Attenuation of pipeline filling over-pressures through trapped air

ABSTRACT

Entrapped air pockets in water pipelines play a significant role in influencing transient over-pressures during filling procedures. Several research is focused on highlighting the attenuation of pressure peaks in pipes with single air pockets. This research studies the air-water interaction during rapid water filling processes in an irregular pipeline and air pockets in different branches, and how the trapped air can attenuate the over-pressure peaks. A three-dimensional computational fluid dynamics (CFD) model was developed, and numerical results of the model were validated through experimental measurements. For a given initial air pocket condition upstream of the high point, the maximum air pocket over-pressure was 11% to 32% lower when the descending pipe segment initially contains air compared to when it contains water. In sum, it was found that entrapped air pockets at high points of water pipelines can help mitigate transient over-pressures considering specific initial hydraulic conditions prior to filling operations.

KEYWORDS:

• Pipeline filling
• air pockets
• entrapped air
• transient flows
• computational fluid dynamics

Nomenclature/Notation

$a_{\mathit{eff}}$	=	= thermal diffusivity (m2/s)
Cs	=	= roughness constant (–)
Dk	=	= diffusion term for $\mathit{k}$ (m2/s)
$D_{\omega }$	=	= diffusion term for $\mathit{\omega }$ (m2/s)
e	=	= internal energy (m2/s2)
F1	=	= blending function (–)
Fs	=	= surface tension force (kg$\cdot$m/s2)
fn	=	= roughness function parameter (–)
G	=	= turbulent kinetic energy generation (m2/s3)
g	=	= gravitational acceleration vector (m/s2)
Ks	=	= absolute roughness (m)
k	=	= turbulence kinetic energy (m2/s2)
P	=	= static pressure (kg/(m$\cdot$s2))
P0	=	= inlet pumping pressure (kg/(m$\cdot$s2))
Pmax	=	= maximum over-pressure peak (kg/(m$\cdot$s2))
q	=	= heat flux (kg/s3)
R	=	= universal gas constant (J/(kg$\cdot$K))
ST	=	= energy source term (kg$\cdot$m2/s2)
T	=	= temperature (K)
t	=	= time (s)
tp	=	= peak over-pressure time instant (s)
$\mathit{\upsilon }$	=	= velocity vector (m/s)
${\upsilon }_{\mathit{in}}$	=	= air inflow velocity (m/s)
${\upsilon }_r$	=	= velocity field (m/s)
${\upsilon }^{\ast }$	=	= shear velocity (m/s)
x0	=	= air pocket size (m)
y+	=	= dimensionless wall distance (–)
${\alpha }_{\omega }$	=	= water volume fraction (–)
$\mathit{\mu }$	=	= dynamic viscosity (N$\cdot$s/m2)
P	=	= density (kg/m3)
$\mathrm{\varnothing }$	=	= pipe diameter (m)
$\mathit{\omega }$	=	= dissipation frequency (s−1)
Subscripts	=
$\mathit{\alpha }$	=	= refers to the air phase (e.g. air density).
W	=	= refers to the water phase (e.g. dynamic water viscosity).
m	=	= refers to the mixture of the air and water phases (e.g. combined density).

Disclosure statement

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