Meifang Zhou,Hao Jiang,Yanjie Hu,Zhimin Lu,Haibo Jiang,*,Chunzhong Li,*

1 Key Laboratory for Ultrafine Materials of the Ministry of Education,School of Materials Science and Engineering,East China University of Science&Technology,Shanghai 200237,China

2 School of Materials Science and Engineering,Yancheng Institute of Technology,Yancheng 224051,China

Keywords:Thickness of injection ring Multiple jets mixing structure Computational fluid dynamics Penetration mode Jet interaction

ABSTRACT The radial multiple jets-in-crossflow mixing structure(RMJCMS)is extensively used in industrial manufacture.In this research,the effects of thickness of injection ring on mixing performance and factors influencing the mixing performance of RMJCMS were discussed based on the results of computational fluid dynamics.The simulation results showed that the dimensionless mixing distance,with the increase of the thickness of injection ring,drops from 1.1 to 0.18 first and then increases to 0.27 while the uniformity of flux monotonously improves,manifesting that the consistency of flux is not the single element determining the mixing performance.Analyzing the simulation results,a conclusion was drawn that the consistency of flux,penetration mode and interaction among injection flows which can be altered by adjusting the thickness of injection ring,determine the mixing performance of RMJCMS jointly.That is to say,in RMJCMS an injection ring with a suitable thickness can realize the function of injection and rectification simultaneously,which not only improves the mixing performance but also reduces the complexity of RMJCMS as well.

1.Introduction

Due to its brilliant mixing performance,jet-in-crossflow is a universal mixing structure used in industrial manufacture[1-7],especially in the field of producing fine nanoparticles with a narrow size distribution[8-10].The schematic diagram of radial multiple jets-in-crossflow mixing structure(RMJCMS)is shown in Fig.1a.In the mixing process induced by RMJCMS,the feeding gas introduced into the gas distributor first,the role of gas distributor is to make the feeding gas forming an annular distribution around the injection ring to realize radial multiple jets.After the feeding gas goes through the injection ring,the mixing between injection flows(feeding gas)and primary flow occurs in the mixing zone.

In the RMJCMS,a zone featured by the rapid production and dissipation of turbulent kinetic energy and fast decrease of the size of segregations is created[8,11]owing to the interaction between injection flows and between the injection flows and primary stream.The existence of characteristic zone is the significant cause for achieving rapid mixing and thus endows the RMJCMS with high mixing efficiency.Many experiments[2,12-22]and simulations[19,22-27]have been done to investigate the flow behavior of RMJCMS.According to previous research[28],it can be found that a nonlinear distribution of flux and pressure was formed along the circumference in the gas distributor (mass variable flow)due to the radial injection of parts of feeding gas and confluence of feeding gas and circulating flow(the other parts of feeding gas which were not jetted into the mixing pipe).The existence of mass variable flow caused the flux of injection flows to be different resulting in the deterioration of mixing performance.To improve the uniformity of flux between injection flows,rectifying accessory has been universally installed in the gas distributor of RMJCMS(Fig.1b and c).Many works have been done to investigate the effect of rectifying accessories on eliminating mass variable flow in the gas distributor[29,30].Li,Yadong[28]simulates the influence of five kinds of rectifying rings on flow distribution and finds that with the installment of rectifying ring,the uniformity of the pressure in the gas distributor and outlet velocity increase obviously,meanwhile a better uniformity is obtained when the aperture ratio of rectifying ring is smaller.Moreover,they summarized that the installment of rectifying ring is necessary for improving the flow uniformity of jet in crossflow.Although the addition of the rectifying ring actually improves the consistency of gas flux between injection flows,it increases the complexity of reactor and the design of an effective rectifying ring also needs to consider the pressure distribution in the gas distributor.As a result,an implementable transformation of injection ring structure without rectifying ring is expected to improve the mixing performance of RMJCMS.

Fig.1.Schematics of the radial multiple jets-in-crossflow mixing structure(RMJCMS):a—schematics of RMJCMS without rectifying ring;b,c—schematics of RMJCMS with rectifying ring(1:gas distributor,2:rectifying ring,3:injection ring,4:mixing pipe)and feeding streams;d—the geometric dimension of RMJCMS.

Based on the current computing power,coupling a realistic reactor geometry(especially with many perpendicular feed jets at multiple feed points)with a detailed complex chemistry and particle model to CFD is out of scope[31].Therefore,there are two popular solutions to investigate the flow behavior induced by a complex reactor geometry under industrial synthesis conditions using CFD,one is considering the detailed reaction kinetics but simplifying the reactor structure[31,32],the other is simulating the mixing with the detailed reactor structure but simplifying or neglecting reaction[33-37].However,if the simplifications of the structure are made,the complexity of flow behavior in the realistic reactor will be underestimated which limits the effect of simulation results on understanding the flow process.Therefore,the way of simulating realistic reactor structure but neglecting the detailed reaction kinetics becomes a common method to investigate mixing behavior in a complex reactor geometry.

The RMJCMS is commonly used as the mixing structure in the industrial chloride process[28,31,32,38].For the chloride process is a mass transfer control process[39],an investigation on intensifying the mass transfer of RMJCMS is required.The main mass transfer process involved in the chloride process is the mixing of reactants—mixing of TiCl4and O2.As a result,a simulation considering the example of the mixing of TiCl4and O2in the industrial chloride process was investigated to explore the effect of thickness of injection ring on the mixing performance and the elements which influence the mixing performance of the radial multiple jets-in-crossflow mixing structure using the commercial code,ANSYS Fluent.Compared with the cold model experiment result,the flow features induced by RMJCMS are accurately captured through simulation with the chosen models.The results show that with the increase of the thickness of the injection ring,the variance of injection flux decreases while the tangential component of the velocity of jet flows reduces monotonically.The dimensionless mixing distance,however,with the increase of the thickness of injection ring,drops from 1.1 to 0.18 first and then goes up to 0.27,manifesting that the uniformity of flux is not the single element influencing the mixing performance,the penetration mode and interaction among jet flows determine the mixing performance as well.Meanwhile,the uniformity of flux,penetration mode and interaction among jet flows can be altered by adjusting the thickness of the injection ring.That is to say,the injection ring can realize the function of injection and rectification simultaneously by the way of adjusting the thickness of injection ring without the rectifying ring,which not only improves the mixing performance of RMJCMS but also reduces the complexity of the mixing structure as well.

2.Model and Methods

2.1.Computational domain and boundary conditions

In the chloride process,the preheated O2(the primary stream)and TiCl4vapor(the feeding gas)are simultaneously fed into the mixing structure from different inlets.The introduced TiCl4vapor enters into the gas distributor and forms an annular flow around the injection ring.After TiCl4goes through the jet holes,O2and TiCl4vapor mix in the mixing zone.The geometry parameters of RMJCMS are listed in Table 1.The boundary conditions of TiCl4-inlet and O2-inlet are velocity-inlet.The flow rates of TiCl4and O2are 0.44 m3·s?1and 1.2 m3·s?1respectively which were calculated according to the presupposition that the yield of TiO2is 15000 tons per year.The turbulence boundary conditions were estimated using the empirical equation where I represents the turbulence intensity and ReDHrefers to the Reynolds number based on corresponding hydraulic diameter.Consequently,the turbulent intensity of TiCl4-inlet was set as 2.8%and O2-inlet was 3.8%.Smooth,no-slip boundary conditions were applied to all walls of the computational domain and the outlet was set as the pressure-outlet.

Table 1 The geometry parameters of RMJCMS

The thickness of injection ring(mixing pipe)n has significant influence on mixing behaviors of RMJCMS.To further reveal and analyze how the thickness influences the mixing performance,a mixing structure with rectifying ring was simulated in Case 6#.The thickness of injection ring in each case is presented in Table 2.For the rectifying ring,the diameter of rectifying hole is 5 mm,and the aperture ratio of rectifying ring installed in Case 6#is calculated based on Formula(2)which describes the proportion of aperture ratio of two adjacent parts(A and B)where Φ represents the aperture ratio,Pinand Poutrefer to the pressure at the inner side (at the radius of 130 mm)and outer side(at the radius of 145 mm)of rectifying ring.

Table 2 The detailed simulation conditions in corresponding case

The standard deviation of the mass fraction of TiCl4was defined as the mixture nonuniformity Δ,

where cipresents the mass fraction of TiCl4at each sampling point i,cmrefers to the facet-average mass fraction of TiCl4at a specified downstream plane and n is the total number of sampling points.When Δ ＜0.05,the mixing of reactants was regarded as sufficient[40],and the mixing distance(y)was defined as the corresponding distance between the injection plane(the plane where y=0 mm as shown in Fig.1c)and the plane where Δ is less than 0.05.Meanwhile,the dimensionless mixing distance was defined as y/D (D is the inner diameter of the mixing pipe and y refers to the mixing distance).

2.2.Computational methods

The commercial code,ANSYS Fluent,was used to simulate the flow behavior.A complex three-dimension turbulence flow mixing process was simulated under the governing equations of the continuity equation,Reynolds-averaged Navier Stokes equations (RANS),realizable k-ε turbulence model,energy equation,and component transport equations.

The continuity equation,RANS equations and energy equation used in this research are shown as follows:where ρ refers to fluid density,p is the static pressure,u presents the time-average velocity,T is the temperature;and τijis the Reynolds stresses,is the turbulent heat fluxes;and the value range of subscripts i,j is (1,2,3).To enclose the governing equations,turbulence model is required.Compared with the RNG and standard k-ε turbulence model,the realizable k-ε model can offer more accurate prediction of the round jets and free-flow of the mixing flow,because the strain and rotation tensors are introduced into the turbulent viscosity calculation[24]and to make the model and turbulent flow physics more consistent,constraints are applied to the Reynolds stress in the realizable k-ε turbulence model.Meanwhile,some precise predictions of the flow field of multiple impinging jets in crossflow and concentration field of multiple tandem jets in mainstream have been made by using the realizable k-ε model[23,24,41].Therefore,the realizable k-ε turbulence model was chosen in this research.Large-eddy simulation(LES)which has been proved that under the same mesh conditions,the computational cost is orders of magnitude higher than the RANS model[23].As a consequence,the LES model has not been adopted in this study,the RANS model with realizable k-ε turbulence equations which also has sufficient accuracy was selected.To verify the availability of the chosen turbulent model,some additional simulations whose geometry and boundary conditions were set according to the cold model experiments were done [42].After comparing with the cold model experiment results,a conclusion can be drawn that with the selected model,the flow features of RMJCMS are well captured by simulation.

To analyze the mixing performance of RMJCMS,the component transport equation which describes the mass transfer process was introduced for solving the concentration field:

Di,mis the laminar diffusion coeffciient for species i in the mixture,μtis the turbulent viscosity and Sctcorresponds to the turbulent Schmidt numberwhere Dtis the turbulent diffusion coeffciient).The laminar diffusioncoefficient and turbulent Schmidt number used here are 2.88×10?5and 0.7respectively.

The physical properties of gas-phase TiCl4were expressed as a function of temperature as shown in Table 3,and the calculating methods of the properties of the mixture(a mixture of TiCl4and O2)are listed in Table 4.Besides,the property parameters of O2in the Fluent database were used.

Table 3 The function expressions of physical properties for gas-phase TiCl4and the corresponding temperature range

Table 4 Calculating methods of physical properties for the mixture of O2and TiCl4

The residual was regarded as the criterion of convergence of the numerical solution.In this research,when residual of energy was less than 10?6and other parameters were smaller than 10?4,the numerical solution was regarded as converged[40].

2.3.Mesh independency tests

The cooperation of tetrahedron and hexahedron grid elements was used to discretize the computational domain.To obtain more exact information on mixing behavior,finer hexahedron grid elements were adopted in the mixing zone.Meanwhile,the dimensionless mixing distance was used as a judgment criterion to eliminate the effect of grid size on simulation results[40].The result of the mesh independence test of Case 3#is shown in Fig.2.With the increase of the number of grid elements,the influence of the number of grid elements on the dimensionless mixing distance is decreased.When the number of grid elements reaches 9399286,the influence is indistinctive which informs a mesh-independent solution is obtained.Therefore,considering the computational efficiency and accuracy of simulation results,the final number of grid elements used in the simulation after the mesh independence test is listed in Table 5.

Fig.2.The relationship between the dimensionless mixing distance and the number of grid elements for Case 3#.

Table 5 The number of grid elements after the mesh independence test

3.Results and Discussion

3.1.Cold model experiment and model validation

Cold model experiments were done in a pilot-scale radial multiple jets-in-crossflow mixing reactor in our previous work[42].In the experiment,compressed air was used as feeding gas and primary stream,and in order to obtain the mixing field,ethanol steam was injected into the feeding gas as the tracer material.To verify the availability of the chosen model,simulations were done under the same geometry parameters and boundary conditions with the cold model experiments.In the experiment,the Reynolds number of the mixture flow in the mixing pipe was maintained at 1.2 ×105and the MR remained at 11.MR is the momentum ratio of injection flow to primary stream which expresses as

where subscripts inj and p refer to the injection flows and primary stream,respectively;A represents the total area of jet holes for injection flow and the sectional area of the mixing pipe for primary stream;ρ denotes the fluid density and u is the velocity.The geometry parameters of the mixing reactor are shown in Table 1.Two kinds of injection rings with same thickness(5 mm)but different number and diameter of jet hole(the diameter of jet hole is 9 mm and 18 mm,the corresponding number of jet hole is 48 and 12 respectively)were adopted.The radial relative concentration distribution curves at different downstream plane(y/D=0.19,0.45 and 0.72)were used to evaluate the effectiveness of simulation.As presented in Fig.3,the flow features of RMJCMS are accurately captured,indicating that a credible prediction of the flow behaviors induced by RMJCMS is obtained through simulation with the chosen models.

3.2.Effect of the thickness of injection ring on the homogeneity of flux of jet flows

The flow in the gas distributor is a mass variable flow which decreases the uniformity of flux between injection flows and thus deteriorates the mixing performance of RMJCMS.The influence of the thickness of injection ring on the uniformity of flux between injection flows is shown in Fig.4(insert),it shows that with the increase of the thickness of the injection ring,the uniformity of flux increases monotonously.It is worth noting that in Case 6# (a mixing structure with rectifying ring and the thickness of injection ring is 5 mm),the variance of injection flux is only 0.0002,while in Case 1#(the thickness of injection ring is 5 mm without rectifying ring)the variance is 0.01,demonstrating the effectiveness of rectifying ring on adjusting the uniformity of flux.

3.3.Effect of the thickness of injection ring on the mixing performance

To evaluate the significance of the uniformity of flux between injection flows on the mixing performance,the relationship between the variance of injection flux and dimensionless mixing distance is presented in Fig.4.The mixing performance of mixing structure with rectifying ring(Case 6#)is almost 10 times higher than the mixing structure without rectifying ring(Case 1#),implying that the improvement of the uniformity of flux indeed improves the mixing performance as mentioned above.However,it also can be found that with the increase of the thickness of injection ring,the dimensionless mixing distance of the RMJCMS without rectifying ring,drops from 1.1 to 0.18 first and then goes up to 0.27.Case 3#(variance of injection flux is 0.07),instead of Case 5#(variance of injection flux is 0.04),has a comparable mixing performance with Case 6# (variance of injection flux is 0.0002)informing that the uniformity of flux between injection flows is not the only element deciding the mixing performance of RMJCMS.Further analysis needs to be done to explore the other elements which have a non-ignorable impact on determining the mixing performance of RMJCMS.

Fig.3.Radial relative concentration distribution curves of tracer material for simulation and cold model experiments.

Fig.4.Effect of the thickness of injection ring on the variance of jet flow flux(insert)and the relationship between the thickness of injection ring and the dimensionless mixing distance.

3.4.Effect of the thickness of injection ring on penetration mode

There are three penetration models to describe the flow field induced by RMJCMS according to the depth of jet flows penetrating into the primary stream.The schematic diagrams of three penetration models and the concentration contours of TiCl4mass fraction on the injection plane are displayed in Fig.5.When the thickness of injection ring is 5 mm(Case 1#)and 7 mm(Case 2#),the mass fraction of TiCl4at the center of the mixing pipe is 0 which demonstrates that the injection flows have not reached the middle of the mixing pipe and a typically under-penetration mode is formed.With the increment of the thickness of injection ring,the depth of jet flows penetrating into the primary stream increases.The over-penetration mode develops in Case 5# where the thickness of injection ring is 20 mm characterized by the collision of jet flows at mixing zone.However,under the over-penetration mode,the impinging of jet flows hinders the primary stream from going downstream,the primary stream has to deflect to the wall and flows towards the downstream through the spacing between adjacent jet flows.Meanwhile,the mixture fraction of TiCl4in the center of the mixing pipe in Case 3#(the thickness of injection ring is 8 mm)and Case 4#(the thickness of injection ring is 10 mm)are approximately 0.5,testifying the occurrence of the moderate penetration mode.A conclusion could be drawn that the variation of the thickness of injection ring changes the penetration mode which in turn influences the distribution of jet flows in the primary stream.

Fig.5.The schematic diagrams of three penetration models and the concentration contours of TiCl4mass fraction on the injection plane(in the legend,the value of 0 refers to pure primary stream-O2and 1 refers to pure injection flow-TiCl4vapor).

Fig.6.Radial relative concentration distribution curves of TiCl4mass fraction for different downstream planes:y/D=0 refers to the injection plane and r/R=0 represents the center of the mixing pipe.

Fig.6 shows the radial relative concentration distribution curves of TiCl4at different downstream planes.Cases 1#and 2#present the features of under-penetration mode — low concentration of TiCl4at the center of the mixing pipe and the penetration depth of jet flows is only a half of radius.Meanwhile,as shown in Fig.5,a relative high concentration of TiCl4is spotted in Cases 3#and 4#,and from the concentration curves,the injection flows almost reach the middle of the mixing pipe,indicating the occurrence of the moderate penetration mode.In contrast with Cases 1#-4#,the relative concentration of TiCl4is higher than 1 in Fig.6-Case 5#,which informs the formation of the collision of jet flows,denoting the existence of the overpenetration mode.

The distinctions between the penetration modes make the distribution of jet flows in the primary stream different,which leads to the disparity of the mixing process,and thus impact the mass-transfer process.The mixing process induced by RMJCMS consisted of convective diffusion,turbulent diffusion,and molecular diffusion [43].In the mixing process of jet-into-crossflow,convection diffusion is an important factor in determining the mixing effect and directly decides the scale of macromixing and segregation at initial stage.Meanwhile,the existence of turbulent diffusion continually decreases the scale of segregation and the scale of segregation finally reaches to molecular scale owing to the existence of molecular diffusion.Convection diffusion is decided by the distribution of the jet flows in the primary stream which can be adjusted by the thickness of injection ring as mentioned above.Though the turbulent diffusion and molecular diffusion are based on the flow condition and the molecular characteristics respectively,both of them can be improved through reducing the scale of segregation and increasing the contacting area of segregations.That is to say,the variation of the penetration mode alters the transfer process not only from the point of intensifying convection diffusion but also from the point of intensifying turbulent diffusion and molecular diffusion as well.Moreover,for the change of thickness of injection ring has a significant effect on determining the penetration mode,it can influence the mixing performance of RMJCMS obviously.

3.5.Effect of the thickness of injection ring on the interaction among jet flows

Fig.7.Average deflection angle(an average value of the angles between the direction of injection flows and radial direction)of injection flows at the injection plane and the contours of tangential component of the velocity:the positive value presents the tangential component of the velocity perpendicular to the paper towards outside while the negative value refers to the velocity towards inside.

The interaction between adjacent injection flows is a feature in the mixing process induced by RMJCMS.When the arrangement of jet holes on the injection ring is the same,the deflection angle of injection flowangle between the direction of injection flow and radial direction -directly reflects the interaction between injection flows.The average deflection angle of injection flows at the injection plane is shown in Fig.7,it can be seen that the deflection angle of injection flow decreases with the increase of the thickness of injection ring,representing the reduction of the interaction between injection flows.Fig.7 also displays contours of the tangential component of the velocity of injection flows along axial direction in which color shows the magnitude of velocity,the larger the absolute value is,the more obvious is the deviation of injection flow direction from radial direction.The tangential component of the velocity lowers distinctly with the increase of the thickness of injection ring as shown in Fig.7,demonstrating that with the increase of the thickness of injection ring,the injection flows are more preferred to penetrate the primary stream radially rather than forming a circulation flow along the wall,which leads to a diminution of interaction among injection flows.The velocity vector at the injection plane is presented in Fig.8 where the direction of the arrow denotes the velocity direction and color refers to the magnitude of velocity.It can be seen in Fig.8 that when the thickness of injection ring is 5 mm(Case 1#),a confluence of injection flows is formed which resulted from the large deflection angle of injection flows and a large velocity is found at the center of the mixing pipe for the flow is under-penetration mode-injection flows do not reach the middle of the primary flow,go downstream helically along the wall of mixing pipe instead.With the increase of the thickness of injection ring,the radial component of the velocity of injection flows increases which makes the penetration mode turn from under-penetration mode to over-penetration mode and thus influence the mixing effect of RMJCMS.When the thickness of injection ring is ＞8 mm,the injection ring generates an over rectification of the injection flows which makes the injection flows penetrate the primary flow in the way of overpenetration.Under the overpenetration mode,injection flows collide with each other at the center of the mixing pipe which impedes the primary flow going downstream.As it can be seen from Fig.8 with the increase of the thickness,velocity at the center of the mixing pipe decreases and gets minimum in Case 5#(thickness is 20 mm)demonstrating the transformation of the penetration mode from under-penetration to overpenetration.

In order to compare the intensity of interaction among injection flows more intuitionistically,the streamlines which describe the flow tracks of injection flows are presented in Fig.9.It is obvious that the change of the thickness of injection ring has the ability to adjust the flow direction of injection flows.When the injection ring is thin enough,the adjustment of injection ring on flow direction could be regarded as negligible,and thus the interaction between injection flows is large,forming a confluence of injection flows which goes downstream helically along the wall of the mixing pipe as shown in Fig.9-Case 1#.In contrast,the adjustment of injection ring is excessive if the injection ring is too thick which dramatically enervates the intensity of interaction among injection flows.As can be seen in Fig.9-Case 5#,the injection flows go downstream severally.Regardless of whether the adjustment of the flow direction is negligible or excessive,it decreases the mixing performance of RMJCMS due to the unsuitable interaction among injection flows and the inhomogeneous distribution of the injection flows in the primary stream.That is to say,a moderate interaction among injection flows is a necessary element in improving the mixing performance of RMJCMS.

The installment of rectifying ring distinctly improves the uniformity of flux between injection flows(Fig.4-Case 6#)and generates a moderate interaction between injection flows (Fig.9-Case 6#),and thus improves the mixing performance of RMJCMS.Compared with the other cases,the penetration mode of Case 3#is moderate penetration mode and the intensity of the interaction between injection flows is familiar with Case 6#which can be observed from Fig.9.Even though the uniformity of flux between injection flows is lower than Cases 4#and 6#,Case 3#—a mixing structure whose thickness of injection ring is 8 mm without rectifying ring,has comparable mixing performance with Case 6#.That is to say,the consistency of flux between injection flows influences the mixing performance of RMJCMS but is not the only element,the penetration mode and the intensity of interaction among injection flows are also elements impacting the mixing performance.

Fig.8.The velocity vector at the injection plane—the direction and color of arrow refer to the direction and magnitude of velocity respectively.

Fig.9.The streamlines of injection flow whose color refers to the magnitude of velocity of the fluid particle.

4.Conclusions

The exhibition of nonlinear distribution of flux and pressure in the gas distributor along the circumference decreases the mixing performance of RMJCMS.To further reveal and analyze the factors which determine the mixing performance of a complex mixing structure,radial multiple jets-in-crossflow mixing structure(RMJCMS),simulations were done considering the mixing of TiCl4and O2in the industrial chloride process using the commercial code,ANSYS Fluent in this research.The variation of the thickness of injection ring and the installment of the rectifying ring have a significant effect on adjusting the consistency of flux between injection flows.However,comparing the mixing performance of the mixing structure with/without rectifying ring,a conclusion was gained that the uniformity of flux has an influence on mixing performance but is not the only element determining it.The penetration mode of the injection flows penetrated into the primary stream and the interaction among injection flows determine the mixing performance of RMJCMS as well.Moreover,the variation of the thickness of injection ring,according to the simulation results,has the ability to change the penetration mode and adjust the intensity of interaction among injection flows.Therefore,the injection ring can realize the function of injection and rectification simultaneously by the way of adjusting the thickness of injection ring instead of the setup of the rectifying ring,which means that the reduction of the complexity of the mixing structure and improvement of mixing performance of RMJCMS can be realized concurrently.