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Effect of the inlet gas void fraction on the tip leakage vortex in a multiphase pump
Renewable Energy 150 (2020) 46e57
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Renewable Energy journal homepage: www.elsevier.com/locate/renene
Effect of the inlet gas void fraction on the tip leakage vortex in a multiphase pump Guangtai Shi a, Zongku Liu a, Yexiang Xiao b, *, Hong Yang c, Helin Li a, Xiaobing Liu a a
Key Laboratory of Fluid and Power Machinery, Ministry of Education, Xihua University, Chengdu, 610039, China State Key Laboratory of Hydroscience and Engineering and Department of Energy and Power Engineering, Tsinghua University, Beijing, 100084, China c China Institute of Water Resources and Hydropower Research, Beijing, 100038, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 10 September 2019 Received in revised form 11 November 2019 Accepted 24 December 2019 Available online 26 December 2019
Inlet gas void fraction (IGVF) played an important role on the flow characteristics in a multiphase pump. To reveal the effect of inlet gas void fraction on the flow characteristics in the tip clearance, a combination of numerical simulation and experiment was carried out and the reliability of numerical method was verified by comparing with the experimental data of the flow field by using high-speed photography. The results showed the accumulated gas was mainly at the impeller inlet near the pressure side (PS), tip clearance near the tip and the suction side (SS). When the IGVF increased, there was an obvious stratified structure and the separated vortex in the tip clearance. Compared to the water case, the gas caused the tip leakage flow velocity to decrease from the blade inlet to the streamwise coefficient of 0.2, and to increase from the streamwise coefficient of 0.2 to the blade trailing edge. At the same time, the IGVF had a significant influence on the tip leakage vortex (TLV) structure and trajectory, and the streamlines and vorticity distribution corresponding to the wake and the TLV were changed. Moreover, the flow characters and the structure of the TLV were more complicated under gas-liquid condition. © 2019 Elsevier Ltd. All rights reserved.
Keywords: Multiphase pump IGVF TLV Leakage flow
1. Introduction With the development of society and industry, the world’s demand for energy is growing, and traditional coal and oil resources are expected to exhaust after 40 or 50 years. At the same time, the subsea oil and gas resources are widely distributed and the reserves are large. Therefore, the development of subsea oil and gas resources has become the only way to solve the energy problem. However, there are many phases such as oil, gas and some small solid particles in crude oil, which brings great challenges to oil and gas development and transportation [1e4]. The multiphase pump has been widely used in oil and gas development because it can efficiently transport gas-liquid mixed medium and has good adaptability to small solid particles [5e7]. Due to the relative motion between the impeller tip and the shroud, a tip clearance is inevitable, as shown in Fig. 1. The leakage flow in the tip clearance and the main flow are mutually entrained to form a tip leakage vortex (TLV). The TLV deteriorates the flow state, which reduces the working performance and efficiency of the
* Corresponding author. E-mail address: [email protected] (Y. Xiao). https://doi.org/10.1016/j.renene.2019.12.117 0960-1481/© 2019 Elsevier Ltd. All rights reserved.
pump, and induces pressure fluctuation, and appears the tip leakage cavitation, noise, vibration, and other serious damages, which seriously affect the safe and stable operation of the unit [8e11]. Since the attention on the tip leakage flow has been paid, many scholars have conducted a lot of researches worldwide. Zhang D. et al. [12e14] used experimental and numerical simulation methods to study the trajectory of the TLV in the axial flow pump, the unsteady leakage vortex cavitation cloud and the cavitation mechanism. Shi W. et al. [15] used shear stress transport (SST) k-u turbulence model simulation and vortex strength method to numerically calculate the flow field near the blade tip and TLV trajectory of an axial flow pump; They found that with the increase of flow rate, the flow direction in the impeller is shifted, and the TLV trajectory changes accordingly under the entrainment of main flow. Liu, Y. et al. [16e18] studied the influence of the tip clearance on the pressure fluctuation and vortex characteristics of the mixed flow pump. The results show that the flow rate has a great influence on the structure and trajectory of the TLV and the starting point of the primary TLV moves 20% of the blade chord length under the high flow rate. Hao Y. et al. [19,20] studied the effects of symmetric and asymmetric tip clearance on the radial force and cavitation of a
G. Shi et al. / Renewable Energy 150 (2020) 46e57
47
2. Experiment and simulation model
Shroud Shroud Blade tip
2.1. Test rig
Pressure side Blade tip
Suction side Suction side
Pressure side
Fig. 1. Tip clearance.
mixed flow pump, and found that the asymmetry tip clearance worsens the pump cavitation performance compared to the symmetric tip clearance. Due to the development of cavitation, the asymmetrical tip clearance affects both the magnitude and direction of the radial force. Li Y. et al. [21,22] investigated the influence of tip clearance on pressure fluctuation and leakage flow with axial flow pump. The research shows that with the increase of the tip clearance, head, shaft power and efficiency of the pump are decreased. At the same time, the leakage flow velocity in the tip clearance gradually increases along the radial direction. In addition, due to the influence of the TLV, the pressure fluctuation amplitude of the pressure side (PS) middle section near the shroud increases with the increase of the tip clearance. Li Y. et al. [23,24] studied the effect of different tip clearances on the performance of the diagonal flow pump. The results showed that the head-flow positive slope characteristic of the diagonal flow pump can be suppressed effectively when tip clearance was 0.5 mm and the efficiency value of diagonal flow pump is highest at this time; At the same time, the larger tip clearance can effectively reduce the high frequency pressure fluctuation in the tip clearance, but the leakage flow caused by it is intensified. You D. et al. [25] used large eddy simulation (LES) to study the tip clearance flow. It was found that the TLV and the tip-leakage jet produced mean velocity gradients. Torre, L. et al. [26] investigated the effect of tip clearance on the performance of a three-bladed axial inducer and found that the intensity of pressure oscillations tends to decrease as the tip blade clearance increases. Many investigations [27e30] have conducted on the effect of tip clearance in other rotating machinery. It can be seen from the above literature that the current research on the tip clearance is mostly focused on performance effects, vortex structure, cavitation and pressure fluctuation, and the flow state in the tip clearance is less analyzed; Moreover, most of the current research is based on single phase medium only. With the further development of submarine oil and gas resources, the application of multiphase pump is more widely expected, and it is more urgent to study the tip clearance flow under gas-liquid two phase conditions. The multiphase pump was always used at the small flow rate in actual operation. Then the effect of the inlet gas void fraction (IGVF) on the flow characteristics in the tip clearance was investigated in a multiphase pump with a tip clearance in present work. The basic structure of the present work was as follows. Firstly, the numerical simulation in a multiphase pump with a tip clearance using ANSYS CFX under different IGVFs was conducted. Then, the reliability of numerical method was proved by comparing with the experimental data of the flow field with the IGVFs of 10%, 15% and 20% using high-speed photography. Finally, the gas distribution, flow characteristics and the evolution of TLV with different IGVF values in the multiphase pump were analyzed in order to make full sense of the effect of the IGVF on flow characteristics in the tip clearance and assist the development of deep sea oil and gas resources, which has an important engineering practical value.
A multiphase pump with 3 impeller and 7 diffuser blades was chosen for analysis. The main design parameters of the pump were listed in Table 1. The test rig for the multiphase pump was comprised of a motor, a multiphase pump, gas-liquid mixing tank, lubrication system, cooling system, control system, water supply system, gas supply system, pipeline and valves, etc. as shown in Fig. 2. In this test, the third compression stage of the multiphase pump was made in a transparent glass. The shape of the pump body was square from outside whereas a circle from inside. The glass refractive index was similar to that of clean water in order to reduce the test error caused by secondary refraction. In order to compare with numerical results, the experimental flow field was shot by a high-speed camera. The transparent glass components used in the test were shown in Fig. 3. The flow field in the multiphase pump at present work was detected with a high speed camera (RDT16-4G), which can capture the fast moving particles and bubbles, and the bursting process of the variable bubbles, as shown in Fig. 4. The camera speed is 500 fps with maximum resolution of 16000 fps, the resolution is 1280 1024 pixels. The test site shown in Fig. 5. 2.2. Governing equations The fluid in the pump was assumed to be incompressible and the governing equations were as follows [31e33]. Continuity equation:
V , ðak rk wk Þ ¼ 0
(1)
Momentum equation:
V , ðak rk wk wk ak tÞ ¼ ak Vp þ Mk þ ak rk fk
(2)
where t denotes the viscous stress tensor; ak , rk , Mk ; fk and wk stand for the void fraction, the density, the interphase force, the mass force, and the velocity of k phase, respectively. 2.3. Computational methods For the convenience of numerical studies, a single compression stage of the pump was selected to conduct the simulation work. In order to ensure that the impeller inlet and the diffuser outlet flow are more adequate, the extension section is added to the impeller inlet and diffuser outlet respectively, and the extension section was added to both impeller inlet and diffuser outlet. The length of the extension was 1.1 and 3.3 times of the inner diameter (D) for impeller inlet and diffuser outlet, respectively. The specific computational model is shown in Fig. 6. The mesh quality in the tip clearance has a large influence in simulating the tip clearance flow and the TLV, so a hexahedral mesh is used for the entire computational domain. In particular, the tip
Table 1 Main design parameters of multiphase pump. Parameters
Symbol
Value
Unit
Design flow rate Design speed Hub/tip ratio
Qd n
100 3000 0.7
m3/h rpm ()
113 85
mm m
Inner diameter Head
d D H
48
G. Shi et al. / Renewable Energy 150 (2020) 46e57 Water injection
3
2
4
5
1
Water pipeline P
P
9 8
12 14
Air injection Gas pipeline
High-speed photography
6
7
P
13
10 P
11
1. Water tank 2. Water supply pump 3. Flow meter 4. Outlet valve 5. Inlet valve 7. Torque meter 8. Gas-liquid mixing tank
6. The motor
9. Outlet pressure gauge 10. Inlet pressure gauge 11.
Multiphase pump 12. Gas valve 13. Air compressor 14. Rotameter Fig. 2. Test rig.
(a) Impeller
(b) Diffuser
(c) Pump Fig. 3. Transparent glass components used in the test.
clearance and the near-wall area mesh are refined to improve the accuracy and convergence of the calculations, as shown in Fig. 7. The blade adopts an O-topology method to control the boundary layer distribution near wall. At the same time, in order to accurately capture the flow characteristics in the tip clearance, 40 layers meshes are arranged in the tip clearance along the radial direction of the blade. The y þ near the impeller is between 0 and 60, which meets the requirements of the SST k-u turbulence model for the near wall [34]. After the mesh independence check, the requirements were met, and the number of mesh finally used was 5,421,110. The k-u based Shear-Stress-Transport (SST) model was designed to give highly accurate predictions of the onset and the amount of flow separation under adverse pressure gradients by the inclusion of transport effects into the formulation of the eddy-viscosity. Based on the RANS equations and the SST k-u turbulence model, the ANSYS CFX software was used to numerically calculate the flow characteristics in a multiphase pump with a tip clearance of 1 mm at the off-design condition and different IGVFs. The offdesign condition (partial discharge of 0.8Qd (Qd is the design flow rate)) and the IGVFs (IGVF ¼ 0, 5%,10%,15% and 20%) were chosen for
Fig. 4. The high speed camera.
the numerical investigation. In the calculations, an EulerianEulerian multiphase model was adopted and the velocity slip between gas and liquid was taken into account. Meanwhile, the liquid phase was considered as a continuous fluid and the gas phase was considered as a dispersed fluid. The settings of boundaries and solution were listed in Table 2. 2.4. Operating condition points In the process of experiment, keeping the gas flow rate Qg unchanged and adjusting the liquid flow rate Ql to adjust the IGVF. IGVF is calculated according to the Eq. (3).
G. Shi et al. / Renewable Energy 150 (2020) 46e57
49
Qg Qg þ Q1
(3)
IGVF ¼
where Qg and Ql represent the volume discharge of gas and liquid, respectively, at the inlet. In order to verify the reliability of the numerical results, the flow field in test results are compare to the results in numerical simulation in multiphase pump at the rotational speed of 3000 rpm, flow rate of 80 m3/h, and the IGVFs of 10%, 15% and 20% in this paper, which intends to verify the reliability of numerical calculation methods.
2.5. Test and numerical tip leakage flow Fig. 8 is a comparison of the test results and the numerical calculation results near the blade tip. The swirling strength is selected to as isosurface and represent the TLV trajectory. It can be seen from Fig. 8 that the leakage flow in the tip clearance entrained the main flow and then evolved into a TLV. The TLV is mainly located on the suction side (SS) of the blade. At the same time, there is also a vortex structure at the blade inlet near the PS. The correspondence between tests and the numerical simulations are as
Fig. 5. The test site.
h Tip clearance Inlet pipe
Impeller
Outlet pipe
Diffuser
IGVF=10% Fig. 6. Computation model.
IGVF=15%
IGVF=20%
Fig. 8. Comparison of test results and numerical results.
Mesh in the tip clearance
Blade tip Blade Blade tip
(a) Impeller blade (b) Tip clearance
(c) Impeller
(d) Diffuser
Fig. 7. Computational domain mesh.
Table 2 Settings of boundaries and solution. Types
Items
Settings
Value
Unit
boundaries
Inlet Outlet Pressure Domain motion Wall Rotor-stator interfaces Convergence criteria
Normal speed Static pressure Reference pressure Rotating No-slip Frozen-rotor Root mean square (RMS) residuala
2.1512 6 1 3000 () () 1 105
m/s atm atm rpm () () ()
solution a
When the RMS residual was below 1 105, the calculation was considered to be converged.
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G. Shi et al. / Renewable Energy 150 (2020) 46e57
shown in common color markers (As shown in red, yellow and blue ellipses). Thus, the numerical calculation results are in good agreement with the experimental results, which verifies the reliability of the numerical calculation method. 3. Effect of IGVF for TLV flow behavior In order to analyze the flow characteristics of different parts of the multiphase pump, 6 cross sections were set in the impeller and diffuser along the axial direction, which were named as Section 1 to Section 6, respectively. At the same time, Section 7 was set to analyze the flow characteristic in tip clearance. In addition, in order to accurately analyze the flow state characteristics of the Section 7, it was divided into two regions A and B. A schematic view of sections was shown in Fig. 9. 3.1. Effect of IGVFs on the impeller cross section The Fig. 10 was a velocity distribution for different sections in the impeller, where Fig. 10 (a) and Fig. 10 (b) were the velocity contour and the streamline distribution, respectively. It can be seen from Fig. 10 (a) that at different IGVFs, the maximum velocity region moved from the shroud to the hub along the flow direction (the flow direction was from Section 1 to Section 3). At the same time, it was found that the maximum velocity appears in Section 1 near the PS. This was because the inflow angle was inconsistent with the blade inlet angle, which caused the flow instability in the region. In addition, it was found that the influence of IGVF in the passage at three sections was different, ie, as the IGVF increases, the maximum velocity in the passage at the Section 1 (except for the unstable flow region of the blade PS) gradually decreased. Simultaneously, the proportion of the high velocity area also reduced gradually, and the high velocity area gradually moved from the shroud to hub. In the Section 2, the proportion of the high velocity area gradually increased and the high velocity area gradually extended to the adjacent blade PS with the increase of the IGVF. In the Section 3, the proportion of maximum velocity increased initially and then decreased with the increase of the IGVF. The relationship between the velocity and IGVF was not linear because it was affected by the rotorestator interaction at the Section 3, which caused that the flow state in the region to become more complicated. It can be seen
from Fig. 10(b) that as the IGVF increased, the streamlines on the sections in the impeller were smooth, and there was no unstable flow phenomenon such as vortex and secondary flow, which indicates that the impeller had a good adaptability to the gas phase medium [1]. The Fig. 11 showed gas distribution of the A region in Section 7. As can be seen from Fig. 11, the accumulated gas was mainly at the impeller inlet near the PS, tip clearance near the tip and the SS both at the Section 2 and Section 3. The gas accumulated at the impeller inlet PS because the flow near the inlet was unstable, while the blade tip and SS were concentrated because of the lower pressure in the region. At the same IGVF, the gas accumulated more and more near the tip and the SS along the flow direction, and it was found that the uneven region of the accumulated gas gradually moved from the shroud to hub. In addition, as the IGVF increased, the proportion of the gas in the main accumulated location also increased. 3.2. Effect of IGVF in the tip clearance Fig. 12 was the velocity vector and pressure distribution of region A in Section 7. It can be seen from Fig. 12 that the IGVF had a great influence on the velocity and pressure distribution in the tip clearance. In the pure water condition (IGVF ¼ 0), the tip clearance leakage flow was from the PS to the SS under the pressure difference between the PS and the SS. Since the angle of the tip near the PS was a right angle, the leakage flow was flowing through the blade tip, then the flow separation occurred, and a tip separated vortex was generated [12]. At this time, the separated vortex was small. In addition, the separated vortex core pressure was lower, which increased the possibility of cavitation in the tip clearance [14]. When the IGVF increased from 5% to 10%, it was found that the separated vortex in the tip clearance was increased until the separated vortex region throughout the entire tip clearance. At the same time, the tip leakage flow velocity was also gradually reduced, and the low pressure area caused by the flow separation around the blade tip was further enlarged. When the IGVF increased to 15%, it was found that the tip leakage flow velocity decreased while the velocity near the tip separated vortex increased slightly, at the same time the low pressure distribution area decreased. When the IGVF was increased to 20%, the low
Section1 Section2 Section3 Section4 Section5 Section7 Section6
B
A
Suction side Pressure side
Inlet pipe Impeller Duffser Outlet pipe
Fig. 9. A schematic view of sections.
G. Shi et al. / Renewable Energy 150 (2020) 46e57
IGVF=0 PS SS
51
SS PS
PS
PS
PS
SS
SS PS
SS
SS
IGVF=10%
IGVF=20%
Section 1 Section 2 Section 3 (a)Velocity contour
Section 1 Section 2 Section 3 (b) Distribution of the streamline
Fig. 10. Velocity distribution in different sections of the impeller.
SS PS
PS
PS
SS
SS
IGVF=0%
IGVF=15%
IGVF=20%
Section 1
Section 2
Section 3
Fig. 11. Gas distribution in the impeller.
pressure area in the tip clearance near the PS gradually disappeared. In summary, at a small IGVF (IGVF ¼ 5%, 10%), the IGVF increased, the separated vortex intensity around the blade tip increases and the low pressure area in the tip clearance near the PS increased. While at the large IGVF (IGVF ¼ 15%, 20%), the increase of IGVF caused the low pressure area in the tip clearance near the PS gradually disappeared, which can effectively reduce the possibility of cavitation in the tip clearance.
The Fig. 13 (a) was a velocity distribution of the region A in Section 7. When the IGVF increased from 5% to 10%, it was found that the velocity in the tip clearance was larger than that in pure water, and when the IGVF increased, the proportion of the maximum velocity in the tip clearance decreased and move forward along the flow direction of the leakage flow. It was also found that the range of the low velocity area near the blade tip was enlarged and the velocity was decreased. When the IGVF increased
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G. Shi et al. / Renewable Energy 150 (2020) 46e57
IGVF=0 SS
PS
SS
PS
IGVF=5%
IGVF=10%
IGVF=15%
IGVF=20% Fig. 12. Velocity vector and pressure distribution in the tip clearance.
IGVF=0
SS
IGVF=5%
PS
SS
PS
IGVF=10%
IGVF=15%
IGVF=20%
(a) Velocity
(b) IGVF
Fig. 13. Velocity and IGVF distribution in the tip clearance.
to 15%, the high velocity area in the tip clearance disappears and the velocity near the blade tip increased. When the IGVF was further increased to 20%, the proportion of the high velocity area was reduced again, and the velocity near the blade tip was also reduced. It can be seen that the IGVF had a great influence on the velocity distribution in the tip clearance. The Fig. 13(b) was a gas distribution of the region A in Section 7.
As can be seen from Fig. 13(b), the gas accumulation mainly occurred around the blade tip and the SS of the blade, and the gas accumulation and the tip separated vortex were consistent. When the IGVF was 5%, the gas accumulation around the blade tip occurs near the PS and consistent with the separated vortex. When the IGVF was 10%, the gas accumulation area was further enlarged and the gas accumulation area was near the blade tip as compared with
G. Shi et al. / Renewable Energy 150 (2020) 46e57
the IGVF of 5%. When the IGVF was 15%, the gas distribution in the gas accumulation area was stratified. When the IGVF was further increased to 20%, the gas accumulation location gradually moved from the blade tip to the shroud in the entire tip clearance. At the same time, there was an obvious stratified structure in the tip clearance [7]. In addition, as the IGVF increases, the gas accumulation near the SS of the blade gradually increased. It can be seen from the above analysis that different IGVFs had different influences on the gas distribution in the tip clearance. This indicated the gas-liquid two-phase interaction was complicated, and the leakage flow state was also disordered. The gas void fraction near the blade tip was displayed in Fig. 14. From Fig. 14, the gas distribution between the pressure side and the suction side at the blade tip was obviously different. The gas distribution variation at the inlet and streamwise coefficient of 0.3 on the pressure side was more obviously and with the increase of inlet gas void fraction, the gas distribution was increased. At same time, there was almost no gas at other locations from the leading edge to the trailing edge. From the inlet to streamwise coefficient of 0.8 on suction side, the gas distribution increased with the increase of the inlet gas void fraction, and the degree gradually decreased. In addition, the gas variation regularity was significantly weakened from the streamwise coefficient of 0.8 to the trailing edge and the gas distribution pulsated near the trailing edge. 3.3. Effect of IGVF on tip clearance leakage flow The TLV was formed by the entrainment between the leakage flow and main flow under the pressure difference between the PS and SS of the blade, so the tip leakage flow velocity was an important quantitative indicator for analyzing the TLV, especially in the two-phase condition. In order to accomplish quantitative analysis, the monitor points were set at the middle of the radial direction along the streamwise direction in the tip clearance. The distance from the blade inlet along center line of blade profile to the blade outlet was normalized, ie, the inlet was 0, the outlet was 1, and it was defined as the streamwise coefficient. Finally, the tip leakage flow velocity was plotted along the streamwise, as shown in Fig. 15. It can be seen from Fig. 15 that the trend of leakage flow velocity along the streamwise was generally similar under the gas and pure
53
water conditions, but the difference was in the magnitude of the leakage velocity. The gas caused the tip leakage flow velocity to decrease from the blade inlet to the streamwise coefficient of 0.2 compared to the pure water condition, whereas it was increased from the streamwise coefficient of 0.2 to the blade trailing edge. At the same time, it can be found that the leakage velocity along the streamwise coefficient of 0.1e0.4 was most affected by the IGVF, whereas the leakage velocity along the streamwise coefficient of 0.6e0.9 was most affected by whether it had gas or not. The flow state in the impeller under gas-liquid two-phase conditions was quite different from that of pure water. In order to qualitatively analyze the flow characteristics of the medium in the impeller passage, the correlation between the velocity streamline and the vorticity distribution in the region B of the Section 7 was analyzed, as shown in Fig. 16. It can be seen from Fig. 16 that, a “jet-wake” structure was formed due to the jet effect at the outlet of the tip clearance. It affected the flow characteristics both in the impeller passage and the near the blade tip to a large extent. The influence of the IGVF on the flow characteristics was analyzed as follows. Under the water condition (IGVF ¼ 0), the wake area and the maximum TLV area were basically coincident. At the same time, a large vorticity appeared in the radial middle of the adjacent blade PS. When the IGVF was 5%, a relatively obvious vortex structure appeared in the development direction of the wake, and the velocity at the vortex was significantly smaller. In addition, the streamlines at the vortex near the hub were slightly curved. At the same time, it can be seen that the vorticity around TLV was larger than that of pure water, and the vorticity at the radial middle of the adjacent blade PS was also significantly increased. As the IGVF increased to 10%, 15%, the vortex core was moved to the shroud and the SS, and the streamlines around the TLV near the hub was more obviously curved. The maximum vorticity area corresponding to the wake in the vorticity diagram also increased rapidly, and the increase in amplitude was most obvious when the IGVF was 15%. At the same time, the area of the maximum vorticity in the middle of the adjacent blade PS gradually became smaller, and moved toward the SS. When the IGVF was 20%, the TLV had further increased and moved toward the adjacent blade PS. At the same time, a small vortex structure appeared in the wake region due to the induction. The streamline deflection of the large vortex near the hub was more obvious. In addition, the maximum vorticity region corresponding to the wake region became larger, and gradually extended to the tip clearance of the adjacent blade PS, interacting with the adjacent tip leakage flow and making the flow state in the tip clearance more complicated. At the same time, the maximum vorticity area at the radial middle near the adjacent blade PS had significantly moved toward the SS. 3.4. Effect of the IGVF on TLV structure
Fig. 14. Gas void fraction near blade tip.
In order to analyze the effect of the IGVF on the TLV in the multiphase pump, the liquid swirling strength was used to represent the TLV structure and it was shown in Fig. 17. It can be seen from Fig. 17 that the TLV trajectory changed with the IGVF. The variation of the TLV trajectory was analyzed as follows. When the GFV was 0, the TLV appeared at the impeller inlet along the flow coefficient of about 0.3. The TLV structure was strip-shaped and close to the SS, ie, the leakage separation angle between the TLV trajectory and the chord was small [18]. In addition, a wake vortex appeared on the trailing edge of the blade. With the increase of the IGVF, the TLV had obviously changed in structure and distribution. When the IGVF was 5%, the initial location of the TLV was moving to the trailing
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G. Shi et al. / Renewable Energy 150 (2020) 46e57
Fig. 15. Leakage flow velocity in the tip clearance.
edge along the streamwise compared with the pure water working condition. The length of the TLV increased and the separation angle became larger. The vortex at the trailing edge of the blade increased, and the vortex structure also appeared on the inlet PS of the blade. When the IGVF was further increased to 10%, the TLV around the blade tip was significantly increased from the streamwise coefficient of about 0.5 to the trailing edge. When the IGVFs were 15%, 20%, the TLV was further enhanced, and the TLV of the adjacent SS at the blade inlet and the vortex at the inlet PS of the blade began to be drawn into a strong vortex structure. In addition, in order to further explore the cause of the vortex structure at the inlet PS of the blade, taking IGVF of 15% and 20% as an example, the liquid velocity streamline and gas distribution of the impeller were made, as shown in Fig. 18. It can be seen from the figure that gas accumulation is observed near the blade inlet, which caused a flow separation phenomenon and to form a vortex structure. It can be seen from the above analysis that the IGVF had a great influence on the three-dimensional structure of the TLV in the multiphase pump and the flow mechanism under gas-liquid condition was more complex, so this research had great significance. Fig. 19 was a velocity distribution of each section in the diffuser. As can be seen from Fig. 19, the velocity in the diffuser was smaller than that in the impeller as a whole, and the flow state was also disordered. At the same IGVF, the proportion of the minimum velocity in the diffuser along the flow direction (Section 4 to Section 6) gradually increased, and the flow state in the passage becomes more and more disordered, and the vortices appeared. In addition, the vortex location was found to correspond to the minimum velocity location, and the vortex was asymmetrically distributed in the circumferential direction in each of the passages. With the increase of IGVF, the proportion of low velocity area in the passage of each section in the diffuser gradually increased, especially at the diffuser inlet (Section 4).
4. Conclusion The gas distribution, flow characteristics and the evolution of TLV with different IGVF values in the multiphase pump were analyzed in present work. Based on experimental results, the accuracy of the numerical simulations on multiphase pumps was validated. From the present study, following conclusions have been drawn. (1) The accumulated gas was mainly at the impeller inlet near the PS, tip clearance near the tip and the SS. When the IGVF increased, there was an obvious stratified structure in the tip clearance and the separated vortex structure near the PS had been found to increased gradually. In addition, the streamlines in the impeller were more smoother than those in the diffuser and the vortex in diffuser corresponded to the minimum velocity. (2) Compared to the pure water condition, the gas caused the tip leakage flow velocity to decrease from the blade inlet to the streamwise coefficient of 0.2, and to increase from the streamwise coefficient of 0.2 to the blade trailing edge. At the same time, the structure of the TLV was changed with the IGVF. With the increase of the IGVF, firstly, the length of the TLV increased and the separation angle became larger. Then, the TLV around the blade tip was significantly increased from the streamwise coefficient of about 0.5 to the trailing edge. Finally, the leakage vortex of the adjacent SS and the vortex at the inlet PS began to be drawn into a strong vortex structure. In addition, the streamlines and vorticity distribution corresponding to the wake and the TLV were also changed. (3) The flow characters and the structure of the TLV were more complicated under gas-liquid condition, and it also deteriorated the flow state in the passage and increased the hydraulic loss in the multiphase pump.
Suction side
Pressure side of adjacent blade
Pressure side of adjacent blade
Suction side
IGVF=0
Suction side
Pressure side of adjacent blade
Pressure side of adjacent blade
Suction side
IGVF=5%
Suction side
Pressure side of adjacent blade
Pressure side of adjacent blade
Suction side
IGVF=10%
Suction side
Pressure side of adjacent blade
Pressure side of adjacent blade
Suction side
IGVF=15%
Suction side
Pressure side of adjacent blade
Pressure side of adjacent blade
Suction side
IGVF=20%
(a) Velocity streamlines
(b) Vorticity distribution
Fig. 16. Velocity streamlines and vorticity distribution.
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G. Shi et al. / Renewable Energy 150 (2020) 46e57
IGVF=0
IGVF=5%
IGVF=15%
IGVF=10%
IGVF=20%
Fig. 17. Three-dimensional structure of the TLV.
IGVF =15%
IGVF =20%
(a) Velocity streamline at the radial coefficient r*=0.6
IGVF =15%
IGVF =20%
(b) Gas volume fraction at radial coefficient r*=0.6
Fig. 18. Velocity streamline and gas volume fraction.
IGVF=0
IGVF=10%
IGVF=20%
Section 4
Section 5
Section 6
Section 4
Section 5
Section 6
Fig. 19. Velocity distribution of each section in the diffuser.
Declaration of competing interest Guangtai Shi and other co-authors have no conflict of interest. Acknowledgment This work was supported by the National Key Research and Development Program(Grant No. 2018YFB0905200), Education department key project of Sichuan province of China (Grant No. 17ZA0366),“Young Scholars Reserve Talents” program of Xihua University, China Postdoctoral Science Foundation (Grant No.
2017T100077) and the Key scientific research fund of Xihua University of China (Grant No. Z1510417). This work was also supported by the Open Research Subject of Key Laboratory of Fluid and Power Machinery, Ministry of Education (Grant No. szjj2016-063), the National Natural Science Foundation of China (Grant No. 51479093), The National Key Research and Development Program of China (Grant No. 2017YFC0404200), the Key Research and Development Program of Tianjin (Grant No. 18YFZCSF00310), and the Key Laboratory of Fluid and Power Machinery (Xihua University) Ministry of Education (Grant No. SZJJ-2018-125).
G. Shi et al. / Renewable Energy 150 (2020) 46e57
Nomenclature D
Inner diameter
d fk H IGVF LE TE LES Mk n PS Qd SST SS TLV wk
Hub/tip ratio Mass force of k phase Head Inlet gas void fraction Leading edge Trailing edge Large eddy simulation Interphase force of k phase Design speed Pressure side Design flow rate Shear stress transport Suction side Tip leakage vortex Velocity of k phase Void fraction of k phase Density of k phase Viscous stress tensor
ak rk t
Author contributions section Guangtai Shi, Zongku Liu and Yexiang Xiao proposed the simulation method and designed the experiment; Hong Yang, Helin Li and Xiaobing Liu performed the experiment; Zongku Liu completed the numerical simulations; Zongku Liu and Guangtai Shi analyzed the data and wrote the paper. References [1] J. Zhang, L. Tan, Energy performance and pressure fluctuation of a multiphase pump with different gas volume fractions, Energies 11 (2018) 1216. [2] M. Liu, L. Tan, S. Cao, Design method of controllable blade angle and orthogonal optimization of pressure rise for a multiphase pump, Energies 11 (2018) 1048. [3] Kim J., Lee H., Yoon J., Lee K., Lee Y., Choi Y. Multi Objective Optimization of a Multiphase Pump for Offshore Plants. ASME. Fluids Engineering Division Summer Meeting, Volume 1B, Symposia: Fluid Machinery; Fluid-Structure Interaction and Flow-Induced Noise in Industrial Applications; Flow Applications in Aerospace; Flow Manipulation and Active Control: Theory, Experiments and Implementation; Multiscale Methods for Multiphase Flow; Noninvasive Measurements in Single and Multiphase Flows:V01BT10A011. [4] J. Kim, H. Lee, J. Kim, Y. Choi, J. Yoon, I. Yoo, W. Choi, Improvement of hydrodynamic performance of a multiphase pump using design of experiment techniques, J. Fluids Eng. Trans. Asme 137 (8) (2015), 081301-081301-15. [5] S. Stuart, Multiphase pumping addressed a wide range of operating problems, Oil Gas J. (2009) 59e71. [6] A.A. Hamoud, A. Adnan, Boudi, et al., Deployment of a rotodynamic multiphasepump in a remote hilly-terrain oil field in Saudi Arabia, in: Abu Dhabi International Petroleum Exhibition and Conference, 2008. SPE117462, Abu Dhabi. [7] W. Zhang, Z. Yu, Y. Li, Analysis of flow and phase interaction characteristics in a gas-liquid two-phase pump, Oil Gas Sci. Technol. (73) (2018) 69. [8] S. Kim, C. Choi, J. Kim, et al., Tip clearance effects on cavitation evolution and head breakdown in turbopump inducer, J. Propuls. Power 29 (6) (2013) 1357e1366. [9] H. Wu, R.L. Miorini, D. Tan, et al., Turbulence within the tip-leakage vortex of an axial waterjet pump, AIAA J. 50 (11) (2012) 2574e2587.
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[10] D. You, M. Wang, P. Moin, et al., Vortex dynamics and low-pressure fluctuations in the tip-clearance flow, J. Fluids Eng. 129 (8) (2007) 1002e1014. [11] S. Gopalan, J. Katz, H.L. Liu, Effect of gap size on tip leakage cavitation inception, associated noise and flow structure, J. Fluids Eng. 124 (4) (2002) 994e1004. [12] D. Zhang, W. Shi, B.P.M.V. Esch, L. Shi, M. Dubuisson, Numerical and experimental investigation of tip leakage vortex trajectory and dynamics in an axial flow pump, Comput. Fluids 112 (2015) 61e71. [13] D. Zhang, L. Shi, W. Shi, R. Zhao, H. Wang, B. van Eschb, Numerical analysis of unsteady tip leakage vortex cavitation cloud and unstable suction-sideperpendicular cavitating vortices in an axial flow pump, Int. J. Multiph. Flow 77 (2015) 244e259. [14] D. Zhang, W. Shi, D. Pan, M. Dubuisson, Numerical and experimental investigation of tip leakage vortex cavitation patterns and mechanisms in an axial flow pump, J. Fluids Eng. Trans. Asme 137 (12) (2015), 121103-121103. [15] W. Shi, P. Shao, D. Zhang, S. Wu, T. Li, Influence of operational condition and tip clearance size on trajectory of tip leakage vortex, J. Drain. Irrig. Mach. Eng. 32 (05) (2014) 373e377. [16] Y. Liu, L. Tan, Tip clearance on pressure fluctuation intensity and vortex characteristic of a mixed flow pump as turbine at pump mode, Renew. Energy 129 (Part A) (2018) 606e615. [17] Y. Liu, L. Tan, B. Wang, A review of tip clearance in propeller, pump and turbine, Energies 11 (9) (2018) 2202. [18] Y. Liu, L. Tan, Y. Hao, Y. Xu, Energy performance and flow patterns of a mixedflow pump with different tip clearance sizes, Energies 10 (2) (2017) 191. [19] Y. Hao, L. Tan, Symmetrical and unsymmetrical tip clearances on cavitation performance and radial force of a mixed flow pump as turbine at pump mode, Renew. Energy 127 (2018) 368e376. [20] Y. Hao, L. Tan, Y. Liu, Y. Xu, J. Zhang, B. Zhu, Energy performance and radial force of a mixed-flow pump with symmetrical and unsymmetrical tip clearances, Energies 10 (1) (2017) 57. [21] Y. Li, J. Shen, H. Yan, Z. Zhang, Investigation of the effects of tip-gap size on the tip-leakage flow in an axial-flow pump using LES, J. Hydraul. Eng. 45 (02) (2014) 235e242. [22] Y. Li, J. Shen, Y. Hong, Z. Liu, Numerical investigation of pressure fluctuations on axial-flow pump blades affected by tip-gap size, Trans. Chin. Soc. Agric. Mach. 45 (05) (2014) 59e64. [23] Y. Li, P. Hu, R. Li, Z. Bi, P. Li, Numerical analysis for effects of different blade tip clearance on performance in mixed-flow pump, Trans. Chin. Soc. Agric. Eng. 30 (23) (2014) 86e93. [24] Y. Li, Z. Bi, R. Li, P. Hu, D. Zhou, Numerical analysis of pressure pulsation characteristics of diagonal flow pump in adjacent area of tip clearance, J. Hydraul. Eng. 46 (04) (2015) 497e504. [25] D. You, M. Wang, P. Moin, et al., Large-eddy simulation analysis of mechanisms for viscous losses in a turbomachinery tip-clearance flow, J. Fluid Mech. 586 (2007) 177e204. [26] L. Torre, A. Pasini, A. Cervone, et al., Effect of tip clearance on the performance of a three-bladed axial inducer, J. Propuls. Power 27 (4) (2011) 890e898. [27] M. Mansour, B. Wunderlich, D. Thevenin, Effect of tip clearance gap and inducer on the transport of two-phase air-water flows by centrifugal pumps, Exp. Therm. Fluid Sci. (2018) 487e509. [28] J.H. Jung, W.G. Joo, Effect of tip clearance, winglets, and shroud height on the tip leakage in axial flow fans, Int. J. Refrig. Revue Internationale Du Froid (2018) 195e204. [29] H. Khaleghi, M.A. Sheikhshahrokh Dehkordi, A.M. Tousi, Role of tip injection in desensitizing the compressor to the tip clearance size, Aero. Sci. Technol. 52 (2016) 10e17. [30] T. Engin, M. Gur, Performance characteristics of a centrifugal pump impeller with running tip clearance pumping solid-liquid mixtures, J. Fluids Eng. 123 (3) (2001) 532e538. [31] J. Pei, M.K. Osman, W. Wang, et al., Unsteady flow characteristics and cavitation prediction in the double-suction centrifugal pump using a novel approach, Proc Inst Mech Eng A J Power Energy 0 (0) (2019) 1e17. [32] J. Pei, F. Zhang, D. Appiah, et al., Performance prediction based on effects of wrapping angle of a side channel pump, Energies 12 (1) (2019) 139. [33] J.W. Such, J.W. Kim, Y.S. Choi, , et al.Y. LeeK, Multi-objective optimization of the hydrodynamic performance of the second stage of a multi-phasepump, Energies 10 (2017) 1e21. [34] F.R. Menter, Review of the shear-stress transport turbulence model experience from an industrial perspective, Taylor Francis 23 (4) (2009) 305e316.
Contents lists available at ScienceDirect
Renewable Energy journal homepage: www.elsevier.com/locate/renene
Effect of the inlet gas void fraction on the tip leakage vortex in a multiphase pump Guangtai Shi a, Zongku Liu a, Yexiang Xiao b, *, Hong Yang c, Helin Li a, Xiaobing Liu a a
Key Laboratory of Fluid and Power Machinery, Ministry of Education, Xihua University, Chengdu, 610039, China State Key Laboratory of Hydroscience and Engineering and Department of Energy and Power Engineering, Tsinghua University, Beijing, 100084, China c China Institute of Water Resources and Hydropower Research, Beijing, 100038, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 10 September 2019 Received in revised form 11 November 2019 Accepted 24 December 2019 Available online 26 December 2019
Inlet gas void fraction (IGVF) played an important role on the flow characteristics in a multiphase pump. To reveal the effect of inlet gas void fraction on the flow characteristics in the tip clearance, a combination of numerical simulation and experiment was carried out and the reliability of numerical method was verified by comparing with the experimental data of the flow field by using high-speed photography. The results showed the accumulated gas was mainly at the impeller inlet near the pressure side (PS), tip clearance near the tip and the suction side (SS). When the IGVF increased, there was an obvious stratified structure and the separated vortex in the tip clearance. Compared to the water case, the gas caused the tip leakage flow velocity to decrease from the blade inlet to the streamwise coefficient of 0.2, and to increase from the streamwise coefficient of 0.2 to the blade trailing edge. At the same time, the IGVF had a significant influence on the tip leakage vortex (TLV) structure and trajectory, and the streamlines and vorticity distribution corresponding to the wake and the TLV were changed. Moreover, the flow characters and the structure of the TLV were more complicated under gas-liquid condition. © 2019 Elsevier Ltd. All rights reserved.
Keywords: Multiphase pump IGVF TLV Leakage flow
1. Introduction With the development of society and industry, the world’s demand for energy is growing, and traditional coal and oil resources are expected to exhaust after 40 or 50 years. At the same time, the subsea oil and gas resources are widely distributed and the reserves are large. Therefore, the development of subsea oil and gas resources has become the only way to solve the energy problem. However, there are many phases such as oil, gas and some small solid particles in crude oil, which brings great challenges to oil and gas development and transportation [1e4]. The multiphase pump has been widely used in oil and gas development because it can efficiently transport gas-liquid mixed medium and has good adaptability to small solid particles [5e7]. Due to the relative motion between the impeller tip and the shroud, a tip clearance is inevitable, as shown in Fig. 1. The leakage flow in the tip clearance and the main flow are mutually entrained to form a tip leakage vortex (TLV). The TLV deteriorates the flow state, which reduces the working performance and efficiency of the
* Corresponding author. E-mail address: [email protected] (Y. Xiao). https://doi.org/10.1016/j.renene.2019.12.117 0960-1481/© 2019 Elsevier Ltd. All rights reserved.
pump, and induces pressure fluctuation, and appears the tip leakage cavitation, noise, vibration, and other serious damages, which seriously affect the safe and stable operation of the unit [8e11]. Since the attention on the tip leakage flow has been paid, many scholars have conducted a lot of researches worldwide. Zhang D. et al. [12e14] used experimental and numerical simulation methods to study the trajectory of the TLV in the axial flow pump, the unsteady leakage vortex cavitation cloud and the cavitation mechanism. Shi W. et al. [15] used shear stress transport (SST) k-u turbulence model simulation and vortex strength method to numerically calculate the flow field near the blade tip and TLV trajectory of an axial flow pump; They found that with the increase of flow rate, the flow direction in the impeller is shifted, and the TLV trajectory changes accordingly under the entrainment of main flow. Liu, Y. et al. [16e18] studied the influence of the tip clearance on the pressure fluctuation and vortex characteristics of the mixed flow pump. The results show that the flow rate has a great influence on the structure and trajectory of the TLV and the starting point of the primary TLV moves 20% of the blade chord length under the high flow rate. Hao Y. et al. [19,20] studied the effects of symmetric and asymmetric tip clearance on the radial force and cavitation of a
G. Shi et al. / Renewable Energy 150 (2020) 46e57
47
2. Experiment and simulation model
Shroud Shroud Blade tip
2.1. Test rig
Pressure side Blade tip
Suction side Suction side
Pressure side
Fig. 1. Tip clearance.
mixed flow pump, and found that the asymmetry tip clearance worsens the pump cavitation performance compared to the symmetric tip clearance. Due to the development of cavitation, the asymmetrical tip clearance affects both the magnitude and direction of the radial force. Li Y. et al. [21,22] investigated the influence of tip clearance on pressure fluctuation and leakage flow with axial flow pump. The research shows that with the increase of the tip clearance, head, shaft power and efficiency of the pump are decreased. At the same time, the leakage flow velocity in the tip clearance gradually increases along the radial direction. In addition, due to the influence of the TLV, the pressure fluctuation amplitude of the pressure side (PS) middle section near the shroud increases with the increase of the tip clearance. Li Y. et al. [23,24] studied the effect of different tip clearances on the performance of the diagonal flow pump. The results showed that the head-flow positive slope characteristic of the diagonal flow pump can be suppressed effectively when tip clearance was 0.5 mm and the efficiency value of diagonal flow pump is highest at this time; At the same time, the larger tip clearance can effectively reduce the high frequency pressure fluctuation in the tip clearance, but the leakage flow caused by it is intensified. You D. et al. [25] used large eddy simulation (LES) to study the tip clearance flow. It was found that the TLV and the tip-leakage jet produced mean velocity gradients. Torre, L. et al. [26] investigated the effect of tip clearance on the performance of a three-bladed axial inducer and found that the intensity of pressure oscillations tends to decrease as the tip blade clearance increases. Many investigations [27e30] have conducted on the effect of tip clearance in other rotating machinery. It can be seen from the above literature that the current research on the tip clearance is mostly focused on performance effects, vortex structure, cavitation and pressure fluctuation, and the flow state in the tip clearance is less analyzed; Moreover, most of the current research is based on single phase medium only. With the further development of submarine oil and gas resources, the application of multiphase pump is more widely expected, and it is more urgent to study the tip clearance flow under gas-liquid two phase conditions. The multiphase pump was always used at the small flow rate in actual operation. Then the effect of the inlet gas void fraction (IGVF) on the flow characteristics in the tip clearance was investigated in a multiphase pump with a tip clearance in present work. The basic structure of the present work was as follows. Firstly, the numerical simulation in a multiphase pump with a tip clearance using ANSYS CFX under different IGVFs was conducted. Then, the reliability of numerical method was proved by comparing with the experimental data of the flow field with the IGVFs of 10%, 15% and 20% using high-speed photography. Finally, the gas distribution, flow characteristics and the evolution of TLV with different IGVF values in the multiphase pump were analyzed in order to make full sense of the effect of the IGVF on flow characteristics in the tip clearance and assist the development of deep sea oil and gas resources, which has an important engineering practical value.
A multiphase pump with 3 impeller and 7 diffuser blades was chosen for analysis. The main design parameters of the pump were listed in Table 1. The test rig for the multiphase pump was comprised of a motor, a multiphase pump, gas-liquid mixing tank, lubrication system, cooling system, control system, water supply system, gas supply system, pipeline and valves, etc. as shown in Fig. 2. In this test, the third compression stage of the multiphase pump was made in a transparent glass. The shape of the pump body was square from outside whereas a circle from inside. The glass refractive index was similar to that of clean water in order to reduce the test error caused by secondary refraction. In order to compare with numerical results, the experimental flow field was shot by a high-speed camera. The transparent glass components used in the test were shown in Fig. 3. The flow field in the multiphase pump at present work was detected with a high speed camera (RDT16-4G), which can capture the fast moving particles and bubbles, and the bursting process of the variable bubbles, as shown in Fig. 4. The camera speed is 500 fps with maximum resolution of 16000 fps, the resolution is 1280 1024 pixels. The test site shown in Fig. 5. 2.2. Governing equations The fluid in the pump was assumed to be incompressible and the governing equations were as follows [31e33]. Continuity equation:
V , ðak rk wk Þ ¼ 0
(1)
Momentum equation:
V , ðak rk wk wk ak tÞ ¼ ak Vp þ Mk þ ak rk fk
(2)
where t denotes the viscous stress tensor; ak , rk , Mk ; fk and wk stand for the void fraction, the density, the interphase force, the mass force, and the velocity of k phase, respectively. 2.3. Computational methods For the convenience of numerical studies, a single compression stage of the pump was selected to conduct the simulation work. In order to ensure that the impeller inlet and the diffuser outlet flow are more adequate, the extension section is added to the impeller inlet and diffuser outlet respectively, and the extension section was added to both impeller inlet and diffuser outlet. The length of the extension was 1.1 and 3.3 times of the inner diameter (D) for impeller inlet and diffuser outlet, respectively. The specific computational model is shown in Fig. 6. The mesh quality in the tip clearance has a large influence in simulating the tip clearance flow and the TLV, so a hexahedral mesh is used for the entire computational domain. In particular, the tip
Table 1 Main design parameters of multiphase pump. Parameters
Symbol
Value
Unit
Design flow rate Design speed Hub/tip ratio
Qd n
100 3000 0.7
m3/h rpm ()
113 85
mm m
Inner diameter Head
d D H
48
G. Shi et al. / Renewable Energy 150 (2020) 46e57 Water injection
3
2
4
5
1
Water pipeline P
P
9 8
12 14
Air injection Gas pipeline
High-speed photography
6
7
P
13
10 P
11
1. Water tank 2. Water supply pump 3. Flow meter 4. Outlet valve 5. Inlet valve 7. Torque meter 8. Gas-liquid mixing tank
6. The motor
9. Outlet pressure gauge 10. Inlet pressure gauge 11.
Multiphase pump 12. Gas valve 13. Air compressor 14. Rotameter Fig. 2. Test rig.
(a) Impeller
(b) Diffuser
(c) Pump Fig. 3. Transparent glass components used in the test.
clearance and the near-wall area mesh are refined to improve the accuracy and convergence of the calculations, as shown in Fig. 7. The blade adopts an O-topology method to control the boundary layer distribution near wall. At the same time, in order to accurately capture the flow characteristics in the tip clearance, 40 layers meshes are arranged in the tip clearance along the radial direction of the blade. The y þ near the impeller is between 0 and 60, which meets the requirements of the SST k-u turbulence model for the near wall [34]. After the mesh independence check, the requirements were met, and the number of mesh finally used was 5,421,110. The k-u based Shear-Stress-Transport (SST) model was designed to give highly accurate predictions of the onset and the amount of flow separation under adverse pressure gradients by the inclusion of transport effects into the formulation of the eddy-viscosity. Based on the RANS equations and the SST k-u turbulence model, the ANSYS CFX software was used to numerically calculate the flow characteristics in a multiphase pump with a tip clearance of 1 mm at the off-design condition and different IGVFs. The offdesign condition (partial discharge of 0.8Qd (Qd is the design flow rate)) and the IGVFs (IGVF ¼ 0, 5%,10%,15% and 20%) were chosen for
Fig. 4. The high speed camera.
the numerical investigation. In the calculations, an EulerianEulerian multiphase model was adopted and the velocity slip between gas and liquid was taken into account. Meanwhile, the liquid phase was considered as a continuous fluid and the gas phase was considered as a dispersed fluid. The settings of boundaries and solution were listed in Table 2. 2.4. Operating condition points In the process of experiment, keeping the gas flow rate Qg unchanged and adjusting the liquid flow rate Ql to adjust the IGVF. IGVF is calculated according to the Eq. (3).
G. Shi et al. / Renewable Energy 150 (2020) 46e57
49
Qg Qg þ Q1
(3)
IGVF ¼
where Qg and Ql represent the volume discharge of gas and liquid, respectively, at the inlet. In order to verify the reliability of the numerical results, the flow field in test results are compare to the results in numerical simulation in multiphase pump at the rotational speed of 3000 rpm, flow rate of 80 m3/h, and the IGVFs of 10%, 15% and 20% in this paper, which intends to verify the reliability of numerical calculation methods.
2.5. Test and numerical tip leakage flow Fig. 8 is a comparison of the test results and the numerical calculation results near the blade tip. The swirling strength is selected to as isosurface and represent the TLV trajectory. It can be seen from Fig. 8 that the leakage flow in the tip clearance entrained the main flow and then evolved into a TLV. The TLV is mainly located on the suction side (SS) of the blade. At the same time, there is also a vortex structure at the blade inlet near the PS. The correspondence between tests and the numerical simulations are as
Fig. 5. The test site.
h Tip clearance Inlet pipe
Impeller
Outlet pipe
Diffuser
IGVF=10% Fig. 6. Computation model.
IGVF=15%
IGVF=20%
Fig. 8. Comparison of test results and numerical results.
Mesh in the tip clearance
Blade tip Blade Blade tip
(a) Impeller blade (b) Tip clearance
(c) Impeller
(d) Diffuser
Fig. 7. Computational domain mesh.
Table 2 Settings of boundaries and solution. Types
Items
Settings
Value
Unit
boundaries
Inlet Outlet Pressure Domain motion Wall Rotor-stator interfaces Convergence criteria
Normal speed Static pressure Reference pressure Rotating No-slip Frozen-rotor Root mean square (RMS) residuala
2.1512 6 1 3000 () () 1 105
m/s atm atm rpm () () ()
solution a
When the RMS residual was below 1 105, the calculation was considered to be converged.
50
G. Shi et al. / Renewable Energy 150 (2020) 46e57
shown in common color markers (As shown in red, yellow and blue ellipses). Thus, the numerical calculation results are in good agreement with the experimental results, which verifies the reliability of the numerical calculation method. 3. Effect of IGVF for TLV flow behavior In order to analyze the flow characteristics of different parts of the multiphase pump, 6 cross sections were set in the impeller and diffuser along the axial direction, which were named as Section 1 to Section 6, respectively. At the same time, Section 7 was set to analyze the flow characteristic in tip clearance. In addition, in order to accurately analyze the flow state characteristics of the Section 7, it was divided into two regions A and B. A schematic view of sections was shown in Fig. 9. 3.1. Effect of IGVFs on the impeller cross section The Fig. 10 was a velocity distribution for different sections in the impeller, where Fig. 10 (a) and Fig. 10 (b) were the velocity contour and the streamline distribution, respectively. It can be seen from Fig. 10 (a) that at different IGVFs, the maximum velocity region moved from the shroud to the hub along the flow direction (the flow direction was from Section 1 to Section 3). At the same time, it was found that the maximum velocity appears in Section 1 near the PS. This was because the inflow angle was inconsistent with the blade inlet angle, which caused the flow instability in the region. In addition, it was found that the influence of IGVF in the passage at three sections was different, ie, as the IGVF increases, the maximum velocity in the passage at the Section 1 (except for the unstable flow region of the blade PS) gradually decreased. Simultaneously, the proportion of the high velocity area also reduced gradually, and the high velocity area gradually moved from the shroud to hub. In the Section 2, the proportion of the high velocity area gradually increased and the high velocity area gradually extended to the adjacent blade PS with the increase of the IGVF. In the Section 3, the proportion of maximum velocity increased initially and then decreased with the increase of the IGVF. The relationship between the velocity and IGVF was not linear because it was affected by the rotorestator interaction at the Section 3, which caused that the flow state in the region to become more complicated. It can be seen
from Fig. 10(b) that as the IGVF increased, the streamlines on the sections in the impeller were smooth, and there was no unstable flow phenomenon such as vortex and secondary flow, which indicates that the impeller had a good adaptability to the gas phase medium [1]. The Fig. 11 showed gas distribution of the A region in Section 7. As can be seen from Fig. 11, the accumulated gas was mainly at the impeller inlet near the PS, tip clearance near the tip and the SS both at the Section 2 and Section 3. The gas accumulated at the impeller inlet PS because the flow near the inlet was unstable, while the blade tip and SS were concentrated because of the lower pressure in the region. At the same IGVF, the gas accumulated more and more near the tip and the SS along the flow direction, and it was found that the uneven region of the accumulated gas gradually moved from the shroud to hub. In addition, as the IGVF increased, the proportion of the gas in the main accumulated location also increased. 3.2. Effect of IGVF in the tip clearance Fig. 12 was the velocity vector and pressure distribution of region A in Section 7. It can be seen from Fig. 12 that the IGVF had a great influence on the velocity and pressure distribution in the tip clearance. In the pure water condition (IGVF ¼ 0), the tip clearance leakage flow was from the PS to the SS under the pressure difference between the PS and the SS. Since the angle of the tip near the PS was a right angle, the leakage flow was flowing through the blade tip, then the flow separation occurred, and a tip separated vortex was generated [12]. At this time, the separated vortex was small. In addition, the separated vortex core pressure was lower, which increased the possibility of cavitation in the tip clearance [14]. When the IGVF increased from 5% to 10%, it was found that the separated vortex in the tip clearance was increased until the separated vortex region throughout the entire tip clearance. At the same time, the tip leakage flow velocity was also gradually reduced, and the low pressure area caused by the flow separation around the blade tip was further enlarged. When the IGVF increased to 15%, it was found that the tip leakage flow velocity decreased while the velocity near the tip separated vortex increased slightly, at the same time the low pressure distribution area decreased. When the IGVF was increased to 20%, the low
Section1 Section2 Section3 Section4 Section5 Section7 Section6
B
A
Suction side Pressure side
Inlet pipe Impeller Duffser Outlet pipe
Fig. 9. A schematic view of sections.
G. Shi et al. / Renewable Energy 150 (2020) 46e57
IGVF=0 PS SS
51
SS PS
PS
PS
PS
SS
SS PS
SS
SS
IGVF=10%
IGVF=20%
Section 1 Section 2 Section 3 (a)Velocity contour
Section 1 Section 2 Section 3 (b) Distribution of the streamline
Fig. 10. Velocity distribution in different sections of the impeller.
SS PS
PS
PS
SS
SS
IGVF=0%
IGVF=15%
IGVF=20%
Section 1
Section 2
Section 3
Fig. 11. Gas distribution in the impeller.
pressure area in the tip clearance near the PS gradually disappeared. In summary, at a small IGVF (IGVF ¼ 5%, 10%), the IGVF increased, the separated vortex intensity around the blade tip increases and the low pressure area in the tip clearance near the PS increased. While at the large IGVF (IGVF ¼ 15%, 20%), the increase of IGVF caused the low pressure area in the tip clearance near the PS gradually disappeared, which can effectively reduce the possibility of cavitation in the tip clearance.
The Fig. 13 (a) was a velocity distribution of the region A in Section 7. When the IGVF increased from 5% to 10%, it was found that the velocity in the tip clearance was larger than that in pure water, and when the IGVF increased, the proportion of the maximum velocity in the tip clearance decreased and move forward along the flow direction of the leakage flow. It was also found that the range of the low velocity area near the blade tip was enlarged and the velocity was decreased. When the IGVF increased
52
G. Shi et al. / Renewable Energy 150 (2020) 46e57
IGVF=0 SS
PS
SS
PS
IGVF=5%
IGVF=10%
IGVF=15%
IGVF=20% Fig. 12. Velocity vector and pressure distribution in the tip clearance.
IGVF=0
SS
IGVF=5%
PS
SS
PS
IGVF=10%
IGVF=15%
IGVF=20%
(a) Velocity
(b) IGVF
Fig. 13. Velocity and IGVF distribution in the tip clearance.
to 15%, the high velocity area in the tip clearance disappears and the velocity near the blade tip increased. When the IGVF was further increased to 20%, the proportion of the high velocity area was reduced again, and the velocity near the blade tip was also reduced. It can be seen that the IGVF had a great influence on the velocity distribution in the tip clearance. The Fig. 13(b) was a gas distribution of the region A in Section 7.
As can be seen from Fig. 13(b), the gas accumulation mainly occurred around the blade tip and the SS of the blade, and the gas accumulation and the tip separated vortex were consistent. When the IGVF was 5%, the gas accumulation around the blade tip occurs near the PS and consistent with the separated vortex. When the IGVF was 10%, the gas accumulation area was further enlarged and the gas accumulation area was near the blade tip as compared with
G. Shi et al. / Renewable Energy 150 (2020) 46e57
the IGVF of 5%. When the IGVF was 15%, the gas distribution in the gas accumulation area was stratified. When the IGVF was further increased to 20%, the gas accumulation location gradually moved from the blade tip to the shroud in the entire tip clearance. At the same time, there was an obvious stratified structure in the tip clearance [7]. In addition, as the IGVF increases, the gas accumulation near the SS of the blade gradually increased. It can be seen from the above analysis that different IGVFs had different influences on the gas distribution in the tip clearance. This indicated the gas-liquid two-phase interaction was complicated, and the leakage flow state was also disordered. The gas void fraction near the blade tip was displayed in Fig. 14. From Fig. 14, the gas distribution between the pressure side and the suction side at the blade tip was obviously different. The gas distribution variation at the inlet and streamwise coefficient of 0.3 on the pressure side was more obviously and with the increase of inlet gas void fraction, the gas distribution was increased. At same time, there was almost no gas at other locations from the leading edge to the trailing edge. From the inlet to streamwise coefficient of 0.8 on suction side, the gas distribution increased with the increase of the inlet gas void fraction, and the degree gradually decreased. In addition, the gas variation regularity was significantly weakened from the streamwise coefficient of 0.8 to the trailing edge and the gas distribution pulsated near the trailing edge. 3.3. Effect of IGVF on tip clearance leakage flow The TLV was formed by the entrainment between the leakage flow and main flow under the pressure difference between the PS and SS of the blade, so the tip leakage flow velocity was an important quantitative indicator for analyzing the TLV, especially in the two-phase condition. In order to accomplish quantitative analysis, the monitor points were set at the middle of the radial direction along the streamwise direction in the tip clearance. The distance from the blade inlet along center line of blade profile to the blade outlet was normalized, ie, the inlet was 0, the outlet was 1, and it was defined as the streamwise coefficient. Finally, the tip leakage flow velocity was plotted along the streamwise, as shown in Fig. 15. It can be seen from Fig. 15 that the trend of leakage flow velocity along the streamwise was generally similar under the gas and pure
53
water conditions, but the difference was in the magnitude of the leakage velocity. The gas caused the tip leakage flow velocity to decrease from the blade inlet to the streamwise coefficient of 0.2 compared to the pure water condition, whereas it was increased from the streamwise coefficient of 0.2 to the blade trailing edge. At the same time, it can be found that the leakage velocity along the streamwise coefficient of 0.1e0.4 was most affected by the IGVF, whereas the leakage velocity along the streamwise coefficient of 0.6e0.9 was most affected by whether it had gas or not. The flow state in the impeller under gas-liquid two-phase conditions was quite different from that of pure water. In order to qualitatively analyze the flow characteristics of the medium in the impeller passage, the correlation between the velocity streamline and the vorticity distribution in the region B of the Section 7 was analyzed, as shown in Fig. 16. It can be seen from Fig. 16 that, a “jet-wake” structure was formed due to the jet effect at the outlet of the tip clearance. It affected the flow characteristics both in the impeller passage and the near the blade tip to a large extent. The influence of the IGVF on the flow characteristics was analyzed as follows. Under the water condition (IGVF ¼ 0), the wake area and the maximum TLV area were basically coincident. At the same time, a large vorticity appeared in the radial middle of the adjacent blade PS. When the IGVF was 5%, a relatively obvious vortex structure appeared in the development direction of the wake, and the velocity at the vortex was significantly smaller. In addition, the streamlines at the vortex near the hub were slightly curved. At the same time, it can be seen that the vorticity around TLV was larger than that of pure water, and the vorticity at the radial middle of the adjacent blade PS was also significantly increased. As the IGVF increased to 10%, 15%, the vortex core was moved to the shroud and the SS, and the streamlines around the TLV near the hub was more obviously curved. The maximum vorticity area corresponding to the wake in the vorticity diagram also increased rapidly, and the increase in amplitude was most obvious when the IGVF was 15%. At the same time, the area of the maximum vorticity in the middle of the adjacent blade PS gradually became smaller, and moved toward the SS. When the IGVF was 20%, the TLV had further increased and moved toward the adjacent blade PS. At the same time, a small vortex structure appeared in the wake region due to the induction. The streamline deflection of the large vortex near the hub was more obvious. In addition, the maximum vorticity region corresponding to the wake region became larger, and gradually extended to the tip clearance of the adjacent blade PS, interacting with the adjacent tip leakage flow and making the flow state in the tip clearance more complicated. At the same time, the maximum vorticity area at the radial middle near the adjacent blade PS had significantly moved toward the SS. 3.4. Effect of the IGVF on TLV structure
Fig. 14. Gas void fraction near blade tip.
In order to analyze the effect of the IGVF on the TLV in the multiphase pump, the liquid swirling strength was used to represent the TLV structure and it was shown in Fig. 17. It can be seen from Fig. 17 that the TLV trajectory changed with the IGVF. The variation of the TLV trajectory was analyzed as follows. When the GFV was 0, the TLV appeared at the impeller inlet along the flow coefficient of about 0.3. The TLV structure was strip-shaped and close to the SS, ie, the leakage separation angle between the TLV trajectory and the chord was small [18]. In addition, a wake vortex appeared on the trailing edge of the blade. With the increase of the IGVF, the TLV had obviously changed in structure and distribution. When the IGVF was 5%, the initial location of the TLV was moving to the trailing
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G. Shi et al. / Renewable Energy 150 (2020) 46e57
Fig. 15. Leakage flow velocity in the tip clearance.
edge along the streamwise compared with the pure water working condition. The length of the TLV increased and the separation angle became larger. The vortex at the trailing edge of the blade increased, and the vortex structure also appeared on the inlet PS of the blade. When the IGVF was further increased to 10%, the TLV around the blade tip was significantly increased from the streamwise coefficient of about 0.5 to the trailing edge. When the IGVFs were 15%, 20%, the TLV was further enhanced, and the TLV of the adjacent SS at the blade inlet and the vortex at the inlet PS of the blade began to be drawn into a strong vortex structure. In addition, in order to further explore the cause of the vortex structure at the inlet PS of the blade, taking IGVF of 15% and 20% as an example, the liquid velocity streamline and gas distribution of the impeller were made, as shown in Fig. 18. It can be seen from the figure that gas accumulation is observed near the blade inlet, which caused a flow separation phenomenon and to form a vortex structure. It can be seen from the above analysis that the IGVF had a great influence on the three-dimensional structure of the TLV in the multiphase pump and the flow mechanism under gas-liquid condition was more complex, so this research had great significance. Fig. 19 was a velocity distribution of each section in the diffuser. As can be seen from Fig. 19, the velocity in the diffuser was smaller than that in the impeller as a whole, and the flow state was also disordered. At the same IGVF, the proportion of the minimum velocity in the diffuser along the flow direction (Section 4 to Section 6) gradually increased, and the flow state in the passage becomes more and more disordered, and the vortices appeared. In addition, the vortex location was found to correspond to the minimum velocity location, and the vortex was asymmetrically distributed in the circumferential direction in each of the passages. With the increase of IGVF, the proportion of low velocity area in the passage of each section in the diffuser gradually increased, especially at the diffuser inlet (Section 4).
4. Conclusion The gas distribution, flow characteristics and the evolution of TLV with different IGVF values in the multiphase pump were analyzed in present work. Based on experimental results, the accuracy of the numerical simulations on multiphase pumps was validated. From the present study, following conclusions have been drawn. (1) The accumulated gas was mainly at the impeller inlet near the PS, tip clearance near the tip and the SS. When the IGVF increased, there was an obvious stratified structure in the tip clearance and the separated vortex structure near the PS had been found to increased gradually. In addition, the streamlines in the impeller were more smoother than those in the diffuser and the vortex in diffuser corresponded to the minimum velocity. (2) Compared to the pure water condition, the gas caused the tip leakage flow velocity to decrease from the blade inlet to the streamwise coefficient of 0.2, and to increase from the streamwise coefficient of 0.2 to the blade trailing edge. At the same time, the structure of the TLV was changed with the IGVF. With the increase of the IGVF, firstly, the length of the TLV increased and the separation angle became larger. Then, the TLV around the blade tip was significantly increased from the streamwise coefficient of about 0.5 to the trailing edge. Finally, the leakage vortex of the adjacent SS and the vortex at the inlet PS began to be drawn into a strong vortex structure. In addition, the streamlines and vorticity distribution corresponding to the wake and the TLV were also changed. (3) The flow characters and the structure of the TLV were more complicated under gas-liquid condition, and it also deteriorated the flow state in the passage and increased the hydraulic loss in the multiphase pump.
Suction side
Pressure side of adjacent blade
Pressure side of adjacent blade
Suction side
IGVF=0
Suction side
Pressure side of adjacent blade
Pressure side of adjacent blade
Suction side
IGVF=5%
Suction side
Pressure side of adjacent blade
Pressure side of adjacent blade
Suction side
IGVF=10%
Suction side
Pressure side of adjacent blade
Pressure side of adjacent blade
Suction side
IGVF=15%
Suction side
Pressure side of adjacent blade
Pressure side of adjacent blade
Suction side
IGVF=20%
(a) Velocity streamlines
(b) Vorticity distribution
Fig. 16. Velocity streamlines and vorticity distribution.
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G. Shi et al. / Renewable Energy 150 (2020) 46e57
IGVF=0
IGVF=5%
IGVF=15%
IGVF=10%
IGVF=20%
Fig. 17. Three-dimensional structure of the TLV.
IGVF =15%
IGVF =20%
(a) Velocity streamline at the radial coefficient r*=0.6
IGVF =15%
IGVF =20%
(b) Gas volume fraction at radial coefficient r*=0.6
Fig. 18. Velocity streamline and gas volume fraction.
IGVF=0
IGVF=10%
IGVF=20%
Section 4
Section 5
Section 6
Section 4
Section 5
Section 6
Fig. 19. Velocity distribution of each section in the diffuser.
Declaration of competing interest Guangtai Shi and other co-authors have no conflict of interest. Acknowledgment This work was supported by the National Key Research and Development Program(Grant No. 2018YFB0905200), Education department key project of Sichuan province of China (Grant No. 17ZA0366),“Young Scholars Reserve Talents” program of Xihua University, China Postdoctoral Science Foundation (Grant No.
2017T100077) and the Key scientific research fund of Xihua University of China (Grant No. Z1510417). This work was also supported by the Open Research Subject of Key Laboratory of Fluid and Power Machinery, Ministry of Education (Grant No. szjj2016-063), the National Natural Science Foundation of China (Grant No. 51479093), The National Key Research and Development Program of China (Grant No. 2017YFC0404200), the Key Research and Development Program of Tianjin (Grant No. 18YFZCSF00310), and the Key Laboratory of Fluid and Power Machinery (Xihua University) Ministry of Education (Grant No. SZJJ-2018-125).
G. Shi et al. / Renewable Energy 150 (2020) 46e57
Nomenclature D
Inner diameter
d fk H IGVF LE TE LES Mk n PS Qd SST SS TLV wk
Hub/tip ratio Mass force of k phase Head Inlet gas void fraction Leading edge Trailing edge Large eddy simulation Interphase force of k phase Design speed Pressure side Design flow rate Shear stress transport Suction side Tip leakage vortex Velocity of k phase Void fraction of k phase Density of k phase Viscous stress tensor
ak rk t
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