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Analytical and Experimental Analysis of the High Pressure Boiler Feed Pump
Available online at www.sciencedirect.com
ScienceDirect Procedia Technology 23 (2016) 472 – 479
3rd International Conference on Innovations in Automation and Mechatronics Engineering, ICIAME 2016
Analytical and Experimental Analysis of the High Pressure Boiler Feed Pump Nilesh Tiwaria *, Krishna Kumarb, Devranjan Kumarc a
Asst. Prof., SVMIT, BHARUCH-392001, India Asst. Prof., SVMIT, BHARUCH-392001, India c Asst. Prof., SVMIT, BHARUCH-392001, India
b
Abstract The present works discuss the comparison between the analytical and experimental performance curve of the high pressure boiler feed pump - a multistage centrifugal pump. The hydraulic loss model stated by J.F. Gulich is widely used for the analytical performance prediction of the single stage centrifugal pumps. In the present work, this methodology is implemented for the analytical performance prediction of the 10-stage industrial centrifugal pump. The given pump is installed as HPBFP (High Pressure Boiler Feed Pump) to carry water from the deaerator to boiler. The H-Q (Head versus Discharge) analytical performance characteristics curve of the pump is compared with the experimental performance characteristics curve. The deviation between the analytical and experimental curve is between 2-13% for the discussed range of discharge. This deviation is due to the assumption of the single dimensional geometry of the different components of the centrifugal pump. Published by by Elsevier Ltd. Ltd. This is an open access article under the CC BY-NC-ND license © 2016 2016The TheAuthors. Authors. Published Elsevier (http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and/or peer-review under responsibility of the Organizing Committee of ICIAME 2016. Peer-review under responsibility of the organizing committee of ICIAME 2016
Keywords: multistage centrifugal pump; hydraulic loss method; high pressure boiler feed pump; performance characteristics curve.
Nomenclature A A1q A2q
cross section area impeller inlet throat area area between vanes at impeller outlet
* Corresponding author. Tel.: +91-9033252898. E-mail address: [email protected]
2212-0173 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICIAME 2016 doi:10.1016/j.protcy.2016.03.052
Nilesh Tiwari et al. / Procedia Technology 23 (2016) 472 – 479
A3q a b cf D, d d3q db dm dn ds e I Hexp Hth Hslip Hwithout slip L n QLa r r3q s sax w w1q Zh zLa zLe α β J ε ζ ν ϕ
473
diffuser/volute inlet throat area distance between vanes width of channel in the meridional section friction coefficient of a flat plate Diameter equivalent diameter of volute throat arithmetic average of diameters at impeller or diffuser geometric average of diameters at impeller or diffuser hub diameter inner diameter of suction nozzle vane thickness incidence (i = blade angle minus flow angle) Experimental pressure head Theoretical pressure head Head with the consideration of slip factor Head without consideration of slip factor Length rotational speed (revolutions per minute) flow rate through impeller Radius equivalent radius of volute throat area gap width axial distance between impeller shrouds and casing relative velocity average velocity in impeller throat area w1q = QLa/(zLa×A1q) hydraulic losses (impeller: ZLa diffuser: ZLe) number of impeller blades number of diffuser vanes angle between direction of circumferential and absolute velocity angle between relative velocity vector and the negative direction of circumferential velocity impeller discharge coefficient (slip factor) equivalent roughness equivalent roughness loss coefficient kinematic viscosity flow coefficient
1. Introduction Centrifugal pumps are one of the most common machines used in the industrial and domestic field. It is turbomachine used for transporting liquids by raising a specified volume flow to a specified pressure level, which uses the dynamic principle of accelerating fluid, through centrifugal activity, and converting the kinetic energy into pressure. Centrifugal pump consists of mechanical and the hydraulic portion, in which impetus would be given on the hydraulic performance of the pump. In the present paper focus would be on the multistage type centrifugal pump. For the performance prediction of the single stage centrifugal pump, hydraulic loss method given by J. F. Gulich [1] has been widely utilized. This is evident in the work done by Li [2-4], Golcu [5], Rababa [6] and Patel and Doshi [7]. For the calculation of the slip factor in the turbomachines, various formulae have been proposed. In the work by Gulich, slip factor is calculated by the formula given by Wiesner [8]. Literature of Memardezfouli and
474
Nilesh Tiwari et al. / Procedia Technology 23 (2016) 472 – 479
Nourbakhsh [9] also conclude that the formula stated in [8] calculates the slip factor more accurately than other formulae. Multistage centrifugal pumps are of two types i.e. series and parallel types multistage pumps. The series type pump is used to increase the pressure head, whereas the parallel type is used for increment in the discharge. In the present work, focus is on the series type of multistage centrifugal pump. The first stage of a multistage centrifugal pump is larger in diameter as compared to remaining stages. This is done to resist the thrust exerted by the other stages of the pump. The analytical performance prediction of the multistage centrifugal pump has been done on the basis of the extension of the work by J. F. Gulich on the single stage centrifugal pump. The work done in [10], calculate the performance of the multistage pump on the basis of the hydraulic loss model discussed in [1]. The analytical work includes the calculation of the Euler head of the pump and subtracting the losses in impeller, diffuser and the return vanes from the Euler head.
Fig. 1. Line diagram of the thermal power plant 2. Analytical Study In this process, various geometric parameters are required for the calculations in this section. These parameters are measured by dismantling of the pump during the maintenance phase of the centrifugal pump. The list of required input geometrical data required for the calculations in the subsequent portions is obtained from Fig. 2 (a) and (b). In the analytical performance prediction of the centrifugal pump, Euler head is calculated with the consideration of slip factor with the following formula. * QLa A 2 d 1m tanE 2 B ½º u 22 ª H th,with slip ®W 2 ¾» «γ (1) A1tanD1 ¿¼ g ¬ A 2 u 2tanE 2 B ¯ In this equation, slip factor is calculated by formula stated by Wiesner [3]. Then the hydraulic losses in impeller, diffuser and return vanes are estimated. Hydraulic loss in impeller includes friction and mixing loss and shock loss at impeller inlet. Friction and mixing loss: ζ La ,R
2g
Z La ,r u 22
4cd
Lsch § wav · ¨ ¸ Dh © u 2 ¹
2
(2)
475
Nilesh Tiwari et al. / Procedia Technology 23 (2016) 472 – 479
(a)
(b)
(* all dimensions are in mm)
Fig.2. (a) Sectional view of the impeller blade and (b) Meridional view of diffuser
Shock loss at impeller inlet 2 Z La ,C § w1m w1q · ζ La ,C 2g 0.3 ¨ (3) ¸ u 22 u2 © ¹ Then, hydraulic loss in the volute includes losses due to friction in inlet region, diffuser loss including overflow channel, discharge nozzle, friction in vaneless diffuser and friction losses in vaneless diffuser with constant width. The losses in the return vanes are estimated through the diffuser loss including overflow channel. Here, overflow loss coefficient is taken as 0.2. π3 φ2 b *2 § c ¨1 2 c f 0.0015 a b * * 3 ¨ c 3q 8 zLe a 3 b 3 © 2
ζ 2 3
Z 2g 223 u2
* 3
* 3
3
· ¸¸ ¹
(4)
Diffuser loss including overflow channel ζ Le
2g
2 2 · §c · 1 ζ ov ½ ° §c ° ζ 23 ¨ 3q ¸ ®0.3 ¨ 2 1¸ 1 c p 2 ¾ ¨ ¸ A u c R © 2 ¹ ° ° ¹ ¯ © 3q ¿
Z Le u 22
(5)
Discharge nozzle 2
§c · § 1 · ζ Sp,D ¨ x ¸ ¨ 1 c p ¸ AR2 ¹ © u2 ¹ © Friction in vaneless diffuser ζ LS
§ b · φ 2, La 2 ¨ W 2 2 ¸ b3 ¹ ©
(6)
2
(7)
Friction losses in vaneless diffuser with constant width ζ LR
2c f r2 § c2u · § r2 · ¨ ¸ ¨1 ¸ b3 sinD 3cos 2D 3 © u2 ¹ © r4 ¹
(8)
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Nilesh Tiwari et al. / Procedia Technology 23 (2016) 472 – 479
Loss in the inlet casing stated in the following equation, is also considered in the summation of the losses in the centrifugal pump. § d 2 d 2 · ζ E 0.75 ¨ 1 2 n ¸ (9) © ds ¹ Here all the formula assumes the single dimensional nature of the components of the centrifugal pump. The losses in impeller, diffuser and casing are subtracted from the Euler head with the consideration of the slip factor. The geometrical parameters required for the theoretical analysis are obtained from Fig. 2 (a) and (b). With the application of these parameters in the formulae in [1], theoretical performance characteristics curve of the pump can be obtained. Fig. 3 shows the analytical performance characteristics curve of the multistage centrifugal pump. Here, trajectory of the curve is parabolic in nature. The maximum pressure head of 1043 m is obtained at the discharge of 44 m3/hr.
Fig.3. Theoretical head with respect to Discharge with consideration of slip factor and all the hydraulic losses 3. Experimental Test Rig In the Fig 1, layout of the power plant is described. The multistage pump used for the analysis in this paper, carries the water from the deaerator to the boiler. This multistage pump is a 10-stage High Pressure Boiler Feed Pump (HPBFP). In this pump, the assembly of impeller, diffuser and casing bowel is connected in a 10-stage series.
Fig.4. Layout of multistage centrifugal pump test rig
Nilesh Tiwari et al. / Procedia Technology 23 (2016) 472 – 479
477
Fig. 4 indicates the layout of experimental test rig. The centrifugal pump transports water from the deaerator to the boiler. For the pressure head, suction pressure, discharge pressure and discharge across the pump have to be measured, to calculate the pressure of the centrifugal pump. The pressure and discharge are measured by Bourdon tube type of pressure gauge and differential pressure type pressure gauge respectively. The accuracy and the range of the inlet pressure gauge are ± 1 % of FSD and 0 to 6 kg/cm2 respectively. For the discharge pressure gauge, accuracy is same as that of inlet pressure gauge, and range is 0 to 160 kg/cm2. The accuracy and the range of the Differential Pressure Flow meter are ± 1 % of FSD and 0 to 165 m3/hr respectively. Fig. 2(a) indicates the sectional view of the impeller blade. This diagram is used to obtain the geometrical parameters for the calculations for the hydraulic loss in the impeller. Similarly Fig. 2(b) indicates the meridional view of the diffuser. These diagrams are used for various calculations according to the hydraulic loss method by J. F. Gulich.
(b) (a) Fig.5. Experimental characteristics curve of the multistage centrifugal pump. (a) H-Q (Head- Discharge) characteristics curve and (b) η-Q (Efficiency - Discharge) characteristics curve 4. Experimental Analysis and Comparative Analysis With the help of the experimental data gathered through the experiments performed on the multistage centrifugal pump, parabolic H-Q performance characteristics curve in the form of Fig. 5, has been obtained. The summary of the comparison between experimental and theoretical data is given in Fig. 6.
Fig.6. Comparison of the Theoretical and Experimental Characteristics curve
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Nilesh Tiwari et al. / Procedia Technology 23 (2016) 472 – 479
This performance characteristics curve is compared with the theoretical performance characteristics curve. Fig. 6 shows the comparison between Euler head without consideration of slip factor, Euler head with consideration of slip factor, theoretical characteristics curve and the experimental characteristics curve. Here the trajectory of the theoretical characteristics curve is in congruence with the experimental characteristics curve. The deviation between the theoretical and the experimental curve is 2-13% for the discharge between 19 m3/hr to 91m3/hr. This deviation is due to non-consideration of secondary losses in centrifugal pump in the analytical study. The secondary losses include disk friction loss, leakage loss and mechanical loss. In the analytical study, one dimensional profile of the pump is considered. But, to calculate the secondary losses 2-dimensional or 3dimensional profile of the pump has been considered. These considerations are complex to include in the theoretical analysis. Also these losses do not have major impact on the performance characteristics curve. 5. Results and Discussions Fig. 5 indicates the experimental performance characteristics curve of the multistage pump. This performance characteristics curve is compared with the theoretical performance characteristics curve in Fig. 6. Fig. 7 shows the comparison between Euler head without consideration of slip factor, Euler head with consideration of slip factor, theoretical characteristics curve and the experimental characteristics curve. Here the trajectory of the theoretical characteristics curve is in congruence with the experimental characteristics curve.
Fig.7. Performance characteristics curve of the multistage centrifugal pump The deviation between the theoretical and the experimental curve is 2-13% for the discharge between 19 m3/hr to 91m3/hr is indicated in Fig. 6. This deviation is due to non-consideration of secondary losses in centrifugal pump in the analytical study. The secondary losses include disk friction loss, leakage loss and mechanical loss. In the analytical study, one dimensional profile of the pump is considered. But, to calculate the secondary losses 2dimensional or 3-dimensional profile of the pump has been considered. These considerations are complex to include in the theoretical analysis. Also these losses do not have major impact on the performance characteristics curve. 6. Conclusion The hydraulic loss calculation method shows deviation with respect to experimental results in the range of about 2% to 13%, for the range of discharge between 19 m 3/hr to 91m3/hr. This deviation between the theoretical and experimental result is due to negligence of the secondary losses in the analytical study to calculate various losses in the centrifugal pump.
Nilesh Tiwari et al. / Procedia Technology 23 (2016) 472 – 479
This method, which is already applied to predict the performance characteristics curve of the single-stage centrifugal pump, can also be applied to the multistage centrifugal pumps to predict its performance for various operation and geometric parameters. Acknowledgment I would like to show my greatest appreciation to the professional staff of G.I.P.C.L. (Gujarat Industries Power Company Limited), for their immense support and involvement throughout the tenure of training. Without their encouragement and guidance this report would not have materialized. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]
Gulich, Johann F., 2008, “Centrifugal pumps." Berlin: Springer. Li, W-G., 2002, "Influence of the number of impeller blades on the performance of centrifugal oil pumps." World Pumps, 427: 32-35. Li, W. G., 2011, "Blade exit angle effects on performance of a standard industrial centrifugal oil pump." Journal of applied fluid mechanics, 4.2: 105-119. Li, Wen-Guang., 2013, “Effects of flow rate and viscosity on slip factor of centrifugal pump handling viscous oils." International Journal of Rotating Machinery. Golcu, Mustafa, and Yaşar Pancar, 2005, "Investigation of performance characteristics in a pump impeller with low blade discharge angle." World Pumps 2005. 468: 32-40. Khalid.S.Rababa, 2002, “The Effect of Blades number and Shape on the Operating characteristics of Groundwater Centrifugal Pumps”, European Journal of scientific research, Vol 2, No.6: 243-251. M.G.Patel and A.V.Doshi, 2013, “Effect of Impeller Blade Exit Angle on the Performance of Centrifugal Pump", International Journal of Emerging Technology and Advanced Engineering, Volume 3, Issue 1:702-706. F.J. Wiesner, 1967, “A review of slip factors for centrifugal impellers", Transactions of the American Society of Mechanical Engineers: J.Eng. Gas Turbines Power, 89:558–572. Memardezfouli, Mohamad, and Ahmad Nourbakhsh. "Experimental investigation of slip factors in centrifugal pumps." Experimental thermal and fluid science 33.5 (2009): 938-945. Foslie, S., 2013, “Design of Centrifugal Pump for Produced Water” (Master of Science in Mechanical Engineering). Norwegian University of Science and Technology. Nemdili, Ali, and Dieter-Heinz Hellmann., 2004, “Development of an empirical equation to predict the disc friction losses of a centrifugal pump." The Sixth International Conference on Hydraulic Machinery and Hydrodynamics, (2004) BP. Vol. 1505:235- 40. Shi, Weidong, Ling Zhou, Weigang Lu, Bing Pei, and Tao Lang., 2013, “Numerical prediction and performance experiment in a deep-well centrifugal pump with different impeller outlet width." Chinese Journal of Mechanical Engineering 26, no. 1: 46-52. Walker, Craig I., and Greg C. Bodkin., 2000, “Empirical wear relationships for centrifugal slurry pumps: Part 1: side-liners." Wear, 242.1: 140-146. Aisenstein, M.D. (1927). “A new method of separating the hydraulic losses in a centrifugal pump.” ASME Transactions 49, 1-7. Aly, S. and S. Al-Zubaidy (1992). “Performance prediction method for centrifugal pumps.” SAE paper 921731. Gulich, J.F. (1999a). “Pumping highly viscous fluids with centrifugal pumps-part 1.” World Pumps 395, 30-34. Gulich. J.F. (1999b). “Pumping highly viscous fluids with centrifugal pumps-part 2.” World Pumps, 396, 39-42. Gulich. J.F. (2003). “Effect of Reynolds number and surface roughness on the efficiency of centrifugal pumps.” ASME Journal of Fluids Engineering 125, 670-679. Iguchi. M. and M. Ohmi (1986). “Loss coefficients for flows through a sudden expansion and a sudden contraction closely placed.” Trans JSME, Series B 52(481), 3252-2258. Li, W.G. (2000). “The “sudden-rising head” effect in centrifugal oil pumps.” World Pumps 409, 34-36. Li, W.G. (2002). “The Influence of number of blades on the performance of centrifugal oil pumps.” World Pumps 427, 32-35. Li, W.G. (2004). “A method analyzing the performance of centrifugal oil pumps.” ASME Journal of Fluids Engineering 126(3), 482-485. Ohta, H. and K. Aoki (1996). “Effect of impeller angle on performance and internal flow of centrifugal pump for high-viscosity liquids.” Proceedings of the School of Engineering, Tokai University 36(1), 159-168.
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ScienceDirect Procedia Technology 23 (2016) 472 – 479
3rd International Conference on Innovations in Automation and Mechatronics Engineering, ICIAME 2016
Analytical and Experimental Analysis of the High Pressure Boiler Feed Pump Nilesh Tiwaria *, Krishna Kumarb, Devranjan Kumarc a
Asst. Prof., SVMIT, BHARUCH-392001, India Asst. Prof., SVMIT, BHARUCH-392001, India c Asst. Prof., SVMIT, BHARUCH-392001, India
b
Abstract The present works discuss the comparison between the analytical and experimental performance curve of the high pressure boiler feed pump - a multistage centrifugal pump. The hydraulic loss model stated by J.F. Gulich is widely used for the analytical performance prediction of the single stage centrifugal pumps. In the present work, this methodology is implemented for the analytical performance prediction of the 10-stage industrial centrifugal pump. The given pump is installed as HPBFP (High Pressure Boiler Feed Pump) to carry water from the deaerator to boiler. The H-Q (Head versus Discharge) analytical performance characteristics curve of the pump is compared with the experimental performance characteristics curve. The deviation between the analytical and experimental curve is between 2-13% for the discussed range of discharge. This deviation is due to the assumption of the single dimensional geometry of the different components of the centrifugal pump. Published by by Elsevier Ltd. Ltd. This is an open access article under the CC BY-NC-ND license © 2016 2016The TheAuthors. Authors. Published Elsevier (http://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and/or peer-review under responsibility of the Organizing Committee of ICIAME 2016. Peer-review under responsibility of the organizing committee of ICIAME 2016
Keywords: multistage centrifugal pump; hydraulic loss method; high pressure boiler feed pump; performance characteristics curve.
Nomenclature A A1q A2q
cross section area impeller inlet throat area area between vanes at impeller outlet
* Corresponding author. Tel.: +91-9033252898. E-mail address: [email protected]
2212-0173 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICIAME 2016 doi:10.1016/j.protcy.2016.03.052
Nilesh Tiwari et al. / Procedia Technology 23 (2016) 472 – 479
A3q a b cf D, d d3q db dm dn ds e I Hexp Hth Hslip Hwithout slip L n QLa r r3q s sax w w1q Zh zLa zLe α β J ε ζ ν ϕ
473
diffuser/volute inlet throat area distance between vanes width of channel in the meridional section friction coefficient of a flat plate Diameter equivalent diameter of volute throat arithmetic average of diameters at impeller or diffuser geometric average of diameters at impeller or diffuser hub diameter inner diameter of suction nozzle vane thickness incidence (i = blade angle minus flow angle) Experimental pressure head Theoretical pressure head Head with the consideration of slip factor Head without consideration of slip factor Length rotational speed (revolutions per minute) flow rate through impeller Radius equivalent radius of volute throat area gap width axial distance between impeller shrouds and casing relative velocity average velocity in impeller throat area w1q = QLa/(zLa×A1q) hydraulic losses (impeller: ZLa diffuser: ZLe) number of impeller blades number of diffuser vanes angle between direction of circumferential and absolute velocity angle between relative velocity vector and the negative direction of circumferential velocity impeller discharge coefficient (slip factor) equivalent roughness equivalent roughness loss coefficient kinematic viscosity flow coefficient
1. Introduction Centrifugal pumps are one of the most common machines used in the industrial and domestic field. It is turbomachine used for transporting liquids by raising a specified volume flow to a specified pressure level, which uses the dynamic principle of accelerating fluid, through centrifugal activity, and converting the kinetic energy into pressure. Centrifugal pump consists of mechanical and the hydraulic portion, in which impetus would be given on the hydraulic performance of the pump. In the present paper focus would be on the multistage type centrifugal pump. For the performance prediction of the single stage centrifugal pump, hydraulic loss method given by J. F. Gulich [1] has been widely utilized. This is evident in the work done by Li [2-4], Golcu [5], Rababa [6] and Patel and Doshi [7]. For the calculation of the slip factor in the turbomachines, various formulae have been proposed. In the work by Gulich, slip factor is calculated by the formula given by Wiesner [8]. Literature of Memardezfouli and
474
Nilesh Tiwari et al. / Procedia Technology 23 (2016) 472 – 479
Nourbakhsh [9] also conclude that the formula stated in [8] calculates the slip factor more accurately than other formulae. Multistage centrifugal pumps are of two types i.e. series and parallel types multistage pumps. The series type pump is used to increase the pressure head, whereas the parallel type is used for increment in the discharge. In the present work, focus is on the series type of multistage centrifugal pump. The first stage of a multistage centrifugal pump is larger in diameter as compared to remaining stages. This is done to resist the thrust exerted by the other stages of the pump. The analytical performance prediction of the multistage centrifugal pump has been done on the basis of the extension of the work by J. F. Gulich on the single stage centrifugal pump. The work done in [10], calculate the performance of the multistage pump on the basis of the hydraulic loss model discussed in [1]. The analytical work includes the calculation of the Euler head of the pump and subtracting the losses in impeller, diffuser and the return vanes from the Euler head.
Fig. 1. Line diagram of the thermal power plant 2. Analytical Study In this process, various geometric parameters are required for the calculations in this section. These parameters are measured by dismantling of the pump during the maintenance phase of the centrifugal pump. The list of required input geometrical data required for the calculations in the subsequent portions is obtained from Fig. 2 (a) and (b). In the analytical performance prediction of the centrifugal pump, Euler head is calculated with the consideration of slip factor with the following formula. * QLa A 2 d 1m tanE 2 B ½º u 22 ª H th,with slip ®W 2 ¾» «γ (1) A1tanD1 ¿¼ g ¬ A 2 u 2tanE 2 B ¯ In this equation, slip factor is calculated by formula stated by Wiesner [3]. Then the hydraulic losses in impeller, diffuser and return vanes are estimated. Hydraulic loss in impeller includes friction and mixing loss and shock loss at impeller inlet. Friction and mixing loss: ζ La ,R
2g
Z La ,r u 22
4cd
Lsch § wav · ¨ ¸ Dh © u 2 ¹
2
(2)
475
Nilesh Tiwari et al. / Procedia Technology 23 (2016) 472 – 479
(a)
(b)
(* all dimensions are in mm)
Fig.2. (a) Sectional view of the impeller blade and (b) Meridional view of diffuser
Shock loss at impeller inlet 2 Z La ,C § w1m w1q · ζ La ,C 2g 0.3 ¨ (3) ¸ u 22 u2 © ¹ Then, hydraulic loss in the volute includes losses due to friction in inlet region, diffuser loss including overflow channel, discharge nozzle, friction in vaneless diffuser and friction losses in vaneless diffuser with constant width. The losses in the return vanes are estimated through the diffuser loss including overflow channel. Here, overflow loss coefficient is taken as 0.2. π3 φ2 b *2 § c ¨1 2 c f 0.0015 a b * * 3 ¨ c 3q 8 zLe a 3 b 3 © 2
ζ 2 3
Z 2g 223 u2
* 3
* 3
3
· ¸¸ ¹
(4)
Diffuser loss including overflow channel ζ Le
2g
2 2 · §c · 1 ζ ov ½ ° §c ° ζ 23 ¨ 3q ¸ ®0.3 ¨ 2 1¸ 1 c p 2 ¾ ¨ ¸ A u c R © 2 ¹ ° ° ¹ ¯ © 3q ¿
Z Le u 22
(5)
Discharge nozzle 2
§c · § 1 · ζ Sp,D ¨ x ¸ ¨ 1 c p ¸ AR2 ¹ © u2 ¹ © Friction in vaneless diffuser ζ LS
§ b · φ 2, La 2 ¨ W 2 2 ¸ b3 ¹ ©
(6)
2
(7)
Friction losses in vaneless diffuser with constant width ζ LR
2c f r2 § c2u · § r2 · ¨ ¸ ¨1 ¸ b3 sinD 3cos 2D 3 © u2 ¹ © r4 ¹
(8)
476
Nilesh Tiwari et al. / Procedia Technology 23 (2016) 472 – 479
Loss in the inlet casing stated in the following equation, is also considered in the summation of the losses in the centrifugal pump. § d 2 d 2 · ζ E 0.75 ¨ 1 2 n ¸ (9) © ds ¹ Here all the formula assumes the single dimensional nature of the components of the centrifugal pump. The losses in impeller, diffuser and casing are subtracted from the Euler head with the consideration of the slip factor. The geometrical parameters required for the theoretical analysis are obtained from Fig. 2 (a) and (b). With the application of these parameters in the formulae in [1], theoretical performance characteristics curve of the pump can be obtained. Fig. 3 shows the analytical performance characteristics curve of the multistage centrifugal pump. Here, trajectory of the curve is parabolic in nature. The maximum pressure head of 1043 m is obtained at the discharge of 44 m3/hr.
Fig.3. Theoretical head with respect to Discharge with consideration of slip factor and all the hydraulic losses 3. Experimental Test Rig In the Fig 1, layout of the power plant is described. The multistage pump used for the analysis in this paper, carries the water from the deaerator to the boiler. This multistage pump is a 10-stage High Pressure Boiler Feed Pump (HPBFP). In this pump, the assembly of impeller, diffuser and casing bowel is connected in a 10-stage series.
Fig.4. Layout of multistage centrifugal pump test rig
Nilesh Tiwari et al. / Procedia Technology 23 (2016) 472 – 479
477
Fig. 4 indicates the layout of experimental test rig. The centrifugal pump transports water from the deaerator to the boiler. For the pressure head, suction pressure, discharge pressure and discharge across the pump have to be measured, to calculate the pressure of the centrifugal pump. The pressure and discharge are measured by Bourdon tube type of pressure gauge and differential pressure type pressure gauge respectively. The accuracy and the range of the inlet pressure gauge are ± 1 % of FSD and 0 to 6 kg/cm2 respectively. For the discharge pressure gauge, accuracy is same as that of inlet pressure gauge, and range is 0 to 160 kg/cm2. The accuracy and the range of the Differential Pressure Flow meter are ± 1 % of FSD and 0 to 165 m3/hr respectively. Fig. 2(a) indicates the sectional view of the impeller blade. This diagram is used to obtain the geometrical parameters for the calculations for the hydraulic loss in the impeller. Similarly Fig. 2(b) indicates the meridional view of the diffuser. These diagrams are used for various calculations according to the hydraulic loss method by J. F. Gulich.
(b) (a) Fig.5. Experimental characteristics curve of the multistage centrifugal pump. (a) H-Q (Head- Discharge) characteristics curve and (b) η-Q (Efficiency - Discharge) characteristics curve 4. Experimental Analysis and Comparative Analysis With the help of the experimental data gathered through the experiments performed on the multistage centrifugal pump, parabolic H-Q performance characteristics curve in the form of Fig. 5, has been obtained. The summary of the comparison between experimental and theoretical data is given in Fig. 6.
Fig.6. Comparison of the Theoretical and Experimental Characteristics curve
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Nilesh Tiwari et al. / Procedia Technology 23 (2016) 472 – 479
This performance characteristics curve is compared with the theoretical performance characteristics curve. Fig. 6 shows the comparison between Euler head without consideration of slip factor, Euler head with consideration of slip factor, theoretical characteristics curve and the experimental characteristics curve. Here the trajectory of the theoretical characteristics curve is in congruence with the experimental characteristics curve. The deviation between the theoretical and the experimental curve is 2-13% for the discharge between 19 m3/hr to 91m3/hr. This deviation is due to non-consideration of secondary losses in centrifugal pump in the analytical study. The secondary losses include disk friction loss, leakage loss and mechanical loss. In the analytical study, one dimensional profile of the pump is considered. But, to calculate the secondary losses 2-dimensional or 3dimensional profile of the pump has been considered. These considerations are complex to include in the theoretical analysis. Also these losses do not have major impact on the performance characteristics curve. 5. Results and Discussions Fig. 5 indicates the experimental performance characteristics curve of the multistage pump. This performance characteristics curve is compared with the theoretical performance characteristics curve in Fig. 6. Fig. 7 shows the comparison between Euler head without consideration of slip factor, Euler head with consideration of slip factor, theoretical characteristics curve and the experimental characteristics curve. Here the trajectory of the theoretical characteristics curve is in congruence with the experimental characteristics curve.
Fig.7. Performance characteristics curve of the multistage centrifugal pump The deviation between the theoretical and the experimental curve is 2-13% for the discharge between 19 m3/hr to 91m3/hr is indicated in Fig. 6. This deviation is due to non-consideration of secondary losses in centrifugal pump in the analytical study. The secondary losses include disk friction loss, leakage loss and mechanical loss. In the analytical study, one dimensional profile of the pump is considered. But, to calculate the secondary losses 2dimensional or 3-dimensional profile of the pump has been considered. These considerations are complex to include in the theoretical analysis. Also these losses do not have major impact on the performance characteristics curve. 6. Conclusion The hydraulic loss calculation method shows deviation with respect to experimental results in the range of about 2% to 13%, for the range of discharge between 19 m 3/hr to 91m3/hr. This deviation between the theoretical and experimental result is due to negligence of the secondary losses in the analytical study to calculate various losses in the centrifugal pump.
Nilesh Tiwari et al. / Procedia Technology 23 (2016) 472 – 479
This method, which is already applied to predict the performance characteristics curve of the single-stage centrifugal pump, can also be applied to the multistage centrifugal pumps to predict its performance for various operation and geometric parameters. Acknowledgment I would like to show my greatest appreciation to the professional staff of G.I.P.C.L. (Gujarat Industries Power Company Limited), for their immense support and involvement throughout the tenure of training. Without their encouragement and guidance this report would not have materialized. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]
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