An analytical investigation of transient imperfectly expanded turbulent jet

Abstract

Supersonic turbulent high-pressure jet flows, which are discharging in low-pressure quiescent ambient, are recognized as imperfectly expanded turbulent jet. Steady-state imperfectly expanded jet flow has been already studied analytically; however, the transient flow has not been thoroughly studied. In the present study, the transient imperfectly expanded jet flow with focus on fuel spray in combustion is investigated analytically employing two-step separation of variables method and Fourier-Bessel expansion. The results are validated using available experimental data. The effects of different parameters such as eddy viscosity and pressure ratio on the behavior of the jet are studied. Results show that increasing the eddy viscosity decreases the velocity magnitude and required time to reach fully developed jet. Increasing the pressure ratio almost linearly increases the required time to reach steady state. The density distribution which affects the combustion performance is reported for different axial and radial positions. In the transient region, tip penetration is obtained and validated with the experimental results in the literature, and the velocity profile at different times is presented. The simplicity and accuracy are key advantages of the developed method compared with the experimental and numerical methods. The analytical method proposed in the present research helps to understand the behavior of jet flows from transient to steady state condition without using expensive and time-consuming numerical or experimental techniques.