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

Despite the presence of a variety of studies dealing with the magnitude of particle Reynolds number, Rep 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, Dp/L, 0.04 ⩽ Dp/L ⩽ 0.72, and bed porosity, ε, 0.36 ⩽ ε ⩽ 0.56. The test cases covered the ranges of particle Reynolds number, Rep 708 ⩽ Rep ⩽ 7772 and particle Froude number; Frp 2.86 ⩽ Frp ⩽ 10.39. The measurements of pressure drop through packed bed; ΔPBed and superficial mean exit velocity; U are used to determine bed frictional effects in reference to the available literature on particle friction factors, fp. The magnitude of Rep 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 fp. The calculated fp for the covered test cases are given as a function of pressure coefficient, ΔP* and Rep, Frp, Φ, ε, Dp/L in the approximate ranges of laminar and turbulent flow for Rep < 2000 and Rep > 2000, respectively. The proposed separate equations of fp = fp(ΔP*, Rep, Frp, Φ, ε, Dp/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 ⩽ Rep ⩽ 4000 and Rep > 5000 with an analogy to the well-known Moody Chart in pipe flows.