Effect analysis of centrifugal pump parameters optimization design on performance

Under the background of energy-saving priority and efficient use of energy, centrifugal pump, as a kind of energy conversion equipment in modern industry and agriculture with liquid as the medium, plays an important role in many occasions. Optimization of performance parameters of centrifugal pump can improve efficiency and save energy. Important parameters include the number of blades and structural optimization of blade tail, etc. These parameters are often selected according to experience in actual production, which lacks accuracy and persuasiveness. The influence of different blade numbers and structural designs on cavitation performance and efficiency of the pump is studied, and the characteristic curve of the pump is drawn. The blade performance is evaluated comprehensively according to the pressure distribution, flow condition, cavitation degree and velocity diagram under different blade numbers, and the conclusion is drawn. The efficiency of the four-blade pump is 6.96% higher than that of the original six-blade pump, 1.96% higher than that of the three-blade pump, and 5.11% higher than that of the five-blade pump. The optimization results are obvious, which provides reference for the determination and setting of the number of centrifugal pumps.


Introduction
In manufacturing, agriculture and other related industries, pump machines play an important role [1].Nowadays, it is an era that attaches great importance to energy saving and energy consumption.As an indispensable energy conversion equipment in modern industry and agriculture with liquid as the medium, pump is widely used in actual production and life [2].In the field of engineering application, centrifugal pump has a high frequency of use in engineering practice because of its stable flow, simple structure, stable work and many other advantages.The optimization and selection of key parameters such as efficiency and blade of centrifugal pump are particularly important.Vane design and cavitation energy of centrifugal pump are closely related to work efficiency.The influence of specific values of the blade on the pump can be described and expressed by characteristic curves [3].Characteristic curves of different types of pumps are generally different and are marked and drawn by basic parameters such as flow rate, head and efficiency.There are many factors affecting the characteristic curve of the pump in the blade, such as the inlet diameter of the impeller, the Angle of blade placement, the number of blades and the density and viscosity of the liquid medium will have a certain influence on the characteristic curve.This paper mainly studies the occurrence of cavitation in the centrifugal pump and the optimization of the blade [4].
Model creation, grid generation, equation setting, boundary condition selection and result processing and analysis were carried out in sequence according to the numerical calculation process.The occurrence process and trend of cavitation in the model pump were simulated and analyzed by changing a single condition and repeating this series of processes.Other conditions were the same.The numerical calculation of flow field and cavitation of the model pump is carried out when the number of blades is 3, 4, 5 and 6 respectively.

Numerical calculation method
With the development of science and technology, the calculation method of fluid has developed to the theory of three-dimensional flow.The three-dimensional turbulent motion of the medium in the centrifugal pump is an irregular flow, and the variation of various parameters of the fluid in the flow field is random and disorganized.For fluid studies [5], the cost of repeated experiments is often high.With the development of information technology means, the related experiment of complex flow in centrifugal pump provides convenience.Under the guidance of finite element volume method, CFD provides users with simulation functions of various fluid machinery, and forms various turbulence calculation methods, such as turbulence simulation method, flow governing equation and cavitation model [6].
Cavitation, in essence, is the process of transformation from liquid phase to gas phase when the pressure of liquid medium at the operating temperature reaches saturation vapor pressure.Therefore, cavitation model is actually a phase transition model, which is used to describe the transition from liquid phase to gas phase.Currently, three types of models are most frequently used in simulation, namely [7][8], Kunz model, Zwart-Gerber-Belamri model and Schnerr-Sauer model.Different cavitation models are used for calculation, and the results are slightly different.Therefore, the most suitable cavitation model should be selected in the calculation process.
(1)Schnerr-Sauer Cavitation model Schnerr-Sauer cavitation formula believes that gas-liquid two-phase flow can be simply regarded as a mixture of liquid and bubble, and the only parameter to be confirmed in the equation is the density generated by bubbles [9].Since empirical constant is not included in the calculation of mass transport rate, the accuracy is low.Schnerr-Sauer formula has some shortcomings in simulating cloud cavitation.The equation is: (2) Kunz Cavitation model Kunz cavitation expression is a proportional model based on practice.When the medium is converted from liquid to gas, the mass transport rate is proportional to the difference between flow field pressure and vaporization pressure; when the medium is converted from gas to liquid, the mass transport rate is related to the cubic power of gas volume fraction [10], and the equation is: (3) Zwart-Gerber-Belamri Cavitation model The biggest feature of Zwart-Gerber-Belamri cavitation model is that the model uses a more accurate correction coefficient in the equation.Considering the relationship between gas volume fraction and bubble density [11], the equation is: In order to prepare for the selection and setting of various models in flow analysis and cavitation simulation, the current widely used turbulence models and cavitation models are compared.

Optimization design of centrifugal pump blade parameters
In actual production, cavitation is a key problem threatening the safe and stable operation of centrifugal pumps.The occurrence of cavitation essentially refers to the formation, development and collapse of hollow bubbles in the flow field.The development of the pump industry is largely limited by cavitation, and there are many hazards brought by cavitation: It will not only reduce the working capacity of the pump and destroy the part in contact with the flow, but also be accompanied by harmful vibration and noise, which are very prominent and important problems in industrial operation [12].Therefore, a model pump with a certain number of blades is taken as the research object to study and verify the cavitation generation process in the model pump and the relationship between the cavitation occurrence area and the anti-cavitation allowance.
In most cases, when the size, design conditions and hydraulic parameters of centrifugal pumps are different, the number of blades Z that best match them are also different.A large number of noncavitation flow field and cavitation flow field solutions have been carried out for model pumps with blade numbers of 3, 4, 5 and 6 respectively.Based on the calculation results, the differences of energy conversion characteristics and internal flow characteristics of the selected model pumps are analyzed in detail when the number of blades Z is different.As shown in FIG. 1, on the premise that the volute watershed body is not changed, the number of pump blades is changed, and then four different impeller watershed bodies are generated.With the help of ICEM, FLUENT, CFX and CFD-POST tools in ANSYS, flow field analysis is carried out on the watershed body in Fig. 1  According to the comprehensive analysis of Fig. 2, 3 and 4, it can be seen that when Z=3, the distribution of low pressure area is general, and the quality of the flow diagram and velocity diagram is moderate.When Z=4, the distribution of low pressure area in the centrifugal pump is ideal, the flow line is smooth and smooth, and the velocity cloud map is relatively average.When Z=5, the low-pressure region has the largest distribution area, and the area where cavitation may occur is the largest.However, the flow condition is good, and the streamline is stable and beautiful.There is only a little streamline distortion at the pump outlet [14], and the velocity diagram distribution is very uniform.When Z=6, the low pressure area at the inlet of the impeller in the centrifugal pump is the most evenly distributed, and the area is also the smallest.However, the flow state of the liquid medium is poor, the streamline is mixed with each other, and there is a certain degree of reflux phenomenon at the outlet of the impeller.

Characteristic curves of pumps with different blade numbers
Considering that cavitation in the pump cannot be completely eliminated in the actual operation of the centrifugal pump, the effect of cavitation can only be weakened by various means.The premise of opening the cavitation equation in the simulation calculation is to fit the real operation of the centrifugal pump, and to carry out the calculation and mapping of each point on the characteristic curve of the model pump.The acquisition of specific parameters under various working conditions in the pump needs to be completed according to the specified calculation formula [15].The head of the pump is: In Formula ( 7), is the density of liquid medium, is the acceleration of gravity, is the total pressure at the inlet of the impeller and is the outlet pressure of the volute.Hydraulic efficiency is: In the efficiency calculation formula (8), M is the sum of torques of blade working face and back outer surface, and is the angular velocity of impeller rotation.The volumetric efficiency calculation formula is as follows: In Equation ( 9), is the specific revolution, and the mechanical efficiency and total efficiency considering bearing seal loss and disc friction loss are According to the characteristic curve analysis of centrifugal pump, the curve change trend of four kinds of vane pump is similar.With the increase of the number of blades, the corresponding head curve has a certain degree of increase.At the design flow point, it is found that the pump head with 6 blades is the highest, the number of blades is large, and the control ability of the liquid medium is strong.With 3 blades, the head decreases obviously, and the control ability of fluid medium is insufficient [16], while the head of 4, 5 and 6 blades pumps all meet the design conditions.Pump efficiency changes are more complex, for the four types of pumps, with the increase of the flow rate, the efficiency rises first and then decreases, there is a maximum efficiency.In the flow-efficiency curve, the optimal efficiency point of the centrifugal pump is offset.The highest efficiency point of the 4-blade pump and 6-blade pump is around 1.2Q, while the efficiency of the 3-blade pump and 5-blade pump still shows an upward trend.Combined with the chart, at the design flow point, the efficiency of the 3-blade pump is 65.62%, that of the 4-blade pump is 67.5%, and that of the 5-blade and 6-blade pumps is 62.5% and 60.6% respectively.The analysis results show that the efficiency of 4-vane pump is the highest at the designed flow rate.
The figure corresponding to the calculation is shown in Fig. 6.

Fig. 6 Cavitation cloud diagram under different blade numbers
According to the graph analysis, we can know: (1) When the number of blades Z=3 and 4, the bubble area is smaller and the performance is better under the same working condition; When the number of blades Z=5, the bubble area in the pump channel is larger than that of blades 3 and 4, but smaller than that of blades 6.In a word, the cavitation resistance performance is not ideal.When the number of blades Z=6, the bubble area is the largest and the performance is the worst.Therefore, the cavitation performance of 3 and 4 vane pumps is better than that of 5 and 6 vane pumps under the same conditions.
(2) Under some working conditions, the size of cavitation area on different blades in the impeller is asymmetrical, which is caused by the uneven distribution of pressure in the impeller caused by the coupling effect between the rotating part of the impeller and the static part of the volute.
(3) Cavitation bubbles of a certain area are generated in each flow condition of the pump, because there is a deviation between the inlet liquid flow Angle of the liquid in the high-speed centrifugal pump and the placement Angle of the blade, resulting in reflux vortex at the inlet end of the blade, resulting in flow loss .The greater the flow loss, the more obvious the drop in pressure, which leads to a significant increase in the possibility of phase transition and cavitation at the inlet end of the blade.

Analysis of numerical calculation results
Based on the fluid simulation calculation software, a more comprehensive calculation and analysis were carried out on the conditions of no cavitation and cavitation under different blade numbers.The results show that the pump has the best anti-cavitation performance when Z = 3, which is specifically manifested as the minimum cavitation area in FIG. 5.However, the head of the 3-blade pump at the designed flow point is 37.8m, with an efficiency of 65.62%.Although the efficiency is high, its head decreases too much, which does not meet the design requirements.When Z = 5 and 6, the pump has a large area of hollow bubble occurrence, strong fluid control ability and relatively high head as shown in Figure 5.Under the design flow, the head of the 5-blade pump and the 6-blade pump are 44.47 and 44.9m respectively, and the efficiency is 62.5% and 60.6% respectively.The head of the two kinds of pumps meet the design requirements, and the efficiency of the 5-blade pump is 1.9% higher than that of the 6-blade pump.When Z = 4, the pump head is 42.5m, and the efficiency is 67.5%.While the head meets the design requirements, the efficiency of the 4-blade pump is 1.88% higher than that of the 3blade pump, 5% higher than that of the 5-blade pump, and 6.9% higher than that of the 6-blade pump.In addition, the distribution of cavitation area of the 4-blade pump in the cavitation diagram is relatively small, and the anti-cavitation performance is relatively ideal.Further performance tuning is possible.In addition, in the calculation of no-cavitation operation when Z = 3, 4, 5 and 6, the pressure distribution of the 4-blade pump and the 6-blade pump is better, but the flow of the 4-blade pump is uniform, while the flow line of the 6-blade pump is seriously distorted.5.The pressure distribution of vane pump is the worst, but the flow condition and velocity diagram distribution are the best.The pressure distribution and streamline distribution of the vane pump are moderate.Therefore, when Z=4, the model pump has higher head, higher efficiency, better anti-cavitation performance and better comprehensive performance.

Conclusion
After studying the regularity of cavitation process in centrifugal pump and the influence of blade number on flow field and cavitation in centrifugal pump, a lot of analysis and calculation have been carried out, and the characteristic curve of model pump has been obtained.After qualitative and quantitative analysis, the optimal choice of pump blade number has been determined.The main conclusions are as follows: (1) In the operation calculation of pumps with different number of blades, the flow-efficiency curves of the four-blade pump and the six-blade pump are closest to the theoretical prediction, which conform to the curve of first rising and then falling.The pump head of the four models has an overall trend of decreasing with the increase of flow; The longitudinal comparison of the same working condition shows that the higher the number of blades, the higher the head.
(2) When the number of blades Z is 3, 4, 5 and 6 respectively, the calculation results according to the flow field without cavitation show that the pressure distribution of 3 vane pump and the streamline quality in the flow passage are moderate.4. The low-pressure region of the vane pump is moderately distributed and the flow condition is good; 5 The flow line and speed display of the vane pump are the most uniform, but the low pressure area at the blade inlet is the largest, and the pressure distribution is the worst.6 The low pressure area of the vane pump is small, but the flow condition is very poor.In summary, the pressure distribution and flow of the 3-blade pump and the 4-blade pump are more ideal than that of the 5-blade pump and the 6-blade pump.
(3) By analyzing the cavitation calculation results when the number of blades Z is 3, 4, 5 and 6 respectively, it is found that when the number of blades Z=4, the low pressure area in the centrifugal pump is small, the flow line is uniform and smooth, and the flow in the pump is good.At the designed flow point, the head and efficiency values of the four vane pumps are as follows: 3 vane pump H=37.67m, =65.64%; 4 vane pump H=42.53m, =67.6%; 5 blade pump H=44.47m, =62.49%;H of 6 vane pump =44.90m, =60.64%.According to the analysis results, when the head of the four-blade pump meets the design requirements and the cavitation performance is better, the efficiency of the four-blade pump is 6.96% higher than that of the original six-blade pump, 1.91% higher than that of the three-blade pump and 5.11% higher than that of the five-blade pump.The optimal number of blades of the pump is determined to be four blades.
(4) The flow field in the pump with different blade tail structures is compared according to the calculation results.When the blade tail thickness is 3.2mm, the cavitation area in the pump cavitation calculation is the smallest, and the maximum cavity volume fraction in the flow passage is only 48.99%.It is much lower than the maximum value of 99.15% when the thickness is 6.5mm and 95.17% when the thickness is 0mm.The minimum part of the most serious cavitation in the flow passage does not block the flow passage.The degree of cavitation is the lightest and the performance of anti-cavitation is the best.

Fig. 5
Fig. 5 Comparison of characteristic curves under different blade numbers