Iranian Journal of Mechanical Engineering Transactions of ISME

Iranian Journal of Mechanical Engineering Transactions of ISME

Exact Solution of Viscous Fluid Velocity and Pressure Due to Kinematic Effect of Two-Dimensional Boundary Propagating Wave

Authors
Mohammad Ehsan Khodaei Meidanshah 1
Khosro Naderan Tahan 1
Mojtaba Dehghan Manshadi 2
Amin Yaghootian 1
1 Department of Mechanical Engineering, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran
2 Department of Mechanical and Aerospace Engineering, Malek-Ashtar University of Technology, Isfahan, Iran
Abstract
In the present study, to extend the Stokes' second problem, the bottom edge of viscous incompressible semi-space resting fluid is excited in two dimension, simultaneously. This two-dimensional excitation which is the effect of velocity of two-dimensional travelling wave, is boundary condition for the two-dimensional linear Navier-Stokes equations. The time-space exact solution for fluid velocity and pressure show that the amplitude of oscillating velocity has fast damping in space till 1.87 micron from excited surface. After this height, the amplitude of oscillating quantities has a slowly damping. In the first region (in fast damping region), phase difference between pressure and velocity is changing, but after that there is a region with constant phase difference. The space variation in velocity components of surface wave, together with the coupling of velocity components in main equations, produces pressure wave. It has been found that kinematic effect of vertical and horizontal harmonic motion cause damped rotational motion in fluid.
Keywords
Analytical Solution
Incompressible Fluid
Wave Propagation
Phase Difference
Vortex

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Iranian Journal of Mechanical Engineering Transactions of ISME
Volume 20, Issue 4 - Serial Number 53
Fluid Mechanics and Heat Transfer
Winter 2019
Pages 210-233

  • Receive Date 21 August 2018
  • Revise Date 11 November 2018
  • Accept Date 12 March 2019