<p>The underexpanded jet issuing from an elliptic convergent nozzle with an aspect ratio of 8 is quantitatively visualized using rainbow schlieren tomography. Flow visualizations are conducted at a nozzle pressure ratio of 4.0 to produce strong shocks within the jet plume. The Reynolds number, based on the equivalent diameter and flow properties at the nozzle exit, is 4.0<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10494_2025_687_Article_IEq1.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(\times\)</EquationSource> </InlineEquation>10<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10494_2025_687_Article_IEq2.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(^5\)</EquationSource> </InlineEquation>. Multi-view rainbow schlieren images with a horizontal filter setting are captured by rotating the nozzle around its central axis at an angular step of 5<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10494_2025_687_Article_IEq3.gif" Format="GIF" Height="7" Rendition="HTML" Resolution="72" Type="Linedraw" Width="9" /> </InlineMediaObject> <EquationSource Format="TEX">\(^\circ\)</EquationSource> </InlineEquation>, ranging from 0<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10494_2025_687_Article_IEq3.gif" Format="GIF" Height="7" Rendition="HTML" Resolution="72" Type="Linedraw" Width="9" /> </InlineMediaObject> <EquationSource Format="TEX">\(^\circ\)</EquationSource> </InlineEquation> to 180<InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10494_2025_687_Article_IEq3.gif" Format="GIF" Height="7" Rendition="HTML" Resolution="72" Type="Linedraw" Width="9" /> </InlineMediaObject> <EquationSource Format="TEX">\(^\circ\)</EquationSource> </InlineEquation>. The jet density field is reconstructed at a spatial resolution of 13 <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10494_2025_687_Article_IEq6.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mu\)</EquationSource> </InlineEquation>m using the convolution back projection method. The near-field flow features of a shock-containing elliptic jet with a high aspect ratio are experimentally demonstrated for the first time. In addition, to examine the effects of angular steps on the reconstructed density field, the rainbow schlieren images taken at 10<InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10494_2025_687_Article_IEq3.gif" Format="GIF" Height="7" Rendition="HTML" Resolution="72" Type="Linedraw" Width="9" /> </InlineMediaObject> <EquationSource Format="TEX">\(^\circ\)</EquationSource> </InlineEquation>, 20<InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10494_2025_687_Article_IEq3.gif" Format="GIF" Height="7" Rendition="HTML" Resolution="72" Type="Linedraw" Width="9" /> </InlineMediaObject> <EquationSource Format="TEX">\(^\circ\)</EquationSource> </InlineEquation>, and 30<InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10494_2025_687_Article_IEq3.gif" Format="GIF" Height="7" Rendition="HTML" Resolution="72" Type="Linedraw" Width="9" /> </InlineMediaObject> <EquationSource Format="TEX">\(^\circ\)</EquationSource> </InlineEquation> intervals are selected from a total of 37 rainbow schlieren images captured at 5<InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10494_2025_687_Article_IEq3.gif" Format="GIF" Height="7" Rendition="HTML" Resolution="72" Type="Linedraw" Width="9" /> </InlineMediaObject> <EquationSource Format="TEX">\(^\circ\)</EquationSource> </InlineEquation> intervals. The density field is then reconstructed for these specific angular steps. The effects of angular steps are clarified on the two-dimensional density fields in the minor-axis and major-axis planes, as well as on the streamwise density profiles along the jet centerline and liplines in both the minor-axis and major-axis planes.</p>

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Quantitative Flow Visualization of Underexpanded Elliptic Jets by Rainbow Schlieren Tomography

  • Takumi Sakashita,
  • Tatsuya Nagata,
  • Shinichiro Nakao,
  • Yoshiaki Miyazato

摘要

The underexpanded jet issuing from an elliptic convergent nozzle with an aspect ratio of 8 is quantitatively visualized using rainbow schlieren tomography. Flow visualizations are conducted at a nozzle pressure ratio of 4.0 to produce strong shocks within the jet plume. The Reynolds number, based on the equivalent diameter and flow properties at the nozzle exit, is 4.0 \(\times\) 10 \(^5\) . Multi-view rainbow schlieren images with a horizontal filter setting are captured by rotating the nozzle around its central axis at an angular step of 5 \(^\circ\) , ranging from 0 \(^\circ\) to 180 \(^\circ\) . The jet density field is reconstructed at a spatial resolution of 13 \(\mu\) m using the convolution back projection method. The near-field flow features of a shock-containing elliptic jet with a high aspect ratio are experimentally demonstrated for the first time. In addition, to examine the effects of angular steps on the reconstructed density field, the rainbow schlieren images taken at 10 \(^\circ\) , 20 \(^\circ\) , and 30 \(^\circ\) intervals are selected from a total of 37 rainbow schlieren images captured at 5 \(^\circ\) intervals. The density field is then reconstructed for these specific angular steps. The effects of angular steps are clarified on the two-dimensional density fields in the minor-axis and major-axis planes, as well as on the streamwise density profiles along the jet centerline and liplines in both the minor-axis and major-axis planes.