Inner-tube shape for diesel exhaust waste heat recovery: a thermal–hydraulic and techno-economic CFD study of circular, hexagonal and elliptical tubes

Recovering the medium-grade heat in internal-combustion-engine exhaust improves overall efficiency and lowers fuel consumption and emissions, and the recuperator is the performance-limiting component of any such system. While fins, inserts and surface texturing have been studied extensively, the influence of the inner-tube cross-sectional shape alone—at an otherwise fixed, fin-free architecture—has received little attention. This study presents a three-dimensional, steady, conjugate-heat-transfer CFD investigation of a double-pipe counter-flow exhaust-gas-to-water heat exchanger whose inner (hot-gas) tube assumes three cross-sectional forms—circular, regular-hexagonal and elliptical—compared under a fixed cross-sectional flow-area constraint, so that the gas mean velocity and mass flux are identical across the three geometries and the performance differences arise from the shape change together with the changes in wetted area and hydraulic diameter that it necessarily entails. The simulations, performed in ANSYS Fluent with the shear-stress-transport (SST) k–ω model on conformal (shared-topology) conjugate meshes, closed the global energy balance to better than 5 %, and grid independence was assessed for the circular and the elliptical configuration, the latter giving an apparent order of convergence of 2.33 and a fine-grid Grid Convergence Index of 6.9 %. The circular baseline was validated against the published water-side experimental measurement, which it under-predicts by 17.8 %, and against the Gnielinski correlation, which its gas-side Nusselt number under-predicts by 17 % — two deficits of similar magnitude, which place the shortfall on the gas side. Since only the circular geometry could be validated experimentally, a bias of this kind is expected, though not demonstrated, to be common to the three cross-sections, and to that extent it affects the absolute duties more than the relative comparison between them. At the full-load design point, relative to the circular tube (heat-recovery rate Q = 303.5 W, effectiveness ε = 15.8 %), the hexagonal and elliptical tubes raised heat recovery by 29.8 % and 38.7 % (to 393.9 W and 420.9 W) and effectiveness to 20.1 % and 21.1 %, at gas-side pressure-drop penalties of 27.9 % and 47.1 %. The comparison was repeated at part load and at idling: the ranking is preserved at every condition, the enhancement spans 22–39 % across the load range, and the effectiveness of each geometry is almost independent of load. Because the absolute pumping penalty was four orders of magnitude smaller than the recovered heat, an indicative techno-economic assessment favored the elliptical tube on absolute energy return, while the hexagonal tube reached an equal effective Nusselt number for roughly half the additional wetted area and wall material.