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Surge Protection Design for Water Conveyance System for the Case of
Power Failure to Pumps in Lift Irrigation Scheme Using SAP2
Ruben Nerella1 E.Venkata Rathnam2 P. Raghuveer Rao3
1Research Scholar, Department of Civil Engineering, National Institute of Technology, Warangal.
(Email: [email protected])
2Associate Professor, Department of Civil Engineering, National Institute of Technology, Warangal.
(Email: [email protected])
3Senior Scientific Officer, Department of Civil Engineering, Indian Institute of Science, Bangalore
(Email: [email protected]) ABSTRACT
The paper presents the results of hydraulic transient (surge) analysis of a water pumping system. The study include formulation of problem with relevant boundary conditions viz., upstream and downstream reservoir, pump, pipe junction, air vessel, surge tank, air valve, stand pipe etc. The surge equations are generally solved by Method of Characteristics (MOC) approach. The main assumption in the analysis is that formulas for computing the steady state friction losses in conduits are valid during the transient state also. A case study of water pumping main of JCR Devaduala Lift Irrigation project of Telangana State is presented. Surge analysis is carried out for the case of tripping of power to pumps. The results for pump trip condition show that there is pressure rise above working pressure and down surge throughout the alignment. The maximum pressure observed is 291 m as against the pump head of 131 m. Surge protection devices for the pumping main are designed using software Surge Analysis Program Version 2 (SAP2).
Keywords: hydraulic transients, pressure main, pump failure, air vessel, surge tanks.
1.0 INTRODUCTION
Many researchers including Wylie and Streeter (1993) and Chaudhry (1987) referred pressure surges as water hammer pressures or hydraulic transients in conduits which may occur due to change in flow conditions. Liggettt et al. (1992) mentioned that most hydraulic transient analysis in pipe networks have been done in feed-water system in power plants. Soares et al. (2013) stressed the need for hydraulic transient analysis in the operation stage of any existing pumping mains for the diagnosis of malfunction problems or the cause of pipe bursts. In a pumping mains, changes in flow may be caused by i) starting or stopping of pumps, ii) opening or closing of valves, iii) Power failure (Pump trip), and iv) single pump failure. The first two conditions (i, ii) fall under planned conditions where as the other two conditions (iii, iv) fall under unplanned conditions which form the most critical surge condition in pumping main. The prediction of maximum transient pressures is used to verify whether pipe materials, pressure classes, and wall thicknesses are sufficient to with stand predicted pressure loads to avoid pipe rupture or system damage. Verification of minimum transient pressures is important to prevent air release, cavitation, and water column separation and consequently, to avoid pipe collapse or pathogenic intrusion into the system. When severe transients cannot be avoided, either the pipe characteristics are changed, or surge-protection devices are specified (e.g., air vessels, surge tank etc.) so as to reduce the extreme pressures to within acceptable limits. Usually, the decision is the most economical and reliable surge protection devices that yield an acceptable transient pressure response. Stephenson (2002) simplified the process of sizing of air vessel with nomographs. Both air volume and total vessel size are calculated.
Hydraulic transients in pump–pipe line system can be solved by widely accepted numerical method called Method of characteristics (MOC) which involves the solving of two non-linear, first order partial differential equations in two unknowns piezometric head (H) and flow velocity (V) in two independent variables like time (t) and distance (x) along the pipe line. Wylie & Streeter (1993) developed the theory and computational methodology for solution by MOC and are available in standard references. In this paper, transient pressures generated in pipe flows
program called Surge Analysis Program Version 2 (SAP2) developed at the Indian institute of Science, Bangalore (IISC) in more than 500 projects. The same has been used for analyzing transient pressures in the present study. Field data of steady state flow rate were collected at Intake pump house of JCR Devadula Lift irrigation scheme located in Telangana state, India. Results obtained with provision of protection devices such as air vessel, one way surge tank, stand pipes and air valves are presented.
2.0 METHODOLOGY AND DESIGN CONSIDERATION
2.1 Dynamic and continuity equations
Analyses of most hydraulic transients in pressurized systems are carried out assuming one dimensional flow and are based on the continuity and momentum equations describing the general behavior of fluids in a closed duct in terms of two variables, namely piezometric head (H), and fluid velocity (V), in two independent variables time and distance along pipe line. Hanif Chaudary (1987) derived the continuity and momentum equation for hydraulic transient conditions which constitute a system of partial differential equations of first order that can be written as
(1)
(2)
Where, H is piezometric head, V is mean velocity, x is the coordinate along the pipe axis, t is time, a is celerity (or pressure wave velocity), D is diameter of pipe, g is acceleration due to gravity, f is Darcy Weisbach friction factor and sin θ is the slope of the pipeline. Wylie & Streeter (1993) confirms that method of characteristics (MOC) can successfully replace by a pair of partial differential equations (Eq.1) and (Eq.2) by an equivalent set of ordinary differential equations. The new set of characteristic equations can be written as
where (3)
(4)
where (5)
(6) (Eq 3 – Eq 6) are the basis for the finite-difference solution of the water hammer problem. A finite difference approximation for the velocity and head (Vp, Hp), at point P is expressed as
(7)
(8)
The subscripts i-1 and i+1 in (Eq.7) and(Eq.8) refers to the sample points to the left and right of P and one time interval ∆t in the past. By combining known variables, We may write Eqns. (7&8) as
(9) 2 0 sin 0 2 H a V t g x fV V V H g g t x θ D ∂ + ∂ = ∂ ∂ ∂ ∂ + + + = ∂ ∂ : 0 2 : 0 2 fV V d V g d H C d t a d t D d x a d t fV V d V g d H C d t a d t D d x a d t + − + + = = − + = = − 1 1) 1 1 1 1) 1 1 ( : 0 2 ( : 0 2 p i p i i i p i p i i i V V g H H fV V C t a t D V V g H H fV V C t a t D − − − − + + + + + − − − + + = Δ Δ − − + + = Δ Δ 1 2 : p p C V+ = −C C H
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(11) (12) (13) (Eq.9) and (Eq.10) can be referred as compatibility equations and are valid for interior points of solution space (2 ≤ i ≤ N) as shown in Figure 1. At any interior grid intersection point (P at section
i), the two compatibility equations (Eq.9) and (Eq.10) are solved simultaneously for the unknowns Vp and Hp.
Figure 1. Method of characteristics - characteristic lines in plane (x, t)
2.2 Design of surge protection system
The design of surge protection system is an iterative process in which protection is proposed, analysis is made, results are evaluated, based on evaluation modification, and process is repeated until an economic protection system is arrived at. The surge protection devices used for pumping mains and their role in surge protection system is shown in (Table 1).
Table 1. Surge Protection Devices and its functions
Surge Protection Devices Functions
Air vessel Controls upsurge & down surge
Surge tank, Air valves Controls down surge directly and upsurge indirectly
Stand pipe Controls down surge only
Zero velocity valves and Surge relief valves
Controls Up surge only
2.2.1 Air vessel
It is a closed vessel with water in the lower part of the vessel and compressed air at working pressure in the upper part Figure 2. The compressed air functions as stored energy cushioning the rate of velocity reduction in the transmission main.
1 1 1 1 1 2 4 3 1 1 1 1 2 , 2 i i i i i i i i where g f t C V H V V a D g C C a g f t C V H V V a D − − − − + + + + Δ = + − = Δ = − + x t P a‐ a+ B A
i ‐ 1 i i + 1 x
t 1 2 3 . . . N N+1 Δt Δt Δt Δx Δx Δx Δx Δx Interior sections Upstream boundary conditions Initial condition Downstream boundary condition t0 t0 + Δt
Figure 2. Schematic diagram of Air vessel
When pump fails, pump head reduces, pressure in the air vessel reduces by expansion of air. As result water is supplied to transmission main which reduces the rate of velocity reduction in transmission mains. The air chamber contribution to the upstream boundary condition must be incorporated with that of pumps. Assume that there are Npu pumps in parallel and the power fails
simultaneously. The equations for these situations are
Upstream: (13)
Conservation of Mass: (14)
Pump Work Energy: (15)
Chamber Work Energy: (16)
Pump Head Increase: (17)
Where Hc is the head in the chamber, Cout is the out flow coefficient, Aout is the out flow cross
sectional area, and, Qc is the discharge from the chamber.
(18)
(19)
(20) Raghuveer Rao (2012) used a non-dimensional size parameter (KAV) instead of actual size of air vessel to specify the volume of the air vessel.
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Where, C0 is air volume under working condition, Q0 is design discharge, L is the length of
transmission main, and is celerity or pressure wave velocity. After repeated analysis is determined with different size parameters, volume of air vessel is determined based on results of surge analysis.
2.2.2 One way surge tank
It is a RCC or feed tank placed at locations where the pipe line undergoes severe down surge pressures Figure 3.When pressure in rising main drops below the water level in OST due to power failure, water from OST starts draining into the rising main, controlling further down surge. Control of down surge avoids column separation and resulting upsurge.
Figure 3. Schematic diagram of one way surge tank
The following equations form the internal boundary Conditions.
Upstream: (22)
Downstream: (23)
Conservation of mass: (24)
Work-Energy: (25)
Where, Cout is loss coefficient for the connecting pipe (0.60-0.98), A, As are cross sectional areas of
pipe and surge tank, Hs is height of tank liquid surface above centre line of the pipe and ZAB is
elevation of centre line of the pipe. Tank discharge Qs is given by
(26)
(27)
(28)
2.2.3 Air Valves
Figure 4. Schematic diagram of Air valves
Air valves are intended for control of down surge in view of their function as vacuum breaker Figure 4. The primary role of air valves is to release/allow air at summits during filling/emptying the pipeline. This can be used as supplement surge control device at locations where there is severe sub-atmospheric pressure is expected. Air valves at proper locations make pipeline free of air pockets. For a cross country pipe line, air valves need to be located at all local peaks and at every 500 to 600 m. Analysis of air valves focuses on a) air inlet capacity of air valve b) air exhaust characteristic of the air valve.
2.2.4 Stand pipe:
Stand pipe may be considered only at a location along the alignment where the hydraulic grade line is within a few meters (usually 3 to 4 m) of ground elevation. Also, the downsurge at the location must be severe enough to require a local protection. Such locations are usually likely to occur towards the delivery Reservoir. Figure 5 gives a schematic diagram of the stand pipe. The design variables for the stand pipe are: a) location of the stand pipe, b) diameter of the stand pipe, c) elevation of the top of the stand pipe. The top of the stand pipe should be fixed 1 to 2 m above the maximum elevation of hydraulic grade line at the location.
Figure 5. Schematic diagram of stand pipe
3.0 SURGE ANALYSIS
3.1 Case Study : Devadula Lift irrigation Project
The Devadula lift irrigation scheme involves seven reaches (approximately 200 km length) to lift water from river Godavari to upper parts of Telangana region. Out of seven reaches, reach 1 which is about 38 km, whose longitudinal alignment and steady state hydraulic grade line is shown in
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Bhimganapuram irrigation tank (RL 166.94 m) with a static lift about 96 m. The design discharge in the 3000 mm size MS pipe line with 16 mm thick wall is 14 m3/s and rated head is 131 m. The system parameters/ field data is given as input and simulated the steady state condition as well as transient condition (Pump trip condition).
Figure 6. Longitudinal alignment and steady state HGL of pipeline
Two pumps of 7 m3/sec discharge at head of 131m are installed whose speed is 500rpm,
efficiency is 91%. The GD2 values of pump and motor are 14920 and 44000 kg-m2. The power of motor is 9.9 MW. Length of transmission main is 38252 m long, mild steel pipeline diameter of 3 m, pipe wall thickness is 16 mm with external cement mortar guiniting of 25 mm thick. The pump characteristics curve is shown in Table 1.
Table 1: Pump characteristics
Discharge (m3/s) 0 1 2 3 4 5 6 7 8 9 9.6
Head (m) 154 152 149 147 145 142.5 139 131 120 103.5 91 Efficiency (%) 0 26.2 45.7 60.3 75.9 84.2 87.97 90.86 90.12 85.4 78.96 When pump trip occurs, discharge and head in the transmission main reduces to zero. In order to prevent reverse flow trough pumps, a hydraulically operated discharge valve (HOPDV) is provided. The closure time, on power failure, for HOPDV valve is 20 sec, with 90% closure in 10 sec and remaining 10% closure in 10 sec.
Wave speed estimation: The Elastic wave speed (a) can be estimated by theoretical formulas with
the modulus of elasticity provided by manufacturer of the pipes (Wylie & Streeter, 1993). The wave speed was estimated as 868 m/s, given by (Eq.29).
(29)
Where, K is bulk modulus of elasticity of water (2.19 GPa), E is modulus of elasticity of pipe (200 GPa), e is pipe wall thickness (16 mm), D is diameter of pipe (3000 mm), ν is Poisons ratio (0.29)
70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 0 4000 8000 12000 16000 20000 24000 28000 32000 36000 Chainage, m Eleva tion, RL, m Alignment HGL
3.2 Overview of SAP2
The design of surge protection system is an iterative process. Surge or water hammer analysis is made for each option by numerical analysis using the method of characteristics. A software is required for such an analysis, as it involves simultaneous solution of two non-linear, first order partial differential equations. The present Surge Analysis Program Version 2 (SAP2) is an offshoot of a software developed in-house at the Indian Institute of Science and used for the design of surge protection system for more than 500 projects. The principal limitations of SAP2 are: (a) The software requires that the steady state flow direction in each pipe is known. (b) It is not applicable for looped networks such as street level pipes in an urban water supply network. (c) The scope of the software is limited to flow shutdown such as power failure, one or more pumps failure and closure of the delivery end valve in gravity main.
4.0 RESULTS
4.1 Steady state analysis
The hydraulic parameters mentioned above were given as input to SAP2 and simulated the steady state analysis i.e., both pumps working as shown in Figure 7.
Figure7. Steady state analysis
4.2 Surge analysis with out protection
The results for pump trip show that there is rise in upsurge and vapour pressure throughout the stretch as shown in Figure 8. This figure presents the pipeline alignment, the HGL and the minimum and maximum piezometric heads obtained from surge analysis. The maximum and minimum pressures at any location in the figure are obtained by deducting the pipe alignment elevation from the corresponding piezometric head. The alignment levels in the figure correspond to pipe invert level. The maximum pressure is 291 m which results in a hoop stress exceeding the yield stress of steel and vapour pressure throughout the alignment. Spurious minimum pressures with negative values in excess of -10 m should be interpreted only qualitatively not quantitatively. Also as the pipeline cannot take full vacuum as per AWWA M11 which specifies minimum thickness of 6 mm for every 1000 mm. As the pipeline is vulnerable to upsurge or pressure rise and down surge or pressure drop and hence need protection.
70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 0 4000 8000 12000 16000 20000 24000 28000 32000 36000 Chainage, m Ele v a ti o n , R L , m Alignment Minimum Head Maximum Head HGL
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Figure 8. Minimum and maximum piezometric heads for no protection
4.3 Surge analysis with protection
The analysis carried out by incorporating surge protection devices viz., Air vessel, surge tank, Stand pipes, Air valves etc. at appropriate locations. After several iterations, the following protection devices are proposed.
a. Four air vessels of 99 m3 each with 27 m3 of initial air volume with connecting pipe of 900 mm size with orifice of 500 mm size. The air vessels are connected to the transmission main through a manifold of 1800 mm size with an orifice of 1000 mm size.
b. One way surge tank of 20 m diameter with storage height of 5 m and staging height of 5 m at Ch. 5971 m. The twin connecting pipe size is 1400 mm with filling pipe size of 600 mm. c. Stand pipes of 300 mm size at Ch. 26337 m and 27742 m with top level extending to RL 181
m.
d. Air valves of 200 mm size at Ch. 2687 m and 7035 m.
Figure 9 shows maximum pressure head and minimum pressure head variation along the pumping main with proposed surge protection on power failure. It can be observed that the maximum pressure is the maximum working pressure only and practically no sub-atmospheric pressure.
-10 40 90 140 190 240 290 340 390 0 4000 8000 12000 16000 20000 24000 28000 32000 36000 Chainage, m El eva ti on, RL, m Alignment Minimum Head Maximum Head HGL 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 0 4000 8000 12000 16000 20000 24000 28000 32000 36000 Chainage, m El evat io n , R L , m Alignment Minimum Head Maximum Head HGL
5. CONCLUSIONS
Surge analysis and design of surge protection system is very important for safe and reliable functioning of water conveyance systems. The paper presents numerical analysis of surge pressures in water transmission main using SAP2. The analysis shows power failure results in maximum pressures in excess of pipe capacity and vapour pressure throughout which the pipeline cannot withstand. The proposed combination of protection devices the maximum pressure is the maximum working pressure and practically no sub-atmospheric pressure any where on the alignment.
6. ACKNOWLEDGEMENTS
Authors gratefully acknowledge the help received from Chief Engineer, JCR Devadula Lift Irrigation Project, Hanamkonda, Warangal district, Telangana State in providing data for the analysis.
7. REFERENCES
AWWA M11 (2004), Steel Pipe – A Guide for Design and Installation, Fourth Edition, American Water Works Association, Denver, USA
Hanif Chaudary, M. (1987) Applied Hydraulic Transients,Van Nostrand Reinhold, New York. Liggettt J A, Li-Chung C. (1992) Inverse Transient Analysis In Pipe Networks. Journal of Hydraulic Enggineering 120 (8):1014-1024.
Raghuveer Rao, P. (2012) Surge Analysis and Design of Surge Protection System - Case Studies,Water Hammer Surge Analysis of Piping System (WHSAPS), (pp. 1-42). Trichur, India.
Soares A K, Covas C. I, & Ramos H. M. (2013). Damping Analysis of Hydraulic Transients in Pump -Rising Main system, Journal of Hydraulic Engineering, 139 (2): 233-242.
Stephenson, D. (2002) Simple guide for design of Air vessels for Water Hammer protection of Pumping mains, Journal of Hydraulic Engineering, 128 (8):792-797.
