Research Article Optimization Design and ...

Hindawi Publishing Corporation Advances in Mechanical Engineering Volume 2014, Article ID 401093, 7 pages http://dx.doi.org/10.1155/2014/401093

Research Article Optimization Design and Performance Analysis of a Pit Turbine with Ultralow Head Chunxia Yang,1 Yuan Zheng,2 and Lingyu Li3 1

College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing, 210098, China National Engineering Research Center of Water Resources Efficient Utilization and Engineering Safety, Hohai University, Nanjing 210098, China 3 College of Energy and Electrical Engineering, Hohai University, Nanjing 210098, China 2

Correspondence should be addressed to Chunxia Yang; [email protected] Received 14 November 2013; Accepted 14 January 2014; Published 3 April 2014 Academic Editor: T. H. New Copyright © 2014 Chunxia Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A developed pit turbine with ultralow head was optimization designed under the design head of about 2 meters to achieve the goal of improving the turbine unit’s efficiency. At the same time, the turbine’s synthetic characteristic curve was drawn to predict the turbine’s overall performance. Navier-Stokes equations and SIMPLEC algorithm were used for pit turbine’s whole flow passage numerical simulation of the 3D, steady, incompressible, turbulent flow field. Through the CFD numerical simulation, the influence to ultralow head turbine’s performance was analyzed by runner blade’s different setting angles and guide vane’s different axes. Considering the hydraulic performance of various methods, the best blade’s setting angle and guide vane’s axis were chosen. The results show that, the turbine unit has the best performance on efficiency, hydraulic loss, and so forth, with the blade’s setting angle 23∘ and the angle 72∘ between the guide vane and the centerline of unit, meeting the power station’s design requirements. The development pit turbine with ultralow head shows the highest efficiency of 87.6% under condition of design head of 2.1 meters and design discharge of 10 m3 /s. The energy performance of pit turbine with ultralow head was researched by the model test of GD-WS-35 turbine. The model turbine’s characteristic curve was drawn. The model turbine’s high efficiency area is wide and the efficiency changes mildly. The numerical simulation results are essentially consistent with the model test results, while the former one is slightly higher than the latter one. The error range is ±3%.

1. Introduction The low water head resource is very rich in China, which usually locates in the economic developed areas of rivers’ middle and lower reaches. With the advantages of runner’s high efficiency, large discharge, short construction cycle, low total investment, and so on, the pit turbine unit becomes a good machine type to develop and utilize the tidal energy and water resource with low head and large discharge [1]. The lowest water head of conventional pit turbine units is mostly above 4 meters. The design discharge is larger than 20 m3 /s and efficiency usually reaches 87%. The highest efficiency is 90% [2]. For the small hydropower station with low water head, shaft-extension tubular type turbine and pit turbine show equivalent technical and economic advantages to the bulb

tubular turbine. In the development of small hydropower under 20-meter water head abroad, the axial flow turbines were substituted gradually. According to the literature [3, 4], the operated shaft-extension tubular type turbine’s runner diameter reached 8.6 meters, and the unit capacity reached 31.5 MW. The largest used water head reached 38 meters. The technology development of shaft-extension tubular type turbine started late in China. The performance of selfdeveloped GZ006, GZ007 (five blades), and so forth reached or exceeded the international advanced level. But they were not technology popularized or formed corresponding production, market scale. Most of the operated shaft-extension tubular type turbines used fixed blade runner. The largest runner diameter was 2.75 meters, unit capacity was 3.5 MW, and the highest used water head was 22 meters. The technology was poor of developing pit turbine and entirely

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Advances in Mechanical Engineering

Y

X

Z

Figure 1: Whole flow passage of the pit turbine.

tubular unit. And the turbine and entirely tubular unit were less applied. Obvious gap existed between China and other countries. Pit turbine unit is a type suitable for low head, large flow rate with simple structure, and convenient maintenance. The pit power station is rare in our country at present. The main reason is insufficient research on flow design and general structure types of shaft tubular units, key technologies to solve the problem of gearbox for increasing speed and oil supply head’s arrangement with double adjusting structure. So, the shaft tubular unit type is not popularization and application, with simple structure, convenient installation and maintenance, and good hydraulic performance and low investment [5, 6]. Jiang [7], Liu Chao, and others, Yangzhou University, carried out the numerical simulation of inner flow in bidirectional symmetric runner pit pump. With short plate guide vanes, both positive and reverse hydraulic performance were considered, decreasing the difference of performance between them. Though using plate guide vanes made the forward efficiency of pump decrease, the reverse efficiency was much higher. Liu [8] and Han Fengqing, South China University of Technology, researched on the runner of bulb turbine with high head based on channel theory. The tubular turbine runner design method based on flow theory was put forward. Using the theory of export, meridian plane for the design plane, a new runner of bulb tubular turbine was designed, under the principle of no-impact entrance point and normal discharge point. Through the 20 years’ development of tubular hydro power station in our country, bulb tubular turbine is suitable for power station with head varying from 5 meters to 25 meters, but using bulb tubular turbine is not worthwhile in ultralow head (Hcp ≤ 3 m) power station. Pit turbine instead of bulb tubular turbine will be the trend in the future [2, 9].

2. Numerical Simulation

Reynolds-averaged Navier-Stokes equation for an incompressible flow have been used in the following form [10–12]: 𝜕𝑈𝑖 = 0, 𝜕𝑥𝑖 𝜕 (𝑈𝑖 𝑈𝑗 ) 𝜕𝑥𝑗

𝜕 (𝑢𝑖󸀠 𝑢𝑗󸀠 ) 𝜕𝑈𝑖 𝜕𝑈𝑗 1 𝜕𝑝 𝜕 =− + [] ( + )] − , 𝜌 𝜕𝑥𝑖 𝜕𝑥𝑗 𝜕𝑥𝑗 𝜕𝑥𝑖 𝜕𝑥𝑗 (1)

where 𝑈, 𝑝, ], and 𝜌 are velocity, pressure, kinematic viscosity, and density. The renormalization group (RNG) 𝑘-𝜀 turbulence model is used to enclose the governing equations [13]. RNG 𝑘-𝜀 turbulence model can obtain a more accurate description of turbulent transfer relationship with the Reynolds number or vortex scale changes, so that the model can better deal with the low Reynolds number zone or near the wall region [14]. 2.1.2. Algorithm and Boundary Conditions. The calculation region contains inlet passage, guide vane part, runner chamber, and outlet passage. Figure 1 shows the whole flow passage of the pit turbine. Unstructured tetrahedron grid with strong adaptability was chosen for computation. Pressure inlet and pressure outlet were chosen as boundary conditions. Mathematical calculation adopted finite volume method and second-order upwind scheme, while coupling numeration of velocity field and tress was based on SIMPLEC [15]. Segregated steady implicit solver was used in the simulation, no-slip condition for solid boundary, and standard wall functions for near wall region. For rotational boundaries, circumferential velocity was given as the velocity of boundaries [16, 17]. 2.2. Optimization Methods 2.2.1. Different Setting Angles of Blades. The blade’s setting angle is the angle of the blade bone of the tangent line along the flow direction and u direction. Different setting angle positions have a significant impact on turbine performance. Figure 2 shows the schematic of blade with setting angles 𝜑 = 15∘ , 23∘ , and 28∘ .

2.1. Simulation Method 2.1.1. Governing Equations. For the fluid flow analysis of the entire pit turbine, the continuity equation and

2.2.2. Different Guide Vane’s Axis Positions. Calculation Condition. The angle 𝜃 between the guide vane and the centerline



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Table 1: Results of different blade’s setting angles. ∘

𝜑/( ) h1 /(m) 𝜂/(%) Q/(m3 /s)

15 0.091 88.9 7.47

23 0.103 87.6 10.05

28 0.121 81.7 10.92

Table 2: Results of different angles between the guide vane and the centerline of unit. 𝜃/(∘ ) h2 /(m) 𝜂/(%) Q/(m3 /s)

90 0.037 87.7 9.38

72 0.053 89.9% 9.33

15∘

23∘ 28∘

Figure 2: Blade’s different setting angles.

of unit was changed for the turbine’s numerical simulation with the same parameters of other flow parts and the same inlet pressure and speed. Figure 3 shows the schematic diagram of the angle between the guide vane and the centerline of unit. 2.3. Results of Different Methods 2.3.1. Results of Blade’s Different Setting Angles. As seen from Table 1, through computational efficiency of the CFD simulation, blade’s different setting angles have influence on the efficiency of the turbine, with the guide vane opening 𝑎 = 65∘ and the geometric similarity flow passage components. The efficiency reduces with the runner blade’s setting angle becoming larger. The turbine shows the highest efficiency with blade’s setting angle 𝜑 = 15∘ . The efficiency slightly declines with the blade’s setting angle 𝜑 = 23∘ and it shows the largest decreasing with blade’s setting angle 𝜑 = 28∘ . At the same time, the flow capacity of the turbine increases with blade’s larger setting angle. The hydraulic loss from runner’s inlet section to runner’s outlet section (hereinafter, using ℎ1 for short) is becoming larger along with the increased setting angle. Generally, the turbine shows the best overall performance with the blade’s setting angle 𝜑 = 23∘ , although the turbine’s efficiency of 𝜑 = 23∘ is lower than the efficiency of 𝜑 = 15∘ and the hydraulic loss ℎ1 of 𝜑 = 23∘ is larger than that of 𝜑 = 15∘ . The differences are small. The turbine’s flow rate increases to 2.58 m3 /s with the blade’s setting angle 𝜑 = 23∘ . And the flow rate increases largely, closing to the design flow rate. The turbine’s conveyance capacity is improved with the blade’s setting angle 𝜑 = 28∘ , but the increasing is not large and the efficiency is low. The hydraulic loss ℎ1 is large. So, the turbine shows the best overall performance with the blade’s setting angle 𝜑 = 23∘ .

2.3.2. Results of Guide Vane’s Different Axis Positions. Table 2 shows the calculation results of different angles between the guide vane and the centerline of unit (hereinafter, using 𝜃 for short), with the same parameters of other flow parts and the same guide vane opening. As seen from the table, the flow capacity was less influenced by different angles between the guide vane and the centerline of unit. Though the hydraulic loss between the guide vane’s inlet section and the runner’s inlet section (hereinafter, using ℎ2 for short) was large with 𝜃 = 72∘ , the total efficiency of the unit was high. The main reason was the small hydraulic loss of other flow parts under the associated condition. The whole flow passage’s efficiency of 𝜃 = 72∘ was higher than that of 𝜃 = 90∘ . Through comprehensive consideration of turbine’s total performance, the turbine unit shows the highest efficiency with 𝜑 = 23∘ and 𝜃 = 72∘ . The discharge is large, closing to the design discharge. 2.4. The Synthetic Characteristic Curve. Through the analysis above, turbine with the best performance was chosen under the condition of actual requirements. Turbine’s other conditions of the best method were predicted by the same numerical simulation. Thus, the overall performance of the turbine was understood more. 2.4.1. Choice of Calculation Condition. Turbine’s discharge can be adjusted by changing the guide vane opening to change the turbine’s output. So, there were many calculation conditions. In this paper, the unit discharge was changed by different guide vane opening. The unit discharge 𝑄11 increased, while the guide vane opening increased. The unit speed 𝑛11 was changed by different inlet total pressure. The unit speed 𝑛11 decreased, while the inlet total pressure increased. Consider 𝑛11 =

𝑛𝐷1 . √𝐻𝜂

(2)

Unit speed 𝑛11 stands for the turbine’s actual speed of 𝐷1 = 1 m, 𝐻𝜂 = 1 m. Also 𝜂 stands for the efficiency of the unit. It relates to 𝐻 (the inlet total pressure = 𝐻 × 9810). Firstly, 𝜂 increases while 𝐻 increases, approaching design point. Then, 𝜂 decreases, while 𝐻 increases away from the design point. On the whole, the value of 𝐻𝜂 increases, while 𝐻 increases because of the little impact of 𝜂’s variation. So, as seen from formula (2), 𝑛11 decreased when 𝐻 increased with 𝐷1 and 𝑛 keeping the same. Six different guide vane conditions were chosen: 𝑎1 = 45∘ , 𝑎2 = 55∘ , 𝑎3 = 65∘ , 𝑎4 = 75∘ , 𝑎5 = 85∘ , and 𝑎6 = 95∘ (hereinafter, using 𝑎1 , 𝑎2 , 𝑎3 , 𝑎4 , 𝑎5 , and 𝑎6 for short).


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Y

Y ZX

ZX (a) 𝜃 = 90∘

(b) 𝜃 = 72∘

Figure 3: Schematic diagram of the angle between the guide vane and the centerline of unit.

55∘

45∘

240

65∘

n11 (r/min)

220 200

84%

85∘ 95∘

75∘

75% 77% 79% 81% 83%

Rated head/(m) Highest water head/(m) Lowest water head/(m) Rated discharge/(m3 /s) Rated speed/(r/min)

85%

180

86% 87%

160

Table 3: Main parameters of GD-WS-35 turbine. 2.1 2.8 0.3 0.4 684.7

140 120 1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3

Q11 (m /s)

3. Model Test 3.1. Experimental Configuration

Figure 4: The synthetic characteristic curve of pit turbine with ultralow head.

Pressure inlet and pressure outlet were chosen as boundary conditions. Under every guide vane condition, the inlet total pressure was set as 𝑝1 = 7848 Pa, 𝑝2 = 14715 Pa, 𝑝3 = 20601 Pa, 𝑝4 = 27468 Pa, 𝑝5 = 34335 Pa, and 𝑝6 = 41202 Pa for calculation. The outlet pressure was set as 0. 2.4.2. Analysis of Turbine’s Performance. According to the calculation conditions above, the highest efficiency point appeared at the guide vane opening 𝑎3 = 65∘ after arranging turbine’s every calculation condition. The calculation conditions were 𝑄11 = 2.265 (m3 /s) and 𝑛11 = 165.5 (r/ min). The highest efficiency is 𝜂max = 87.6%, at the moment, the turbine’s discharge is 𝑄 = 10.05 m3 /s, inlet total pressure is 𝑝 = 20601 Pa, and output is 𝑃 = 181.11 kW. Figure 4 shows the synthetic characteristic curve of pit turbine with ultralow head, which was drawn according to calculation results. As seen from the figure, the pit turbine’s high efficiency region concentrated in three conditions with guide vane opening: 𝑎2 = 55∘ , 𝑎3 = 65∘ , and 𝑎4 = 75∘ . On the most region of calculation condition, the turbine’s efficiency was higher than 80%. And the highest efficiency reaches 87.6%.

3.1.1. Turbine Investigated. Six pit turbines GD-WS-175 were used in the Gu Huanghe hydrojunction project in Huai’an city. The design generation discharge was 60 m3 /s. The total output power was 840 kW. The diameter of prototype turbine GD-WS-175 was 1.75 m. The prototype turbine was scaled down to a model turbine GD-WS-35 with a 0.35 m diameter runner for the model test. There were 3 blades and 15 guide vanes of the model turbine. The main working diameters were shown in Table 3. The head parameters of the power station were design water head 2.1 m, highest water head 2.8 m, lowest water head 0.3 m, and rated water head 2.10 m. 3.1.2. Experiment Apparatus. The model test was based on a multifunction hydromechanical experimental bench at Hohai University. The measuring instruments were as follows: (1) head measurement: EJA110A pressure difference sensor made by CYS, precision of ±0.1%; (2) discharge measurement: RFM4110-500 electromagnetic flow meter made by SGAIC, precision of ±0.2%; (3) torque and speed measurement: JCZ-200 torque meter made by XYDC, precision of ±0.1%; (4) vacuum, atmospheric pressure, and temperature measurement: EJA430A pressure transmitter made by CYS for measuring vacuum, precision of ±0.075%; level 0.5 aneroid barometer for measuring atmospheric pressure; mercury thermometer for measuring temperature.



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Table 4: The model turbine unit’s test data of the highest efficiency of 𝜑 = 23∘ .

Table 6: The model turbine unit’s test data with water head 𝐻 = 2.1 m.

a/(∘ ) H/(m) Q/(m3 /s) P/(kW) Q11 /(m3 /s) n11 /(r/min) 𝜂/(%)

a/(∘ ) H/(m) Q/(m3 /s) P/(kW) Q11 /(m3 /s) n11 /(r/m) 𝜂/(%)

45 3.09 0.339 8.371 1.573 136.17 81.51

55 2.70 0.384 9.052 1.910 145.29 88.90

65 2.50 0.416 8.544 2.146 151.50 83.82

75 3.09 0.486 11.939 2.257 136.61 81.04

85 2.49 0.493 8.828 2.552 152.20 73.25

Table 5: Data of prototype turbine’s highest efficiency of 𝜑 = 23∘ . a/(∘ ) H/(m) Q/(m3 /s) P/(kW) Q11 /( m3 /s) n11 /(r/min) 𝜂/(%)

45 3.09 8.47 213.9 1.573 136.17 83.31

55 2.70 9.61 230.9 1.910 145.29 90.71

65 2.50 10.39 218.2 2.146 151.50 85.63

75 3.09 12.15 305.1 2.257 136.61 82.85

85 2.49 12.34 226.1 2.552 152.20 75.05

3.2. Experimental Analysis 3.2.1. Results and Analysis of Energy Characteristic Testing. Contents of turbine model test are as follows: (1) keeping the GD-WS-35 turbine’s speed at 684.7 r/min and measuring the turbine’s discharge and output of 𝜑 = 10∘ , 15∘ , 20∘ , 23∘ , 30∘ , and 35∘ ; (2) keeping 𝜑 unchanged and measuring the turbine’s discharge and output of 𝑎 = 35∘ , 45∘ , 55∘ , 65∘ , 75∘ , and 85∘ ; (3) keeping the guide vane opening 𝑎 unchanged and testing the turbine’s discharge and output of water head 𝐻 varying from 0.7 m to 3.1 m; (4) calculating the unit speed 𝑛11 , unit discharge 𝑄11 , and model turbine’s efficiency 𝜂 under every condition; (5) drawing turbine’s synthetic characteristic curve. The model turbine unit’s test data of the highest efficiency, the model turbine unit’s test data of 2.1 m water head, and the prototype turbine unit’s efficiency data of the blade’s setting angle 𝜑 = 23∘ are given in this paper. Table 4 shows the model turbine unit’s test data of the highest efficiency of blade’s setting angle 𝜑 = 23∘ under different guide vane opening𝑎. Table 5 shows the conversed data of prototype turbine’s highest efficiency under different guide vane opening 𝑎. Table 6 shows the model turbine unit’s test data of blade’s setting angle 𝜑 = 23∘ under every guide vane opening 𝑎, water head 𝐻 = 2.1 m. Table 7 shows the conversed data of prototype turbine under different guide vane opening 𝑎. As seen from the test data of Tables 4, 5, 6, and 7 we get the following. (1) With the blade’s setting angle 𝜑 = 23∘ , the guide vane opening 𝑎 = 65∘ , and the design water head 2.1 m, the model turbine’s discharge is 0.398 m3 /s, and the corresponding prototype turbine’s discharge is 9.96 m3 /s. The model unit’s efficiency is 83.34%, and the corresponding prototype turbine’s efficiency is 85.14%. The prototype turbine’s power is 174.7 kW.

45 2.10 0.300 4.353 1.691 165.27 70.39

55 2.11 0.358 6.268 2.010 164.83 84.65

65 2.10 0.398 6.838 2.244 165.30 83.34

75 2.09 0.435 7.012 2.457 166.15 78.58

85 2.10 0.473 6.911 2.666 165.66 70.88

Table 7: Data of prototype turbine with water head 𝐻 = 2.1 m. a/(∘ ) H/(m) Q/(m3 /s) P/(kW) Q11 /(m3 /s) n11 /(r/m) 𝜂/(%)

45 2.10 7.51 111.6 1.691 165.27 72.19

55 2.11 8.94 160.0 2.010 164.83 86.45

65 2.10 9.96 174.7 2.244 165.30 85.14

75 2.09 10.88 179.3 2.457 166.15 80.38

85 2.10 11.33 177.2 2.666 165.66 72.68

With the blade’s setting angle 𝜑 = 23∘ , the guide vane opening 𝑎 = 75∘ , and the design water head 2.1 m, the model turbine’s discharge is 0.435 m3 /s, and the corresponding prototype turbine’s discharge is 10.88 m3 /s. The model unit’s efficiency is 78.58%, and the corresponding prototype turbine’s efficiency is 80.38%. The prototype turbine’s power is 179.3 kW. Figures 5 and 6 were the synthetic characteristic curve of model turbine and prototype turbine with the blade’s setting angle 𝜑 = 23∘ . (2) The high efficiency region of model turbine is wide and the efficiency changes slowly. The turbine shows obvious economic significance while applied in power station with low head. Under the condition of design water head of 2.1 m, guide vane opening 𝑎 = 65∘ , and blade’s setting angle 𝜑 = 23∘ , the original data was calculated by transforming rules between original turbine and model turbine. The original flow rate is 9.96 m3 /s, and the power is 174.7 kW, with the efficiency of 85.14%. As seen from the test results, turbine’s flow rate is 9.96 m3 /s, closing to the design flow rate 10 m3 /s under the design water head. The efficiency reached up to 85.14%, slightly lower than the efficiency of 87.6% of numerical simulation. It is shown that the result of simulation is slightly higher, basically consistent with the result of model test. The efficiency range of error is ±3%. The error of numerical simulation was increased without considering the clearance and frictional force between the runner and runner chamber. The clearance between the guide vane and stay ring was not taken into account either. The main reasons of error are, while calculating, the poor quality grids, the choosing of calculation model, parameter settings, and so forth. They are related to the error. The size of error is easy to control. In addition, too small inner edge of guide was not easy to process through the model turbine production. The inner edge was thick properly. At the same time, the shaft tubular turbine’s thrust bearing


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According to the test bench equipment, we can see that the systematic errors are as follows: systematic errors of discharge measurement 𝐸𝑄,𝑆 = ±0.2%; systematic errors of water measurement 𝐸𝐻,𝑆 = ±0.1%; systematic errors of speed measurement 𝐸𝑛,𝑆 = ±0.05%; systematic errors of moment measurement 𝐸𝑀,𝑆 = ±0.2%. By formula (3), the systematic error of efficiency measurement in the model test 𝐸𝜂,𝑆 = 0.304% can be obtained.

𝜑 = 23∘

n11 (r/min)

270 45∘

240 210

80% 75% 81% 78% 83% 85%

180 150 120 1.4

65∘

55∘

72%

75∘

85∘

69%

88.9% 1.6

2.0

1.8

2.2

2.4

2.6

2.8

3.0

3.2

3.4

Q11 (m3 /s)

H (m)

Figure 5: Model turbine’s synthetic characteristic curve with blade’s setting angle 𝜑 = 23∘ . 3.6 3.2 2.8 2.4 2.0 1.6 1.2 0.8 0.4 0

81% 83% 80% 85% 78% 75%

𝜑 = 23∘

45∘

5

6

55∘

7

65∘

8

75 ∘

9

180 kW 160 kW 140 kW 120 kW

85∘

10

11

12

13

𝑆𝑥 = √

𝐸𝑅 = ±

14

3

Q11 (m /s)

Figure 6: Prototype turbine’s synthetic characteristic curve with blade’s setting angle 𝜑 = 23∘ .

just bears axial thrust. The weight of rotation part was borne by guide bearing. In order to improve the stability, pillar was added. So, the high efficiency point of model test is slightly lower than the numerical simulation but almost the same. The practical operation feasibility of tubular turbine with ultralow head is verified. 3.3. Error Analysis 3.3.1. Experimental Error Analysis. The test error is divided into two parts: the systematic errors and random errors. (1) Systematic Error (𝐸𝑆 ). Systematic error is to obey a certain law rather than offsetting the error. It mainly depends on the error of measuring instruments. Efficiency of system error in the model test can be calculated as follows: 2 + 𝐸2 + 𝐸2 + 𝐸2 , 𝐸𝜂,𝑆 = ±√𝐸𝑄,𝑆 𝐻,𝑆 𝑛,𝑆 𝑀,𝑆

𝑛 1 2 [∑ (𝑥𝑖 − 𝑥) ], 𝑛 − 1 𝑖=1

(4)

where 𝑆𝑥 is standard deviation; 𝑥𝑖 is the measured values; 𝑥 is the arithmetic mean values of the measured values; 𝑛 is number of measurements. Nine consecutive repeat test data were chosen near the highest efficiency point. The results were shown in Table 8. Random error using the relative error (𝐸𝑅 ) value is calculated using the formula

88.9%

72%

(2) Random Error (𝐸𝑅 ). Random error is subject to statistical laws with compensation, commonly used in probability and statistics treatment. The error shows student distribution. The standard deviation is calculated by

(3)

where 𝐸𝜂,𝑆 are systematic errors of efficiency in the model test, %; 𝐸𝑄,𝑆 are systematic errors of discharge measurement, %; 𝐸𝐻,𝑆 are systematic errors of water measurement, %; 𝐸𝑛,𝑆 are systematic errors of speed measurement, %; 𝐸𝑀,𝑆 are systematic errors of moment measurement, %.

𝑡𝑛−1 𝑆𝑥 × 100% , 𝑥√𝑛

(5)

where 𝐸𝑅 is relative error,%; 𝑡𝑛−1 is confidence coefficient, generally using the 95% confidence probability. The random error of efficiency is 2 + 𝐸2 2 2 𝐸𝜂,𝑅 = ±√𝐸𝑄,𝑅 𝐻,𝑅 + 𝐸𝑛,𝑅 + 𝐸𝑀,𝑅 ,

(6)

where 𝐸𝑛,𝑅 are random errors of efficiency in the model test, %; 𝐸𝑄,𝑅 are random errors of discharge measurement, %; 𝐸𝐻,𝑅 are random errors of water head measurement, %; 𝐸𝑛,𝑅 2 are random errors of speed measurement, %; 𝐸𝑀,𝑅 are random errors of moment measurement, %; for the calculation results of the standard deviation 𝑆𝑥 and random error 𝐸𝑅 see Table 8. ( 3) Total Error of Efficiency (𝐸𝑅 ). The total error of the efficiency of the test is 2 + 𝐸2 , 𝐸𝜂 = ±√𝐸𝜂,𝑆 𝜂,𝑅

(7)

where 𝐸𝜂 is the total error of the efficiency in the model test, %. The total error of efficiency in test can be calculated by formula (7), 𝐸𝜂 = 0.359%.

4. Conclusions The Reynolds-averaged N-S equation, the RNG 𝑘-𝜀 turbulence model, and second-order upwind scheme were used to discrete the equation for solution. SIMPLEC algorithm for



7

Table 8: Nine repeated test data. Measurement parameters Discharge Water head Moment Speed H/(m) N/(N⋅m) n/(r/mim) Q/(m3 /s) 1 0.3806 1.70 72.17 684.8 2 0.3806 1.70 72.15 684.9 3 0.3804 1.70 72.23 685.0 4 0.3805 1.70 72.20 685.0 5 0.3805 1.69 72.30 685.1 6 0.3806 1.70 72.39 684.9 7 0.3805 1.69 72.36 685.0 8 0.3806 1.69 72.20 684.8 9 0.3807 1.70 72.27 684.9 0.380556 1.697 72.252 684.933 Mean value 𝑥 0.005 0.084 0.100 Standard deviation 𝑆𝑥 0.088 0.014 0.183 0.072 0.009 Random error 𝐸𝑅 Number

pressure-velocity coupling, pressure inlet, and pressure outlet for boundary conditions were chosen. Numerical simulation was used for the research of the pit turbine with ultralow head in the following areas: (1) analyzing the impact of the runner blade’s setting angle on the turbine performance, the results show that, in this case, meeting the requirements of power design, the blade’s setting angle 23∘ , the turbine’s performance, efficiency, hydraulic losses, and blade static pressure show the best performance; (2) analyzing the impact of the guide vane axis inclination on turbine performance and obtaining the best turbine guide vane. Studies show that the angle 72∘ between the guide vane and the centerline of unit has optimal performance in terms of efficiency, water loss and flow capacity. By model test of pit turbine GD-WS-35 with ultralow head, we study the performance of pit turbine with ultralow head under the different blade’s setting angles, different guide vane opening, and different heads. Analysis was done on the results of model test and numerical simulation of pit turbine GD-WS-175 with ultralow head, according to the conversion principle. The efficiency error range is ±3%. The test proved that the pit turbine with ultralow head can better develop and utilize low head hydropower resources.

Conflict of Interests All the authors declare that there is no conflict of interests regarding the publication of this paper. All the authors do not have a direct financial relation with the commercial identities mentioned in this paper that might lead to a conflict of interests for any of the authors.

References [1] C. Qian and Y. Sun, “Types of tubular units and development of dfem’s large shaft tubular turbine,” Dongfang Electrical Machine, no. 1, pp. 1–12, 2005. [2] China Water Resources Pearl River Planning Surveying & Designing Co., LTD, Bulb Turbine Hydropower Station, China water power press, Beijing, China, 2009. [3] J. Zhang, H. Duan, and S. Tian, “Optimum selection of water turbine generator units with ultra-low head,” Northwest Hydro Power, vol. 4, pp. 77–79, 2006. [4] Y. Fang, G. Song, and Q. Zhang, “The flow passage design and type selection of pit type tubular turbine,” Large Electric Machine and Hydraulic Turbine, vol. 1, pp. 49–52, 2009. [5] Q. Lin, “Design of vertical circulating water turbine group,” Manufacture Information Engineering of China, vol. 40, no. 17, pp. 81–83, 2011. [6] C. Qian and Y. Sun, “Type of tubular unit and development of large shaft tubular turbine units of Tokyo electric power company,” Dongfang Electrical Machine, vol. 1, pp. 1–12, 2005. [7] N. Jiang, The Flow Numerical Simulation in Through-Flow Pump with Intallation-Pit with Reversible Syrnrnetric Aerofoil Impeller, Yangzhou University, 2010. [8] P. Liu, Channel Theory for High-Head Bulb Runner, South China University of Technology, 2010. [9] Y. Zeng, “Compare characteristics of hydropower plants with high-head Francis turbines and low-head bulb turbines,” Guangxi Water Resources & Hydropower Engineering, vol. 2, pp. 49–51, 2008. [10] R. A. Saeed and A. N. Galybin, “Simplified model of the turbine runner blade,” Engineering Failure Analysis, vol. 16, no. 7, pp. 2473–2484, 2009. [11] A. Reprecht, “Unsteady flow simulation in hydraulic machinery,” Task Quarterly, vol. 6, no. 1, pp. 187–208, 2002. [12] Z.-D. Qian, J.-D. Yang, and W.-X. Huai, “Numerical simulation and analysis of pressure pulsation in francis hydraulic turbine with air admission,” Journal of Hydrodynamics, vol. 19, no. 4, pp. 467–472, 2007. [13] V. Yakhot and S. A. Orszag, “Renormalization group analysis of turbulence. I. Basic theory,” Journal of Scientific Computing, vol. 1, no. 1, pp. 3–51, 1986. [14] C. Lu, Numerical Simulation for Cavitations Flow inside Fluid Machinery, Xihua University, 2006. [15] W. Feng, L. Song, L. Zuo, and B. Yuan, “3D numerical simulation on unsteady turbulence flow in axial flow pump system,” Journal of Drainage and Irrigation Machinery Engineering, vol. 28, no. 6, pp. 531–536, 2010. [16] R. A. Saeed, A. N. Galybin, and V. Popov, “Modelling of flowinduced stresses in a Francis turbine runner,” Advances in Engineering Software, vol. 41, no. 12, pp. 1245–1255, 2010. [17] R. Xiao, Z. Wang, and Y. Luo, “Dynamic stresses in a Francis turbine runner based on fluid-structure interaction analysis,” Tsinghua Science and Technology, vol. 25, no. 2, pp. 587–592, 2008.

Acknowledgment The work is financially supported by the Project Special Funds for MRE, GHME2011CX02.
