Transition nozzle-pressure ratio in quiescent underexpanded jets

Determine the nozzle pressure ratio at which an underexpanded sonic jet issuing into a quiescent ambient transitions from regular reflection to Mach reflection, resolving the discrepancy among reported transition values.

Background

The paper reviews experimental, theoretical, and numerical studies of Mach-disk formation in underexpanded jets issuing into a quiescent ambient. Reported transition values, defined by the nozzle pressure ratio at which the Mach-disk diameter vanishes, range approximately from 3.1 to 3.9. This unresolved variation motivates careful distinction between transition criteria and computational or experimental configurations.

References

The transition NPR for a jet in a quiescent ambient thus remains unsettled, with reported values ranging from approximately 3.1 to 3.9.

— Mach-disk formation and shock-structure transitions in underexpanded coflowing jets  (2608.18923 - Dhungana et al., 19 Aug 2026) in Section 1, Introduction