Identifying Head Accumulation due to Transient Wave Superposition in Pipelines

Abstract

Fluctuations in pressures are part of the normal behavior of water distribution systems. The common perception is that transient events dissipate quickly in a network without significant consequences; however, under certain circumstances, the superposition of waves from a transient event can magnify the pressure response, effectively accumulating head in a pipeline. This paper studies this accumulation phenomenon in a single pipeline from a theoretical point of view, with supporting numerical simulation and laboratory validation. Transient wave propagation analysis shows that after the generation of a transient event, multiple wave reflections induce an increase in the head. A cycle of accumulation is defined and the potential maximum number of cycles is studied for a pipeline connected to a long, large impedance pipe section. The analysis is then extended to a system connected to a shorter large impedance pipe section where the maximum head accumulation is not reached. Expressions to calculate the potential maximum head accumulation in pipeline systems are proposed and numerically validated. A general classification for the head accumulation is presented to specify how severe a head accumulation event may be. Experimental validation of the phenomenon has been conducted, showing that under a proposed configuration, the head in the pipeline increases significantly after the first small head rise due to a valve closure. A comparison between the maximum measured head in the laboratory and the theoretical expected maximum head has been undertaken. More realistic configurations that could result in the same phenomenon are briefly discussed.

Consumption Change‐Induced Transients in a Water Distribution Network: Laboratory Tests in a Looped System

“…The so called “head accumulation”—already tested in Bohorquez et al. (2020) but in a single pipe (with a connection in series) for transients generated in the larger diameter pipe (low impedance)—happens also in a WDN for transients generated in the downstream end section of a service line.…”

“…On the other hand, this remark cannot explain the different behavior of test series #2 and #3, since junctions 6 and 7 have the same shape. However, it is worthy pointing out the crucial role of the ratio between the main pipe cross‐sectional areas connected to the service line, and the service line itself, for a given pipe material: the smaller this ratio—that is, the higher the pipe impedance ratio—the larger the transmitted pressure wave (Bohorquez et al., 2020; Swaffield & Boldy, 1993). This is the reason why series #3 experiences the largest range of the no‐cavitating flow in the service line.…”

Improved Analytical Solution for Water Hammer in Viscoelastic Pipes

“…partial closing of the valve. Recently, an approximate analytical method was derived [11] for the accumulated pressure head at the valve, during the first half pressure wave cycle. This method considers, only, frictionless elastic pipes consisting of two reaches with lower hydraulic impedance for the reach associated to the valve.…”

“…for the Kelvin element i. Different terms of ( 10) are compensated as: the viscoelastic term is substituted from (11),…”

Energy Reduction with Application of Shaft in Water Supply Systems

“…A pumped piped network results in more wear and tear than a gravity-based system due to transitional pressures (Zaman et al 2021), and water hammer is the primary problem responsible for the deterioration (Bohorquez et al 2020). Numerous studies have reported the theory of water hammer and solution to minimize its impact on the network (Boulos et al 2005; Nault and Karney 2016; Wan and Zhang 2018).…”