<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">${50\,\mathrm{\%}}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>50</mn> <mspace width="0.166667em" /> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> in flow angles, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">${70\,\mathrm{\%}}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>70</mn> <mspace width="0.166667em" /> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> in total pressure, and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">${60\,\mathrm{\%}}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>60</mn> <mspace width="0.166667em" /> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> in dynamic pressure. Artificial neural network-based regression provides a further reduction of approximately <InlineEquation ID="IEq4"> <EquationSource Format="TEX">${30\,\mathrm{\%}}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>30</mn> <mspace width="0.166667em" /> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> 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.</p>

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

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2026年7月31日

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Jonas Stürznickel,
Romuald Skoda,
Maximilian Passmann

摘要

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 ${50\,\mathrm{\%}}$ $50 %$ in flow angles, ${70\,\mathrm{\%}}$ $70 %$ in total pressure, and ${60\,\mathrm{\%}}$ $60 %$ in dynamic pressure. Artificial neural network-based regression provides a further reduction of approximately ${30\,\mathrm{\%}}$ $30 %$ 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.