Experimental Nusselt number correlations for heat transfer of a single spherical particle in turbulent flow

Gas-solid heat transfer is crucial in industrial reactors. The classic Ranz-Marshall correlation works well under low turbulence intensity but underestimates the Nusselt number Nu when turbulent fluctuations match or exceed the mean flow. This study delves into the heat transfer of a single spherical particle in turbulent flows through extensive experiments and develops unified Nusselt number correlations. A custom-designed four-fan turbulent heating setup is employed to create homogeneous and isotropic turbulence region (u_rms ≤ 4.18 m/s, integral length scale L ≈ 14 mm), effectively isolating the pure turbulent effect. By conducting heating experiments on a single copper sphere at different furnace temperatures and turbulent fluctuation velocities, and employing the lumped-parameter method to measure particle temperature, the Nusselt number is inversely determined via a zero-dimensional energy balance model. The results indicate a sub-linear relationship between the Nusselt number and the particle turbulent Reynolds number Re_t. An improved correlation for pure turbulent environments is derived from experimental data, as $Nu=2+0.6R{e}_t^{1/2}P{r}^{1/3}{\left(C/d\right)}^{1/5}{\left(T_f/T_p\right)}^{1/5}$. Furthermore, a coupled correlation considering both mean flow and turbulent fluctuation is proposed, capable of seamlessly transitioning between mean flow-dominated and turbulence-dominated regimes via a nonlinear composite formulation. Comparisons with the references validates the proposed correlations with an acceptable error of 10 % over a wide Reynolds range. This research highlights the significant role of turbulent fluctuations in enhancing heat transfer under high turbulence intensity. The developed correlations provide a more accurate tool for predicting Nu in complex gas-solid flows, aiding in understanding and modeling heat and mass transfer processes in turbulent multiphase flows, and offering critical guidance for subsequent reaction processes in industrial combustors.