A numerical study is carried out to predict the velocity and temperature distributions in fully developed, constant property, laminar flows in tubes containing twisted-tape inserts. The tape inserts are characterized by the twist ratio y(ratio of 180° twist pitch of the tape H to the tube inner diameter d), and the ratio of tape thickness δ to the tube diameter, δ / d. The swirl flow is simulated by following the helically twisted flow path in the partitioned tube represented by a semi-circular cross-section geometry. In this model, the tape thickness is neglected (δ = 0), which is a reasonable first-order approximation as δ / d˜ ~ Ο[10-2] for most inserts used in practice.
For the numerical solution of the velocity problem, the stream function and vorticity formulation is employed. The corresponding non-linear governing differential equations for the stream function, vorticity, axial velocity and temperature distributions are discretized using the finite control-volume method. This procedure essentially retains the conservative forms of the governing equations, and provides second-order discretization accuracy for the numerical solution. For the heat transfer problem both the uniform wall temperature (UWT) and uniform heat flux (UHF) boundary conditions at the tube wall are considered. In addition, two variations of the tape surface condition are considered, namely, uniform temperature and zero heat flux. These two cases model the tape as having infinite and zero fin efficiency, respectively.
Results for the variations in the velocity and temperature fields with flow Reynolds number Re and tape twist ratio y are presented; the temperature distributions also reflects the influence of fluid Prandtl number Pr. The twisted-tape induced swirl flow field is characterized by a single longitudinal vortex that breaks up into two counter-rotating helical vortices with increasing Re or decreasing y. Correspondingly, both the friction factor f and Nusselt number Nuincrease substantially; in the case of heat transfer, Nusselt number also increases with Pr. The results for f and Nu are found to agree very well with the respective Manglik and Bergles (1993) correlations. This verifies the scaling of swirl flow effects by the parameter Sw as proposed by them.