Nonclassical effects in two-dimensional transonic flows

The scientific interest and motivation for the investigation of Bethe-Zel'dovich-Thompson (BZT) fluids follows from the fact that all the nonclassical phenomena for these fluids occur for single phase standard fluids in equilibrium when the perfect gas law is replaced by a more realistic equation of state. Among others there are two most immediate and interesting engineering applications for these fluids, as working fluids in Rankine cycles of power systems and for proper design of fuel injectors in typical automotive or aircraft engines. Here we study transonic flows of BZT fluids and present exact solutions to the steady, two-dimensional transonic small disturbance equation in the physical and in the hodograph plane. The equations of the characteristics in the hodograph plane are obtained for the transonic small-disturbance equation of the second-, third-, and fourth-order nonlinearity. The solutions for inviscid, shock-free, transonic vortex flow, Ringleb flow, subsonic and sonic jets, and viscous radial flow are presented for BZT fluids.