General Unsteady Circulatory Flow outside a Porous Circular Cylinder with Suction or Injection

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Abstract

An exact solution of the Navier-Stokes equations is established for a general initial/boundary-value problem which describes the development of an incompressible circulatory flow outside an infinite circular cylinder with uniform suction or injection. An asymptotic evaluation of the solution, valid after a long time, reveals the effects of suction or injection upon the ultimate flow behavior; for R>2, the circulation at infinity remains unchanged throughout the process if it is finite initially; for R≤1, all of the vorticity, even if its amount is infinite, is blown away to infinity and the flow becomes irrotational in the final state; intermediate between them is the case of 1<R≤2. Here R=Va/v, with V, a and v being the suction velocity, radius of the cylinder and the kinematic viscosity, respectively.

Original languageEnglish
Pages (from-to)918-926
Number of pages9
JournalJournal of the Physical Society of Japan
Volume59
Issue number3
DOIs
Publication statusPublished - 1990
Externally publishedYes

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suction
circular cylinders
injection
infinity
potential flow
boundary value problems
Navier-Stokes equation
vorticity
kinematics
viscosity
radii
evaluation

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

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title = "General Unsteady Circulatory Flow outside a Porous Circular Cylinder with Suction or Injection",
abstract = "An exact solution of the Navier-Stokes equations is established for a general initial/boundary-value problem which describes the development of an incompressible circulatory flow outside an infinite circular cylinder with uniform suction or injection. An asymptotic evaluation of the solution, valid after a long time, reveals the effects of suction or injection upon the ultimate flow behavior; for R>2, the circulation at infinity remains unchanged throughout the process if it is finite initially; for R≤1, all of the vorticity, even if its amount is infinite, is blown away to infinity and the flow becomes irrotational in the final state; intermediate between them is the case of 1<R≤2. Here R=Va/v, with V, a and v being the suction velocity, radius of the cylinder and the kinematic viscosity, respectively.",
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T1 - General Unsteady Circulatory Flow outside a Porous Circular Cylinder with Suction or Injection

AU - Fukumoto, Yasuhide

PY - 1990

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N2 - An exact solution of the Navier-Stokes equations is established for a general initial/boundary-value problem which describes the development of an incompressible circulatory flow outside an infinite circular cylinder with uniform suction or injection. An asymptotic evaluation of the solution, valid after a long time, reveals the effects of suction or injection upon the ultimate flow behavior; for R>2, the circulation at infinity remains unchanged throughout the process if it is finite initially; for R≤1, all of the vorticity, even if its amount is infinite, is blown away to infinity and the flow becomes irrotational in the final state; intermediate between them is the case of 1<R≤2. Here R=Va/v, with V, a and v being the suction velocity, radius of the cylinder and the kinematic viscosity, respectively.

AB - An exact solution of the Navier-Stokes equations is established for a general initial/boundary-value problem which describes the development of an incompressible circulatory flow outside an infinite circular cylinder with uniform suction or injection. An asymptotic evaluation of the solution, valid after a long time, reveals the effects of suction or injection upon the ultimate flow behavior; for R>2, the circulation at infinity remains unchanged throughout the process if it is finite initially; for R≤1, all of the vorticity, even if its amount is infinite, is blown away to infinity and the flow becomes irrotational in the final state; intermediate between them is the case of 1<R≤2. Here R=Va/v, with V, a and v being the suction velocity, radius of the cylinder and the kinematic viscosity, respectively.

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