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

UR - http://www.scopus.com/inward/record.url?scp=0024072298&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0024072298&partnerID=8YFLogxK

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 -