Junctions between pipes can involve the mixing or splitting of fluids. In single phase flow, the flows about the junction are very complex with recirculation possible in the outlet pipe(s), features first observed by Leonardo da Vinci, Figure 1.
Figure 1. Recirculation during single phase flow split at a T-junction as observed and recorded by Leonardo da Vinci.
In dividing junctions, the actual division of the flow will depend on the pressure drops in the two downstream legs. Apart from the usual losses in the pipes and other downstream equipment, there are specific losses at the junction itself. These are best illustrated in Figure 2. As the velocity in pipe 2 is lower than that in pipe 1, the pressure rises. The junction pressure drops are defined from the extrapolation of pressure profiles from the undisturbed regions far from the junction back to the junction. Gardel (1957, 1971) has produced equations describing these pressure losses and the effect of parameters such as flow split, diameter ratio, angle between the pipes and degree of rounding of the corner. Obviously, the junction pressure drops are most important when the pressure drops in the downstream lines are small.
For flow combining, there are equivalent pressure drops for which Gardel has proposed equations. In addition, there is considerable interest in the distance along the outlet pipe required to achieve mixing of the two streams.
When the split at a junctions involves more than one phase, the process has the added complication that the ratio of the phases in the outlet pipes is almost inevitably different to that at inlet. This process is controlled by the momentum fluxes of the phases. For example, for gas/liquid annular flow, the portion of the liquid traveling as a film on the wall has a much lower velocity and hence momentum flux than that traveling as drops. Consequently, it is not surprising that the liquid film and the gas nearest the junction are taken off through the side arm while the drops carry on along the main pipe. A thorough review of the behavior of gas/liquid split at junctions is given by Azzopardi and Hervieu (1994) who discuss other mechanisms together with available data and models for the prediction of the phase split. For other combinations of phases, date on the maldistribution is given by Nasr-El-Din and Shook (1986) (solid/liquid) and Lempp (1966) (gas/solids).
As in single phase flow, combination of two-phase flows at junctions involves extra pressure changes at the junction itself. There is much less information about other aspects such as mixing length etc., Azzopardi (1986).
Azzopardi, B. J. (1986) Two-Phase Flow in Junctions, Encyclopedia of Fluid Mechanics, Vol. 3, Ch. 6 Gulf, Houston.
Azzopardi, B. J. and Hervieu, E. (1994) Phase Separation at T-Junctions, Multiphase Science and Technology, Vol 8, Ch. X, pp. 645-714, Begell House, Inc., New York.
Da Vinci, L., I manuscritti e disegni di Leonardo da Vinci, (Reale Commissione Vinciana) Vol. IV, folio 32 verso, Rome (1934) = the edition of the Codiee Forster, III in the Victoria and Albert Museum.
Gardel, A. (1957) Les Pertes de Charge dans les Ecoulements au Travers de Branchments en Te, Bulletin Technique de la Suisse Romande, 9, 122–130 and 10, 143–148.
Gardel, A. and Rechstiener, G. F. (1971) Les Pertes de Charge dans les Branchments en Te des Conduites Circulaires, Bulletin Technique de la Suisse Romande, 25, 363–391.
Lempp. M. (1966), Die strömungsverhältnisse von Gas-Feststoff-Gemischen in Verzweigungen pneumatischer Förderanlagen, Aufbereitungs-Technik, 7, 81–91.
Nasr-El-Din, H. and Shook, C. A. (1986) Particle segregation in slurry flow through vertical tees, Int. J. Multiphase Flow, 12, 427–443. DOI: 10.1016/0301-9322(86)90016-9