Frequency-Dependent Interfacial Instability and Vortex Dynamics of a Disturbed Liquid Jet in Crossflow

This study investigates the primary atomization dynamics of a sinusoidal-disturbed liquid jet in a gaseous crossflow, focusing on perturbation frequencies spanning <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>−</mml:mo> <mml:mn>1500</mml:mn> </mml:mrow> </mml:math> kHz (Strouhal number <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m2"> <mml:mrow> <mml:mi mathvariant="normal">S</mml:mi> <mml:mi mathvariant="normal">t</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mo>−</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:math> ). A high-fidelity numerical framework combining the Volume of Fluid (VOF) interface capturing method and octree-based adaptive mesh refinement is employed to resolve interfacial instabilities, vortex dynamics, and droplet formation mechanisms. For the undisturbed jet, Rayleigh-Taylor (RT) instability dominates surface wave formation, producing characteristic “ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m3"> <mml:mrow> <mml:mi mathvariant="normal">Λ</mml:mi> </mml:mrow> </mml:math> ”-shaped structures and governing ligament/droplet shedding. Under forced perturbations, four distinct frequencies are systematically analyzed to elucidate modulation effects. Key findings reveal that low-frequency disturbances <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m4"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mi mathvariant="normal">S</mml:mi> <mml:mi mathvariant="normal">t</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.22</mml:mn> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> induce periodic flapping, suppress RT-driven waves, and reduce breakup length remarkably, while frequency-matching RT instability <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m5"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mi mathvariant="normal">S</mml:mi> <mml:mi mathvariant="normal">t</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> amplifies surface undulations, accelerating column disintegration. High-frequency perturbations <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m6"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mi mathvariant="normal">S</mml:mi> <mml:mi mathvariant="normal">t</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> exhibit rapid near-nozzle damping, restoring unperturbed breakup characteristics. Vorticity analysis identifies counter-rotating vortex pairs as critical drivers of interfacial destabilization, with perturbation frequency non-monotonically modulating annular vortex dynamics. Trajectory comparisons demonstrate breakup length minima at intermediate Strouhal numbers, linked to wavelength-dependent wave topology transitions. These insights establish a frequency-dependent mechanism for controlling jet atomization, offering direct applications for reducing combustion instabilities through targeted flow modulation in propulsion systems.