Mach Wave Noise of a Supersonic Jet

Supersonic jets emit noise to the outside in form of Mach waves which are long, straight and have about equal angles. Experiments done by Oertel sen. visualized clearly these Mach waves and he publicized moreover that such Mach waves exist also inside the jet. Experimental and theoretical studies in the past did not allow a complete understanding of the phenomenon up to now, wherefore the need for further research is obvious. In this study the observations of Oertel sen. are described and an assumption is given for illuminating theoretically the experimental outcomes. The Mach waves inside and outside are visualized by single frames, by immobilization images and by streak records. Differential interferometry (DI) is used for visualizing density differences by light intensity variations. Measuring the Mach wave angles from many shock tube experiments revealed the existence of three wave families. They move with different speeds, denoted as w, w’ and w’’, which depend only on the jet Mach number Mi and the ratio aa/ai of the sound speed aa outside and ai inside the jet. A theory is proposed which explains the three speeds found. Its central point is the production of Mach waves by pairs of vortices moving inside of the jet mixing layer. Each pair is built by a front and a rear vortex. The front vortices create the w’-Mach waves outside the jet and the rear vortices are accompanied by the w’’-Mach waves inside. The w-Mach waves go together with the notch in-between both and are finally also formed when a front vortex combines with an overtaking preceding rear vortex, both creating only one big vortex which moves with w. The processes mentioned are mainly suggested by the immobilizations and by the streak records taken. For both the flow is observed through a slit on a rotating drum camera. Immobilizations use a wide opened slit and the camera turns with the speed of the Mach waves to be observed. Streak records show clearly with a narrow adjusted slit the Mach wave traces. The explanations given are only valid for the beginning of a supersonic jet up to about ten jet diameters downstream. Nomenclature flow velocity u = general, u* = special, ui = inside the jet propagation velocity w = centre of vortex pair, w’ = front vortex, w” = rear vortex speed of sound a = general, a* = special, ai = jet gas inside, aa = gas outside Mach numbers Mj = jet Mach number, Mi=ui/ai = inside the jet with Mi = Mj w/aa = of the w-Mach wave outside, w’/aa = of the w’-Mach wave outside (ui-w)/ai = of the w-Mach wave inside, (ui-w”)/ai = of the w”-Mach wave inside Mach angles  = w-Mach wave inside and outside, ’ = w’-Mach wave outside, ” = w”-Mach wave inside other parameter e = optical beam separation inside the differential interferometer H. OERTEL SEN., F. SEILER, J. SRULIJES ISFV15 – Minsk / Belarus – 2012