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Although curved pipes are used in a wide range of applications, flow in curved pipes is relatively less well known than that in straight ducts. This paper presents a computational fluid dynamics study of isothermal laminar single-phase flow of water in a hollow helical pipe at various Reynolds numbers. The ranging of Reynolds numbers of fluid was from 703.2 to 1687.7. The three dimensional governing equations for mass and momentum have been solved. It was found that with increasing Reynolds number and creation of centrifugal forces, a high velocity and pressure region occurs between two tubes, at the outer side of the hollow helical pipe walls. Friction factor decreases as the tendency for turbulence increases.

Although curved pipes are used in a wide range of applications, flow in curved pipes is relatively less well known than that in straight ducts. In recent years, Helical coiled tubes have been more attention because of their practical applications such as compactness, easy manufacture and high efficiency in heat and mass transfer. They are extensively used in compact heat-exchangers, heat-exchanger network, heating or cooling coils in the piping systems, intake in air-crafts, fluid amplifiers, coil steam generators, refrigerators, nuclear reactors, thermo siphons, and other heat transfer equipment involving phase change, chemical plants as well as in the food and drug industries [

In particular, helical coils are also used as steam generators in some “generation IV” nuclear reactors like IRIS [

During the designing and operating processes of helical coiled tubing steam generators, the prediction of pressure drop of single-phase flow and two-phase mixtures is an essential step for the adjustment of pump pressure head and even calculation of heat transfer conditions. Despite considerable progress that has been made in the past several decades this, and many different correlations (such as that of Berger and Talbot [

Naphon and Wongwises [

M. Moawed [_{o} (Pitch of coil tube/Outer diameter of coil tube), the higher values of Nusselt number can be obtained with a high value of D/d_{o} (Coil diameter/Outer diameter of coil tube) while the small value of Nusselt number can be obtained with a small value of D/d_{o}.

Austen and Soliman [

Choi et al. numerically studied the steady laminar flows in coiled hollow ducts and observed the evolution of secondary flow and the effect of radius ratio on the flow development. It was concluded that the flow in a curved hollow duct was not necessarily fully developed earlier when the radius ratio was larger owing to the complicated interaction between the viscous and centrifugal forces [

The schematic of hollow helical pipe

At the inlet according to different Reynolds numbers for laminar flow, corresponding normal speeds were used. No turbulence option was chosen for analysis (laminar flow). At outlet, pressure boundary condition was applied. No slip boundary condition was used at walls.

Convergence criterion of 1.0E−5 for RMS of all of the equations was used. Hybrid scheme was used for discretization of all equations and SIMPLEC algorithm was used for pressure-velocity coupling. The effect of gravitational force is applied in this analysis. In this analysis, a superficial velocity of 0.101, 0.113, 0.162 and 0.243 ms^{−1} for Reynolds numbers of 703.2, 787.6, 1125.3 and 1687.7 at the inlet are specified, respectively.

The friction factor for single phase flow is determined using:

The contour plots of velocity at different positions

The contour plots of pressure gradient at different positions

Friction factor of laminar single liquid phase flow of water in hollow helical pipe versus various Reynolds number

. Values of friction factor versus Reynolds number with computed average and mean average errors.

Reynolds No. | f (CFD Method) | f (Experimental) | AE^{a} |
---|---|---|---|

703.2 | 0.153 | 0.16 | 0.04375 |

787.6 | 0.161 | 0.17 | 0.05294 |

1125.3 | 0.089 | 0.1 | 0.11 |

1687.7 | 0.065 | 0.079 | 0.1772 |

MAE^{b} | 0.09597 |

^{a}; ^{b}; NP, number of data points.

It seems that the friction factor results can be predicted with reasonable accuracy in the complete laminar flow regions. The critical Reynolds numbers predicted by Srinivasan’s equation (Srinivasan et al. 1970) is 1139 for this test section.

The calculated and experimental values of friction factor with computed average and mean average errors can be observed in

Therefore, we would like to present and suggest a new technique namely CFD method, for simulation and prediction of various processes in industrial applications. In this approach, we are able to design the best geometry of equipments in different industries with the highest accuracy and maximum of efficiency.

Laminar single-phase of water flow through a hollow helical pipe is simulated using computational fluid dynamics (CFD) model. It was found that centrifugal forces created a high velocity region at the outer side of the hollow helical pipe walls. The acceleration forces acting on the fluid flow in the pipe create high pressure region at outer side of the pipe wall. Friction factor decreases with tend to increasing turbulency, although the results of MAE of correlations—CFD model showed a very close values compared with experimental data.