Comparative analysis of 2D simulations and isentropic equations for compressible flow in experimental nozzles

Abstract

Experimental studies for supersonic airflow in different supersonic nozzle geometries are recurrent, and the turbulence of the flow can be reproduced with the CFD tool by applying the RANS model and suitable turbulence models. The objective of this investigation is to carry out a comparative analysis of 2D numerical simulation curves for viscous flow with averaged data against equation curves for quasi-one-dimensional isentropic flow, for three experimental supersonic nozzle geometries that are used in the laboratory, for the flow condition without the presence of shock waves in the divergent. For the numerical simulations, three computational domains were discretized with structured grids, the Spalart-Allmaras turbulence model was used, and the Sutherland's law equation was used for the viscosity as a function of temperature. The results of the curve trajectories for Mach number, pressure and temperature obtained with averaged data from the 2D simulations are close to the curves of the analytical and empirical equations for isentropic flow. It is concluded that the numerical error of the total temperature for the planar nozzle with 𝛼𝛼 = 11.01° and NPR = 8.945 reports 0.008%; for the conical nozzle with 𝛼𝛼 = 15° and NPR = 14.925 it reports 1%; and, finally, for the conical nozzle with 𝛼𝛼 = 4.783° and NPR = 7, it reports 0.04%.