Near-Field Shock Structure of Underexpanded Coflowing Jets and a Gas-Kinetic Framework for Multiscale Jet Flows

Abstract

A propulsive nozzle operating in flight during take-off is surrounded by a freestream flow, referred to as coflow. For a choked convergent nozzle exhausting an underexpanded jet in high subsonic flight, the literature lacks a systematic study of how the coflow velocity, characterized by the coflow-to-jet-exit velocity ratio $U_c$, and the nozzle pressure ratio (NPR) together shape the near-field flow structures of the jet. Moreover, when the surrounding ambient is rarefied, as for a rocket operating on the Moon or Mars, its effect on the jet flow structures remain unclear. This thesis characterizes the former and develops a multiscale solver to address the latter. The former study in the continuum regime serves as the interpretable baseline against which rarefied jet flow behavior can eventually be compared and contrasted.

This thesis first characterizes the effect of a subsonic coflow over a range of NPR and $U_c$ representative of a choked convergent nozzle in high subsonic flight, in a continuum environment. Time-averaged statistics from direct numerical simulations (DNS) and an inviscid method-of-characteristics (MOC) analysis are used to understand how the coflow alters the Mach-disk and shock-cell structures. While the transition from regular to Mach reflection with increasing NPR is well known, coflow exerts the opposite effect. A strong coflow reverts the centerline Mach reflection to regular reflection and shrinks the Mach disk until it vanishes, so that the NPR for the transition from regular to Mach reflection increases with $U_c$. This effect has previously been attributed solely to a reduction in the initial jet-boundary inclination, which confines the lip Prandtl--Meyer fan to a smaller angle and weakens the embedded shock. A second mechanism, driven by the static pressure at the jet boundary, is shown here to be equally important. Coflow imposes a non-uniform pressure along the jet boundary that orients the boundary-reflected compression waves at shallower angles and inhibits their coalescence into an embedded shock, so that the shock either reflects regularly or fails to form. An MOC analysis using simulation-informed jet-boundary inclination and boundary-pressure profiles confirms this two-factor effect. The coflow also lengthens the first shock cell approximately linearly, which is captured by a simple correction to Prandtl's classical shock-cell-length scaling.

To extend the study beyond the continuum to the rarefied regime, where the shock structure and flow statistics of the jet are expected to change substantially, two gas-kinetic solvers are developed on the Bhatnagar--Gross--Krook model of the Boltzmann equation. The first, an axisymmetric gas-kinetic scheme for the Navier--Stokes equations (GKS-NS), reproduces the continuum coflowing-jet results using fluxes built from the kinetic description of the gas. The second, based on the unified gas-kinetic wave-particle (UGKWP) method, extends the same description from the continuum to the rarefied regime by carrying the non-equilibrium part of the flow with stochastic particles. The UGKWP solver is validated in the continuum regime against well-characterized underexpanded jets from the literature, and its performance in the rarefied regime is assessed qualitatively against a vacuum-plume configuration from the literature. A detailed quantitative validation in the rarefied regime, a three-dimensional extension of the solver, and its application to coflowing jets exhausting into a rarefied ambient are left for future work.