Long-Zhou Xiao，Xin-Ping Long，Xue-Long Yang

(1.School of Power and Mechanical Engineering，Wuhan University，Wuhan 43000 China; 2.Key Lab of Jet Theory and New Technology of Hubei Province，Wuhan 43000 China)

1 Introduction

Jet pump is a sort of particular pump and mixing device working by the primary flow’s entrainment of the secondary flow.For the good sealing ability and the absence of rotating parts，jet pump has been widely used in engineering fields.According to the mode of jetting，it can be classified into two categories:center type jet pump and annular type jet pump(CJP and AJP for short).The jet in CJP is the confined compound circular jet，and the nozzle with a circular cross section is positioned at the center of suction chamber.While for AJP，the nozzle cross section is annular and encircles the suction pipe and the main flow in AJP is the confined turbulent annular jet.For this reason，AJP is suitable to convey the liquid with solid particles，such as potato，onion and capsule，even the live fish.

Thereare a large numberofstudies about turbulent jets in annular type nozzle［1-7］.Annular jets are frequently applied in bluff-body stabilized burner for the central recirculation zone which can help in flame stabilization and flue gas recirculation.The core issue of annular jet is the confined mixing process with the negative pressure gradient.Chan［1］studied the effects of the centrebody in annular jet.They found that the presence of the central recirculation zone and the wake vortices behind the centrebody had the effect of accelerating the annular jet into a fully developed state. Through flow visualization and LDA， Sheen［3］discovered the hysteresis phenomenon of flow reattachment occurred between Re=230 and 440 in annular air jet over an axisymmetric sudden expansion. In addition，a lot of studies aim on the annular swirling jet which is widely adopted in combustion for fuel jet［4-7］.

Nevertheless，there are few studies on AJP.The annular jet pump is a particular jet pump with the secondary flow surrounded by the primary flow.The internal flow is the sort of annular turbulent wall jet spreading in a pipe with great negative axial pressure gradient.Shimizu et al.carried out experiments on AJP and demonstrated the correlation between the structure parameters and the performance of AJP［8］. Elger et al.studied the recirculation in AJP with the area ratio varied from 2.19 to 3.86［9］.Long et al. investigated the optimum structural design of AJP［10］.

As indicated in the previous studies，the flow field within AJP is basically controlled by area ratio A and flow ratio q［9-11］resembling that in CJP［12］，and nearly all the studies on AJP concentrates on the influence of A and q on the pump performance regardless of the nozzle lip thickness［8，10，13］.However，only A and q are not enough to describe the flow detail and performance in AJP in the consideration of the nozzle lip thickness t.Through varying t under the same A and q，the mean velocity ratio V will be altered.Even when q is low and the difference is negligible，the velocity gradient at nozzle exit also differs greatly with different t.Long et al.investigated the lip thickness of nozzle on the performance and flow field of CJP，andthey found that the lip thickness greatly affects the development of the recirculation near the nozzle lip［14］.Similarly，for AJP，the thickness of the suction duct，responsible for the performance of an AJP to some extent，also has great influence on the flow field near the nozzle exit.

So，in this work，numerical method is adopted to analyze and figure out the influence of the nozzle lip thickness on the flow field and performance of AJP with different t.

2 Numerical Simulation Details

2.1 Simulated Pump Model

Shimizu［8］carried out many experiments on AJP with various structural parameters.One of his tested AJP with A=1.75(the area ratio of the throat and annular nozzle，Ath/Aj)，as shown in Fig.1，is chosen as the simulating prototype. The corresponding structural parameters in Fig.1 are given in Table 1，where，D is the outer diameter of annular nozzle;D0is the diameter of outlet pipe;Dsois the inner diameter of suction conical duct;Lcis the length of suction chamber;Ltis the length of throat;p0is the static pressure at suction duct exit;Vjis the velocity at nozzle exit;Vsis the velocity at suction duct exit;V is the velocity ratio Vj/Vs;α is the angle of suction chamber; β is the angle of diffuser.

Fig.1 Configuration of AJP

Table 1 Structural parameters of AJP［8］

In order to figure out the effect of the lip thickness completely and accurately，the thickness of the suction conical duct is set as 0.1，0.5，1.0，1.5，2.5 and 3.0 mm respectively besides the original t=2.0 mm. The schematic diagram of thickening strategy is shown in Fig.2， where t1and t2represent different thicknesses.The strategy for adjusting the nozzle lip is to keep D and the cross section area of annular nozzle constant and thicken the suctionpipe inward.

Fig.2 Schematic diagram of the strategy for thickening the nozzle lip

To analyze the correlation between t and the mean velocity ratio V precisely，the following equations are derived.The mean velocity of secondary flow is

where Qsis the volume flow rate of secondary flow. And Asois the cross sectional area of suction conical duct which can be obtained through

Combine Eqs.(1)and(2)，Vscan be expressed as

where Dstis the outer diameter of thesuction conical duct. Dividing Eq.(3)by the mean velocity of primary flow (Vj)，the following scalar equation is obtained:

With Eq.(4)，the variation of Vs/Vjwith t can be calculated.The result is shown in Fig.3.Obviously the effect of t is marginal when q is small.However as q increases，the deviation of Vs/Vjcaused by t gradually develops.Table 2 lists the values of Vs/Vjfor different t when q=0.58.

When q increases to 0.58 corresponding to the optimum working condition by Shimizu et al.［8］，the deviation of Vs/Vjbetween t=0.1 mm and 3.0 mm is as large as 28.4%.This significantly affects the recirculation in suction chamber.The effect of t，denominated as thickening effect，will be discussed in the following section.

Fig.3 Vs/Vjversus q under different t

Table 2 Comparison of Vs/Vjfor different t

2.2 Simulation Strategy

Assumed to be steady and incompressible，the flow inside AJP is controlled by the Reynolds averaged Navier-Stokers equations and continuity equations.The standard，RNG and realizable k-ε model and RSM model have been adopted to govern the turbulence characteristics.

For the boundary conditions，the inlet boundary is chosen to be mass flow inlet and the outlet condition is designed as pressure outlet.The wall is no-slip and standard wall function is adopted as the wall treatment. The maximum wall y+value was around 65 and for most of the wall regions，y+was around 35.

The commercial CFD code FLUENT 12.0 was used in this paper.The momentum equations were discretized by a second-order upwind scheme and the SIMPLEC algorithm was applied to solve the coupling of the pressure and velocity.

3D modeling was adopted. One of the most popular mesh tools，ICEM CFD，was used to generate the hexahedral grids.The calculation domain and grid system of AJP CFD model are shown in Fig.4.The grid number was initializedaround 1.8 million.Then the mesh at nozzle outlet and the suction chamber were doubled in three directions and the grid number increased to about 2.5 million to confirm that the grid was independent.The center point at nozzle exit was set as origin.Since the flow field at nozzle exit was complicated，the mesh was refined at the nozzle exit.

2.3 Experimental Validations

The experimental data presented by Shimizu［8］，including wall pressure coefficient(Cp)distribution and pump efficiency(η)，were utilized to validate the simulation results. The comparison resultsof Cpbetween experimental data and CFD results under four turbulent models when q=0.58 are shown in Fig.5.It can be found that Cpof each k-ε model along x direction is basically in line with the experimental data，while that of RSM suffers a considerable deviation.Therefore RSM model was excluded from the later simulation.

Fig.4 Calculation domain and grid detail of AJP

Fig.5 Comparison of Cpdistribution

Fig.6 illustrates the comparison ofAJP performance between the simulation results and the experiment data.The performance from the realizable k-ε model accorded extremely well with the experimental result when q＜0.4.When q＞0.4，the realizable k-ε model sees a certain deviation，while the results of the standard k-ε model compares well with experimental data.However，the actual condition of Shimizu’s experiment［8］is that the cavitation initiated at q～0.58.Nevertheless the cavitation was not taken into account in this CFD investigation，so the CFD result should be a little greater than the experimental result when q～0.58.Furthermore，based on the previous study［10］，the realizable k-ε model issuitable to predict the inner flow field and performance of AJP.

Hence it can be concluded that the results calculated by the realizable k-ε model agree well with the experimental data and the realizable k-ε model was utilized in the later simulation.

Fig.6 Comparison of AJP performance

3 Results and Discussion

3.1 Flow Field Details in AJP

The flow in AJP resembles that of the confined annular jet，while the main distinction of them is caused by the suction chamber and the diffuser. According to the position of recirculation in axial，the flow field can be divided into four regions A，B，C and D，which are presented in Fig.7.

Fig.7 Sketch of inner flow in AJP

Region A is the region where the potential core of the primary flow is completely consumed.In this region，the jet velocity distribution develops a nearly constant shape.Due to the convergent structure，the annular jet core disappears quickly and the region is drastically small.

Region B is the section before the separation point.The annular jet keeps entraining the secondary flow，while it has lost its characteristic completely.As the jet entrains the secondary flow rapidly to reduce the velocity of the central flow，there is a positive axial pressure gradient generated in this region.However the axial pressure gradient is not apparent，because it was confined by the convergence ofthe suction chamber.

Region C is the possible recirculation zone and the reverse flow generated here.The recirculation zone occurs only when the entrainment“appetite”of the jet cannot be satisfied by the secondary flow［15］.In this region the jet entrains all the secondary flow before spreading to the centerline.

Region D is downstream of the point where the jet attaches to the centerline.It consists of two parts:the stream in throat and in diffuser.Any longitudinal pressure gradient in this region is nearly zero.The flow tends to be uniform along the centerline.Through the diffuser，the flow will obtain a higher static pressure and then be pumped out.

It is noteworthy that regionsA and B will disappear and region C can even extend upstream into the suction duct with rather low q.Conversely，region C can disappear when q increases to a critical value［9］. However this will not be discussed in this paper.

The streamlines near the nozzle lip，with q ranging from 0.04 to 0.58，are shown in Fig.8.When q～0.3 and t～1.5 mm，the induced vortex appears near the nozzle lip.Then，with either q or t increasing，the vortex enlarges.In contrast，if t decreases to 0.1 mm which can nearly be neglected，the vortex vanishes thoroughly regardless of q.

The velocity profile along the radial direction with different t，0.1 and 3.0 mm，at different axial position x(0 and 3 mm)，is compared in Fig.9 where q is 0.04 for Fig.9(a)and 9(b)and 0.23 for Fig.9(c)and 9 (d). The nozzle lip separates the primary and secondary flow and leads to a“velocity collapse”on the velocity profile at nozzle exit.As depicted in Fig.9 (a)and 9(c)，the collapse appears to be the mutation of the velocity gradient at the intersection of the primary and secondary flow.The extent of the sudden change is mainly determined by t.So，induced by the primary flow，the entrainment effect with t=3.0 mm will be conveyed to the secondary flow more slowly than that with t=0.1 mm.Meanwhile，regarding the velocity profile at x=3.0 mm，it is apparently shown in Fig.9(b)and 9(d)that the sudden change of the velocity gradientstill exists for t=3.0 mm while completely disappears for t=0.1 mm.

In order to compensate the sudden change of the velocity gradient，the primary flow consumes more time on conveying the momentum and the delay is longer under the larger t.Thus，it is the delay that exerts a significant effect on the recirculation in the suction chamber and this will be discussed in the following section.Additionally，the mutation of the velocity gradient impacts little on the entraining ability of the primary flow，because it consumes little momentum for the primary flow to fill the“velocitycollapse”.

Fig.8 Stream trace near nozzle lip with different q

Fig.9 Velocity profile along the radial direction with t=0.1 and 3.0 mm

Due to the considerable large velocity gradient in the suction chamber，the recirculation emerges when q drops to a critical value which is determined by the structure of AJP.This is a serious issue in AJP design，which should be avoided inpractical operation. The size of recirculation increases with the decreasing q and the recirculation even stretches into the suction duct with considerably low q.Area ratio A is also responsible for the onset andshape of the recirculation.

The sketch of recirculation in the suction chamber is depicted in Fig.10.The secondary flow in the center begins to separate at the separation point and join together at reattachment point.With q increasing，the recirculation tends to be weakened and disappears at a certain q.

Fig.10 Sketch of recirculation in suction chamber

Fig.11 presented the separation and reattachment points of recirculation in AJP along the centerline with four different t(0.1，1.0，2.0 and 3.0 mm).With the increasing q，the separation point quickly moves away from the nozzle exit，while the reattachment point slowlyapproaches toward the nozzle exit. As t increased，the reattachment point moves away from the origin regardless of q.When q is low，the separation point even stretches into the suction duct and the smaller the t is，the more it stretches.When q＞0.13，the separation point with t=0.1 mm surpasses the othersand moves much further away from the nozzle exit.Even though，the recirculation vanishes when q= 0.23 regardless of t.

Fig.11 Location of recirculation in suction chamber with different t

The correlation between q and the width of recirculation W is shown in Fig.12.When q≤0.13，the nozzle thickness matters great on the size of the recirculation and the smaller t corresponds to a larger W.While the nozzle thickness exerts little effects on the recirculation size when q＞0.13.

There are two ways for t to affect the profile of the velocity gradient and then to influence the recirculation in suction chamber.One effect，the thickening effect，caused by thickening the nozzle lip，leads to the deviation of Vs/Vj.When q～0.58，the deviation of Vs/Vjwill be greater with larger t.This contributes to the reduction of the recirculation width.

Fig.12 Width of recirculation versus q with different t

The other effect，caused by the existence of the nozzle lip separating the primary and secondary flow，leads to the sudden change of the velocity gradient on the velocity profile.The primary flow has to smooth the sudden change of the velocity gradient and deliver the momentum to the secondary flow subsequently.Hence，the entrainment of the secondary flow was impeded and the delay lasts longer with the greatersudden change for the higher t.As a result，the separation point moves downstream with the increasing t.

As shown in Fig.11 and Fig.12，when q is low，which means that the thickening effect is so weak that can be neglected，and the separation point is far away from the inlet and the width of recirculation decreases with the increasing t.This is consistent with the preceding analysis.

As q increases，the thickening effect becomes stronger. When q approaches to 0.23 where the recirculation disappears nearby，the thickening effect and the sudden change of the velocity gradient both influence a lot on the inner flow.And because of that，the W-q curves for each t gradually converge into one curve and the separation point with t=3.0 mm moves away from the inlet faster than that with the other t.

3.2 Effect of t on the Mixing Process

In order to analyze the mixing process in suction chamber，two kinds ofvortex， streamwise and spanwise vortex，are adopted which are applied by Yang et al.［16］and Hu et al.［17］.They are defined in Eqs.(5)and(6)respectively.

where u，v and w are velocities in the x，y and z directions;D is the outer diameter of the annular nozzle and it is 55.0 mm in this work.Vjis the mean velocity in annular nozzle.

3.2.1 Spanwise vortex

The spanwise vortex in AJP is mainly caused by the shearing force between the flow and the wall.It can be classified into two types:one caused by primary flow and the other by secondary flow.

Fig.13 illustrates the decay of the maximum spanwise vortex.Apparently，when x/D ＜0.2，the four decay profiles of the maximum spanwise vorticity value are greatly different from each other.Then they quickly decay to a similar low value downstream.For t =0.1 mm the spanwise vortex value，at x/D=0.018，close to nozzle exit，is as much as 200 while only 100 for t=2.0 mm and 3.0 mm respectively.

Fig.13 Decay of the maximum spanwise vortex in the suction chamber

Fig.14 depicts the spanwise vorticity distribution at each cross section in suction chamber with t=0.1，1.0，2.0 and 3.0 mm.The shape of the spanwise vorticity distribution is same with that of the nozzle exits as expected in Ref.［16］.

When t=3.0 mm and x/D=0.018，the spanwise vortex is divided into two layers as shown in Fig.14. The spanwise vortices at the outer layer are much greater than that at the inner one.As the flow moves downstream，two layers join together and the strength of the spanwise vortex weakens gradually until it vanishes.

Fig.14 reveals that the spanwise vortex distribution tends to be more concentrated near nozzle exit with a smaller t.That is because the two layers of spanwise vortex will merge together more rapidly with lower t.When t=0.1 mm，as shown in the lower left corner of Fig.14，the two layers merge with each other immediately at nozzle lip which greatly enhances the entrainment of the secondary flow.On the contrary，if the distance between the two layers is large，the mixing of two layers will substantially consume the spanwise vorticity.For this reason，when x/D=0.091 where the two layers are completely merged，the maximum spanwise vortex with t=0.1 is still much greater than that with other t(Fig.13). Consequently，the entrainment of the secondary flow by the primary flow with a lower t is much stronger than other cases and the corresponding pump performance is better.

Fig.14 Spanwisevortex distribution in thesuction chamber of AJP

3.2.2 Streamwise vortex

Fig.15 illustrates the decay of the maximum streamwise vortex in the suction chamber of AJP. Compared with the spanwise vortex in AJP，the tiny streamwise vortex is negligible. The maximum streamwise vortex is less than 1% of the maximum spanwise vortex(Fig.13 and Fig.15).It is because that the nozzle shape boundary is regular and circular and the streamwise vortex is only caused by turbulence. Consequently the streamwise vortex contributes little to the internal flow field in suction chamber.

Fig.15 Decay of the maximum streamwise vortex in the suction chamber of AJP

Fig.16 shows the streamwise vortex distribution at each cross section with t=3.0 mm when q=0.58.The distribution of streamwise vortex for each t is nearly the same，so only one case with t=3.0 mm is presented. Four pairs of the smaller and weaker streamwise vortices in suction chamber form at x/D=0.091，which are called“horseshoe vortex”［17］，and they gradually disappear with the increasing downstream distance.

Fig.16 Streamwise vortex distribution in the suction chamber of AJP(t=3.0 mm)

3.3 Performance Comparisons

It has been validated that the AJP performance is greatly correlated with pump geometry and flow ratio q［13］.Fig.17 depicts the efficiency of AJP versus q under different t.Since the efficiency deviation under different t is less than 0.005 when q＜0.2，F(xiàn)ig.17 only displays η with q＞0.2.The AJP performance is better with the smaller t and the increment of η increases with the increasing q.The greatest increment of η caused by t is between t=0.1 mm and 3.0 mm when q=0.58，which is of great influences in engineering applications.So，providing the insurance of the structural strength，it is important to choose an appropriate tforbetterpump performance when designing an AJP.

Fig.17 Pump efficiency η versus q for different t

4 Conclusions

The flow inside AJPunder different nozzle lipthickness is numerically investigated in this work. The important conclusions are drawn as follows:

As the nozzle lip thickened，the AJP pump efficiency decreases correspondingly，and the reduction of pump efficiency tends to be greater when q～0.58 (the optimum working condition in Ref.［8］).

A small vortex is induced at the nozzle lip when q and t both reach to certain values.With the greater q and t，the vortex tends to be larger.However，the vortex disappears completely with t≤0.1 mm or q≤0.4.

The recirculation in suction chamber is affected by the nozzle lip thickness through the thickening effect and the mutation of velocity gradient.The thickening effect strengthens with the increasing t，while it is negligible when q≤ 0.1.The mutation of velocity gradient makes the separation and reattachment point moving downstream.The larger t is，the greater the sudden change of velocity gradient is and the further the separation and reattachment point shift downstream.

As the primary flow is entraining the secondary flow，the effect of spanwise vortex plays an important role，while the effect of streamwise vortex is negligible. Two layers of spanwise vortex are created by the primary and secondaryflow. Asthe flow moves downstream，the two layers merge together and the strength of spanwise vortex decays gradually until it vanishes.The existence of nozzle thickness hindered the mixing process.

Finally，it is found that the vortex zone for t= 3.0 mm at the nozzle lip is larger than that with other t and the spanwise vortex tends to be more intensive for the smaller t.Since the larger vortex zone accounts for more friction loss and the greater spanwise vortex contributes to fiercer mixing process， the AJP efficiency is higher for the smaller t.

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