Climate-Change Mitigation Through Efficient Convergent–Divergent Nozzles: Influence of Divergent Straight-Section Length and Symmetric Double Secondary Injection

Abstract

Improving nozzle energy conversion can reduce the propellant needed to deliver a given impulse and, consequently, propulsion-related carbon dioxide emissions. This study uses steady two-dimensional Reynolds-averaged Navier–Stokes simulations to examine a planar convergent–divergent nozzle with 1150 mm inlet and exit heights, a 300 mm throat, and an overall length of 2775 mm. Air enters at 800 kPa gauge and 500 K. Symmetric secondary hot-air injection is supplied through opposed 30 mm wall ports at 38 kPa gauge and 1000 K. Five divergent shapes are considered: a fully curved contour and contours with straight portions occupying 10%, 20%, 25%, and 30% of the divergent length. Double-injection predictions are compared against baseline and single-injection results for the same geometries. Integrated wall forces match a control-volume momentum balance within 1.9%. The straight-section cases yield velocity coefficients of 98.9%–99.2% and exit Mach numbers of 2.86–2.89, compared with the isentropic value of 2.90; the fully curved case yields 97.7% and Mach 2.80. With total secondary-to-primary mass-flow ratios of 0.13%–0.71%, double injection changes exit-plane thrust by −0.33% to +0.42% relative to single injection and limits residual side force to 0.04%–0.29% of axial force. Nonetheless, nominally identical ports do not always deliver equal flow: the 10% case has a 73% imbalance, and one port reverses in the 30% case. These findings indicate that an injector stagnation-pressure ratio near 0.155 is marginal. Hot injection raises adiabatic wall temperature by 42–92 K and lowers viscous axial force by 16%–23%. Across the cases examined, divergent-contour selection has a stronger association with efficiency than low-pressure injection.