An Approach to Measurement of Volumetric Fill and Flow Rate in a Discharging Hopper Using Helmholtz Resonance

The response of a partially enclosed cavity to acoustic excitation is related to the volume of fluid enclosed, and Helmholtz resonance is increasingly finding application in the measurement of the volume of nonporous objects. Simplistically, an object placed in a cavity changes the free volume of the cavity, and the volume of the object can be found from theory and empirical calibration. Determination of the volume of particulate materials brings challenges which arise from the properties of the individual particles, their size and size distribution. The exploratory work we report here was carried out with a cylindrical discharge vessel 300 mm in diameter and 700 mm high, discharging mustard seeds (approximately spherical, diameter ~2 mm) and agricultural lime (polydisperse). The system was excited by a series of chirps each with a frequency range chosen to span the expected resonant frequency. The response to each chirp was recorded, and resonant frequency determined. Computation time was reduced by using the measured resonant frequency of each excitation chirp as the basis for setting the frequency span of the next chirp in the series; typically, a measurement cycle took less than one second. The material leaving the discharge vessel was also continuously weighed using laboratory scales enabling volumetric discharge rate to be estimated using a (nominal) bulk density, for comparison with the acoustic measurements. The agricultural lime behaved similarly to a solid object, and degree of fill could be found with an accuracy of approximately 2%. The response of the mustard seeds was different, exhibiting a negative correlation with degree of fill. This is thought to result from the open structure of the particle bed, and the interaction of this with the free volume in the discharge vessel.