Pressure variations in rocket nozzles. Part 2: Analytical predictions during blowdown

We consider the one-dimensional equations that delineate the operating modes of a converging-diverging nozzle over a range of chamber pressures. The main purpose of this study is to characterize the flow regimes experienced in the nozzle during the blowdown process at mission's end. Blowdown transients can lead to sideloads in the nozzle due to flow asymmetries including normal and oblique shock transitions, shock movement and excursions, flow separation, and the formation of recirculatory zones. By characterizing the nozzle flowfield with one-dimensional equations, we can achieve a direct analytical representation of the key pressure ratios that dictate the ensuing flow regime: supersonic with external shocks, supersonic with optimal expansion, supersonic with internal shocks, or subsonic throughout. These dividing pressure ratios are obtained using asymptotic methods that enable us to estimate the duration of the sideload flow regime by comparing the blowdown pressure profile to the delimiting pressure values projected by their corresponding asymptotic solutions. In fact, Part 1 of this investigation details the analytical methodology leading to closed-form representations of the pressure to an arbitrary level of precision (see Maicke, B. A., and Majdalani, J., "Pressure Variations in Rocket Nozzles. Part 1: Direct Asymptotic Predictions," AIAA Paper 2010-7072, July 2010). In this study, these solutions are inverted to the extent of predicting the nozzle flow conditions associated with an evolving chamber pressure, rather than a varying back pressure. The flow attributes of the various regimes and their corresponding shock transitions are subsequently explained in view of the pressure descent that accompanies chamber blowdown. We retire with a discussion of experimental observations involving slag accumulation and its effects on spin generation during tail off in the upper stage of a sounding rocket.