On the in-series and branching dual-technique - based water-hammer control strategy

ABSTRACT

This study developed the concept of a dual strategy combining the inline and branching techniques; used to upgrade the capacity of existing steel pipe-based hydraulic systems, with respect to the compromise between the attenuation of surge-magnitude and the limitation of period-expansion of the pressure-wave oscillations. Basically, this concept was based on adding a plastic short-penstock to the main steel-pipe and replacing a short in-series short-section of the main-pipe by another one made of plastic material. In this study, the extended 1D water-hammer solver based on the method of characteristics was used for numerical computations. Investigations addressed two plastic material types including High- and Low-Density PolyEthylene (HDPE and LDPE). Results argued that the specific layout of the dual technique using an LDPE material is the most prominent configuration providing an acceptable trade-off between attenuation of the pressure-head surge and limitation of excessive expansion of the period of pressure-wave oscillations.

KEYWORDS:

• Branching
• design
• dual
• hdpe/ldpe
• in-series
• water-hammer

Nomenclature

$A$ = cross-sectional area of the pipe(m²)

$a_0$ = elastic-wave-speed(m/s)

$D$ = diameter of the main steel piping system(m)

$d$ = diameter of the inline (or branched) short-section(m)

$E_0$ = Young’s modulus(Pa)

$e$ = pipe-wall thickness(m)

$g$ = acceleration due to gravity(m/s²)

$h_f$ = pressure-head loss per unit length(–)

$H$ = pressure-head, $h=p/\gamma +z$(m)

$k_v$ = Vitkovsky et al.’s unsteady decay coefficients(–)

$L$ = length of the main piping system(m)

$l$ = length of the inline (or branched) plastic short-section(m)

$Q$ = flow rate(m³/s)

$t$ = time(s)

$T_1$ = period of the first cycle or pressure-wave oscillations(s)

$x$ = coordinate along the pipe axis(m)

z = elevation(m)

Greek symbols

$\mathrm{\Delta }$ = surge magnitude of the first cycle of pressure-wave oscillations(m)

$\delta$ = attenuation of the first pressure-peak or -crest(m)

$\alpha$ = ratios between the relative attenuation of positive (or negative) pressure-surge and the phase-shift, for the first cycle of pressure-wave oscillations(ms⁻¹)

$\varphi$ = phase-shift(s)

Subscripts

0 = steady state

short-section = characteristics of the inline (or branched) plastic short-section

Superscripts

± = characteristics of positive-/negative-surge pressure-wave

Acronyms

HDPE/LDPE = High- or Low- Density PolyEthylene

Disclosure statement

No potential conflict of interest was reported by the author(s).