A 2 litre bottle part filled with water and pressurised with air is a two phase blowdown with three thrust regimes. The launch tube as a piston, the water impulse driven by the expanding gas, and the gas impulse after water exhaustion. The physics is Wheeler 2002 in the bottle fixed frame1, and the archived Simulink implementation of it ran on a quasi steady Bernoulli velocity and dry air5.
The water phase is momentum limited and the gas phase is energy limited, and that asymmetry decides every finding below.
Wheeler's Appendix B, the condensation of the water vapour carried in the pressurising gas, and Appendix A, the nozzle boundary layer, were both left incomplete in the source. I completed both, here1.
The axisymmetric profile with closed form volume and inertia integrals.
Ambient state and waterProperties.
Named parameter sets verbatim from their sources.
DryAdiabatic, the parity baseline. WheelerCondensation, Appendix B all at once1. GommesMoistAdiabat, the continuous moist adiabat2.
Choked and subsonic compressible outflow.
Through launch tube, water impulse and gas impulse.
Fill fraction and pressure sweeps.
Flight performance.
against the archived trace5, launch tube, water, gas
0.64, 0.001 and 7.84 percent, impulse over the archived window 1.14 percentthe closed form volume round trip
exact to 1e-12, and 11 times fasterWheeler's own worked example1
reproduced to 0.007 percentthe archive truncated its own gas tail at 0.088 s with 6.33 N still flowing
7.84 percent, stated, not smoothedThe framework run on the legacy geometry against reference_thrust.csv, 1764 points at 50 microseconds, like for like5.
The standard 2 litre case behind every sweep.
Dry baseline against both moist closures12.
Bore diameter and neck length swept to find where Appendix A starts to matter3.
Thrust against time, archive and framework overlaid, three phases shaded. The water phase matches to 0.001 percent while the gas phase reads 7.84 percent high against an archive that its own Stop block truncated at 0.088 s with 6.33 N still flowing.
Drawn from the page's own march of the same equations. The exported parity run against reference_thrust.csv will replace it.
Two treatments of the same vapour, all at once against the continuous moist adiabat12. Measured on the reference case, water impulse moves 0.802 percent and gas impulse 0.155 percent.
The completed Appendix A splits the effect. The displacement thickness area reduction on its own is impulse neutral at +0.000 percent, because narrowing the exit lowers mass flow and raises velocity in almost equal measure, while the wall shear costs 0.579 percent on the standard bottle, 1.8 percent at a 4 mm bore and 8.1 percent at a 300 mm neck34. The laminar method carries a caveat at the measured nozzle Reynolds number of 8.8e5.
Restrictions and vapour physics move the water phase, which is momentum limited, and barely touch the gas phase, which is energy limited, because the same stored gas energy eventually leaves whatever the restriction. The 7.84 percent gas phase gap against the archive and the laminar caveat are the two open edges, and both are stated where they occur.
With a pressure transducer and controlled initial humidity, which separates the two condensation treatments.
The measured Reynolds number sits past transition, so the laminar result is a lower bound on the friction.
The instant where the archive and the framework disagree about the handover.
Laminar boundary layer only, so the friction numbers are lower bounds. No spray, foaming or two phase expulsion at water exhaustion. Rigid bottle, no compliance. One dimensional nozzle flow. No validation against a measured thrust trace.