Design of converging-diverging nozzles with constant-radius centerbody

Abstract

Several flow phenomena, such as recirculating wake flows or noise generation, occur in aerodynamic configurations with backward facing steps. In this context, subsonic nozzles with constant-radius centerbodies exist, which enable fundamental research of these phenomena for M < 1. For the supersonic regime, however, the existing database and knowledge are limited. Therefore, this work presents a design approach for a converging-diverging nozzle with constant-radius centerbody. For the nozzle throat, Sauer's method is modified to include a centerbody. The method of characteristics is used for the subsequent supersonic portion. Comparing the analytical calculations to numerical simulations results in very good agreement and therefore underlines the feasibility of the chosen approach. Viscosity reduced the Mach number on the exit plane by 1.0-1.2% and therefore had little influence. Keywords Wind tunnels • Method of characteristics • Supersonic List of symbols a Speed of sound, m/s A Area, m 2 cbr Centerbody ratio D Diameter, m dm/dt Mass flow rate, kg/s L Length, m M Mach number p Pressure, Pa r Radius, m Re Reynolds number T Temperature, K u, v, w Velocity in x, y, z direction, m/s x, y, z Spatial coordinates, m Greek symbols Angle, deg Difference Rotational displacement, deg Superscripts * Critical condition Subscripts 0 Reservoir condition cb Centerbody iv Initial value sub Subsonic sup Supersonic th Throat * Andreas K. Flock

Analysis of the convergent section of a C-D nozzle and its influence on airflow performance using evolutionary strategies

“…Recently, there is another paper written by Flock et al 14 that corroborates the design of a convergent-divergent nozzle using Sauer’s research. It is necessary to solve the following set of formulas to define the design parameters according to the concept of sonic line propagation proposed by Sauer.…”

Real-Time Motion Planning for Quadcopter Using Adaptive Spherical Expansion and Sequential Convex Optimization

“…These characteristics result in reflective Mach waves or expansion fan waves generated in the expansion section of the nozzle (region 3 of Figure 1) as the flow is being locally turned in a direction parallel to the nozzle walls, and propagate further downstream along the supersonic section nozzle in the straightening section of the nozzle (region 4 in Figure 1). MoC based design methods were previously applied to two-dimensional [3] or axisymmetric [4] nozzle configurations, with and without the presence of center bodies [5].…”