Numerical investigation of fully developed laminar flow in irregular annular ducts: Triangular–circular combinations

The aim of this study is to reduce the required pumping energy by obtaining accurately the friction factor – Reynolds number product (fRe) of the steady fully developed laminar flow in annular ducts. The study is focused on the annular region between equilateral triangular and circular ducts under all possible combinations. For this purpose, the governing equations are solved using high order finite element method. For regular annuli, it is found that higher values of area ratio lead to monotonic increase in (fRe) value, with (fRe)max = (24, 42.67,96) at the respective values of (Dh) = (0.5,0.75,1) regardless of the particular geometry. For irregular annuli, higher values of area ratio lead to an increase followed by a decrease in (fRe) value, with (fRe)max = (79.631,35.392,19.921) at the respective values of (Dh) = (0.5, 0.75, 1) for the (CT) case, and correspondingly (fRe)max = (91.02,40.45,22.85) for the (TC) case. On the other hand, it is found that (fRe) value inversely proportional with the hydraulic diameter (Dh). For all cases considered in this study, the largest (fRe) at the representative values (AR) = 30% is found for the (CC) case with (fRe)max = 95.43 whereas the smallest (fRe) is found for the (CT) case with (fRe)min = 17.544. More importantly, irregular annuli outperformed the regular annuli and thus are recommended to replace the classical regular annuli currently used in double duct heat exchangers. This in turn will significantly decrease the pumping energy required in such applications in industry.