Modeling of turbulent flows through annuli with smooth and rough walls; drag reduction and heat transfer

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A model of a turbulent flow in an annular channel with rough walls is developed. An effect of roughness on hydraulic resistance of the channel is accounted for through the formal dimensionless negative velocity shift at the wall by using an empirical function linking this velocity shift to the dimensionless sandgrain wall roughness. The developed annular flow model is validated by experimental data found in literature for both smooth walls, both rough walls, smooth outer wall and rough inner wall as well as vice versa. The same flow model is applied also to a polymer solution turbulent flow in annular channel with hydraulically smooth walls. A turbulent drag reduction effect, observed in this case, is accounted for by a positive velocity shift at the wall determined for a certain drag reduction chemical from experiments in a round cross-section pipe. Also, an engineering approach for modeling heat transfer through either outer or inner wall of an annular channel with rough walls is suggested. This approach is based on the known analogy of heat transfer in a hydraulically smooth annular channel and a pipe. This analogy is extended to an annular channel with rough walls by using the developed flow model. The heat transfer model developed is validated, discussed and illustrated by calculation examples. Key attention is paid to analyzing an effect of the Reynolds number on both a Nusselt number increase and an efficiency change for different wall roughening cases.