Reynolds analogy in compressible turbulent flow over rough surface

Understanding heat and momentum transfer in compressible turbulent flows over rough surfaces is critical for the design and performance of high-speed aerodynamic systems. The classical Reynolds analogy, which assumes that the same turbulent motions responsible for friction also govern heat transfer, breaks down in high-speed, rough-wall flows, rendering the conventional temperature–velocity relationship invalid. This work aims to investigate the effects of compressibility and surface roughness on the Reynolds analogy and to develop a DNS-informed, machine-learning-based model for the Reynolds analogy factor that accounts for both influences. We constructed a direct numerical simulation (DNS) database of compressible turbulent flow over irregular rough surfaces, covering regimes from subsonic to supersonic and from transitionally to fully rough conditions. We observe that the Reynolds analogy factor decreases with increasing roughness Reynolds number, effective roughness slope, and Mach number. A model for the Reynolds analogy factor is developed using a feedforward neural network trained on the DNS database. The model is tested on previously unseen rough-wall cases and outperforms existing empirical correlations. Finally, a modified temperature–velocity relationship is proposed for rough-wall conditions by leveraging the Reynolds analogy model. This revised relation is validated across a range of rough surfaces and flow conditions.