TY - JOUR
T1 - Distribution Patterns of Eigenvalues of Laminar Pipe Flow 3rd Report, Effect of the Reynolds Number
AU - Suematsu, Yoshikazu
AU - Hayase, Toshiyuki
AU - Hase, Kenji
AU - Ito, Tadaya
PY - 1988
Y1 - 1988
N2 - This study investigates the structure and dynamic behavior of a linear system which describes the perturbation of a laminar pipe flow. In the preceding papers a numerical method for calculating the eigenvalues with sufficient accuracy was proposed, and the characteristic distribution pattern of eigenvalues for Poiseuille pipe flow and the classification of the modes of the perturbations were presented. This paper discusses the effects of the Reynolds number on the distribution pattern of eigenvalues. In the first place, for the Poiseuille pipe flow, it is shown how the distribution of eigenvalues in a complex phase velocity plane takes a tree like shape as the Reynolds number increases. Then the distributions of eigenvalues are calculated for the laminar developing pipe flow and the Poiseuille pipe flow with rigid rotation, which are known to be unstable for high Reynolds number. It is found that these distribution patterns take the same shape as that of Poiseuille pipe flow, and that the unstable eigenvalues belong to the specified modes of perturbations, as predicted in the former report.
AB - This study investigates the structure and dynamic behavior of a linear system which describes the perturbation of a laminar pipe flow. In the preceding papers a numerical method for calculating the eigenvalues with sufficient accuracy was proposed, and the characteristic distribution pattern of eigenvalues for Poiseuille pipe flow and the classification of the modes of the perturbations were presented. This paper discusses the effects of the Reynolds number on the distribution pattern of eigenvalues. In the first place, for the Poiseuille pipe flow, it is shown how the distribution of eigenvalues in a complex phase velocity plane takes a tree like shape as the Reynolds number increases. Then the distributions of eigenvalues are calculated for the laminar developing pipe flow and the Poiseuille pipe flow with rigid rotation, which are known to be unstable for high Reynolds number. It is found that these distribution patterns take the same shape as that of Poiseuille pipe flow, and that the unstable eigenvalues belong to the specified modes of perturbations, as predicted in the former report.
KW - Developing Flow
KW - Distribution of Eigenvalues
KW - Fluid Mechanics
KW - Hagen-Poiseuillle Flow
KW - Laminar Pipe Flow
KW - Poiseuile Flow with Rigid Rotation
KW - Stability
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U2 - 10.1299/kikaib.54.2433
DO - 10.1299/kikaib.54.2433
M3 - Article
AN - SCOPUS:0024072298
VL - 54
SP - 2433
EP - 2440
JO - Nihon Kikai Gakkai Ronbunshu, B Hen/Transactions of the Japan Society of Mechanical Engineers, Part B
JF - Nihon Kikai Gakkai Ronbunshu, B Hen/Transactions of the Japan Society of Mechanical Engineers, Part B
SN - 0387-5016
IS - 505
ER -