<p>This study investigates and quantifies the soot free length (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14234_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\({L}_{\rm b}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi mathvariant="normal">b</mi> </msub> </math></EquationSource> </InlineEquation>) and soot free length fraction (<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14234_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text{SFLF}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext>SFLF</mtext> </math></EquationSource> </InlineEquation>) of methane laminar diffusion flames at sub-atmospheric pressures (20–100&#xa0;<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14234_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text{kPa}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext>kPa</mtext> </math></EquationSource> </InlineEquation>), which are rarely reported in literature. Methane-buoyant laminar diffusion flames are produced using a circular aperture burner with an inner diameter of 8&#xa0;mm, and a series of fire tests is conducted in a hypobaric chamber with internal dimensions of <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14234_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="86" /> </InlineMediaObject> <EquationSource Format="TEX">\(3\times 2\times 2\text{ m}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>3</mn> <mo>×</mo> <mn>2</mn> <mo>×</mo> <mn>2</mn> <mspace width="0.333333em" /> <mtext>m</mtext> </mrow> </math></EquationSource> </InlineEquation>. The mass flow rates in this study are set to 2.988–8.365&#xa0;mg s<sup>−1</sup>. The results indicate that for steady and tip-flickering flames, the total flame length increases with pressure <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14234_Article_IEq6.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="72" /> </InlineMediaObject> <EquationSource Format="TEX">\({L}_{\rm f}\sim {P}^{1/5}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>L</mi> <mi mathvariant="normal">f</mi> </msub> <mo>∼</mo> <msup> <mrow> <mi>P</mi> </mrow> <mrow> <mn>1</mn> <mo stretchy="false">/</mo> <mn>5</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>. However, for bulk-flickering flames, the total flame length is nearly constant with <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14234_Article_IEq7.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="60" /> </InlineMediaObject> <EquationSource Format="TEX">\({L}_{\rm f}\sim {P}^{0}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>L</mi> <mi mathvariant="normal">f</mi> </msub> <mo>∼</mo> <msup> <mrow> <mi>P</mi> </mrow> <mn>0</mn> </msup> </mrow> </math></EquationSource> </InlineEquation>. Additionally, both <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14234_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\({L}_{\rm b}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi mathvariant="normal">b</mi> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14234_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text{SFLF}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext>SFLF</mtext> </math></EquationSource> </InlineEquation> decrease with an increasing ambient air pressure. For a given pressure, both the <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14234_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\({L}_{\rm b}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi mathvariant="normal">b</mi> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14234_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text{SFLF}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext>SFLF</mtext> </math></EquationSource> </InlineEquation> decrease with an increasing mass flow rate (or heat release rate). The Reynolds number (<InlineEquation ID="IEq12"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14234_Article_IEq12.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text{Re}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext>Re</mtext> </math></EquationSource> </InlineEquation>), which has been successfully used to characterize the <InlineEquation ID="IEq13"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14234_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\({L}_{\rm b}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi mathvariant="normal">b</mi> </msub> </math></EquationSource> </InlineEquation> and the <InlineEquation ID="IEq14"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14234_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text{SFLF}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext>SFLF</mtext> </math></EquationSource> </InlineEquation> of buoyant turbulent jet flames, fails with buoyant laminar diffusion flames. The dimensionless soot free length correlates well with the nondimensional heat release rate. Moreover, a prediction correlation for the <InlineEquation ID="IEq15"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10973_2025_14234_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\(\text{SFLF}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext>SFLF</mtext> </math></EquationSource> </InlineEquation> of methane-buoyant laminar diffusion flames is developed, which could effectively unify the experimental data in the current work.</p>

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Experimental investigation of the soot free lengths of methane laminar diffusion flames at sub-atmospheric pressures

  • Jinfei Zhao,
  • Tengjiao Zhou,
  • Di Meng,
  • Jian Wang

摘要

This study investigates and quantifies the soot free length ( \({L}_{\rm b}\) L b ) and soot free length fraction ( \(\text{SFLF}\) SFLF ) of methane laminar diffusion flames at sub-atmospheric pressures (20–100  \(\text{kPa}\) kPa ), which are rarely reported in literature. Methane-buoyant laminar diffusion flames are produced using a circular aperture burner with an inner diameter of 8 mm, and a series of fire tests is conducted in a hypobaric chamber with internal dimensions of \(3\times 2\times 2\text{ m}\) 3 × 2 × 2 m . The mass flow rates in this study are set to 2.988–8.365 mg s−1. The results indicate that for steady and tip-flickering flames, the total flame length increases with pressure \({L}_{\rm f}\sim {P}^{1/5}\) L f P 1 / 5 . However, for bulk-flickering flames, the total flame length is nearly constant with \({L}_{\rm f}\sim {P}^{0}\) L f P 0 . Additionally, both \({L}_{\rm b}\) L b and \(\text{SFLF}\) SFLF decrease with an increasing ambient air pressure. For a given pressure, both the \({L}_{\rm b}\) L b and \(\text{SFLF}\) SFLF decrease with an increasing mass flow rate (or heat release rate). The Reynolds number ( \(\text{Re}\) Re ), which has been successfully used to characterize the \({L}_{\rm b}\) L b and the \(\text{SFLF}\) SFLF of buoyant turbulent jet flames, fails with buoyant laminar diffusion flames. The dimensionless soot free length correlates well with the nondimensional heat release rate. Moreover, a prediction correlation for the \(\text{SFLF}\) SFLF of methane-buoyant laminar diffusion flames is developed, which could effectively unify the experimental data in the current work.