synergistic control of supersonic jet flows: numerical investigation of multiple protuberance and coanda effect integration

This study numerically investigates transonic jet control in a rectangular nozzle with mach (m) = 1 at the throat, issuing at nozzle pressure ratio (npr = p0/pa) = 2.5 (p0 = 210 kpa, pa = 84 kpa, t = 300 k; fully expanded m ≈ 1.22). a two-dimensional steady rans framework (sst k–ω, density-based implicit solver, roe flux; cfl ramp 0.5 → 2) is employed in a 100 × 75 throat-based domain with adiabatic no-slip walls and a hybrid mesh (≈ 2.3 – 2.5×105 elements). we vary the number, placement (throat and/or coanda flaps), and penetration depth (pen.) of protuberances. with two protuberances (throat + flap), the system exhibits discrete deflection plateaus: deflection angle (da) ≈ 35 – 37° (flap slot 22.5°) and da ≈ 68 – 75° (slots 7.5° or 37.5°), with resultant-force ratio (fr/fr0) ≈ 0.95 – 0.99. introducing a third protuberance enables intermediate deflections (e.g., da ≈ 51°, −5° to −21°) at fr/fr0 ≈ 0.86 – 0.89 (efficiency trade-off). removing the throat protuberance while retaining two flap-mounted elements yields da ≈ 6.5° at near-zero loss (fr/fr0 ≈ 1.0). overall, across the explored layouts, da spans −21° to 75° while fr/fr0 spans 0.86 – 1.0, quantifying how strategic multi-protuberance layouts expand the deflection spectrum beyond binary attachment/detachment and clarify efficiency trade-offs for integrated protuberance–coanda control at npr = 2.5.