Flow energetics and wake dynamics in compressible laminar heated bluff-body flows

In our previous work [Kula et al., PoF 2025], it was shown that aerodynamics and heat transfer characteristics of a flow over a two-dimensional (2D) cylinder are significantly affected by the surface-to-free-stream temperature ratio (TR). To better understand the underlying physics, we investigate flow energetics and vorticity using high-fidelity Direct Numerical Simulations (DNS) of the compressible Navier–Stokes equations. DNS are performed for TR ranging from 1.0 (Boussinesq) to 3.0 (non-Boussinesq), Reynolds numbers of 40, 80, and 150, and free-stream Mach numbers of 0.2 and 0.4. The three-dimensional (3D) geometry effects are also examined by comparing the flows over a 2D cylinder and a 3D sphere. Investigation of the terms that appear in the internal energy, kinetic energy, and vorticity transport equations reveals that the dominant mechanism of energy exchange between internal and kinetic energy is pressure dilatation, and increasing TR enhances internal energy generation through heat diffusion and its subsequent conversion into kinetic energy. At high TR, flow compressibility and variable-density effects become significant, especially in front of the body, which leads to an increased contribution of baroclinic torque to the vorticity generation.