Formation and vortex breakdown of the counter-rotating vortex pair in square and circular laminar jets in crossflow

Laminar jets in crossflow are analyzed using direct numerical simulation to identify the source of vorticity leading to the formation of the counter-rotating vortex pair. A vorticity transport analysis conducted on steady cases shows that all counter-rotating vortex pair vorticity is generated in the nozzle walls for large velocity ratio jets (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>R</a:mi></a:math>), but that additional boundary layer vorticity is entrained at low <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>R</b:mi></b:math>. The transport mechanisms are quantified and discussed in detail, including the influence of having a square jet cross section. The study also examines the effect of varying the velocity ratio in the range <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mn>0.25</c:mn><c:mo>≤</c:mo><c:mi>R</c:mi><c:mo>≤</c:mo><c:mn>5</c:mn></c:mrow></c:math> and the jet Reynolds number in the range <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mn>100</d:mn><d:mo>≤</d:mo><d:msub><d:mtext>Re</d:mtext><d:mtext>jet</d:mtext></d:msub><d:mo>≤</d:mo><d:mn>300</d:mn></d:mrow></d:math>. Increasingly complex flow patterns are revealed, even in the steady regime, including the onset of bubble vortex breakdown of the counter-rotating vortex pair. Breakdown onset is quantified and analyzed in detail, revealing that it is a gradual process that depends on the jet vorticity and the adverse pressure gradient formed downstream of the jet inlet. Additionally, breakdown is discovered to precede the onset of unsteady flow for decreasing <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mi>R</e:mi></e:math> and fixed <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:msub><f:mtext>Re</f:mtext><f:mtext>jet</f:mtext></f:msub></f:math> for jets with both cross sections. A newly discovered asymmetric instability is identified at <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:msub><g:mtext>Re</g:mtext><g:mtext>jet</g:mtext></g:msub><g:mo>=</g:mo><g:mn>300</g:mn></g:mrow></g:math> and characterized, where each of the counter-rotating vortices undergoes breakdown while oscillating laterally at low frequency. Hairpin vortex shedding, typical of low <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mi>R</h:mi></h:math> laminar jets in crossflow, is captured in our simulations. Breakdown bubbles are identified for <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mrow><i:mi>R</i:mi><i:mo>&gt;</i:mo><i:mn>0.4</i:mn></i:mrow></i:math>, where the flow remains approximately steady in the near field. For <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mrow><j:mi>R</j:mi><j:mo>≤</j:mo><j:mn>0.4</j:mn></j:mrow></j:math>, the increasing fluctuation amplitude in the near field results in the rollup of fluid and the destruction of the breakdown bubbles in the instantaneous flow field.