The Unsteady Laminar Flow between Two Parallel Discs with Arbitrarily Varying Gap Width

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概要

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• A theoretical analysis is presented for the unsteady laminar flow of an incompressible fluid in a narrow gap between two parallel discs of which gap-width h (t) varies arbitrarily with time. An infinite set of the non-dimensional time-dependent parameters [numerical formula], …… is introduced providing that the function h (t) is continuously differentiable, and the exact solutions of the Navier-Stokes equations and the thermal energy equation are obtained as the "multifold"series of these non-dimensional parameters. As an application, a detailed numerical study has been made of the fundamental case when the walls perform reciprocating harmonic oscillations with finite amplitudes {h (t)=h_0 (1+asinωt)}. The flow characteristics are governed by the two non-dimensional parameters a and R_ω=(h_0^2ω)/υ. As compared with the sinusoidal velocity of the gap-width change, (dh)/(dt)=aωh_0cosωt, the varying hydrodynamical force acting on the wall surface becomes more distorted in wave form as a increases, and becomes more advanced in phase as R_ω increases. Heat is generated in the fluid between the walls through viscous friction : when the fluid is cooled by only one wall surface the fluid temperature becomes very much higher than when the cooling is done by both the two walls.

• 一般社団法人日本機械学会の論文

著者

• Ishizawa Shingo

  Mechanical Engineering Research Laboratory Hitachi Ltd.

関連論文

• A New Multifold Series General Solution of the Steady, Laminar Boundary Layers : 2nd Report, Application Theory of the Euler Transformation
• A New Theory and its Extensive Application of the Multifold Series Expansion Analysis for the Boundary Layer Equations
• A New Multifold Series General Solution of the Steady, Laminar Boundary Layers : 3rd Report, Extension of the Solution to the Case of Not Smoothly joining Mainstream-Velocities
• The Flow of a Viscous Fluid through a Porous Wall into a Narrow Gap : A Consideration of the Slip of Fluid on a Porous Wall Surface
• The Unsteady Laminar Flow between Two Parallel Discs with Arbitrarily Varying Gap Width
• A New Multifold Series General Solution of the Steady, Laminar Boundary Layers : 1st Report, Theory of the Multifold Series Expansion
• On the Momentum-Integral Method of Solution for the Laminar Entrance-Flow Problems

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