Jing Zhang,Zhongyi Ge,Wei Wang,Bin Gong,Yaxia Li,Jianhua Wu,*

1 New Chemical Technology Transfer and Promotion Center of Liaoning Province,Shenyang University of Chemical Technology,Shenyang 110142,China

2 School of Chemical Engineering &Technology,Tianjin University,Tianjin 300350,China

Keywords:Concave-wall jet Baffle component Curvature Concentration Numerical simulation

ABSTRACT The concave-wall jet was formed in the vertical cylinder separator with inlet baffle component.The effect of curvature of radial baffle on the jet flow in the separator was investigated by the experiment of concentration and the numerical simulation of species transport.The results show that the concave-wall jet was confined within the narrow region near the concave-wall and the flow disturbance in the center of separator was weakened.The distribution of concentration and the flow region of wall jet depended on the curvature of radial baffle(K).Compared with the turbulent intensity of the plate baffle(K=0),that of concave baffle(K=2)reduced by 6.1%and the turbulent intensity of convex baffle(K=-2)increased by 13.5%.The best flow stability was obtained by the concave baffle because the baffle outlet was similar to convergent nozzle.The outlet convergent angle was between 0°and 19.5°when 0 ≤K ≤2.The secondary vortices were caused by the tangential velocity irregularity on the cross-section of two axial baffles in the separator with convex baffle.The baffle with K ≥0 was more suitable in separator inlet than that with K ＜0.

1.Introduction

Gravity sedimentation and centrifugal sedimentation were traditional mechanical separation methods for heterogeneous separation.However,the deposition rate and hydraulic efficiency of separation device were weakened by short-circuiting,circulation zones and inlet free jet.By arraying the inlet baffle in the vertical cylindrical heterogeneous separator,the free jet was transformed to the wall jet.A uniform and stable flow field was formed by the wall jet for improving fine particle separation [1,2].The baffle component of separator was composed of a radial plate baffle and two axial plate baffles,a vertical cylindrical separator with the inlet baffle was showed in Fig.1.The conventional radial baffle was designed as plane surface.The flow stability was improved [3,4]and the phase separation time was reduced [5] in the separator with inlet baffle.But the research on the effect of baffle structure on flow in vertical cylindrical separator was limited.The performance of separator with curved baffle should be investigated in detail for improving separation effect.

Fig.1.The vertical cylinder separator with inlet baffle component.

As the design of separator depended on many process parameters,the perfect design standards were not available for the optimal design of baffle configuration.The numerical simulation was widely applied for determining the optimal structure and position of separator baffle for practical engineering.Tamayolet al.[6,7]studied the effects of baffle configuration in primary settling tanks by RNG (renormalization group)k-ε and the species transport model.The optimal inlet position and baffle height were determined by the flow through curves in order to spoil circulation region.Razmiet al.[8] usedk-ε model combining with VOF (volume of fluent model)to simulate the hydrodynamics and sedimentation.It is indicated that the inlet jet energy was dissipated efficiently with the decreasing distance between baffle and inlet because the maximum velocity and sediment re-suspension were diminished.Husseinet al.[9]investigated the effect of baffles position on oil and water separation by the velocity measurement and oil removal efficiency experiment.The highest removal efficiency was obtained when the baffle was placed at the inlet to tank length ratios of 0.12.However,Nasiri and Abdolzadeh [10] simulated the flow in the gravitational settling separator with baffles,it is found that the particulate removal efficiency in separator with curved baffle+plate baffle was better than that with single vertical baffle.Haitham and Abdulrasool [11] investigated the thermal stratification in hot water storage with inlet baffle by RANS turbulence model.The result shows that the inlet jet momentum and mixing efficiency within the tank were reduced by arranging curved baffle.Prmmvongeet al.[12] proposed the three-dimensional isothermal wall square-channel fitted with V-baffle.The impingement/attachment flows on the wall were induced by the longitudinal counterrotating vortex flows by V-baffle.In authors’earlier study[13],the local flow in the baffle component of separator was analyzed.The result showed that the effects of curvature of baffle on velocity distribution and energy dissipation were significant.However,further investigation should be carried out for the effect of curvature of baffle on hydraulic efficiency in the separator.

In the present work,the numerical model of vertical cylinder separator with inlet baffle component is established.The distribution of the concentration is studied experimentally and numerically in the vertical cylinder separator.The influence of radial baffle curvature and separator structure on the velocity distribution and flow regime is analyzed.The optimal design of the vertical cylindrical separator with baffle is provided for the engineering design of separator baffle.

2.Numerical Models and Methods

2.1.Physical model

The physical model of separator and the cylindrical coordinates system are shown in Fig.2.The separator consisted of vertical cylinder,baffle component and inlet pipe.The baffle component including a radial baffle and two axial baffles was installed at separator inlet.Two symmetrical rectangular cross-sections were generated by the baffles and inner wall of separator,namely the baffle outlet.The separator inlet was used a section of pipe.The main dimensions of physical model were presented in Table 1.

Fig.2.The physical model(K ＞0).(a)is the isometric view and(b)is the horizontal symmetry plane of separator.

In order to analyze the effect of radial baffle curvature on the wall jets flow in the concave wall,two important dimensionless parameters were defined.The ranges of the relative curvature of baffleK=R0/Rand the aspect ratio of baffle outletAr=B/Hare showed in Table 1.According to the value ofK,the radial baffles were divided into concave baffle (K＞0),plate baffle (K=0) and convex baffle(K＜0),which are illustrated in Table 2.In the study,the range of Reynolds number wasRe=2347-14080,and Reynolds number was defined as follow:

where ρ is the fluid density,dis the inner diameter of separator inlet pipe,uinis the velocity of separator inlet cross-section,and μ is the fluid viscosity.

2.2.CFD grids

The half of the computational domain was discretized into grids for the symmetrical structure of separator about the vertical symmetry plane,as shown in Fig.3.The multi-block grid system[14,15] was used to improve the accuracy of results in the study for the calculation efficiency (Fig.3(a)).Fig.3(b) shows the distribution of cells on the horizontal symmetry plane in detail.The flow domain was split into two regions by the baffle outlet longitudinal section.The baffle outlet downstream region (Block-1) was meshed by hexahedral cell (size=10 mm).The tetrahedral cell(size=10 mm) was used to mesh the region between the vertical symmetry plane and baffle outlet longitudinal section (Block-2).Block-1 and Block-2 were linked by the grids of baffle outlet longitudinal section which was set as internal boundary.The refined grids near the wall were required to adapt the velocity variation in numerical model.The characteristics of wall jet depended on the grids density and nodes distribution near the separator wall.The boundary layer was made up ofNrows of equal number of cells with a growth factor of 1.2,the grids near wall were created by the uniform algorithm in GAMBIT.The first layer cells were equal in size to each other and the distance from cell centroid to wall was defined asyp.The radial thickness of the boundary layer grids in Table 3 were calculated,which was about 15.5-17.9 mm.

In order to improve the accuracy of the simulation results,the dependence of the grid density was investigated and the calculated tangential velocity was compared with the experimental data reported by Kobayashi and Fujisawa[16].A grid independence test was conducted under the turbulent condition,the geometric parameters of concave wall for the grid test wereR0=250 mm,B=8 mm.The comparison between grid-independent simulation data and experimental data [16] is shown in Fig.4.The number of cells and standard deviation based on the rows of the boundary layer cellsNand the distance from the adjacent cell centroid to the wallypwere summarized in Table 3.It can be seen that the standard deviation of velocity was less than 5% when the number of cells was 1.28 million.Therefore,N=10 (yp=0.5 mm,Fig.3)was selected,y+adaption was used to refine the grids near separator wall.The near-wall resolution was achieved for the requirements of non-equilibrium wall model [17].All flow domains of separators with different type baffle were meshed about 1.3 million grids in the study.

Table 1The characteristic dimensions of the separator as defined in Fig.2

Table 2The types of radial baffles

Table 3Comparison of meshing scheme at Re=7040

2.3.Numerical simulation

The incompressible water (T=285.15 K) was selected as flow medium and the segregated pressure-based solver was used for the computation in this study.The non-equilibrium wall modeling was adopted to treat near-wall flow in the separator.The SIMPLEC method[18,19]was used as the solution for pressure-velocity coupling.The pressure discretization was taken by the Standard scheme,and the momentum equation and turbulent governing equations were discretized by the second-order scheme.The inlet boundary for separator was set as the velocity-inlet withuin=constant and the turbulent intensity wasI?0.16(Re)-1/8=4.85%-6.06% [20].No-slip shear condition imposed in the separator wall and the baffle surfaces.The symmetry boundary was used in the vertical symmetry plane.The pressure-outlet boundary was applied to the top and bottom outlet cross-sections.

The Realizablek-ε turbulence model was suggested by Reynolds[21]and Shihet al.[22]in the case of large mean strain rate.The results of some studies such as references [23-25] show that the Realizablek-ε model appropriately predicted the hydrodynamic behavior of wall jet.The Realizablek-ε turbulence model was adopted because of the large mean strain rate of η ＞3.7 in this paper.The governing equations were solved by the finite volume method using ANSYS FLUENT.The continuity and Navier-Stokes equations were given as:

In the Realizablek-ε turbulence model,the modeled transport equations forkand ε were as follows [22]:

whereGkrepresents the generation of turbulent kinetic energy due to the mean velocity gradients.σk=1.0 is the turbulent Prandtl number for kinetic energy.

For the realizablek-ε model,Cμ was computed from

After the steady calculation of flow field,the model of species transport without reactions was used to solve the incompressible fluids mixing.The non-reacting species transport equation[26,27] was described as:

whereCis the concentration.Γtis the turbulent diffusivity coefficient.

Fig.3.Isometric view of grids.(a) and details near the baffle (K ＞0);(b) at horizontal symmetry plane.

Fig.4.Analysis of the grid independence at Re=7040.

In the study,the influence of gravity in the simulation was ignored because the mixing material consisted of two volumetric species and the second species also used the incompressible water.The self-diffusion coefficient is Γ=2.222×10-9m2·s-1of water at 285.15 K[28].The mass fraction of second species was set as 1.0 at the inlet boundary for unsteady species transport calculation.The area of different concentration was monitored on the crosssections of 2Z/H=-1,0,1.The distribution of concentration was calculated untilt*=15,where the dimensionless time was definedt*=t/(πR0/uin).

3.Experimental

3.1.Experimental system

In this research project,the dye-tracer visualization technology[29-32]was adopted to track wall jet.The experimental setup was composed of water circulation,tracer injection and image acquisition system,shown in Fig.5.The test equipment consisted of separator and tank,the separator was placed inside a tank (1000 mm×1000 mm×1000 mm).The separator was designed as same as the numerical model,the sizes referred in Table 1.The distance between the bottom outlet cross-section of cylinder and the bottom plate of tank was 100 mm.The tank was filled with water(T=285.15 K),and its level was 100 mm above the top outlet cross-section of the cylinder.A multi-orifice plate was installed before the circulated water inlet to ensure a uniform velocity distribution at the inlet cross-section.In the experiment,the concave baffle(K=2,as shown in Fig.5(a)),the plate baffle (K=0) and the convex baffle (K=-2,as shown in Fig.5(b)) were printed by UP BOX 3D printer.The hot melt extrusion method (MEM) was used by the 3D printer with 0.1 mm precision of printing,and the printing material was the ABS (acrylonitrile-butadiene-styrene) white wire.

3.2.Measurement

The visualization of the flow field measurement was a noncontact method using laser technique in the experiment.Visualization of fuel distributions in premixed ducts in a low-emission gas turbine combustor using laser techniques The jet region was illuminated by a λe=532 nm laser sheet of thicknesseL?3.0 mm using a stability Argon-Ion continuous wave laser.The central plane of laser sheet was set at the horizontal symmetry plane of the cylinder.The laser source was placed at the circumferential angle θ=90° from the fluid inlet and closed to the outer wall of tank.A CCD (charge-coupled device) camera was placed at the cylinder axis 750 mm from the horizontal symmetry plane of the cylinder for tracking the tracer along streamwise of wall jet.The frame rate of camera was set as 30 fps and the pixel size was 0.4 mm × 0.4 mm per pixel.The Value component was extracted from HSV (Hue,Saturation and Value) color space of the experiment video.

The visualization technology based on tracer was used to measure the flow field.The solution,5 g of Acid Ink Blue G was added in 1000 ml of water,was used as tracer in this experiment.A stainless steel pipe with the length 500 mm long and inner diameter 2 mm was used as tracer injection.The pipe was connected with the peristaltic pump by a hose.The tracer outlet was placed 80 mm distance before the multi-orifice plate to ensure thoroughly mixed between the tracer and water.The average velocity of the tracer was same as the water circulation inlet,the ratio of tracer flowrate to separator inlet flowrate was less than 5‰.

The operation process was carried out in this experiment.The visualization measurement was begun when the water circulation reached steady state in the tank.The laser and camera were started,and then the peristaltic pump was activated for injecting the tracer.The peristaltic pump was shut down after the tracer reached the circumferential 180°.Finally,laser,camera and recirculating pump were shut down.Fluid in the tank was discharged and the tank was cleaned for the next experimental test.

3.3.Experimental uncertainty

In these experiments,the low frame rate (30 fps (frames per second)) was selected for improving pixel recognition because the potential source of deviation was image post-processing.The mass fractions were calibrated at the same conditions before experiments to improve the accuracy of the post-processing.But the color near of the wall was deepened by the background under the laser sheet,and the error of the instantaneous images was caused by the laser pulse.To solve problems,the tracer diffusion area values from experiments involving repeated measures were obtained whent*=10 forK=0,Ar=0.25 andRe=7040.The standard deviation of the area difference was calculated with the Eq.(9).

wherenis the number of observation andSiis the tracer area measured.

The standard deviation was 2.1%and the calculation accuracy of image post-processing was set as 3σ=6.4%.The measurement accuracy of flowmeter used to obtain wall jet is 0.5%.The flow accuracy error of peristaltic pump (UIP,Kamoer,Shanghai,China)is less than 5%.The layer thick of UP BOX 3D printer was set as 0.1 mm,the minimum size of the baffles is 5 mm.The relative uncertainty was calculated that the maximum uncertainty was about 8.4% for all experiment.

Fig.5.Experimental device for the vertical cylinder separator with baffle component.Radial baffles with(a)K=2 and(b)K=-2 printed by the UP BOX 3D printer.

3.4.Comparison of simulated and experimental results

To verify the accuracy of simulated results,the simulated and experimental results forAr=0.25 andRe=7040 were compared.Fig.6 shows the distributions of dimensionless tracer mass fraction in the horizontal symmetry plane att*=10.The tracer mass fraction near the separator wall was higher than that in the center of separator.There is a significant difference in the tracer diffusion boundary in separator with different baffle.The tracer diffusion rate ofK=-2 was the fastest along streamwise and the region of tracer ofK=2 was the largest at θ ≤90°.In order to verify with numerical simulation and experimental values of tracer distribution,the tracer diffusion area with time of experiment and simulated was analyzed in Fig.7.For the concave,plate and convex baffles,the deviation ofC/Cin≥0.1 diffusion area were 5.6%,6.5%,4.3%.ForC/Cin≥0.3,the deviation was 9.0%,6.1%,7.3%in separator with different baffles (K=2,0,-2).Thus,the simulated results were reliable and the numerical calculation model was feasible in this study.

4.Results and Discussion

4.1.Distributions of concentration in separator with baffle of different types

The distribution of concentration was an important parameter for evaluating the mixing quality in the jet mixer [32-37].Fig.8 described the distributions of tracer concentration in the horizontal symmetry plane and the concave-wall with dimensionless timet*.The concentration near concave-wall was far higher than that in the center of separator whent*≤15.It is indicated that the concave-wall jet was formed near the inner surface of cylindrical vessel with baffle component.

In Fig.8,the tracer flowed from both side of baffle outlets and then converged at θ=180°.The expansion speed ofC/Cin≥0.3 along streamwise was the fastest.However,the regions ofC/Cin-≥0.5 changed barely at the radial direction,streamwise and spanwise whent*≥6.The distribution of tracer concentration near wall was affected by radial baffle type.The spread rate with concave baffle (K＞0) was the largest along radial direction,K=0 was the fastest along spanwise,andK＜0 was the largest speed along streamwise.There was the maximum concentration on the horizontal symmetry plane along streamwise of concave-wall jet forK≥0 in Fig.8(a) and (b).But the maximum existed in the planes of upper and lower axial baffles forK＜0,as shown in Fig.8(c).

In order to analyze the spread rate of wall jet in the separator,the effects of baffle component structure parameters on the tracer volume distribution withC/Cin≥0.3 whent*=10 at the range ofRe=2347-14080 were shown in Fig.9.The effect on the tracer expansion volume obviously increased with the increase of Reynolds number of separator inlet.The average of the volume distribution(C/Cin≥0.3 andt*=10) with the same outlet cross-section widthBwas calculated.Compared with the tracer volume distribution of the plate baffle(K=0),the volume ofK=2 increased by 1.4%and that ofK=-2 was higher 2.6%.The effect of the radial baffle curvatureKon the concave-wall jet was more important than the aspect ratio of baffle outletArand Reynolds number of separator inlet.The results about the local flow in inlet baffle of separator was proposed from our previous work [13],the structure of baffle(K＞0) was similar to the convergent nozzle andK＜0 was the divergent nozzle,the flow sections ofK=0 was about constant.Theobald[38]proposed that the free jet has the best stability when the angle of nozzle profile approximated to 15°.The outlet convergent angle of the side of the radial baffleK=2 was 19.5° in this study.Three baffle components (Ar=0.25 andH=80 mm) were selected to reveal the flow characteristic with the types of radial baffle (K=2,0,-2) whenRe=7040.

4.2.Distribution of the tangential velocity in separator with baffle component

Fig.6.The distributon of dimensionless tracer mass fraction in the horizontal symmetry plane at t*=10 for Re=7040, Ar=0.25.

Fig.7.Comparison of simulated and experimental results of tracer diffusion area with the injection time for Re=7040, Ar=0.25.

Fig.10 shows the tangential velocity distribution for explaining the effect of radial baffle type.The tangential velocity in the horizontal symmetry plane developed(Streamwise)and that in the cylindrical surface(R0-r=0.5B)was unfolded(Spanwise)along the circumferential direction.The dimensionless tangential velocity was calculated by using the average velocity of baffle outletubafto analyze the characteristics of wall jet.The velocity of concavewall jet was calculated by Eq.(10).

The radial expansion of streamwise was 1.8Band the spread of spanwise was 4.7Hin Fig.10(a) (K=2) whenut/ubaf≤0.1.The radial expansion was 1.0Band the spanwise spread was 5.1HwhenK=0 (Fig.10(b)).The radial expansion was 1.6Band the spanwise spread was greater than 5.0HwhenK=-2(Fig.10(c)).The conclusion of velocity irregularities in the three-dimensional convex wall jet of this study was coincided with the research of Patankar and Sridhar[39].In this study,the tangential velocity in the horizontal symmetry plane was smaller than that in the planes of upper and lower axial baffles.

The maximum tangent velocity of wall jet along streamwise is shown in Fig.11.Here,the term maximum velocity was the maximum value of velocity in the plane of 2Z/H=0,the real maximum velocity was searched in the calculation domain along streamwise.The real maximum velocity was not in the horizontal symmetry plane because of the velocity irregularities in three-dimensional jet flows.The three-dimensional concave-wall jet was divided into three regions based on the streamwise decay of the maximum velocity [40-42].As shown in Fig.11,the potential core region was not found.In the characteristic decay region,the power law relation depended onKwas excited between the maximum velocity decay rate and streamwise distance.The characteristic decay region was in θ ＜45° whenK≥0 and the region was in θ ＜90°whenK＜0.The real maximum velocity was higher than the term maximum velocity and gradually approaches.The term maximum velocity ofK＜0 was lower than that ofK≥0 radial baffles in θ ＜60°,but the real maximum velocity ofK＜0 was higher than that ofK≥0.EspeciallyK＜0,the term maximum velocity was 0.023ubaf,and the real maximum velocity was 0.676ubafat θ=25°.Theutmof concave-wall jet withK＜0 was the most seriously affected in the range of θ ＜60°.In the radial decay region,the effect on maximum velocity by the baffle outlet was weakened and the term and real maximum velocities were equal.Compared with the baffle ofK=0,the mean ofutmofK＞0 andK＜0 increased by 17.4% and 66.2% in θ ＞90° respectively.Theutmdecreased rapidly to zero when θ ＞160 °.

Fig.8.Distribution of the tracer mass fraction in 5 time-steps for (a) K=2,(b) K=0 and (c) K=-2 (Re=7040, Ar=0.25).

Fig.9.Effect of K and Ar on the tracer volume distribution of C/Cin ≥0.3 when t*=10 (H=80 mm).

The half-value width in the radial directionbtand spanwisebzalong streamwise was analyzed to illustrate the difference of concave-wall jet expansion.The half-value widthbtof the baffle ofK≥0 in the horizontally symmetric plane was divided into two sections,btofK＞0 was more than that ofK=0 in the range of θ ＜65° andK≥0 were nearly value ofbtin the range of θ ＞65°,as shown in Fig.12(a).ButbtofK＜0 was different from the radial baffle ofK≥0 because the flow instability of divergent nozzle.The spanwise expansion of the tangential velocity is described in Fig.12(b).The half-value widthbzgrowth rate of the concave-wall jet withK=0 was the fastest.The different baffle of typesK=2 andK=-2 in separator descended by 29.5% and 41.2% respectively.

Comparing the distributions of tracer concentration and the tangential velocity,it is concluded that the concave-wall jet of baffle withK=0 was the slowest of streamwise velocity,the narrowest of radial extension region and the widest of spanwise expansion region.The streamwise velocity of concave-wall jet with convex baffle (K=-2) was the fastest,and the narrowest of spanwise expansion region.

4.3.Distribution of the vortices in separator with baffle component

The flow stability near concave-wall was the primary factor for the enhancement separation in the vertical cylindrical heterogeneous separator [43,44].Therefore,the vortex characteristics near concave-wall in the separator with different type radial baffle were studied to reveal the relationship between the heterogeneous separation and the concave-wall jet.The distributions of axial vorticity and secondary vorticity with streamlines are shown in Fig.13 and Fig.14.The axial and secondary vorticity were given by the following Eq.(11) and Eq.(12).

Fig.13 describes the axial vorticity and streamlines in the horizontal symmetry plane.It is found that the radial range of ωz/(ubaf/R) ＞ 1 was contracted along streamwise,but that of ωz/(ubaf/R) ＞0.1 was expanded.There is an axial vortex for each type of baffles,and the position and intensity of vortex are illustrated in Table 4.It was indicated the circumferential angle θ of vortex center increased with the decreasing ofKvalue.The distance between vortex center and concave-wall was the narrowest forK=0 and the widest forK＞0.The vortex ofK＞0 was the strongest and that ofK＞0 was the weakest for the vorticity of vortex center in Table 4.For the radial baffles withK=2,0,-2,the areas ratios of ωz/(ubaf/R) ＞1 were 4.9%,7.3%,7.3% on the horizontal symmetry plane,and the areas ratios of ωz/(ubaf/R)＞0.1 were 50.7%,49.0%,47.0%,respectively.A triangular region with ωz/(ubaf/R)＜0 was formed from the baffle to the center of the cylinder.For the radial baffles withK=2,0,-2,the area ratios of ωz/(ubaf/R) ＜ 0 are 38.7%,31.5%,33.8% respectively.It is indicated that the axial higher vorticity region(ωz/(ubaf/R) ＞1) of the concave baffle was the smallest,and the region (ωz/(ubaf/R) ＞0) of the plane baffle was the largest.

Fig.14 describes the secondary vorticity and streamlines on the cross-sections θ=15°,45°,90°,135°.It can be seen that the distribution of secondary vorticity was different in the range of θ ＜90°for three types of radial baffles.There were multiple longitudinal vortices along streamwise,the position and vorticity of the vortex center are listed in Table 5.Fig.14 shows that the longitudinal vortices in pairs were found,which were symmetrical about the horizontal symmetry plane and the absolute value of the secondary vorticity was equal.There are four vortices formed byK=0,2 radial baffles in the cross-section of θ=15°,but vortex cannot be found in the cross-section of θ=45°,90°.There are four vortices formed byK=-2 in the cross-section of θ=15°,two vortices in the crosssection of θ=45°,one vortex in the cross-section of θ=90°,the vortices were close to the upper and lower axial baffles (i.e.± 1H).

Table 4The position and vorticity of axial vortices (Re=7040, Ar=0.25)

The region of ωt＞1 was analyzed in the cross-section of θ=15°,the radial ranges ofK=2,0,-2 are 1.12B,1.14B,1.83Band the spanwise ranges were 3.55H,2.45H,1.27H.The high vorticity region ofK=2 rapidly expanded along spanwise near the concave-wall.The local high vorticity region ofK=-2 rapidly expanded in the radial direction at the baffle outlet cross-section,the complex secondary vortices were formed in the near concave-wall.The secondary vortices ofK=-2 caused by the velocity near the upper and lower axial baffles was faster than that in the horizontal symmetry plane.

Fig.15 compares the effects of radial baffle types on the distribution of axial vorticity and secondary vorticity along streamwise in the separator.The absolutely vorticity flux has been defined by Zhuet al.[45],it can be expressed in the followings

Fig.15(a) shows that the absolutely axial vorticity flux was affected byKin the circumferential direction,ΩzofK=-2 was more than 4.42% ofK=0,and ΩzofK=2 was only less than 4.32%.The absolutely axial vorticity flux ΩzofK=-2 was the lowest when θ ＜75°and the highest when θ ＞90°,ΩzofK=2 was the lowest when 75° ＜θ ＜135°.Fig.15(b) depicts the distribution of absolutely secondary vorticity flux in the circumferential direction,ΩtofK=-2 was less than 12.9%ofK=0 and ΩtofK=2 was more than 0.56%.However,ΩtofK=2 was lower than that ofK=0 when 40° ＜θ ＜140°,the average value of ΩtofK=-2 was more than 29.5%ofK=0 when θ ＞90°.It is concluded that the absolutely vorticity flux ofK=2 was the lowest at the range of θ ＜30°and that ofK=-2 is the highest at the range of θ ＞90°.

4.4.The turbulent intensity in separator with baffle component

Fig.10.Distribution of the tangential velocity for (a) K=2,(b) K=0 and (c) K=-2 (Re=7040, Ar=0.25).

The distribution of tracer mass fraction was related to the turbulent intensity[46,47],and the distribution of turbulent intensity was used to evaluate the fluid disturbance of the jet [48,49].The turbulent intensity was calculated in the region of 0 ＜2Z/H＜5 along streamwise,radial direction and spanwise,as shown in Fig.16.Compared with the turbulent intensity of the radial baffleK=0,the turbulent intensity ofK=2 is reduced by 6.1% andK=-2 increased by 13.5%.Specifically,the turbulent intensity ofK=2 was less than that ofK=0 in the range of 30°＜θ ＜120°,2.5 ＜(R0-r)/B＜10,2Z/H＞1.The turbulent intensity ofK=-2 was more than that ofK≥0 in the range of θ ＞45°,(R0-r)/B＞4,2Z/H＞0.75.It can be seen that the disturbance was seriously near baffle outlet and the fluid was disturbed slightly away from the baffle outlet in the separator with radial baffle ofK＞0,andK＜0 was considerable to the contrary.

Fig.11.Decay of the maximum tangential velocity (Re=7040, Ar=0.25).

Fig.12.The half-value width of tangential velocity for (a) Radial expansion at the horizontal symmetry plane and (b) Spanwise expansion at (R0-r)/B=0.5 cylinder surface (Re=7040, Ar=0.25).

Fig.13.Distribution of the streamlines and axial vorticity in the horizontal symmetry plane for (a) K=2,(b) K=0 and (c) K=-2 (Re=7040, Ar=0.25).

Fig.14.Distribution of the streamlines and secondary vorticity for (a) K=2,(b)K=0 and (c) K=-2 (Re=7040, Ar=0.25).

The average turbulent intensity was affected by the baffle component structure parameters,as shown in Fig.17(a).The turbulent intensity ofK=2 decreased by 11.3%,and the turbulent intensity ofK=-2 was higher 14.7% than that ofK=0.The concave-wall jet velocity decreased with the increasing ofArwhen the Reynolds number of separator inlet was constant.The influence of the baffle component parameters (R,B,Hin Table 1) on the turbulent intensity was investigated,the dimensionless area of baffle outlet crosssection was defined asBH/(πd2/4).The effect of baffle outlet area on the average turbulent intensity in the separator is shown in Fig.17(b).It is found that the increasing area of outlet crosssection was an effective means to reduce the average turbulence intensity in the separator.Furthermore,the baffle curvatureKwas an important structural parameter for the influence of turbulent kinetic energy in separator.It is concluded that the turbulent kinetic energy with different type of baffle was variable,concave baffle ＜plate baffle ＜convex baffle.

Table 5The position and vorticity of longitudinal vortices (Re=7040, Ar=0.25)

Fig.15.Effect of the vorticity along streamwise for (a) Absolutely axial vorticity flux and (b) Absolutely secondary vorticity flux (Re=7040, Ar=0.25).

Fig.16.Variations of the turbulent intensity for (a) Streamwise,(b) Radial direction and (c) Spanwise (Re=7040, Ar=0.25).

Fig.17.Effect of K and Ar on the average turbulent intensity (H=80 mm).Abscissa of (a) is Reynolds number of separator inlet and (b) is the dimensionless area of baffle outlet cross-section.

5.Conclusions

In this paper,the flow characteristic of concave-wall jet in the vertical cylinder separator with inlet baffle component was investigated by numerical simulation and experiment.The effect of baffle component on the concentration and velocity distribution was analyzed,and the influence of the radial baffle curvature on the concave-wall jet was more significant than the aspect ratio of baffle outlet and Reynolds number of separator inlet.The spread rates of concentration were the fastest along radial direction for concave baffle (K＞0),along spanwise for plate baffle (K=0),and along streamwise for convex baffle (K＜0).The spanwise expansion region of concave-wall jet velocity with concave baffle (K＞0)was the narrowest and the velocity irregularity was weakest.The regions of axial vorticity ωz＞1 and ωz＜0 were the smallest in the separator with concave baffle.The average value of absolutely axial vorticity flux increased with the decrease of the radial baffle curvature,but that of absolutely secondary vorticity flux was contrary.However,the absolutely vorticity flux withK=2 was the lowest at the range of θ ＜30°and that withK=-2 was the highest at the range of θ ＞90°.The turbulent kinetic energy in the separator with different types of baffle was compared and the conclusion was concave baffle ＜plate baffle ＜convex baffle.The results in the study were very useful in predicting the concave-wall jet behavior of the vertical cylinder separator with radial baffle.The concave surface was considered as the radial baffle at separator inlet for engineering design and for increasing the hydraulic efficiency in future work.

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

This work was supported by the National Natural Science Foundations of China(51506133);Natural Science Foundation of Liaoning Province of China(2019ZD0078,2019MS259);and Key projects of Liaoning Province education department of China (LZ2019001).

Nomenclature

Araspect ratio of baffle outlet

Bbaffle outlet width,mm

bthalf-value width in the radial direction,mm

bzhalf-value width in the spanwise,mm

Cmass fraction of tracer

D0separator diameter,mm

dseparator inlet diameter,mm

eLlaser-sheet thickness,mm

Hbaffle height,mm

H0separator height,mm

Iturbulent intensity

Krelative curvature of baffle

kturbulent kinetic energy,m2·s-2

Lbaffle length,mm

Nrows of the boundary layer cells

nnumber of repeated measurements

ppressure,Pa

Rbaffle radius,mm

R0separator radius,mm

Rereynolds number

rradial coordinate,mm

S,Sidiffusion area of tracer,mm2

Ttemperature,K

ttime,s

t*dimensionless time

utmmaximum tangential velocity,m·s-1

xcoordinate,mm

y+near-wall mesh non-dimensional parameters,

ypdistance from the adjacent cell centroid to the wall,mm

Zaxial coordinate,mm

Γ self-diffusion coefficient

Γtturbulent diffusivity coefficient.

ε turbulent dissipation rate,m2·s-3

η the time scale ratio of the turbulence to the mean strain,

θ circumferential angle coordinate,(°)

λelaser excitation wavelength,nm

μ dynamic viscosity,Pa·s

ν viscosity,m2·s-1

vtturbulent viscosity,m2·s-1

ρ density,kg·m-3

σ standard deviation,

ωtsecondary vorticity,s-1

ωzaxial vorticity,s-1

Ω absolutely vorticity flux,s-1

Subscripts

avg average

baf baffle

i,jdirections in the Cartesian coordinate system

in inlet

m maximum

r radial direction

t tangential direction