Experimental correlations on critical Reynolds numbers and friction factor in tubes with wire-coil inserts in laminar, transitional and low turbulent flow regimes

This paper analyses 23 circular helicoidal wire-coils with different geometric characteristics ranging from: dimensionless pitch p/d = [0.25-3.37], dimensionless thickness e/d = [0.071-0.286] and a Reynolds number interval from 50 to 8000. This interval widely includes the Reynolds number range in which rigid wire-coil inserts present better performance as passive enhancement technique for tubular heat exchanger applications Re = [200-2000]. Based on their hydraulic performance, the wire-coil inserts are categorized according to a new dimensionless parameter: the Transition Shape Parameter (TSP). A new set of correlations are obtained to predict the Fanning friction factor coefficient as a function of Reynolds number and geometrical characteristics of the insert within the three flow regimes: laminar, transitional and low turbulent. Additional correlations are proposed to estimate the critical Reynolds number at the beginning and ending of the transition region, which allows to select the most adequate friction factor correlation as a function of the operational Reynolds number for a heat exchanger design application. Finally, a comparative between the proposed and the published correlations in the open literature for laminar and turbulent regimes is presented. This brings to light the need and interest of having the suitable and reliable set of correlations presented in this paper to compute the friction coefficient covering all the wire-coil applicability range as an enhancement technique.