Thermal Drifts of Capacitive Flow Meters: Analysis of Effects and Model-Based Compensation

Capacitive sensing has become a favorable measurement technology for flow metering in pneumatic conveying systems. Multielectrode sensing structures and tomographic signal evaluations enable spatially resolved flow parameter estimation, which is of particular interest for pneumatically conveyed solids due to inhomogeneous particle distributions within the pipeline. The noninvasive working principle of capacitive sensors is an important feature for the application in industrial processes with harsh environments. However, cross sensitivities of the capacitive probe cause effects, such as temperature drifts of the measurements. For a reliable operation of capacitive flow meters in harsh environments, induced drifts have to be compensated. In this article, we present the detailed analyses of thermal effects within capacitive sensors. Based on the findings, a model-based temperature compensation approach is developed within the Bayesian framework. The performance of the proposed compensation approach is analyzed by a measurement-based validation within a climate chamber and by a simulation-based uncertainty quantification. The capability to obtain temperature-independent estimates with calibration measurements acquired at room temperature is demonstrated.