Analytical investigation into simultaneous effect of friction and heating on a supersonic nucleating Lavalnozzle

In supersonic water vapor ow of low pressure turbines, nucleation phenomena and consequent condensation are commonly observed. Internal heat transfer, which is caused by phase change, is strongly irreversible and has unwanted eects on turbine eciency. Also, the strike of formed droplets on the surfaces results in large amounts of mechanical damage. Condensation heat release to supersonic ow, named condensation shock, leads to considerable pressure rise, which, in turn, reduces outlet velocity and occasionally causes severe oscillations, making the ow supercritical. The authors have presented a novel analytical approach for the reduction of these unwanted results in Laval nozzles by volumetric heating of the convergent section. In this paper, and in continuation of the series of papers by the same authors, one dimensional, supersonic and two-phase ow is modeled analytically, and the simultaneous eects of volumetric heat transfer and friction in the convergent nozzle are investigated. It is concluded that the simultaneous use of friction and volumetric heating can be an appropriate and useful technique for the control of two-phase ow conditions, keeping them within the desired range.