Investigation of Near-Wall Coherent Structures by Stereo Particle Image Velocimetry

Abstract

We consider issues of camera calibration and measurement validation for a stereo P.I.V. system designed for high-resolution measurements at 15 Hz in a cross-stream plane of an open channel flow, in which Willert’s “front-and-rear” stereo camera arrangement is applied with a new three-dimensional calibration target. The most commonly used mathematical expression of the pinhole camera model contains eleven constants, even though an ideal camera, i.e. one free from lens aberrations and with a uniform and rectilinear distribution of pixels on the sensor face, is characterized by only seven constants with respect to a given physical coordinate system. Thus this mapping function is in fact more general than the pinhole model, and four of its constants are in principle determined by the other seven. However, it has the advantage that the constants may be found from calibration photographs by linear least squares, and in a previous communication (10th International Symposium on Flow Visualization, 2002), we verified experimentally that this form of the pinhole model may by applied without modification to a Scheimpflug camera as used in our setup. In the present paper, we show that when looking through an air-water interface at an angle close to 90 degrees, for which the pinhole model is not valid, this redundant camera model is still applicable, thus explaining why our experimental check gave very good results. We also provide refined data from a previously reported cross-check on the two horizontal components of instantaneous velocity vectors, using a third camera viewing from below with beam illumination (rather than sheet illumination).