<p>This study investigated the performance of hot-wire anemometry and a multi-hole Cobra pressure probe for turbulence characterization in a small-scale, 3D-printed wind tunnel operating at a Reynolds number of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$2.6 \times 10^{4}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2.6</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>4</mn> </msup> </mrow> </math></EquationSource> </InlineEquation>. Experiments were conducted under passive grid-generated turbulent conditions, resulting in freestream turbulence (FST) levels of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$2\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$4\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>4</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation>, and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$8\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>8</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation>. Despite the Cobra’s practical advantages (robust, geometry-dependent pre-calibration and simultaneous three-component velocity measurements), it showed limitations due to a restricted sampling frequency and the probe’s head geometry, leading to spectral deviation and biased turbulence estimates. Post-processing strategies were devised to mitigate these effects. A second-order polynomial spectral correction improved estimates of RMS fluctuations and the integral length scale (<i>L</i>). At the same time, an approach based on equilibrium dissipation laws enabled consistent estimation of dissipation-related quantities, including the Taylor microscale (<InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\lambda$</EquationSource> <EquationSource Format="MATHML"><math> <mi>λ</mi> </math></EquationSource> </InlineEquation>), Kolmogorov scale (<InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\eta$</EquationSource> <EquationSource Format="MATHML"><math> <mi>η</mi> </math></EquationSource> </InlineEquation>), and dissipation rate (<InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\varepsilon$</EquationSource> <EquationSource Format="MATHML"><math> <mi>ε</mi> </math></EquationSource> </InlineEquation>), without relying on velocity gradients, which are highly dependent on the pressure probe’s limitations. Validation in a large-scale wind tunnel confirmed that corrected Cobra-based dissipation estimates could achieve relative errors below <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$30\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>30</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> compared with hot-wire data. Overall, the results demonstrate that, when combined with the proposed corrections, the Cobra probe can provide a good estimate of turbulence features despite its intrinsic frequency limitations, offering a practical alternative to hot-wire anemometry in low-Reynolds-number turbulent flows.</p>

Comparative study of hot-wire and multi-hole pressure probe performance in low-Reynolds-number turbulent flows

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发表日期：

2026年2月24日

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Simon Dehareng,
Thomas Gemine,
Geoffroy Lumay,
Thomas Andrianne

摘要

This study investigated the performance of hot-wire anemometry and a multi-hole Cobra pressure probe for turbulence characterization in a small-scale, 3D-printed wind tunnel operating at a Reynolds number of $2.6 \times 10^{4}$ $2.6 \times 10^{4}$ . Experiments were conducted under passive grid-generated turbulent conditions, resulting in freestream turbulence (FST) levels of $2\%$ $2 %$ , $4\%$ $4 %$ , and $8\%$ $8 %$ . Despite the Cobra’s practical advantages (robust, geometry-dependent pre-calibration and simultaneous three-component velocity measurements), it showed limitations due to a restricted sampling frequency and the probe’s head geometry, leading to spectral deviation and biased turbulence estimates. Post-processing strategies were devised to mitigate these effects. A second-order polynomial spectral correction improved estimates of RMS fluctuations and the integral length scale (L). At the same time, an approach based on equilibrium dissipation laws enabled consistent estimation of dissipation-related quantities, including the Taylor microscale ( $\lambda$ $λ$ ), Kolmogorov scale ( $\eta$ $η$ ), and dissipation rate ( $\varepsilon$ $ε$ ), without relying on velocity gradients, which are highly dependent on the pressure probe’s limitations. Validation in a large-scale wind tunnel confirmed that corrected Cobra-based dissipation estimates could achieve relative errors below $30\%$ $30 %$ compared with hot-wire data. Overall, the results demonstrate that, when combined with the proposed corrections, the Cobra probe can provide a good estimate of turbulence features despite its intrinsic frequency limitations, offering a practical alternative to hot-wire anemometry in low-Reynolds-number turbulent flows.