Towards Quantitative Wall Shear Stress Measurements: Considering the Flow Behavior of Liquid Crystals

Liquid crystal diagnostics is a capable tool for determining quantitative wall shear stress distributions with high spatial resolution, which may be applied to almost any surface shape. To determine a wall shear stress vector field, the state-of-the-art calibration procedure requires taking multiple images of the liquid crystal-coated surface from different points of view. In the literature, it is reported that this data acquisition is usually performed using multiple, up to six, commercially available consumer cameras to synchronously record the liquid crystal signal. However, the need for multiple recording devices makes measurement diagnostics unsuitable even for laboratory measurements, as often only one (identical) camera is available. Using a single camera results in a different wall shear stress vector field due to the time-dependent liquid crystal signal, which results from the time offset between the individual exposures compared to the synchronous exposures under otherwise identical boundary conditions. This time dependence follows from the thixotropic behavior of the liquid crystals. On top of that, two other effects, one of which is not described in the literature, affect the liquid crystal color signal. In order to record physical and reliable data even with a single camera, it is essential to record images only when the liquid crystal signal is quasi-stationary. The main objective of this paper is to provide recommendations for the acquisition of liquid crystal data using a single camera. For this purpose, in a first step, a start time is defined from which quasi-stationary liquid crystal data can be experimentally acquired within a certain time interval. A flat plate wind tunnel is used for this purpose. The specified time constraints are valid for measurements, in which liquid crystal mixtures, with a viscosity ≤ 750...1 250 mPa s are used, e. g. BCN/192 from LCRHallcrest Ltd., at a maximum wall shear stress of ≤ 34 Pa. Using the derived time constraints, the error with respect to the wall shear stress magnitude and its direction can be reduced. The concluding discussion serves as a guide for reliable liquid crystal data acquisition to make the measurement technique applicable in practice even with a single camera