THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS 345 E. 47th St New York, N.Y. 10017 The Society shall not be responsible for statements or opinions advancedin papers or &Scission at meetings of the Society or of its Divisions or Sections, or printed in its publications. Discussion is printed only if the paper is published in an ASME Journal. Authorization to photocopy material for internal. or personal use under circumstance not falling within the fair use provisioneof the Copyright Act is granted by ASME to libraries and other users registered with the Copyright Clearance Center (CCC) Transactional Reporting Service provided that the base fee of $0.30 per page Is paid directly to the CCC, 27 Congress Street Salem MA 01970. Requests for spaal permiszicii or bulk reproduction shottkl be addressed to the ASME Technical Publishing Department Copyright 0 1997 by ASME All Flights Reserved. Printed in U.S.A "FLUID TRANSIENT RESPONSES WITH CHECK VALVES IN PIPE FLOW SYSTEM WITH AIR ENTRAINMENT" EN4111111411111111M ' BREAK T.S.Lee and L.C.Leow Mechanical and Production Engineering Department National University of Singapore SINGAPORE 119260 ABSTRACT A common flow system arrangement in piping system consists of a lower reservoir, a group of pumps with a check valve in each branch, and a pipeline discharging into a upper reservoir. In earlier studies of check valves performances in transient flow, none considered the effects of air entrainment into a pipeline system and the subsequent effects on the. check valve performances in transient flow. Studies on pressure surges during pump tripped in pumping systems showed that by including an air entrainment variable wave speed model, reasonable predictions of fluid transient responses with proper phasing and attenuation of pressure peaks can be obtained. The most severe case where all the pumps in the station fail simultaneously due to power failure was analysed for their maximum and minimum pressure variation along the pipeline. A numerical model is now set up in the present work to investigate the check valve performances in transient flow for a pumping system with air entrainment. The analyses examine a fluid system with a variable air entrainment content (c) and studied numerically it effects on the flow reversal time and hence determine the appropriate valve selection for a given fluid system to minimize problems of check valve slamming. Present numerical computations show that the air content in a fluid system can adversely affect the check valve transient responses. With the fluid system operating within a critical range of air entrainment values, analysis showed that there is a possibility of "check valve slamming" when the check valves were selected based on the analysis of an air free system. The above phenomena is confirmed through physical field measurements. Presented at the ABE ASIA '97 Congress dt Exhibition Singapore - September 30-October 2,1997
1. INTRODUCTION A common flow system arrangement in fluid engineering consists of a lower reservoir, a group of pumps with a check valve in each branch, and a pipeline discharging into an upper reservoir. In earlier studies of check valve performances in transient flow Wrovoost(1980-83), Thorley(1983-89)J, none considered the effects of air entrainment into a pipeline system and the subsequent effects on the check valve performances. A pipeline contour of a pumping station with possible air entrainment is shown in Figure 1. This profile was also chosen among some other previous studies due to its known check valve slamming characteristics. Possible air entrainment into this pumping station was also due to its frequent operation near low cut-out water levels in the sump [Lee (1991, 1994)]. The most severe case of all the pumps in the station fail simultaneously due to power failure was analysed for their maximum and minimum pressure variation along the pipeline. A numerical model was set up in the present work to investigate the check valve performances in a pumping system with air entrainment. The present analysis examines a fluid system with an air entrainment content (c). Nuumerical studies show that effects on the flow reversal time, and hence, the appropriate valve selection for a given fluid system to minimize the problem of check valve slamming. From the study by Thorley(1989), it is observed that the rate of decrease for a given flow rate is approximately linear over the interval when the flow rate starts to decrease and eventually reverses. This physical observation is implemented in the present numerical calculation procedures in order to better determine the suitability of a check valve type for a given pumping system. 2. METHOD OF CHARACTERISTICS WITH VARIABLE WAVE SPEED The method of characteristics applied to the above pressure tfansient problem with variable wave speed (ai), can be described by the C and C characteristics lines: C + characteristics g H) (V1" 1 - V) g fi + a At k At k a i 2D R V IV I = 0 R R X -x At k - v +a R R 2
and C - characteristics g ) (V /" 1 -V s ) g fl s s 1 V s sin a + V IV 1 = 0 s s a s At " At " a 2D X -x at " - V s -a s With air entrainment, the transient computation of the fraction of air content (CI ) along the pipeline depends on the local pressure and local air volume and is given in [Lee(1994)]. The loss factor fl used in conjunction with the Method of Characteristics with air entrainment and gas released in a pipeline system is evaluated at the local point (i) using the characteristics of the flow at that point. The steady state overall loss factor at the operating point of a system can be determined from the pump characteristic curve and the system curve [Lee(1991)]. 3. NUMERICAL COMPUTATION OF PUMPS RUN DOWN WITH DYNAMIC CHECK VALVE RESPONSES Downstream of the pipeline profile [Figure 11 of the pumping station, a constant head reservoir is assumed for all time level. The upstream pumping station is modelled by an equivalent pump characteristics with number of pumps (np) running in parallel. During pumps stoppage and pumps run down, the homologous relationship for np number of pumps in the form of an equivalent pump is numerically modelled [Lee[1994]. When the reversed flow is encountered in the pump, the check valve response is modelled here according to the experimental data obtained by Thorley(1989) on the dynamic characteristics of the check valves: Vx/ Vo = Di + D2 (A * ) + D3 (A * ) + D4(A* ) 3 where A s = reverse flow deceleration parameter through the check valve = IdV/dt1/ [ (V0) 2/ D] Vo = steady state flow velocity dv/dt = reverse flow velocity gradient D = check valve nominal diameter Di, D2, D3 are the characteristic parameters of the type of check valve Da is the characteristic parameter of the check valve due the effects of the air entrainment. For no air entrainment, 1)4 = 0.0. Check valves serve to prevent the reversal of the flow in a pumping system. If however, the reversal of the flow occurs in a very short time the valve may close when the flow already has been reversed. Depending on the type of check valve used, a sudden decrease of the reversal flow will 3
occur, resulting in undesirable pressure variations and slamming of the valve. Thorley(1989) gave some very good examples of check valve slamming in pumping systems. To theoretically predict whether slamming of a check valve is to be expected, data under dynamic conditions of the valve must be known. In most cases these data are not known. However, the possibility of a check valve slamming may be estimated through a numerically predicted "flow reversal time (tr)". Prototype valve tests showed that the fluid velocity gradient IdV/dt1 variation with time is of decisive importance when considering the valve slam problem. Obviously, the shorter the time for transient flow reversal from pump trip, the more likely that valve slamming will occur. This again depends on the type of check valve used. Nozzle type of recoil check valves tend to have a better dynamic response than the conventional swing type check valve. It is thus important to know the "flow reversal time" during pump trip so that at the design stage, it is possible to predict whether the chosen type of check valve will satisfy the design specifications of the pumping system. Specifically, the aim of this study is to determine the air entrainment effects on the "flow reversal time" and its effects on the check valve selection and the consequences of pressure surges for a pumping system. 4. RESULTS AND DISCUSSIONS Initially, the effects of air entrainment on pressure transients generated by the simultaneous pump trip of all pumps operating in a pumping station with the undulating pipeline contour as shown in Figure 1 were investigated for a selected swing check valve configuration. The pumping station uses three parallel centrifugal pumps to supply 1.08 m Is of water to a tank 19.7 m above the sump level, through a 0.985 m diameter main of 4720 m length. Swing check valves were installed downstream of the pumping station. The pumpset moment of inertia (including the flywheel) were studied for an equivalent pumpset moment of inertia of Ie = 0.1, 0.1, 1.0, 2.0, 5.0 and 10 of a reference pumpset inertia (I) of 99.9 kg-m. The air void fraction (c) studied were in the range of 0.00 to 0.03. Figure 2 shows the effects of air entrainment on the pressure transients at a point A (immediate downstream of the check valves) and at a point B (at the peak) of the pipeline contour for an equivalent pumpset moment of inertia (Ie). Several distinct pressure transient characteristics were observed from the above numerical experiments: (i) The magnitude of the maximum pressure surges varies with c and is very often larger than that predicted by the constant wave speed model (c=0.000) (ii) The damping of surge pressure is noticeably larger with 00.000 when compared with the constant wave speed model (c=0.000) (iii) With 00.000, the pressure surges are asymmetric with respect to the static head, while the pressure transients for the constant wave speed model were symmetric with respect to the static head. (iv) When air was entrained into the system, the pressure transient showed long periods of downsurge and short periods of upsurge when compared with the gas-free constant wave speed case. From past experiences, surge measurements (Lee(1994)) indicate that the damping is faster in the actual system indicating that more energy dissipating mechanisms than ordinary friction are at hand. (v) The degree 4
of amplification of the first pressure peak is dependent upon the rate of deceleration of the flow after the pump trip. An increased pump inertia (by attaching a flywheel to the drive-shaft) generally produces a slower rate of deceleration of the flow after pump trip and a smaller amplification of the first pressure peak as compared with the constant wave speed model. Figure 3 showed that the entrained, entrapped or released gases significantly altered the flow reversal time. From the available flow' reversal time, the reverse flow velocity gradient with respect to time is obtained. The maximum reverse flow gradient and the corresponding maximum reverse flow for a given pumping configuration at various air entrainment levels for a swing check valve is shown in Figure 4. The results show that although the selection of the swing check valve is in general satisfactory for the above pumping system, there is still a possibility of the "valve slamming" problem unless the pumpset inertia is significantly increased. The results presented in Figure 3 show that the effects of the check valves in transient flow can be predicted by means of numerical computation of the equivalent flow reversal time. When analysing these effects, both steady flow rate and fluid velocity gradient with time must be considered. For systems with large flow rates ' the fluid velocity gradient is of decisive importance. The time interval necessary for flow reversal and mode of the flow rates versus time variation during the flow reversal period gives an indication of the necessary characteristics for a satisfactory flow and pressure prediction of the check valve closure. The above observations made through numerical experiments are consistent with field measurements and observations (Lee(1994)) of pressure surges in prototype pumping stations at various mode of pump normal operations and pumps operating near low water cut-out levels with air entrainment due to attached surface vortex. Observations showed that the commonly used swing check valve closed when flow reversed. At the instant of valve closure, a large pressure variation was initiated. S. CONCLUSIONS The present analysis show that the effects of air entrainment on the check valve performances in transient flow with various mode of pumps operations may be predicted by means of a numerical computation of the equivalent flow reversal time. Both steady flow rate and fluid velocity gradient with time need to be considered in the computation. The time. interval needed for flow reversal, and mode of the flow rates versus time variation during the flow reversal period, gives an indication of the required check valve characteristics necessary for a satisfactory pressure transient in a pumping system without valve slamming problem. From the analysis, it is seen that in order to find the most severe conditions of pressure surges and valve slamming for a given fluid system, it is necessary to perform a complete air entrainment computional study. The reason is that for a given system, the maximum pressure peaks and valve slamming phenomena may not always occur at the minimum or maximum air entrainment levels, and can occur within a range of intermediate air entrainment values. This range of critical air entrainment values can only be obtained through numerical 5
experimentation. Physical experiments with a model setup for air entrainment investigation are not reliable [Lee and Pejovic (1996)1. 6. ACKNOWLEDGEMENTS The author gratefully acknowledges the kind assistance of the personnel from the Ministry of the Environment, Singapore for providing valuable information on pumping stations for this investigation. The support of the National University of Singapore Research Grant ( No. RP890633 ) is also gratefully acknowledged. 7. REFERENCES Lee, T.S., "Numerical computation of fluid pressure transients in pumping installations with air entrainment", Int. J. for Numerical Methods in Fluids, Vol.12, pp.747-763 (1991). Lee, T.S., "Numerical Modelling and Computation of Fluid Pressure Transients with Air Entrainment in Pumping Installations", Int. J. for Numerical Methods in Fluids", Vol.18, pp.89-103 (1994). Lee, T.S. and Pejovic, S., "Air Influence on Similarity of Hydraulic Transients and Vibrations", ASME Journal of Fluids Engineering, Vol.118, December 1996. pp.706-709. Provoost, G.A., "The Dynamic behaviour of Non-Return Valves", Proceedings of the Third International Conference on Pressure Surges, Canterbury, England, March 24-27, 1980. pp.415-427. Provoost, G.A., "The Dynamics Characteristics of Non-Return Valves", Paper 14, 11th IAEA Symposium of the Section on Hydraulic Machinery, Equipment and Cavitation Operational Problems of Pump Stations and Power Plants, Amsterdam, Sept. 1982. Provoost, G.A., "A Critical Analysis to Determine the Dynamic Characteristics of Non-Return Valves", Paper F4, Proceedings 4th Int. Conf. on Pressure Surges, BHRA, Bath, Sept. 1983, pp.275-286. Thorley, A.R.D., "Dynamic Response of Check Valves", Paper fl, Proceedings of 4th Int. Conf. on Pressure Surges, BHRA, Bath, Sept. 1983, pp.231-242. Thorley, A.R.D., "Check Valve Behavior Under Transient Flow Conditions : A State-of-the-Art Review", ASME Journal of Fluid Engineering, June 1989, Vol.111, pp.178-183. 6
PIPELINE CONTOUR ELEVATION (METERS ) ttl A 0 500 1000 1500 2000 2500 3000 3500 4000 4500 CHAINAGE (METERS) FIGURE 1. A TYPICAL PIPELINE CONTOUR OF PUMPING STATION WITH POSSIBLE AIR ENTRAINMENT
(a) c = 0.000 (b) c = 0.001 10 0 60 5 141 1= ID 1 14 SO 1111 lir& I. SCROK5 *._./..., 0.0 LZ CAI GO.L C.0 =A MA MA MO MA 71z: In SCCONCI5 (c) c = 0.005 (d) c = 0.010 a.. 0... I\ /r/....k 0.7 al 41 WA WO 4111 MO MA 1111 M.: TRR N SECON25 S..,. R \...--- (...... 0.0 n:.o U, MI MI M., 1:1 Mt MA. e TIC in SCC0.75 (e) c = 0.020 S Cl) c = 0.030 ----- -.... _ F 0.0 AA OA CO Ma 103.0 MA la a.r.. it- TM: IN SECOROS R 71./ N SECCRO5 FIGURE 2. AIR ENTRAINMENT EFFECTS ON TRANSIENT PRESSURE HEADS DOWNSTREAM OF PUMPING STATION AT A ( ) PEAK OF PIPELINE ELEVATION AT B ( - - - - ): (i) c=0.000 (ii) c=0.001 (iii) c=0.005 (iv) c=0.010 (v) c=0.020 (vi) c=0.030
100 80 8 60 EOLINALD1T PUMPSCI IMETITIA.34 I. 0.1 1 4. I. 0.5 I Agaj 40 i 1.02 20 I. 2. 0 I if. 5.0 e li 0.005 0.01 0.015 0.02 0.025 0.03 0.035 AIR ENTRAINMENT (c) FIGURE 3. EFFECTS OF AIR CONTENT c ON FLOW REVERSAL TIME
2.0 (i) It = 0.11 0 If CC (iii) Ie = 101 I 0 SWING ON 100 (ii) IC = 1.01 SPLIT DISK (w) ON 200 0-0 /' SPLIT DISK (s) ON 200...>,---- NOZZLE (s) - -------6. DN 300 0 0 0... i...,...--- 0 4 12 16 DECELERATION PARAMETER, A= ICW/dt1/1(W0) 2 /pi FIGURE 4. EFFECTS OF AIR CONTENT c ON SELECTION OF CHECK VALVES (1) Ie = 0.11 (ii) Ie = 1.01 (iii) Ie = 101