Numerical simulations of the laminar flow in pipes with wire coil inserts

Helical wire coils fitted inside a round pipe is a simple and well-known heat transfer enhancement technique in order to improve the overall performance of heat exchangers. Three-dimensional numerical simulations of the incompressible laminar flow that develops into smooth round pipes of diameter, d, with wire coil inserts of helical pitch, p, and diameter, e, have been accomplished with the finite volume method. In particular, we describe the behaviour of the Fanning friction factor, f, as a function of the Reynolds number, Re = ρUd/μ, where, U = 4Q/πd2, is the mean velocity based in the flow rate, Q, and ρ and μ the density and dynamic viscosity of the fluid, respectively. For a wire coil of 40 pitches in length with dimensionless pitch p/d = 2.5 and dimensionless wire diameter e/d = 0.074, both pitch-periodic and full domain numerical results have been validated with experiments. We have found an excellent agreement with both numerical models and experimental results for Re < 500, showing the friction factor a quasi-linear dependence on Re when is plotted in log–log axes. For 500 < Re < 600 both experimental and full domain numerical results of the values for the friction factor leave the quasi-linear trend observed for Re < 500. Our full domain numerical calculations reveal the onset of a linear instability into the range 500 < Re < 550 that becomes the flow unsteady and breaks the periodic axial pattern of the flow. The friction factor becomes constant in the range, 600 < Re < 850, and only the full numerical model shows a good agreement with the experimental results, but periodic numerical simulations fail. For 850 < Re, even the full domain laminar model fails due to the onset of turbulent outbreaks. Finally, the effect of the pitch on the friction factor has been addressed by performing a parametrical study with a pitch-periodic computational domain for wire coils within the dimensionless pitch range, 1.50 ⩽ p/d ⩽ 4.50, and dimensionless wire diameter, e/d = 0.074, showing that the increase of the nondimensional pitch, p/d, decreases the friction factor.