A linearized theory for unsteady flow along vaneformed fillets driven by surface tension
Abstract
A mathematical model was formulated for the flow through the fillets of liquid propellant formed in the intersections of vanes and tank walls. In addition, based on a small perturbation approximation, firstorder linear equations for the surface tension driven flow in zerog condition were obtained. The resulting equations are useful for predicting an unsteady inviscid flow along the fillets. These equations are analogous to the well known acoustic equation and the linearized potential equation for supersonic flow. The linearized equations show that a small disturbance will travel along the vane at a wave speed equal to the square root of the fraction of the kinematic surface tension coefficient divided by two x the liquid layer thickness h sub 0, i.e., a = (beta/2 h sub 0) sup 1/2, where beta is the surface tension divided by the liquid density. A solution of these equations for a case of a uniform fillet with a small step increase in thickness delta shows that the liquid flows from the thicker portion of the fillet toward the thinner portion at a fraction (delta/h sub 0) of the wave speed.
 Publication:

In Johns Hopkins Univ
 Pub Date:
 October 1990
 Bibcode:
 1990jann....2..333D
 Keywords:

 Fillets;
 Fuel Control;
 Interfacial Tension;
 Liquid Sloshing;
 Mathematical Models;
 Unsteady Flow;
 Wall Flow;
 Inviscid Flow;
 Kinematics;
 Linear Equations;
 Liquid Rocket Propellants;
 Perturbation Theory;
 Potential Flow;
 Supersonic Flow;
 Vanes;
 Weightlessness;
 Fluid Mechanics and Heat Transfer