Tripping transients in a complex pumping system with ...

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Procedia Engineering (2011) Procedia Engineering 00 31 (2012) 428000–000 – 434

Procedia Engineering

www.elsevier.com/locate/procedia

International Conference on Advances in Computational Modeling and Simulation

Tripping transients in a complex pumping system with multi pumps in parallel Jianping Guoa, Lixiang Zhangb* a

Yunnan Province Hydraulic Investigation and Design Research Institute , Kunming 650051, China Department of Engineering Mechanics, Kunming University of Science and Technology, Kunming 650051, China

b

Abstract The paper reports the analysis and application of a large scale pumping station with complex machinery, electrical, and hydraulic systems. The interaction between the pump system and transient flow in case of a sudden tripping of power to the system was investigated by numerically solving governing equations of multi pumps in parallel operation. The transient flow in the hydraulic system and the dynamics of the pumps, for example, oscillation of the surge tank, water hammer wave propagation, dynamical fluid torque acting on the pump impeller, and dynamical pump speed, were obtained on the complete pump model. Results obtained with the present approach show a promising reference for operation of a large scale pumping station with complex system in undulating case due to a sudden power tripping.

© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Kunming University of Science and Technology Keywords: Pumping station; tripping pump; transient flow ; coupling dynamics

1. Introduction Fluid and machinery transients in pumping station with complex hydraulic, machinery and electric system involve high pressure variations with time and rotational dynamics of hydraulic machinery system, which may cause considerable oscillation of pressure and vibration of solid structure due to fluid-structure interaction in system. Although water hammer in pipe and flow-induced vibration of turbine machinery are probably well known and extensively studied phenomenon in this respect [1-6], the problem of the rapid * Corresponding author. Tel.: +86-871-3303561; fax: +86-871-3303561. E-mail address: [email protected]

1877-7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2012.01.1047

Jianping Guo andetLixiang ZhangEngineering / Procedia Engineering 31 (2012) 428 – 434 Jianping Guo al./ Procedia 00 (2011) 000–000

change of flow with undulating machinery system is still challenge to complex system in tripping power. At the same time, the negative flow of the water column in pipe by a high head drives a reversed speed of pump. For a large scale pumping station with multi pumps in parallel operation, the interaction between transient flow and pump system in tripping pump is strong enough to induce a severe fluid oscillation and structure vibration in system. In this paper, we consider interaction between pumps in parallel and transient flow by a tripping pump for a large scale pumping station equipped with a complex hydraulic system and high head, which involves 4 large power pumps in parallel, upstream reservoir, surge tank, long and branching pipe system, and downstream reservoir. Results show a promising reference for operation of a large scale pumping station with

complex system due to power tripping.

2. Governing equations For the pumping station as sketched in Fig.1 ( with numbered pipe segments ). We make assumptions:  The pipe segment that has been filled with water remains full and a well-defined system in analysis exists. This assumption allows for a one-dimensional model to be used.  The Darcy-Weisbach friction law developed for steady pipe flow can be used. This is a reasonable assumption for turbulent pipe flows.  The fluid compressibility is taken into account by the wave speed, while the mass density is considered to remain constant in transient analysis.

Fig. 1. Sketch of pump station system

The transient flow in a pipe segment is simplified by 1D flow and the continuity and momentum equations of the incompressible fluid are stated as: V H fV V g  0, (1) z 2D t  f g H V 2 u R   0 , (2) K f t z R t in pressure form p (3)  h, H f g

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where p = pressure, V = velocity, ρf = water mass density, g = gravitational acceleration, f = friction factor, D = pipe diameter, R = pipe radius, h = datum height at the control point, Kf = bulk modulus of the water, uR = pipe wall velocity in radius direction, z and t denote spatial coordinate and time, respectively. Using Hook’s law, the stresses in the pipe wall are written as u u E   ( z  R ) , (4) 2 R z 1  u u E z  ( z  R ) , (5) 2 R z 1  where E = Young modulus,  = Poisson ratio,  = stress in pipe wall, subscripts  and z are hook and longitudinal directions of the pipe. Conventional assumptions of the pressure wave propagation and pipe wall vibration are herein used, thus we obtain governing equations as fQ Q H 1 Q (6) g  0, A f t z 2 DA 2f 1 H 1 Q  0,  2 t cf gA f z

(7)

where Af = wet area of pipe, Q = flow rate, cf = speed of sound. The solution on MOC is expressed as fc f t n n cf (Qin1  Qin1 )  Qi 1 Qi 1  0 , C  : H in1  H in1  gA f 2 gDA 2f

C  : H in1  H in1 

cf gA f

(Qin1  Qin1 ) 

fc f t 2 gDA 2f

Qin1 Qin1  0 ,

The boundary conditions for serial and branching pipes as shown in Fig. 2 are respectively written as Q1n, N1s  Q2n,11 , H1n, N1s  H 2n,11 , N

 i 1

Qin1 

M

Q

n 1 j ,

H in1  H nj1

(i  1, N ; j  1, M ) ,

(8) (9)

(10) (11)

j 1

Fig. 2. Serial and branching pipes

3. Speed and head equations of tripping pump The dynamics of tripping pump depend upon transient flow in the pipe and dynamical characteristics of pumping system. For a single pump system with control points indicated A, B, and C as shown in Fig.3, the head and rotational speed of single pump trip are respectively affined by the Suter characteristics of the

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Jianping Guo andetLixiang ZhangEngineering / Procedia Engineering 31 (2012) 428 – 434 Jianping Guo al./ Procedia 00 (2011) 000–000

pump as H A  H B  H r ( 2  q 2 )WH  0 , ( 2  q 2 )WB 

(12)

T0 N   I r ( 0   )  0 , Tr Tr 30t

(13)

where WH and WB = Suter characteristics curves of pump, T = torque, N = rotational speed, I  = polar inertia of pump,  = dimensionless rotational speed, q = dimensionless flow rate, t = time step, subscript r and 0 are rated and initial values of pump. V P Fig. 3. Single pump system

For two parallel pumps as shown in Fig. 4, governing equations of pumps in tripping case are defined as

H A  H P1  H A  H P2 

H V 1q P1 q P1

 V21

H V 2 q P 2 q P 2

 V2 2

 HC  0 ,

（14）

 HC  0 ,

（15）

( P21  q P21 )WB P1 

TP10 N   I P1 P1r ( P10   P1 )  0 , TP1r TP1r 30t

（16）

( P2 2  q P2 2 )WB P 2 

TP 20 N   I P 2  P 2r ( P 20   P 2 )  0 , TP 2 r TP 2 r 30t

（17）

Fig. 4. Two pumps in parallel

By the same way, we can obtain tripping governing equations for three and four pumps in parallel work, and solve them in numerical scheme. The details on the derivation of the governing equations are in [1]. 4. Numerical results The characteristics of the centrifugal pumps used for the pumping station under consideration are plotted in Fig. 5 in QHE and Suter forms. The computational case is described as:

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 Three pumps are running in 606.2r/min, 606.1r/min, and 606r/min, respectively, and the total discharge of water supply is 23m3/s. the pressured tunnel to the surge tank from the upstream reservoir is 3332.1m long, and the pipe from the surge tank to the downstream reservoir is 829.6m through Pump 4 and 831.7m through Pump 1, respectively. The difference of the water levels of the reservoirs is 224.8m.  When the tripping for all three pumps happens, the valves are closed in duration of 40s of bilinear law.  The time step t is 0.01s, and the computation duration 1400s. The convergence controls for relative accuracy of discharge and head are 0.001 and 0.01, respectively. The main computational results are shown in Fig.6 through Fig.11.

Fig. 5 QHE curves and WH and WB curves of pump

Fig. 6. Head history at inlet of pump 1

Fig. 8. Discharge history of pump 1

Fig. 7. Head history at outlet of pump 1

Fig. 9. Rotational speed history of pump 1

Jianping GuoGuo andetLixiang Zhang Engineering / Procedia Engineering 31 (2012) 428 – 434 Jianping al./ Procedia 00 (2011) 000–000

Fig. 10. Flow velocity history at ball valve 1

Fig. 11. Head history at ball valve 1

Figs. 6 and 7 are pressure histories in head at the inlet and outlet of pump 1 after tripping. The head at inlet of the pump performs an oscillation with low frequency and long term due to the surge tank wave. The pressure at the outlet decreases suddenly to 135m from 254.2m in 5s because of tripping, and then rises up around 250m within time of 10s. It is clear that the tripping pump produces a big shock to the pump system in pressure. Figs. 8 and 9 show the flow rate history through the pump and the characteristics of the rotational speed change of the pump with time. From Fig.8, it is seen that maximum discharge is minus 10m3/s through the pump, which means that inversed flow in system happens before the valve is completely closed. Therefore, the reversed rotation of the pump occurs and the peak reversed speed is up to 683.1r/min as shown in Fig. 9. Figs. 10 and 11 present the fluid torque acting on the pump impeller and the characteristics of the transient flow at the valve. From Fig.10, it is seen that the change of the fluid torque is first down to 25 kNm rapidly because of tripping of the pump, and then the reserved torque increases into 350 kNm, more than normal torque of 300 kNm, and due to action of the back flow, the speed of the machinery set with GD2 of 94 tm2 (electrical machine plus pump) changes to minus 683.1r/min(reserved rotation) from plus 600 r/min (normal rotation) within 15s. Fig.11 plots the feature of the waterhammer wave in the pipe at the valve. The results have a valuable reference for operation of a large scale pumping station with complex system due to power tripping.

5. Conclusions The tripping transient characteristics of a large scale pumping station with a high head and complex system was analyzed. The influence of the interaction between pumps on the transient characteristics of the pumping system was investigated by numerically solving governing equations of the tripping pumps, and a valuable result to the control of the pumping station in tripping case was achieved. Acknowledgements The authors gratefully acknowledge the support from the National Natural Science Foundations of China (No. 50839003) and Yunnan (No. 2008GA027).

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References [1] Wylie EB, Streeter VL, Suo LS. Fluid Transients in Systems. Prentice-Hall, Englewood Cliffs, 1993. [2] Zhang LX, Tijsseling AS, Vardy AE, FSI analysis of liquid-filled pipes. J. Sound Vib, 224,1(1999): 69-99 [3] Weaver D S. Ziada S, Au-Yang M K, Chen S S. Paidoussis M P, Pettigrew M J. Flow-induced vibration in power and process plants components- Progress and prospects. ASME J. Pressure Vessel Technology, 122(2000): 339-48. [4] Li QS, Yang K, Zhang LX, Analytical solution for fluid-structure interaction in liquid-filled pipes subjected to impact-induced water hammer. ASCE J. Eng Mech. 129,12(2003): 1408-17 [5] Bergant A, Simpson AR, Tijsseling AS. Water hammer with column separation: A historical review. J. Fluid. Struct., 22 (2006), 135–71. [6] Malekpour A, Karney BW. Rapidly filling analysis of pipelines using an elastic model. 10th Int. Conf. on Pressure Surges, Edinburgh, UK, 2008, 539–52.