Effect of Divergent-Section Straight-Segment Length on Secondary-Injection Thrust Vector Control in a Planar Convergent–Divergent Nozzle: A RANS Study

Abstract

Fluidic thrust vector control (FTVC) can redirect a propulsion jet without moving nozzle components, although its performance is sensitive to the nozzle contour near the injection location. This study presents steady, two-dimensional Reynolds-averaged Navier–Stokes (RANS) simulations of a planar convergent–divergent nozzle at a nozzle pressure ratio of approximately 8.9. The primary stagnation conditions are about 899 kPa and 500 K, while a hot secondary stream at approximately 139 kPa and 1000 K is introduced through a single port in the upper wall. Five divergent contours are considered: one fully curved contour and four variants with straight portions occupying 10%, 20%, 25%, or 30% of the divergent length. Each contour is evaluated with and without injection, for a total of ten cases. Integrated wall forces are checked against a control-volume momentum balance, with differences no greater than 3.5%; exit-plane thrust coefficients are within ±1.4% of the corresponding isentropic estimates. At secondary-to-primary mass-flow ratios of 0.16%–0.37%, the calculated side-force increments are 140–1078 N·m−1, the thrust-vector-angle increments are 0.01°–0.09°, and the amplification factors range from 0.29 to 1.92. For the geometrically consistent 10%, 20%, and 30% pairs, the exit-plane thrust change remains below 0.12%. Side force decreases monotonically with increasing straight-segment length across those three pairs, while the hot secondary flow reduces the viscous axial wall force by 5%–11%. The low secondary-to-primary stagnation-pressure ratio (approximately 0.155) restricts jet penetration, and the baseline side-force asymmetry is comparable in magnitude to the injection-induced change. These findings motivate grid-converged and three-dimensional follow-up studies.