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.

Truncated nozzles are used for tight packing of the rocket engine. Such nozzles have a profiled tip to maximize the filling of space and reduce the overall weight. This paper is concerned with the study the effect of the tip geometry of a truncated supersonic nozzle on its characteristics. The features of the gas flow at different initial pressures and different environmental conditions in the supersonic area of a nozzle with a bell-shaped tip of different lengths are considered. The flow inside the nozzle followed by the jet outflow into the surrounding space was simulated. The flow simulation for tips at sea level showed a similar structure of the Mach number isolines, and the only difference was in the intensity of the vortex structure near the tip wall. As the pressure at the nozzle inlet increases, the length of the first “barrel” increases proportionally, and the vortex structure near the tip walls decreases. For the upper atmosphere, the flow pattern is different. The supersonic flow in the nozzle does not undergo separation, and therefore there are no vortex structures from the external environment. The flow downstream of the tip exit deflects from the axis through the angle determined by the Prandtl–Meier flow at the corner point of the tip exit, and the shape of the first “barrel” is distorted by a hanging shock. An analysis of the obtained results shows that the ambient pressure downstream the nozzle exit significantly affects the flow pattern in the nozzle. It is established that the thrust coefficient of both circuits at sea level decreases with increasing pressure at the nozzle inlet, which is explained by a decrease in the effect of the ambient pressure on the tip wall. In the upper atmosphere, the flow is adjacent to the tip wall, and the thrust coefficient for nozzles of different lengths has almost the same constant value at different inlet pressures. It is shown that a decrease in the length of the nozzle, all other geometrical dimensions of the nozzle being equal, does not significantly affect the impulse characteristics.

This work is concerned with studying the static and dynamic characteristics of the gas-dynamic (interceptor) subsystem of a combined system for thrust vector control and identifying ways to increase its efficiency. The combined control system includes a mechanical and a gas-dynamic subsystem. The gas-dynamic thrust vector control subsystem is the most important and reliable part of the combined control system. Consideration is given to disturbing the supersonic flow by installing a solid obstacle (interceptor) in the middle part of the rocket engine nozzle. An important advantage of this method to gas-dynamically control the rocket engine thrust vector is that the thrust vector control loss of the specific impulse is nearly absent because the control force is produced without any consumption of the working medium. Injection through the interceptor protects it against exposure to the nozzle supersonic flow and produces an additional lateral force. By now, the optimum height of the mass supply opening in the interceptor that maximizes the control force has not been determined, and the dynamic characteristics of this system have not been studied. The aim of this work is to find the optimum position of the opening for working medium supply through the interceptor that maximizes the added control force and to determine the effect of the transfer functions of the interceptor system components on the characteristics of the control force production transient. As a result of the study of the static characteristics of the supersonic flow disturbance in a nozzle with an interceptor through which a secondary working medium is injected, it is concluded that in terms of thrust vector control efficiency and interceptor protection the injection opening should be situated in the upper part of the interceptor. The transfer function of interceptor control of the liquid-propellant rocket engine thrust vector is obtained with account for the production of an additional control force by the injection of a liquid propellant component. It is found that the loss of stability of the operation of an injection interceptor unit depends on the transient of the working medium injection control valve.

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In recent years, more and more attention has been paid to nozzles with an unconventional profile, which differs from that of the classical streamline-profiled Laval nozzle. In such nozzles, the flow fields typically include interacting supersonic and subsonic flows, often with recirculation regions and a complex wave structure of the flow. This work is concerned with a numerical study of the wave structure of the gas flow in a truncated supersonic nozzle with an elliptical bell-shaped tip whose length is long in comparison with the conical section upstream of the tip. The gas flow inside the nozzle and in the surrounding space was simulated using the ANSYS software package. The calculations were carried out in a non-stationary axisymmetric formulation based on the Reynolds-averaged Navier–Stokes equations closed with the use of the SST turbulence model with near-wall functions and a compressibility correction. In the calculations, the nozzle inlet pressure and the ambient pressure were varied. The correctness of the methodological approaches to the solution of the problem was confirmed in the authors’ previous works. The study showed the following. At low values of the nozzle inlet pressure (P0 < 50 bar) and an ambient pressure of 1 bar, the tip wall exhibits a developed separation zone with a large-scale vortex and a small-scale one (near the tip exit). The first "barrel" of the outflowing gas shows a "saddle" low-intensity compression wave structure. In the case of a separated flow, the tip wall pressure in the separation zone is about 15% less than the ambient pressure. At P0 > 100 bar, the tip wall pressure is nearly proportional to the nozzle inlet pressure. In the upper atmosphere, when going in a radial direction from the nozzle axis at the tip exit cross-section, the static pressure monotonically decreases, reaches a minimum, and then increases linearly to the its maximum value on the tip wall. In the case of a separated flow in the tip at a sea-level ambient pressure, the static pressure at the tip exit cross-section behaves in the same manner for inlet pressures P0 > 50 bar. At P0 = 50 bar, there exist two extrema: the pressure first deceases to its minimum value, then increases to its maximum value, and then decreases slightly to its value on the tip wall.