TY - JOUR
T1 - Existence of dual solutions and three-dimensional instability in helical pipe flow
AU - Datta, Anup Kumer
AU - Kouchi, Toshinori
AU - Hayamizu, Yasutaka
AU - Nagata, Yasunori
AU - Yamamoto, Kyoji
AU - Yanase, Shinichiro
N1 - Funding Information:
A. K. Datta would like to acknowledge gratefully the financial support from the Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) for study in Japan. Y. Hayamizu and S. Yanase would like to give their cordial thanks to MEXT for the financial support through the Grant-in-Aid for Scientific Research, No. 15K05814 .
Publisher Copyright:
© 2021 The Physical Society of the Republic of China (Taiwan)
PY - 2021/10
Y1 - 2021/10
N2 - Three-dimensional (3D) direct numerical simulations (DNS) of the viscous incompressible fluid flow through a helical pipe with circular cross section were performed. The flow is governed by three parameters: the Dean number (or the Reynolds number), curvature, and torsion. First, we obtained steady solutions by steady 3D calculations, where dual solutions were found, one was uniform in the pipe axial direction and the other varied very slowly, if torsion exceeded a critical value. Then, the instability of the steady solutions obtained was studied by unsteady 3D calculations. We obtained critical Reynolds numbers of steady to unsteady transition by observing the behaviors of the unsteady solutions. The present results of the critical Reynolds number nearly agreed with those by the 2D linear stability analysis (Yamamoto et al. [9]) except for the lowest critical Reynolds number region, where the present study gave the critical Reynolds number much less than that obtained by the 2D linear stability analysis. We found the vortical structures in the form of a standing wave slightly above the marginal instability state, which is a trigger of explosive 3D instability.
AB - Three-dimensional (3D) direct numerical simulations (DNS) of the viscous incompressible fluid flow through a helical pipe with circular cross section were performed. The flow is governed by three parameters: the Dean number (or the Reynolds number), curvature, and torsion. First, we obtained steady solutions by steady 3D calculations, where dual solutions were found, one was uniform in the pipe axial direction and the other varied very slowly, if torsion exceeded a critical value. Then, the instability of the steady solutions obtained was studied by unsteady 3D calculations. We obtained critical Reynolds numbers of steady to unsteady transition by observing the behaviors of the unsteady solutions. The present results of the critical Reynolds number nearly agreed with those by the 2D linear stability analysis (Yamamoto et al. [9]) except for the lowest critical Reynolds number region, where the present study gave the critical Reynolds number much less than that obtained by the 2D linear stability analysis. We found the vortical structures in the form of a standing wave slightly above the marginal instability state, which is a trigger of explosive 3D instability.
KW - Critical Reynolds number
KW - Helical pipe flow
KW - Three-dimensional instability
KW - Torsion effect
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U2 - 10.1016/j.cjph.2021.07.002
DO - 10.1016/j.cjph.2021.07.002
M3 - Article
AN - SCOPUS:85111253329
VL - 73
SP - 154
EP - 166
JO - Chinese Journal of Physics
JF - Chinese Journal of Physics
SN - 0577-9073
ER -