Example II: Numerical Simulation of Axisymmetric Jet Screech

Experimentally, it is found that an imperfectly expanded supersonic jet invariably emits strong tones called screech tones. Jet screech is a fairly complex phenomenon involving several modes of oscillations. When a convergent nozzle is used, it is observed experimentally that the screech modes are axisymmetric at low supersonic Mach numbers. There are two axisymmetric modes. They are usually designated as the A1 and A2 modes (see Figure 15.51). At Mach number 1.3 or higher, the jet screech switches to flapping or helical modes. They are designated as the B and C modes. In Figure 15.51 Xs is the wavelength of the screech tone. Mode switching or staging is quite abrupt. The staging Mach number is found to be very sensitive to ambient experimental environment and also sensitive to upstream conditions of the jet flow. Largely because of this sensitivity, it is known that the staging Mach numbers differ slightly from experiment to experiment. Even in the same facility, they tend to differ somewhat when the experiment is repeated at a later time.

It is known, since the early work of Powell (1953), that screech tones are gen­erated by a feedback loop. Recent works show that the feedback loop is driven by the instability waves of the jet flow. In the plume of an imperfectly expanded jet is a quasiperiodic shock cell structure. Figure 15.52 shows schematically the feedback loop. Near the nozzle lip where the jet mixing layer is thin and most receptive to

Figure 15.52. Schematic diagram of the feedback loop of jet screech.

external excitation, acoustic disturbances impinging on this area excite the instability waves. The excited instability waves, extracting energy from the mean flow, grow rapidly as they propagate downstream. After propagating a distance of four to five shock cells, the instability wave, having acquired a large enough amplitude, interacts with the quasiperiodic shock cells in the jet plume. The unsteady interaction gen­erates acoustic radiation, part of which propagates upstream outside the jet. Upon reaching the nozzle lip region, they excite the mixing layer of the jet. This leads to the generation of new instability waves. In this way, the feedback loop is closed.