， , ,2*

(1.School of Mechanical and Aerospace Engineering,Gyeongsang National University,Jinju 52828,S.Korea;2.Research Center for Aircraft Parts Technology,Gyeongsang National University,Jinju 52828,S.Korea)

Abstract:Two-phase flow in a horizontal pipe was investigated by using numerical and experimental visualization methods.A horizontal pipe was built for qualitative and quantitative flow visualization.The length of horizontal pipe flow system was 9.5 m and the inner diameter was 51 mm.High-speed video method was used for the qualitative visualization and PIV method was applied for the quantitative visua-lization.The same geometry model was used for the numerical study.Three flow regimes including stratified flow,elongated bubble and slug flow field were generated and visualized by using numerical and experimental methods.The results show that the numerical simulation results are qualitatively si-milar to that of the experimental results.In addition,more quantitative results can be analyzed by numerical method.Development and decay process of slug flow was investigated,showing that the decay of slug heavily depends on the magnitude of nose velocity and its lasting time.It can also be found that the liquid superficial velocity plays a significant role in affecting the slug frequency.When keeping the gas superficial velocity constant,the frequency will increase with the liquid superficial velocity.

Key words:two-phase flow;CFD;PIV;slug flow;slug frequency

Two-phase flow,for example,liquid and gas flow in a straight pipe is popular in many engineering applications such as oil and gas transportation or nuclear power plant.The modeling of gas-liquid flow especially slug flow in horizontal pipelines and channels is of considerable importance.Due to large fluctuation of the momentum formed behind liquid slugs,it has the potential to destroy the structure of the pipe system or apparatus.So,slug flow has received quite a large interest by the researchers due to its role in the structural stability.

Fig.1 Flow regime map of gas-liquid in horizontal pipe flow

Two-phase slug flow may appear in several pipe topologies and previous studies have explained the ori-gination of this slug based on Kelvin-Helmholtz instability and effect of Bernoulli.Slug flows can divide into two main groups:hydrodynamic and terrain slugging.Hydrodynamic slugging is the normal slugging pattern encountered in straight flow lines.Terrain slugging has a variety of topography due to liquid accumulation in local dips of flow lines.In the current research,hydrodynamic slug flow is the key point.CZAPP et al.[4]has studied the hydrodynamic slug formation in a pipe as shown in Fig.2.It begins with wave flow for its small perturbation (see Fig.2a).Later on account of Kelvin-Helmholtz instabilities and superposition of water waves,water level rises and air is accelerated because of the cross section reduction of air (see Fig.2b).Next,due to the Bernoulli effect,water is sucked to the top of the pipe (see Fig.2c),forming a short slug,and referring to as a ″pseudo-slug″ or a ″slug precursor″[5].Finally,the water completely fills the cross section at a certain axial position,which is also called plug onset.With that,slug length will increase meaning that water is accelerated and accumulates downstream for the compression of air (see Fig.2d).

Fig.2 Slug initiation process

Many numerical investigations have performed to investigate two-phase flow physics in horizontal pipes[6-8].The numerical studies presented are focused on the feasibility or validation stage of the numerical scheme[9].Recently,some qualitative comparisons of result between experiment and simulation in slug flow were presented[10]and they showed that the results match with each other very well and CFD can be a useful tool in studying horizontal two-phase flow.In quantitative studies,VALLéE et al.[11]had recorded the pressure signal which indicated a sudden pressure increase when the slug passed by HUSSAIN et al.[12]and ABDALELLAH et al.[13],who had found that the slug frequency increased with increasing the superficial liquid velocity at constant superficial gas velocity.Due to the complicated interphase shape and the incorporation of bubbles,the study of multiphase flow in the pipe is limited.The former studies had proved that CFD had the feasibility to simulate the slug flow.However,the verification is just from the aspect of morphology and there are few quantitative analyses to verify the applicability.Hence,the stratified flow,elongated bubble and slug flow regimes were investiga-ted by using experimental and numerical visualization method quantitatively.

In this study,the numerical study of two-phase flow in a horizontal pipe was carried out.The target of this paper is to develop the numerical method of gas and liquid two-phase flow in a horizontal pipe.To achieve this goal,it is necessary to validate the numerical method qualitatively and quantitatively.The transition process of slug flow was simulated and the different states in slug flow were detected.Furthermore,it is of interest to understand the general fluid dynamic mechanism of slug flow and identify the critical parameters affecting the main slug flow parameters (such as slug length,frequency,velocity distribution and pressure).

1 Numerical Method

The numerical simulation is performed in ANSYS Fluent 17.1.ANSYS Geometry is used to design three-dimensional models.Hexahedral grids are generated in the ICEM CFD.The VOF approach which bases on a fixed Eulerian computational mesh uses a fractional VOF scheme to track free boundary (interfaces).In this technique,it is assumed that fluids participating in the modelled flows are immiscible but inside the computational mesh[14].

In addition,the VOF technique uses a single set of momentum equations for each dimension and single coupling pressure equation.It creates shared velocity field in modelled multiphase flow.The modeling is based on mass-weighted averaged mass and momentum transport equations.Regarding both phases as continua,these equations without mass transfer between phases are defined as

(1)

(2)

For numerical simulations,the 3-D modeling with the diameterD=0.051 m and lengthL=9.5 m is made to capture the fully physics of slug flow.As can be seen in Fig.3,the high-quality structural grid is applied to improve the accuracy of the simulation.The half cylinder model is used,showing that there is no diffe-rence in the mean properties such as slug length of slug frequency.DEENDARLIANTO et al.[10]has presented the validity of half cylinder model.The boundary conditions are shown in Tab.1.In this work,the constant superficial inlet velocities of airvSGand watervSLare set during the simulations.The superficial velocity is a hypothetical fluid velocity,calculated as a single phase that fills the whole pipe cross section.Based on the flow regime map as shown in Fig.1,a certain range of values in stratified and intermittent parts is choose.These values are selected from the preliminary experimental results.For the present simulations,three pairs of superficial inlet velocities for gas and liquid two-phase are used (Tab.1).The wall of the horizontal pipe has been set as hydraulically smooth wall with no-slip boundary conditions for the gas and liquid two-phase.Average static pressure outlet conditions with a relative pressure ofprel=0 Pa according to ambient atmosphere have been applied to the downstream outlet cross section of the pipe.The volume fraction for liquid and air at the inlet are initialized torG=rL=0.5.The transient simulation has been carried out with a constant time step size ofdt=0.005 s.

Fig.3 Grids of computational domain (0.5 million nodes)

Tab.1 Boundary conditions for flow characteristics analysis

The realizablek-εturbulence model is applied.The comparisons of different turbulent models are shown in Tab.2.As can be seen,there is no slug flow under the turbulent condition of standardk-ωand BSLk-ω.While in the RNGk-εand standardk-εturbulent model,the time step sizedtis smaller than other cases which means that it will cost much more time than other cases.Then the realizablek-εand SSTk-ωis suitable.According to other simulation studies,k-ωis applied more in CFX[9,15],however,researchers prefer to usek-εin Fluent[16].Based on the above analysis,the realizablek-εmodel is chosen for turbulence flow.Grid independence test,defined as a solution error range which can be accepted by the end-user,is carried out in the present CFD calculation.The principle of verifying the grid independence is that a parameter will not change as the grids increases.The former studies uses the slug appea-rance[4],length and velocity of elongated bubble[10]as the criterion of judgment.In the mesh independence study of DEENDARLIANTO,it is found that the modest number of grid is 161 000 in the pipe of 9.5 m in length and 26 mm in diameter.According to researches,the modest grid number is nearly 0.50 million because the diameter is approximately twice.In order to validate that the grid number of 0.50 million is reasonable,four test cases are run with different mesh nodesNwhich are 0.10 million,0.25 million,0.50 million and 1.00 million.All four cases are run in the case of slug,the gas and liquid velocity of which arevSG=0.45 m/s andvSL=0.48 m/s.Moreover,same physical parameters are set in the calculations such as control factors,time step size,turbulent model and so on.In this study,the time of first slug appearance is set as the parameter to validate number the grid independence.Fig.4 shows that with the mesh number increases,the time of first slug appearances will decrease and the time is almost constant after the 0.5 million mesh nodes.

Tab.2 Comparison of different turbulent models

Fig.4 Time of first slug appearances

In order to reduce the time of slug occurrence,the patch grids are used to supplement the initial condition where water and air are each half in the pipe.In addition,the other physical parameters are the same with the unpatched condition.The number of elongated bubbles,the number of generated slug,the velocity of elongated bubble and the velocity of slug flow are the parameters which are used to check the mesh independence under the patch condition.In Tab.3,Neb,veb,Nsf,vsftrepresent the number of elongated bubble,the velocity of elongated bubble,the number of slug flow and the tail velocity of slug flow respectively.Tab.3 shows that only a small difference in the nodes 0.25,0.50 and 1.00 million whereas the nodes of 0.10 million has the obvious distinction.This means that the grid number of 0.25 million is the optimum point for the calculations.Close observation of the results between patch and unpatched condition reveals that it can use less meshes in calculation when the initial condition is sufficient.Combing these two conditions,the mesh of 0.50 million is applied to this study.

Tab.3 Comparison parameters under different meshes

2 Results and Discussion

Stratified flow is the most regular two-phase flow regime where the interface has a continuous boundary making liquid and gas flow completely separate.When the water superficial velocity increases to 0.48 m/s and the gas superficial velocity keeps the same with the stratified flow condition,it will appear the elongated bubble (Fig.5) which the elongated bullet-shaped gas and plugs of liquid alternately flow along the upper part of the pipe.The shedding of the gas bubble shows the periodic appearance.The nose and tail of bubble shows the distinctive shapes.The nose is blunt and the bubble has the long narrow tail[17].In addition,φLin Fig.5 means the water volume fraction.

Fig.5 Comparison of elongated bubble shape between experiment and simulation

Fig.6 shows the consistent qualitative flow visua-lization of slug flow between experiment and simulation.The slug flow will appear when the water superficial velocity remains the same with elongated bubble case and the gas velocity is increased to 0.45 m/s.As can be seen that the visualization between experiment and si-mulation is similar.Slug flow can divide into four parts,nose,body,tail and Taylor bubble part.These two qualitative comparisons can validate the feasibility of CFD method,and the quantitative parameters can also demonstrate it.The average length of elongated bubble and slug are 0.94 m and 1.25 m respectively,while the results of experiment and simulation are nearly the same.These qualitative and quantitative comparisons verify that the gas-liquid two-phase flow in horizontal circular pipes can be simulated using the commercial CFD software.In the two-phase flow,the flow regime is very complex.Especially in the slug slow,it has highly unsteady features.With its movement along the pipe,the slug flow properties such as the length,frequency change.However,some initiated slug will decay to wave.This phenomenon has been detected in the simulation.

Fig.6 Comparison of slug flow shape between experiment and simulation

Fig.7 shows the process of developing and decaying slug flow.The front slug in Fig.7a is developing and its length increases as the slug moving to the downstream.However,the rear one shows the decaying process and finally it becames the wave flow.These two different phenomena can be explained from the perspective of the distribution of velocity.

Fig.7 Evolution of developing and decaying slug flow

Fig.8 shows the corresponding velocity distribution of the developing one (the front slug).Thevwin Fig.8 represents the velocity along the axis direction.When enlarging the nose part,it can be found easily that the axial velocity in the nose part is faster than the tail part.The liquid entrainment rate at the slug front is greater than the shedding rate at the tail,then the slug precursor length grows into a ″fully developed″ slug.When analyzing the velocity distribution of decaying one (Fig.9),the speed of nose is gradually decrea-sing.If the rate of pick-up liquid at the front is nearly or even less than the rate of shedding at the tail,the slug precursor is ephemeral and collapses back into a large wave.The velocity of nose and tail part is all-important in the development of slug flow,so it is necessary to extract the speed value at nose and tail part.As can be seen from the Fig.10 which extracts the velocity from Fig.8,the difference between nose and tail at the slug precursor is nearly 1.7 m/s and the velocity can sustain for a period timetwith the developing of slug flow.While in the Fig.11 which extracts the velocity from Fig.9,the difference of velocity at the slug precursor is about 1.2 m/s and the velocity drop,imme-diately.The means of the axial velocity in the slug nose needs an enough velocity to sustain its development.

Fig.8 Nose axial velocity change of developing slug flow

Fig.9 Nose axial velocity change of decaying slug flow

Fig.10 Comparison of axial velocity between nose and tail part in developed slug flow

Fig.11 Comparison of axial velocity between nose and tail part in decaying slug flow

One of the differences between slug flow and elongated bubble flow is the amount of bubbles within the liquid body.This phenomenon can also be explained in Fig.12.As previously analyzed,the velocity in the upper part is bigger than the bottom part at nose,so it can push the air to move forward.Then,in the upper part,the water will accumulate (Fig.12a).With further development,it will form a concave shape for the uneven distribution of velocity (Fig.12b).Last,the water of this part will fall down because of the gra-vity (Fig.12c,12d) and the bubbles will be entrained into slug flow.This tumbling motion causes the large air entrainment to the slug body.The pressure signal with the movement of slug flow on top of the pipe is extracted and spectral analysis is applied using FFT method.By doing this,the slug frequency Fig.12f is calculated and the graph of amplitudeMand frequency is got,as seen in Fig.13.

Fig.12 Gas entrainment phenomena in slug nose area

Fig.13 Comparison of slug frequency by varying liquid superficial velocity (vSG=1.0 m/s)

Under various liquid and gas superficial veloci-ties,the slug frequency change due to the different superficial velocity condition is investigated.First,the gas superficial velocity does not affect the slug frequency.On the other hand,the liquid superficial velocity causes the large variation of the slug frequency.Fig.13 shows the change of frequenciesfby varying the liquid superficial velocity under the constant gas superficial velocity of 1.0 m/s.The frequency is about 0.3 Hz when liquid superficial velocity is 0.5 m/s.When the liquid superficial velocity increases to 1.0 m/s,the frequency becomes 0.68 Hz.This means that the large liquid superficial velocity increases the generation of the slug flow.This conclusion is also confirmed by HUSSAIN[12]and ABDALELLAH[13].

3 Conclusions

In this study,two-phase flow including stratified flow,elongated bubble and slug flow were predicted successfully with the VOF multiphase model of Fluent.The results show qualitatively similar between experi-ment and simulations.This work demonstrates that the formation and propagation of slug flows in horizontal circular pipes could be simulated using the commercial CFD software package Fluent.The validation of nume-rical results can from the structure and from the specific parameters such as the length of slug flow and elonga-ted bubble,whose average length are 0.94 m and 1.25 m respectively.In numerical study,it can easily get the transition process of slug flow rather than the mean results using the transient model.Also,the numerical method of gas and liquid two-phase in a horizontalpipe has been developed.The further understanding of the general fluid dynamic mechanism leading to slug flow and the critical parameters affecting the main slug flow parameters (such as slug length,frequency,velocity distribution and pressure) can be achieved.

The flow regime is very complex in the two-phase flow,especially in the slug slow.With the slug movement,it changes from developing slug to developed slug,where the liquid rate picked up at the slug front is greater than the liquid rate shed at the tail.Then the slug precursor grows in length to form a ″fully developed″ slug.Whereas,some of the slug precursors are ephemeral and will collapses back into a large wave,because the rate of pick-up at the front is nearly or even less than the rate of shedding at the tail.This kind of phenomenon is detected by the simulation.The reason for the decay of slug is that the velocity cannot hold for a time period.The pressure signal of slug flow is recorded.From the pressure signal,it can be detected that the rise point represents the appearance of slug nose and the drop point means that the slug reaches the exit.The frequency was calculated.The liquid superficial velocity plays a significant role in affecting the slug frequency.When keeping the gas superficial velocity constant,the frequency will increase with the liquid superficial velocity.

Acknowledgement

The work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) under the Ministry of Science,ICT &Future Planning (2018R1A2B6003623).