Cavitation performance of high-speed centrifugal pump with annular jet and inducer at different temperatures and void fractions ＊

Jin Jiang, Yan-hui Li, Chong-yan Pei, Lin-lin Li, You Fu, Hong-gui Cheng, Qiang-qiang Sun

1. Key Laboratory of Hydraulic Machinery Transient, MOE, Wuhan University, Wuhan 430072, China

2. Science and Technology on Scramjet Laboratory, The 31st Research Institute of CASIC, Beijing 100074, China

Abstract: The cavitation is very common in a centrifugal pump, especially when the speed is very high, and it seriously influences the centrifugal pump performance. In this investigation, the RNG k-ε turbulence model and the cavitation model with consideration of the mass transferring are first used to simulate the cavitation performance of the high-speed centrifugal pump without taking any measure for improving the pump cavitation performance. The calculation results reveal that a number of bubbles appear in the centrifugal pump flow channel, and the head as well as the flow rate of the high-speed centrifugal pump are far from its design condition. The cavitation performance can be improved effectively by arranging a variable pitch inducer and adopting an annular nozzle scheme. The flow field analysis of the pump is conducted to obtain the suitable working temperature distribution at different void fractions. On one hand, with the same void fraction, the head of the centrifugal pump drops slowly with the increase of temperature. However, when the temperature exceeds 90°C, the head of the pump drops rapidly. On the other hand, at the constant temperature, the higher the void fraction, the worse the cavitation performance. This research conducted under different temperatures and void fractions provides some guidance for designing an effective high-speed centrifugal pump.

Key words: High-speed centrifugal pump, cavitation performance, inducer, annular nozzle, void fraction

Introduction

A high-speed centrifugal pump with a good cavitation performance is a main part of the hypersonic engine fuel supply system[1], and an inducer is a key component which can improve the suction performance of the high-speed centrifugal pump[2]. An inducer can protect the centrifugal pump against damage due to vibration and noise caused by the cavitation[3]. There have been huge amount of investigations on cavitation. For instance, Ji et al.[4]found that the cavitation can result in the flow separation, the increase of the boundary layer thickness and the instability of the flow. Huang et al.[5]investigated the multistage centrifugal pump performance under developed cavitation conditions numerically and experimentally, where numerical data were validated with experimental data and a good comparison of results was achieved. Okita et al.[6]performed numerical simulations to clarify the influences of the tip clearance flows on the unsteady cavitating flow,and flow conditions in both the two-dimensional cascades and the three-dimensional inducer with and without tip clearance were considered respectively.Lee et al.[7]conducted experiments and numerical investigation of the cavitation instability for a two-bladed inducer and found that the local flow around the cavity closure significantly contributes to the occurrence of the asymmetric cavitation. Tamura and Matsumoto[8]presented a new bubble flow dynamics to increase the accuracy of the numerical simulation. Choi et al.[9], Saha et al.[10-11]proposed shallow grooves structure, names “J-Grooves”, and arranged them on a casing wall of a centrifugal pump in the pressure gradient direction of the main flow as countermeasures to various abnormal flow phenomena such as the rotating stall in vane and vaneless diffusers and for the rising head performance with increasing the flow in the axial flow pumps. Flores et al.[12]studied the three-bladed inducer performance in three kinds of flow and analyzed the head, the efficiency,the blade load and the power of the centrifugal pump when the cavitation occurs, with the simulation results in good agreement with the experimental data.Yoshida et al.[13]investigated the rotor dynamics for the three-bladed inducer with synchronous or super-synchronous rotating cavitations and found that the instability of the rotating cavitation would lead to the vibration of the shaft. Zhang et al.[14]proposed a thermodynamic cavitation model for the cavitation flow simulation in a wide range of water temperatures and analyzed the thermodynamic effects of the cavitation, where the simulation values were in good agreement with the experiment. Yu et al.[15]simulated the cavitation flow around a cylinder vehicle using a new simulation method, where the interactions between the water and the air, the water and the vapor are fully considered. The good agreement between the simulation and experiment indicates that the new method is accurate enough. Li et al.[16]used the vortex identified Zwart-Gerber-Belamri (VIZGB) cavitation model coupled with the SST-CC turbulence model to investigate the unsteady tip-leakage cavitating flow induced by a NACA0009 hydrofoil and results indicate that the cavitation accelerates the fusion of the tip-leakage vortex and the tip-separation vortex.

In spite of the effort to investigate the inducer performance and the cavitation instability, there is lack of the device investigation for improving the centrifugal pump cavitation performance. Therefore, a suitable variable pitch inducer and several annular nozzles are designed and investigated in the research.The new device can effectively suppress the cavitation and improve the centrifugal pump cavitation performance for different temperatures and void fractions.

1. Numerical simulation model

1.1 Governing equations

In this paper, the fluid is considered to be incompressible and the steady-state RANS equations are used. The continuity equation and the momentum equations are given as follows:

In order to achieve the closure of Eq. (2), the Reynolds stress term is modeled. The modeling is based on the Boussinesq hypothesis and the relation between the Reynolds stresses and the mean velocity gradients within the flow. The Reynolds stress term is given by

wheretμ is the turbulent viscosity and k is the turbulent kinetic energy.

1.2 Turbulence model

The turbulent effective viscosity is simulated by the RNG k- ε turbulence model[17]in which the turbulent kinetic energy k and its dissipation rate ε are defined as:

wherekG is the production term of turbulent kinetic energy k while the corresponding empirical constantskα ,εα and2Cεrespectively equal to 1.39,1.39 and 1.68.

In addition, the effective viscosity μeffand the modified empirical coefficientare respectively given by:

where Cμ,1Cε,0η and β are empirical constants and their valves are 0.0845, 1.42, 4.377 and 0.012 respectively.

And another complementary equations are needed:

1.3 Cavitation model

The Schnerr-Sauer cavitation model[18-20]is used to simulate the cavitating flow. The expression for the phase change rate is defined as

wherevR is the vaporization rate andcR is the condensation rate. And they are expressed respectively as follow:

where r is the radius of a typical bubble with a value of 1×10-6, p,vp are the actual pressure and the saturated vapor pressure respectively,lρ,vρ are the densities of liquid and gas phases respectively, and vα is the volume fraction of the gas phase.

2. Design of variable pitch inducer and annular nozzle

2.1 Design parameters of variable pitch inducer

Design parameters of the high-speed centrifugal pump are given as follows: the impeller diameter Dim= 0.1m , the rotation speed n = 40 000 r/min ,and the flow rate Q = 0.004 m3/s . The Reynolds number based on the diameter of the centrifugal pump inlet and the inlet velocity is 2.3×105approximately.

Fig. 1 Variable pitch inducer

The 3-D physical model of the two-bladed variable pitch inducer is depicted in Fig.1. This inducer located at the upstream of the impeller is designed to guide the fluid smoothly into the pump and improve the pressure of the impeller inlet to suppress the cavitation. The main design parameters of the variable pitch inducer are indicated in Table 1.

Table 1 Characteristic parameters of variable pitch inducer

2.2 Design of annular nozzle

In a high-speed centrifugal pump, the cavitation likely appears at the inducer inlet. Thus, in this investigation, a portion of high-energy liquid is guided to flow back from the pump volute to the annular ejector through the diversion tube, to improve the pressure of the inducer inlet and suppress the cavitation effectively. There are six nozzles on the ejector toward the variable pitch inducer, as shown in Fig. 2,and the angle between each two nozzles is 60°.

Fig. 2 (Color online) Configuration of annular nozzle scheme

3. Simulation settings and grid generation

3.1 Grid generation and boundary conditions

In the computational domain, the unstructured mesh is adopted. The mesh generation details near the special structures such as the nozzle and the inducer tip are shown in Fig. 3. In addition, the fuel oil is used as the working material in this investigation with the molecular formula of C19H30. For the calculation temperature, different parameters are adopted according to the thermal properties of the fuel oil at different temperature levels.

Boundary conditions are as follows: the uniform velocity and the turbulence intensity for the inlet, the average total pressure for the outlet, the non-slip condition for the walls.

Fig. 3 (Color online) Mesh details near inducer tip and nozzle

3.2 Grid independent test

The numerical simulations are performed by three mesh schemes to satisfy the requirement of grid independence, respectively including the amounts of grids of 4.286×106, 5.323×106and 6.742×106. The performance parameters of the centrifugal pump,including the inducer inlet static pressure, the impeller inlet static pressure as well as the inducer head, are listed in Table 2.

Table 2 Characteristic parameters of variable pitch inducer

According to Table 2, the calculation results of the centrifugal pump performance are almost the same as each other in these three different situations. For instance, the relative errors of the inducer inlet static pressure, the impeller inlet static pressure and the centrifugal head are all less than 5%.

4. Results and discussions

4.1 Results based on different structural schemes

Fig. 4 (Color online) Vapor volume fractions in centrifugal pump with or without a variable pitch inducer and an annular nozzle scheme: (a) Situation in impeller without inducer and nozzle scheme, (b) Situation in impeller with a variable pitch inducer and annular nozzle scheme, (c)Situation in pump without inducer and nozzle scheme, (d)Situation in pump with a variable pitch inducer and annular nozzle scheme

Fig. 5 (Color online) Pressure distributions in centrifugal pump with or without a variable pitch inducer and an annular nozzle scheme: (a) Situation in impeller without inducer and nozzle scheme, (b) Situation in impeller with a variable pitch inducer and annular nozzle scheme, (c) Situation in pump without inducer and nozzle scheme, (d) Situation in pump with a variable pitch inducer and annular nozzle scheme

For the centrifugal pump without an inducer and a nozzle scheme, as shown in Fig. 4(a), the cavitation not only appears in the impeller but also the volute.The impeller is full of bubbles, which will damage the performance of the pump seriously, as shown in Fig.4(c). The head and the flow rate are only 0.4 MPa, 0.1 l/s respectively, which are far below the design values.While adding a variable pitch inducer and an annular nozzle scheme on the high-speed centrifugal pump,only a few bubbles, as shown in Figs.4 (b), 4(d), are located on the impeller blade inlet and the variable pitch inducer blade suction surface. And the cavitation in the centrifugal pump is suppressed effectively. As a satisfactory result, the head and the flow rate are within the design limits.

Figures 5(a), 5(c) show the pressure distributions in the high-speed centrifugal pump without any anticavitation scheme to suppress the cavitation. The pressures in almost all locations are really low except some local areas of the impeller blade tip. However,the pressure in most area in the centrifugal pump with a variable pitch inducer and an annular nozzle scheme is significantly high as shown in Figs. 5(b), 5(d). The lower pressure area between the inducer outlet and the impeller inlet is recognized. And the pressure of the centrifugal pump outlet is 8.0 MPa which meets the design requirements. Comparing with the centrifugal pump without taking any measure, it is an effective way to improve the pump suction performance by adding a suitable variable pitch inducer and an annular nozzle scheme.

4.2 Results based on different temperatures and void fractions

As mentioned above, an appropriate variable pitch inducer and an annular nozzle scheme are mounted on the high-speed centrifugal pump to increase the pump pressure and improve its cavitation performance.In this section, the high-speed centrifugal pump cavitation performance at different temperatures and void fractions are investigated based on the scheme of suppressing cavitation to obtain the temperature distribution for the pump operating normally.

The numerical simulation is conducted for three kinds of void fractions ( =α 0, 0.01and 0.03) and six different temperatures ( T= 50°C, 70°C, 80°C, 90°C,100°C, 110°C)

Figure 6 illustrates the gas-phase volume fraction of the high-speed centrifugal pump impeller at different temperatures and void fractions. When α=0 and T = 50 °C , both of the cavitation scope and the extent of the impeller channel are really tiny. The bubbles are only distributed on the impeller blade inlet and there are more bubbles found near the blade suction surface rather than the pressure surface.However, there is no cavitation between the variable pitch inducer outlet and the impeller inlet. When T = 70 ° C, the cavitation area becomes larger and the bubbles can be found not only on the impeller blade inlet but also on the impeller blade tip. The degree of the cavitation is more serious and the cavitation also appears on the contact area between the variable pitch inducer outlet and the impeller inlet at 90°C. With temperature increasing, the cavitation becomes more and more severe. When T = 100° C, it is obvious that the whole impeller channel is full of bubbles and in the contact location between the variable pitch inducer and the impeller also huge amount of bubbles is found,indicating the serious cavitation appears in the high-speed centrifugal pump. The cavitation scope and extent at the temperature larger than 100°C is similar to the situation when T = 100 °C . At this moment the head of the high-speed centrifugal pump is only about 0.3 MPa. However, this head is far from meeting the design requirements.

With all calculation temperatures, the variations of the cavitation scope and extent in the high-speed centrifugal pump when =α 0.01, 0.03 are almost the same as that when α=0 . On the other hand, the cavitation in the high-speed centrifugal pump becomes more serious with the void faction increasing in one temperature.

Fig. 6 (Color online) Gas-phase volume fractions of centrifugal pump impeller at different temperatures and void fractions

Fig. 7 (Color online) Pressure distributions on the centrifugal pump impeller blade walls at different temperatures and void fractions

In addition, the distribution of the centrifugal pump cavitation is asymmetrical in the impeller flow channel. More bubbles are found in two impeller blade runners rather than in other six channels. The similar case is also found on the area between the variable pitch inducer outlet and the impeller inlet.These may be caused by the axial distance between the inducer and the impeller, which will be explored in other investigations.

When α =0 and T = 50° C , the pressure in the area near the impeller blade tip wall is significantly high, but this is not really true for the impeller blade inlet including the pressure surface and the suction surface. Therefore, the cavitation occurs on the impeller blade inlet, as shown in Fig. 7. When T is less than 90°C, both the pressure on the impeller blade tip wall and in the area of high pressure decrease with the increase of the temperature. Besides, the impeller inlet pressure also decreases. When the temperature is increased to 100°C, the pressure on almost all the impeller blade wall is really low except for a very little area near the impeller blade tip wall. In addition,the case of 110°C is similar with that of 100°C.

The variations of the pressure distributions on the impeller blade wall at different temperatures, when=α 0.01 or 0.03, are similar to the case when α=0 .Furthermore, at one temperature, the pressure on the high-speed centrifugal pump impeller blade wall decreases slowly with the increase of the void fraction,but not significantly.

When α=0 , the area and the extent of the cavitation at all calculation temperatures in the variable pitch inducer flow passage are similar, as shown in Fig. 8. The bubbles are generated on all two inducer blade suction surface. There are more bubbles on the inducer blade inlet as compared with the blade outlet.In addition, the cavitation also occurs in the tip clearance between the inducer blade tip and the wall.The area and the level of the cavitation in the variable pitch inducer flow channel and the tip clearance between the inducer blade tip and the wall go with serious problems of cavitation with the increase of the temperature.

The variations of the gas-phase volume fraction in the inducer runner at different temperatures, when α = 0.01 or 0.03, is similar to the case when α =0.Their difference is that the cavitation becomes more serious with the increase of the void fraction at a high temperature.

With respect to pressure distribution as illustrated in Fig. 9, the numerical simulation results show that when α =0, the pressure on the variable pitch inducer blade pressure surface close to the outlet edge is relatively high and the area of the high pressure nearly covers fifty percent of all pressure surface when T = 50° C. However, in the inlet of the variable pitch inducer, low-pressure area is recognized on the pressure surface and all the suction surface. With the temperature increasing to 100°C, on the pressure surface or the suction surface, the pressure on the entire wall is extreme low, as shown in Fig. 9 (a).

The variations of the pressure distributions on the inducer blade wall at different temperatures, when α =0.01 or 0.03, is similar to the case when α =0.Furthermore，at the same temperature, the pressure on the high-speed centrifugal pump inducer blade wall decreases slowly with the increase of the void fraction.

Fig. 8 (Color online) Gas-phase volume fractions of high-speed centrifugal pump inducer at different temperatures and void fractions

Fig. 9 (Color online) Pressure distributions on the high-speed centrifugal pump inducer blade walls at different temperatures and void fractions

Table 3 lists the numerical simulation results of the head of the high-speed centrifugal pump at different temperatures and void fractions. At the same void fraction, the head of the high-speed centrifugal pump decreases slowly with the increase of the temperature, while it decreases rapidly when the temperature is higher than 90°C. In view of the above analysis about the flow field in the high-speed centrifugal pump impeller and the variable pitch inducer, lots of bubbles would appear in the impeller and the variable pitch inducer flow passage, as shown in Figs. 5, 7. When the temperature is higher than 100°C, the head of the centrifugal pump is so low and keeps constant that it is far away from the normal operation condition. At the same temperature, the head of the high-speed centrifugal pump decreases with the increase of the void fraction.

Table 3 Heads at different temperatures and void fractions

5. Conclusions

The RNG k- ε turbulence model and the masstransfer cavitation model are used to simulate the cavitation performance of the high-speed centrifugal pump with a suitable variable pitch inducer and an annular nozzle scheme at different temperatures ( T=50°C, 70°C, 80°C, 90°C, 100°C and 110°C) and void fractions ( =α 0, 0.01 and 0.03). Conclusions can be drawn based on simulation results:

(1) The cavitation of the high-speed centrifugal pump without the inducer and the annular nozzle is very serious. Therefore, the head and the flow rate are significantly smaller than those in the normal operation condition. When an appropriate variable pitch inducer and an annular nozzle scheme are adopted in the pump, the cavitation is suppressed effectively. Its head and flow rate can meet the design requirements.

(2) For the impeller flow channel, the cavitation mainly occurs on its blade inlet and spreads towards the blade tip gradually with the increase of the void fraction and the temperature. The bubbles are mostly distributed on the two-bladed suction surface and the tip clearance between the blade tip and the wall of the inducer. The higher the temperature and the void fraction, the more the bubbles.

(3) At the same void fraction, when the temperature is lower than 90°C, the heads and the cavitation performance of the high-speed centrifugal pump decrease slowly with the increase of the temperature and the pump can work normally. However, the heads will significantly drop and finally tend to be stable when the temperature is higher than 90°C. On the other hand, the cavitation in runners becomes more serious with the increase of the void fraction at the same temperature. Above all, the highest temperature of the pump with inducer and annular nozzle scheme is 90°C.

In addition, the cavitation area is asymmetrical in the impeller, and the cavitation is more serious in the flow channel between the two impeller blades, as compared with other regions. The similar phenomenon also emerges on the area between the inducer outlet and the impeller inlet.