Characteristics of underexpanded free jet under periodic pressure perturbation

Abstract

Combustion takes place in the engine combustor of high-speed aircraft engines, and exhaust gas escapes through a nozzle providing thrust for propulsion. During the typical operation of such engines, the combustor undergoes different transient combustion processes due to the initial ignition process, changes in fueling scheme, ignition delay, inefficient flame holding and combustion instability. These processes induce changes in combustor pressure and results in transient nozzle pressure ratio (NPR) conditions. In the present study, computational investigation of flow structures of underexpanded supersonic free jet under periodic pressure perturbation condition has been carried out, where the jet exits from nozzle at a pressure higher than the ambient pressure and further expands supersonically outside the nozzle. To mimic the combustor thermal conditions, the flow structure at high temperature flow conditions has been explored including the cold flow condition. Reynolds Averaged Navier-Stokes (RANS) equation with single-equation Spalart-Allmaras (SA) turbulence model has been used for the computation. The numerical scheme has been validated using available numerical and experimental data under identical flow conditions. Static pressure at the nozzle inlet has been modeled with steady as well as time-dependent fluctuating pressure profiles. Sinusoidal oscillation of pressure with varying frequency has been considered to impose fluctuating pressure perturbation to the inlet of nozzle. In both steady and fluctuating cases, it is found that the shock cell structure is significantly affected by variation of pressure. The flow properties like static pressure, static temperature etc. in the compression and expansion zones of shock cells tend to move toward extremes at higher NPR conditions. Lengths of shock cell and supersonic core have been found to increase with the increase of inlet pressure. Higher stagnation temperature makes the supersonic core length significantly smaller and hardly affects the shock cell sizes. For fluctuating inlet pressure, hysteresis behavior in several flow parameters especially the shock cell length and supersonic core length has been noted between increasing and decreasing half cycles of NPR oscillation. The sonic lines at same NPR as well as centerline properties from the two halves of oscillation does not overlap on one another. Hysteresis for both shock cell length and supersonic core length appears to rise at higher frequency for both cold flow and high temperature flows. For a specific frequency, hysteresis is found to reduce at higher temperature. Thus, the maximum hysteresis occurs at high frequency cold flow; 28.6% for first shock cell length and 20.6% for supersonic core length. The generated thrust at different conditions tends to vary linearly with NPR with a very low dependence on stagnation temperature. It does not show a hysteretic behavior (below 1%) in oscillating NPR conditions except at low stagnation temperature and high frequency where it shows maximum 4.7% deviation. Although there is almost no hysteresis in thrust, specific impulse is subjected to hysteresis and shows greater difference between increasing and decreasing NPR processes at low frequency and low temperature flow.