Image Based Sensor for Distributed Wall Shear Stress Measurement

Abstract

There is a need for a sensor to measure global, spatially and temporally resolved wall shear stress on wall bounded ∞ows in various engineering flelds. A wall shear stress sensor using a micro pillar array made out of silicone rubber is presented. This sensor is based on the principle that, if such a pillar is inside the viscous sub layer the de∞ection of the pillar is proportional to the drag forced experienced by the pillar, which in turn is proportional to the wall shear stress. The displacements of individual pillars in the array are tracked to obtain the wall shear stress fleld in a turbulent boundary layer ∞ow. Design and manufacturing considerations are discussed along with typical sensor calibrations in a fully developed turbulent channel ∞ow. Based on the resolution needed the sensor can be tuned for various applications. To demonstrate the feasibility of these types of sensors, the turbulent statistics in a fully developed channel ∞ow is studied. The instantaneous wall shear stress distribution around a cylinder in cross ∞ow was also mapped. I. Introduction The measurement of skin friction or wall shear stress is important for several everyday engineering problems. The time averaged values of the wall shear stress are a measure of the global state of wall bounded ∞ows and is used to determine quantities such as skin friction drag on a body moving in a ∞uid. The time resolved measurement of wall shear stress gives an estimate of the turbulent activity in the ∞ow and describes the momentum transfer events between the body and the ∞uid. The instantaneous wall shear stress is a foot print of the individual unsteady ∞ow structures that transfer momentum to the wall. 14 Wall shear stress is signiflcant especially in improving the performance and e‐ciency of transportation vehicles by reducing drag. In the airline industry skin friction drag accounts for about 45 % of the drag on an aircraft at cruise conditions. 4 Measurement of skin friction, thus assumes signiflcance as a reduction in drag directly results in a reduction in fuel consumption. Likewise, skin friction is responsible for a great part of the power expended in pumping oil and natural gases through pipes across countries and even continents. These ∞ows fall under the broad classiflcation of ∞ows called high Reynolds number ∞ows. The flnancial implications of measuring wall shear stress in a spatially and temporally resolved manner in a high Reynolds number ∞ow is hence signiflcant. Skin friction is also an important measured quantity because it helps in characterizing the state of the turbulent boundary layer, which is important both to the fundamental understanding of these ∞ows and also to assist in the fleld of ∞ow control. Flow control deals with the controlling of these ∞ows by using spatially distributed values of the instantaneous wall shear stress in manner such as to efiect changes in the boundary