Investigation of thrust augmentation and nozzle exit pressure in starting jets from a tube nozzle

TL;DR

This study uses numerical simulations to investigate the role of nozzle exit pressure in thrust augmentation of starting jets, finding that it is negligible or negative, contrary to previous assumptions, and identifying vortex dynamics affecting thrust.

Contribution

It provides the first detailed numerical analysis challenging prior beliefs about nozzle exit over-pressure's role in thrust enhancement in starting jets.

Findings

No significant thrust augmentation from nozzle exit over-pressure.

Both over-pressure and under-pressure occur during different jet phases.

Counter-rotating vortices are linked to thrust reduction.

Abstract

It has been widely accepted that nozzle exit over-pressure is responsible for thrust augmentation in starting jets over steady jets and a few pulsed jet propulsion systems have been developed based on this finding. However, no other study has been conducted to confirm the nozzle exit over-pressure effect. In this paper, thrust and nozzle exit pressure are numerically investigated under different jet velocity programs (negative slope (NS), positive slope (PS) and impulsive). Starting jets are generated for fluid slug length to diameter (L/D) ratios of 2-5 at each jet velocity program. In contradiction to the findings presented in [P. Krueger and M. Gharib, J. Phys. Fluids, 15, 1271 (2003)] the results in this paper reveal that the time-averaged thrust due to nozzle exit pressure in starting jets from a tube nozzle is negligible or negative resulting in no thrust augmentation when compared to steady jets with hypothetical identical velocity programs. Also, nozzle exit experiences both over-pressure and under-pressure in accelerating and decelerating portions of jet velocity programs respectively in both NS and PS velocity programs. Furthermore, it is found that secondary counter-rotating vortex is generated during decelerating portion of jet velocity programs which may be linked to the nozzle exit underpressure explaining the reduced thrust during starting jets generated by different velocity programs.