The Development of a Dual-Axis Wall Shear Stress Sensor

The accurate measurement of time-resolved wall shear stress has been a heavily-researched topic in the fluid dynamics community for decades. Understanding the behavior of wall shear stress in different fluid environments empowers researchers to learn more about complex flow phenomena, including turbulent boundary layer physics, viscous drag, and flow separation. With these topics better understood, vehicles may be further optimized, and flow-control applications may be improved.

Traditional technologies for wall-shear stress sensing rely on empirical relationships and assumptions that may be inaccurate in different flow fields. These shortcomings motivate the need for a direct sensor, i.e., one that is capable of producing an output that is calibrated directly to the input wall shear stress. Strides have been made in the development of direct, one-dimensional wall shear stress sensors that take advantage of MEMS technologies. More specifically, several iterations of devices that utilize capacitive transduction have been disclosed in the literature. Research into these devices features the appropriate modeling, optimization, fabrication, packaging, and calibration prior to full-scale wind tunnel testing. Despite the significant advancements in the MEMS-based 1D sensors, little progress has been made in the development of two-dimensional transducers. The ability to make point-measurements of wall shear stress in two orthogonal directions reveals additional information on the spanwise behavior of wall-bounded flow fields, furthering the knowledge in the fluid dynamics world.

This poster presentation will cover the development of a direct, dual-axis, capacitive device, with an emphasis on the modeling and optimization of the structure. The dual-axis sensor contains a proof mass that is free to move in response to an incident wall shear stress vector. Supported by crab-leg tethers, the proof mass features comb finger extrusions along its perimeter that form variable-gap capacitors with mechanically static electrodes. As the proof mass moves, the capacitance of the device changes and a voltage is produced. The modeling that will be discussed includes theory in the mechanical and electrical domains, along with the formation of a lumped element model. The mechanical modeling is used to accurately capture the physics of the crab-leg tethers and to predict the deflection of the proof mass per unit wall shear stress. Electrical modeling converts that mechanical deflection to a capacitance change, which is converted to a voltage using either voltage- or charge-amplifier topologies. Lastly, lumped element modeling couples the electrical and mechanical domains, leading to theoretical expressions for the sensitivity and resonance of the device.

With theoretical relations derived and design goals in mind, a sequential quadratic programming algorithm is used to determine the optimal sensor geometry. For this optimization scheme, the optimizer looks to minimize the minimum detectable signal of the device, ultimately leading to a maximum sensitivity value. The optimizer does this while ensuring that constraints in performance are met, e.g., the resonance of the structure is sufficiently high in order to maximize the sensor bandwidth.

Following the modeling and optimization, the sensors are fabricated, packaged, and calibrated. Each of these steps is crucial towards the final device; however, there is literature that exists on dual-axis fabrication, packaging, and calibration and very little in dual-axis modeling and optimization. This poster hopes to provide more information on such topics.