Chunhui Li,Bin Wu,Junjie Zhang,Peicheng Luo,*

1 School of Chemistry and Chemical Engineering,Southeast University,Nanjing 211189,China

2 Hubei Sanjiang Aerospace Jianghe Chemical Technology Co.,Ltd,Yichang 444200,China

Keywords:Mixing T-jets mixer Swirling Computational fluid dynamics (CFD)Large eddy simulation

ABSTRACT Swirling addition to the stream is beneficial for the fluid mixing.This work aims to study the mixing process intensification in a conventional T-jets mixer by the swirling addition.After experimental verification by the planar laser-induced fluorescence technique,large eddy simulation with the dynamic kinetic energy sub-grid stress model is used to predict how the swirling strength (in terms of swirling number,Sw)and swirling directions affect the mixing performance,e.g.the tracer concentration distribution,mixing time,and turbulent characteristics in the T-jets mixers.Predictions show that the swirling strength is the key factor affecting the mixing efficiency of the process.The overall mixing time,τ90,can be significantly reduced by increasing Sw.Vortex analysis shows that more turbulent eddies appear in the collision zone and the turbulent kinetic energy dissipation rate increases obviously with the swirling addition.When Sw is kept constant,the mixing process can be accelerated and intensified by adding swirling to only one stream,to both streams with the opposite swirling directions,or to both streams with the same swirling directions.Amplification of the mixing process by enlarging the mixer size or increasing the flow rates is also optimized.Thus,this work provides a new strategy to improve the mixing performance of the traditional T-jets mixers by the swirling addition.

1.Introduction

Impinging jets(IJ)reactors have been widely used in the mixing process[1],absorption[2],crystallization[3],as well as heat transfer process [4] to enhance the mass and heat transfer rates.The confined impinging jets reactor (CIJR) [5] and T-jets mixer [6] are two typical IJ reactors,which have attracted extensive attention and research because of their simple structures.The CIJR can be used not only for the mixing of low viscosity fluids,but also for the mixing of high viscosity fluids.Whereas the T-jets mixer is usually used for mixing low viscosity fluids.Liet al.[7] have studied the flow regimes in a three-dimensional CIJR in the Reynolds number(Re)range of 100 ≤Re ≤2000.WhenReincreases,a segregated flow regime,a radial deflective oscillation,an axial oscillation,and a vortex shedding regime appear successively in the CIJR.Gaoet al.[8] have focused on the turbulent mixing in the CIJR with various configuration parameters in theRerange of 10620 ≤Re ≤21210.Liu and Fox [9] have investigated the chemical reaction process in the CIJR using numerical simulation and have found that the zone of intense mixing is only limited to a small region of the total volume of the CIJR.Although the mixing process is fast,the outlet stream has not been thoroughly mixed,and the complete mixing at all scales is not achieved in the CIJR.

Compared with CIJR,the T-jets mixer has a much simpler configuration with only two opposed jets and one mixing pipe.The impingement of two streams can produce a relatively narrow region with high turbulence intensity and mass transfer rate,which can achieve a faster mixing process than those in traditional reactors at a small mixing time scale [10,11].Thus,many studies have focused on the flow and mixing phenomena in the T-jets mixers.For example,Engleret al.[12]have investigated the liquid mixing in a T-jets mixer and found that the mixing performance in the engulfment flow regime can be improved significantly compared with those in the laminar and vortex flow regimes.Wonget al.[13] have found that the mixing times of micro T-jets mixers are in milliseconds,which are orders of magnitude faster than those achieved in the conventional micromixers.Zhaoet al.[14] have found that the overall volumetric mass transfer coefficients with Tee-junction microchannel contactors are two or three orders of magnitude higher than those of conventional liquid-liquid contactors.

However,a big challenge in practical applications is the absolute mixing time will increase significantly when the mixer is enlarged,although the dimensionless mixing time might remain essentially the same[15].To further enhance the mixing efficiency and reduce the mixing time,many researchers have improved the mixer configurations,or used external driving forces to increase perturbations,e.g.electrical field [16],acoustic wave [17],and magnetic field [18].Applying the integrated components to introduce the external force complicates the structure of the mixer[19],thus,modifying the mixer configuration becomes a preferable method to intensify the mixing process.In recent years,the introduction of the swirling flow to intensity the mixing process of single-phase flow or multi-phase flow has become an attractive topic.Due to the presence of centrifugal force,the swirling flows can cause the pressure gradient in the radial direction and improve the mixing efficiency significantly [20-22].

In our previous study for the liquid mixing in the multi-orificeimpinging transverse jet mixer,it is found that the interaction of the swirling crossflow with no-swirling-injected streams,or with swirling-injected streams in the opposite direction is beneficial for the fast mixing of fluids in a few milliseconds [23].For the gas-liquid two-phase flow in a self-suction jet reactor,swirling addition can significantly increase the gas suction rate compared with that without swirling addition [24].Thus,it is expected that the swirling-addition design can improve the mixing performance of other traditional mixers or reactors.

The objective of this work is to study how the swirling addition affects the turbulent liquid mixing characteristics in the T-jets mixer.Non-invasive planar laser-induced fluorescence(PLIF)technique is used to measure the tracer concentration distribution field,thus,providing basic data for validation of numerical simulation using the large eddy simulation (LES) approach.LES predictions are then used to analyze time-averaged concentration distribution,intensity of segregation,mixing time of the process,and turbulent characteristics in the T-jets mixers with different swirling strength of the jet streams,thus,providing a fundamental understanding of the flow characteristics in the T-jets mixers with swirling addition.Moreover,we intend to provide a new strategy to improve the mixing performance of the traditional T-jets mixers by the swirling addition.

2.Experimental

2.1.Mixer configurations and operation conditions

Fig.1 shows the core structure of the T-jets mixers,which consists of two configurations,i.e.two fluids flow in a no-swirling mode (Fig.1(a)),or in a swirling mode (Fig.1(b)).Four identical orifices with different angles are embedded symmetrically in the wall of the branch pipes.The swirling flow is created by designing certain jet angles (θ1and θ2) between the centerline of the jet orifice and the radial direction.In order to distinguish the swirling directions,we define the jet angle as positive when the swirling is counterclockwise from the left view.Otherwise,the jet angle is negative if the swirling is clockwise.Streams A and B are injected through the orifices into the branch pipes and then impinge with each other in the mixing pipe of the T-jets mixer.The mixing pipe diameter,D,is the same as the diameters of the branch pipes.The velocity ratio of stream B to stream A,is fixed at 1.The diameter of injecting orifices,d,is fixed at 4 mm,and the number of orifices,n,is 4.In order to describe the mixers with different configuration parameters,the mixer is named as TD(θ1,θ2),e.g.a mixer with the name of T16(30°,30°),represents the mixing pipe diameter is 16 mm,and the swirling angles and directions of the two streams are the same.The Reynolds numbers of stream A and stream B,ReAandReB,are in the range of 5300-42300 to ensure the flow in a turbulent regime.The configuration parameters and the operation conditions of the T-jets mixers are listed in Table 1.

Table 1 Operating conditions for the T-jets mixer with different configuration parameters.

2.2.Experimental setup and calibration of the PLIF technique

Fig.2 shows the schematic diagram of the experimental system.PLIF technique is used to study the mixing process of the T-jets mixer.Tap water is used as the working fluid,and Rhodamine 6G is used as the fluorescent tracer which is added into stream A.Two streams enter the buffer chambers around the jetting orifices by two centrifugal pumps.The flow rates are controlled and measured by the valves and the rotameters,respectively.A continuous laser (KSPL05) is used to excite the fluorescence,and the emitted fluorescence light is captured by a CCD camera (TXG14NIR,Baumer,Switzerland).The fluorescence intensity distribution on the measurement plane can be converted into the tracer concentration distribution.In each experimental run,about 500 images are captured,corresponding to a total sampling time of 5-10 s.More detailed experiments can be found in our previous work [25].

3.Numerical Methods

The LES approach is used for the numerical simulation.In the LES model,the transport of mass,momentum,energy,and other physical quantities in the system is mainly affected by largescale eddies,which are high anisotropy and defined by the geometry and boundary conditions.However,the small-scale eddies are not closely related to the specific problems solved and tend to be isotropic.Therefore,the transient simulation of eddies on the whole scale is abandoned,and only the turbulent motion larger than the grid-scale is predicted by solving the instantaneous Navier-Stokes equation.The influence of smallscale eddies on the motion of large-scale eddies is reflected in the instantaneous Navier-Stokes equation of large-scale eddies by sub-grid scale (SGS) turbulent model.In this work,the dynamic kinetic energy SGS model,which has been proposed by Kim and Menon [26],is applied to simulate the turbulent mixing process.

The governing equations in the LES model are obtained by filtering the time-dependent Navier-Stokes equations in Fourier space.The resolved-scale component of a quantity φ is given as:

whereGis the filtering function and determines the scale of the resolved eddies,and Λ is the fluid domain.The discretization finite-volume method provides the filtering operation as:

whereVis the volume of the computational domain.The basic governing equations are given as:

whereuiis the velocity component inidirection,ρ is the density,pis the pressure,and ν is the kinematic viscosity.τijis the SGS stress tensor,which represents the effect of the unresolved scales in the resolved ones and is given as:

Fig.1.Schematic diagrams of the T-jets mixer: (a) no-swirling addition design;(b) swirling addition design.

Fig.2.Schematic diagram of the PLIF measurement system.(1) Rhodamine 6G tank;(2) Tap water tank;(3) Centrifugal pumps;(4) Flow valves;(5) Rotameters;(6) Laser sheet;(7) KSPL05 laser;(8) T-jets mixer;(9) High-pass optical filter;(10)CCD camera;(11) Data acquisition and image processing system.

In order to close the equations,this additional stress is expressed in terms of the grid-scale velocity field,which is related to the filtered strain tensor,Sij,in the eddy viscosity model:

The dynamic kinetic energy model is chosen as the SGS model,and the SGS kinetic,ksgs,is given by:

The SGS eddy viscosity,νt,is defined as:

where Δfis the filter size computed asV1/3.τijis expressed as:

Then,the transport equation for the SGS kinetic energy is expressed as:

whereCkandC?,are determined dynamically by solving the transport of the sub-grid scale turbulence kinetic energy,and σkis equal to 1.0.

The mixing process is modeled by a passive scalar,f,which is controlled by fluid advection and molecular diffusion.The passive scalar transport equation is expressed as:

where Γ is the molecular diffusivity andJi,sgsis the subgrid scalar flux vector,which can be modeled using the gradient diffusion hypothesis as:

where νsgsis the viscosity or eddy viscosity,andScsgsis the turbulent Schmidt number.

In this simulation,the geometry of the T-jets mixer is created by Auto CAD.The commercial software ANSYS FLUENT 14.5.7 is used to solve the governing equations based on the finite volume method.The SIMPLE algorithm is adopted for pressure-velocity coupling.The bounded central differencing method is used for the spatial discretization of the momentum,turbulent kinetic energy,and concentration.The velocity boundary conditions are imposed on the inflows.The pressure outlet boundary condition is assumed at the outflow of the mixing pipe.A no-slip wall boundary condition is used on the wall.The time step is set to be 0.0002 s.To ensure the accuracy of the simulation,the time averaging must begin after some simulated time.Thus,when the pseudo-steady state is reached,the sampling settings are made and the data is collected continuously for 2-10 s,corresponding to the distance that the fluid flows through the mixing pipe is more than 200 times its diameter.

4.Results and Discussion

4.1.Validation of LES predictions

LES needs a high spatial resolution grid to ensure the accuracy of the solution.The influence of grid size on the simulation results has been studied in our previous work [27].It is found that whenD/Δxis equal to or larger than 55,the simulation results are in good agreement with the experimental data.Therefore,we adopt this grid generation strategy in this work.The grids consisting of about three million unstructured poly-hexcore cells are generated by Fluent Meshing.The minimum and maximum grid lengths are 0.05 mm and 0.3 mm,respectively.The dimensionless wall distance,Y+,is used to evaluate the grid resolution near the wall,andY+＜5 is a consensus criterion for LES prediction [28].In this work,theY+values of all T-jets mixers are less than 5,implying that the flow adjacent to the wall is in the laminar regime,and the grid resolution can satisfy the requirement of the simulation.

In order to have a further assessment,the time-dependent power spectrums are calculated (data not shown).According to the Kolmogorov -5/3 theory,the characteristic slop (-5/3) of the inertial range can be used for the test.The decreasing line with a slope of -5/3 appears at the intermediate frequencies of 100-1000 Hz,which lies in the range of more than one order magnitude of the frequency.Whenfk＞1000,it has a sharp decrease due to the energy dissipation,which indicates that the large-scale eddies and small-scale eddies are separated successfully in the numerical simulation.

Fig.3 provides a further comparison of the time-averaged concentration distribution between PLIF experiments and LES predictions.The predicted concentration distributions of the three selected T-jets mixers are all in good agreement with the experimental results,indicating that the LES approach can provide a reasonable prediction of the mixing process.

4.2.Effect of the swirling strength and swirling direction

The effect of the swirling strength on the macromixing performance of the T-jets mixer is first investigated.Here,the mixing pipe diameter is fixed atD=16 mm,andReM=21000.The jetting angle,θ,is changed from 0° (without swirling addition design) to 2°,15°,30°,and 45° to increase the swirling strength of the impinged streams.Fig.4(a)-(f) compare the time-averaged concentration distributions when two streams have opposite swirling directions.It is observed that there is an intense collision zone at the initial contact between the two streams.At a smaller jetting angle(e.g.θ=0°or 2°),the two streams continue to flow in a similar segregated flow pattern in the initial part of the mixing pipe,and then mix into each other to a stream of uniformly distributed concentration.When θ increases,the collision zone gradually expands,and the segregated flow pattern gradually disappears,implying that the two streams interact with each other more intensively and the mixing process is significantly accelerated.

To have a quantitative analysis,the intensity of segregation,IOS0.5,is used to evaluate the spatial unmixedness of the mixing process,which is expressed as [25]:

whereL90is the distance from the point ofy=0 to the point where IOS0.5=0.1,anduMis the mean velocity of the mixed fluid.The dimensionless mixing time,θM,is defined by Eq.(14).Combining with Eq.(13),θMis the ratio ofL90to the mixing pipe diameter,which represents the dimensionless distance required to reach the 90 % mixing uniformity in terms of the number ofD.

Fig.3.Comparison of the time-averaged concentration distributions between the PLIF results and the LES predictions.(1) T16(0°,0°);(2) T16(45°,0°);(3) T16(45°,45°),1 ＜x/R ＜1;(1a-3a): y/D=0.5;(1b-3b): y/D=1.0;(1c-3c): y/D=1.5.

Fig.4.Comparison of the time-averaged concentration distributions predicted by LES, ReM=21,000.

To quantitatively elucidate the effect of θ on the mixing process,we calculate IOS0.5and τ90for different T-jets mixers.It is seen from Fig.5(a) that all the IOS0.5profiles move downwards as the dimensionless distance (y/D) increases,indicating that the mixing uniformity increases.Each profile has two stages: the initial stage where IOS0.5decreases sharply withy/D,and the tailing stage where IOS0.5decreases slowly.In addition,the profiles in the case of larger jetting angles have markedly different trends from those with smaller jetting angles.For a larger θ,the tailing stage starts at a smallery/Dvalue,indicating the strong effect of the swirling strength on the mixing performance of the T-jets mixer.By using the location information with a value of IOS0.5=0.1,the 90%mixing time,τ90,is calculated and plotted against the jetting angle,as shown in Fig.5(b).It is seen that a larger swirling angle leads to a shorter mixing time,i.e.the mixing process can be accelerated by swirling addition into the impinged streams.Moreover,the effect of θ on τ90becomes smaller by further increasing the jetting angle when θ reaches 5°,which should be further analyzed.

Fig.5.Effects of the jetting angle (or swirling strength) on the IOS0.5 and the mixing time: (a) IOS0.5 vs y/D;(b)τ90 vs θ;(c) Sw vs θ;(d)τ90 vs Sw.

In general,the swirling number,Sw,is used to account for the swirling strength,which can be defined as the ratio of the tangential velocity component to the axial one [29],i.e.

wherewis the tangential velocity component,uis the axial velocity component,andRis the hydraulic radius of the tube.wanducan be calculated from the jetting angle,θ.The distributions of pressure can be neglected and the definition ofSwcan be simplified by the formula [30,31]:

Fig.5(c)shows the relationship betweenSwand θ for generating swirling flow.It is seen that the curve has an obvious inflection point at an angle of θ=5°,which is a good explanation for why the effect of θ on τ90becomes smaller when θ reaches 5°.Then the mixing time,τ90,is replotted against the swirling number,Sw,as shown in Fig.5(d).We can see that there is an approximately inverse proportional linear relationship between τ90andSw.This provides a strong support that the mixing process in the T-jets mixer can be significantly accelerated by swirling addition.

In order to understand mechanically how the swirling addition enhances the mixing process,turbulent vortex distributions and sub-grid kinetic energy dissipation rate distributions for different T-jets mixers are compared in Figs.6 and 7,respectively.TheQcriterion is generally used to evaluate the formation and development of the vortex structures,which is a widespread criterion to visualize the flow structure by identifying the invariants of the velocity gradient tensor [32].It represents the local balance between vorticity and strain rate,which can be used to identify the core location of the turbulent vortices.When no swirling is employed or the swirling strength is weak,there are few vortexes in the initial contact zone of the two streams(see Fig.6(a)-(c)),and the sub-grid kinetic energy dissipation rate is also relatively low(see Fig.7(a)-(b)).When θ increases,i.e.the swirling strength becomes stronger,turbulent vortexes gradually become more numerous,and the kinetic energy dissipation rate increases gradually.All these imply that the intensity of the interaction between the two streams increases due to swirling addition into the streams.Moreover,the stronger the swirling strength,the more intensive the interaction between the two streams.

Fig.6.Visualization of the turbulent vortex structures by three-dimensional isocontours of Q-criterion (Q ≥5 × 106),colored by the concentration distribution.

Fig.7.Comparison of the sub-grid scale kinetic energy dissipation rate.

To investigate whether the mixing process can be intensified by adding swirling to the two streams in the same directions,or adding swirling to only one of the two streams,the mixing performance of T16(45°,-45°),T16(45°,45°) and T16(45°,0°) in the case ofReM=21,000 are compared in Figs.4,6 and 7.It is seen that the tracer concentration distributions in the initial collision zone of the two streams are significantly different.However,in the mixing pipe,the two streams soon reach a uniform mixed stream,and no obvious segregated flows are observed in the three cases.The calculated τ90values for T16(45°,-45°),T16(45°,45°)and T16(45°,0°)are 21.0,20.0 and 22.1 ms,respectively,indicating that the macromixing performance of the three cases is similar.Adding swirling to two streams in the same swirling directions has a slight advance in the mixing intensification.

When two streams are in the same swirling directions,vortex visualization shows that a large number of jet shear vortices appear in the collision zone and the vortexes develop over a longer distance in the mixing pipe of T16(45°,45°),as shown in Fig.8(g).When the swirling is added to only one stream,the number of vortices is relatively less,and the sub-grid kinetic energy dissipation rate is relatively lower than those in the mixers of T16(45°,45°)and T16(45°,-45°) (see Fig.8(f)-(h)).

4.3.Amplification of the mixing process

The mixing process can be amplified by increasing the flow rates of two streams when the mixer configuration is fixed,or increasing the mixer size when the flow velocities are kept constant.Thus,the mixer,T16(45°,-45°)is first selected to investigate how the mixing performance changes when the flow rates of the two streams increase proportionally.Because the liquid properties are constant and the velocity ratio of two streams is fixed,the change ofReMcan reflect the change of flow rates.Thus,four cases withReMof 1.06 × 104,2.11 × 104,3.17 × 104and 4.23 × 104are compared to study the amplification effect.It is found that the time-averaged concentration distributions in these cases are almost the same,and four curves of IOS0.5vs y/Dalmost overlap each other (data not shown),implying that the dimensionless distance required to reach the 90 % mixing uniformity in terms ofDremains essentially the same.Plotting of the dimensionless mixing time,θM,againstReMin Fig.8(b)provides a strong support for this point.Although θMdoes not change significantly withReM,the absolute overall mixing time,τ90,decreases significantly with the increase ofReM,as shown in Fig.8(a).This provides an effective strategy to reduce the overall mixing time,i.e.increasing the flow rates of the mixed streams when the mixer configuration is fixed.

Another strategy for the amplification of the mixing process is to increase the diameters of the branch pipes and the mixing pipe,whereas keep the flow velocities of the two streams constant.Fig.8(d)shows that θMdoes not change significantly whenDis enlarged by 2 and 4 times.However,the overall mixing time increases linearly with the increase ofD,as shown in Fig.8(c).

Fig.8.Effect of ReM with a fixed mixer configuration of T16(45°,-45°)(a,b)or the size of the mixer at a fixed flow rate of uM=1.33 m·s-1(c,d)on the overall mixing time(a,c) and the dimensional mixing time (b,d).

To offset the significant increase in the overall mixing time,one can increase the fluid velocity (orReM) when the mixer size is enlarged.To check this strategy for the amplification of the mixing process,three T-jets mixers,T16 (45°,-45°),T32 (45°,-45°),and T64 (45°,-45°),are selected and the flow velocities in the mixing pipe are 1.33,2.65,and 5.30 m·s-1,respectively.The values of τ90are 21.9,18.6,and 15.5 ms,respectively,i.e.the absolute overall mixing time still has a decrease tendency when the mixer size is enlarged.The mixing process in the mixer of T64 (45°,-45°) can be faster than that in the mixer of T64 (45°,-45°).It is noted that the flow rates of two streams in this case are 7.68 m3·h-1.This indicates that industrial-scale material mixing could be achieved in milliseconds.

5.Conclusions

Following our previous work using swirling to enhance the mixing process,we investigate the mixing process intensification in a conventional T-jets mixer by swirling addition in this work.The swirling flow is generated by four identical orifices with different jet angles between the jet orifice and the radial direction around the branch pipes of the T-jets mixer.The swirling number,Sw,for different mixer configurations is calculated to provide a quantitative description of the swirling strength.The prediction accuracy of large eddy simulation using the dynamic kinetic energy subgrid stress model is assessed by analyzing theY+values and time-dependent power spectrum.The predictions are also validated by the time-averaged concentration distributions by the PLIF technique.

The effects of the swirling strength and swirling directions on the mixing performance are evaluated by the tracer concentration distribution,the mixing time in terms of the overall mixing time,τ90,and the dimensionless mixing time,θM,and turbulent characteristics.It is found that the swirling strength is the key factor affecting the mixing efficiency of the process,and τ90can be significantly reduced by increasingSw.Vortex analysis shows that more turbulent eddies appear in the collision zone and the turbulent kinetic energy dissipation rate increases obviously when the swirling strength becomes stronger.WhenSwis kept constant,the mixing process can be accelerated and intensified by adding swirling to only one stream,to both streams with the opposite swirling directions,or to both streams with the same swirling directions.

In addition,the amplification of the mixing process in the T-jets mixer has also been investigated.At a fixed mixing pipe diameter,increasing the flow rates of two streams proportionally has a small effect on the time-averaged concentration distributions,however,τ90decreases significantly with the increase ofReM.When the flow velocities of two streams are constant,the overall mixing time increases sharply with the increase of the mixing pipe diameter,D.To offset this significant increase in the overall mixing time,increasing the fluid velocity (orReM) is an effective strategy to reduce the mixing time when the mixer size is enlarged.Using an optimized design,industrial-scale material mixing could be achieved in milliseconds.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

We acknowledge the financial support from the National Natural Science Foundation of China(22078058).We also thank the Big Data Center of Southeast University for providing the facility support on the numerical simulations in this work.