Dynamic calibration technique for the micro-pillar shear-stress sensor MPS³

Abstract

Based on magnetic excitation a dynamic calibration technique for the micro-pillar shear-stress sensor MPS 3 , which allows one to determine the local wall-shear stress in turbulent flows by optically measuring the velocity gradient within the viscous sublayer of turbulent flows, is described. The proposed dynamic calibration technique allows one to assess the micro-pillar dynamic response for different flow media up to approximately 10 kHz. The results convincingly agree with the findings of a second-order analytical approximation based on experimentally determined damped eigenfrequencies and damping coefficients. Measurements for different sensor geometries and in various fluids show the sensor to possess transfer functions ranging from a flat low-pass filtered response to strong resonant behavior.

Microsphere-assisted fabrication of high aspect-ratio elastomeric micropillars and waveguides

“…Its governing equation models the motion of a uniform, homogeneous, single-clamped cantilever beam due to a massflow by taking the impacts of inertia, bending, drag and viscous damping into consideration. It has been adopted by a number of researchers for flexible micropillars [31][32][33] . Traditionally, it has been used for absolutely linear bending for which the cantilever's tip displacement d tip is below 5% of the cantilever length.…”

“…where m, c, k, F o and u(t) are to be determined from the structural and material characteristics of the cantilever, the magnitude and waveform of the driving force, and the axial profile of the massflow 33 . As described in Supplementary Note 2, we utilized both linearly varying and constant axial massflow profiles 34 .…”

Improvement of The Measurement Range of The Micro-Pillar Shear-Stress Sensor MPS3

“…27 Brücker et al 21 and Große et al 22 deduced in their work that the added mass due to the movement of the structure is included by their methods of calibration. Große et al 22 assumed Stokes flow around the micro-structure. In doing so, they accounted for a frequency dependent term for the added massm(f ).…”

“…In addition, the microstructures possess a pronounced resonance for measurements in air. 22 The eigenfrequency of the sensor depends on the geometry of the cylindrical structures and can reach several kHz.…”

“…This is an intrinsic task. This is why Große et al 22 developed a calibration technique in which an permanent magnetic layer is attached to the pillar tip such that the pillar can be magnetically excited by an oscillating magnetic field in order to determine the frequency response. The usable frequency bandwidth reaches about 2 kHz since the maximum eigenfrequency is about 5 kHz.…”