An Optical Fiber Bundle Sensor for Tip Clearance and Tip Timing Measurements in a Turbine Rig

When it comes to measuring blade-tip clearance or blade-tip timing in turbines, reflective intensity-modulated optical fiber sensors overcome several traditional limitations of capacitive, inductive or discharging probe sensors. This paper presents the signals and results corresponding to the third stage of a multistage turbine rig, obtained from a transonic wind-tunnel test. The probe is based on a trifurcated bundle of optical fibers that is mounted on the turbine casing. To eliminate the influence of light source intensity variations and blade surface reflectivity, the sensing principle is based on the quotient of the voltages obtained from the two receiving bundle legs. A discrepancy lower than 3% with respect to a commercial sensor was observed in tip clearance measurements. Regarding tip timing measurements, the travel wave spectrum was obtained, which provides the average vibration amplitude for all blades at a particular nodal diameter. With this approach, both blade-tip timing and tip clearance measurements can be carried out simultaneously. The results obtained on the test turbine rig demonstrate the suitability and reliability of the type of sensor used, and suggest the possibility of performing these measurements in real turbines under real working conditions.

Fractional Reserve Banking

Economic point of view about fractional reserve banking

On Nonnegative Solutions of Fractional q-Linear Time-Varying Dynamic Systems with Delayed Dynamics

This paper is devoted to the investigation of nonnegative solutions and the stability and asymptotic properties of the solutions of fractional differential dynamic linear time-varying systems involving delayed dynamics with delays. The dynamic systems are described based on q-calculus and Caputo fractional derivatives on any order.