Determination of laminar and turbulent flow ranges through vertical packed beds in terms of particle friction factors

Abstract

Despite the presence of a variety of studies dealing with the magnitude of particle Reynolds number, Re p defining transition from laminar to turbulent regime for flow through packed beds, the manner is still one of the unknowns. An approach based on the experimental data concerning upward airflow through fixed cylindrical packed beds is presented in this paper. The utilized packed beds had the following ranges of; sphericity, Φ, 0.55 ⩽ Φ ⩽ 1.00, packing material diameter to bed length ratio, D p/ L, 0.04 ⩽ D p/ L ⩽ 0.72, and bed porosity, ε, 0.36 ⩽ ε ⩽ 0.56. The test cases covered the ranges of particle Reynolds number, Re p 708 ⩽ Re p ⩽ 7772 and particle Froude number; Fr p 2.86 ⩽ Fr p ⩽ 10.39. The measurements of pressure drop through packed bed; Δ P Bed and superficial mean exit velocity; U are used to determine bed frictional effects in reference to the available literature on particle friction factors, f p. The magnitude of Re p defining transition is assumed to be 2000 with particular emphasis to the flow dynamics. The definitions of Bird et al. [R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena , John Wiley and Sons, NY, 1960] are used to calculate f p. The calculated f p for the covered test cases are given as a function of pressure coefficient, Δ P* and Re p, Fr p, Φ, ε, D p/ L in the approximate ranges of laminar and turbulent flow for Re p < 2000 and Re p > 2000, respectively. The proposed separate equations of f p = f p(Δ P*, Re p, Fr p, Φ, ε, D p/ L) are satisfied for laminar and turbulent flows with corresponding average error margins of ±7.6% and ±18%. Furthermore ranges of transitional and fully rough flow through packed beds are estimated as 2000 ⩽ Re p ⩽ 4000 and Re p > 5000 with an analogy to the well-known Moody Chart in pipe flows.