Direct numerical simulation of the amplification of a 2D temporal disturbance in plane Poiseuille flow
✍ Scribed by G. J. Hwang; S. J. Wu
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 229 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0271-2091
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✦ Synopsis
A direct numerical scheme is developed to study the temporal ampli®cation of a 2D disturbance in plane Poiseuille ¯ow. The transient non-linear Navier±Stokes equations are applied in a region of wavelength moving with the wave propagation speed. The complex amplitude involved in the perturbation functions is considered as the initial input of the non-linear stability equations. In this study a fully implicit ®nite difference scheme with ®ve points in the ¯ow direction and three points in the normal direction is developed so that numerical simulation of the ampli®cation of a two-dimensional temporal disturbance in plane Poiseuille ¯ow can be investigated. The growth and decay of the disturbance with time are presented and neutral stability curves which are in good agreement with existing solutions can be determined. The critical conditions as a function of the amplitude A 0 of the disturbance are presented. Fixing the wavelength, the Navier±Stokes equations are solved up to Re 10,000 a friction factor increasing with Reynolds number is observed. The 2D non-linear behaviour of the streamfunction, vorticity and velocity components at Re 10,000 are also exhibited.