Flow in a truncated supersonic Laval nozzle with a bell-shaped tip (“bell”) is investigated. This nozzle configuration can be used in tight layouts of multistage rockets of short length with improved energy-mass characteristics. Similar types of nozzles were developed at the Institute of Technical Mechanics of the National Academy of Sciences and the State Space Agency of Ukraine in the 1990s. Using approximate methods, the parameters of variously configured truncated nozzles were calculated, and their models were made. Some of the models were blown with cold air, and their characteristics were measured. Shadow patterns of gas flow downstream of the nozzle and soot-oil patterns of streamlines on the nozzle wall were obtained. These results were used in the formulation of this work. In this work, a numerical study with the ANSYS package was carried out for gas flow in a truncated Laval nozzle with a spherical tip. For this nozzle configuration, its model was blown with cold air. The calculated results were verified by comparing the velocity distribution in the gas flow downstream of the nozzle exit with the experimental shadow patterns. An additional confirmation of the correctness of the calculated results was a comparison of the flow downstream of a streamline-profiled Laval nozzle with the underexpanded flow pattern downstream of the nozzle exit in the first “cask” (up to the Mach disk) studied in detail. The same initial data and initial conditions that give the best results in terms of verifiability were chosen in both cases. The study of flow in a truncated supersonic nozzle showed the following results. Downstream of the corner exit point of the truncated section of a Laval nozzle, flow separation is observed where the gas flow enters the “bell”. The separation is retained as the pressure upstream of the nozzle increases up to a certain critical (for a given tip type) value of the underexpansion ratio, after which (with a further increase in the underexpansion ratio) the flow attaches to the nozzle wall and remains attached with a further increase in the pressure upstream of the nozzle. The impulse response of a truncated nozzle with a bell-shaped tip is lower than that of a streamline-profiled Laval nozzle of the same geometric expansion ratio.

This paper presents the results of a thrust performance study of an unconventionally shaped supersonic nozzle in the form of a truncated Laval nozzle with a bell-shaped tip. This nozzle shape may be used in the development of compact layouts of multistage rockets. The study was carried out using the ANSYS software package in a 3D formulation. The methodological approaches to the numerical calculation of a complex separated gas flow used in this study were verified in a previous study of the flow pattern in similar nozzle. Some results of exact calculations were compared with the results of experimental studies carried out at the Institute of Technical mechanics of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine for a model of a similar truncated nozzle with a bell-shaped tip blown with a cold air. This study detailed the features of the separated gas flow in a spherical tip connected (at the corner point) to a truncated supersonic Laval nozzle of conical shape. It was found that the pattern of the separated flow in the tip depends on the nozzle flow expansion degree (nozzle inlet pressure). At a relatively low nozzle inlet pressure, a developed separation zone is observed in the nozzle tip (between the jet boundary and the nozzle wall) with a subsonic flow from the external environment, which forms an almost constant static pressure from the tip inlet cross-section to the tip exit. At a nozzle inlet pressure at which the free boundary of the jet flowing from the truncated nozzle adjoins the nozzle wall, the static pressure in the tip varies almost linearly along the tip length from the corner point with the minimum pressure to the tip exit. The dependence of the thrust of a tipped nozzle on the nozzle inlet pressure is nonlinear. As the pressure upstream of the nozzle increases (or the ambient pressure decreases), the effect of the external environment on the tipped-nozzle thrust diminishes. It is shown that under "terrestrial conditions" the thrust of a truncated nozzle with a tip exceeds the thrust of a profiled nozzle with the same geometric expansion degree (due to the atmosphere “entering” the tip). Under "vacuum” conditions, the former is 8% less than the latter.