<p>Effective quantitative visualization of compressible flows across the full field of view is essential for understanding the flow topology and dynamics of supersonic jet oscillations, shock-boundary-layer interactions, and shock reflection and diffraction. The present study provides a methodology for obtaining the time-dependent density field of transient shock-dominated flows within a confined duct. A shock strong enough to induce flow separation and exhibiting unsteady behavior is introduced downstream of the throat within a divergent half duct. The incoming flow Mach number just upstream of the shock is approximately 1.47, and the Reynolds number calculated based on the height and flow properties at the throat is 1.35 <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="348_2025_4131_Article_IEq1.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> <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="348_2025_4131_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">$10^5$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>10</mn> <mn>5</mn> </msup> </math></EquationSource> </InlineEquation>. We employ Mach-Zehnder interferometry with a finite-fringe setup to capture the time-resolved density field including the shock motion, utilizing a He-Ne laser as the light source and a high-speed camera as the recording device. A two-dimensional Fourier fringe analysis is employed to extract the phase information over the entire density field. Fascinating visual representations, such as the pseudo-infinite interferogram and the density field with phase information known as domain coloring, are introduced to illustrate flow topology. The oscillatory characteristics of shock motions are analyzed using both Lagrangian and Eulerian approaches, and the results are compared quantitatively. Furthermore, an uncertainty analysis is conducted to assess the accuracy of the density measurements and to reveal how shock oscillations affect density uncertainty.</p>

Mach–Zehnder interferometry for transient shock-dominated flows in a confined duct

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发表日期：

2025年10月18日

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Takahiro Yamashita,
Masaki Okajima,
Hiroki Kodama,
Shinichiro Nakao,
Yoshiaki Miyazato

摘要

Effective quantitative visualization of compressible flows across the full field of view is essential for understanding the flow topology and dynamics of supersonic jet oscillations, shock-boundary-layer interactions, and shock reflection and diffraction. The present study provides a methodology for obtaining the time-dependent density field of transient shock-dominated flows within a confined duct. A shock strong enough to induce flow separation and exhibiting unsteady behavior is introduced downstream of the throat within a divergent half duct. The incoming flow Mach number just upstream of the shock is approximately 1.47, and the Reynolds number calculated based on the height and flow properties at the throat is 1.35 $\times$ $\times$ $10^5$ $10^{5}$ . We employ Mach-Zehnder interferometry with a finite-fringe setup to capture the time-resolved density field including the shock motion, utilizing a He-Ne laser as the light source and a high-speed camera as the recording device. A two-dimensional Fourier fringe analysis is employed to extract the phase information over the entire density field. Fascinating visual representations, such as the pseudo-infinite interferogram and the density field with phase information known as domain coloring, are introduced to illustrate flow topology. The oscillatory characteristics of shock motions are analyzed using both Lagrangian and Eulerian approaches, and the results are compared quantitatively. Furthermore, an uncertainty analysis is conducted to assess the accuracy of the density measurements and to reveal how shock oscillations affect density uncertainty.