Solution of Navier-Stokes equations in squeezing flow between parallel plates in two-dimensional case

0447948 - ÚH 2016 eng C - Konferenční příspěvek (zahraniční konf.)
Petrov, A.G. - Kharlamova, Irina
Solution of Navier-Stokes equations in squeezing flow between parallel plates in two-dimensional case.
2015.
[The 16th International Conference on Fluid Flow Technologies. Budapest (HU), 01.09.2015-04.09.2015]
Grant ostatní: Russian science foundation(RU) 14-19-01633
Institucionální podpora: RVO:67985874
Klíčová slova: closed form solution * counterflow * Navier-Stokes equations * squeezing flow between plates * two-dimensional viscous flow
Kód oboru RIV: BK - Mechanika tekutin

The velocity profile in a layer of a twodimensional viscous Newtonian fluid between two parallel plates, where one plate is immobile and other is either moving away or moving to the first one, is studied. The distance between plates changes in time according to arbitrary power-law: h ∼ |t|s. The unsteady Navier-Stokes equations in three independent variables with some special substitutions were reduced to a system of ordinary differential equations. As result, a new boundary value problem of the third order with two variables was found. Precise solutions of the Navier-Stokes equations are constructed as series in powers of Reynolds number. The cases of motion with s = 0.5, 1, 2 are studied in detail. In the case s = 0.5 the series is convergent and the self-similar, one-parametric solution can be obtained; in other cases the series is asymptotic. For some Reynolds numbers greater than critical, the velocity of flow near the boundaries has opposite direction to the average velocity; it is the counterflow phenomenon. The critical Reynolds numbers corresponding to the appearance of counterflow for all three cases were determined.
Trvalý link: http://hdl.handle.net/11104/0249703