Semi-analytical solution of transient imperfectly expanded turbulent supersonic jet

Although the steady state flow has been taken into the account widely, studying the transient flow is not a common investigation through the published analytical researches. In the present work, deriving an analytical solution, the transient behavior of imperfectly expanded supersonic jet flow has been studied in detail. In this regard applying Laplace transform method, the Favre-averaged Navier-Stokes equations for turbulent compressible flow have been solved. Then the results are validated with the available experimental data in the literature. Furthermore, the effects of eddy viscosity on steady state flow is discussed. It is found that velocity increases by decreasing the eddy viscosity. Moreover, tip penetration, radial velocity and velocity profile are studied and plotted. As expected results show that pressure ratio has direct relationship with tip penetration length. So, in can be concluded that the present analytical solution can have profound impact on developing future studies.