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.