(186o) Analytical Analysis of Flow Distribution Uniformity As a Design Criteria for a Novel Micro Packed-Bed Bionic Reactor

The Micro Packed-bed Bionic Reactor (MPBR) is a novel configuration aiming for fast catalytic gas-solid reactions. Hierarchical distributed fluid channel and microscale permeable framework packed with small particle catalysts can realize a higher reaction effectiveness, a lower pressure drop and a better heat transfer.The flow distribution uniformity substantially affect the performance of MPBR, which is determined by operating conditions and especially size parameters. This work endeavors to use analytical methods to seek a theoretical instruction of structure design.

The elementary unit of MPBR consists of a catalyst bed with two halves of fluid channel on both sides, which is governed by Berman’s equation in fluid channels and Darcy’ law in catalyst bed. The one-dimensional simplified mathematical model is obtained by integration of channel equations along radial direction and coupling through Darcy’s flow equation. The resulting expression turns out to be a second order homogeneous linear differential equation of pressure difference between the two fluid channels, and the analytic solution is the function of three dimensionless parameters, the inlet Reynolds number, the aspect ratio of fluid channel and the unit permeability. The analytic solution makes it possible to quantitatively estimate the distribution uniformity by the relative standard deviation of pressure difference, which is proved, under reasonable conditions, to be linear to P_re , a new dimensionless parameter extracted from the analytic solution indicating the relative proportion between the pressure drop of fluid channel and catalyst bed. Deduction demonstrates that P_re equals the product of the three aforementioned dimensionless parameters, meaning that giving a maximum restriction for the relative standard deviation, the operating conditions and structure size can be designed correspondingly.

Further numerical simulations have been carried out to estimate the accuracy of the analytic solution, and verify that the error is tolerant even in certain parameter ranges where some of the assumptions the analytic solution is based on is invalid.