DETERMINATION OF DISCHARGE COEFFICIENTS OF SONIC NOZZLES OBTAINING LOW UNCERTAINTY WITHOUT KNOWLEDGE OF THROAT DIAMETER

摘要

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 c_D = a +b·Re~(-0.5) to figure out a relationship of the parameter b as a function of the parameter a and to define a new parameter β with b = f(a,β). It is shown in the paper by theory as well as by experimental results, that the parameter β can be determined only from measurements of flow rate and gas parameters without any knowledge about throat diameter. With parameter a as a parameter which is very well known with low uncertainty from past research and theoretical studies, the discharge coefficient c_D = a +b·Re~(-0.5) = a+ f(a, β)·Re~(-0.5) can be determined now also for very small nozzles down to a Reynolds number Re = 1000 (throat diameter roughly 0.1 mm) with a very low uncertainty. Additional to this, it is shown based on measurements of more than 300 nozzles, that the new parameter β is related to the inner geometry of the nozzle and a sensitive indicator of the quality of manufacturing and/or the measurements.