<p>An investigation was conducted on a rectangular supersonic jet (Mach 1.8) grazing past a flat wall to study, separation, spillage, and entrainment aspects of the flow over the wall and the deflection of the jet at the wall trailing edge (WTE). The work presented in this paper is of relevance to exhaust flows over an aft-deck of rectangular nozzle and useful in thrust vectoring research. The investigation was conducted by varying the flat wall length (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40430_2025_5446_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="28" /> </InlineMediaObject> <EquationSource Format="TEX">\({L}_{\text{w}})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>L</mi> <mtext>w</mtext> </msub> <mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> as <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40430_2025_5446_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">\({0.5D}_{\text{h}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mrow> <mn>0.5</mn> <mi>D</mi> </mrow> <mtext>h</mtext> </msub> </math></EquationSource> </InlineEquation>,<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40430_2025_5446_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">\({1D}_{\text{h}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mrow> <mn>1</mn> <mi>D</mi> </mrow> <mtext>h</mtext> </msub> </math></EquationSource> </InlineEquation>,<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40430_2025_5446_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">\({2D}_{\text{h}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mrow> <mn>2</mn> <mi>D</mi> </mrow> <mtext>h</mtext> </msub> </math></EquationSource> </InlineEquation>,<InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40430_2025_5446_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">\({4D}_{\text{h}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mrow> <mn>4</mn> <mi>D</mi> </mrow> <mtext>h</mtext> </msub> </math></EquationSource> </InlineEquation>, and <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40430_2025_5446_Article_IEq6.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">\({8D}_{\text{h}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mrow> <mn>8</mn> <mi>D</mi> </mrow> <mtext>h</mtext> </msub> </math></EquationSource> </InlineEquation>, where <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40430_2025_5446_Article_IEq7.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\({D}_{\text{h}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>D</mi> <mtext>h</mtext> </msub> </math></EquationSource> </InlineEquation> was the hydraulic diameter of the nozzle rectangular exit with aspect ratio 2). Numerical simulations at three nozzle pressure ratios, i.e., 4, 6, and 8, with a set of experiments on oil flow visualization and wall pressure distributions along the length of the flat wall were carried out. The results of the present investigation indicate that for <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40430_2025_5446_Article_IEq8.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="79" /> </InlineMediaObject> <EquationSource Format="TEX">\({L}_{\text{w}}&gt;{2D}_{\text{h}},\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>L</mi> <mtext>w</mtext> </msub> <mo>&gt;</mo> <msub> <mrow> <mn>2</mn> <mi>D</mi> </mrow> <mtext>h</mtext> </msub> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> both spillage and entrainment of the flow recur along the wall length and the locations at which they occur depend upon the expansion conditions at the nozzle exit. The jet flow leaving the WTE contains asymmetric total pressure profiles about the nozzle extended centerline, and the strong cross-flow pressure gradients between the jet flow leaving WTE and the surrounding flow affect the quantum and direction of the jet deflection. The change in <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40430_2025_5446_Article_IEq9.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\({L}_{\text{w}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mtext>w</mtext> </msub> </math></EquationSource> </InlineEquation> at over-expansion conditions does not significantly affect flow separation point on the mid-width line of the wall, whereas at under-expansion conditions increase in <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40430_2025_5446_Article_IEq10.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\({L}_{\text{w}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mtext>w</mtext> </msub> </math></EquationSource> </InlineEquation> from <InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40430_2025_5446_Article_IEq11.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">\({2D}_{\text{h}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mrow> <mn>2</mn> <mi>D</mi> </mrow> <mtext>h</mtext> </msub> </math></EquationSource> </InlineEquation> to <InlineEquation ID="IEq12"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40430_2025_5446_Article_IEq12.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">\({4D}_{\text{h}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mrow> <mn>4</mn> <mi>D</mi> </mrow> <mtext>h</mtext> </msub> </math></EquationSource> </InlineEquation> shifts the separation point toward WTE.</p>

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Deflection, spillage, and flow separation aspects of a rectangular supersonic jet grazing past a flat wall

  • T. V. S. Manikanta,
  • B. T. N. Sridhar

摘要

An investigation was conducted on a rectangular supersonic jet (Mach 1.8) grazing past a flat wall to study, separation, spillage, and entrainment aspects of the flow over the wall and the deflection of the jet at the wall trailing edge (WTE). The work presented in this paper is of relevance to exhaust flows over an aft-deck of rectangular nozzle and useful in thrust vectoring research. The investigation was conducted by varying the flat wall length ( \({L}_{\text{w}})\) L w ) as \({0.5D}_{\text{h}}\) 0.5 D h , \({1D}_{\text{h}}\) 1 D h , \({2D}_{\text{h}}\) 2 D h , \({4D}_{\text{h}}\) 4 D h , and \({8D}_{\text{h}}\) 8 D h , where \({D}_{\text{h}}\) D h was the hydraulic diameter of the nozzle rectangular exit with aspect ratio 2). Numerical simulations at three nozzle pressure ratios, i.e., 4, 6, and 8, with a set of experiments on oil flow visualization and wall pressure distributions along the length of the flat wall were carried out. The results of the present investigation indicate that for \({L}_{\text{w}}>{2D}_{\text{h}},\) L w > 2 D h , both spillage and entrainment of the flow recur along the wall length and the locations at which they occur depend upon the expansion conditions at the nozzle exit. The jet flow leaving the WTE contains asymmetric total pressure profiles about the nozzle extended centerline, and the strong cross-flow pressure gradients between the jet flow leaving WTE and the surrounding flow affect the quantum and direction of the jet deflection. The change in \({L}_{\text{w}}\) L w at over-expansion conditions does not significantly affect flow separation point on the mid-width line of the wall, whereas at under-expansion conditions increase in \({L}_{\text{w}}\) L w from \({2D}_{\text{h}}\) 2 D h to \({4D}_{\text{h}}\) 4 D h shifts the separation point toward WTE.