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Research Papers: Fundamental Issues and Canonical Flows

# Numerical Study of Turbulent Helical Pipe Flow With Comparison to the Experimental Results

[+] Author and Article Information
Anup Kumer Datta

and Technology,
Okayama University,
3-1-1 Tsushima-naka, Kita-Ku,
Okayama 700-8530, Japan
e-mail: akd_math_02@yahoo.com

Yasutaka Hayamizu

National Institute of Technology,
Yonago College,
4448 Hikona-cho,
Yonago-shi 683-8502, Tottori, Japan
e-mail: hayamizu@yonago-k.ac.jp

Toshinori Kouchi

and Technology,
Okayama University,
3-1-1 Tsushima-naka, Kita-Ku,
Okayama 700-8530, Japan
e-mail: kouchi@mech.okayama-u.ac.jp

Yasunori Nagata

and Technology,
Okayama University,
3-1-1 Tsushima-naka, Kita-Ku,
Okayama 700-8530, Japan
e-mail: ynagata@okayama-u.ac.jp

Kyoji Yamamoto

and Technology,
Okayama University,
3-1-1 Tsushima-naka, Kita-Ku,
Okayama 700-8530, Japan
e-mail: tetsukyo8801@earth.ocn.ne.jp

Shinichiro Yanase

and Technology,
Okayama University,
3-1-1 Tsushima-naka, Kita-Ku,
Okayama 700-8530, Japan
e-mail: yanase@mech.okayama-u.ac.jp

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received August 7, 2016; final manuscript received April 5, 2017; published online June 20, 2017. Assoc. Editor: Satoshi Watanabe.

J. Fluids Eng 139(9), 091204 (Jun 20, 2017) (13 pages) Paper No: FE-16-1503; doi: 10.1115/1.4036477 History: Received August 07, 2016; Revised April 05, 2017

## Abstract

Turbulent flow through helical pipes with circular cross section is numerically investigated comparing with the experimental results obtained by our team. Numerical calculations are carried out for two helical circular pipes having different pitches and the same nondimensional curvature δ (=0.1) over a wide range of the Reynolds number from 3000 to 21,000 for torsion parameter $β$ (=torsion $/2δ$  = 0.02 and 0.45). We numerically obtained the secondary flow, the axial flow and the intensity of the turbulent kinetic energy by use of three turbulence models incorporated in OpenFOAM. We found that the change to fully developed turbulence is identified by comparing experimental data with the results of numerical simulations using turbulence models. We also found that renormalization group (RNG) $k−ε$ turbulence model can predict excellently the fully developed turbulent flow with comparison to the experimental data. It is found that the momentum transfer due to turbulence dominates the secondary flow pattern of the turbulent helical pipe flow. It is interesting that torsion effect is more remarkable for turbulent flows than laminar flows.

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## Figures

Fig. 1

(a) Helical pipe with circular cross section and (b) coordinate system

Fig. 2

Mesh on the cross section of the helical pipe

Fig. 3

Axial flow distribution on the x-axis for β = 0.02 and δ = 0.1

Fig. 4

A view of the 3.2 pitch helical pipe showing the three-pitch downstream cross section for β = 0.02 and δ = 0.1

Fig. 5

Axial velocity distribution on the x-axis for β = 0.02 at δ = 0.1. The outer wall is on the right-hand side: (a) Re = 5320, (b) Re = 6880, (c) Re = 12,140, and (d) Re = 20,850.

Fig. 6

Axial velocity distribution on the y-axis for β = 0.02 at δ = 0.1. The upper wall is on the right-hand side: (a) Re = 5320, (b) Re = 6880, (c) Re = 12,140, and (d) Re = 20,850.

Fig. 7

Vector plots of the secondary flow for β = 0.02 and δ = 0.1. Two figures on the left-hand side are the results of numerical simulations and one on the right-hand side is the experimental result: (a) is for Re = 12,140 and (b) for Re = 20,850. The outer wall is on the right-hand side.

Fig. 8

Numerical result of vector plots of the secondary flow for β = 0.02 and δ = 0.1 at Re = 200

Fig. 9

Contours of the axial velocity for β = 0.02 and δ = 0.1. Two figures on the left-hand side are the results of numerical simulations and one on the right-hand side is the experimental result: (a) is for Re = 12,140 and (b) for Re = 20,850.

Fig. 10

Turbulent intensity, (2k)1/2/〈w¯〉 for β = 0.02 and δ = 0.1 at Re = 12,140 and 20,850, where k is the intensity of turbulent kinetic energy and 〈w¯〉 the mean axial velocity. Two figures on the left-hand side are the results of numerical simulations and one on the right-hand side is the experimental result: (a) is for Re = 12,140 and (b) for Re = 20,850.

Fig. 11

Axial velocity distribution on the x-axis for β = 0.45 at δ = 0.1. The outer wall is on the right-hand side: (a) Re = 3060, (b) Re = 5550, (c) Re = 9340, and (d) Re = 19,910.

Fig. 12

Axial velocity distribution on the y-axis for β = 0.45 at δ = 0.1. The upper wall is on the right-hand side: (a) Re = 3060, (b) Re = 5550, (c) Re = 9340, and (d) Re = 19,910.

Fig. 13

Contours of the axial velocity for β = 0.45 and δ = 0.1. Two figures on the left-hand side are the results of numerical simulations and one on the right-hand side is the experimental result: (a) is for Re = 9340 and (b) for Re = 19,910.

Fig. 14

Turbulence intensity, (2k)1/2/〈w¯〉, for β = 0.45 and δ = 0.1 at Re = 9340 and 19,910, where k is the intensity of turbulent kinetic energy and 〈w¯〉 the mean axial velocity. Two figures on the left-hand side are the results of numerical simulations and one on the right-hand side is the experimental result. (a) is for Re = 9340 and (b) for Re = 19,910.

Fig. 15

Friction factor of the helical pipe for β = 0.45 and δ = 0.1

Fig. 16

Equi-Q-value surface for β = 0.02 and δ = 0.1: (a) shows the pipe wall, (b) the case for Re = 200, where Q = 0.5, and (c) the case for Re = 20,850, where Q = 70

Fig. 17

Equi-Q-value surface for β = 0.45 and δ = 0.1: (a) shows the pipe wall, (b) the case for Re = 200, where Q = 0.5, and (c) the case for Re = 19,910, where Q = 70

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