Hydraulic transients in pumping systems with air chambers

Abstract

This thesis presents the results of an extensive computational study of the transients in pumping mains following power failure and singlepump tripping. The studies are of practical relevance to pumping mains of watersupply systems provided with an air chamber for surge protection. The influence of various parameters on the transients following power failure in systems provided with air chambers has been studied by earlier investigators. However, there is disagreement regarding the effect of the loss parameter for flow out of the air chamber, DHOR1, on the downsurge following power failure. Some investigators assert the existence of an optimum value of DHOR1 that minimises downsurge, while others advocate providing DHOR1 = 0.0. The traditional design procedure for air chambers ignores pumpmotor inertia and assumes instantaneous closure of the nonreturn valve (NRV) upstream of the air chamber following power failure. Although nonreturn valve malfunction is known to have deleterious effects in pumping systems, these are usually ignored in airchamber design. It is also typically assumed that power failure produces the most critical transient condition, but several accidents show that tripping of a single pump out of multiple pumps operating in parallel can also result in severe transient pressures. With this background, the present study was undertaken with the following scope:

To study the influence of the loss parameter for outflow from the air chamber (DHOR1) on the downsurge following power failure.

To examine the effects of: (a) delayed closure of pump and/or airchamber nonreturn valves, (b) pumpmotor inertia, and (c) airchamber location on the transients following power failure, both in the transmission main and the short reach between the pump and the air chamber.

To study the effects of: (a) delay in pump NRV closure, (b) pumpmotor inertia, (c) number of pumps, (d) deliverypipe size and length, and (e) valveclosure pattern on the transients following singlepump tripping.

Computational Method The method of characteristics with a finitedifference scheme was used to solve the hyperbolic partialdifferential equations of motion and continuity governing unsteady flow. The dependent variables-head and velocity-were computed at selected pipe locations and time intervals. Boundary conditions at pump end, reservoir end, and internal elements such as junctions, air chambers, and surge tanks were applied. Steadystate head and velocity prior to power failure or pump tripping were used as initial conditions. Newton-Raphson iteration was employed wherever nonlinear equations arose.

Influence of DHOR1 on Downsurge A parametric study covering over 400 computational cases was carried out. DHOR1 was varied from 0.0 to 0.3. Key findings:

The optimum value of DHOR1 varies along the pipeline; it decreases with increasing distance from the air chamber. Near the reservoir end, the optimum DHOR1 = 0.0 for all practical parameter combinations. The deterioration in downsurge as DHOR1 increases beyond its optimum value is far more significant than the improvement gained by increasing DHOR1 from 0.0 up to the optimum. This effect is especially pronounced for small airchamber capacities and locations near the reservoir.

Effects of Valve Closure Delay, PumpMotor Inertia and AirChamber Location Three systems were analysed:

System I: 3.15 m³/s, 19.6 km, 1750 mm pipe, 170 m head System II: 1.87 m³/s, 3.2 km, 1450 mm pipe, 88 m head System III: 0.40 m³/s, 660 m, 600 mm pipe, 112 m head

Over 50 cases were analysed. Major conclusions:

Ideal closure of either airchamber or pump NRV is sufficient to prevent deterioration of pressures in the transmission main. Delay in closure of both valves can cause significant pressure deterioration-except in very long pipelines. Pressures in the short reach between the pump and the air chamber become considerably higher than downstream pressures when NRVs close late. A critical delay dcd_cdc exists that results in the maximum head rise:

1.5 × working head (Systems I & II) 1.8 × working head (System III)

Maximum expandedair volume, important for airchamber sizing, increases considerably when NRVs close late. High pressures decay only very close to the air chamber. NRVs should therefore be placed near the air chamber when it must be located away from the pump.

Transients Following SinglePump Tripping A large system (similar to System I) was analysed. Over 100 computational cases were performed, varying:

NRV delay pumpmotor inertia number of pumps deliverypipe size and length valveclosure pattern

Key observations:

Severe transients are localised between the pump’s delivery NRV and the delivery manifold. Transients due to singlepump tripping are often more severe than those due to power failure. Even a 0.5sec delay in NRV closure results in a head 1.9 × working head. Maximum head 2.6 × working head occurs for NRV closure delay dc=2.9d_c = 2.9dc=2.9 sec. Pumpmotor inertia significantly influences singlepumptripping transients. Reducing the number of pumps reduces maximum pressure significantly only when no air chamber is present. Pressure decay after pump tripping occurs very close to the manifold.

Valveclosure pattern effects:

Multidoor valve: maximum pressure depends mainly on closure time of the last door. Uniform gradual closure helps only for sufficiently long closure times; however, long closures risk large reverserotation speeds. A twospeed closure (rapid initial + slow final closure) is effective in controlling pressure rise without causing reverse rotation. Increasing deliverypipe diameter reduces the severity of transients.