A method for determining orifice loss coefficients in strongly transient compressible liquid flows

Abstract

The aim of the current work was to devise a method of establishing orifice loss coefficients in highly transient liquid flows. This was motivated by the fact that (i) many physical systems involve liquid transfer through narrow channels between cavities under unsteady conditions, and (ii) such data does not exist in the literature. A test facility was constructed, consisting of a drop-weight tester which operates in conjunction with a test cell comprising a vertically mounted thick-walled cylinder blanked off at the bottom, and containing upper and lower water-filled cavities separated by a plate with a small, sharp-edged orifice (thickness to diameter ratio of four). The upper cavity is enclosed at its top surface by a piston which protrudes beyond the upper section of the cylinder. When a weight is dropped onto the piston, a variation of pressure (p1) occurs in the upper cavity, approximating the shape of a half sinusoid with time, and with a typical half cycle (T) in the range 1.34–2.73 ms. Mass transfer takes place from the upper to the lower cavity, with a commensurate increase of pressure (p2) in the latter. At a certain time p1 and p2 become equal, at which the latter is at its maximum and the former is close to the end of its sinusoidal half cycle. Thereafter, p1 rapidly diminishes to ambient pressure and p2 approaches ambient pressure over a period of about 5T. During this latter phase, p2 exceeds p1, which is consistent with flow reversal. A comprehensive analysis of the system, in conjunction with pressure measurement, enabled experimental loss coefficients to be determined during that time when mass transfer was taking place between the upper and lower cavities (with p1>p2). Values of cd obtained were in the range 0.85–1.2, increasing for the smaller values of T. These data are viewed in the context of the expected steady flow value of 0.79 for this configuration of orifice, and confirm the hypothesis that flow unsteadiness of a sufficiently small time scale has a significant effect on loss coefficients.