CFD Study on the Influence of Liquid Viscosity on the Swirling Gas-Liquid Flow
Ryan Anugrah Putra a,1,*, Habib Luthfi Ash Shiddiqie a,2, Indro Pranoto a,3
a Department of Mechanical and Industrial Engineering, Faculty of Engineering, Universitas Gadjah Mada, Jalan Grafika No. 2, 55281 Yogyakarta, Indonesia
1 [email protected]*; 2 [email protected]; 3 [email protected]
* corresponding author
I. Introduction
Swirling flow is commonly found in nature and in various industrial applications, such as in static mixers and combustors, as well as in separation processes, such as in cyclones and inline swirl separators [1]–[7]. In inline separators and mixers, swirl elements are installed in the pipe to create swirling flow in the region downstream the swirl elements. Putra et al. in [9] has conducted experimental research on the air-water flow in a vertical pipe with a swirl component. They measured the two-phase flow properties, which in their study were represented by the radial distribution of the gas fraction, using the High-resolution Gamma-ray Computed Tomography (HireCT) technique created by the German Helmholtz-Zentrum Dresden-Rossendorf (HZDR) organization. This study's measurement data are highly helpful for analyzing flow characteristics. Researchers [8]–[14] have also conducted experiments on pipes featuring swirl elements for the two-phase flow of water and air. It is known from this literature that the discussion of these articles did not address the impact of liquid viscosity on flow characteristics including gas volume fraction distribution, velocity, and pressure.
The experimental results can then be combined with CFD to explain the flow-related phenomena [15]. CFD can also be used to determine the effect of swirl element geometry. Different swirl element geometries can produce different flow behavior. This was investigated by [16], who used single-phase CFD to see the streamlined shape of the flow velocity in a vertical pipe equipped with three different types of swirl elements, namely coil, single helix and double helix. A discussion of the difference in rotational strength produced by the three swirl elements was also reported by them [16]. The weakness of their study is the use of single-phase CFD which cannot provide a direct picture of the distribution of gas fractions in the pipeline. This weakness was later addressed by [17], who used a two-phase CFD simulations based on the Euler-Euler model to study the effect of different geometries of swirl elements on the gas-water flow characteristics in vertical pipes. They found the unique flow shape generated by each swirl element investigated in their study. They also observed that under certain conditions swirl elements can be used for gas-water mixing processes,
ARTICLE INFO A B S T R A C T
Article history:
Accepted
Swirling two-phase flow is important in industrial mixing and separation systems. In this work, the effect of liquid viscosity was investigated computationally using the Euler-Euler model where the liquid and the gas acted as the continuous and dispersed phases, respectively. CFD simulations were performed to model the gas-liquid flow inside a horizontal pipe with a static mixer element with liquid viscosities of 1, 5, 10, and 50 cP. The axial gas fraction profiles show that the gas distribution dynamic is strongly affected by the liquid viscosity, especially in the region downstream of the element. The calculated results show that the higher the viscosity, the shorter the gas core downstream of the element. Gas separation after the element occurs over a shorter distance with higher liquid viscosity. A possible explanation is that the swirling flow decays faster at higher liquid viscosities, and the buoyancy force dominates over the centrifugal force.
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Keywords:
Swirling flow CFD Gas-liquid Rotating flow Viscosity
but under other conditions for separation processes [17]. This agrees with the observations of an experimental study by [20], who used ultrafast electron beam X-ray tomography to investigate the flow behavior in a vertical tube with a helical static mixer. Helical static mixers are intended for the mixing processes, but have potential to separate gases and liquids under certain conditions, as performed in experimental studies by [18], [21].
In a numerical study using the Euler-Euler CFD model [19], gas-water mixing characteristics inside a vertical pipe were investigated for three different length-to-diameter (L/D) ratios. In their study, it was concluded that all static mixers tested in the numerical simulations provided better mixing conditions compared to a pipe without a static mixer. The study also shows that the static mixer with the lowest tested L/D yielded the highest velocity curl which indicated the rotational strength of the flow. Furthermore, the static mixer with the lowest L/D in their study showed the best gas-water mixing characteristics. This is indicated by the radial distribution of the gas inside the pipe [19]. Their work was carried over to the next numerical study investigating gas-water flow in a horizontal pipe with a single helical static mixer reported in [20]. The results of this study agree that the superficial liquid velocity has a strong effect on the gas-liquid mixing conditions in the pipe. The study also shows that good mixing conditions can be achieved at relatively high superficial liquid velocities (greater than 0.8 m/s), under the operating conditions used in this study [20].
Numerical studies using two-phase CFD were also performed by [21] to study the gas-liquid separation characteristics in a vertical pipe. They placed a swirl element with the shape of double helix in the pipe. The result show that the gas distribution profile is significantly affected by the liquid superficial velocity similar to the one reported in [20] which use a single helix. The study [21]
shows that in a single helix static mixer, the mixing or contacting of gas and liquid conditions tend to be better with higher liquid superficial velocities while in a double helical swirl separator gas and liquid tend to separate better at higher superficial liquid velocities. In their study, the best separation conditions were achieved at a superficial liquid velocity of 1 m/s. They found that at this velocity, a gas core was formed steadily up to the exit of the tube [21].
From this literature study, it is concluded that research to determine the effect of fluid viscosity on gas-liquid flow behaviors such as gas fraction and velocity profiles as well as the pressure both experimental and computational fluid dynamics (CFD) studies is still very limited in the existing literature. Therefore, more studies in this regard are needed. The deeper knowledge gained from research on this topic will be useful for the process of optimizing the design of equipment or systems that involve swirling two-phase flows.
From this literature review, it can be concluded that both experimental and numerical studies investigating the influence of liquid viscosity on the flow characteristics such as the gas volume fraction distribution are still very limited. Therefore, further research is needed in this regard. Deeper knowledge gained from research on this topic will help in the process of optimizing the design of devices or systems involving swirling two-phase flow. In this work, the liquid viscosity effects on the gas volume fraction distribution inside a horizontal pipe with a single static mixer element was investigated using the Euler-Euler two-phase CFD model.
II. Method
The computational domain of the CFD simulations performed in this study (see Fig.1) is a horizontal pipe of 24 mm diameter and 1 m length, which is equipped with a static mixer element of 24 mm diameter and 50 mm length. The element entrance is 100 mm from the liquid inlet. Gas is injected using a source point placed at the top of the tube with 10 mm from the liquid inlet. In addition to observing the gas distribution from the CFD results using the axial center plane, we also used several cross-sectional planes, namely P1-P9, to analyze the change of gas distribution along the pipe.
Table 1 shows the axial distance of these planes relative to the fluid inlet.
Fig. 1. The domain for CFD simulation.
Table 1. Axial distance of the cross-sectional planes relative to the fluid inlet.
Plane Distance [mm]
P1 5
P2 50
P3 100
P4 125
P5 150
P6 200
P7 350
P8 500
P9 900
In this study, the two fluid model was used in which liquid and gas were defined as continuous and dispersed phases, respectively. A uniform bubble size of 3 mm in diameter was chosen for the dispersed phase. To investigate the effect of liquid viscosity, viscosities of 1, 5, 10 and 50 cP were tested in simulations. The ANSYS CFX software (Student License) was used to calculate the continuity and momentum equations for each computational cell given by the equations given in Table 2 [22]:
Table 2. The governing equations.
Equations Continuity equation: !
!"!𝛼#𝜌#$ + ∇. !𝛼#𝜌#𝒖#$ = 𝑆#
where 𝛼#, 𝜌#, 𝒖# represent the volume fraction, the density and the velocity vector of phase 𝑗 , respectively.
(1)
Momentum equation:
𝜕
𝜕𝑡!𝛼#𝜌#𝒖#$ + ∇. -𝛼#!𝜌$𝒖#× 𝒖#$/ = −𝛼#∇𝑝 + ∇. 2𝛼#𝜇#-∇𝒖#+ !∇𝒖#$%/4 + 𝑴#+ 𝑆&#
Variables 𝜇#, t, 𝑆#, 𝑆&# and p represent the viscosity, the time, the mass source, the momentum sources due to external body forces and the pressure, respectively. The term 𝑴# represents the sum of the bubble forces including the drag force 𝑭'()*, lift force 𝑭+,-", wall lubrication force 𝑭.)++, turbulent dispersion force 𝑭%/ and virtual mass force 𝑭0& and can be expressed as [22]:
(2)
𝑴#= 𝑭'()*+ 𝑭+,-"+ 𝑭.)+++ 𝑭%/+ 𝑭0&
In this CFD work, 𝑭'()*, 𝑭+,-", 𝑭.)++ and 𝑭%/ are defined based on the Ishii-Zuber model [23], Tomiyama model [24], Hosokawa model [25], and the Burns model [26], respectively, and 𝑭0&
was defined based on [27]–[29]. For modeling the turbulence of the continuous phase, k‒ω-based shear stress transport (SST) model proposed by Menter [30] was selected. To take into account the bubble induce turbulence, the Sato model [31] was used in the simulation.
(3)
All calculations in this study were performed in steady-state and adiabatic modes (i.e., heat transfer is ignored). We used the following arrangement as boundary conditions: a liquid velocity of 1 m/s was used at the liquid inlet. Gas injected at a mass flow rate of 1.36 mg/s from the source point.
An average static pressure was implemented as a boundary condition at the outlet. Boundary conditions for all other parts were defined as non-slip and free-slip walls for liquid and gas, respectively.
III. Results and Discussion
The significant effect of the fluid viscosities on the gas distribution along the pipeline equipped with a static mixer can be observed in Fig.2. The CFD simulation results show that the longest gas core downstream of the element is obtained for the case of 1 cP. The increase in viscosity results in a decrease in the gas core length. It can be observed from this figure that the shortest gas core occurs in the case of 50 cP. The centrifugal force responsible for the rotational flow is important in facilitating mixing or contact between gas and liquid downstream of the element. It must be able to resist buoyancy that tends to push the gas vertically toward the upper part of the tube. After a certain axial distance, the magnitude of the centrifugal force seems to decrease and no longer dominates the buoyancy force. This results in gas and liquid separation, where the gas will stay in the upper part of the pipe forming a film-like structure and move to the outlet as a separate flow.
Fig. 2. Contours of axial gas distribution for different liquid viscosities.
Fig. 3. Gas distribution porfiles on the crosss-sectional planes upstream the static mixer element for different liquid viscosities.
To get a clearer picture of the evolution of the gas distribution over the axial distance, gas volume fraction contours plotted on some cross-sectional planes are shown in Figs. 2-4. Fig. 2 focuses on the gas distribution in the upstream region (i.e., upstream of the static mixer element). As can be seen from this figure, there is no significant difference in the radial gas distribution at planes P1 and P2 for all viscosities tested in this study. The gas distribution of P1 is highly influenced by the gas injection point near this plane. The gas then spreads at the top of the pipe, as seen at P2. In this area, the separate flow is likely to occurs. Buoyancy keeps the gas at the top and prevents the downward motion which results in a negligible gas-water mixing process.
Fig. 4. Gas distribution profiles on some crosss-sectional planes around the static mixer element for different liquid viscosities.
Contours of the gas volume fraction at several planes around the static mixer element for different liquid viscosities are presented in Fig.4. Here we can observe the change in gas distribution due to the presence of the mixer element. The gas distribution at P3 is similar to the previous plane (i.e., P2). As soon as the flow passes the mixer element, it twists, leading to a very different gas distribution as observed at P4. Although the distribution patterns at P4 are similar between different viscosities, non-negligible difference are still seen. The gas at P5 accumulated at the center of the pipe and its distribution are nearly identical for all tested viscosities.
Fig.5 shows the contours of gas distribution at several planes downstream of the element. The patterns of gas distribution at P6 are similar, but the size or value of gas peaks differ among them.
The higher the viscosity, the lower the gas peak. In the case of 1cP and 5cP, a relatively good mixing still can be maintained up to P7. However, for 10 cP and 50 cP, the gas appears to move to the top of the tube. Separation is starting to occur as the rotational strength appears to decrease in this plane.
A segregation similar to that described above also occurs at P8 for 5 cP. In contrast, in the case of 1 cP a similar gas distribution as in the previous plane still can be maintained up to P8. The movement of the gas toward the upper part of the pipe further progressing for 10 cP and 50 cP. Contours at P9 show that the gas has been separated at this axial distance for all tested viscosities.
Fig. 5. Gas distribution profiles on several crosss-sectional planes downstream the static mixer element for different liquid viscosities.
IV. Conclusion
The co-current gas-liquid flow in a horizontal pipe with a static mixing element was numerically studied. The calculated results show that the liquid viscosity strongly affected the gas volume fraction distribution around and downstream of the mixer element. As the liquid viscosity increases, the gas core formed downstream of the element becomes shorter. Swirling flow appears to decay faster in viscous liquid flows. Rotational strength may not be sufficient to prevent the buoyancy driven gas separation after a certain axial distance downstream of the element. CFD simulations show that the separation distance downstream of the element decreases as the viscosity of the liquid increases.
Acknowledgment
The authors would like to thank to Universitas Gadjah Mada, Yogyakarta, Indonesia for financing this research under a research grant with contract number: 2559/UN1.P.III/Dit- Lit/PT.01.03/2022.
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