Scaling analysis of the pressure distribution in shock wave/boundary layer interactions on convex surfaces with extended free-interaction theory

Predicting the pressure distribution in shock wave/boundary layer interaction (SWBLI) over convex surfaces is critical for hypersonic vehicle design, yet a unified theoretical model remains absent. This work extends the classical free-interaction theory by introducing two dimensionless parameters: normal upper Delta p overbar Subscript r Δ p ¯ r Δ p̄ᵣ , which quantifies the cumulative effect of downstream curvature on reattachment pressure, and normal upper Delta p overbar Subscript s Δ p ¯ s Δ p̄ₛ , which captures the upstream displacement delay due to boundary-layer growth on the curved wall. Based on the relative position of the separation point with respect to the curvature onset, the interaction is classified into two distinct types: type-I, where separation occurs on the flat plate upstream of the curved section ( normal upper Delta p overbar Subscript s Baseline equals 0 Δ p ¯ s = 0 Δ p̄ₛ = 0 ), and type-II, where separation occurs on the curved surface itself ( normal upper Delta p overbar Subscript s Baseline less than 0 Δ p ¯ s < 0 Δ p̄ₛ < 0 ). Scaling methods are developed to reconstruct the entire pressure distribution within the separation region from the flat-plate baseline for both interaction types. Comprehensive validation using numerical simulations and experimental measurements demonstrates that the normalised pressure rise normal upper Delta upper F Subscript c Superscript asterisk divided by upper F Subscript p Superscript asterisk Δ F c ∗ / F p ∗ Δ F^*c/F^*ₚ collapses linearly onto alpha Subscript r Baseline normal upper Delta p overbar Subscript r plus alpha Subscript s Baseline normal upper Delta p overbar Subscript s α r Δ p ¯</mml:m