Hydrodynamic forces on two moving discs

Abstract

We give a detailed presentation of a flexible method for constructing explicit expressions of irrotational and incompressible fluid flows around two rigid circular moving discs. We also discuss how such expressions can be used to compute the fluid-induced forces and torques on the discs in terms of Killing drives. Conformal mapping techniques are used to identify a meromorphic function on an annular region in C with a flow around two circular discs by a Mobius transformation. First order poles in the annular region correspond to vortices outside of the two discs. Inflows are incorporated by putting a second order pole at the point in the annulus that corresponds to infinity.U radu se daje detaljna prezentacija jednog prilagodljivog metoda za konstrukciju eksplicitnih izraza za irotaciona i nestisljiva fluidna tecenja oko dva kruta pokretna kruzna diska. Takodje se diskutuje kako takvi izrazi mogu da se iskoriste za izracunavanje fluidom iza zvanih sila i spregova na diskove pomocu Kilingovih diskova. Zatim se Mebijusovom transformacijom koristeci tehniku konformnog preslikavanja izvodi identifikacija meromorfne funkcije na anularnoj oblasti u C sa tecenjem oko dva kruzna diska. Ovde polovi prvog reda odgovaraju vrtlozima van diskova. Tecenja ka unutrasnjosti se uzimaju u obzir postavljanjem pola drugog reda u anulus koji odgovara beskonacnosti. .