<p>The wake characteristics of a solid particle featuring a through-hole were investigated using particle image velocimetry. The particle had a diameter of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$d = 25.4$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>d</mi> <mo>=</mo> <mn>25.4</mn> </mrow> </math></EquationSource> </InlineEquation> mm, with a through-hole diameter ratio of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\gamma = d_h/d = 0.24$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>γ</mi> <mo>=</mo> <msub> <mi>d</mi> <mi>h</mi> </msub> <mo stretchy="false">/</mo> <mi>d</mi> <mo>=</mo> <mn>0.24</mn> </mrow> </math></EquationSource> </InlineEquation>, where <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$d_h$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>d</mi> <mi>h</mi> </msub> </math></EquationSource> </InlineEquation> represents the diameter of the through-hole. The particle was placed in a uniform flow with a velocity <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$U_0 = 3.6$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>U</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>3.6</mn> </mrow> </math></EquationSource> </InlineEquation> m/s, yielding a Reynolds number of approximately 6000. The orientation of the through-hole relative to the uniform flow <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\alpha$</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> was varied from 0 deg to 90 deg. For the solid particle without a hole, the wake demonstrated a pronounced velocity deficit and a pair of symmetric vortices behind the particle. Introducing a through-hole resulted in the formation of a jet emerging from the hole into the wake at <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$10 \le \alpha \le 60$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>10</mn> <mo>≤</mo> <mi>α</mi> <mo>≤</mo> <mn>60</mn> </mrow> </math></EquationSource> </InlineEquation> deg. The jet velocity decreased as <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\alpha$</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> increased, and the jet disappeared for <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$\alpha \ge 70$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>≥</mo> <mn>70</mn> </mrow> </math></EquationSource> </InlineEquation> deg. Downstream of <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$x/d \ge 2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>x</mi> <mo stretchy="false">/</mo> <mi>d</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>, the velocity field became independent of <InlineEquation ID="IEq10"> <EquationSource Format="TEX">$\alpha$</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>. At <InlineEquation ID="IEq11"> <EquationSource Format="TEX">$\alpha =0$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>=</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> deg, two pairs of vortices were generated by the interaction of the shear layers and hole jet. For <InlineEquation ID="IEq12"> <EquationSource Format="TEX">$\alpha \ge 10$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>≥</mo> <mn>10</mn> </mrow> </math></EquationSource> </InlineEquation> deg, one vortex of each pair disappeared. For <InlineEquation ID="IEq13"> <EquationSource Format="TEX">$20 \le \alpha \le 40$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>20</mn> <mo>≤</mo> <mi>α</mi> <mo>≤</mo> <mn>40</mn> </mrow> </math></EquationSource> </InlineEquation> deg, the vortex size associated with the hole jet increased with increasing <InlineEquation ID="IEq14"> <EquationSource Format="TEX">$\alpha$</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>. For <InlineEquation ID="IEq15"> <EquationSource Format="TEX">$\alpha \ge 70$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>≥</mo> <mn>70</mn> </mrow> </math></EquationSource> </InlineEquation> deg, the wake structure closely resembled that of a solid particle. These findings demonstrate that the through-hole angle exerts a significant influence on the near-wake structure, and they provide further support for the interference model between the hole jet and shear layer proposed in previous studies.</p> Graphical abstract <p></p>

Effect of through-hole angle on particle wake

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2026年7月14日

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Kotaro Takamure,
Tomomi Uchiyama,
Tomohiro Degawa

摘要

The wake characteristics of a solid particle featuring a through-hole were investigated using particle image velocimetry. The particle had a diameter of $d = 25.4$ $d = 25.4$ mm, with a through-hole diameter ratio of $\gamma = d_h/d = 0.24$ $γ = d_{h} / d = 0.24$ , where $d_h$ $d_{h}$ represents the diameter of the through-hole. The particle was placed in a uniform flow with a velocity $U_0 = 3.6$ $U_{0} = 3.6$ m/s, yielding a Reynolds number of approximately 6000. The orientation of the through-hole relative to the uniform flow $\alpha$ $α$ was varied from 0 deg to 90 deg. For the solid particle without a hole, the wake demonstrated a pronounced velocity deficit and a pair of symmetric vortices behind the particle. Introducing a through-hole resulted in the formation of a jet emerging from the hole into the wake at $10 \le \alpha \le 60$ $10 \leq α \leq 60$ deg. The jet velocity decreased as $\alpha$ $α$ increased, and the jet disappeared for $\alpha \ge 70$ $α \geq 70$ deg. Downstream of $x/d \ge 2$ $x / d \geq 2$ , the velocity field became independent of $\alpha$ $α$ . At $\alpha =0$ $α = 0$ deg, two pairs of vortices were generated by the interaction of the shear layers and hole jet. For $\alpha \ge 10$ $α \geq 10$ deg, one vortex of each pair disappeared. For $20 \le \alpha \le 40$ $20 \leq α \leq 40$ deg, the vortex size associated with the hole jet increased with increasing $\alpha$ $α$ . For $\alpha \ge 70$ $α \geq 70$ deg, the wake structure closely resembled that of a solid particle. These findings demonstrate that the through-hole angle exerts a significant influence on the near-wake structure, and they provide further support for the interference model between the hole jet and shear layer proposed in previous studies.

Graphical abstract