INTRODUCTION
Water conservancy is the foundation of the national economy. Pump station is the important section of water conservancy project and is the key to protect and develop grain production. Compared to other water conservancy projects, it plays an irreplaceable role to solve the three water resource issues today, such as flood, water shortage and deterioration of water environment. To improve the efficiency of pump station is the most basic question in the process of design, technical reform and operation and also this is unified with the national sustainable development strategy. Chinese electromechanical drainage and irrigation industry started late, thus many questions exist, for example: Low efficiency of pump device, exceeding standard of unit energy consumption , reduction of project benefits, abates of antidisaster ability and so on.
The actual flow in axial pump is so complex that the rules were not be understanded
clearly. So far, the design of axial pump is at the stage of half theory and
half experience. Generally, manufactures adopt the process containing design,
trialproduce, experiment and improving. The process is cockamamie and the consumptions
of manpower, financial resources and times are massive. According with the pipe
parameters of axial pump station and the structure parameters of axial pump,
if the sundry performances can be predicted and the primary performance curves
can be mastered, not only the interrelated costs can be reduced significantly
but also the cycle of design, manufacture and renovation can be shorten availably
and huge social and economic benefits can be produced at the same time.Therefore,
researchers have a long pursuit goal to gain the complete performance curves
economically and reliably (He et al., 2003).
Now, the complete performance curves could be acquired through model experiment
and transform calculation. Several important curves also could be obtained through
performance transform calculation based on existed data. The curves gained by
the former method were true and reliable but the experiment costs were very
expensive and the period was very long. The latter could reduce experiments
but the predicted accuracy could be ensured only in the vicinity of the known
data points, due to the over reliance on the accuracy and the satisfied degree
of similarity assumption.
Qian Xiao’s research was about the mixedflow pump comparison with predicted
and actual efficiency, indicated that the predicted method was simple and practical
(Qian et al., 1999). Liu Guanlin predicted
the complete characteristics of pump by using BP neural network and got the
reliable conclusion on prediction (Liu et al., 2000).
Wang Guoyu discussed the numerical simulation of 3D turbulent flow and performance
prediction of a pump turbine runner (Wang et al.,
2001). The result showed that the method was suitable for the performance
and flow field analysis at the runner design stage (Liu
et al., 2000). Tan Minggao expounded the predicted theory of centrifugal
pump and develope the program to predict the performance in his master’s
dissertation. He proved that the prediction theory was correct and the software
was practical (Tan, 2006). Ge Qiang studied water conservancy
characteristic conversion and performance prediction for lowleft pumping station
in his doctor’s dissertation. He predicted the characteristics of pump
station successfully and gave some reasonable advice for lager pump station
in stable operation (Ge, 2006). In summary, the previous
research focused on the centrifugal pump and mixedflow pump. But the study
on axial pump was few. The author’s team took hard work on axial pump and
gained some achievements.
So far, there are three methods on performance prediction: Hydraulic loss method,
neural network method and flow field analysis method. In this article, the
research was based on the hydraulic loss method.
METHODOLOGY
The first step of hydraulic loss method is to analyze the physical essence and influence factor of hydraulic loss. The second is to seek the relation between the loss and pump structure parameter and the last is to build the mathematic mode of hydraulic loss. Thus the performance parameters could be predicted and the essential performance curves could be gained. So the method key and base are the analysis and calculation. And the aim function is the comprehensive performance of pump station device. Because of the whole consideration of various factor’s effect in pump, the hydraulic loss method has practicality and accuracy. So it is the common method to predict the pump’s performance currently.
MATHEMATIC MODE
Loss and efficiency of pump: During the operation of axial flow pump,
there are three types of loss: Mechanical loss, volume loss and hydraulic loss.
The last one accounted for the largest proportion of loss and was the definitive
factor to influence the pump efficiency. According to literature (He
and Guo, 2008), the expressions of mechanical efficiency η_{m}
and volume efficiency η_{v} were given below:
In the last written, mechanical loss ΔP_{m} was about 315% of pump shaft power P and leakage q was about 410% theoretical flow Q_{T}.
The theoretical head of finite number lamina pump can be denoted by H_{T}, then the expression of power loss caused by the flow leakage was as follow:
According to massive references, hydraulic loss occurred mainly in the suction chamber, impeller channel and casing of axial flow pump. The detailed accounts follow:
• 
The suction chamber loss mainly includes local loss and friction
loss. But the figure of friction loss was very small, especially at the
design condition. Based on literature (Chen and Wu, 2003),
the expression of local loss was as follow: 
In the equation, k_{x} was the hydraulic loss coeffic ient of the
suction chamber and v_{0} was the velocity of pump in the suction chamber
inlet.
• 
The loss in impeller channel mainly includes impact loss at
the entrance, friction loss, divergence loss and hydraulic loss at the export
(Liu, 2001). In most cases, using the semiempirical
and semitheory formula to calculate the loss 
Owing to the changes of operating conditions, rate of flow Q deflected design flow Q_{d}, the entrance flow angle β_{1} was not equal to the entrance blade incidence β_{1a}, so the impact loss occurred. The entrance impact loss of impeller could be expressed as:
In the above formula, k_{1} was the impeller entrance impact loss coefficient and w_{1} was the opposite velocity at impeller entrance which could be solved based on the fluid flow in axial pump meet the cylindrical layer independence hypothesis.
According with the number of impeller and the structure size of channel, the friction loss in impeller channel Δh_{2} could be calculated by the next formula:
In the last written, z was the number of impeller, k_{2} was the channel friction loss revise coefficient, λ was the onway friction coefficient, l_{a} was the channel length, D_{a} was the average diameter of channel and w_{a} was the average opposite velocity of fluid in channel.
The parameters in Eq. 5 formula could be calculated by the following expressions:
In the above formulas, D_{1} was the impeller entrance diameter, D_{2} was the impeller export diameter, δ was the impeller surface roughness, w_{2} was the impeller export opposite velocity and β_{2a} was the export blade incidence.
Based on the absolute value of square difference about w_{1} (the impeller entrance opposite velocity) and w_{2} (the impeller export opposite velocity), Δ_{h3} (local loss in impeller) could be solved as follow:
The hydraulic loss at impeller export Δ_{h4} was re lated to the circumferential velocity v_{2u} and axial velo city v_{2m} of fluid at the impeller export which could be solved as follow:
So, the total hydraulic loss in axial pump impeller Δ_{hl} could be expressed as follow:
• 
Hydraulic loss of chamber pressure mainly includes local loss
and onway friction loss. The common formula to calculate onway friction
loss was: 
In the equation, f was the friction resistance coefficient, L was the length
of outlet pipeline, D was the overage diameter of discharge elbow, b was the
pipe diameter index and m was the flow index. According to literature (Qiu,
2001), the number of f, m and b could be detected.
The common formula to calculate local loss was:
In the last written, ζ was the local resistance coefficient of discharge
elbow and v was the average velocity of discharge elbow. Based on literature
(Qiu, 2001), ζ and v could be solved.
So, the total hydraulic loss in chamber pressure Δ_{hy} was:
From (a), (b) and (c), it could be seen that the total hydraulic loss in axial pump Δh was:
Then the power loss caused by the hydraulic loss ΔP_{h} was:
Therefore, hydraulic efficiency of axial pump η_{h} was the ratio of actual and theoretical head, that was:
In summary, the power loss ΔP and the overall efficiency η of axial pump were given below:
In the equation, P_{e} was the effective efficiency of pump, that meaned the actual gained power of fluid and the number was ρgQH.
Based on literature (Tan, 2006; Zhang
et al., 1996; Guo and Wang, 1983; Yang,
2001; Wang et al., 1997), it could be initially
confirmed the number of various loss correction coefficient, such as k_{x},
k_{1}, k_{2}, k_{3} and k_{4}.
Pipeline loss and efficiency: The energy suppled from pump station,
not only needs to raise the water to the requisite height and pressure but also
needs to overcome various resistance of pipeline. Therefore, the pipeline head
loss should be calculated (Qiu, 2004). Generally, pipeline
loss mainly includes onway friction loss and local loss.
Onway friction loss Δh_{f} and local loss Δh_{j} could be calculated by the general formula of friction loss and local loss, that were:
In the above equation, ζ_{i} was the local resistance coefficient
of the i section of pipeline which can be solved based on literature (Qiu,
2001; Qiu, 2004) and v_{i} was the average
velocity of the i section of pipeline.
Therefore, pipeline loss Δh_{p} and power loss ΔP_{p} were:
Generally, the loss flow of pipeline was negligible (Luan,
1993), so the pipeline efficiency η_{n} was:
Efficiency of pump device and pump station: Device efficiency of axial pump η_{sy} was the technical and economic index to reflect operation condition and decided by pump efficiency and pipeline efficiency together, that was:
Many factors affect pump station efficiency, such as electric machine, the driving mode, pump, pipeline, inlet pool, outlet pool etc. So the axial pump station efficiency η could be expressed as follow:
In the last written, η_{g} was the electric motor efficiency,
η_{tm} was the driving efficiency and η_{0} was the
efficiency of inlet and outlet pool that the approximate number was 1.0 (Liu,
2001).
Head character expression: H_{T}∞was the theoretical head of theoretical inviscid fluid gained under the condition of infinite number and thin blade. If the number of blade was finite and the theoretical head was H_{T}, the expression of H_{T}∞ and H_{T} were:
In the equation, μ_{1} and μ_{2} were the circumferential velocities at entrance and export of impeller, v_{1μ∞} and v_{2μ∞} were the components of absolute velocity on the circumferential velocity at entrance and export of impeller, K was the circulation coefficient of finite number blade pump and it could be calculated by the Stehekin equation.
Therefore, the actual head of fluid in axial pump H was:
The axial pump device head H_{sy} was the total head that the pipeline system conveying fluid requires, its number was equal to the sum of design net head and water piping system loss, that was:
In the last written, Z_{i} and Z_{0} were the water level of inlet and outlet pool.
Power character expression: The shaft power of axial pump P should be the sum of effective power and various power loss in pump, that was:
And the device power of axial pump P_{sy} should be the sum of shaft power and loss power in pipeline, that was:
PERFORMANCE PREDICTION AND EXPERIMENT
According to Eq. 126 formula, the mathematic
model of axial pump and axial pump station could be established. Using Visual
C++ software, the visual program of performance prediction could be developed.
With inputting the basic parameters of axial pump or pump device, various function
could be achieved, such as hydraulic loss calculation, performance prediction,
drawing and revising curve and so on.
The Tianshan grade 1 pump station diverting water from the Yellow River built
in 1972. 12 sets axial pump device were installed, the pump design head was
7.7 m and the design flow was 2.8 m^{3} sec^{1}. Accompanied
by the operation, 0.7 billion stere water were raised and the local economy
development was promoted greatly. But, due to the 30 years operation, a series
of trouble of the pump station appeared, for example: Facilities aging, poor
safety performance and low efficiency. To study the reasons and improve the
operation conditions, site tests were carried out based on the site test procedures.
One photograph of site test was as shown in Fig. 1. At the
rated speed and different flow, the predicted data in contrast with actual measured
data of pump head, shaft power and efficiency were as shown in Fig.
2(ac), pump device’s contrast were as shown in Fig.
3(ac) and the essential performance curves of pump and
pump device drew based on predicted data were as shown in Fig.
4ab.

Fig. 1: 
Photograph of site test 

Fig. 2(ac): 
Pump’s performance contrast of predicted data and actual
data (a) Head, (b) Shaft power and (c) Efficiency 

Fig. 3(ac): 
Pump device performance contrast of predicted data and actual
data (a) Head, (b) Power and (c) Efficiency 

Fig. 4(ab): 
Cruves draw by the program based on predicted data (a) Pump
curves and (b) Pump device curves 
CONCLUSIONS
Analyzing Fig. 24, it could be found: The difference of predicted data and actual measured data was small, especially at the design conditions. But the difference amplified when the flow deflected the design condition flow and the off design conditions, the greater the difference. The performance curves of pump and pump device drew by performance prediction program were reasonable and practicable after the contrast of actual measured data. In view of the error in site test and the increasing complexity of axial pump inner flow produced some adverse effects on the actual operation especially deflecting design condition, the predicted data was credible, the predicted model and application program was practical and the selection of various loss correction coefficient was reasonable. The study result can provide beneficial reference for design, technical reform and operation etc. It basically meets the needs of engineering and it has important reference value and practical significance.
Actually, the reform time of Tianshan pump station was shorten obviously. The efficiency was increased by 5% and the economic benefits were about 50 million yuan. So, it can be said that the aim of the research study was achieved.
Expectations: Based on the background of the technology renewal reform about TianShan grade 1 pump station, performance prediction using the hydraulic loss method for axial pump station device has a certain practicality but the difference between prediction data and actual measured data is larger as soon as deflecting design flow: The off design flow, the greater the difference. The main cause is the actual fluid flow in axial pump is very complex while deflecting design flow, so the actual loss is obvio usly larger than the prediction model loss based on design flow. Given all that, the following aspects of performance prediction study on axial pump and axial pump station need further development:
• 
Carry out more site tests, combine with the theoretical analysis
to improve the practicability and accuracy of the loss model, consider adequately
the internal loss reflection of axial pump in the prediction model as deflecting
design flow and further improve hydraulic loss theory 
• 
Combine with flow field calculation and analysis and build
more precise mathematical relationships reflecting efficiently between the
internal parameters and external characters 
• 
Improve the universality of prediction software and develope
higher practical integrated software for design and flow field analysis
of axial pump 
ACKNOWLEDGMENTS
This study was supported by the National Natural Science Foundation of China (Grant No. 90410019), the public industry scientific special fund of Ministry of water conservancy of PRC (Grant No. 201201085) and the science Technology Research major project of the Education department of Henan province, China (Grant No. 12A570003). The test scheme draft and the data measurement and record in this article were completed in Jinan city, Tianshan pump station management office, supported by Shi Liwen, Liu Wei etc. The authors sincere thanks to them. In the end, the authors are also grateful for the anonymous reviewers who made constructive comments.