<p>Shock propagation at microscales has been an area of utmost interest in recent years due to the recent developments in the fields of micro-electro-mechanical systems (MEMS) and medical science. In the present investigation, post-shock boundary layer flow is numerically examined for shock wave propagation in micro-ducts of 1000 <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="193_2024_1214_Article_IEq1.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\upmu \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">μ</mi> </math></EquationSource> </InlineEquation>m <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="193_2024_1214_Article_IEq2.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(\times \)</EquationSource> <EquationSource Format="MATHML"><math> <mo>×</mo> </math></EquationSource> </InlineEquation> 150 <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="193_2024_1214_Article_IEq3.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\upmu \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">μ</mi> </math></EquationSource> </InlineEquation>m, 1000 <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="193_2024_1214_Article_IEq4.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\upmu \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">μ</mi> </math></EquationSource> </InlineEquation>m <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="193_2024_1214_Article_IEq5.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(\times \)</EquationSource> <EquationSource Format="MATHML"><math> <mo>×</mo> </math></EquationSource> </InlineEquation> 300 <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="193_2024_1214_Article_IEq6.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\upmu \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">μ</mi> </math></EquationSource> </InlineEquation>m, and 1000 <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="193_2024_1214_Article_IEq7.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\upmu \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">μ</mi> </math></EquationSource> </InlineEquation>m <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="193_2024_1214_Article_IEq8.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(\times \)</EquationSource> <EquationSource Format="MATHML"><math> <mo>×</mo> </math></EquationSource> </InlineEquation> 400 <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="193_2024_1214_Article_IEq9.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\upmu \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">μ</mi> </math></EquationSource> </InlineEquation>m cross sections at incident shock Mach numbers ranging from 1.97 to 2.31, similar to the experimental investigations of Giordano et al. (Shock Waves 28:1251–1262, 2018). The shock is introduced using the stagnation properties corresponding to the Mach number of shock-induced flow. The shock position and the shock wave attenuation parameter are compared with the experimental findings of Giordano et al. Numerical results suggest the existence of a turbulent boundary layer behind the shock wave similar to the experimental findings.</p>

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Post-shock flow in micro-channels: a numerical investigation and analysis

  • S. Lokhande,
  • A. Deshpande

摘要

Shock propagation at microscales has been an area of utmost interest in recent years due to the recent developments in the fields of micro-electro-mechanical systems (MEMS) and medical science. In the present investigation, post-shock boundary layer flow is numerically examined for shock wave propagation in micro-ducts of 1000 \(\upmu \) μ m \(\times \) × 150 \(\upmu \) μ m, 1000 \(\upmu \) μ m \(\times \) × 300 \(\upmu \) μ m, and 1000 \(\upmu \) μ m \(\times \) × 400 \(\upmu \) μ m cross sections at incident shock Mach numbers ranging from 1.97 to 2.31, similar to the experimental investigations of Giordano et al. (Shock Waves 28:1251–1262, 2018). The shock is introduced using the stagnation properties corresponding to the Mach number of shock-induced flow. The shock position and the shock wave attenuation parameter are compared with the experimental findings of Giordano et al. Numerical results suggest the existence of a turbulent boundary layer behind the shock wave similar to the experimental findings.