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The transient flow in a centrifugal pump during the discharge valve rapid opening process
Nuclear Engineering and Design 240 (2010) 4061–4068
Contents lists available at ScienceDirect
Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
The transient flow in a centrifugal pump during the discharge valve rapid opening process Wu Dazhuan ∗ , Wu Peng, Li Zhifeng, Wang Leqin Institute of Process Equipment, Zhejiang University, 38 Zheda Road, Hangzhou 310027, PR China
a r t i c l e
i n f o
Article history: Received 6 May 2010 Received in revised form 29 July 2010 Accepted 16 August 2010
a b s t r a c t During the rapid opening period of the discharge valve in the pump system commonly used in nuclear reactor operation, the flow-rate of the pump increases impulsively. In this paper, we report on experiment and numerical simulations which were implemented to investigate the external transient hydrodynamic performance and the internal flow mechanism of the pump during this transient process. External and internal characteristics under different flow-rates were measured with an experimental system. The simulation for steady conditions was based on detached eddy simulation (DES) and sliding mesh was verified by comparing the simulation with test results. More importantly, the transient characteristics during the valve’s rapid opening process were simulated using a similar method. Results show that the Q–H curve deviates from the steady-state value. The external characteristics are further explained by analyzing the relative velocity on the middle stream surfaces S1 m and S2 m between blades. The pump performance during the valve’s rapid opening process is influenced both by the fluid acceleration and instantaneous evolutions of the vortex structure. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Pumps play important roles in nuclear reactor coolant systems. Transient operations are commonly found, such as the pump’s starting and stopping, the flow-rate increasing and decreasing, and power failures in the centrifugal pump motors. The responses of the pump system in these operations show transient effects due to changes in the operating conditions. Boyd et al. (1961) performed a mathematical simulation for various transient conditions of coolant flow and pump speeds in a multiloop nuclear reactor system. They studied the transient phenomena due to power failure, starting pumps in idle loops, and the opening of an active pump’s discharge valve. They emphasized that one must consider all the components offering resistance change in the full primary coolant flow. Rapid changes in flow-rate will lead to sudden changes in pressure which propagate from the change point to the pipe system at the speed of sound in a liquid. This is called the water hammer phenomenon. In some pipeline systems, where a pump is used to lift liquid into a reservoir with a static head, the check valve downstream of the pump does not open until the static head is higher than the reservoir. Joseph and Hamill (1972) investigated the water hammer effects caused by valve openings in these operations.
∗ Corresponding author. Tel.: +86 139 89880802; fax: +86 571 87952406. E-mail address: [email protected] (D. Wu). 0029-5493/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2010.08.024
For theoretical analysis, many researchers have used hybrid models to solve the water hammer problem. Among them, the method of characteristics line (MOC) is the most popular one in modeling the valve-induced water hammer equations, because of its feasibility and advantages for complex systems (Kaliatka et al., 2007; Werner et al., 2008). Wenxi et al. (2008) evaluated the valve-induced water hammer phenomena in a parallel pumps feedwater system (PPFS) during the alternate startup process of parallel pumps. A code was developed to compute the transient phenomena, including the pressure wave vibration, local flow velocity, slamming of the check valve disc, etc. Most studies have focused on the water hammer in pipes when the valve is opening or closing, while the flow status in pumps has been given little attention. In a valve’s opening process, the flow-rate increases from zero to maximum rapidly, so most of the time pumps operate under off-design conditions. The flow fields under off-design conditions are influenced by complex separation and recirculation, thus making them highly turbulent and unsteady. Numerical calculations of performance for off-design conditions are extremely difficult using traditional steady-state methods, because of the need to control complex physical phenomena such as the boundary layer separation, vortex dynamics, interactions between rotational and stationary components, vibrations and noise, etc. (Felix et al., 2002; Rikke et al., 2003). There are many ways that cause the flow-rate increasing or decreasing. In this paper, rapid opening of the discharge valve is chosen as a way to achieve the process that flow-rate is increas-
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Nomenclature A0 CFL d2 H Hc Hd Hi Leq n ns Q Qd Qi R Re t t h
cross sectional area (m2 ) Courant Friedrichs Lewy number, CFL = Wt/x outer diameter of the impeller (mm) total head of the pump (m) apparent static head (m) total head of the pump at design condition (m) indicated total head (m) length of equivalent pipe (m) rotational speed (rpm) specific speed, ns = 3.65n Q /H 3/4 flow-rate (m3 /h) flow-rate at design condition (m3 /h) instantaneous flow-rate (m3 /h) radius (m) Reynolds number, Re = U2 D2 /v time (s) time step size (s) hydraulic efficiency
ing rapidly. During this period, the valve is opened within a few seconds, the flow rate of the pump increases rapidly. Numerical and experimental results of external and internal characteristics show significant transient effects, which differ from steady-state processes. These unsteady phenomena are not predictable with the conventional steady-state simulation approach. During recent years, with the expansion of centrifugal pump applications, studies on transient characteristics during start-up period have received increased attention (Lefebvre and Barker, 1995; Kazem et al., 2007). Analysis methods for transient processes can be understood for flow-rate changes caused by fast opening and closing valves. Wang et al. (2008) used the dynamic mesh method for 2D simulation of a centrifugal pump during the start-up period, but this method requires considerable computational resources for the large deformation and update load of the mesh in rotational regions. Wu et al. (2009) developed a method to simulate the flow field during the start-up period, based on the sliding mesh technique, in which interfaces were used to connect the rotational impeller and the stationary components. And experiments were also carried out to verify the reliability of the simulation. Wu et al. (2010) also reported some experimental studies on hydrodynamic performance of a cavitating centrifugal pump during transient operation. In order to improve the accuracy of the numerical simulations and better understand the flow in the centrifugal pumps during transient processes, a numerical method for simulations at off-design conditions is proposed and then the simulation is carried out. The method is validated by comparing with the experimental results both from the aspects of external and internal characteristics. Based on the experimental and numerical results of steady-state performances, a simulation model of the unsteady state is built, and a similar simulation method is applied for the simulation of the valve’s rapid opening processes. Both the external and internal characteristics are analyzed. The results can be used as references for future studies and applications. 2. Numerical simulations at steady flow-rate 2.1. Model and parameter The pump under investigation, shown in Fig. 1, is a shrouded centrifugal pump with a specific speed of ns = 103 and hydraulic
Fig. 1. Geometry of the centrifugal pump.
efficiency of h = 70%. The impeller has an outer diameter of d2 = 238 mm and four backswept blades. In order to measure the flow field by the particle image velocimetry (PIV) technique, the case is designed like a box with a diffuser. The diameter of inlet pipe is 200 mm and outlet is 156 mm. The pump is designed to rotate at n = 1475 rpm, operate at a flow-rate of Qd = 332 m3 /h and provide a pressure rise equivalent to a head of Hd = 7.1 m. The rated Reynolds number (Re = U2 D2 /v) based on the outer diameter of the impeller is 4.4 × 106 . 2.2. CFD code The flow fields at off-design conditions are highly turbulent and unsteady. Due to the complex separation and recirculation, numerical simulations of the performances for off-design conditions will be extremely difficult. Therefore, a reliable turbulence model must be chosen to simulate the performances more accurately. Most of the numerical simulations for engineering applications at high Reynolds numbers are performed using the Reynolds averaged Navier–Stockes (RANS) turbulence models. Tutar and Hold (2001) and Benim et al. (2008) have pointed out, however, that the RANS model is not appropriate for computations of transient turbulent separated flow. While the RANS models are appropriate for simulations of attached flows, they fail to accurately capture the complex flow structures in regimes substantially different from the thin shear and attached boundary layers. Thus, they are not suitable for calculating the flow with separation and recirculation under off-design conditions. Simulation strategies such as direct numerical simulation (DNS) and large eddy simulation (LES) are attractive as an alternative for predictions of flow fields where RANS is deficient. But they will carry a prohibitive computational cost for resolving boundary layer turbulence at high Reynolds numbers. The detached eddy simulation (DES) has been recently developed, and is one of the most widely used models for high speed turbulent flows with massive separations. The DES model was developed to combine RANS in the attached boundary layers with LES in the shear layers and separated flow regions (Spalart et al., 1997). It is a unified approach based on the adoption of a single turbulence model. It functions as a sub-grid scale LES model in the separated flow regions where the grid is nearly isotropic, and as a RANS model in the attached boundary layer regions (Basu et al., 2005). It retains the essential features of LES type method as well as employs a computationally cheaper RANS method in regions where it is appropriate.
D. Wu et al. / Nuclear Engineering and Design 240 (2010) 4061–4068
Applications of the DES models for a wide variety of problems involving separated flow configurations have shown certain degrees of success relative to the RANS predictions. But DES models have not been so widely used in pumps, thus further trials are necessary for pump applications. Realizable-DES is available in the software package FLUENT 6.3. The time dependent term scheme is 2nd-order implicit. The pressure–velocity coupling is calculated through the SIMPLEC algorithm. A second-order upwind scheme with numerical underrelaxation is applied for the discretization of convection term and central difference schemes for diffusion terms. 2.3. Computational domain and grid The pump is divided into four parts: inlet, impeller, diffuser and case. Impeller is rotary and the other parts are stationary. The geometry of the centrifugal pump is discretized by unstructured tetrahedral meshes. In order to check the influence of different grids on the results, meshes with different quantities of elements are tested. 2.4. Boundary conditions at operating conditions Simulations are carried out over a wide range of operating points, from shutoff to the maximum flow rate. Walls are modeled using the standard wall functions. Velocity in axial direction is specified as inlet boundary, while the average static pressure field is defined as the outlet boundary. The inlet and outlet boundary conditions are placed far away from the impeller component in order to minimize the influence of the boundary conditions on the flow field. The flow in the impeller is defined as moving mesh zone, while the flow in the inlet pipe, diffuser, and outlet pipe is calculated in the stationary reference frame. The connection between the rotary impeller and the stationary components is linked by interfaces. That means that the node of each side of the interface does not have to match while the meshes are moved. This method is called sliding mesh method which is commonly used for unsteady flow field simulation of pumps (Croba and Kueny, 1996; Gonzalez et al., 2002). Six different flow-rates with a rotational speed of 1475 rpm are simulated: 0, 70, 130, 186, 233, and 332 m3 /h.
Table 1 Characteristics of the mesh structure, boundary conditions, and numerical setup of the steady flow simulations. Mesh structure Total number of cells Cells in inlet section Cells in impeller Cells in diffuser Cells in outlet section Cells in case section
3,702,328 395,116 518,836 319,287 80,512 2,388,577
2,334,914 226,818 329,344 183,893 43,266 1,551,593
1,436,774 118,694 171,570 97,985 20,500 1,028,025
Boundary condition Velocity inlet (m/s) Pressure outlet (Pa) Wall
0.619 0 No-slip
1.149 0
1.644 0
2.060 0
2.935 0
Numerical setup Number of time steps Time step (s) Time steps per revolution CPU time per time step (min) Total computational time (h)
2000 5e−4 80 10 333
4.5 150
3.3 110
Table 2 numerical setup of the unsteady flow simulations. Numerical setup
1s
0.5 s
0.25 s
Number of time steps Time step (s) Time steps per revolution CPU time per time step (min) Total computational time (h)
2400 5e−4 80 10 400
1200 5e−4 80 10 200
600 5e−4 80 10 100
same except the inlet velocity, which is defined by a UDF program. During the period of increasing flow-rate in a centrifugal pump, the flow-rate increases rapidly from shut-off to its operating flow-rate and then remains at this flow-rate. Variations of the flow-rate under three different valve’s opening times are defined by functions (1)–(3). The previously calculated result of flow field at shut-off condition is used as the initial flow field for unsteady flow simulations.
Q (t) =
2.5. Numerical setup In order to resolve the real temporal variation of the flow, the time-step has been adjusted to t = 5 × 10−4 s, which ensures a reasonable CFL number based on physical time less than 1.0. This time-step is equivalent to 80 time-steps per impeller revolution. The flow fields at different flow-rates have been iterated for 2000 time-steps, respectively, equivalent to 24 revolutions. Simulations have been parallelly performed on a Linux PC cluster of eight Intel Xeon processors (3.2 GHz) at institute of process equipment in Zhejiang University. An overview of mesh structure, boundary conditions, and numerical setup of the simulations is provided in Table 1.
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Q (t) =
Q (t) =
⎧ ⎪ ⎨ ⎪ ⎩ ⎧ ⎪ ⎨ ⎪ ⎩
0 233(t
233
t < 0.07 s 0.07 s ≤ t < 1.07 s
0
t < 0.07 s 0.07 s ≤ t < 0.57 s
233
t ≥ 0.57 s
0
t < 0.07 s
932(t
− 0.07) (m3 /h) 233
(1)
t ≥ 1.07 s
466(t − 0.07) (m3 /h)
⎧ ⎪ ⎨ ⎪ ⎩
− 0.07) (m3 /h)
0.07 s ≤ t < 0.32 s
(2)
(3)
t ≥ 0.32 s
An overview of the numerical setup is provided in Table 2. 4. Results and discussion
3. Numerical simulations of valve rapid opening process In practical applications, flow-rate may be increased impulsively from shutoff to maximum. In these operations, pumps operate under off-design conditions. Based on the simulated method above, this special transient operation can be simulated using a similar method. To compare different phenomena between steady flow-rate and increasing flow-rate operations, all of the numerical setups are the
4.1. Comparison of external characteristics between steady flow-rate simulations and experimental results Six different operating conditions at a flow-rate of 0, 70, 130, 186, 233 and 332 m3 /h are simulated under a rotational speed of 1475 rpm. Because the simulation method is unsteady, rotor–stator interaction phenomena between impeller and case can be captured (Gonzalez et al., 2002). One impeller revolution has 80 time-steps
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Fig. 2. Fluctuant curve of the instantaneous head. Fig. 5. Internal flow comparison between simulation and PIV test.
Fig. 3. General view of the pump. Fig. 6. Comparison between steady and unsteady flow-rate simulation.
Fig. 4. Comparison between experimental result and simulated results with different grid quantity.
Fig. 7. Total head comparison between steady and unsteady flow-rate simulation.
D. Wu et al. / Nuclear Engineering and Design 240 (2010) 4061–4068
and the impeller has four vanes, so the period of head oscillations caused by rotor–stator interaction is about 20 time-steps. Take the curve of Q = 233 m3 /h in Fig. 2 as an example. There are four obvious peaks which are nearly 14 m, and the time-steps are 126, 150, 173 and 190. So the period of the curve oscillation is nearly 20 time steps, it is equal to the rotor–stator interaction period. Beside, the amplitude of the instantaneous head gradually increases as the flow-rate increases. This is because fluid discharged from diffuser includes two parts: fluid circularly flowing in diffuser and that discharged from impeller. The former flow is steady and the latter fluctuates, which causes a fluctuant head. As the flow-rate is decreased, fluid which flows from impeller to diffuser is also decreased. Accordingly, the fluctuation of head is decreased. In order to compare with experimental results, the instantaneous head was averaged in a rotational period of impeller, which
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is called available head. Steady performance of the pump was tested in a test rig, and the case part is shown in Fig. 3. The accuracy of the flow rate and pressure sensor is 0.5%. Fig. 4 shows simulated results of three different grid quantities and the corresponding experimental results. Through comparison, one concludes that a grid quantity of 3.7 × 106 can accurately simulate the external characteristics. As shown in Fig. 4, the maximum error comparing between simulated and experimental results is about 7% at shut-off condition. This is because the flow field at shutoff condition is so complex that some vortices cannot be captured accurately. As the flow-rate increases, simulated results are well in agreement with experimental results. At the flow rate of 70 m3 /h, the error is 3%. The steady state simulation is only used for method validation, such accuracy is enough for unsteady flow rate simulation and engineering applications.
Fig. 8. Velocity vector graphs at unsteady condition of different flow-rate.
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4.2. Internal flow comparison of steady flow-rate between simulations and experiments The velocity vector graph on cross-section of the pump shown in Fig. 3 is caught by a 2D PIV device. The comparison between simulations and PIV experimental results at shutoff condition is shown in Fig. 5. The maximum velocity in simulation is about 3 m/s, while at the same position of the measured velocity is 2 m/s. An anticlockwise vortex exists above the diffuser in the two graphs, because at shut-off condition the fluid is blocked off by valves and cannot discharge out. It continues to circulate in the pump. Comparing with the flow structure of simulated results shown in Fig. 5, flow captured by the PIV method is a little flat. This is because bubbles produced in the pump at start-up affect the PIV results. In addition, the simulated model has its own error. So the PIV result can only be a qualitative comparison. By comparing the internal and external characteristics of the pump between experiment and simulation, this simulation method can be used for pump simulation from shutoff to maximum flowrate.
In the present paper, as shown in Fig. 1, the passage area of the pump does not change so significantly, so the average of the area is taken as the passage area A(s), and length of the middle streamline is taken as Leq . Following Eq. (4), the total head of the pumps can be calculated. As shown in Fig. 7, at low flow-rate, the head of 1 s opening time is the lowest and is highest at 0.25 s, with 0.5 s being intermediate. Meanwhile, at high flow-rates, the three different opening ways are nearly the same. To explain this phenomenon, the internal flow of the pump must be analyzed. 4.4. Internal flow simulation result of valve rapid opening process To analyze the transient evolution of the flow field during the process of variable flow-rates, simulated results of flow-rate at 1.163, 82.44, 164.14 and 251.72 m3 /h were undertaken. Comparison between different flow-rates of velocity vector graphs on cross-section near the diffuser is shown in Fig. 8. As can be seen from the graphs, large-scale vortices exist in impeller and diffuser at
4.3. External characteristic simulation result of valve rapid opening process The method mentioned above can accurately calculate the external characteristics and internal flow at conditions from shutoff to maximum flow-rate. Based on this method, unsteady flow is simulated with the shut-off condition as the initial flow field. Similarly, instantaneous head is also averaged to obtain the available head. Simulated results of steady state and increased flow-rate with different valve opening times are shown in Fig. 6. The unsteady Q–H curve lies under the steady Q–H curve. With increases in flow-rate, the velocity of the fluid in pipes increases, and part of the energy exported by the pump is used to provide fluid acceleration. Thus, the faster the valve opens, the greater the head loss. With increases in flow-rate, the transient head curve approaches the steady-state curve gradually. This phenomenon agrees well with the experimental results of Wang et al. (2003). With increases in flow-rate, velocity of the fluid in pipes increases, part of the energy exported by the pump is used to provide fluid acceleration, so at the same flow-rate unsteady flow process has a smaller head. This is because the flow-rate increases to the design operating point, the flow separation phenomenon in the impeller lessens, causing the transient curves to move closer to the steadystate curve. In order to analyze the transient effect in the process of flowrate increases, it is necessary to differentiate the total head of the pump H(t) from the indicated total head between the suction port and the discharge of the pump Hi (t). The total head is affected by the acceleration of the water contained in the pump casing. So the true total head rise H(t) is obtained by subtracting the apparent static head Hc (t) due to the acceleration from the indicated total head Hi (t), as the following equation shows (Tsukamoto and Ohashi, 1982): H(t) = Hi (t) − Hc (t) = Hi (t) +
L dQ (t) eq i gA0
dt
(4)
where the pump is represented by a straight pipe with cross sectional area A0 and length Leq . The equivalent pipe Leq of the pump is calculated by the equation:
L
Leq = s=0
A 0 A(s)
ds
(5)
where s is the distance measured from the suction port, and L is the total path length.
Fig. 9. Relative velocity evolutions of different conditions on the middle stream surfaces S1 m .
D. Wu et al. / Nuclear Engineering and Design 240 (2010) 4061–4068
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5. Conclusion Based on the experimental and simulated results of internal and external characteristics at steady operation from shutoff condition to design condition, DES and silding mesh were used to explore the transient characteristic of the process when valve was rapidly opened. The results show that: (1) Simulated results of steady operation using DES model agree well with the experimental results, and the phenomenon of head fluctuation caused by the impeller–volute interation is well predicted. The results indicate that the proposed method is capable of solving complex flow in the centrifugal pump under off-design conditions. (2) The Q–H curve of valve opening process lies under the steady Q–H curve, which reflects the acceleration effect when the flowrate is increasing. (3) Besides the acceleration effect, a transits effect of the vortics revolution is also a main factor which influences the performance of the pump. In this context, flow-rate variations are defined as linear functions and outlet pressure is set to constant, which is different from the actual situation. the pipelines and pump should be coupled together for further study so that the boundary conditions of flow-rate and pressure better approximate the actual situation. The contents and conclusions of the current work can provide references for the performance prediction, design optimization and fluid control of the pump used in the transient process of valve rapid opening. Acknowledgement Fig. 10. Relative velocity evolutions of different conditions on the middle stream surfaces S2 m .
low flow-rate. As the flow-rate increases gradually, more compact vortices are generated in the flow passage of the impeller, while vortices in the case are smaller, fluid flowing to the outlet more intensively. The main reason is that at off-design conditions, due to the liquid viscosity, flow separation occurs on the blade surface, and thus vortices are generated. As the flow-rate increases, flow separation on the blade surface decreases, and vortices in the impeller are also decreased. Fig. 9 shows the relative velocity evolutions of different opening times at flow-rate of 100 m3 /h (left) and 233 m3 /h (right) on the middle stream surfaces S1 m in the impeller. As can be seen from the graphs, when the valve is opened in 0.25 s, at a flowrate of 100 m3 /h, vortices on the middle stream surfaces S1 m are small and compact; when valve is opened in some vortices develop at the trailing edge of the suction face; when valve is opened in large vortices can be observed on the pressure face. At the flowrate of 233 m3 /h, there is almost no difference on the middle stream surfaces S1 m , and the internal flow is very smooth along the blades. Fig. 10 shows the relative velocity evolutions of different opening times at a flow-rate of 100 m3 /h and 233 m3 /h on the middle stream surfaces S2 m in the impeller. As the opening time increases, the structure of the vortices becomes more complex at a flow-rate of 100 m3 /h, while the internal flow is very smooth along the blades at a flow rate of 233 m3 /h. As was stated above, the internal flow shown in Figs. 9 and 10 agrees with Q–H curve shown in Fig. 7 on the whole. Pump performances in valve opening processes are both influenced by the acceleration of the fluid and transits effect of flow revolution.
This study was performed as part of National Natural Science Foundation of China, the project numbers are 50776077, 50979095 and 50906074. This support is gratefully acknowledged. References Basu, D., Hamed, A., Das, K., 2005. DES Hybrid RANS/LES and PANS model for unsteady separated turbulent flow simulations. In: Proceedings of FEDSM 5, pp. 19–23. Benim, A.C., Pasqualotto, E., Suh, S.H., 2008. Modeling turbulent flow past a circular cylinder by RANS, URANS LES and DES. Progress in Computational Fluid Dynamics 8, 299–307. Boyd, G.M., Rosser, R.M., Cardwell, B.B., 1961. Transients flow performance in a multiloop nuclear reactor system. Nuclear Science and Engineering 9, 442–454. Croba, D., Kueny, J., 1996. Numerical calculation of 2D, unsteady flow in centrifugal pumps: impeller and volute interaction. International Journal for Numerical Method in Fluids 22, 467–481. Felix, A., Peter, H., Philippe, D., 2002. CFD calculation of a mixed flow pump characteristic from shutoff to maximum flow. Journal of Fluid Engineering 124, 798–802. Gonzalez, J., Fernandez, J., Blanco, E., 2002. Numerical simulation of the dynamic effects due to impeller–volute interaction in a centrifugal pump. Journal of Fluid Engineering 124, 348–354. Joseph, L., Hamill, F.A., 1972. Start-up pressures in short pump discharge lines. Journal of the Hydraulic Division, Proceedings of ASCE 98, 1117–1125. Kaliatka, A., Uspuras, E., Vaisnoras, M., 2007. Benchmarking analysis of water hammer effects using RELAP5 code and development of RBMK-1500 reactor main circulation circuit model. Annals of Nuclear Energy 34, 1–12. Kazem, F., Anis, B., Franscesco, D., 2007. A model for the analysis of pump start-up transients in Tehran Research Reactor. Progress in Nuclear Energy 49, 499–510. Lefebvre, P.J., Barker, W.P., 1995. Centrifugal pump performance during transient operation. Journal of Fluid Engineering 117, 123–128. Rikke, K., Christian, B., Nicholas, P., 2003. Flow in a centrifugal pump impeller at design and off-design conditions. Part II. Large eddy simulations. Journal of Fluid Engineering 125, 73–83. Spalart, P.R., Jou, W.H., Allmaras, S.R., 1997. Comments on the feasibility of LES for wings, and on a hybrid RANS/LES approach. In: First AFOSR International Conference on DNS/LES. Tsukamoto, H., Ohashi, H., 1982. Transient characteristics of a centrifugal pump during starting period. Journal of Fluid Engineering 104, 6–13.
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Tutar, M., Hold, A.E., 2001. Computational modelling of flow around a circular cylinder in sub-critical flow regime with various turbulence models. International Journal for Numerical Methods in Fluids 35, 763–784. Wang, L., Wu, D., Zheng, S., 2003. Experimental study on transient performance of a mixed-flow-pump. Fluid Machinery 31, 1–3. Wang, L., Li, Z., Dai, W., et al., 2008. 2-D numerical simulation on transient flow in centrifugal pump during starting period. Journal of Engineering Thermophysics 29, 1319–1322. Wenxi, T., Su, G.H., Wang, G., 2008. Numerical simulation and optimization on valveinduced water hammer characteristics for parallel pump feedwater system. Annals of Nuclear Energy 35, 2280–2287.
Werner, B., Audrius, J., Annalisa, M., 2008. Analysis of the capability of system codes to model cavitation water hammers: simulation of UMSICHT water hammer experiments with TRACE and RELAP5. Nuclear Engineering and Design 238, 1129–1145. Wu, D., Xu, B., Li, Z., et al., 2009. Numerical simulation on internal flow of centrifugal pump during transient operation. Journal of Engineering Thermophysics 30, 1319–1322. Wu, D., Wang, L., Hao, Z., et al., 2010. Experimental study on hydrodynamic performance of a cavitating centrifugal pump during transient operation. Journal of Mechanical Science and Technology 24, 575–582.
Contents lists available at ScienceDirect
Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
The transient flow in a centrifugal pump during the discharge valve rapid opening process Wu Dazhuan ∗ , Wu Peng, Li Zhifeng, Wang Leqin Institute of Process Equipment, Zhejiang University, 38 Zheda Road, Hangzhou 310027, PR China
a r t i c l e
i n f o
Article history: Received 6 May 2010 Received in revised form 29 July 2010 Accepted 16 August 2010
a b s t r a c t During the rapid opening period of the discharge valve in the pump system commonly used in nuclear reactor operation, the flow-rate of the pump increases impulsively. In this paper, we report on experiment and numerical simulations which were implemented to investigate the external transient hydrodynamic performance and the internal flow mechanism of the pump during this transient process. External and internal characteristics under different flow-rates were measured with an experimental system. The simulation for steady conditions was based on detached eddy simulation (DES) and sliding mesh was verified by comparing the simulation with test results. More importantly, the transient characteristics during the valve’s rapid opening process were simulated using a similar method. Results show that the Q–H curve deviates from the steady-state value. The external characteristics are further explained by analyzing the relative velocity on the middle stream surfaces S1 m and S2 m between blades. The pump performance during the valve’s rapid opening process is influenced both by the fluid acceleration and instantaneous evolutions of the vortex structure. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Pumps play important roles in nuclear reactor coolant systems. Transient operations are commonly found, such as the pump’s starting and stopping, the flow-rate increasing and decreasing, and power failures in the centrifugal pump motors. The responses of the pump system in these operations show transient effects due to changes in the operating conditions. Boyd et al. (1961) performed a mathematical simulation for various transient conditions of coolant flow and pump speeds in a multiloop nuclear reactor system. They studied the transient phenomena due to power failure, starting pumps in idle loops, and the opening of an active pump’s discharge valve. They emphasized that one must consider all the components offering resistance change in the full primary coolant flow. Rapid changes in flow-rate will lead to sudden changes in pressure which propagate from the change point to the pipe system at the speed of sound in a liquid. This is called the water hammer phenomenon. In some pipeline systems, where a pump is used to lift liquid into a reservoir with a static head, the check valve downstream of the pump does not open until the static head is higher than the reservoir. Joseph and Hamill (1972) investigated the water hammer effects caused by valve openings in these operations.
∗ Corresponding author. Tel.: +86 139 89880802; fax: +86 571 87952406. E-mail address: [email protected] (D. Wu). 0029-5493/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2010.08.024
For theoretical analysis, many researchers have used hybrid models to solve the water hammer problem. Among them, the method of characteristics line (MOC) is the most popular one in modeling the valve-induced water hammer equations, because of its feasibility and advantages for complex systems (Kaliatka et al., 2007; Werner et al., 2008). Wenxi et al. (2008) evaluated the valve-induced water hammer phenomena in a parallel pumps feedwater system (PPFS) during the alternate startup process of parallel pumps. A code was developed to compute the transient phenomena, including the pressure wave vibration, local flow velocity, slamming of the check valve disc, etc. Most studies have focused on the water hammer in pipes when the valve is opening or closing, while the flow status in pumps has been given little attention. In a valve’s opening process, the flow-rate increases from zero to maximum rapidly, so most of the time pumps operate under off-design conditions. The flow fields under off-design conditions are influenced by complex separation and recirculation, thus making them highly turbulent and unsteady. Numerical calculations of performance for off-design conditions are extremely difficult using traditional steady-state methods, because of the need to control complex physical phenomena such as the boundary layer separation, vortex dynamics, interactions between rotational and stationary components, vibrations and noise, etc. (Felix et al., 2002; Rikke et al., 2003). There are many ways that cause the flow-rate increasing or decreasing. In this paper, rapid opening of the discharge valve is chosen as a way to achieve the process that flow-rate is increas-
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Nomenclature A0 CFL d2 H Hc Hd Hi Leq n ns Q Qd Qi R Re t t h
cross sectional area (m2 ) Courant Friedrichs Lewy number, CFL = Wt/x outer diameter of the impeller (mm) total head of the pump (m) apparent static head (m) total head of the pump at design condition (m) indicated total head (m) length of equivalent pipe (m) rotational speed (rpm) specific speed, ns = 3.65n Q /H 3/4 flow-rate (m3 /h) flow-rate at design condition (m3 /h) instantaneous flow-rate (m3 /h) radius (m) Reynolds number, Re = U2 D2 /v time (s) time step size (s) hydraulic efficiency
ing rapidly. During this period, the valve is opened within a few seconds, the flow rate of the pump increases rapidly. Numerical and experimental results of external and internal characteristics show significant transient effects, which differ from steady-state processes. These unsteady phenomena are not predictable with the conventional steady-state simulation approach. During recent years, with the expansion of centrifugal pump applications, studies on transient characteristics during start-up period have received increased attention (Lefebvre and Barker, 1995; Kazem et al., 2007). Analysis methods for transient processes can be understood for flow-rate changes caused by fast opening and closing valves. Wang et al. (2008) used the dynamic mesh method for 2D simulation of a centrifugal pump during the start-up period, but this method requires considerable computational resources for the large deformation and update load of the mesh in rotational regions. Wu et al. (2009) developed a method to simulate the flow field during the start-up period, based on the sliding mesh technique, in which interfaces were used to connect the rotational impeller and the stationary components. And experiments were also carried out to verify the reliability of the simulation. Wu et al. (2010) also reported some experimental studies on hydrodynamic performance of a cavitating centrifugal pump during transient operation. In order to improve the accuracy of the numerical simulations and better understand the flow in the centrifugal pumps during transient processes, a numerical method for simulations at off-design conditions is proposed and then the simulation is carried out. The method is validated by comparing with the experimental results both from the aspects of external and internal characteristics. Based on the experimental and numerical results of steady-state performances, a simulation model of the unsteady state is built, and a similar simulation method is applied for the simulation of the valve’s rapid opening processes. Both the external and internal characteristics are analyzed. The results can be used as references for future studies and applications. 2. Numerical simulations at steady flow-rate 2.1. Model and parameter The pump under investigation, shown in Fig. 1, is a shrouded centrifugal pump with a specific speed of ns = 103 and hydraulic
Fig. 1. Geometry of the centrifugal pump.
efficiency of h = 70%. The impeller has an outer diameter of d2 = 238 mm and four backswept blades. In order to measure the flow field by the particle image velocimetry (PIV) technique, the case is designed like a box with a diffuser. The diameter of inlet pipe is 200 mm and outlet is 156 mm. The pump is designed to rotate at n = 1475 rpm, operate at a flow-rate of Qd = 332 m3 /h and provide a pressure rise equivalent to a head of Hd = 7.1 m. The rated Reynolds number (Re = U2 D2 /v) based on the outer diameter of the impeller is 4.4 × 106 . 2.2. CFD code The flow fields at off-design conditions are highly turbulent and unsteady. Due to the complex separation and recirculation, numerical simulations of the performances for off-design conditions will be extremely difficult. Therefore, a reliable turbulence model must be chosen to simulate the performances more accurately. Most of the numerical simulations for engineering applications at high Reynolds numbers are performed using the Reynolds averaged Navier–Stockes (RANS) turbulence models. Tutar and Hold (2001) and Benim et al. (2008) have pointed out, however, that the RANS model is not appropriate for computations of transient turbulent separated flow. While the RANS models are appropriate for simulations of attached flows, they fail to accurately capture the complex flow structures in regimes substantially different from the thin shear and attached boundary layers. Thus, they are not suitable for calculating the flow with separation and recirculation under off-design conditions. Simulation strategies such as direct numerical simulation (DNS) and large eddy simulation (LES) are attractive as an alternative for predictions of flow fields where RANS is deficient. But they will carry a prohibitive computational cost for resolving boundary layer turbulence at high Reynolds numbers. The detached eddy simulation (DES) has been recently developed, and is one of the most widely used models for high speed turbulent flows with massive separations. The DES model was developed to combine RANS in the attached boundary layers with LES in the shear layers and separated flow regions (Spalart et al., 1997). It is a unified approach based on the adoption of a single turbulence model. It functions as a sub-grid scale LES model in the separated flow regions where the grid is nearly isotropic, and as a RANS model in the attached boundary layer regions (Basu et al., 2005). It retains the essential features of LES type method as well as employs a computationally cheaper RANS method in regions where it is appropriate.
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Applications of the DES models for a wide variety of problems involving separated flow configurations have shown certain degrees of success relative to the RANS predictions. But DES models have not been so widely used in pumps, thus further trials are necessary for pump applications. Realizable-DES is available in the software package FLUENT 6.3. The time dependent term scheme is 2nd-order implicit. The pressure–velocity coupling is calculated through the SIMPLEC algorithm. A second-order upwind scheme with numerical underrelaxation is applied for the discretization of convection term and central difference schemes for diffusion terms. 2.3. Computational domain and grid The pump is divided into four parts: inlet, impeller, diffuser and case. Impeller is rotary and the other parts are stationary. The geometry of the centrifugal pump is discretized by unstructured tetrahedral meshes. In order to check the influence of different grids on the results, meshes with different quantities of elements are tested. 2.4. Boundary conditions at operating conditions Simulations are carried out over a wide range of operating points, from shutoff to the maximum flow rate. Walls are modeled using the standard wall functions. Velocity in axial direction is specified as inlet boundary, while the average static pressure field is defined as the outlet boundary. The inlet and outlet boundary conditions are placed far away from the impeller component in order to minimize the influence of the boundary conditions on the flow field. The flow in the impeller is defined as moving mesh zone, while the flow in the inlet pipe, diffuser, and outlet pipe is calculated in the stationary reference frame. The connection between the rotary impeller and the stationary components is linked by interfaces. That means that the node of each side of the interface does not have to match while the meshes are moved. This method is called sliding mesh method which is commonly used for unsteady flow field simulation of pumps (Croba and Kueny, 1996; Gonzalez et al., 2002). Six different flow-rates with a rotational speed of 1475 rpm are simulated: 0, 70, 130, 186, 233, and 332 m3 /h.
Table 1 Characteristics of the mesh structure, boundary conditions, and numerical setup of the steady flow simulations. Mesh structure Total number of cells Cells in inlet section Cells in impeller Cells in diffuser Cells in outlet section Cells in case section
3,702,328 395,116 518,836 319,287 80,512 2,388,577
2,334,914 226,818 329,344 183,893 43,266 1,551,593
1,436,774 118,694 171,570 97,985 20,500 1,028,025
Boundary condition Velocity inlet (m/s) Pressure outlet (Pa) Wall
0.619 0 No-slip
1.149 0
1.644 0
2.060 0
2.935 0
Numerical setup Number of time steps Time step (s) Time steps per revolution CPU time per time step (min) Total computational time (h)
2000 5e−4 80 10 333
4.5 150
3.3 110
Table 2 numerical setup of the unsteady flow simulations. Numerical setup
1s
0.5 s
0.25 s
Number of time steps Time step (s) Time steps per revolution CPU time per time step (min) Total computational time (h)
2400 5e−4 80 10 400
1200 5e−4 80 10 200
600 5e−4 80 10 100
same except the inlet velocity, which is defined by a UDF program. During the period of increasing flow-rate in a centrifugal pump, the flow-rate increases rapidly from shut-off to its operating flow-rate and then remains at this flow-rate. Variations of the flow-rate under three different valve’s opening times are defined by functions (1)–(3). The previously calculated result of flow field at shut-off condition is used as the initial flow field for unsteady flow simulations.
Q (t) =
2.5. Numerical setup In order to resolve the real temporal variation of the flow, the time-step has been adjusted to t = 5 × 10−4 s, which ensures a reasonable CFL number based on physical time less than 1.0. This time-step is equivalent to 80 time-steps per impeller revolution. The flow fields at different flow-rates have been iterated for 2000 time-steps, respectively, equivalent to 24 revolutions. Simulations have been parallelly performed on a Linux PC cluster of eight Intel Xeon processors (3.2 GHz) at institute of process equipment in Zhejiang University. An overview of mesh structure, boundary conditions, and numerical setup of the simulations is provided in Table 1.
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Q (t) =
Q (t) =
⎧ ⎪ ⎨ ⎪ ⎩ ⎧ ⎪ ⎨ ⎪ ⎩
0 233(t
233
t < 0.07 s 0.07 s ≤ t < 1.07 s
0
t < 0.07 s 0.07 s ≤ t < 0.57 s
233
t ≥ 0.57 s
0
t < 0.07 s
932(t
− 0.07) (m3 /h) 233
(1)
t ≥ 1.07 s
466(t − 0.07) (m3 /h)
⎧ ⎪ ⎨ ⎪ ⎩
− 0.07) (m3 /h)
0.07 s ≤ t < 0.32 s
(2)
(3)
t ≥ 0.32 s
An overview of the numerical setup is provided in Table 2. 4. Results and discussion
3. Numerical simulations of valve rapid opening process In practical applications, flow-rate may be increased impulsively from shutoff to maximum. In these operations, pumps operate under off-design conditions. Based on the simulated method above, this special transient operation can be simulated using a similar method. To compare different phenomena between steady flow-rate and increasing flow-rate operations, all of the numerical setups are the
4.1. Comparison of external characteristics between steady flow-rate simulations and experimental results Six different operating conditions at a flow-rate of 0, 70, 130, 186, 233 and 332 m3 /h are simulated under a rotational speed of 1475 rpm. Because the simulation method is unsteady, rotor–stator interaction phenomena between impeller and case can be captured (Gonzalez et al., 2002). One impeller revolution has 80 time-steps
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Fig. 2. Fluctuant curve of the instantaneous head. Fig. 5. Internal flow comparison between simulation and PIV test.
Fig. 3. General view of the pump. Fig. 6. Comparison between steady and unsteady flow-rate simulation.
Fig. 4. Comparison between experimental result and simulated results with different grid quantity.
Fig. 7. Total head comparison between steady and unsteady flow-rate simulation.
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and the impeller has four vanes, so the period of head oscillations caused by rotor–stator interaction is about 20 time-steps. Take the curve of Q = 233 m3 /h in Fig. 2 as an example. There are four obvious peaks which are nearly 14 m, and the time-steps are 126, 150, 173 and 190. So the period of the curve oscillation is nearly 20 time steps, it is equal to the rotor–stator interaction period. Beside, the amplitude of the instantaneous head gradually increases as the flow-rate increases. This is because fluid discharged from diffuser includes two parts: fluid circularly flowing in diffuser and that discharged from impeller. The former flow is steady and the latter fluctuates, which causes a fluctuant head. As the flow-rate is decreased, fluid which flows from impeller to diffuser is also decreased. Accordingly, the fluctuation of head is decreased. In order to compare with experimental results, the instantaneous head was averaged in a rotational period of impeller, which
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is called available head. Steady performance of the pump was tested in a test rig, and the case part is shown in Fig. 3. The accuracy of the flow rate and pressure sensor is 0.5%. Fig. 4 shows simulated results of three different grid quantities and the corresponding experimental results. Through comparison, one concludes that a grid quantity of 3.7 × 106 can accurately simulate the external characteristics. As shown in Fig. 4, the maximum error comparing between simulated and experimental results is about 7% at shut-off condition. This is because the flow field at shutoff condition is so complex that some vortices cannot be captured accurately. As the flow-rate increases, simulated results are well in agreement with experimental results. At the flow rate of 70 m3 /h, the error is 3%. The steady state simulation is only used for method validation, such accuracy is enough for unsteady flow rate simulation and engineering applications.
Fig. 8. Velocity vector graphs at unsteady condition of different flow-rate.
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4.2. Internal flow comparison of steady flow-rate between simulations and experiments The velocity vector graph on cross-section of the pump shown in Fig. 3 is caught by a 2D PIV device. The comparison between simulations and PIV experimental results at shutoff condition is shown in Fig. 5. The maximum velocity in simulation is about 3 m/s, while at the same position of the measured velocity is 2 m/s. An anticlockwise vortex exists above the diffuser in the two graphs, because at shut-off condition the fluid is blocked off by valves and cannot discharge out. It continues to circulate in the pump. Comparing with the flow structure of simulated results shown in Fig. 5, flow captured by the PIV method is a little flat. This is because bubbles produced in the pump at start-up affect the PIV results. In addition, the simulated model has its own error. So the PIV result can only be a qualitative comparison. By comparing the internal and external characteristics of the pump between experiment and simulation, this simulation method can be used for pump simulation from shutoff to maximum flowrate.
In the present paper, as shown in Fig. 1, the passage area of the pump does not change so significantly, so the average of the area is taken as the passage area A(s), and length of the middle streamline is taken as Leq . Following Eq. (4), the total head of the pumps can be calculated. As shown in Fig. 7, at low flow-rate, the head of 1 s opening time is the lowest and is highest at 0.25 s, with 0.5 s being intermediate. Meanwhile, at high flow-rates, the three different opening ways are nearly the same. To explain this phenomenon, the internal flow of the pump must be analyzed. 4.4. Internal flow simulation result of valve rapid opening process To analyze the transient evolution of the flow field during the process of variable flow-rates, simulated results of flow-rate at 1.163, 82.44, 164.14 and 251.72 m3 /h were undertaken. Comparison between different flow-rates of velocity vector graphs on cross-section near the diffuser is shown in Fig. 8. As can be seen from the graphs, large-scale vortices exist in impeller and diffuser at
4.3. External characteristic simulation result of valve rapid opening process The method mentioned above can accurately calculate the external characteristics and internal flow at conditions from shutoff to maximum flow-rate. Based on this method, unsteady flow is simulated with the shut-off condition as the initial flow field. Similarly, instantaneous head is also averaged to obtain the available head. Simulated results of steady state and increased flow-rate with different valve opening times are shown in Fig. 6. The unsteady Q–H curve lies under the steady Q–H curve. With increases in flow-rate, the velocity of the fluid in pipes increases, and part of the energy exported by the pump is used to provide fluid acceleration. Thus, the faster the valve opens, the greater the head loss. With increases in flow-rate, the transient head curve approaches the steady-state curve gradually. This phenomenon agrees well with the experimental results of Wang et al. (2003). With increases in flow-rate, velocity of the fluid in pipes increases, part of the energy exported by the pump is used to provide fluid acceleration, so at the same flow-rate unsteady flow process has a smaller head. This is because the flow-rate increases to the design operating point, the flow separation phenomenon in the impeller lessens, causing the transient curves to move closer to the steadystate curve. In order to analyze the transient effect in the process of flowrate increases, it is necessary to differentiate the total head of the pump H(t) from the indicated total head between the suction port and the discharge of the pump Hi (t). The total head is affected by the acceleration of the water contained in the pump casing. So the true total head rise H(t) is obtained by subtracting the apparent static head Hc (t) due to the acceleration from the indicated total head Hi (t), as the following equation shows (Tsukamoto and Ohashi, 1982): H(t) = Hi (t) − Hc (t) = Hi (t) +
L dQ (t) eq i gA0
dt
(4)
where the pump is represented by a straight pipe with cross sectional area A0 and length Leq . The equivalent pipe Leq of the pump is calculated by the equation:
L
Leq = s=0
A 0 A(s)
ds
(5)
where s is the distance measured from the suction port, and L is the total path length.
Fig. 9. Relative velocity evolutions of different conditions on the middle stream surfaces S1 m .
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5. Conclusion Based on the experimental and simulated results of internal and external characteristics at steady operation from shutoff condition to design condition, DES and silding mesh were used to explore the transient characteristic of the process when valve was rapidly opened. The results show that: (1) Simulated results of steady operation using DES model agree well with the experimental results, and the phenomenon of head fluctuation caused by the impeller–volute interation is well predicted. The results indicate that the proposed method is capable of solving complex flow in the centrifugal pump under off-design conditions. (2) The Q–H curve of valve opening process lies under the steady Q–H curve, which reflects the acceleration effect when the flowrate is increasing. (3) Besides the acceleration effect, a transits effect of the vortics revolution is also a main factor which influences the performance of the pump. In this context, flow-rate variations are defined as linear functions and outlet pressure is set to constant, which is different from the actual situation. the pipelines and pump should be coupled together for further study so that the boundary conditions of flow-rate and pressure better approximate the actual situation. The contents and conclusions of the current work can provide references for the performance prediction, design optimization and fluid control of the pump used in the transient process of valve rapid opening. Acknowledgement Fig. 10. Relative velocity evolutions of different conditions on the middle stream surfaces S2 m .
low flow-rate. As the flow-rate increases gradually, more compact vortices are generated in the flow passage of the impeller, while vortices in the case are smaller, fluid flowing to the outlet more intensively. The main reason is that at off-design conditions, due to the liquid viscosity, flow separation occurs on the blade surface, and thus vortices are generated. As the flow-rate increases, flow separation on the blade surface decreases, and vortices in the impeller are also decreased. Fig. 9 shows the relative velocity evolutions of different opening times at flow-rate of 100 m3 /h (left) and 233 m3 /h (right) on the middle stream surfaces S1 m in the impeller. As can be seen from the graphs, when the valve is opened in 0.25 s, at a flowrate of 100 m3 /h, vortices on the middle stream surfaces S1 m are small and compact; when valve is opened in some vortices develop at the trailing edge of the suction face; when valve is opened in large vortices can be observed on the pressure face. At the flowrate of 233 m3 /h, there is almost no difference on the middle stream surfaces S1 m , and the internal flow is very smooth along the blades. Fig. 10 shows the relative velocity evolutions of different opening times at a flow-rate of 100 m3 /h and 233 m3 /h on the middle stream surfaces S2 m in the impeller. As the opening time increases, the structure of the vortices becomes more complex at a flow-rate of 100 m3 /h, while the internal flow is very smooth along the blades at a flow rate of 233 m3 /h. As was stated above, the internal flow shown in Figs. 9 and 10 agrees with Q–H curve shown in Fig. 7 on the whole. Pump performances in valve opening processes are both influenced by the acceleration of the fluid and transits effect of flow revolution.
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