DOI: https://doi.org/10.36347/sjet.2026.v14i07.003

Pages: 386-402

Recently derived analytical area-Mach relation of quasi-one-dimensional isentropic flow for fully expanded supersonic flow inside a convergent-divergent conical nozzle is used to investigate shock formation and characteristics of numerically computed flow fields of the conical and the contour nozzles having identical area ratios and length. The flow fields inside the nozzles are numerically obtained by solving quasi-one-dimensional Euler equations and as well as axisymmetric turbulent compressible Navier-Stokes equations using finite volume method and explicitly integrated using multistage Runge-Kutta time marching method. Computed flow fields are analysed with the help of velocity vector and Mach contour to determine the influence of the geometry of the nozzle on flow behaviour. The variations of pressure and Mach number along the centre line and wall of the contour and conical nozzle are plotted to distinguish the flow characteristics. Formation of a hump in the centre line of pressure and Mach distributions due to shock formation of inside the conical nozzle is analysed using newly derived area-Mach relation. It can be extended to investigate the sonic boom of supersonic aircraft. The difference between CFD and quasi-one-dimensional isentropic results of centre line exit Mach number for conical and contour nozzle is found about -7.86% and 9%, respectively. Nomogram can be converted as a slide-rule for compressible gas dynamics.