Vapor-generating surfaces in the form of a coiled tube have advantages in compactness, in compensation for thermal expansion and in giving enhanced heat transfer.

Inertial forces perpendicular to the axis of liquid flow act on the liquid in *curvilinear channels*, in particular in a coiled tube. A larger centrifugal force acts on the faster-moving fluid near the tube center than on the slower moving fluid near the wall. As a result, the fluid in the central part of the tube moves towards the outer generatrix, while that near the wall moves towards the inner generatrix. *Secondary flow* arises in the form of a pair of symmetrical vortices in the cross-section (Figure 1); along the tube axis, the fluid trajectory is in the form of a double coil. The maximum axial flow velocity in a coiled tube takes place near the outer generatrix (Figures 2 and 3) the secondary flow velocity V(r/r_{0}) is constant in the core, but changes near the wall.

**Figure 2. Typical variation of axial velocity Ua with radial position (ζ = r/r _{0}, where r_{0} is the radius of the tube and U is the velocity for z = 0).**

In a coiled tube, the distribution of turbulent fluctuations is nonuniform. Near the outer generatrix, turbulence intensity is lowest.

The *friction factor* for a coiled tube with a relative diameter (D_{coil}/D) > 4 (D_{coil} is the coil diameter, D is the tube diameter) is calculated as:

where f_{0} is the *friction factor* in a straight tube with the same diameter, as determined from the Reynolds Number and K_{φ} is the coefficient of a coiled tube. The value of coefficient K_{φ} depends on the flow regime. In laminar flow, K_{φ} = 1.

In curvilinear channels, turbulent flow begins at a higher Reynolds number Re given by

and in turbulent flow, the coiled tube coefficient K_{φ} is given by the equation

In two-phase flow, the *flow pattern in a coiled tube* (*) has peculiarities determined by the inertial force in the cross-section and by the secondary circulation. The centrifugal force promotes phase stratification and liquid transfer to the outer generatrix; secondary circulation in the gas phase leads to phase mixing and liquid shifts to the inner generatrix. These processes depend on mass velocity, pressure, ratio D*_{coil}/D, and vapor content. A more detailed discussion is given by Hewitt and Jayanti (1992).

Pressure losses of a two-phase flow in a coiled tube are determined by the equation

where f_{LO} is the Fanning friction factor (corrected as above for the coiled tube flow) for the total mass flux flowing with liquid properties, L the length of the tube, m the mass flux of the fluid in the tube, D the tube diameter, ρ_{L} and ρ_{G} the liquid and gas densities and x the quality. ψ is a factor which connects the equation for departures from homogeneous flow (x = 1 for homogeneous flow). (See Pressure Drop, Two-Phase Flow.)

#### REFERENCES

Hewitt, G. F. and Jayanti, S. (1992) Prediction of film inversion in two-phase flow in coiled tubes. *J. Fluid Mech.,* vol. 236, pp 497-511.

Schlichting, M. (1973) *Grenschicht-Theorie*. Verlag G. Brawn. Karlsruhe. Heat Exchange Design Hand Book. v.1,2. Hemisphere Publishing Corporation.

#### References

- Hewitt, G. F. and Jayanti, S. (1992) Prediction of film inversion in two-phase flow in coiled tubes.
*J. Fluid Mech.,*vol. 236, pp 497-511. DOI: 10.1017/S0022112092001502 - Schlichting, M. (1973)
*Grenschicht-Theorie*. Verlag G. Brawn. Karlsruhe. Heat Exchange Design Hand Book. v.1,2. Hemisphere Publishing Corporation.