Numerical Simulation of Fully Developed Laminar Flow and Heat Transfer in Isothermal Helically Twisted Tubes with Elliptical Cross-Sections

Periodically fully-developed swirling laminar flows in twisted tubes with elliptical cross sections are numerically simulated. The tubes are helically twisted along the axis perpendicular to their cross-section. The helical twist geometry is described by the 180 degree twist ratio and the elliptical cross-section is described by the ellipse aspect ratio. The geometries considered for this study have twist ratios with values {3,4.5,6} and ellipse aspect ratios with values {0.3, 0.5, 0.7}. Constant-property flow with a nominal Prandtl number of 3 (e.g. water at 60 degree Celsius) and Reynolds numbers in the range 10 ≤ Re ≤ 1000 was considered.

The analysis quantifies the improvement in the Nusselt number as well as the increase in friction factor in order to map the effective heat transfer enhancement due to the twisted-tube-geometry-induced swirl flows. To this effect, the numerical results are compared, for a given aspect ratio, with the case of a straight elliptical tube (i.e. twist ratio tends to infinity) for which well established correlations are available.

The results were also compared with those of circular tubes with twisted tape inserts for any given twist ratio. Numerical results show that the friction factor and the Nusselt number are strong functions of the twist ratio, aspect ratio and the Reynolds number. The increase in the friction factor and Nusselt number is higher for more tightly twisted tubes and for tubes with a lower ellipse aspect ratio. For Reynolds numbers below 100, the heat transfer results do not deviate significantly from the straight-tube values, but at higher values of Re, significant enhancement in heat transfer is evident for all twist ratios considered here. For example, for tubes with aspect ratio α = 0.3 and a twist ratio y = 3, the enhancement of the Nusselt number relative to the straight tube Nusselt number Nu/Nu_y=∞ = 2.7. For the same aspect ratio, but with a twist ratio y=6, the enhancement Nu/Nu_y=∞ = 2. On the other hand, for nearly round cross sections (e.g. α = 0.7) and nearly straight tubes (e.g. y=6) the enhancement Nu/Nu_y=∞ ~ 1; i.e. there is no enhancement.

The friction factor and Nusselt number results provided in this paper will give practicing engineers the necessary data to integrate twisted elliptical tubes in various heat transfer applications.