A Rotary Flow Channel for Shear Stress Sensor Calibration

*† A proposed shear sensor calibrator consists of a rotating wheel with the sensor mounted tangential to the rim and positioned in close proximity to the rim. The shear stress generated by the flow at the sensor position is simply τw = µ rω /h, where µ is the viscosity of the ambient gas, r the wheel radius, ω the angular velocity of the wheel, and h the width of the gap between the wheel rim and the sensor. With numerical values of µ = 31 µPa . s (neon at room temperature), r = 0.5 m, ω = 754 s -1 (7200 rpm), and h = 50.8 µm, a shear stress of τw = 231 Pa can be generated. An analysis based on one-dimensional flow, with the flow velocity having only an angular component as a function of the axial and radial coordinates, yields corrections to the above simple formula for the curvature of the wheel, flatness of the sensor, and finite width of the wheel. It is assumed that the sensor mount contains a trough (sidewalls) to render a velocity release boundary condition at the edges of the rim. The Taylor number under maximum flow conditions is found to be 62.3, sufficiently low to obviate flow instability. The fact that the parameters entering into the evaluation of the shear stress can be measured to high accuracy with well-defined uncertainties makes the proposed calibrator suitable for a physical standard for shear stress calibration.