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Favourable breakdown of the Reynolds analogy in turbulent heat transfer over streamwise-aligned longitudinal rib arrays
Published online by Cambridge University Press: 11 June 2026
Abstract
We performed a direct numerical simulation study on the breakdown of the Reynolds analogy over streamwise-aligned longitudinal rib arrays caused by Kelvin–Helmholtz (K–H) instability-induced turbulence. The purpose of this study was to elucidate the underlying physics responsible for the favourable breakdown of the Reynolds analogy, and gain better insight into the scaling of the dissimilar heat transfer enhancement and characteristics of the K–H instability-induced turbulence structure. Temperature was treated as a passive scalar with a Prandtl number of unity. The thermal and flow boundary conditions were prescribed such that the non-dimensional streamwise momentum and energy equations were similar. The results showed that the Reynolds analogy factor attains its maximum value when the spanwise-oriented turbulent structure associated with the K–H instability becomes energetic. The slip-to-bulk velocity ratio serves as an effective scaling parameter not only for the Reynolds analogy factor but also for quantifying the significance of turbulence structures induced by the K–H instability, and a moderate slip-to-bulk velocity ratio yields the largest Reynolds analogy factor. A conditional averaging analysis reveals that the K–H instability generates a counter-rotating vortex pair accompanied by streamwise-alternating turbulent fluctuations. The associated streamwise-alternating perturbations in pressure, velocity and temperature exhibit phase differences between them. The phase difference strengthens the negative correlation between the vertical velocity and temperature fluctuations, while reducing that between the vertical and streamwise velocity fluctuations within the rib arrays. As a result, the vertical turbulent heat flux is more significantly enhanced than the Reynolds shear stress within the rib arrays. Another consequence of the phase differences is the dissimilar modifications of the pressure correlation terms in the transport equations for turbulent heat and momentum fluxes. A budget analysis indicates that modifying the pressure correlation terms also serves to enhance the vertical heat flux more than the Reynolds shear stress, thereby reinforcing the favourably dissimilar heat transfer enhancement.
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