GAO Bo and YANG Minguan

School of Energy and Power Engineering, Jiangsu University, Zhenjiang 212013, China

1 Introduction

Salt-out flow is a liquid-solid two-phase flow[1]. When crystal particles suspending in the transporting salt solution flow into a vortex pump, they mostly concentrate in the front clearance. The existence of these particles has an effect on heterogeneous nucleation, secondary nucleation,coalescence and sediment activities during the salt-out process in the pump. Different particle concentrations lead to various salt-out speed and features[2]. But the concentration distribution is mainly determined by particle flow structure in the volute. If temperature is not taken into account, it is of practical importance to measure the particle motion in the front clearance.

With the development of flow measurement technology,non-intrusive optical test techniques have become the main methods for two-phase flow measurements. Since laser Doppler anemometer(LDA) becomes a reliable means for accurate velocity measurements in single-phase flows,many scholars attempt to apply it to multiphase flows from 1980s. LEE, et al[3], carried out LDA measurements on the motion of particles in turbulent duct flows by an additional photodiode. SHENG, et al[4], combined LDA and an electrical probe to determine the bubbly motion.VELIDANDLA, et al[5], measured the gas-liquid two-phase flows in a pipe by means of discriminating the amplitude of LDA signals. LIU[6]and LI, et al[7], also did similar work.But all above were performed in relatively simple geometries. The first ones to apply LDA to complex pump internal two-phase flows measurements is CADER, et al[8]who successfully measured the liquid-solid two-phase flows in a centrifugal slurry pump, combining amplitude discrimination and velocity filtering. There are still limitations when LDA applied to two-phase flows measurements. The particle size and concentration information can not be obtained. Phase Doppler particle analyzer(PDPA) is an extension of LDA for measuring the particles diameter together with their velocity at defined locations, which becomes the first choice for multiphase flows measurements. PREVOST, et al[9], used PDPA to measure fluid/particle correlated motion in a jet. Spherical and nonspherical particles were measured by BLACK, et al[10]. AISA[11], et al, applied PDPA on particle concentration and local mass flux measurements. But studies on two-phase flows in complex geometries (such as turbomachinery) using PDPA are not generally available.ZHAO, et al[12], used PDPA in an axial flow rotor, but two-phase flows measurements were not involved in fact.

Vortex pump has a simple structure, making it possible for PDPA two-phase measurements. But there are very complicated flow patterns. There is an interaction between circulating-flow and through-flow. The axial and tangential vortexes coexist in the pump. In Refs. [13–15], the internal flow field in the vortex pump volute is measured using a five-hole probe. Several typical flow models have been proposed. The relative research work has also been done in Refs. [16–18]. However, very few reports on liquid-solid two-phase flow pattern in the pump have been published to date.

This paper describes a research on the salt-out two-phase flow in a model vortex pump by means of PDPA measurement. Accurate crystal particle motion and concentration distribution features are carried out as an investigative step towards the salt-out flow mechanism in this type pump.

2 Experiment System for Internal Flow Measuring

2.1 Experimental set and test pump

The experimental arrangement in Fig. 1 comprises the model pump, the circuit for the temperature-controlled solution and measurement instruments. The pump is driven by an electric motor running at 1 450 r/min and circulated solution from and to a 1 500 L tank through inlet and outlet pipes made of PVC. Electric heater, temperature control system and stirring apparatus are mounted in the tank to make sure the solution temperature is maintained within error ±0.1℃ in the test period. The flow is regulated by a stainless valve downstream of the exit pipe and measured by an electromagnetic flow meter. Pressure gauge and vacuum gauge are used to monitor the pump outlet and inlet pressure, respectively. The flow meter and gauges are all calibrated to an accuracy of more than 3%.

Fig. 1. Experimental set

The test pump sectional view and nomenclature are shown in Fig. 2. The diameter of the impeller 2r2is 120 mm, inlet diameter 2r1=40 mm, the vane width b=24 mm and the front clearance l=35 mm. The casing peripheral wall is a coaxial cylinder with a diameter 2r3of 170 mm.The impeller is equipped with back shroud and contains 8 radial vanes of uniform width. The design discharge Q0=14 m3/h, pump head H=4.5 m, rotational speed n=1 450 r/min and non-dimensional specific speed ns=105. The suction cover of the pump is made of polymethyl methacrylate to satisfy the PDPA measurement requires. Measuring window is also used at the right side of the pump body. In the figure, r is radial direction towards the casing peripheral wall and z axial direction towards the suction cover.

Fig. 2. Test pump sectional view

2.2 Experimental apparatus and measurement method

Two-dimensional point velocity and diameter measurements are performed with a two-color PDPA(Dantec) system. A 6 W argon-ion laser (Spectra-phsics Stabilite 2017) generates a multi-line beam containing both the 514.5 nm green and 488 nm blue lines. PDPA optical parameters are shown in Table. According to the methods proposed in Ref. [19], the velocities are obtained by two measuring patterns (axial and radial ones), and the point liquid and solid phase velocities are determined with a particle size discrimination approach. Glass beads (8–12 μm) with good following performance are chosen as tracer particles for liquid phase. Crystal particles with average diameter 100 μm are classified as the solid phase.

Supersaturated sodium sulfate solution, which has typical salt-out features, is chosen as the transporting medium. The solution is maintained at a constant temperature of 30±0.1℃, with density ρs=1 300 kg/m3and dynamic viscosity μ=3 mPa·s. After salt-out takes place,sodium sulfate decahydrate particles are separated out with mass density ρp=1 460 kg/m3. Measurement is carried out at the section Ⅷ of the volute. Measuring volume moves along radial direction point by point to acquire data.

Table. PDPA optical parameters

3 Results and Discussions

Velocity distribution of crystal particles affects the concentration result directly. First of all, velocity distribution curves are discussed. Then, particle size and PND distribution are analyzed. Symbols of normalized values in the following figures are defined. The radial position R=r/r2, axial position Z=z/b, discharge Q′=Q/Q0,peripheral velocity component U=u/r2ω, radial velocity component V=v/r2ω, and axial velocity component W=w/r2ω. Q is the actual pump discharge, ω is the rotating angular velocity of the impeller, and u, v, w is the actual peripheral, radial and axial velocity component,respectively.

3.1 Velocity distribution

3.1.1 Different operating conditions

Fig. 3 shows the peripheral, radial and axial velocity component distributing curves at Z=1.25 under three different discharges Q′=1.2, 1, 0.8.

In Fig. 3(a), peripheral component of particle velocity magnitude climbs up almost linearly at 0.5＜R＜0.75. But the velocity gradients under different discharges are not the same. Gradient of low discharge is smaller than that of high one. The peripheral velocity component increases as the discharge decreases in this region. The lower discharge is,the higher velocities are. As the radius increases, velocity differences among discharges are getting small because of the various velocity gradients, till R=0.75, nearly the same.This is the turning point of relation between peripheral velocity component and discharge. The velocity curves turn to fall down at 0.75＜R＜1. It reaches the maximum velocity value near R=0.85. The relation between peripheral velocity and discharge is changed into the opposite side of the former at R＞0.75. That is the higher discharge, the higher velocities. The velocity decreases and has a tendency to be constant at R＞1 beyond the impeller diameter.

Fig. 3. Three velocity components under different discharges

In Fig. 3(b), the magnitude of radial velocity along the direction r is negative. In other words, the positive value of velocity represents the reverse flow with the direction towards the pump axis. It is mainly the reverse flow at 0.5＜R＜0.75. Radial velocity decreases rapidly after it gets to the maximum value which indicates that the flow in this region is affected badly by the tangential vortex and circulating-flow flowing towards the impeller. The dividing point of circulating-flow and through-flow flowing into impeller is moved with the discharge. As pump discharge increases, the point moves towards the larger radial positions, leading to the increasing of through-flow flow rate. Radial velocity decreases as discharge increases at R＜0.65. It is indicated that the reverse flow is strengthened at the low pump discharge. It is the main reason that the pump efficiency is very low at this point. Radial velocity tends to be zero at R=0.75, and it has nothing to do with the discharge. Particle motion is turned into radial flow at R＞0.75. The velocity curves in this region are like a saddle shape due to the effect of the particle circulating-flow flowing out of the impeller. The larger discharge is, the greater radial velocity is.

The axial components of velocity distribution are shown in Fig. 3(c). The negative value means the velocity direction towards the negative z axis. That is the inflow direction from suction cover to the impeller. The positive value represents the outflow from the impeller. As R increases, axial velocity component increases gradually until R=1 because of the junction flow here between the through-flow and parts of particle circulating-flow flowing out of the impeller. Then it is turned from axial direction to radial direction, leading to the decreasing of the axial velocity but increasing of the radial velocity. It is the particle flow out of the impeller at R＞1.25. Axial velocity magnitude is changed into positive value. It varies with the pump discharge but the difference is much smaller than that of radial velocity.

3.1.2 Different axial positions

According to the classical flow models, flow patterns in the vortex pump are different at different axial sections. In order to understand the changing law of particle flow with axial positions, three velocity components of crystal particles are given at Q′=1 and Z=1.08, 1.25 in Fig. 4.

It can be concluded from the velocity curves shown in Fig. 4(a) that peripheral velocity at Z＝1.25 is a little larger than that at Z＝1.08 at R＜0.75. Besides, the difference is getting larger with the pump discharge and disappears at 0.75＜R＜1.1. Because of the circulating-flow the difference of radial velocity at two positions is much larger, especially at R＞0.8.

In Fig. 4(b), radial velocity magnitude just in front of the impeller is obviously greater than that far from the impeller.The value of the former is nearly twice as large as that of the latter. The position of the junction flow is also changed with the axial position. Relations of axial velocity components vary alternatively at two positions. The point W=0 is also different with the position. So far, thorough analysis on velocity changing with the axial positions can not be taken until more experiments are done in the future

3.1.3 Non-equilibrium velocity feature between two phases

Particles motion is closely related to the solution flow.The non-equilibrium velocity feature between liquid and solid phase is shown at Z=1.25 and Q′=1 in Fig. 5.

It can be seen from the figure that slip velocities of peripheral and axial components between liquid and solid phases are not significant (Figs. 5(a), 5(c)). It may relate to the characteristics of crystal particles and solution. The settling velocity can be estimated by Stokes law v∞=(ρp–ρs)gD2/18μ (with the particle diameter D). The particle terminal velocity is v∞= 0.3 mm/s. Furthermore, the particle hydrodynamic response time tp=ρpD2/18μ is very short,about 0.27 ms. Compared with the characteristic velocity(the circumferential velocity, about 9 m/s), slip velocities on the two directions are much smaller. But on the radial direction, slip velocity is a little larger. This difference is probably due to the centrifugal and Coriolis forces formed by the axial and tangential vortexes. The density difference between phases (ρp/ρs=1.13) produces a noticeable slip velocity between the solid and liquid phase. However,radial velocities of two phases tend to be equilibrium at R＞1.25 (Fig. 5(b)). But the relations of velocity between two phases in the pump are still unclear. More experimental and theoretical studies need to be taken in the future works.

Fig. 4. Three velocity components at different axial positions (Q′＝1)

Fig. 5. Three velocity components at different axial positions (Z=1.25, Q′＝1)

3.2 Particle concentration distribution

Particle concentration distribution is formed after the particle movement. Investigation on that is of significance for salt-out flow analysis and prediction in the pump.

3.2.1 Particle size distribution

The diameters of crystal particles salt-out from the solution are not all the same. They are affected by many factors, such as supersaturation, temperature, and flow condition, and so on. Particles with different sizes have different path-lines in the volute. Fig. 6 shows the particle size distributing curves on the radial direction at various discharges and axial positions. The diameter D at every point is a statistical average size of the particles passing through this point. Here, Sauter mean diameter(SMD) is used and given by

where Dkis the diameter of size class k, nkthe number of particles in each size class and N the total number of size classes.

Fig. 6. Particle size distribution

Particle size curves show an open-up parabola distribution in Fig. 6. They firstly decrease gradually to the minimum values. The values always appear at R=0.85 and never change with the pump discharge. The diameters then increase from these values rapidly. The closer it moves to the casing peripheral wall, the larger the diameters are. It is suggested that after particles with different sizes entering the volute, particles with larger size are easy to move to the casing peripheral wall and particles with smaller size distribute in the impeller diameter region. That is due to the particle circulating flow. Under the influence of the tangential vortex, large particles move along the radial flow and the opposite directions. In the small radius region, the reverse flow of particles meets the through-flow, which leads to a smaller statistical diameter of the flow than that around the casing wall. It is also the main reason why the largest particles aggregate in vicinity of the casing wall.Furthermore, the diameter decreases as the pump discharge decreases at this axial position. It can be predicted from the flow characteristics of the pump that large particles tend to move towards the suction cover as the discharge decreases.Under the same operating condition, the diameters at different axial positions have little diversity (Fig. 6(b)).

3.2.2 PND distribution

Fig. 7 shows the PND curves at various discharges and axial positions. The value of PND C means the total particle number per cubic centimeter. It is calculated as follows:

where ?t is the particle transmitting time through the measuring volume, or the residence time in the volume, Akthe section area of the volume perpendicular to the transmitting direction of the particles with size class k.

Fig. 7. PND distribution

PND increases at R＜0.8 in Fig. 7(a). However, particle size in this region decreases, which creates the condition for crystal particle aggregation. The aggregation of small particles under high concentration leads to the PND decreasing in a later certain region. A low ebb of the concentration curve comes out and its position varies at different discharges. For example, it is around R=0.95 at Q′=1.2, and R=1.05 at Q′=1. The PND firstly rises quickly to a maximum value due to the particles flowing out from the impeller at R＞1. Then, it falls down rapidly due to the function of particles aggregation. But the particle volume concentration increases because the particle size still keeps increasing. Moreover, the PND increases as the discharge increases. It can be proposed that particles tend to move towards the impeller as the discharge increases. At different axial positions, there are differences of the PND observed in Fig. 7(b). Larger PND values are near the suction cover of the pump. It is also proved that particles are easy to move towards the suction cover after they enter the pump.

Based on the results of particle concentration distribution described above, it can be found that particles salt-out from the solution mostly move to the vicinity of the casing peripheral wall and suction cover. Secondary and heterogeneous nucleation happened at these regions accelerate the formation and growth progress of crystal particles. The aggregated particles deposit on the boundary to form the salt-out layer, and the layer thickens continuously. The results can be used to predict the growth process of salt-out layer in the pump volute.

Based on the results of particle concentration distribution described above, it can be found that particles salt-out from the solution mostly move to the vicinity of the casing peripheral wall and suction cover. Secondary and heterogeneous nucleation which happens at these regions accelerates the formation and growth progress of crystal particles. The aggregated particles deposit on the boundary to form the salt-out layer, and the layer thickens continuously. The results can be used to predict the growth process of salt-out layer in the pump volute.

4 Conclusions

(1) The particle velocity gradient of peripheral component changes with the pump discharge on radial direction. A turning point of relation between peripheral velocity component and discharge appears at R=0.75. There are little differences of the velocity at two axial positions.The velocity slip between liquid and solid phase is not large.

(2) The particle radial and reverse flows coexist. The dividing point of circulating-flow and through-flow flowing into impeller is changing with discharges. The reverse flow is strengthened at low pump discharge. The velocity curves have a saddle shape. Differences of radial velocity at two positions are much larger, especially at R＞0.8.Non-equilibrium radial velocity component between two phases is remarkable.

(3) As R is increasing, axial velocity component increases gradually on the direction towards the impeller with R＜1. The velocity differences at three discharges and two axial positions are smaller than that of the radial velocity component. Non-equilibrium axial velocity component between two phases is not significant.

(4) Particle size curve shows an open-up parabola distribution. The larger particles are at the vicinity of the casing peripheral wall. Particle sizes vary with the discharge at the same axial position. PND is increasing with the discharge. The closer to the suction cover, the larger the PND values are. Crystal particle aggregation phenomenon can be revealed from the analysis of particle size and PND distribution.

[1] JIA Weidong, YANG Minguan, GAO Bo, et al. Crystal mechanism in pipelines while conveying green liquid[J]. Journal of Jiangsu University (National Science Edition), 2005, 26(6): 514–517. (in Chinese)

[2] ANASTASIOS J Karabelas. Scale formation in tubular heat exchangers-research priorities[J]. International Journal of Thermal Sciences, 2002, 41(7): 682–692.

[3] LEE S L, DURST F. On the motion of particles in turbulent duct flow[J]. International Journal of Multiphase Flow, 1982, 8(2):125–146.

[4] SHENG Y Y, IRONS G A. A combined laser-Doppler anemometry and electrical probe diagnostics for bubbly two-phase flow[J].International Journal of Multiphase Flow, 1991, 17(5): 585–598.

[5] VELIDANDLA V, PUTTA S, ROY R P. Velocity field in isothermal turbulent bubbly gas-liquid flow through a pipe[J]. Experiments in Fluids, 1996, 21(5): 347–356.

[6] LIU Qingqua. LDV measurements and experimental study of water and sediment two phase flow[J]. Journal of Sediment Research,1998, 23(2): 72–80. (in Chinese)

[7] LI Ling, LI Jingyin, XU Zhong. Study of LDV measurement technology of gas solid two phase flow[J]. Chemical Engineering and Machinery, 1998, 25(6): 311–365. (in Chinese)

[8] CADER T, MASBERNAT O, ROCO M C. LDV measurement in a centrifugal slurry pump: Water and dilute slurry flows[J]. Journal of Fluid Engineering, 1992, 114(4): 606–615.

[9] PREVOST F, BOREE J, NUGLISCH H J, et al. Measurements of fluid/particle correlated motion in the far field of an axisymmetric jet[J]. International Journal of Multiphase Flow, 1996, 22(4):685–701.

[10] BLACK D L, MCQUARY M Q. Laser-based particle measurement of spherical and nonspherical particles[J]. International Journal of Multiphase Flow, 2001, 27(8): 1 333–1 362.

[11] AISA L, GARCIA J A, CERECEDO L M, et al. Particle concentration and local mass flux measurements in two-phase flows with PDA. Application to a study on the dispersion of spherical particles in a turbulent air jet[J]. International Journal of Multiphase Flow, 2002, 28(2): 301–324.

[12] ZHAO Yan, ZU Xiaocheng, DU Caohui. Several PDA application problems in measurement of an axial flow rotor[J]. Fluid Machinery,2002, 30(5): 8–12. (in Chinese)

[13] SCHIVLEY G P. Analytical and experimental study of a vortex pump[J]. Trans ASME, Ser. D,1970, 92(4): 889–900.

[14] OHBA Hideki, NAKASHIMA Yukitoshi, SHIRAMOTO Kazuaki,et al. A study on performance and internal flow pattern of a vortex pump[J]. Bulletin of the JSME, 1978, 21(162): 1 741–1 749.

[15] AOKI Masanori. Studies on the vortex pump (1st report)[J]. Bulletin of the JSME, 1983, 26(213): 387–393.

[16] CHEN Hongxun. Reserch on turbulent flow within the vortex pump[J]. Journal of Hydrodynamics, Ser. B, 2004, 16(6): 701–707.

[17] SHA Yi, YANG Minguan, KANG Can, et al. Design and performance experiment of sewage and slurry vortex pump[J].Journal of Jiangsu University (National Science Edition), 2005,26(2): 153–157. (in Chinese)

[18] SHI Weidong, WANG Yongzhi, SHA Yi. Research on the internal flow of vortex pump[J]. Transactions of the Chinese Society for Agricultural Machinery, 2006, 37(1): 67–70. (in Chinese)

[19] YANG Minguan, GAO Bo, LIU Hui, et al. Simulation and experimental research on salt-out two-phase flow field in a vortex pump[J]. Chinese Journal of Mechanical Engineering, 2008, 44(12):42–48. (in Chinese)