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An experimental study on leakage flow in different geometrical disk seals
9th International Conference on Hydrodynamics October 11-15, 2010 Shanghai, China
370
2010, 22(5), supplement :381-385 DOI: 10.1016/S1001-6058(09)60223-7
An experimental study on leakage flow in different geometrical disk seals
1
Wei Zhao 1*, Torbjørn K. Nielsen1,Jan Tore Billdal2 Norwegian University of Science and Technology, Trondheim, Norway 2 Rainpower ASA, Kjeller, Norway * E-mail: [email protected]
ABSTRACT: This paper presents an experimental study on the leakage flow in rotor-stator system. The experimental setup of the rotor-stator system is a simplification of a Francis turbine runner with focus on the seals. It consists of a motor, a bearing, a shaft, a fixed rotor made of steel, a pump and a plastic ring fixed on the steel rotor, which can be replaced with different geometrical pads to test various seals. A small radial clearance (0.2mm) between the rotational disk and stator is settled. Leakage loss, pressure variation under the rotational disk and pressure difference between above and below the disk for various geometrical seals is measured at different rotational speeds. The results indicate that the rotational disk can reduce the leakage loss as the speed increases and the performance of disk without pads is better than the disk with straight pads under the same supply flow. KEY WORDS: Seals; leakage loss; disk friction; experiment; Francis turbine.
1 INTRODUCTION The efficiency performance of Francis turbines has been continuously improved over the last century, and state-of-the-art prototypes today reach above 96% of the total efficiency at best efficiency point[1]. A further improvement in efficiency is of course possible by optimizing the different geometrical components. This can be combined with a detailed understanding of the different flow related losses. However, the potential for a higher best efficiency point is somewhat limited. Two of the largest single losses in Francis turbines are respectively the volumetric seal leakage loss and the disc friction loss in the water filled annulus between the runner and the upper/lower head covers. Based on prototype measurements, the leakage loss is at least 0.5% for a prototype with tight seal gaps while the disc friction will vary strongly with the specific speed [2]. The same author states that for high head Francis turbines the efficiency loss due to disc friction can be more than 1.0%. Hence, in order to substantially improve the efficiency level on the next generation of
Francis turbines, a reduction of these two loss components is probably required. Labyrinth seals are the primary type of seals for hydraulic turbines and have been used for over 100 years [3]. The labyrinth seal is the type of non-contact seal which is widely used in turbo machinery to suppress leakages. However, for traditional labyrinth seals, the space between the crown and upper cover is filled with water, which results in the high disk friction loss [4]. Therefore a new seal should be developed which is located at the inlet of the runner, rendering the space between the crown and upper cover larger. However, it is necessary to design a new seal which can be located at the inlet of the runner and also reduce the leakage loss of Francis turbine. Thus a seal with different kinds of pads may be a good solution.
This present work is about the preliminary experimental investigation of the performance of seals with different geometric pads. The experimental setup, experimental method and some preliminary results are presented in the paper. Based on an analysis of the preliminary experimental results, the experimental setup will be improved more in order to provide more credible experimental proof for designing a new seal technology. The new seal device is to be applied on the Francis turbine instead of the labyrinth seal to improve the efficiency. The investigation is part of PhD work that is planned to be finished in 2010. 2 EXPERIMENT 2.1 Experimental set-up Fig. 1 illustrates the schematic of the experimental apparatus. This experimental set-up of the rotor-stator system is a simplification of a Francis turbine runner with focus on the seals. The apparatus consists of a
9th International Conference on Hydrodynamics October 11-15, 2010 Shanghai, China motor, a bearing, a shaft, a stator, a fixed rotor made of steel, a pump and a plastic ring fixed on the steel rotor, which can be replaced with different geometrical pads to test diverse seals. This plastic ring could be different geometric seals. As Fig. 1 shows, the radius of shaft, fixed rotor, plastic disk and stator are R1, R2, R3 and R4, respectively; C represents the clearance between the rotor and stator; P1, P2 and P3 demonstrate pressure points that are measured. The values of these parameters are given in Table 1.
a.
Plastic disk without pads
b.
Plastic disk with straight pads
c.
Plastic disk with left tilting pads
d.
Plastic disk with right tilting pads
371
Fig. 2 Schematic diagram of different geometrical plastic disks
Fig. 1 Schematic diagram of the experimental set-up Table 1 Parameter of experimental set-up Parameters Radius of shaft (R1) Radius of fixed rotor (R2) Radius of plastic disk (R3) Radius of the stator (R4) Clearance (C)
Fig. 3 Vertical view of plastic disk with straight pads Values 25 mm 98 mm 100 mm 100.2 mm 0.2 mm
Fig. 2 represents examples of different geometric seals. Fig. 2 (a) is the round plastic disk without pads; Fig. 2 (b) is the plastic disk with straight pads and Fig.2 (c) and (d) are the plastic disk with tilting pads which can be tilted in left or right directions. The most significant point is that the tilting direction should be also achieved by changing the direction of rotation of motor. With the purpose of good understanding, Fig. 3 shows the example of the vertical view of plastic disk with straight pads. The pump is used to supply the water flow. There is one inlet and two outlets, one of which is defined as the leakage flow outlet. When the water flows in the tank, some water will flow out from the outlet 1 and some will leak through clearance between the rotor and stator. The different geometrical plastic disks are designed to influence the leakage loss; for the same type of geometric plastic disk, there are two aspects that can affect the leakage loss, such as the angle of tilting pads and number of the pads.
2.2 Experimental method The test method is as follows: First, the plastic disk with straight pads was chosen and fixed on the test rig; the water was supplied into the tank with the constant velocity by the pump. Second, the water was discharged from the outlet 1 and the surface went up; and then the water effused from the outlet 2 as well. Next, the motor was started with a low rotational speed. The outflow through outlet 2 was suppressed when increasing the rotational speed of motor. The leakage flow and the pressure in the tank, P1, P2 and P3, as shown in the Fig. 1, are measured. In the process, the rotational speed of the disk was changed; the leakage flow was measured by recording the time of filling a barrel of water, which was weighed before the experiment. For the sake of reducing artificial error as much as possible, the time was recorded three times for each flow and rotational speed. The pressure was measured by a pressure sensor, rotational speed by the speed sensor, the total flow by a measuring cylinder. These sensors were calibrated before the experiment. During testing, the measurements of the pressure and rotational speed were controlled and recorded by a LabVIEW program.
372
9th International Conference on Hydrodynamics October 11-15, 2010 Shanghai, China
3 RESULTS AND DISCUSSION In the following, some preliminary results of the disk without pads and with straight pads, see Fig. 2 (a) and (b) are presented. The dimension of this disk is displayed in Tables 2~3. Table 2 Parameters of plastic disk without pads Parameters Values Radius of disk without pads 100 mm Thickness of disk 20 mm Clearance 0.2 mm Table 3 Parameters of plastic disk with straight pads Parameters Values Radius of disk with straight pads 96 mm Thickness of disk 20mm Clearance 0.2 mm Thickness of pads 4 mm Number of pads 40
The rotational disk can suppress the leakage flow through outlet 2 at certain rotational speed, which is depended on the supply flow. In the experimental process, 800 rpm was proved to suppress the leakage flow through outlet 2 for supply flow of 10 and 12 L/min and 1200 rpm for supply flow of 14 L/min. Hence, the 800 and 1200 rpm were chosen as the initiative speeds for the measurements. 3.1 Disk without pads Fig. 4 reveals the relationship between the leakage flow rate QL/Qin and the rotational speed of disk, n rpm, in the case of the constant supply flow for the disk without pads. It gives the results under the supply flows of 10, 12 and 14 L/min. In general, the leakage loss decreases as the rotational speed increases at the constant flow. The leakage loss rate at the supply flow of 10 L/min is reduced from 6.5% to 3.4% when the rotational speed increases from 800 r/min to 2400 r/min. However, for the supply flows of 12 and 14 L/min, the leakage loss rate decreases gradually as the rotational speed increases from 800 r/min to 2600 r/min. Fig. 5 presents the relationship of the pressure (P1) below the disk and the rotational speed for three different supply flows (10, 12 and 14 L/min). The pressure, P1, rises up as the rotational speed increases for the supply flows of 12 and 14 L/min. However, for the supply flow of 10 L/min, the pressure increase first and then declines rapidly. For the supply flow of 14 L/min, it shows a much higher pressure than for the other two supply flows.
Fig. 4 Leakage loss rate vs. rotational speed for disk without pads
Fig. 5 Pressure P1 vs. rotational speed for disk without pads
Fig. 6 shows the relationship of the pressure difference among P1, P2 and P3 and the rotational speed at the constant supply flow, 10, 12 and 14 L/min. All of the pressure differences, P1-P2, P1-P3 and P3-P2, show a gradual rise as the rotational speed increases. Moreover, the growth rate of the pressure difference between P1 and P2 is the fastest one. It presents the pressure P3 is higher than the pressure P2. That is because the point P2 is closer to rotational disk than the point P3. The velocity at point P2 rises gradually as the rotational speed increases, which results in the pressure P2 decreases.
9th International Conference on Hydrodynamics October 11-15, 2010 Shanghai, China
373
Fig. 7 Leakage loss rate vs. rotational speed for disk with straight pads
Fig. 6 Pressure difference vs. rotational speed for disk without pads
3.2 Disk with straight pads Fig. 7 discloses the relationship between the leakage flow rate QL/Qin and the rotational speed of disk, n rpm, in the case of the constant supply flow for the disk with straight pads. Fig. 8 and Fig. 9 gives the relationship of the pressure (P1) below the disk and the rotational speed for three different supply flow (10, 12 and 14 L/min) and the relationship of the pressure difference among P1, P2 and P3 and the rotational speed at the constant supply flow, 10, 12 and 14 L/min for disk with straight pads respectively. The pressure, P1, rises up by increasing the rotational speed for the disk with straight pads. In generally, the results of disk with straight pads are almost the same as the disk without pads.
Fig. 8 Pressure P1 vs. rotational speed for disk with straight pads
3.3 Comparison Comparing the results of both disk with straight pads and disk without pads, the trend of the leakage loss rate, the pressure and the pressure difference is generally agreement. The leakage loss rate is reduced as the rotational speed increases and the pressure and pressure difference rise up as the rotational speed increases. However, the leakage loss rate is lower for disk without pads than for disk with straight pads at the same supply flow. For instance, the leakage loss rate is 5.86%-5.26% under the supply flow of 14 L/min for disk without pads when rotational speed is from 1200 rpm to 2400 rpm while the leakage loss rate is 9.28-7.45% for disk with straight pads. The reason is the disk with straight pads gives more space between the rotor and stator than the disk without pads. However, the decreasing rate of leakage loss rate is obviously higher for disk without pads than for disk with straight pads, see Fig. 4 and Fig. 7. It means the influence from the rotational speed on the leakage loss for disk with straight pads is larger than for disk without pads. Hence, it could be possible to optimize disk with tilting pads to reduce the leakage loss.
374
9th International Conference on Hydrodynamics October 11-15, 2010 Shanghai, China 4 CONCLUSIONS A test rig of rotor-stator system is designed and set up to study the new seal technology, which is made up of disk with different geometrical pads. A series of simple and basic laboratory tests were performed to study the leakage characteristic of disk without pads and disk with straight pads. The preliminary results indicate the leakage flow rate is inverse proportional to the rotational speed for these two disks. The pressure below the disk rises as the rotational speed increases while the pressure difference between the above and below disk increases. However, the leakage loss rate is lower for disk without pads than for disk with straight pads at the same supply flow. Moreover, the influence from the rotational speed on the leakage loss for disk with straight pads is larger than for disk without pads. It could be possible to optimize disk with tilting pads to reduce the leakage loss. 5 FURTHER WORK Further experiments are needed to test more types of disk with different geometrical pads in order to study the effect from the geometry of the pads on the leakage flow and measure the disk friction loss. ACKNOWLEDGEMENTS This paper is a partial result from a research project sponsored by Research Council of Norway and Rainpower Norway AS. The assistance of Mr. Bård Aslak Brandåstrø and Mr. Joar Gristad, engineers in the waterpower lab in the Norwegian University of Science and Technology, is gratefully appreciated. Gratitude also goes to Mr. Trygve Opland and Mr. Per Eivind for helping me set up the test rig in the laboratory. REFERENCES
Fig. 9 Pressure difference vs. rotational speed for disk with straight pads
[1] J L Gordon. Hydraulic turbine efficiency [J]. Canadian Journal of Civil Engineering, 2001, 28(2): 238-253. [2] Hermod Brekke. Analysis of losses in hydraulic turbines [C]. 18th IAHR Symposium on Hydraulic Machinery and Cavitation, Valencia, Spain, 1996: 294-303. [3] H Martin. Labyrinth Packing [M]. The Engineer, 1908: 3536. [4] Frank M W. Viscous Fluid Flow [M]. McGraw-Hill, 2006: 155-161.
370
2010, 22(5), supplement :381-385 DOI: 10.1016/S1001-6058(09)60223-7
An experimental study on leakage flow in different geometrical disk seals
1
Wei Zhao 1*, Torbjørn K. Nielsen1,Jan Tore Billdal2 Norwegian University of Science and Technology, Trondheim, Norway 2 Rainpower ASA, Kjeller, Norway * E-mail: [email protected]
ABSTRACT: This paper presents an experimental study on the leakage flow in rotor-stator system. The experimental setup of the rotor-stator system is a simplification of a Francis turbine runner with focus on the seals. It consists of a motor, a bearing, a shaft, a fixed rotor made of steel, a pump and a plastic ring fixed on the steel rotor, which can be replaced with different geometrical pads to test various seals. A small radial clearance (0.2mm) between the rotational disk and stator is settled. Leakage loss, pressure variation under the rotational disk and pressure difference between above and below the disk for various geometrical seals is measured at different rotational speeds. The results indicate that the rotational disk can reduce the leakage loss as the speed increases and the performance of disk without pads is better than the disk with straight pads under the same supply flow. KEY WORDS: Seals; leakage loss; disk friction; experiment; Francis turbine.
1 INTRODUCTION The efficiency performance of Francis turbines has been continuously improved over the last century, and state-of-the-art prototypes today reach above 96% of the total efficiency at best efficiency point[1]. A further improvement in efficiency is of course possible by optimizing the different geometrical components. This can be combined with a detailed understanding of the different flow related losses. However, the potential for a higher best efficiency point is somewhat limited. Two of the largest single losses in Francis turbines are respectively the volumetric seal leakage loss and the disc friction loss in the water filled annulus between the runner and the upper/lower head covers. Based on prototype measurements, the leakage loss is at least 0.5% for a prototype with tight seal gaps while the disc friction will vary strongly with the specific speed [2]. The same author states that for high head Francis turbines the efficiency loss due to disc friction can be more than 1.0%. Hence, in order to substantially improve the efficiency level on the next generation of
Francis turbines, a reduction of these two loss components is probably required. Labyrinth seals are the primary type of seals for hydraulic turbines and have been used for over 100 years [3]. The labyrinth seal is the type of non-contact seal which is widely used in turbo machinery to suppress leakages. However, for traditional labyrinth seals, the space between the crown and upper cover is filled with water, which results in the high disk friction loss [4]. Therefore a new seal should be developed which is located at the inlet of the runner, rendering the space between the crown and upper cover larger. However, it is necessary to design a new seal which can be located at the inlet of the runner and also reduce the leakage loss of Francis turbine. Thus a seal with different kinds of pads may be a good solution.
This present work is about the preliminary experimental investigation of the performance of seals with different geometric pads. The experimental setup, experimental method and some preliminary results are presented in the paper. Based on an analysis of the preliminary experimental results, the experimental setup will be improved more in order to provide more credible experimental proof for designing a new seal technology. The new seal device is to be applied on the Francis turbine instead of the labyrinth seal to improve the efficiency. The investigation is part of PhD work that is planned to be finished in 2010. 2 EXPERIMENT 2.1 Experimental set-up Fig. 1 illustrates the schematic of the experimental apparatus. This experimental set-up of the rotor-stator system is a simplification of a Francis turbine runner with focus on the seals. The apparatus consists of a
9th International Conference on Hydrodynamics October 11-15, 2010 Shanghai, China motor, a bearing, a shaft, a stator, a fixed rotor made of steel, a pump and a plastic ring fixed on the steel rotor, which can be replaced with different geometrical pads to test diverse seals. This plastic ring could be different geometric seals. As Fig. 1 shows, the radius of shaft, fixed rotor, plastic disk and stator are R1, R2, R3 and R4, respectively; C represents the clearance between the rotor and stator; P1, P2 and P3 demonstrate pressure points that are measured. The values of these parameters are given in Table 1.
a.
Plastic disk without pads
b.
Plastic disk with straight pads
c.
Plastic disk with left tilting pads
d.
Plastic disk with right tilting pads
371
Fig. 2 Schematic diagram of different geometrical plastic disks
Fig. 1 Schematic diagram of the experimental set-up Table 1 Parameter of experimental set-up Parameters Radius of shaft (R1) Radius of fixed rotor (R2) Radius of plastic disk (R3) Radius of the stator (R4) Clearance (C)
Fig. 3 Vertical view of plastic disk with straight pads Values 25 mm 98 mm 100 mm 100.2 mm 0.2 mm
Fig. 2 represents examples of different geometric seals. Fig. 2 (a) is the round plastic disk without pads; Fig. 2 (b) is the plastic disk with straight pads and Fig.2 (c) and (d) are the plastic disk with tilting pads which can be tilted in left or right directions. The most significant point is that the tilting direction should be also achieved by changing the direction of rotation of motor. With the purpose of good understanding, Fig. 3 shows the example of the vertical view of plastic disk with straight pads. The pump is used to supply the water flow. There is one inlet and two outlets, one of which is defined as the leakage flow outlet. When the water flows in the tank, some water will flow out from the outlet 1 and some will leak through clearance between the rotor and stator. The different geometrical plastic disks are designed to influence the leakage loss; for the same type of geometric plastic disk, there are two aspects that can affect the leakage loss, such as the angle of tilting pads and number of the pads.
2.2 Experimental method The test method is as follows: First, the plastic disk with straight pads was chosen and fixed on the test rig; the water was supplied into the tank with the constant velocity by the pump. Second, the water was discharged from the outlet 1 and the surface went up; and then the water effused from the outlet 2 as well. Next, the motor was started with a low rotational speed. The outflow through outlet 2 was suppressed when increasing the rotational speed of motor. The leakage flow and the pressure in the tank, P1, P2 and P3, as shown in the Fig. 1, are measured. In the process, the rotational speed of the disk was changed; the leakage flow was measured by recording the time of filling a barrel of water, which was weighed before the experiment. For the sake of reducing artificial error as much as possible, the time was recorded three times for each flow and rotational speed. The pressure was measured by a pressure sensor, rotational speed by the speed sensor, the total flow by a measuring cylinder. These sensors were calibrated before the experiment. During testing, the measurements of the pressure and rotational speed were controlled and recorded by a LabVIEW program.
372
9th International Conference on Hydrodynamics October 11-15, 2010 Shanghai, China
3 RESULTS AND DISCUSSION In the following, some preliminary results of the disk without pads and with straight pads, see Fig. 2 (a) and (b) are presented. The dimension of this disk is displayed in Tables 2~3. Table 2 Parameters of plastic disk without pads Parameters Values Radius of disk without pads 100 mm Thickness of disk 20 mm Clearance 0.2 mm Table 3 Parameters of plastic disk with straight pads Parameters Values Radius of disk with straight pads 96 mm Thickness of disk 20mm Clearance 0.2 mm Thickness of pads 4 mm Number of pads 40
The rotational disk can suppress the leakage flow through outlet 2 at certain rotational speed, which is depended on the supply flow. In the experimental process, 800 rpm was proved to suppress the leakage flow through outlet 2 for supply flow of 10 and 12 L/min and 1200 rpm for supply flow of 14 L/min. Hence, the 800 and 1200 rpm were chosen as the initiative speeds for the measurements. 3.1 Disk without pads Fig. 4 reveals the relationship between the leakage flow rate QL/Qin and the rotational speed of disk, n rpm, in the case of the constant supply flow for the disk without pads. It gives the results under the supply flows of 10, 12 and 14 L/min. In general, the leakage loss decreases as the rotational speed increases at the constant flow. The leakage loss rate at the supply flow of 10 L/min is reduced from 6.5% to 3.4% when the rotational speed increases from 800 r/min to 2400 r/min. However, for the supply flows of 12 and 14 L/min, the leakage loss rate decreases gradually as the rotational speed increases from 800 r/min to 2600 r/min. Fig. 5 presents the relationship of the pressure (P1) below the disk and the rotational speed for three different supply flows (10, 12 and 14 L/min). The pressure, P1, rises up as the rotational speed increases for the supply flows of 12 and 14 L/min. However, for the supply flow of 10 L/min, the pressure increase first and then declines rapidly. For the supply flow of 14 L/min, it shows a much higher pressure than for the other two supply flows.
Fig. 4 Leakage loss rate vs. rotational speed for disk without pads
Fig. 5 Pressure P1 vs. rotational speed for disk without pads
Fig. 6 shows the relationship of the pressure difference among P1, P2 and P3 and the rotational speed at the constant supply flow, 10, 12 and 14 L/min. All of the pressure differences, P1-P2, P1-P3 and P3-P2, show a gradual rise as the rotational speed increases. Moreover, the growth rate of the pressure difference between P1 and P2 is the fastest one. It presents the pressure P3 is higher than the pressure P2. That is because the point P2 is closer to rotational disk than the point P3. The velocity at point P2 rises gradually as the rotational speed increases, which results in the pressure P2 decreases.
9th International Conference on Hydrodynamics October 11-15, 2010 Shanghai, China
373
Fig. 7 Leakage loss rate vs. rotational speed for disk with straight pads
Fig. 6 Pressure difference vs. rotational speed for disk without pads
3.2 Disk with straight pads Fig. 7 discloses the relationship between the leakage flow rate QL/Qin and the rotational speed of disk, n rpm, in the case of the constant supply flow for the disk with straight pads. Fig. 8 and Fig. 9 gives the relationship of the pressure (P1) below the disk and the rotational speed for three different supply flow (10, 12 and 14 L/min) and the relationship of the pressure difference among P1, P2 and P3 and the rotational speed at the constant supply flow, 10, 12 and 14 L/min for disk with straight pads respectively. The pressure, P1, rises up by increasing the rotational speed for the disk with straight pads. In generally, the results of disk with straight pads are almost the same as the disk without pads.
Fig. 8 Pressure P1 vs. rotational speed for disk with straight pads
3.3 Comparison Comparing the results of both disk with straight pads and disk without pads, the trend of the leakage loss rate, the pressure and the pressure difference is generally agreement. The leakage loss rate is reduced as the rotational speed increases and the pressure and pressure difference rise up as the rotational speed increases. However, the leakage loss rate is lower for disk without pads than for disk with straight pads at the same supply flow. For instance, the leakage loss rate is 5.86%-5.26% under the supply flow of 14 L/min for disk without pads when rotational speed is from 1200 rpm to 2400 rpm while the leakage loss rate is 9.28-7.45% for disk with straight pads. The reason is the disk with straight pads gives more space between the rotor and stator than the disk without pads. However, the decreasing rate of leakage loss rate is obviously higher for disk without pads than for disk with straight pads, see Fig. 4 and Fig. 7. It means the influence from the rotational speed on the leakage loss for disk with straight pads is larger than for disk without pads. Hence, it could be possible to optimize disk with tilting pads to reduce the leakage loss.
374
9th International Conference on Hydrodynamics October 11-15, 2010 Shanghai, China 4 CONCLUSIONS A test rig of rotor-stator system is designed and set up to study the new seal technology, which is made up of disk with different geometrical pads. A series of simple and basic laboratory tests were performed to study the leakage characteristic of disk without pads and disk with straight pads. The preliminary results indicate the leakage flow rate is inverse proportional to the rotational speed for these two disks. The pressure below the disk rises as the rotational speed increases while the pressure difference between the above and below disk increases. However, the leakage loss rate is lower for disk without pads than for disk with straight pads at the same supply flow. Moreover, the influence from the rotational speed on the leakage loss for disk with straight pads is larger than for disk without pads. It could be possible to optimize disk with tilting pads to reduce the leakage loss. 5 FURTHER WORK Further experiments are needed to test more types of disk with different geometrical pads in order to study the effect from the geometry of the pads on the leakage flow and measure the disk friction loss. ACKNOWLEDGEMENTS This paper is a partial result from a research project sponsored by Research Council of Norway and Rainpower Norway AS. The assistance of Mr. Bård Aslak Brandåstrø and Mr. Joar Gristad, engineers in the waterpower lab in the Norwegian University of Science and Technology, is gratefully appreciated. Gratitude also goes to Mr. Trygve Opland and Mr. Per Eivind for helping me set up the test rig in the laboratory. REFERENCES
Fig. 9 Pressure difference vs. rotational speed for disk with straight pads
[1] J L Gordon. Hydraulic turbine efficiency [J]. Canadian Journal of Civil Engineering, 2001, 28(2): 238-253. [2] Hermod Brekke. Analysis of losses in hydraulic turbines [C]. 18th IAHR Symposium on Hydraulic Machinery and Cavitation, Valencia, Spain, 1996: 294-303. [3] H Martin. Labyrinth Packing [M]. The Engineer, 1908: 3536. [4] Frank M W. Viscous Fluid Flow [M]. McGraw-Hill, 2006: 155-161.