The calibration of five-hole probes for use in low-Reynolds number flows

Five-hole probes are a well-established measurement technique for flow surveys in fluid mechanics and fluid machinery, where the probe calibration is known to become sensitive to Reynolds number below a probe-geometry-specific critical Reynolds number. Nevertheless, probes are typically calibrated at a single Reynolds number—particularly for use in incompressible flow-resulting in significant measurement errors in typical technical flows with strong velocity and Reynolds number variations. To address this limitation, this paper presents a Reynolds number-dependent calibration method based on repeated probe calibration over Reynolds numbers ranging from 2000 to 20000. A novel Reynolds number coefficient is introduced, extending conventional two-dimensional calibration maps into a three-dimensional calibration space. Two data-reduction strategies are investigated: three-dimensional interpolation and artificial neural networks. The proposed method is evaluated using the open-access Oxford Probe and compared against conventional probe calibrations at constant Reynolds number. Compared with conventional constant-Reynolds number calibrations, the proposed Reynolds number-dependent approach reduced the errors by up to 50\,% 50 % in flow angles, 70\,% 70 % in total pressure, and 60\,% 60 % in dynamic pressure. Artificial neural network-based regression provides a further reduction of approximately 30\,% 30 % relative to the interpolation-based calibration in all flow quantities. A parametric study demonstrates the effects of network architecture and size on the calibration errors.