Comparison of the Models of the Air Gauge Static Characteristics

Abstract

In the article, the authors analyze and discuss several models used to the calculation of air gauge characteristics. The model based on the actual mass flow (which is smaller than the theoretical one) was proposed, too. Calculations have been performed with a dedicated software with the second critical parameters included. The air gauge static characteristics calculated with 6 different models were compared with the experimental data. It appeared that the second critical parameters model (SCP) provided the characteristics close to the experimental ones, with an error of ca. 3% within the air gauge measuring range.

Recent Development of Air Gauging in Industry 4.0 Context

“…In a steady-state empirical-mechanistic modeling, the mathematical calculations based on available theoretical background were combined with the empirical polynomial approximating functions of the first and second orders [ 64 ]. Jermak et al [ 65 ] compared several models, usually used for the calculation of air gauge characteristics, such as the one proposed by Balakshin [ 66 ], Gluchow [ 67 , 68 ] or the model based on Saint Venant-Wenzel equations. The latter approach distinguished between different flow conditions in the pneumatic cascade, where sonic air flow velocity can be reached independently in the inlet restriction (I) and the outlet flapper-nozzle area (II).…”

“…Depending on the conditions above, relations of air flow coefficients α and pressure ratios would look different. For instance, when the pressure ratio is below β kr in both areas I and II, i.e., in the inlet restriction and the outlet flapper-nozzle area, the equation could be written as follows [ 65 ]: where b = p a / p k is the normalized steady-state back-pressure, i.e., ratio of the atmospheric pressure p a to the back-pressure p k ; x denotes the relation between flow coefficients and respective flow-through areas of inlet nozzle and flapper-nozzle slot, as follows: where air flow coefficients α 1 and α 2 correspond with inlet restriction and flapper-nozzle restriction of respective flow-through areas A 1 and A 2 . The latter, in turn, depends on respective nozzle diameters d 1 and d 2 , as well as on the actual displacement z , as shown schematically in Figure 1 .…”

“…The authors [ 65 ] from their investigations proposed also a model based on the measurement of the actual mass flow , which appeared to be smaller than the one calculated theoretically due to the stream contraction and respective losses of pressure. They used term ‘second critical parameters’ to describe the difference between the pressure ratio for actual maximal mass flow and the theoretical one, as follows:…”