Improved Stability-Based Transition Transport Model for Airships Incorporating Wall Heating Effects

Laminar drag reduction is a critical technology for enhancing the endurance and station-keeping capabilities of airship platforms. However, existing transport-based transition models fail to account for the premature transition induced by wall heating, a limitation that significantly hinders the robust engineering application of laminar-flow technology in realistic thermal environments.To address this deficiency, this study first develops stability-based correction for transition modeling that explicitly incorporates wall-to-freestream temperature ratios. Leveraging the Falkner--Skan--Cooke (FSC) equations and linear stability theory (LST) with the $e^N$ method, we derive physics-based correlations for the transition criteria as functions of the temperature ratio, pressure gradient, and turbulence intensity. These corrections are integrated into a simplified stability-based transition transport model proposed by \citet{franccois2023simplified} and validated against the classic Schubauer and Klebanoff flat-plate experiments, demonstrating accurate prediction of transition locations under adiabatic, heated, and cooled conditions. Crucially, wind-tunnel experiments on a heated airship model show that wall-heating sensitivity is strongly influenced by local pressure-gradient variations, which is due to Reynolds-number-driven transition-location shifts. The proposed model successfully reproduces the experimentally observed transition advancement caused by wall heating. This framework, covering both heating and cooling regimes, provides a capability to support future laminar-flow control technologies based on wall-temperature modulation.