Optimization Design and Performance Analysis of a Pit Turbine with Ultralow Head

Abstract

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 self-developed 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 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 hydropower 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

2.1. Simulation Method

2.1.1. Governing Equations

For the fluid flow analysis of the entire pit turbine, the continuity equation and Reynolds-averaged Navier-Stokes equation for an incompressible flow have been used in the following form [10 –12]:

\begin{matrix} \frac{\partial U_{i}}{\partial x_{i}} = 0, \\ \frac{\partial (U_{i} U_{j})}{\partial x_{j}} = - \frac{1}{ρ} \frac{\partial p}{\partial x_{i}} + \frac{\partial}{\partial x_{j}} [ν (\frac{\partial U_{i}}{\partial x_{j}} + \frac{\partial U_{j}}{\partial x_{i}})] - \frac{\partial (\bar{u_{i}^{'} u_{j}^{'}})}{\partial x_{j}}, \end{matrix}

(1)

where U, p, ν, 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].

Figure 1:

Whole flow passage of the pit turbine.

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°.

Figure 2:

Blade's different setting angles.

2.2.2. Different Guide Vane's Axis Positions

Calculation Condition. The angle θ between the guide vane and the centerline 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.

Figure 3:

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^°.

Table 1:

Results of different blade's setting angles.

φ/(°)	15	23	28
h1/(m)	0.091	0.103	0.121
η/(%)	88.9	87.6	81.7
Q/(m³/s)	7.47	10.05	10.92

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^°.

Table 2:

Results of different angles between the guide vane and the centerline of unit.

θ/(°)	90	72
h2/(m)	0.037	0.053
η/(%)	87.7	89.9%
Q/(m³/s)	9.38	9.33

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

n_{11} = \frac{n D_{1}}{\sqrt{H η}} .

(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). 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 η_max = 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%.

Figure 4:

The synthetic characteristic curve of pit turbine with ultralow head.

3. Model Test

3.1. Experimental Configuration

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.

Table 3:

Main parameters of GD-WS-35 turbine.

Rated head/(m)	2.1
Highest water head/(m)	2.8
Lowest water head/(m)	0.3
Rated discharge/(m³/s)	0.4
Rated speed/(r/min)	684.7

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.

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 opening a. Table 5 shows the conversed data of prototype turbine's highest efficiency under different guide vane opening a.

Table 4:

The model turbine unit's test data of the highest efficiency of φ = 23°.

a/(°)	45	55	65	75	85
H/(m)	3.09	2.70	2.50	3.09	2.49
Q/(m³/s)	0.339	0.384	0.416	0.486	0.493
P/(kW)	8.371	9.052	8.544	11.939	8.828
Q11/(m³/s)	1.573	1.910	2.146	2.257	2.552
n11/(r/min)	136.17	145.29	151.50	136.61	152.20
η/(%)	81.51	88.90	83.82	81.04	73.25

Table 5:

Data of prototype turbine's highest efficiency of φ = 23°.

a/(°)	45	55	65	75	85
H/(m)	3.09	2.70	2.50	3.09	2.49
Q/(m³/s)	8.47	9.61	10.39	12.15	12.34
P/(kW)	213.9	230.9	218.2	305.1	226.1
Q11/(m³/s)	1.573	1.910	2.146	2.257	2.552
n11/(r/min)	136.17	145.29	151.50	136.61	152.20
η/(%)	83.31	90.71	85.63	82.85	75.05

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.

Table 6:

The model turbine unit's test data with water head H = 2.1 m.

a/(°)	45	55	65	75	85
H/(m)	2.10	2.11	2.10	2.09	2.10
Q/(m³/s)	0.300	0.358	0.398	0.435	0.473
P/(kW)	4.353	6.268	6.838	7.012	6.911
Q11/(m³/s)	1.691	2.010	2.244	2.457	2.666
n11/(r/m)	165.27	164.83	165.30	166.15	165.66
η/(%)	70.39	84.65	83.34	78.58	70.88

Table 7:

Data of prototype turbine with water head H = 2.1 m.

a/(°)	45	55	65	75	85
H/(m)	2.10	2.11	2.10	2.09	2.10
Q/(m³/s)	7.51	8.94	9.96	10.88	11.33
P/(kW)	111.6	160.0	174.7	179.3	177.2
Q11/(m³/s)	1.691	2.010	2.244	2.457	2.666
n11/(r/m)	165.27	164.83	165.30	166.15	165.66
η/(%)	72.19	86.45	85.14	80.38	72.68

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.

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^°.

Figure 5:

Model turbine's synthetic characteristic curve with blade's setting angle φ = 23^°.

Figure 6:

Prototype turbine's synthetic characteristic curve with 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 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 (E_S). 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:

E_{η, S} = \pm \sqrt{E_{Q, S}^{2} + E_{H, S}^{2} + E_{n, S}^{2} + E_{M, S}^{2}},

(3)

where E_{η, S} are systematic errors of efficiency in the model test, %; E_Q,S are systematic errors of discharge measurement, %; E_H,S are systematic errors of water measurement, %; E_n,S are systematic errors of speed measurement, %; E_M,S are systematic errors of moment measurement, %.

According to the test bench equipment, we can see that the systematic errors are as follows: systematic errors of discharge measurement E_Q,S = ± 0.2%; systematic errors of water measurement E_H,S = ± 0.1%; systematic errors of speed measurement E_n,S = ± 0.05%; systematic errors of moment measurement E_M,S = ± 0.2%.

By formula (3), the systematic error of efficiency measurement in the model test E_{η, S} = 0.304% can be obtained.

(2) Random Error (E_R). 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

S_{x} = \sqrt{\frac{1}{n - 1} [\sum_{i = 1}^{n} {(x_{i} - \bar{x})}^{2}]},

(4)

where S_x is standard deviation; x_i is the measured values; $\bar{x}$ 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.

Table 8:

Nine repeated test data.

Number	Measurement parameters
	Discharge	Water head	Moment	Speed
	Q/(m³/s)	H/(m)	N/(N·m)	n/(r/mim)

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
Mean value $\bar{x}$	0.380556	1.697	72.252	684.933
Standard deviation S_x	0.088	0.005	0.084	0.100
Random error E_R	0.014	0.183	0.072	0.009

Random error using the relative error (E_R) value is calculated using the formula

E_{R} = \pm \frac{t_{n - 1} S_{x}}{\bar{x} \sqrt{n}} \times 100 %,

(5)

where E_R is relative error,%; t_n–1 is confidence coefficient, generally using the 95% confidence probability.

The random error of efficiency is

E_{η, R} = \pm \sqrt{E_{Q, R}^{2} + E_{H, R}^{2} + E_{n, R}^{2} + E_{M, R}^{2}},

(6)

where E_n,R are random errors of efficiency in the model test, %; E_Q,R are random errors of discharge measurement, %; E_H,R are random errors of water head measurement, %; E_n,R are random errors of speed measurement, %; E_M,R² are random errors of moment measurement, %; for the calculation results of the standard deviation S_x and random error E_R see Table 8.

(3) Total Error of Efficiency (E_R). The total error of the efficiency of the test is

E_{η} = \pm \sqrt{E_{η, S}^{2} + E_{η, R}^{2}},

(7)

where E_η is the total error of the efficiency in the model test, %.

The total error of efficiency in test can be calculated by formula (7), E_η = 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 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.

Footnotes

Acknowledgment

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

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