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Turbulent mixing and trajectories of jets in a supersonic cross-flow with different injectants

Published online by Cambridge University Press:  01 February 2021

Dan Fries Open the ORCID record for Dan Fries [Opens in a new window] ,
Devesh Ranjan Open the ORCID record for Devesh Ranjan [Opens in a new window]  and
Suresh Menon
Dan Fries*
Affiliation:
School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA
Devesh Ranjan*
Affiliation:
School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA
Suresh Menon
Affiliation:
School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA
*
†Email addresses for correspondence: dfries@gatech.edu, devesh.ranjan@me.gatech.edu
†Email addresses for correspondence: dfries@gatech.edu, devesh.ranjan@me.gatech.edu
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Abstract

We investigate flow fields and trajectories of sonic jets in a supersonic cross-flow with different injectant properties. The cross-flow is held at a fixed condition with Mach number 1.71, static temperature $\sim$375 K and static pressure $\sim$76 kPa. Jet conditions cover momentum flux ratios $J$ from 1 to 6, molecular weights from $\sim$4 to 44 g mol$^{-1}$ and specific heat ratios from $\sim$1.24 to 1.66. Mie-scattering images are used to study turbulent mixing and trajectory development. Qualitative trends suggest that, at $J=4\text {--}6$, the convective Mach number concept applies as discussed in previous literature. At lower $J$, however, trends for changing molecular weights seem to reverse and the boundary layer might influence turbulent mixing. Analytically estimated jet velocities suggest the suppression of hydrodynamic instabilities changes at different rates for different injectants, as $J$ increases. A newly developed, semi-empirical jet trajectory scaling explicitly considers the momentum flux ratio, boundary layer effects and the existence of the jet bow shock. For validation, this scaling is applied to our trajectory data and those of existing literature, extending the covered parameter space. Quantifying the degree of trajectory correlation shows the scaling is specifically relevant at $J \leq 6$ in this study, where the boundary layer and bow shock influence are important. On the other hand, at higher $J$ and for thin boundary layers, the momentum flux ratio plays a more dominant role. The results in this study can guide the design of injection systems for supersonic applications and improve prediction of jet trajectories.

JFM classification

Compressible Flows: Shock waves Wakes/Jets: Jets Mixing: Turbulent mixing

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JFM Papers
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Journal of Fluid Mechanics , Volume 911 , 25 March 2021 , A45
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© The Author(s), 2021. Published by Cambridge University Press

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