Critical-Flow Nozzle Meter and Its Application to the Measurement of Mass Flow Rate in Steady and Pulsating Streams of Gas

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Abstract
Simple theory indicates that when critical flow of a gaseous fluid is established in a given passage, the rate of mass flow becomes dependent only on the absolute pressure and temperature upstream, and changes in downstream conditions no longer have any influence. In practice, some modifications of the theoretical conclusions may sometimes be necessary. The discharge coefficient of a simple plate orifice, for instance, is greatly dependent on the amount of jet contraction, and this may be influenced by changes in downstream pressure even under critical-flow conditions. However, a properly shaped flow nozzle is not affected in this way, and is well suited for flow measurement under critical conditions. In the experiments described, a large number of small-diameter nozzles with quadrant entrances was tested, and the effects of nozzle length/throat diameter ratio and entry radius/throat diameter ratio were carefully examined. A range of simple cylindrical nozzles was also tested. Such nozzles are easily reproduced and are to be recommended in cases where a rather low discharge coefficient is not a disadvantage. The above experiments were made with smoothed steady flows but in addition a number of trials with pulsating flows was carried out and it was found that the observed coefficients of discharge for pulsating flow differed very little from those applying to steady-flow conditions. In view of the acknowledged difficulty in metering unsteady flows, this is a most valuable property, and it is thought that critical flow meters are very suitable for measuring the output of reciprocating compressors, free piston gasifiers and other plant delivering gas at high pressure.
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