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A numerical study over the effect of curvature and adverse pressure gradient on development of flow inside gas transmission pipelines

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Abstract

In order to inspect the effects of adverse pressure gradient (APG) and curvature on the corrosion in the main gas transmission pipelines, the mean velocity and turbulence boundary layer on the walls of six different geometries including a straight pipe (A), a convex pipe (B1), a concave pipe (B2), a convex diffuser (C1), a concave diffuser (C2) and a straight diffuser (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 flow 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 affected quantities in the shear region are independent.

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Abbreviations

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 diffuser

C1:

Flow in a curved diffuser with boundary layer developing on the convex side

C2:

Flow in a curved diffuser with boundary layer developing on the concave side

D :

Flow in a straight diffuser

H :

Shape factor

K :

Turbulent kinetic energy per unit mass (m2/s2)

\(k_{r}\) :

The inverse of curvature radius (m−1)

p :

Pressure (kgm/s2)

R :

Centerline radius of curvature in the curved pipe/diffuser (mm)

t :

Time (s)

u′, v′, w′:

Turbulent normal stress (m/s)

\(\overline{{u^{{\prime}} v^{{\prime}}}}\) :

Turbulent shear stress (m2/s2)

\(u_{c}\) :

Centerline velocity (m/s)

\(u_{e}\) :

External velocity of the flow (m/s)

\(u_{p}\) :

Velocity profile in the potential flow region (m/s)

\(U_{\text{ref}}\) :

Reference velocity (m/s)

\(u_{w}\) :

Potential velocity on the wall (m/s)

\(u_{\tau}\) :

Friction velocity (m/s)

x :

Along stream-wise direction (m)

y :

Normal direction(m)

\(\beta\) :

Clauser’s pressure gradient parameter

\(\delta^{*}\) :

Boundary layer thickness (mm)

\(\delta\) :

Displacement thickness (mm)

\(\varepsilon\) :

Dissipation rate of the turbulent kinetic energy per unit mass (m2/s2)

\(\theta\) :

Momentum thickness (mm)

\(\kappa\) :

Von Karman constant (\(\kappa\) = 0.41)

\(\vartheta_{t}\) :

Kinematic eddy viscosity (m2/s)

\(\vartheta\) :

Kinematic viscosity (m2/s)

\(\rho\) :

Density (kg/m3)

\(\omega\) :

Specific dissipation rate (1/s)

APG:

Adverse pressure gradient

CR:

Centerline radius

STBL:

Supersonic turbulence boundary layer

TBL:

Turbulence boundary layer

ZPG:

Zero pressure gradient

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Authors and Affiliations

  1. Department of Mechanical Engineering, Hakim Sabzevari University, Sabzevar, Iran

    Mitra Yadegari & Abdolamir Bak Khoshnevis

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  1. Mitra Yadegari
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  2. Abdolamir Bak Khoshnevis
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Correspondence to Abdolamir Bak Khoshnevis.

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Technical Editor: Daniel Onofre de Almeida Cruz, D.Sc.

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Yadegari, M., Bak Khoshnevis, A. A numerical study over the effect of curvature and adverse pressure gradient on development of flow inside gas transmission pipelines. J Braz. Soc. Mech. Sci. Eng. 42, 413 (2020). https://doi.org/10.1007/s40430-020-02495-z

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