Units, N
vH2 (m/s)
0.75 20 1~7

3. Experimental Setup
In order to verify the model, this paper chooses helium and air source to verify the
reliability of the helical static mixer results. Note that the helium and air, which are safer
and more accessible than the hydrogen and natural gas, are chosen to validate the model
due to the similar densities. Figure 3 presents a schematic diagram of the experimental
test system device. Helium (the volume fraction is 20%) and air (the volume fraction is
80%) flows in a helical static mixer, and then the data is recorded by a flow meter and a
pressure gauge and the final mixed gas is discharged into the atmosphere. SY-9321 mass
flow meter is selected as the flow meter in the experimental device, and the instrument
measurement accuracy is ±1.5% F.S. The LCD digital pressure gauge is HG-808XB high-
precision pressure gauge, with a measurement accuracy of ±1% F.S. The helical static mixer
uses SK-68650 static mixer with an inner diameter of 50 mm and a maximum pressure
of 1 Mpa. Table 5 presents a detailed list of experimental system instruments. The gas
flow tube has a diameter of 12 mm, and each instrument is connected by a tracheal quick
plug interface.

Figure 3. Schematic diagram of experimental test system device.1—Helium tank, 2—Air pump, 3—Pressure reducing valve,
4—Pressure gauge, 5—Rubber pipe, 6—Flow meter, 7—Flow digital display instrument, 8—Pressure gauge, 9—Helical
static mixer, 10—Computer.

Figure 4 shows a schematic diagram of the gas mixing experiment for verifying the
helical static mixer model. During the experiment, we firstly open the air pump valve and
keep the tube ventilated for 1 min to fully exhaust the impurity gas. Secondly, we slowly
Sustainability 2021, 13, 4255 8 of 17

adjust the pressure gauge of the helium gas tank to maintain the pressure P0 = 0.2 Mpa,
and then adjust the gas inlet flow rate by adjusting the number of revolutions of the flow
meter n (n = 1, 2, 3, 4, 5 . . . ). Finally, under different inlet flow rates q1 , we record the value
of the outlet flow rate q2 flowing out of the helical static mixer. At the same time, record
the inlet and outlet pressure values P1 and P2 under the same conditions.

Table 5. List of instruments of the test system.

Instruments Quantity Information

Helium tank 1 Volume: 22 L
Air pump 1 Gas flow rate: 35 L/min
Pressure reducing vavle 2 Accuracy: ±0.5%
Pressure gauge 2 Accuracy: ±1% F.S
Flow meter 2 Accuracy: ±1.5% F.S
Flow digital display instrument 2 Accuracy: ±1%
Helical static mixer 1 Maximum Pressure: 1 Mpa

Figure 4. Schematic diagram of gas mixing of helical static mixer model.

Model Validation
In the experiment, the number of mixing units of the helical static mixer is seven. Since
the flow of the mixed gas is a steady incompressible flow, which satisfies the Bernoulli
principle, so its expression of equation is as follows [36]:

1
P + ρv2 + ρgh = const (8)
2
where
P—Pressure loss (Pa)
ρ—Density (kg/m3 )
v—Fluid velocity (m/s)
g—Acceleration of gravity (m/s2 )
h—Height (m)
const—Constant.
Further, we define the inlet pressure of the helical static mixer is P1 , the outlet pressure
is P2 and the inlet velocity is v1 , the outlet velocity is v2 . In addition, we assume that the
fluid outlet velocity v2 is λ times that of inlet velocity v1 , its expression is as follows:

v2 = λv1 (9)
Sustainability 2021, 13, 4255 9 of 17

qv1 = A · v1 (10)
qv2 = A · v2 (11)
1
A= π · D2 (12)
4
where
qv1 —Inlet flow rate (m3 /s)
qv2 —Outlet flow rate (m3 /s)
D—Equivalent diameter (m)
A—Cross-sectional area (m2 )
Therefore, from Equation (8) we can further obtain the following expression:

ρ λ2 −1) 2
∆P = f (qv ) = · qv1 (13)
2 · A2
Figure 5 presents the relationship between the inlet flow rate and pressure loss between
the inlet and outlet of the helical static mixer. The tube pressure loss between the inlet
and outlet of helical static mixer is increasing as the inlet flow rate increases. Through
experiments and numerical simulation analysis, the accuracy of the three-dimensional
model is verified.

Figure 5. Verification of experimental results and numerical simulation results.

4. Results and Discussion

Through the experimental research mentioned above, the reliability of the numerical
simulation and experimental results has been verified for the helical static mixer model, and
further parametric discussion of this model is carried out. As the number of mixing units,
the torsion angle of the mixing units and the distance of the mixing units are important
to determine the helical static mixer performance, parametric study has been conducted
to investigate the effects of pressure loss and coefficient of variation changes of natural
gas mixed with hydrogen. In addition, we also further discuss the radial velocity and
the change of methane volume fraction of the outlet section of the helical static mixer.
Considering the symmetry condition, we choose the data in the radius direction to study.
Sustainability 2021, 13, 4255 10 of 17

4.1. Effect of the Number of Mixing Units

In order to investigate the effect of number of mixing units N on the mixing charac-
teristics of methane and hydrogen in the helical static mixer under the steady flow, which
includes pressure loss between inlet and outlet in the helical static mixer, the proportion of
methane composition and the change of outlet coefficient of variation, N is varied from 0 to
7 while other conditions are fixed in Table 6. The study of this section under the condition
of hydrogen mixing ratio at 20% (The volume fraction of methane in the mixed phased
is 80%) that achieved by the methane inlet velocity 3 m/s and hydrogen inlet velocity
0.75 m/s.
Figure 6 shows the variation of pressure loss and COV with the number of mixing
units. As the number of units increases, the pressure loss of the helical static mixer
gradually increases, while the coefficient of variation (COV) continues to decrease. When
the number of mixing units is two, the COV value is 2.13%. When the number of mixing
units is three, the COV value is 1.45%. Considering the application cost, three units is more
appropriate. The coefficient of variation with three mixing units is 1.45%, and the pressure
loss is 52.8 Pa. Figure 7 shows the methane volume fraction (Phase 1) of outlet section
with different number of mixing units. With the number of mixing units increasing, the
methane component concentration distribution becomes more uniform. Without the mixer,
the outlet methane is obviously stratified, i.e., 80% of methane is mainly concentrated in
the middle and lower parts while the upper part is mainly hydrogen. Correspondingly,
the coefficient of variation (COV) reaches its maximum of 10.3%. On the other hand, the
volume fractions of methane for five and seven units are stable at about 80%.

Table 6. Related parameters of different mixing units of helical static mixer.

Number of Mixing Units Hydrogen Mixing Unit

vCH4 (m/s) vH2 (m/s)
of Helical Static Mixer Ratio, X H2 (%) Length, Lmix (m)
N=0 0
N=1 0.094
N=3 3.0 0.75 20 0.282
N=5 0.47
N=7 0.658

Figure 6. Pressure loss and coefficient of variation (COV) change with different number of mixing units.
Sustainability 2021, 13, 4255 11 of 17

Figure 7. Variation of outlet section methane volume fraction with different mixing units: (a) N = 0; (b) N = 1; (c) N = 3;
(d) N = 5; (e) N = 7.

4.2. Effect of the Torsion Angle of Mixing Unit

As mentioned above, the units inside the mixer are arranged perpendicular to each
other at 90◦ , and the numerical simulation results prove that the three units structure
performs better in the mixing of the natural gas with hydrogen. Therefore, the mixing
characteristics of methane and hydrogen under different torsion angles θ (θ = 60◦ ,90◦ ,
Sustainability 2021, 13, 4255 12 of 17

120◦ , 150◦ , 180◦ ) in a three units helical static mixer are further studied. Figure 8 depicts
the torsion angle arrangements, and the effect of the torsion angle θ on the pressure loss
and the coefficient of variation during the mixing process through numerical simulation
is further investigated. Table 7 presents the boundary condition parameters set in the
numerical simulation process. The numerical simulation process is still carried out under
the condition of 20% hydrogen mixing ratio.

Figure 8. Schematic diagram of the arrangement model of different torsion angles (60◦ , 90◦ , 120◦ ,
150◦ , and 180◦ ).

Table 7. Numerical simulation boundary conditions related parameters of 3-units helical static mixer.

Number of Mixing Units, N vCH4 (m/s) vH2 (m/s) X H2 (%) P (Pa)

3 3 0.75 20 1.01 × 105

It can be seen from Figure 9 that as the torsion angle θ of the mixing unit arrangement
increases, the pressure loss of the helical static mixer decreases with the torsion angle.
When θ = 180◦ , it has a minimum value of 38.1 Pa. The coefficient of variation shows
a trend of first decreasing and then increasing as the torsion angle increases. When the
torsion angle θ = 120◦ , the COV minimum value is 0.66%. When θ = 60◦ , the maximum
value of COV is 8.54%.

Figure 9. Pressure loss and COV change with different torsion angle.
Sustainability 2021, 13, 4255 13 of 17

Figure 10 shows the influence of different torsion angles on the outlet methane volume
fraction. As shown in Figure 10, the methane volume fraction with a torsion angle of
60◦ has the largest amplitude range. The changes in the methane volume fraction with
torsion angles of 90◦ and 120◦ are stable, i.e., the methane volume fraction fluctuates quite
little around 80%. When the torsion angle is 180◦ , the outlet methane volume fraction
exhibits obvious stratification with the coefficient of variation (COV) of 6%. Considering
the coefficient of variation and pressure loss parameters, it is more appropriate to select the
torsion angle of 120◦ .

Figure 10. Variation of outlet methane volume fraction with different torsion angle: (a) θ = 60◦ ; (b) θ = 90◦ ; (c) θ = 120◦ ;
(d) θ = 150◦ ; (e) θ = 180◦ .
Sustainability 2021, 13, 4255 14 of 17

4.3. Effect of Mixing Units Distance

In order to explore the gas mixing characteristics, different distance conditions of
mixing units are set. According to the different distances of the mixing units, we have
established four 3D models with different distances. The distances between different
mixing units are marked as ∆Li (i = 1, 2). Figure 11 shows the schematic diagram of
different mixing unit distances. From the figure, it can be seen that the Case A, Case B, Case
C, and Case D are selected for investigating the influence of the distances of the mixing
units on the gas mixing effect of the helical static mixer. Figure 12 shows the pressure loss
and coefficient of variation of the four solutions with the distances of the mixing units. The
pressure loss of the four programs has little change. However, Case A has the smallest
COV value, and Case C has the largest COV value.

Figure 11. Schematic diagram of different mixing units distance: (Case A: ∆L1 = ∆L2 = 0; Case B:
∆L1 = 0, ∆L2 = 60 mm; Case C: ∆L1 = 60 mm, ∆L2 = 0; Case D: ∆L1 = 60 mm, ∆L2 = 60 mm).

Figure 12. Pressure loss and COV change with different arrangements.

Figure 13 shows the change of the outlet methane volume fraction for different ar-
rangements. Among the four arrangements, the outlet methane volume fractions of Case B
and Case C change more strongly. Essentially, the hydrogen in Case B, Case C, and Case D
Sustainability 2021, 13, 4255 15 of 17

is mainly concentrated in the middle. Hence, the arrangement of mixing units has a great
influence on the mixing behavior and Case A is relatively better with less fluctuation.

Figure 13. Variation of outlet methane volume θ fraction with different arrangements: (Case A: ∆L1 = ∆L2 = 0; Case B:
∆L1 = 0, ∆L2 = 60 mm; Case C: ∆L1 = 60 mm, ∆L2 = 0; Case D: ∆L1 = 60 mm, ∆L2 = 60 mm).

5. Conclusions
In this paper, the feasibility of hydrogen blended to natural gas via the helical static
mixer in gas network is verified. The mixing of natural gas and hydrogen through the gas
network can be widely used in gas stations, factories, domestic, and commercial appliances.
The addition of the gas mixer proposed in this article will improve the stratification of
the gas mixture, meanwhile the pressure loss of the pipe will not increase too much.
According to the multiphase flow mixing evaluation index and numerical calculation
method, this article discusses the influence of the number of mixing units, the torsion angle,
and the distance of mixing units on the gas–gas (Methane–Hydrogen) mixing. Further, the
optimization design criteria for the structure of the mixing device for the natural gas mixed
with hydrogen system are proposed to provide a guiding baseline for the subsequent
industrial operation. Through the above analysis, following conclusions are obtained:
(1) The pressure loss increases with the number of mixing units increases, while the
coefficient of variation gradually decreases. There is an optimum number of mixing
units for a good mixing performance with relatively lower pressure loss. Based on
our results, optimum number of mixing units are three, corresponding to the pressure
loss of 52.8 Pa and the coefficient of variation of 1.45%.
Sustainability 2021, 13, 4255 16 of 17

(2) As the torsion angle θ (θ = 60◦ , 90◦ , 120◦ , 150◦ , and 180◦ ) increases, the coefficient of
variation firstly decreases and then increases, while the pressure loss keeps decreasing.
When θ = 120◦ , the COV has a minimum value of 0.66% and the pressure loss become
52.26 Pa.
(3) Through the comparison of the three arrangements, it is found that the distance of
the mixing unit has little effect on the pressure loss of the helical static mixer but has
a greater effect on the coefficient of variation. The coefficient of variation (COV) from
Case A to Case D increases first and then decreases, with a maximum value of 14.68%
at Case C and a minimum value of 1.45% at Case A. Therefore, Case A (consecutive
arrangement) is most appropriate.

Author Contributions: Conceptualization, C.C. and M.K.; funding acquisition, C.C.; methodology,
S.F. and Q.X.; software, S.F.; validation, M.K. and S.F.; formal analysis, M.K. and Z.P.; resources, Z.G.;
writing—original draft preparation, M.K.; All authors have read and agreed to the published version
of the manuscript.
Funding: This research was funded by Natural Science Foundation of Zhejiang Province (No. LY20E060007).
Data Availability Statement: Data sharing is not applicable to this article.
Conflicts of Interest: The authors declare no conflict of interest.

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