Two-dimensional over-expanded jet flow parameters in supersonic nozzle lip vicinity

• Analytical model to calculate flow field derivatives behind a shock is proposed.
• Parameters of over-expanded jet in vicinity of nozzle tip are studied analytically.
• Incident shocks convex upwards and downwards are theoretically predicted.
• Shock curvature and direction turned to be strongly dependent on jet symmetry type.
• Dependences on Mach number, incalculability, nozzle angle and gas adiabatic parameter is also considerable.

The mathematical model for two-dimensional (plane or axis-symmetric) over-expanded jet flow parameters analysis in the vicinity of supersonic nozzle lip is proposed. The variation of the key parameters of this problem (e.g., the geometrical curvature of oblique shock emanating from the nozzle edge) is studied parametrically depending of jet flow parameters, such as Mach number, jet incalculability, and the ratio of gas specific heats. It was proved that differential parameters of the flow field crucially depend not only of the key parameters, but on the symmetry type as well.