| Summary: | The present work investigates the impact of steady micro-jet blowing on the performance of a planar micro-nozzle designed for both liquid micro-thrusters and nitrogen cold-gas micro-resistojets. Two micro-injectors have been placed into the divergent region along the sidewalls, injecting a secondary flow of propellant perpendicularly to the wall where they have been located. The micro-jet actuator configuration is characterized by the dimensionless momentum coefficient <i>c<sub>μ</sub></i>. The best performance improvement is retrieved at the maximum <i>c</i><i><sub>μ</sub></i> for both water vapor (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="sans-serif">Δ</mi><msub><mo>%</mo><mrow><mstyle mathvariant="bold" mathsize="normal"><mi>T</mi></mstyle><mo>,</mo><mstyle mathvariant="bold" mathsize="normal"><mi>j</mi><mi>e</mi><mi>t</mi></mstyle></mrow></msub></mrow></semantics></math></inline-formula> = +22.6% and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="sans-serif">Δ</mi><msub><mo>%</mo><mstyle mathvariant="bold-italic"><mrow><mi>I</mi><mi>s</mi><mi>p</mi><mo>,</mo><mi>T</mi><mi>j</mi><mi>e</mi><mi>t</mi></mrow></mstyle></msub></mrow></semantics></math></inline-formula> = +2.9% at <i>c</i><i><sub>μ</sub></i> = 0.168) and nitrogen gaseous flows (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="sans-serif">Δ</mi><msub><mo>%</mo><mrow><mstyle mathvariant="bold" mathsize="normal"><mi>T</mi></mstyle><mo>,</mo><mstyle mathvariant="bold" mathsize="normal"><mi>j</mi><mi>e</mi><mi>t</mi></mstyle></mrow></msub></mrow></semantics></math></inline-formula> = +36.1% and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="sans-serif">Δ</mi><msub><mo>%</mo><mstyle mathvariant="bold-italic"><mrow><mi>I</mi><mi>s</mi><mi>p</mi><mo>,</mo><mi>T</mi><mi>j</mi><mi>e</mi><mi>t</mi></mrow></mstyle></msub></mrow></semantics></math></inline-formula> = +9.1% at <i>c</i><i><sub>μ</sub></i> = 0.297). The fields of the Mach number and the Schlieren computations, in combination with the streamline visualization, reveal the formation of two vortical structures in the proximity of secondary jets, which energize the core flow and enhance the expansion process downstream secondary jets. The compressible momentum thickness along the width-wise direction <i>θ<sub>xy</sub></i> in presence of secondary injection reduces as a function of <i>c<sub>μ</sub></i>. In particular, it becomes smaller than the one computed for the baseline configuration at <i>c<sub>μ</sub></i> > 0.1, decreasing up to about and -57% for the water vapor flow at <i>c<sub>μ</sub></i> = 0.168, and -64% for the nitrogen gaseous flow at <i>c<sub>μ</sub></i> = 0.297.
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