Jin Zhao,Zhi Ning*,Ming Lü,Geng Wang

College of Mechanical and Electrical Engineering,Beijing Jiaotong University,Beijing 100044,China

Keywords:Flow focusing Pattern transformation Morphological changes Numerical simulation

ABSTRACT The flow focusing nozzle is a new type of nozzle that performs effective atomization of the discrete phase by means ofhigh-speed motion of the continuous phase.The flowpattern and its morphologicalchanges have a significant effect on the atomization,but the in fluence of different parameters on the morphological change of the flowpattern remains unclear.The flow focusing pattern and morphologicalchanges in the two-phase flowinside the nozzle were simulated numerically,based on the volume of fluid method.The results demonstrate that the ratio of the nozzle-to-capillary distance and capillary diameter,the gas–liquid velocity ratio,and capillary diameter have significant effects on the flow pattern.When the ratio of the nozzle-to-capillary distance H and capillary diameter D increases,or the capillary diameter D increases,the flow pattern tends to transform into a laminar form;however,when the gas–liquid velocity ratio V increases,the flow pattern tends to transform into a turbulence form.Furthermore,we define the cone-shaped expansion rate,cone-shaped focusing rate,and cone angle in order to study the morphological changes in the cone shape inside the nozzle.The results indicate that the morphological change of the cone shape and flow pattern transformation is interrelated.When the cone shape tends to be unstable,the flow pattern changes towards flow blurring,whereas,a stable cone indicates that the flow tends to exhibit a droplet pattern.

1.Introduction

The use ofenergy has always occupied a highly importantposition in the development of human society.In recent years,the lack of fossil fuels has resulted in us facing the problem of energy shortages once again,and the impact of fossil fuels on the environment is also an issue to consider[1].There are two options for addressing the above problems: find a cleaner,new energy source,or improve the current usage efficiency of fossil energy.In the field of internal combustion engines,various new fuels are available for use,and the means by which to improve their atomization efficiency has become a significant research topic.

Clean and efficient combustion is largely dependent on the spray produced by atomization,which contributes to effective fuel evaporation and its uniform mixing with the air.However,the viscosities of new alternative fuels such as biodiesel,glycerol,and others are high,making them difficult to atomize.Therefore,numerous different atomization methods have been used for these liquid fuels in order to achieve effective atomization[2–7].

The pressure-atomizing nozzle has a simple structure,but cannot obtain a fine atomization effect for high-viscosity liquid.Ultrasonic atomization nozzles exhibit effective atomization only for low- flow liquids.The air blast nozzle provides effective atomization for highviscosity liquids,but this requires preheating of high-viscosity fuels.The effervescentatomizing nozzle assists liquid atomization by forming small bubbles inside the nozzle.However,the internal two-phase flow regime may transit from bubbly to slug flow with large bubbles or annular flow with no bubbles.Thus,for high-viscosity liquid,the above nozzles cannot achieve effective atomization[8–11].

A new two-phase flow nozzle known as the flow blurring nozzle was proposed by Ga?án-Calvo in 2005.The structure of this nozzle is illustrated in Fig.1.It consists of a capillary and an exit orifice with the same diameter D.A gap of height H exists between the capillary tip and orifice.This structure was originally used in the flow focusing nozzle.However,Ga?án-Calvo experimentally determined that,when H/D is less than 0.25,a new phenomenon which he called flow blurring will occur,as indicated in Fig.2.For a set atomizing air flow rate,the FB injection concept creates a “ five to fifty times”larger fuel surface area than a plain-jet AB atomizer,which is highly beneficial for improving atomization efficiency[12,13].

Fig.1.Nozzle structure.

Two factors determine whether flow blurring can be achieved:the structure of the nozzle,and the two-phase flow parameters.The size of the flow blurring nozzle applied to the internal combustion engine is obviously different from the flow blurring nozzle proposed by Ga?án-Calvo's[14–16].The flow parameters are also very different relative to the flow focusing.In the flow blurring nozzle used in the internal combustion engine,when the H/D is less than 0.25,it is still unknown whether the flow blurring phenomenon appears,and the transformation mechanismof the flow focusing and flow blurring remains unclear.The change in the cone inside the nozzle leads to the flow focusing transforming into flow blurring;however,its transformation law and mechanism are not clear.

In this study,the impact of the structural and operating parameters on the cone of the flow focusing and blurring nozzle was numerically simulated,based on the volume of fluid(VOF)method.The remainder of this paper is organized as follows.The VOF method,governing equations,and numerical method are outlined in Section 2.The solvability conditions and validation of the numerical method are provided in Section 3.Results and discussions are presented in Section 4,which includes a study on the flow focusing pattern and the morphological changes in the internal two-phase flow of the nozzle.Finally,conclusions are provided in Section 5.

2.Governing Equations and Numerical Method

2.1.Governing equations

This paper introduces a preliminary study on the in fluence of structural and operating parameters on flow focusing and internal nozzle two-phase flow.The research object includes two components:the gas and liquid phase fluids.It is assumed that the gas and liquid phases are viscous and incompressible.Furthermore,the following assumptions are reasonably made:(1)no heat transfer occurs at the interface,and(2)the effect of gravity is neglected.

Under micro-scale conditions,the gas–liquid two-phase flow speed is low,so the gas–liquid can be regarded as incompressible viscous fluid.The study of Ling Zhiyong demonstrated that,under microscale conditions,the in fluence of gravity on the flow rate and velocity is small and thus negligible[17].Therefore,the continuity and momentum equations can be reduced to:

Fig.2.Two different phenomena at varying H/D.

Table 1 Summary of physical parameters

The VOF model introduces the fluid volume function α,which is used to calculate the volume fraction of the two phases in each grid cell in order to capture the gas–liquid interface.Taking the gas liquid two phase flow as an example(where g represents the gas and l represents the liquid),αl=1(αg=0)indicates that the control volume is fully occupied by the liquid phase;αl=0(αg=1)indicates that the control volume is fully occupied by the gas phase;and 0＜αl＜1 indicates that the gas–liquid interface is present in this control volume.In this control volume,parameters such as density and viscosity in Eqs.(1)and(2)are calculated by the average of the two-phase volume,as illustrated in Eqs.(3)and(4).

In the VOF method,the diffusion equation of volume fraction α in VOF method is used to solve its variation[18–20].Use liquid phase as an example:

In the VOF method,the continuous surface force model is used to simulate the surface tension under micro-scale conditions;that is,the source term in Eq.(2).

In this equation,γ is the two-phase surface tension coefficientand κlis the interface curvature.

2.2.Numerical method and parameter settings

In the numerical calculation used in this paper,the air is the continuous phase,while the distilled water is the discrete phase.Assuming that the nozzle is full of air at the initial flow moment,the air and water flow from the two-phase inlet at a constant flow rate from t=0 s.Numerical simulations were carried out for three cases in which D=1 mm,1.5 mm,and 2 mm.In each case,we changed the nozzle-to-capillary distance H and the air and water velocities.A numerical simulation was carried out on the two-phase flow pattern inside and outside the nozzle.

The governing equations presented above are solved by using the computational fluid dynamics software Fluent.A first-order implicit scheme is used to discretize the temporalterms,and a second-order upwind differential scheme is used to discretize the momentum equation.The time step,Courant number,and sub-relaxation iteration factor are selected according to the stability and convergence of the calculated results.The solution procedure employs the pressure implicit with splitting of operators algorithm,which used for transient problems.

3.Solvability Conditions and Verification

3.1.Computational domain and solvability conditions

The physical parameters of the distilled water and air are set at a temperature of 15°C.The values of these parameters as used in the calculation are displayed in Table 1.

The study object consists water and air;thus,the calculation area consists of the interior nozzle area and external flow field.As the research object is axisymmetric,and we are only concerned with the axial direction change,our issues can be reduced into a 2D problem and we solve the equations in two-dimensions.Furthermore,for changes regarding the jet morphology,a rectangular mesh can easily cause all mesh cells to be equal,while polar mesh cannot,as it results in dense internal cells and sparse outside cells.Therefore,rectangular mesh is more appropriate than polar mesh.Finally,the calculation area consists of the inner nozzle area and external field,as illustrated in Fig.3.In the figure,it can be observed that the calculation area contains two air inlets and one water inlet,and we define the gas–liquid interaction region as the gas–liquid mixing chamber.The two-phase flow change in this region is one of the focus points of this study,as is the morphological changes in the external jet outside the hole area.

Fig.3.The calculation area consists of the nozzle inner area and external field.

Fig.4.Comparison of calculation results of jet diameter at different flow rates with data in the literature[12].

Fig.5.Comparison ofjetdiameter calculation results atdifferentgas pressures with data in the literature[12].

Both the air and water inlets use the velocity inlet boundary condition,while the nozzle far field uses the pressure far field boundary condition.The initial pressure of the pressure far field is set to 1×105Pa,while the remaining boundary conditions are set to varying initial values according to the different cases.

As the research focus is on the nozzle vicinity,different dense grids are used for various regions of the physical model.A cone-shape is generated between the capillary portand orifice,which belongs to the focus area of this paper;thus,this part of the mesh is dense.As the nozzle far field edge is notnecessary forthe research,this grid is sparse.The calculated region is splitby a structured grid.Grid independence analysis was performed;the nozzle area grid size is 0.01×0.01 mm2,and the remaining region grid sizes increase in turn.

3.2.Numerical validation

In order to study the accuracy of the numerical method proposed in this paper,the effects of the liquid flow rate and gas pressure difference on the jet diameter was investigated numerically,and compared to the original data in the literature[12]and the theoretical formula,as illustrated in Figs.4 and 5.In Fig.4,the triangular logo provides the theoretical formula result for the relationship between the liquid flow and jet diameter.The rectangular logo provides the experimental results of the jet diameter at different flow rates.The simulation results of this study exhibit strong agreementwith the theoretical formula and experimentalresults provided in the literature,and although there are certain small deviations,these are within an acceptable range.

Fig.6.Flow focusing pattern at different times.

Furthermore,Fig.5 illustrates the effect of gas pressure on jet diameter and provides the theoretical formula,experimental,and simulation results.Although there is significantdeviation among the simulation results ofthis paper,the experimentalresults,and the theoretical formula results,the overall trend is consistent.As it is more difficult to control the constant pressure difference atthe gas inletin the experiment,a deviation is observed between the experimental and theoretical formula results.For the simulation model in this paper,the inlet of the gas use in the pressure inlet model is unstable,which exerts a certain in fluence on the simulation results.The selection of the working conditions point is lower,which also affects the accuracy of the simulation and experimental results.The errors between the current simulation and experimental results,as well as the theoretical formula results,are within 6%.Therefore,the simulation model used in this paper for the overall trend provides higher accuracy.

In general,the simulation model proposed in this paper can effectively simulate the in fluence ofliquid flow on the jetdiameter.Although certain deviations exist in the simulation of the effects of gas pressure and jet diameter,little effect is observed on the overall trend.Overall,the simulation model in this paper is accurate.

4.Results and Discussions

4.1.Flow pattern evolution of flow focusing nozzle jet

In order to study the in fluence of the operating and structural parameters on the flow focusing phenomenon,we define the capillary diameter D,nozzle-to-capillary distance H,and gas–liquid velocity ratio V.Firstly,a numerical flow pattern simulation is carried out at D=1 mm and V=4,as in Fig.6.As indicated in the figure,the meniscus area variation has certain rules to follow for the given calculation parameters.Our numerical simulations begin from the interface and arrive at the capillary port.The meniscus increases in the nozzle area from 0.1 ms to 0.4 ms,following which the discrete phase generates a droplet that is gradually deformed while leaving the nozzle area,from 0.5 ms to 0.8 ms.After 0.9 ms,the systembegins to produce a second droplet,and thereafter to generate droplets steadily.

As we have learned from studies of other scholars,when the H/D value changes,the flow focusing pattern will change,from a droplet and jet pattern,to a turbulent flow focusing pattern,as illustrated in Fig.7.This numerical simulation is carried out under the condition of V=5.When H/D=0.8 or H/D=1,both are expressed as a droplet pattern,but the droplet frequencies differ.When H/D is reduced to 0.6,the flow pattern is changed to a jet pattern.When H/D continues to decrease,the jet begins to be unstable and eventually becomes a turbulent flow focusing pattern,as illustrated in Fig.7(e),and the meniscus area also becomes unstable.

However,H/D is notthe only factor determining the flow pattern.As illustrated in Fig.8,when V is reduced to 3,even when H/D=0.2,the flow pattern is also expressed as a droplet,which differs from the dropletpattern ata large H/D.Comparing Fig.8(a)and(b),itcan be observed that,in the small H/D dropletpattern,the dropletbreak distance is short.

Fig.8.The flow pattern of the flow focusing at different H/D,at the same V.

Moreover,the capillary diameter D has a significant effect on the flow pattern.When V=5 and D=2 mm,the flow is expressed as a jet pattern,as indicated in Fig.9(a).With a decrease in capillary diameter,the jet begins to appear unstable,as illustrated in Fig.9(b).If the capillary diameter is suf ficiently small,a turbulent flow focusing pattern will occur.

Fig.9.The flow pattern of the flow focusing at different D.

H/D,V,and D are the only surface factors that cause different flow patterns.We calculated the Reynolds and Weber numbers of the flow underthe differentcases,and identified certain disciplines,asillustrated in Fig.10.A clear dividing line can be observed between each of the three flow patterns,which are marked with dashed lines in the figure in order to divide the entire image into areas I,II,and III.Obviously,the ratio of We and Re,which represent the relative size of the surface tension and the inertial force,determines the nozzle flow pattern.When this ratio is below line 1,the flow exhibits a droplet pattern;when the ratio is between line 1 and line 2,the flow exhibits a jet pattern;and when the ratio is above line 2,the flow exhibits a turbulent flow focusing pattern.

Fig.7.Flow focusing pattern at different H/D.

Fig.10.Flow pattern under different Reynolds and Weber numbers.

4.2.Analysis of two-phase flow evolution inside nozzle and its relationship with flow pattern of flow focusing nozzle jet

The flow pattern changes in the flow focusing are largely owing to the variation in the two-phase flow pattern inside the nozzle.Therefore,a numerical simulation was carried out on the two-phase flow pattern inside the nozzle is carried out.Firstly,the internal conical cone angle,cone-shaped expansion rate,and cone-shaped focusing rate are defined,as illustrated in Fig.11.The ratio of the capillary diameter D to d(jet diameter at the hole area,as shown in the figure)is defined as the cone-shaped focusing rate,and the phenomenon indicated in Fig.11(b)causes the cone diameterto be largerthan the capillary diameter.Therefore,we define the ratio of the cone and capillary diameters as the cone expansion rate.The cone and jet diameters can also be used to study flow pattern changes,butfor differentcapillary diameters,these two parameters do not exhibit comparative significance.Thus,we define the cone-shaped expansion rate and cone-shaped focusing rate.

Firstly,the relationship between the operating and structural parameters with the cone angle is studied.Figs.12 and 13 illustrate the relationship between V and H/D with the cone angle.It can be seen that,with an increase in V,the cone angle also increases,and the flow pattern tends to transform into the turbulent pattern(turbulent flow focusing and flow blurring);however,the change trend of the cone angle differs.It can be seen from Fig.12(b)that the cone angle increasing trend is constant when D=2 mm,while it decreases at D=1.5 mm in Fig.12(a).Analysis of the dimensionless number reveals that the Reynolds and Weber numbers increase when V increases,indicating an increasing inertial force effect.This will eventually lead to a transformation of the flow pattern into flow blurring,and the cone angle concept is no longer present.Furthermore,the reduction in capillary diameter will accelerate this process,so that the increasing trend of the cone angle decreases.

Fig.13 indicates that,as the H/D increases,the cone angle decreases,and the flow pattern tends to transform into a laminar(droplet and jet)pattern.The same dimensionless analysis was performed,and differs from the situation in which the gas–liquid velocity ratio is changed.As the gas–liquid velocity ratio increases,the Reynolds and Weber numbers increase simultaneously,indicating that the inertial force dominates at this point,leading to an increase in the cone angle.However,when the H/D increases,although the Reynolds number also increases,the Weber number does not increase or even reduce.This indicates that the surface tension effect is more pronounced during this process,leading to a decrease in the cone angle.At D=1.5 mm,when H/D is greater than 0.8,the Weber number increases significantly,which leads to an increase in the cone angle at gas–liquid velocity ratios of V=3 and 3.5.This is because,although the gas phase velocity is relatively low at this time,the gas phase does not flow out of the hole quickly,owing to the large nozzle-to-capillary distance H.Thus,the gas phase begins to squeeze the liquid phase.The liquid phase surface tension interacts with the gas phase squeezing action,causing the cone angle to begin to increase.However,when D=2 mm,at the same gas–liquid velocity ratio,the gas phase velocity is too small,resulting in the squeezing action of the gas phase not being obvious;therefore,the cone angle does not increase.

Fig.11.De finition of two-phase flow cone inside nozzle.

Fig.12.Relationship between cone angle and the gas–liquid velocity ratio under different capillary diameters.

Fig.13.Relationship between cone angle and H/D under different capillary diameters.

Figs.14 and 15 illustrate the relationship between V and H/D,and the cone-shaped expansion rate.With an increase in V,the cone-shaped expansion rate decreases,and the flow pattern tends to transform into the turbulent pattern,which is also a result of the inertial force dominating this process.With an increase in H/D,the flow pattern tends to transform into a laminar pattern,and although the coneshaped expansion rate also increases,the trend is constantly changing.This is owing to the surface tension role increasing relatively at this time,there by affecting the cone-shaped expansion rate.When the capillary diameter differs,the effect of the H/D on the cone-shaped expansion rate also varies,which will be discussed later.

Figs.16 and 17 illustrate the relationship between V and H/D,and the cone-shaped focusing rate.It can be observed from the figure that the trend of the cone-shaped focusing and expansion rates is consistent.The flow focusing pattern changes are mainly a result of the interaction between the gas phase inertial force and the liquid phase surface tension.From analysis of the gas velocity diagram inside the nozzle,as illustrated in Fig.18,we can draw the following conclusions.When H/D remains constant,the increase in capillary diameter means that the nozzle diameter and downstream distance increase.According to the fluid mechanics formula,we can observe that this will lead to low gas velocity in the two-phase flow region,while the large nozzle diameter will cause the gas phase flow out of the nozzle more easily.This,in turn,will make the cone-shaped expansion and focusing rates increase.However,if D remains constant,the increase in H/D will also lead to the gas phase velocity of the two-phase flow region decreasing,which will eventually increase the cone-shaped expansion and focusing rates.

Fig.14.Relationship between the cone-shaped expansion rate and gas–liquid velocity ratio under different capillary diameters.

Fig.15.Relationship between cone-shaped expansion rate and H/D under different capillary diameters.

Fig.16.Relationship between cone-shaped focusing rate and the gas–liquid velocity ratio under different capillary diameters.

Fig.17.Relationship between cone-shaped focusing rate and H/D under different capillary diameters.

Overall,the three parameters of cone-shaped expansion rate,coneshaped focusing rate,and cone angle can be used to study the flow pattern transition of the flow focusing.When the cone-shaped expansion and focusing rates decrease,the flow pattern tends to transform into the turbulence pattern(turbulent flow focusing and flow blurring);when the cone angle decreases,the flow pattern tends to transform into a laminar(droplet and jet)pattern.When the flow pattern transforms into flow blurring,the gas velocity in the two-phase flow region is high,producing strong turbulence.At this point,the cone has disappeared and the above parameters have no practical significance.At present,no suitable dimensionless number has been determined for studying the two-phase region when the flow pattern is flow blurring.This will be studied in future.

Fig.18.The gas velocity diagram inside nozzle.

5.Conclusions

In this study,the flow focusing pattern and two-phase flow changes inside the nozzle were simulated numerically,based on the VOF method.

The flow focusing pattern can be divided into the droplet,jet,turbulent,and flow blurring patterns.The changes are a result of the interaction between the inertial forces and surface tension.The gas–liquid velocity ratio V,the ratio of the nozzle-to-capillary distance H and capillary diameter D,and capillary diameter D have a significant impact on the flow pattern transition.When the ratio of the nozzle-to-capillary distance H and capillary diameter D orthe capillary diameter D increase,the flow pattern tends to transform into a the laminarpattern;however,when the gas–liquid velocity ratio V increases,the flow pattern tends to transform into a turbulent pattern.

We define three parameters for the research on the morphology of the two-phase flow inside the nozzle,namely the cone-shaped expansion rate,cone-shaped focusing rate,and cone angle,in order to study the cone shape change.Through the discipline of these three parameters,we determine the relationship between the two-phase flow morphology inside the nozzle and the flow patterns.When the cone-shaped expansion and focusing rates decrease,the flow pattern tends to transform into the turbulent pattern;when the cone angle decreases,the flow pattern tends to transform into the laminar pattern.

For flow blurring,the gas velocity in the two-phase flow region is large,producing strong turbulence.At this point,the cone has disappeared,the gas phase is mixed with the liquid phase,and many bubbles are produced under the inertial force effect.The change in morphology of the two-phase flow of the flow blurring,and its effect on the dispersion effect of the discrete phase,will be studied further in the future.