Determination of Discharge Coefficients of Sonic Nozzles Obtaining Low Uncertainty without Knowledge of Throat Diameter
Abstract
The paper presents a new approach for the determination of discharge coefficients of sonic nozzles. Innovating the conventional way, where the knowledge of throat diameter is always necessary, the new approach utilises a special mathematical characteristic of the equation <i>c</i><sub>D</sub> = <i>a</i> +<i>b</i>·<i>Re</i><sup>-0.5</sup> to figure out a relationship of the parameter <i>b</i> as a function of the parameter <i>a</i> and to define a new parameter <i>β</i> with <i>b</i> =<i>f</i>(<i>a</i>,<i>β</i>).<BR />It is shown in the paper by theory as well as by experimental results, that the parameter <i>β</i> can be determined only from measurements of flow rate and gas parameters without any knowledge about throat diameter.<BR />With parameter <i>a</i> as a parameter which is very well known with low uncertainty from past research and theoretical studies, the discharge coefficient <i>c</i><sub>D</sub> = <i>a</i> +<i>b</i>·<i>Re</i><sup>-0.5</sup> = <i>a</i> + <i>f</i>(<i>a</i>, <i>β</i>)·<i>Re</i><sup>-0.5</sup> can be determined now also for very small nozzles down to a Reynolds number <i>Re</i> = 1000 (throat diameter roughly 0.1 mm) with a very low uncertainty.<BR />Additional to this, it is shown based on measurements of more than 300 nozzles, that the new parameter <i>β</i> is related to the inner geometry of the nozzle and a sensitive indicator of the quality of manufacturing and/or the measurements.
Event details
- Event
- tc9-2004