Supersonic Nozzle Research Articles

Modeling and simulation of supersonic nozzle gas jet laden with polydisperse fire suppressant particles injected from a bypass injector

Dry powder fire extinguishing techniques are widely used due to the environmental friendliness and high efficiency. An Eulerian-Lagrangian interphase coupled modeling is performed for 2D axisymmetric nozzle supersonic gas jets laden with polydisperse fire suppressant particles complying with a Rosin-Rammler distribution injected from a bypass injector. A corrected drag model is developed applicable for very large ranges of particle Reynolds and Mach numbers. A parametric study on performance indexes of jet determining the fire extinguishment efficiency indicates that an increase in injected particle velocity vp,inj, mean diameter dp,m or spread parameter ns, or decrease in mass flow rate qm,p usually causes a monotonous increase of particle streamwise average velocity vp,a, decrease of velocity inhomogeneity Φvp and dispersion Ψp. However, the monotonicity of parametric dependency is probably violated under extreme conditions. It is exemplified by the vp,a, Φvp or Ψp at very large vp,inj, or the Ψp at extremely large ns.

Experimental investigation of nozzle submergence depth on steam cavity thermal characteristics in direct contact condensation

Direct contact condensation has found wide applications in an industrial sector because of its enormous mass and heat transfer capabilities. In the current experimental investigation, effect of submergence depth has been analyzed on the thermal characteristics of steam plume issuing into water tank from two geometrically different steam spray nozzles i.e. converging–diverging (CD) nozzle and straight pipe (SP) nozzle. The steam cavity images were taken using high-speed camera which were processed by MATLAB image-processing tool for the measurement of steam-water interfacial area. It was observed that axial temperature distribution rises with the increase in submergence depth while for radial temperature distributions reverse was found to be true. Additionally, the temperatures at nozzle exit were noted to be independent of submergence depth. The heat transfer coefficient decreases as the steam pressure, water temperature and submergence depth is increased for both the nozzles and found in range of 1.661–2.91 MW/m2·K and 1.472–1.989 MW/m2·K for the CD and SP nozzle, respectively. Moreover, the effect of submergence depth was found to be almost negligible at the higher submergence depth values.

Analysis on Propulsive Performance of Hollow Rotating Detonation Engine with Laval Nozzle

In the present study, an experimental performance analysis of hollow rotating detonation engines (RDEs) with Laval nozzles is carried out for the first time. Experiments of a hollow rotating detonation engine with a Laval nozzle were performed with a modular RDE at a backpressure condition of 1 atm. Two configurations with area ratios of the outlet throat to the inlet of and 2.7 have been tested with gaseous methane/oxygen as propellants. Three normalized metrics, usually used for evaluating the performance of conventional rocket engines, are introduced to analyze the performance deficit between the measured value of an RDE and the ideal value of an isobaric-combustion-based engine. These metrics allow for assessing the entire engine and each component separately. The metric analysis suggests a small outlet-to-inlet area ratio () is detrimental to the propulsive performance. To explain the mechanism, a gas-stratification flowfield model is further proposed. It is found that the unchoked region in the combustible gas layer, which is caused by unchoked injection on the injecting plate, is responsible for the performance deficit of the combustion chamber. This model is then validated by one-dimensional numerical simulations and experimental data. In addition, we also focus on the global performance, including the gross thrust, the specific impulse, and the utilization of the supplied stagnation pressure. The result implies a tradeoff space when choosing an appropriate .

Effect of the tip geometry of a truncated supersonic nozzle on its characteristics

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.

Design Process and Flow Field Analysis of a Double Divergent Supersonic Nozzle: Enhancing Efficiency and Performance

The dual bell nozzle concept's primary goal is to increase performance through the idea of selfadaptation for two operating regimes without mechanical activation. The dual bell nozzle type known asthe planar double divergent nozzle (DDN) has a rectangular cross section. In this study we propose anumerical method for the design of the nozzle profile with double planar divergent. The design of the doubledivergent nozzle is carried out in two parts. The first divergent is a contour of a two-dimensional supersonicnozzle with a sharp-edged throat that gives uniform parallel flow at the exit. The method of characteristicapplied to the two-dimensional isentropic flow of an ideal gas was used for the design of a supersonic planarnozzle. The contour of the second divergent (nozzle extension) is a polynomial. This is achieved using thedirect method of characteristics. A numerical analysis of a double divergent nozzle, and a planar nozzlewith the same area ratio and the same length using ANSYS-Fluent software. The analysis's findingsindicated that the double divergent nozzle had a weight decrease of 0.61%. The thrust increase is estimatedat 3.88% in the low-altitude operating mode for the double divergent nozzle.

Additive manufacturing of Inconel-625: from powder production to bulk samples printing

PurposeFor metal additive manufacturing, metallic powders are usually produced by vacuum induction gas atomization (VIGA) through the breakup of liquid metal into tiny droplets by gas jets. VIGA is considered a cost-effective technique to prepare feedstock. In VIGA, the quality and the morphology of the produced particles are mainly controlled by the gas pressure used during powder production, keeping the setup configuration constant.Design/methodology/approachIn VIGA process for metallic additive manufacturing feedstock preparation, the quality and morphology of the powder particles are mainly controlled by the gas pressure used during powder production.FindingsIn this study, Inconel-625 feedstock was produced using a supersonic nozzle in a close-coupled gas atomization apparatus. Powder size distribution (PSD) was studied by varying the gas pressure.Originality/valueThe nonmonotonic but deterministic relationships were observed between gas pressure and PSD. It was found that the maximum 15–45 µm percentage PSD, equivalent to 84%, was achieved at 29 bar Argon gas pressure, which is suitable for the LPBF process. Following on, the produced powder particles were used to print tensile test specimens via LPBF along XY- and ZX-orientations by using laser power = 475 W, laser scanning speed = 800 mm/s, powder layer thickness = 50 µm and hatch distance = 100 µm. The yield and tensile strengths were 9.45% and 13% higher than the ZX direction, while the samples printed in ZX direction resulted in 26.79% more elongation compared to XY-orientation.

Altitude-compensating axisymmetric supersonic nozzle design and flow analysis

Altitude-adapted nozzles are designed to facilitate flow adaptation during rocket ascent in the atmosphere, without requiring mechanical activation. As a consequence, the performance of the nozzle is significantly improved. The aim of this study is to develop a new profile of axisymmetric supersonic nozzles adapted at altitude (Dual Bell Nozzle with Central Body), which is characterized by an E-D nozzle as a basic profile. The performances obtained for this nozzle (E-D Nozzle) are then compared to those of a Plug nozzle. The E-D nozzle shows significant performance advantages over the Plug nozzle, including a 13.02% increase in thrust, knowing that the length of the E-D nozzle is half that of the Plug nozzle under the same design conditions. Finally, viscous calculations using the k-ω SST turbulence model were conducted to compare the performance of the dual bell nozzle with central body (DBNCB) and the E-D nozzle with the same cross-sectional ratio, and to assess the impact of nozzle pressure ratio (NPR) variations on the operation mode of the DBNCB. The results obtained show that the DBNCB offers the best performance in most phases of flight.

Optimization of Aircraft Fuel Dump Rate towards the Mitigation of Post-Impact Fire

This study seeks to improve the utilization of compressed air towards a faster fuel jettisoning, to increase the survival rate of passengers in the event of an accident or aborted takeoffs by augmenting the already existing means of dumping fuel with no considerable increase in overall weight. The aircraft fuel dump sub-system was isolated, this process was achieved with the aid of the venturi effect. The engine compressor marks the start of the aircraft fuel dump sub-system while an exterior nozzle for displacing the fuel marks its end. This system achieved jettisoning through bled-off air from the compressor, passing through a converging-diverging nozzle (primary supersonic nozzle), thereby creating a vacuum in the mixing chamber. A jet which provides a direct connection between the fuel tank and the mixing chamber sucks fuel from the tank, where bypassed air from the compressor expels the sucked air in fine particles. After running the simulation, the mass flow rate was computed. The compressed air inlet has a mass flow rate of 58.5193(Kg/S), the kerosene inlet 1.2385(Kg/S) while the outlet has a relative value of-59.6541(Kg/S).This study seeks to improve the utilization of compressed air towards a faster fuel jettisoning, to increase the survival rate of passengers in the event of an accident or aborted takeoffs by augmenting the already existing means of dumping fuel with no considerable increase in overall weight. The aircraft fuel dump sub-system was isolated, this process was achieved with the aid of the venturi effect. The engine compressor marks the start of the aircraft fuel dump sub-system while an exterior nozzle for displacing the fuel marks its end. This system achieved jettisoning through bled-off air from the compressor, passing through a converging-diverging nozzle (primary supersonic nozzle), thereby creating a vacuum in the mixing chamber. A jet that provides a direct connection between the fuel tank and the mixing chamber sucks fuel from the tank, where bypassed air from the compressor expels the sucked air in fine particles. After running the simulation, the mass flow rate was computed. The compressed air inlet has a mass flow rate of 58.5193(Kg/s), and the kerosene inlet 1.2385(kg/s) while the outlet has a relative value of -59.6541(kg/s).

Study of fluid-dynamic behavior in a convergent–divergent nozzle by shape optimization using evolutionary strategies algorithms

The performance and thrust of a rocket propulsion system are based mainly on the utilization of the enthalpy of the propellants in the combustion chamber. This accumulated energy is transformed into kinetic energy by the expansion and acceleration of the gases produced by the chemical reaction of combustion, using a device known as a nozzle. This project studies the aerodynamic profile to trace the wall contour of a C-D nozzle based on the technical operating conditions of a rocket engine. The wall contour is traced using different design methods and, for each nozzle section, the behavior of the fluid-thermal properties of the flow field along the flow trajectory of the aerospace nozzle is analyzed. This is necessary because, in each wall contour suggested by the models, the angle of inclination of the curvature is different (the concavity or shape of the curve changes) and, therefore, the physical magnitudes of the properties vary according to the contour. To determine which design complies with the concept that processes occurring within a nozzle are isentropic and reversible, a statistical analysis of data dispersion is performed to choose the design with the lowest energy losses as a function of friction and entropy. An unconstrained optimization is applied to maximize or minimize the cross-sectional area of the nozzle geometric profile through genetic algorithms. To corroborate the nozzle wall contour and the design methodology used, a simulation is performed to evaluate the similarities between the operating characteristics and Mach number with another nozzle of a J-2 rocket engine.

Characterization of surface cratering and particle deformation during high speed microparticle impact events

Simple-to-use damage models are important in predicting the outcome of high speed particle impacts for high speed vehicles traveling in particle laden flows. Such models largely hinge upon experimental data from well-characterized single-impact events. In this study we developed and applied an experimental system to systematically examine surface cratering and particle deposition driven by high speed micrometer particle impacts onto Aluminum 6061-T6 substrates and Inconel 718 substrates. Monodisperse ferrous sulfate particles 1.8 and 6.2 micrometer in diameter were accelerated using a converging-diverging nozzle to achieve varying impact velocities in the range of 0.29–0.84 km s-1 as measured by laser Doppler velocimetry. Post-mortem surface characterization was carried out using a combination of atomic force microscopy and scanning electron microscopy. For the aluminum samples, we then utilize traditional non-dimensional groups to develop scaling relationships between crater size, particle size, velocity and incident angle. Measurement results are found to agree with data from previous studies at higher impact velocities, but notably with a sharper slope between dimensionless crater size and dimensionless impact energy, indicative of a non-negligible amount of particle elastic rebound influencing the outcome of the impact process. In addition, in contrast to crater formation observed on aluminum, equivalent impacts onto Inconel 718 led to no discernible crater formation and instead adhesion and deformation of the impacting particles.

Flow structure and parameter evaluation of conical convergent–divergent nozzle supersonic jet flows

Supersonic gas jets in conical convergent–divergent nozzles are studied numerically using the OpenFOAM rhoCentralFoam solver. The spatiotemporal evolution of the jet flow field is analyzed. The influence of the operating conditions on the flow field is studied parametrically, including the nozzle pressure ratio (NPR), area ratio, and throat position. The behaviors and mechanisms of the double-diamond structure, throat wave, and exit wave are interpreted in detail. The results show that a conical convergent–divergent nozzle always generates shock waves. The throat shock reaches its maximum length during the initial stage, then becomes slightly shorter before becoming stationary, dominated by the exit velocity. Furthermore, it is shown that the jet flow changes from overexpansion to underexpansion with increasing NPR. With an increasing area ratio, the trend is the opposite. The throat position affects the jet divergence angle at the nozzle exit, consequently causing a variation in the core radius of the jet. It is further shown that the double-diamond structure does not always appear. The throat shock angle, exit wave angle, and shear layer width directly affect the shape of the double-diamond structure. The favorable pressure gradient of the nozzle ultimately dominates the changes in the length of the throat wave and exit wave.

Proposal of a New Double-Nozzle Technique for In-Gas-Jet Laser Resonance Ionization Spectroscopy

This paper proposes a new double-nozzle technique for in-gas-jet laser resonance ionization spectroscopy. We explored the functionality of this new technique through detailed gas dynamic and Monte Carlo atom-trajectory simulations, in which results are presented and discussed. The results of similar computer simulations for JetRIS setup (as a typical representative of the conventional in-gas-jet technique nowadays) are also presented and discussed. The direct comparison of calculation results for the proposed new technique with the conventional one shows that the double-nozzle technique has many advantages compared with the one used in the JetRIS setup at GSI for future high-resolution laser spectroscopic study of heaviest elements. To fully implement the proposed new technique in all existing (or under construction) setups for in-gas-jet laser resonance ionization spectroscopy, it will be enough to replace the used supersonic nozzle with the miniature double-nozzle device described in the paper.

Effect of free boundary on the performance of single expansion nozzle

Abstract Effect of free boundary on the flow field characteristics of a single expansion nozzle has been studied experimentally and computationally. The single expansion nozzles studied in this investigation are a convergent-divergent nozzle of rectangular cross-section with convergent-divergent wall on one side and a flat wall on the opposite side, and an identical convergent-divergent ramp with its top open to atmosphere. The studies have been carried out at nozzle pressure ratios 2, 3, 4 and 5. The results show that the single expansion nozzle with wall boundary is able to deliver the flow with Mach number around 1.5, at nozzle pressure ratios of 4 and 5 even with the single expansion. The nozzle with free boundary, the wall static pressure is appreciably lower than that of nozzle with closed boundary and the exit Mach number is 1.5 for NPR 4 and 1.75 for NPR 5. That is, at the exit, the single expansion nozzle with free boundary delivers higher Mach number compared to single expansion nozzle with wall boundary for NPR 5.

Study of the flow structure during the injection of detonation products into the supersonic nozzle

The gradual unloading of the space stage by undocking objects from it or an emer-gency situation due to the undocking of one of the spacecraft leads to mass asymmetry. In outer space there is also the problem of the collision of a space object with elements of space debris. Therefore, the relevance of the topic of this work is determined by the need to develop a system for avoiding the collision of a rocket with elements of space de-bris and controlling the flight, observing the programmed trajectory of movement. The gas-dynamic aircraft system is characterized by the highest speed control. Injection of detonation products into the supercritical part of the nozzle was used as a gas-dynamic system. Modeling was carried out in the SolidWorks application software package. The purpose of the work is to develop alternative methods of the thrust vector control of the upper stage rocket engine. The scheme of the system for the thrust vector control of a rocket engine by the effect of a detonation wave on the gas flow in its nozzle has been developed. The simulation was carried out in a non-stationary flat model at angles to the axis of the combustion chamber of 90°, 60°, 45°, 30° and parallel to the axis, - 0°. The location of the detonation gas generator was near the nozzle section. Numerical simulation revealed that the impact of the detonation wave on the main gas flow in the nozzle causes two power factors. The first force factor is due to the reactive force when detonation products are thrown into the nozzle and on the wall of the high pressure zone where the detonation gas generator is located. The second force factor is due to the change in pressure distribution on the nozzle surface, where high pressure zone creates reflecting on it. The dependence of the relative lateral force on the injection angle of detonation products into the combustion chamber over time has been obtained. The structure of the flow according to the patterns of the velocity distribution in the nozzle during the injection of detonation products is also considered. In cases when the injec-tion is blown at 900 and 450, the release of detonation products initiates a shock wave of high intensity, which moves against the supersonic flow, retarding it. The developed scheme can be used for maneuvering the upper stage of a prospective launch vehicle to avoid its collision with elements of space debris.

Regression analysis of impulse characteristics shorted supersonic nozzle

When designing and testing rocket engines, an important problem is the choice of the contour of the supersonic part of the nozzle. Recently, with the development of rock-et and space technology, different contours of nozzles have appeared that meet new tasks, requirements for the density of the layout, the need to increase the momentum co-efficient, accounting for various operating conditions, etc. Therefore, the relevance of the work is determined by the need to choose the contour of the supersonic part of the nozzle to increase the impulse characteristics of the flow in the shortened nozzle. The goal of the work is to choose the optimal contour of a shortened nozzle with a bell-shaped nozzle, taking into account geometric and technological parameters. The regres-sion model of the supersonic flow in a shortened nozzle with a nozzle considered in the work was created on the basis of previously obtained simulation results in the ANSYS package. It has been found that the flow patterns in the nozzle are affected by the length of the inlet cone, the total length of the nozzle and the operating conditions of the noz-zle, i.e. inlet pressure and ambient pressure. The nature of the separation flow in the nozzle, and hence the momentum coefficient depends on the degree of expansion of the flow from the shortened nozzle, therefore it is necessary to identify the main geometric and technological parameters of the flows in the shortened nozzle with a bell-shaped tip and determine the dependence of the momentum coefficient on them. Data analysis was carried out on the basis of the STATGRAPHICS Plus program. The influence values of each adopted factor and their mutual influence on increasing the flow impulse charac-teristics in the shortened nozzle are obtained. Three-dimensional graphs of the depend-ence of the momentum coefficient on the geometric parameters, the pressure at the noz-zle inlet, and the pressure of the external environment were obtained. The formula for the dependence of the impulse coefficient on the length of the conical part, the total length of the nozzle, the pressure at the nozzle inlet and the pressure of the external space was determined. It was established that an increase in the pressure of the external space leads to an increase in the impulse characteristic at the average value of the pres-sure at the nozzle inlet. The built regression model allows you to choose the optimal contour of a shortened nozzle with a tip.

A Study on Converging-Diverging Nozzle Design for Supersonic Spraying of Liquid Droplets Toward Nanocoating Applications

Abstract Supersonic cold spray (CS) of functional nanomaterials from atomized droplets has attracted significant attention in advanced thin-film coating as it enables particle deposition with high-adhesion strength. In CS, optimum design of the supersonic nozzle (i.e., converging-diverging nozzle) is essential for accelerating particles to desired velocities. However, research on the nozzle design for supersonically spraying of “liquid droplets” for nanocoating applications is limited. To this end, we investigate the effect of nozzle geometrical parameters, including throat diameter, exit diameter, and divergent length on droplets impact velocity by numerical modeling and experimental validation, followed by a case study on nanocoating. The discrete-phase modeling was employed to study droplets’ flow behavior in continuous gas flow for various nozzle geometries. The results reveal that the nozzle expansion ratio, defined as a function of throat and exit diameters, has a significant influence on droplet velocity, followed by divergent length. Noteworthy, to correctly accelerate “low-inertia liquid microdroplets,” it was found that the optimum nozzle expansion ratio for axisymmetric convergent-divergent nozzles should be in a range of 1.5–2.5, which is different and way smaller than the recommended expansion ratio (i.e., 5–9) for CS of conventional micron-scale “metal” powders. Based on the simulation results, an optimum design of supersonic nozzle is established and prototyped for the experimental studies. Particle image velocimetry (PIV) was used to experimentally investigate the spray flow field and to validate the numerical modeling results. Moreover, coating experiments using the optimized nozzle confirmed the effective supersonic spraying of droplets containing nanoparticles, thereby showing the potential for advanced nanocoating applications.

Numerical study on two-phase supersonic expansion refrigeration in novel CO2 refrigeration technology

The serious environmental problems have promoted the development of CO2 natural working fluid refrigerants. The supersonic two-phase expander with supersonic nozzle as the key component is proposed. A novel CO2 supersonic two-phase expansion refrigeration cycle is constructed and its cycle performance is also calculated. Then, the numerical simulation of the flow condensation and liquefaction process of CO2 in the nozzle is carried out. The results show that the inlet parameters of the supersonic two-phase expander have an important effect on the cycle performance. With the increase of inlet pressure, COP first increases and then decreases. The optimal inlet pressure of the system is 5.3 MPa with the corresponding maximum COP by 2.50, and the Relative Carnot Efficiency decreases from 0.809 to 0.755. With the inlet temperature increase, the maximum COP and the Relative Carnot Efficiency are 2.49 and 0.826, respectively. The established model can reasonably describe the supersonic expansion refrigeration characteristics and condensation phase transition characteristics of CO2. With the increase of nozzle inlet pressure and the decrease of temperature, the inlet degree of supercooling increases, while the initial nucleation position moves forward further and the peak nucleation rate decreases. Meanwhile, the droplet number decreases, both the droplet radius and the liquid mass fraction increases. The ideal cycle performs well, which provides a valuable reference for CO2 utilization.

Hysteresis behavior of shock train driven by continuous incoming Mach number variation in an isolator with background waves

Shock train hysteresis was investigated through wind tunnel experiments and numerical simulations of the internal flow in a supersonic isolator under background waves generated by a 14° wedge. An adjustable Laval nozzle was developed so that the throat area could be continuously changed and the incoming Mach number was varied between 1.8 and 2.4. Under the continuous decrease of the incoming Mach number, the impingement points of the background waves are observed to move uniformly upstream and the pressure of the relaxing boundary layer that is not swept by the impingement point decreases linearly. The pressure in the region that is swept by the impingement point first undergoes an adverse pressure gradient that results from the presence of the background wave, and then undergoes the favorable pressure gradient in the relaxing boundary layer. Hysteresis occurs when the shock train moves near the impingement point of the background wave, which is an inherent property of a bistable system. The triggering factor of the bistable system is that the adverse pressure gradient region that results from the background wave/boundary layer interaction cannot resist the pressure rise generated by the shock train leading edge, and the shock train can only stabilize upstream or downstream of the impingement point of the background wave. The maintenance factor of the bistable system is that the two positions of the shock train upstream and downstream of the impingement point of the background wave can match the same backpressure.

Laser ionization scheme development for in-gas-jet spectroscopy studies of Th+

The in-gas laser ionization and spectroscopy (IGLIS) technique has been a cornerstone in the study of heavy elements. The addition of a convergent–divergent (de Laval) nozzle to perform laser ionization in a cold hypersonic gas jet greatly improves the achievable resolution. Recent efforts have focused on preparing the in-gas-jet method for the study of the low-lying 229Th isomer. Tailor-made recoil sources of 233U are installed inside a fast extraction gas cell to provide the (isomeric) thorium ions. A level search above the second ionization potential (IP) uncovered several auto-ionizing states, greatly improving the laser ionization efficiency of singly charged thorium ions.

Research on transonic flow of nozzle contractions for providing an asymptotic solution

The effect of a contraction on the flow in a supersonic nozzle is investigated, and improvements are made to provide an accurate asymptotic solution of transonic flow. Owing to the elliptical characteristic of the governing equation, supersonic nozzle contractions are not rigorously designed from aerodynamics theory. The contraction effect is often masked by the design defects of the supersonic nozzle contours and, therefore, is hard to evaluate independently. In this study, the authors use a sufficiently advanced supersonic contour to support numerical and theoretical research on various contractions. The results show that the commonly used contractions lead to abrupt changes in transonic flow field parameters, and the degree does not vary with the nozzle Mach number. Based on the work of Hall, the accurate asymptotic solution of the sonic line in the nozzle is derived. Most practical sonic lines provided by various contractions are inconsistent with the accurate asymptotic solution, which further affects the uniformity of the supersonic flow. By iterating the shift of the Witoszynski contraction, the end point curvature is found to be the core parameter. On this basis, three improved contractions are proposed. These new contractions allow discontinuities in wall curvature and avoid the problem inherent in Sivells' cylindrical-quartic–conical-quartic contraction. Each improved contraction successfully coincides with theoretical transonic flow, helping the supersonic nozzle eliminate waves completely and achieve a high degree of flow uniformity.