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arXiv · 1609.05392

Unsteady rotating laminar flow: analytical solution of Navier-Stokes equations

Alessio Bocci·Giovanni Mingari Scarpello·Daniele Ritelli
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Abstract

We provide a integration of Navier-Stokes equations concerning the unsteady-state laminar flow of an incompressible, isothermal (newtonian) fluid in a cylindrical vessel spinning about its symmetry axis, say $z$, and inside which the liquid velocity starts with a non-zero axial component as well. Basic physical assumptions are that the pressure axial gradient keeps itself on its hydrostatic value and that no radial velocity exists. In such a way the PDEs become uncoupled and can be faced separately from each other. We succeed in computing both the unsteady velocities, i.e. the axial $v_z$ and the circumferential $v_\theta$ as well, by means of infinite series expansions of Fourier-Bessel type under time exponential damping. Following this, we also find the unsteady surfaces of dynamical equilibrium, the wall shear stress and the Stokesian streamlines

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Alessio Bocci, Giovanni Mingari Scarpello, Daniele Ritelli. 2016-09-17. Unsteady rotating laminar flow: analytical solution of Navier-Stokes equations. https://arxiv.org/abs/1609.05392

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