Mathematical modelling and experimental validation of electrostatic sensors for rotational speed measurement

Recent research has demonstrated that electrostatic sensors can be applied to the measurement of rotational speed with excellent repeatability and accuracy under a range of conditions. However, the sensing mechanism and fundamental characteristics of the electrostatic sensors are still largely unknown and hence the design of the sensors is not optimised for rotational speed measurement. This paper presents the mathematical modelling of strip electrostatic sensors for rotational speed measurement and associated experimental studies for the validation of the modelling results. In the modelling, an ideal point charge on the surface of the rotating object is regarded as an impulse input to the sensing system. The fundamental characteristics of the sensor, including spatial sensitivity, spatial filtering length and signal bandwidth, are quantified from the developed model. The effects of the geometric dimensions of the electrode, the distance between the electrode and the rotor surface and the rotational speed being measured on the performance of the sensor are analyzed. A close agreement between the modelling results and experimental measurements has been observed under a range of conditions. Optimal design of the electrostatic sensor for a given rotor size is suggested and discussed in accordance with the modelling and experimental results

Measurement of Flow Characteristics in a Bubbling Fluidized Bed Using Electrostatic Sensor Arrays

Fluidized beds are widely applied in a range of industrial processes. In order to maintain the efficient operation of a fluidized bed, the flow parameters in the bed should be monitored continuously. In this paper, electrostatic sensor arrays are used to measure the flow characteristics in a bubbling fluidized bed. In order to investigate the electrostatic charge distribution and the flow dynamics of solid particles in the dense region, time and frequency domain analysis of the electrostatic signals is conducted. In addition, the correlation velocities and weighted average velocity of Geldart A particles in the dense and transit regions are calculated, and the flow dynamics of Geldart A and D particles in the dense and transit regions are compared. Finally, the influence of liquid antistatic agents on the performance of the electrostatic sensor array is investigated. According to the experimental results, it is proved that the flow characteristics in the dense and transit regions of a bubbling fluidized bed can be measured using electrostatic sensor arrays

On the Leibniz rule and Laplace transform for fractional derivatives

Taylor series is a useful mathematical tool when describing and constructing a function. With the series representation, some properties of fractional calculus can be revealed clearly. This paper investigates two typical applications: Lebiniz rule and Laplace transform. It is analytically shown that the commonly used Leibniz rule cannot be applied for Caputo derivative. Similarly, the well-known Laplace transform of Riemann-Liouville derivative is doubtful for n-th continuously differentiable function. By the aid of this series representation, the exact formula of Caputo Leibniz rule and the explanation of Riemann-Liouville Laplace transform are presented. Finally, three illustrative examples are revisited to confirm the obtained results

Nonlinear thermal transport and negative differential thermal conductance in graphene nanoribbons

We employ classical molecular dynamics to study the nonlinear thermal transport in graphene nanoribbons (GNRs). For GNRs under large temperature biases beyond linear response regime, we have observed the onset of negative differential thermal conductance (NDTC). NDTC is tunable by varying the manner of applying the temperature biases. NDTC is reduced and eventually disappears when the length of the GNR increases. We have also observed NDTC in triangular GNRs, where NDTC exists only when the heat current is from the narrower to the wider end. These effects may be useful in nanoscale thermal managements and thermal signal processing utilizing GNRs.Comment: 5 pages, 4 figure

Two Case Reports of Familial Chylomicronemia Syndrome

Familial chylomicronemia is a rare autosomal recessive disorder which is also called Hyperlipoproteinemia type I. Here we report two cases with this rare disorder that were admitted to our hospital in recent years