Leading characteristic in conical nozzle flows and the effect of manufacturing errors

Abstract

Shown in Fig. 3 are the results of the investigation of the stability of the interface in the rectangular channel for two different plate spacings. The average interface velocity was obtained by measuring the distance and time required for the gas-liquid interface to move from the starting position to the tank outlet. The solid lines represent the predictions of Eq. (3) for the conditions of the experiment and for an infinite tank. The three states of the interface have been labeled stable, neutral, and unstable. The stable interface condition existed when the interface remained flat with very little penetration of the gas into the liquid, while the neutral case had moderate penetration of the gas. The unstable case represents large penetration of fingers2 into the liquid fuel. Agreement of the data points and theory is seen to be good. The major difference is due to the large neutral region, and is the result of funnelling pressure gradients caused by the finite tank geometry. The neutral region was larger for the lowgravity tests where funnelling would be more influential. For the tests with higher gravitational forces (0.01 g) the experimental results were dominated by the gravitational forces, and the region of neutral stability became very small. Changing the plate spacing b did not cause any observable qualitative changes in the comparison between theory and experiment, and the correct quantitative changes were predicted by Eq. (3). All the tests were carried out at a creeping flow Reynolds numbers1 for which the Hele-Shaw assumptions were justified. The major source of experimental error was due to small inaccuracies in the leveling of the channel in the direction transverse to the flow. This error resulted in a tendency of the fluid to flow slightly down one side of the channel more than the other. The maximum magnitude of the transverse gravitational field at any point in the channel was 0.001 g, and the influence of this field was the greatest for the very low-gravity tests. Another important characteristic of a fuel tank system is the amount of fluid left in the tank after the driver gas reaches the exit. Figure 4 shows the results of the measurement of the percentage of fluid left remaining in the system. The tests were carried out with three outlet geometries in order to determine the influence of funnelling on the data. These outlet geometries consisted of the following: a) no exit constriction; b) single row of spacers in the exit; and c) a large rounded plug in the exit. It was found that both the spacers and the plug improved the performance of the Hele-Shaw cell. The greatest improvement occurred with the large plug in the exit and this indicates that funnelling can be reduced, since the plug changes the exit pressure distribution. The exit spacers also reduced the amount of fluid left in the tank, and this was a result of increased surface tension in the exit. For low velocity (V > 2 cm/sec) and moderate gravitational force (g > 0.005) it was found that the percent of fluid left in the tank could be kept under 5%, which is a respectable result.