Comparative numerical study on pressure drop in helically coiled and longitudinally C-shaped pipes
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Comparative numerical study on pressure drop in helically coiled and longitudinally C‑shaped pipes Yassine Demagh1 · Elwardi Bitam1 · Lyes Bordja2 Received: 15 October 2019 / Accepted: 17 August 2020 © Springer Nature Switzerland AG 2020
Abstract In the present work, the shear stress transport (SST) k − 𝜔 model is used to simulate internal turbulent flows in curved tubular heat exchangers and the resulting friction factors Cf are calculated. A helically coiled configuration was used in the validation process of the model that showed a good agreement between numerical results of the friction factors Cf and the standard experimental correlations of the literature, with a maximum relative error of 4.24%. A comparative study was performed to investigate the possibility of applying friction factor correlations, established mainly for helical coils, to longitudinally C-shaped pipes. Preliminary results confirm the inability of coil-specific correlations to predict the friction factor Cf inside C-shaped pipes. It was also noted that, unlike helical coils, the C-shaped pipe friction factor appears to be affected by ratios other than the curvature ratio as highlighted in this study by introducing the effect of the amplitude ratio 𝛽 defined as the ratio of the amplitude to the curvature radius.
( ) Keywords Pressure drop · Fanning friction factor Cf · Helically coiled pipes · Longitudinally C-shaped pipes 𝜇 Dynamic viscosity (kg m−1 s−1) 𝜇t Turbulent viscosity 𝜔 Turbulent dissipation rate (m2 s−3) k Turbulent kinetic energy (m2 s−2) 𝜌 Density (kg m−3)
List of symbols A Amplitude of the C-shaped pipe (m) Cf Friction coefficient cp Heat capacity (J kg−1 K−1) Di Inner diameter of the pipe (m) f Darcy friction factor Nu Nusselt number Pr Prandlt number Prt Turbulent Prandtl number Rc Curvature radius (m) Re Reynolds number T Temperature (K) u Velocity field (m s−1)
Subscripts b Bulk f Fluid i Inner in Inlet s Straight w Wall
Greek letters 𝛽 Amplitude ratio 𝛿 Curvature ratio 𝜆 Periodicity length (m). Heat conductivity (W K−1 m−2)
* Yassine Demagh, y.demagh@univ‑batna2.dz; Elwardi Bitam, [email protected]; Lyes Bordja, [email protected] | 1LESEI, Department of Mechanics, University Batna 2, Batna, Algeria. 2Department of Mechanics, Faculty of Science and Applied Sciences, University Larbi Ben M’hidi, Oum El Bouaghi, Algeria. SN Applied Sciences
(2020) 2:1570
| https://doi.org/10.1007/s42452-020-03355-0
Vol.:(0123456789)
Research Article
SN Applied Sciences
(2020) 2:1570
1 Introduction Due to improved heat transfer rate, the most widely used tubular heat exchangers in industrial processes are the helically coiled pipes (Fig. 1a). Nevertheless, they produce significant and undesirable pressure drop because of the generation of second flows (vortices) within the mainstream. In fact, concern about pressure drop in curved configurations is common, with particular attention to the helical coils (Hart et al. [1], Guo et al. [2] and Mori and Nakayama [3]). For most cases, the curvature ra
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