Uskov V., Chernyshov M., Erofeev V., Genkin P.

Generation of intensive discrete noise by supersonic gas jets depends on their shock-wave structure. For example, auto-oscillations evidently occur at small supersonic Mach numbers where solutions for both stationary regular and Mach reflections do not exist. Incidence of shock wave from the nozzle edge into the first barrel of overexpanded jet is studied initially. It is analytically proven that the oblique shock can be curved upstream or downstream of the flow. Shock strength decreases at the significant part of its length. Jet boundary curvature, flow velocity rotor vector, gradients of Mach number, full and static pressures at the compressed layer are also changed depending on the jet incalculability. These features influence on the development of Taylor-Gõrtler boundary instability. Incident shock geometry is supposed to be key parameter defining shock-wave noise frequency. Unlike popular Powell’s scheme, proposed physical model of discrete noise generation is based on treatment with jet barrels like volumes with elastic walls and corresponding natural frequencies. Shock-wave structures are treated like three-dimensional Helmholtz resonators or systems with two or three resonance frequencies, etc. Natural frequencies can be calculated according to classical works of Rayleigh, Helmholtz and others. Comparison of the numerical (modified Godunov-type schemes were used) and experimental data reveals that natural frequencies were successfully (with 4-8% error) estimated analytically. For jet Mach number M=2.5 and incalculabilities n=0.6 and n=0.7 calculated frequencies are 11970 Hz and 11600 Hz. Experimental data: 11950 Hz and 11600 Hz, correspondingly. Enormous difference of some parameters (stagnation pressures, gas velocity) of flows separated by the slipstream emanating from the triple point of Mach reflection is also expected to be source of auto-oscillating effects. This analytical study also defines extremal (dozens and hundred times) differences of flow parameters downstream triple configurations. This work was supported by Russian Foundation for Basic Research (project 04-01-00713).