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A low-Reynolds-number k–ε model for polymer drag-reduction prediction in turbulent pipe flow

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Abstract

Pipeline transport at high Reynolds number can result in significant turbulent losses. One of the most effective methods for turbulent drag reduction is adding a very small amount of polymer drag-reducing agent to the pipeline. However, due to the complex interaction between polymers and turbulence, turbulence models incorporating polymer additives remain to be studied and developed. In the present work, we investigated the turbulence model using Reynolds averaged numerical simulation (RANS) to describe polyacrylamide drag reduction flow. A low-Reynolds-number k–ε model in turbulent flow has been developed by considering the concentration and type of polymers, which can be applied for polymer drag reduction prediction in the pipe. Mean velocity profile Uf, turbulent intensity, turbulent kinetic energy k, and turbulent dissipation rate ε in the regions of viscous sublayer, buffer layer and logarithmic layer have been predicted with various concentration θ, Reynolds number Re, degradation degrees, and changing laws of these factors have been revealed with wall distance. The developed turbulence model showed a good capability to qualitatively forecast mean velocity profile, turbulent intensity, turbulent kinetic energy, and turbulent dissipation rate, and the prediction error between the experimental and simulated values falls along the y = x curve, which can be used for the investigation and prediction of varies water-soluble, oil-soluble polymers in turbulent drag reduction flow in pipes with other parameters such as pipe diameter, pipe length, and the Reynolds number.

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Data availability

Data supporting the results of the study will be made available subject to an internal approval process. The data underlying this article are available at https://doi.org/10.1017/S0022112097004850.

Abbreviations

A:

Types of polymers

L :

Pipe length (m)

D :

Pipe diameter (m)

H :

Characteristic length (m)

y + :

Distance from the wall was normalized

u 0 :

Initial velocity (m/s)

u τ :

Friction velocity (m/s)

\(u^+\) :

Velocity normalized using friction velocity

U f :

Mean velocity (m/s)

Re:

Reynolds number

Reτ :

Characteristic Reynolds number

DR:

Drag reduction efficiency (%)

θ :

Concentration (%)

μ t :

Turbulent viscosity (kg/(m s))

k :

Turbulent kinetic energy (J)

ε :

Turbulent dissipation rate

τ ij :

Reynolds stress (Pa)

\(\tau_{\text{w}}\) :

Wall shear stress (Pa)

f μ :

Damping function

f(θ, A) :

Additional correction function

f(c kk):

Function related to the molecular deformation rate tensor

f w :

Wall friction resistance coefficient

M :

Molecular weight (g/mol)

u + rms :

The root mean square (RMS) value of the velocity fluctuationsy

LDA:

Laser Doppler Anemometry

PIV:

Particle Image Velocimetry

DNS:

Direct Numerical Simulation

RANS:

Reynolds averaged numerical simulation

ppm:

Parts per million

Exp:

Experimental

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Acknowledgements

We would like to acknowledge support from assistance from Ufa State Petroleum Technological University and Southwest Petroleum University. This work was supported by the National Natural Science Foundation of China (No. 52004241), the Natural Science Foundation of Sichuan Province (No. 2022NSFSC1018), the Open Fund Project of SINOPEC Key Laboratory for EOR of Fractured-vuggy Reservoir (34400000-22-ZC0607-0006) and the China Scholarship Council (No. 201508090094).

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Authors and Affiliations

  1. Petroleum Engineering School, Southwest Petroleum University, Chengdu, 610500, China

    Yang Chen, Meiyu Zhang & Changjun Li

  2. Institution of Oil-Gas Storage and Transportation, Ufa State Petroleum Technological University, Ufa, Russia, 450062

    Yang Chen, A. R. Valeev & A. M. Nechval

  3. National Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, 610500, China

    Yang Chen, Meiyu Zhang & Changjun Li

  4. Sinopec: China Petrochemical Corporation, Beijing, 100728, China

    Peng Yang

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Correspondence to Yang Chen.

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Chen, Y., Zhang, M., Valeev, A.R. et al. A low-Reynolds-number k–ε model for polymer drag-reduction prediction in turbulent pipe flow. Korea-Aust. Rheol. J. (2024). https://doi.org/10.1007/s13367-024-00087-0

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