Computation of Shock Induced Noise in Imperfectly Expanded Supersonic Jets

Abstract

Screech noise exists in imperfectly expanded jets. When the exit pressure of imperfectly expanded jet does not match its backpressure, expansion or compression waves appear out of the nozzle and generate shock cell patterns. Screech is generated by the interaction of shock cells and instability waves. Although many studies have been conducted to model screech noise, it still is not yet a well-understood phenomenon. In the present computational study, the results help better understand screech generation mechanisms and they are compared with the latest available experiments. First, axisymmetric models are constructed for underexpanded jets of 25.4 mm diameter and Mach numbers of 1.19 and 1.43. Then, three dimensional (3D) models are computed for jets with Mach numbers of 1.43 and 1.80. The mathematical model consists of full Navier-Stokes equations in cylindrical coordinates, and large-eddy-simulation turbulence modeling. For spatial discretizations, a fifth-order, weighted essentially non-oscillatory scheme is used, as it is deemed the most suitable method for capturing shocks. Time discretization is a third-order total-variation-diminishing scheme. This methodology does not require artificial viscosity or “tuning up” of parameters. The experimental results predict that the solution is in axisymmetric mode for Mach 1.19 and in helical mode for 1.43. The experimental screech frequencies of 8.4 kHz for Mach 1.19 and 5.4 kHz for Mach 1.43 are verified with the present axisymmetric results. Computed shock cell structure is in agreement with experiments and other published computations in all cases. As in the experiments, the present screech waves emerge from the second and third shock cells. The screech wavelength is roughly estimated as 1.5 D, which is close to other published computational studies. Axisymmetric results for Mach number 1.43 could predict general flow quantities, like shock cell pattern and screech frequency prediction. Therefore, three-dimensional helical effects are investigated by creating a simulation of planes with varying azimuthal angles. This has been useful to detect shock generation locations. In Mach 1.80 case, a barrel shock structure is observed just as in the experimental studies. In conclusion, this study is deemed as a good verification of experimental results.