Exact non local expression for the wall heat transfer coefficient in tubular catalytic reactors

Pseudo-homogeneous 1D RANS radial model for heat transfer in tubular packed beds

“…Figure 26: Correlations for the wall heat transfer coefficient. Nu1: [26]; Nu2: [4]; Nu3: [58]; Nu4: [59], Nu5: [60]; Nu6: [61]; Nu7: [62]; Nu8: Correlation derived in this study.…”

“…The present study can be seen as an elaboration and an extension of the previous work achieved namely by [26] and [21]. Here, a flow dynamic based two-zonal pseudo-homogeneous 1D radial heat transfer model is derived with a deep insight into the near wall zone heat resistance, which is the most critical point as far as heat control in tubular catalytic reactors is concerned.…”

“…It is also referred to as the REV, the Representative Elementary Volume [39,40]. A methodology to define the appropriate REV for wall bounded medium presenting radial heterogeneity has been developed in [26] and is used in the present study to upscale unequivocally pore scale data to the observation scale (bed scale). When one uses the right REV for volume averaging, it can be showed [38] that the two averaging operators defined above permute φ i = ϕ i .…”

“…The porous medium framework is used to up-scale unequivocally pore scale relevant data obtained via high-fidelity 3D simulations to the reactor scale. This is practically achieved extending the concept of Representative Elementary Volume (REV) to anisotropic wall bounded porous medium [26]. Afterwards, turbulent flow governing pseudo-homogeneous equations including mechanical dispersion are derived and validated against 3D detailed numerical simulations.…”

“…Indeed, global modifications can lead errors on porosity and so on the pressure drop of 4% and 12−15% respectively [37]. The strategy employed here [26] consists in first detecting particles one close to another with a distance less than 1% of d p . For those particles, radius is then increased by 2% of d p .…”