Vol.:(0123456789) 1 3
Journal of the Brazilian Society of Mechanical Sciences and Engineering (2020) 42:413
https://doi.org/10.1007/s40430-020-02495-z
TECHNICAL PAPER
A numerical study over the efect of curvature and adverse pressure
gradient on development of fow inside gas transmission pipelines
Mitra Yadegari
1
· Abdolamir Bak Khoshnevis
1
Received: 19 September 2019 / Accepted: 4 July 2020 / Published online: 17 July 2020
© The Brazilian Society of Mechanical Sciences and Engineering 2020
Abstract
In order to inspect the efects of adverse pressure gradient (APG) and curvature on the corrosion in the main gas transmis-
sion pipelines, the mean velocity and turbulence boundary layer on the walls of six diferent geometries including a straight
pipe (A), a convex pipe (B
1
), a concave pipe (B
2
), a convex difuser (C
1
), a concave difuser (C
2
) and a straight difuser
(D) are calculated. The values of pressure gradient and curvature parameters are chosen 0.62 and 0.023, respectively. The
results indicate that the corrosion in the concave curvature is greater than that the corrosion in the convex curvature, since
the turbulence intensity increases in the concave curvature while it is suppressed in the convex curvature. In addition, when
the boundary layer is exposed to APG and concave curvature simultaneously, the corrosion is greater than the situation
when there is only APG or concave curvature. Ultimately, it was found that for the six studied geometries, there are two fow
regimes (for velocities lower than 36 m/s) that the turbulence quantities are dependent on velocity. However, for velocities
more than 36 m/s, the turbulence quantities and other afected quantities in the shear region are independent.
Keywords Curvature · Adverse pressure gradient (APG) · k - - SST turbulence model · Corrosion
List of symbols
A Flow in a straight pipe
B Flow in a curved pipe
B1 Flow in a curved pipe with boundary layer
developing on the convex side
B2 Flow in a curved pipe with boundary layer
developing on the concave side
C Flow in a curved difuser
C1 Flow in a curved difuser with boundary layer
developing on the convex side
C2 Flow in a curved difuser with boundary layer
developing on the concave side
D Flow in a straight difuser
H Shape factor
K Turbulent kinetic energy per unit mass (m
2
/s
2
)
k
r
The inverse of curvature radius (m
−1
)
p Pressure (kgm/s
2
)
R Centerline radius of curvature in the curved
pipe/difuser (mm)
t Time (s)
u′, v′, w′ Turbulent normal stress (m/s)
u
v
Turbulent shear stress (m
2
/s
2
)
u
c
Centerline velocity (m/s)
u
e
External velocity of the fow (m/s)
u
p
Velocity profle in the potential fow region
(m/s)
U
ref
Reference velocity (m/s)
u
w
Potential velocity on the wall (m/s)
u
Friction velocity (m/s)
x Along stream-wise direction (m)
y Normal direction(m)
Clauser’s pressure gradient parameter
∗
Boundary layer thickness (mm)
Displacement thickness (mm)
Dissipation rate of the turbulent kinetic energy
per unit mass (m
2
/s
2
)
Momentum thickness (mm)
Von Karman constant ( = 0.41)
t
Kinematic eddy viscosity (m
2
/s)
Kinematic viscosity (m
2
/s)
Density (kg/m
3
)
Specifc dissipation rate (1/s)
Technical Editor: Daniel Onofre de Almeida Cruz, D.Sc.
* Abdolamir Bak Khoshnevis
khoshnevis@hsu.ac.ir
1
Department of Mechanical Engineering, Hakim Sabzevari
University, Sabzevar, Iran