Divergent Nozzle Research Articles

Effect of Nozzle Type on Combustion Characteristics of Ammonium Dinitramide-Based Energetic Propellant

The present study explores the influence of diverse nozzle geometries on the combustion characteristics of ADN-based energetic propellants. The pressure contour maps reveal a rapid initial increase in the average pressure of ADN-based propellants across the three different nozzles. Subsequently, the pressure tapers off gradually as time elapses. Notably, during the crucial initial period of 0–5 μs, the straight nozzle exhibited the most significant pressure surge at 30.2%, substantially outperforming the divergent (6.67%) and combined nozzles (15.5%). The combustion product variation curves indicate that the contents of reactants ADN and CH3OH underwent a steep decline, whereas the product N2O displayed a biphasic behavior, initially rising and subsequently declining. In contrast, the CO2 concentration remained on a steady ascent throughout the entire combustion process, which concluded within 10 μs. Our findings suggest that the straight nozzle facilitated the more expeditious generation of high-temperature and high-pressure combustion gases for ADN-based propellants, expediting reaction kinetics and enhancing combustion efficiency. This is attributed to the reduced intermittent interactions between the nozzle wall and shock waves, which are encountered in the divergent and combined nozzles. In conclusion, the superior combustion characteristics of ADN-based propellants in the straight nozzle, compared to the divergent and combined nozzles, underscore its potential in informing the design of advanced propulsion systems and guiding the development of innovative energetic propellants.

Quantitative and Qualitative Experimental Assessment of Water Vapor Condensation in Atmospheric Air Transonic Flows in Convergent–Divergent Nozzles

Atmospheric air, being also a moist gas, is present as a working medium in various areas of technology, including the areas of airframe aerodynamics and turbomachinery. Issues related to the condensation of water vapor contained in atmospheric air have been intensively studied analytically, experimentally and numerically since the 1950s. An effort is made in this paper to present new, unique and complementary results of the experimental testing of moist air expansion in the de Laval nozzle. The results of the measurements, apart from the static pressure distribution on the nozzle wall and the images obtained using the Schlieren technique, additionally contain information regarding the quantity and quality of the condensate formed due to spontaneous condensation at the transition from the subsonic to the supersonic flow in the nozzle. The liquid phase was identified using the light extinction method (LEM). The experiments were performed for three geometries of convergent–divergent nozzles with different expansion rates of 3000, 2500 and 2000 s−1. It is shown that as the expansion rate increases, the phenomenon of water vapor spontaneous condensation appears closer to the critical cross-section of the nozzle. A study was performed of the impact of the air relative humidity and pollution on the process of condensation of the water vapor contained in the air. As indicated by the results, both these parameters have a significant effect on the flow field and the pressure distribution in the nozzle. The results of the experimental analyses show that in the case of the atmospheric air flow, in addition to the pressure, temperature and velocity, other parameters must also be taken into account as boundary parameters for possible numerical analyses. Omitting information about the air humidity and pollution can lead to incorrect results in numerical simulations of transonic flows of atmospheric air. The presented results of the measurements of the moist air transonic flow field are original and fill the research gap in the field of experimental studies on the phenomenon of water vapor spontaneous condensation.

A Free Boundary Problem in an Unbounded Domain and Subsonic Jet Flows from Divergent Nozzles

A Free Boundary Problem in an Unbounded Domain and Subsonic Jet Flows from Divergent Nozzles

Numerical investigation on secondary injection and thrust vector control in a planar double divergent nozzle

In this work, the performance of secondary injection thrust vector control of an altitude adaptive planar double divergent supersonic nozzle is numerically investigated. The compressible turbulent flow is solved using the kT−kL−ω transition-sensitive eddy-viscosity model. An analytical model to predict the separation distance and penetration height due to secondary fluid injection is developed based on the blunt-body theory, and it shows good agreement with the numerical estimation. The computational results indicate that injection pressure, injector location and injection angle significantly impact the thrust vector control performance. The core flow is disrupted by the momentum injection from the secondary fluid, causing the flow field structure to become asymmetrical. The wall pressure imbalance between the upper and lower nozzle increases as the secondary jet pressure elevates. Further, the thrust vectoring amplification factor is improved when the injector is placed downstream near the outlet since the shock reflection is circumvented. Indeed, that resulted in the generation of a large lateral thrust force. Most importantly, for a high injector slot angle, the primary downstream vortex disappears, and a strong secondary upstream vortex is generated, which shifts the primary upstream vortex opposite to the core flow, subsequently the shock separation is advanced. In addition, a secondary injector fitted near the exit with high inclination angles and injection pressure generated a lateral thrust of 20%.

Carbon dioxide separation from natural gas using a supersonic nozzle

Carbon Dioxide (CO2) is often released in the process of natural gases and is one of greenhouse gases that are being treated as the most troublesome environmental issues. One of the promising ways to economically remove CO2 in natural gas processes is to use the technology of supersonic separation that makes use of non-equilibrium condensation in supersonic swirling flows in convergent-divergent nozzle using wet outlet. In the present study, the mixture of Methane (CH4) and CO2 was considered as natural gas. Two-dimensional convergent–divergent nozzle was employed to produce supersonic swirling flow with non-equilibrium condensation. The Peng–Robinson real gas model was used for the mixture gas. A nucleation equation and a droplet growth equation were incorporated into the governing equations of the compressible Navier–Stokes with the k-ω turbulence closure. The predicted results were verified and validated with existing experimental data. The convergent–divergent nozzle was varied to investigate its effect on the non-equilibrium condensation of CO2 in the mixture flow. The Technique for Order of Preference by Similarity to Ideal Solution method was applied to achieve the optimum case with amounts of wetness (the mass fraction of liquid CO2 to the summation of the mass fraction of liquid and vapor CO2 at the outlet of the nozzle) and kinetic energy. Three locations of wet outlets for the optimum case were analyzed. The results show that an increase in the divergent angle of the nozzle, swirling intensity, and inlet supply pressure results in more nucleation of CO2. However, the enhancement of mole fractions of CO2 decreases the nucleation rate and wetness. The exit wetness from wet outlets was increased with increasing distance from the throat.

Accuracy and performance evaluation of low density internal and external flow predictions using CFD and DSMC

The Direct Simulation Monte Carlo (DSMC) method was widely used to simulate low density gas flows with large Knudsen numbers. However, DSMC encounters limitations in the regime of lower Knudsen numbers (Kn<0.05). In such cases, approaches from classical computational fluid dynamics (CFD) relying on the continuum assumption are preferred, offering accurate solutions at acceptable computational costs. In experiments aimed at imaging aerosolized nanoparticles in vacuo a wide range of Knudsen numbers occur, which motivated the present study on the analysis of the advantages and drawbacks of DSMC and CFD simulations of rarefied flows in terms of accuracy and computational effort. Furthermore, the potential of hybrid methods is evaluated. For this purpose, DSMC and CFD simulations of the flow inside a convergent–divergent nozzle (internal expanding flow) and the flow around a conical body (external shock generating flow) were carried out. CFD simulations utilize the software OpenFOAM and the DSMC solution is obtained using the software SPARTA. The results of these simulation techniques are evaluated by comparing them with experimental data (1), evaluating the time-to-solution (2) and the energy consumption (3), and assessing the feasibility of hybrid CFD-DSMC approaches (4).

CFD Investigation of a Co-Flow Nozzle for Cold Spray Additive Manufacturing Applications

This current work evaluates the efficacy of a co-flow nozzle for cold spray applications with the aim of mitigating nozzle clogging issues, which can occur during long-duration operations, by replacing the solid wall of a divergent nozzle section with an annular co-flow fluid boundary. Simulations were conducted on high-pressure nitrogen flowing through convergent–divergent (C–D) axisymmetric nozzles, with a stagnation pressure of 6 MPa and a stagnation temperature of 1273 K. In these simulations, Inconel 718 particles of varying sizes (15 µm to 35 µm) were modeled using a 2-way Lagrangian technique, and the model’s accuracy was confirmed through validation against experimental results. An annular co-flow nozzle with a circular cross section and straight passage covering the primary C–D nozzle has been designed and modeled for cold spray application. Co-flow was introduced to the reduced nozzle length to compensate for particle velocity loss at higher operating conditions. It was found that co-flow facilitates momentum preservation for primary flow by providing an annular gas boundary, resulting in increased particle speed for a longer axial distance beyond the nozzle exit of the reduced divergent length nozzle. The particle acceleration performance of the reduced divergent section nozzle, when combined with co-flow, is comparable to the original length nozzle.

Analysis of aero engine plume potential core infrared signature

Purpose Aero-engine exhaust plume length can be more than the aircraft length, making it easier to detect and track by infrared seeker. Aim of this study is to analyze the effect of free stream Mach number (M∞) on length of potential core of plume. Also, change in infrared (IR) signature of plume and aircraft surface with variation in elevation angle (θ) is examined. Design/methodology/approach Convergent divergent (CD) nozzle is located outside the rear fuselage of the aircraft. A two dimensional axisymmetric computational fluid dynamics (CFD) study was carried out to study effect of M∞ on potential core. The CFD data with aircraft and plume was then used for IR signature analysis. The sensor position is changed with respect to aircraft from directly bottom towards frontal section of aircraft. The IR signature is studied in mid wave IR (MWIR) and long wave IR (LWIR) band. Findings The potential plume core length and width increases as M∞ increases. At higher altitudes, the potential core length increases for a fixed M∞. The plume emits radiation in the MWIR band, whereas the aerodynamically heated aircraft surface emits IR in the LWIR band. The IR signature in the MWIR band continuously decreases as the sensor position changes from directly bottom towards frontal. In the LWIR band the IR signature initially decreases as the sensor moves from the directly bottom to the frontal, as the sensor begins to see the wing leading edges and nose cone, the IR signature in the LWIR band slightly increases. Originality/value The novelty of this study comes from the data reported on the effect of free stream Mach number on the potential plume core and variation of the overall IR signature of aircraft with change in elevation angle from directly below towards frontal section of aircraft.

Numerical solution of steady nonlinear differential equations for compressible flow through a spinning convergent divergent nozzle

Many projectiles tend to spin about their longitudinal axis while progressing in the forward direction. It helps in providing stability and a reference direction for guidance during their run. Many different projectiles employ a supersonic convergent-divergent nozzle to produce thrust for their forward motion; hence, the nozzle and overall whole propulsion system tend to spin about its axis of rotation. The main aim of this study is to observe the effect of spin on the nozzle. In this research, a converging bell-shaped diverging nozzle is numerically designed using a method of characteristics (MOC) for exit Mach number 3.21. Viscous simulations are performed for both two- and three-dimensional cases. The analysis is then performed with nozzle spinning about its axis of symmetry with a constant angular velocity of 10 revolutions per second. The analysis is repeated for the value of constant angular velocities to be 15 and 20 revolutions per second, and the behavior of flow with increasing angular velocity is examined. It has been observed that the exit Mach number and velocity decrease due to the radial protrusion of the boundary layer, and it has a negative impact on the performance of the nozzle. Moreover, the decrease of exit Mach number is in direct relation to increasing angular velocity.

Influence of Cavity on Base Pressure Manipulation in Suddenly Expanded Flow from Converging Diverging Nozzle for Area Ratio 5.29

This study delves into the intricate interplay of cavity placement, Nozzle Pressure Ratio (NPR), and Mach numbers, examining their collective influence on manipulating base pressure within a duct. Employing numerical simulations, the research explores the cavity's effectiveness in altering base pressure dynamics in the duct's base area. The investigation comprehensively studies various factors, including length-to-diameter ratio, nozzle pressure ratio, Mach number, and cavity location. The simulations are conducted for a singular cavity at multiple positions concerning the duct's diameter, maintaining a fixed cavity width-to-height ratio of 1. The NPR ranges from 2 to 8, and the Mach numbers under scrutiny span from 1.2 to 1.8. The study meticulously analyses variations in base pressure and alterations in the pressure field resulting from these variables. Notably, the findings demonstrate the cavity's adeptness in controlling base pressure, particularly at NPR values of 4 and 6 for Mach numbers 1.2 and 1.4. In contrast, ineffectiveness is observed at NPR 2 and 8 due to specific flow reattachment points. However, the cavity effectively influences base pressure at NPR values of 4, 6, and 8 for Mach numbers 1.6 and 1.8. These discernments offer invaluable insights for the optimization of duct designs in diverse engineering applications.

A comprehensive investigation on the internal flow and outflow characteristics of GDI elliptical divergent nozzles

The substantial demand for enhanced combustion efficiency and achieving near-zero emissions in GDI engines has spurred the introduction of a novel approach employing elliptical divergent nozzle spray technology. This innovative method, which marries the elliptical shape with a divergent nozzle, not only elevates downstream atomization quality but also mitigates nozzle tip wetting. Nevertheless, there exists a dearth of documented research regarding the internal flow and outflow characteristics related to the atomization potential of elliptical divergent nozzles. Numerical investigations have been carried out to scrutinize alterations in the three-dimensional cavitation morphology, the dispersion of turbulent vortex structures, and the nozzle exit flow parameters across a range of cavitation number conditions for both circular and elliptical divergent nozzles. The research findings demonstrate that the cavitation intensity of the elliptical divergent nozzle consistently surpasses that of the circular divergent nozzle. Also, the elliptical divergent nozzle consistently exhibits a greater number of turbulent vortex structures compared to the circular divergent nozzle across all cavitation number conditions. Additionally, as the cavitation number decreases, the difference in turbulence vorticity magnitude between the exits of the circular and elliptical divergent nozzles gradually increases. Furthermore, the elliptical diverging orifices are more susceptible to cavitation compared to their circular counterparts. The elliptical divergent nozzle outperforms the circular nozzle with a substantial 24.6% increase in exit velocity, especially at a cavitation number of 1.016.

Design and CFD Simulation of Supersonic Nozzle by Komega turbulence model for Supersonic Wind Tunnel

This paper presents an impressive design of a convergent divergent (C-D) nozzle using the method of characteristics for a Mach number 2 test section. The nozzle’s geometry was meticulously crafted in SolidWorks, and its performance was evaluated through a CFD simulation in Ansys Fluent R22 software. Results showed excellent agreement between the simulation and analytical data, with the Mach number ranging from 1.78 to 2. The study also compared turbulence modeling techniques, concluding that the k-omega model produced superior results. The supersonic wind tunnel achieved remarkable efficiency, completing a run at 1.8 Mach number in just 6 seconds. Overall, the study showcased exceptional accuracy and meticulousness.

Tracking plume-regolith interactions in near-vacuum conditions

An experiment to track and measure the transient phenomenon of plume-liberated regolith in near-vacuum conditions was performed in a dedicated plume-regolith facility housed at the University of Glasgow. This facility with a total volume of around 82 m3 can simulate a soft or hard landing event on “extraterrestrial” sub-atmospheric pressures. Particle image velocimetry method was used to estimate the ejection velocity and ejected angle of regolith particles, and its limitations are discussed. Glass microspheres that are matched with the size of the Lunar and Martian moon “Phobos” surface regoliths are used as simulants. With an exit Mach number of 6.6, a heated convergent–divergent nozzle represents the lander nozzle. Preliminary results capture ejecta development up to 30 ms from plume impingement. Flow visualization reveals the initial moments of plume boundary growth and regolith ejection. The vector images indicate a triangular-shaped sheet of particles sweeping from the regolith bed at a positive inclination with a local maximum velocity close to 100 m/s. The low-density “Phobos” simulant advances at a higher speed, reaches higher elevations, and covers a larger spatial area compared to a higher-density “Lunar” simulant. Observation of the crater formation reveals the difference in cohesive forces between the selected simulants. A higher inclination of particle ejection of more than 50° adjacent to the jet indicates particle entrainment originating from the interior of the crater. Stream traces reveal the deflection of ejected particles upon impingement on the lander surface at close proximity.

Influence of uniform wall corrugations on convective heat transfer through a convergent–divergent nozzle by using mono and hybrid nanofluids

Influence of uniform wall corrugations on convective heat transfer through a convergent–divergent nozzle by using mono and hybrid nanofluids

Asymptotic analysis of transonic shocks in divergent nozzles with respect to the expanding angle

In this paper we study the asymptotic behavior of the transonic shock solutions in divergent nozzles as the expanding angle goes to zero. It is well-known that there exist infinite shock solutions for steady 1-D flows in a flat nozzle with the position of the shock front being arbitrary, while there exists a unique shock solution in an divergent nozzle as the pressure at the exit is given within an appropriate interval. By analyzing the asymptotic behavior of the shock solutions as the expanding goes to zero, we are also trying to figure out a criterion which may be used to select the physical one among all shock solutions in the flat nozzle. It finally turns out that the limit shock solution as the expanding angle goes to zero strongly depends on the asymptotic behavior of the receiver pressure, which is assumed to be a function of the expanding angle, imposed at the exit. In particular, as the Mach number of the flow at the entrance is larger than γ+32, the function of the receiver pressure can be set identical to the value of the pressure behind the shock front for the flat nozzle. Then the limit shock solution may be considered as the physical one for the flat nozzle, and the limit position of the shock front being the admissible position of the shock front. To show these results, one of the key steps is to establish quantitative estimates for the position of the shock front for the given pressure at the exit. To this end, a free boundary problem for the linearized Euler system will be proposed which gives an approximation of the shock solution, then a nonlinear iteration scheme could be carried out to approach the shock solution. Moreover, the error estimates between the exact shock solution and the approximation are also established, which give quantitative information on the position of the shock front.

Transport of Steam-Gas Mixture in Hydrodynamic Devices: A Numerical Study of Steam Reforming of Methane

The paper introduces a mathematical model that describes the cavitation process occurring during the passage of a water steam flow in various geometric configurations of a hydrodynamic device. The flow experiences a localized constriction (convergent nozzle) followed by expansion (divergent nozzle), exemplified by a Venturi tube or a Laval nozzle. A narrow flow channel connecting the convergent and divergent sections is equipped with a narrow-section nozzle for injecting methane molecules into the high-speed steam flow. As the steam-gas mixture passes through this zone, it is irradiated with an electron beam and sprayed into a cylindrical chamber at atmospheric pressure, where the distribution of methane molecules in water vapor forms an aerosol. Key geometric parameters of the constriction and expansion zones of the hydraulic system (cavitation-jet chamber) are determined to ensure the uniform distribution of dispersed-phase particles (methane) in the dispersion medium (water vapor). Velocity and pressure distributions of the mixed steam-gas flow are calculated using a turbulent mathematical model, specifically the k-ω model, while the motion of methane particles is simulated using a particle tracing method. The uniformity of methane molecule distribution in water vapor is assessed using Ripley’s K-function. The best performance of the hydrogen-producing chamber was observed when the cavitation-inducing nozzle’s convergence angle exceeded 50 degrees. The divergence angle of the nozzle within the range of 30–40 degrees provided the best distribution in terms of uniformity of the methane particles in the chamber.

Supersonic Reacting Jet Flows from a Three-Dimensional Divergent Conical Nozzle

Supersonic Reacting Jet Flows from a Three-Dimensional Divergent Conical Nozzle

Convergent Divergent Nozzle Design and Analysis to Increase Working Effectiveness

Abstract: Our project's major goal is to develop and examine a Convergent- Divergent rocket nozzle in order to lower nozzle costs. Here, convergent divergent nozzle uses an alternative material. The design is based on earlier designs that served as a guide for our own. A nozzle is a crucial component that merits consideration in this era of expanding rocket propulsion for a variety of uses, including the launch of satellites into space or human missions. With this in mind, a fundamental design is created utilising the understanding of compressible flow, and the resulting thrust is estimated. use the layout established by hand computations. Utilising the ANSYS Fluent programme, the work is done in, the calculations and results are validated.

Development of Composite Ablative Liners for Solid Rocket Motor Flex Nozzles

Solid Rocket Motor generates high thrust by accelerating high pressure gases to supersonic velocities in convergent divergent nozzle, thus converting pressure energy to kinetic energy of propulsion. As exhaust gas from chamber is of high temperature, the structural steel members of nozzle should be protected from hot gases by highly erosion resistant thermal liners. For this purpose, ablative composite liners made up of Phenolic resin matrix based combined with reinforcement material like carbon fabric is extensively used [1]. Divergent being largest component and contributes more to nozzle weight, the thickness of liner should be as least as possible at the same time; it should be more erosion resistant. The erosion resistant due to hot gases can be increased by fabricating the liner in such a way that the flame only touches the edge of the composite ply of liner and liner has more density. This can be achieved by tape winding of composite prepreg tapes at Zero degrees on tapered metal mandrel using tape winding machine followed by Autoclave curing [2]. This paper gives the details of prepreg, Tape winding, Autoclave Curing and NDT of ablative liner.

CFD Analysis of Over-Expanded Flow in Convergent Divergent Nozzles

The classical one-dimensional inviscid theory does not reveal the complex flow features in an over-expanded nozzle accurately. The code Fluent has been used to simulate the viscous fluid (air) flow passing through three different 2-D Convergent-Divergent (C-D) nozzles for nozzle pressure ratios (NPR) corresponding to over-expanded flow. The steady state RANS equation with five different turbulence models has been simulated for turbulence model study. Two different types of boundary layer grids: grid1 (y&lt;sup&gt;+&lt;/sup&gt;=1) and grid 2 (y&lt;sup&gt;+&lt;/sup=50) have been simulated. Shear Stress Transport k-w (SSTKW) turbulence model with grid 1 has been chosen for turbulence modeling. Both inviscid and viscous flows have been simulated. The converged solutions captured asymmetric lambda shock in all the three nozzles at higher NPRs for viscous flows. It also predicted aftershock and flow separation depending upon NPR. The shock wave angle of the incident and reflected shock generally reduces with increase in NPR for NPR£1.92. The thrust co-efficient of all the theoretical, predicted inviscid and predicted viscous solutions reduce with increase in NPR upto a certain value of NPR and then starts increasing. The predicted viscous results (shock structure, shock location, size of normal shock, aftershock and asymmetric lambda shocks) are close to the experiments in most of the cases. The aftershock phenomenon provides dual mode flow at the exit of the nozzle.