Divergent Section Research Articles

Rutherford scattering of quantum and classical fields

Quantum Rutherford scattering and the scattering of classical waves by black holes have similar formal structures and can be studied using the same mathematical techniques. In both contexts, the long-range nature of the interaction leads to a divergent total cross section, which has been interpreted and regularized in various ways in the past literature. We review in detail the origin of this divergence, in both real and multipole spaces, and show that it arises from the incorrect use of approximations outside their domain of validity. We also stress that although black hole and quantum Rutherford scattering share the same formalism, the natures of the associated physical observables differ. We comment on the role of interference: while interference may be safely neglected in the context of quantum Rutherford scattering (due to the fact that the observable quantity is a flux, and the incoming flux is collimated), it should not be neglected in the context of classical waves scattered by a black hole, where one expects to see a superposition of transmitted and scattered waves in a broad region downstream from the target and a cross section is not connected to any physically observable quantity.

The impacts of structural parameters on performance and energy loss of the supersonic separator: A sensitivity analysis

The supersonic separator uses pressure energy to achieve highly efficient carbon capture and water vapor separation from the natural gas mixture. Structural parameters are crucial in determining both separation performance and pressure energy loss of the supersonic separator. However, a comprehensive understanding of how them influence flow behaviors and performance is hindered by their coupling effects and the limitations of numerical methods. This study introduces Euler-Lagrange-Euler model to predict separation performance and pressure energy loss of supersonic dehydration process with varying structural parameters. The results show that the expansion ratio of the divergent section, length of the convergent section, inlet radius of the inner body, and throat radius of the inner body significantly impact separation performance and pressure energy loss. Especially the first parameter, the swirl strength and centrifugal acceleration decay to 0.044 and 2.41 × 104 m s−2 as it increases. At the same time, the droplet removal rate significantly improves, but the separation performance does not increase indefinitely due to the shock waves. The dehydration efficiency first increases to 95.09 % at Er= 1.5 and then decreases; the dew point depression also expands to 25.28 K and then drops, and the corresponding pressure loss rises to 0.47 and then falls.

Optimization of Process Parameters for Flow Nozzle with Different Geometry using Computational Fluid Dynamics Method

A nozzle is a tubular structure designed to facilitate the flow of hot gases. Rocket nozzle designs typically consist of a stationary convergent section and a stationary divergent section. The term "CD" is an abbreviation for "convergent-divergent" and is used to refer to this specific nozzle type. Upgrades are being made to nozzles and other engine components in order to enhance performance and optimise thrust delivery. Application-specific improvements will be made to rocket nozzles and other current combustion expansion systems. An instance of such progress is the implementation of the bell and twin bell nozzle. This study conducted a comparative analysis of two kinds of nozzles, namely bell and conical, at different Mach speeds to ascertain which one yields the most optimal flow. Subsequently, the flow parameters were modelled with computational fluid dynamics (CFD). Ensuring optimal pressure thrust integral throughout the supersonic zone of the nozzle surface while taking the base pressure into account was the aim of the problem formulation. The research focused on irrotational flow, taking into consideration the impacts of boundary layers.

Large Eddy Simulation of Laminar and Turbulent Shock/Boundary Layer Interactions in a Transonic Passage

Abstract Shock/boundary layer interactions (SBLI) are a fundamental fluid mechanics problem relevant in a wide range of applications including transonic rotors in turbomachinery. This paper uses wall-resolved large eddy simulation (LES) to examine the interaction of normal shocks with laminar and turbulent inflow boundary layers in transonic flow. The calculations were performed using GENESIS, a high-order, unstructured LES solver. The geometry created for this study is a transonic passage with a convergent-divergent nozzle that expands the flow to the desired Mach number upstream of the shock and then introduces constant radius curvature to simulate local airfoil camber. The Mach numbers in the divergent section of the transonic passage simulate single stage commercial fan blades. The results predicted with the LES calculations show significant differences between laminar and turbulent SBLI in terms of shock structure, boundary layer separation and transition, and aerodynamic losses. For laminar flow into the shock, significant flow separation and low-frequency unsteadiness occur, while for turbulent flow into the shock, both the boundary layer loss and the low-frequency unsteadiness are reduced. The time period of the unsteadiness was hypothesized to align with the time it takes for turbulent structures to convect from the shock to the trailing edge and acoustic disturbances to travel back from the trailing edge to the shock, and this is supported by the LES results.

Study on the bubble breakup and internal flow characteristics in the pulsed jet ejector

To intensify the bubble breakup in the ejector, a novel pulsed jet ejector is designed in this work. The pulsed jet is introduced into the ejector by one fluidic oscillator. A high-speed camera experiment is conducted to capture the progress of bubble breakup. The intensification mechanism of pulsed jet on bubble breakup in ejector is investigated by numerical simulation. The experimental results indicate that the introduction of the pulsed jet effectively induces the occurrences of pressure fluctuations and vortex collision, prompting the deformation of bubbles to produce microbubbles. It is also found that the bubble diameter and number of microbubbles mainly depend on the process of bubble breakup in the divergent section, and the bubble diameter distribution is significantly influenced by the variation of Reynolds number. The variations of the vortex structure are induced by the pulsed jet, which is a key factor influencing mixing efficiency and bubble breakup effects. In addition, pulsed jet ejectors have superior mixing performance compared to conventional ejectors.

Glory interference spectroscopy in Sr atom

Slow (meV) photoelectron imaging spectroscopy is employed in the experimental study of near-threshold photoionization of strontium atoms in the presence of an external static electric field. Specifically, the study is devoted to the glory effect, that is, the appearance of an intense peak at the center of the recorded photoelectron images, when dealing with m= 0 final ionized Stark states (m denoting the magnetic quantum number). This critical effect is formally identical to that encountered in classical scattering theory, where, for a nonzero value of the impact parameter, the zero-crossing of the deflection function leads to a divergent classical differential cross section. By recording the magnitude variation of this glory peak as a function of electron excitation energy, we observe that, besides the traces of classical origin, it also exhibits intense quantum interference and beating phenomena, above and below the zero-static-field ionization threshold. We study both, single- and two-photon ionization of Sr, thus enabling a comparison not only between the different excitation schemes, but also with an earlier work devoted to two-photon ionization of Mg atom by Kalaitzis et al (2020 Phys. Rev. A 102 033101). Our recordings are analyzed within the framework of the Harmin–Fano frame transformation Stark effect theory that is applied to both the hydrogen atom and a non-hydrogenic one simulating Sr. We discuss the various aspects of the recorded and calculated glory interference and beating structures and their ‘short time Fourier transforms’ and classify them as either atom-specific or atom independent. In particular, we verify the ‘universal’ connection between the glory oscillations above the zero-field threshold and the differences between the origin-to-detector times of flight corresponding to pairs of classical electron trajectories that end up to the image center.

Aerodynamic Characteristics of the Novel Two-Dimensional Enhanced Shock Vector Nozzle

Fluid thrust vectoring (FTV) control has obvious advantages in structural quality and stealth performance because of its fast response and light weight. However, improving FTV vector performance will cause a loss in engine performance due to the need to draw airflow from the engine. In order to alleviate the above problems and further improve the vector performance of FTV, a nozzle combined with throat skewing and shock vector control is proposed, and the secondary flow of the nozzle comes from the throat and is injected into the nozzle divergence section. The numerical results indicate that compared with the original configuration, the vector angle and vector efficiency of the new configuration are more linear with the nozzle pressure ratio (NPR), and the vector angle and vector efficiency are improved by 163% and 218%, respectively, while experiencing a maximum reduction in the thrust coefficient of 1.4%. Compared with the only bypass-type shock vector nozzle, the new configuration utilizes the diversion of the two jets to eliminate the reattachment of the separation bubble after the jet and its resulting abrupt change in vector performance, improving the performance while having good control characteristics. Additionally, a sensitivity analysis of the spacing between two jets is also carried out. The spacing between two jets should be increased to make the flow pass through two weaker shock waves to improve the vector performance while ensuring that the separation after the jet is no longer attached.

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.

Numerical study on the influence of turbine swirl on exhaust system

This article employed numerical methods to investigate the aerodynamic, thermal, and infrared characteristics of last-stage turbine swirl on a two-dimensional convergent divergent (2D-CD) exhaust system with an afterburner under varying bypass ratios. The research results indicate that the swirl diminishes the thrust coefficient and flow coefficient of the 2D-CD exhaust system with an afterburner. At a bypass ratio of 0.2, the thrust coefficient and flow coefficient decrease by 0.65% and 1.07%, respectively. When the bypass ratio is relatively small, the swirl flow leads to a decrease in the temperature of the afterburner heat shield. Conversely, when the bypass ratio is relatively large, the opposite occurs. The maximum temperature of the heat shield increases by up to 7.2% (bypass ratio = 0.35), while the average temperature decreases by up to 7.1% (bypass ratio = 0.2). The swirl causes an increase in the temperature of the divergent section heat shield, with the most significant deterioration observed at a bypass ratio of 0.25, resulting in a maximum temperature increase in 12.2%. Swirling flow shortens the length of the jet flow, and as the bypass ratio reduces, this attenuation effect becomes more pronounced. When the bypass ratio is 0.2, the length of the core area decreases by 40.3%, and the infrared intensity of the narrow-side jet flow decreases by 12.5%. Overall, on the XOY detection plane, the maximum decrease in infrared intensity is 11.5%, and the maximum increase is 11.7%. On the XOZ detection plane, the maximum decrease in infrared intensity is 15.9%, and the maximum increase is 5.7%.

Numerical Analysis of Convergent-Divergent Angles and Operating Conditions Impact on Rocket Nozzle Performance Parameters

Comprehensive numerical analysis was conducted to elucidate the exhaust performance of rocket engine nozzles. The study focused on unravelling the intricate relationship between convergence and divergence angles and their impact on the exhaust performance parameters, including velocity coefficient (cv), angularity coefficient (Ca), and gross thrust coefficient (Cfg). In contrast to conventional studies that focus mainly on the divergent section, this research delved into both convergent and divergent aspects of nozzle geometry. For the convergent section, a range of angles from 20° to 45° was systematically examined. For the divergent section, a wide spectrum of angles was explored, ranging from small (10°-13°), medium (14°-19°) and large (20°-25°) divergent angles. Further, we venture beyond geometry, investigating the influence of nozzle pressure ratio (NPR) on these key metrics. Realisable 𝑘𝑘−𝜀𝜀, enhanced wall traitement was used to simulate nozzle flow. The study identified the optimal convergent angle at 37.5°. The 15° diverging angle provides good overall performance, while the 23° angle strikes the ideal compromise: maximizing thrust and efficiency while minimizing weight and maintaining optimal performance.

The impact of the Laval nozzle shape on thrust production, using the method of characteristics

This investigation examines the influence of Laval nozzle geometry on thrust production using the method of characteristics. It explores various divergent section configurations, analyzing their impact on nozzle design and performance. Comparative analysis of software tools, study of supersonic flow phenomena, and application of the method of characteristics form the core of this research. Findings showcase strong agreement between computational tools, emphasizing the Mach number's role in divergent section shape variations and thrust force. Additionally, the study scrutinizes over-expansion and under-expansion phenomena, validated through computational simulations. Future research should be aimed at enhancing computational methodologies and investigating additional parameters affecting nozzle performance, promising advancements in rocket propulsion technology.

Effect of Convergent Angle on different Flow Parameters of a Convergent-Divergent Nozzle

Nozzle is defined as a device which is being used to convert the pressure energy into the kinetic energy. It basically controls the mass flow rate, pressure and velocity of the fluid stream. Consisting of three sections convergent, throat and divergent section, this device basically converts subsonic flow into supersonic flow. An extensive study have been conducted by the authors in the past about the divergent angle effect on flow parameters of a C-D (Convergent-Divergent) nozzle. In this paper, detailed study have been done to find the most optimum value of convergent angle of a C-D nozzle for the best flow parameters. Convergent angles under consideration are 15°, 20°, 25°, 30° and 35°.

Effect of kerosene injection states on mixing and combustion characteristics in supersonic combustor at high equivalent ratio

Previous studies have found that the difference in combustion characteristics of gaseous and liquid kerosene injection in supersonic combustor is sensitive to the equivalent ratio. In this paper, the previous work is extended to a high equivalent ratio to gain a deeper understanding of the effect of injection states on combustion performance via numerical computation. The simulation results match well with the experiments and demonstrate that due to the different jet structures, the cavity shear layer of liquid injection penetrates deeply into the cavity, forming two recirculation zones therein. As a result, the majority of droplets enter the cavity and exist at a low streamwise velocity, which is favorable to droplet vaporization and combustion. Therefore, when the liquid fuel is injected at a high equivalent ratio, the fuel residence time increases, the droplet evaporation distance decreases, and the fuel vapor accumulates in the cavity. Compared to the gaseous injection with the same equivalent ratio, the liquid injection exhibits similar mixing efficiency in the cavity but slightly higher mixing efficiency in downstream divergent sections. This unique fuel distribution causes the liquid injection to have a higher combustion efficiency than that of the gaseous injection. The weak advantage in mixing and combustion makes the liquid injection capable of compensating for the effects of the fuel atomization and evaporation on combustion performance. As a result, the combustion structure and static pressure distribution of liquid injection with the high equivalent ratio is similar to those of the gaseous injection.

Численное исследование полидисперсных двухфазных течений в осесимметричном сопле Лаваля с учетом силы Магнуса, действующей на вращающиеся капли

The available papers on two-phase flows in de Laval nozzles are focused on the effect of various initial conditions, models of coagulation, fragmentation, and rotation of droplets on their local and integral characteristics. Some papers note that due to the difference in the velocities of the gas and droplets along the nozzle axis, the Magnus force acts on the rotating droplets perpendicular to the specified difference and deflects the trajectories of the droplets toward the nozzle wall. In an earlier paper, the authors proposed a mathematical model of a two-phase flow in an axisymmetric de Laval nozzle that accounts for the Magnus force on the basis of the kinetic equation. The present article is devoted to a numerical study of a polydisperse two-phase flow in a de Laval nozzle with account for the coagulation, fragmentation, and rotation of droplets and the Magnus force. This study is based on the “monodisperse” model of fragments developed by I.M. Vasenin and A.A. Shreiber, the method of labeled drops (the Lagrange method), and the finite-difference schemes of second order accuracy. The calculations are carried out for a test nozzle configuration with condensate formation on the nozzle wall both with and without the Magnus force accounted. The calculated results show that the Magnus force has different impacts on the trajectories of droplets of various sizes. It should be noted that the limiting trajectories of the droplets approach the nozzle wall due to the Magnus force, resulting in the earlier dropout on the wall. Therefore, when designing the divergent section of the nozzle, it is necessary to consider the revealed approach of the location of the dropout, which is associated with the Magnus force, to the nozzle throat.

SPH simulations and experimental investigation of water flow through a Venturi meter of rectangular cross-section

The flow of water through a horizontal small-scale Venturi tube of rectangular cross-section is simulated using a modified version of the open-source code DualSPHysics, which is based on Smoothed Particle Hydrodynamics (SPH) methods. Water is simulated using the Murnaghan-Tait equation of state so that weak compressibility is allowed. The hydrodynamics is coupled to a Large-Eddy Simulation (LES) turbulence model. The convergence properties of SPH are improved by adopting a C2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{2}$$\\end{document} Wendland function as the interpolation kernel, increased number of neighboring particles and non-reflective open boundary conditions at the outlet of the Venturi tube. The flow structure and differential pressure as well as the mainstream velocity profiles at different stations are compared with calibrated experimental data. A resolution independence test shows that good convergence to the experimental measurements is achieved using four million particles. At this resolution the simulations predict the experimental centerline velocity profile along the Venturi meter for a volumetric flow rate of ten liters per minutes (lpm) with a root-mean-square error of 4.3%. This error grows to 7.1% when the volumetric flow rate increases to 25 lpm. The predicted differential pressure matches the experimental data with errors varying from 1.4% (for 10 lpm) to 6.8% (for 25 lpm). Cross-sectional velocity profiles within the throat and divergent sections differ from the experimental measurements in less than 5.5%. In general, it is shown that the SPH model can provide an efficient and accurate method for recalibrating flow meters at moderately high Reynolds numbers instead of using costly experimental tests.

High efficiency separation of fine coke powders by the novel jet-swirl scrubber: Characteristics and mechanisms

The deep removal of fine coke powders is an urgent need and remains a great challenge for the stable operation of the delayed coke system. Herein, a novel jet-swirl scrubber was developed. A combined approach utilizing CFD and DPM was employed to investigate the mechanism of droplet fragmentation. The results indicated that droplets underwent two stages of fragmentation in the convergent and throat sections under the influence of turbulent vortex structures. This leaded to a rapid reduction in droplet size and an effective dispersion. Thorough mixing with the gas phase occurred in the divergent section, facilitating enhanced capture of coke powders. Cold model experiments were conducted to examine the relationship between droplet size, coke powders capture efficiency, and gas-liquid separation efficiency. Under the condition of optimized critical droplet size 0.106 mm by adjusting the flow rate, the removal efficient of coke powders was up to 99.57 %. This work provides valuable technical support for further development and process optimization of the decoking powder unit in delayed coking system.

Numerical prediction of the two-phase flow and radiation effects on the thermal environment and ablation of solid rocket nozzle

The effects of two-phase flow and radiative heat transfer have a significant impact on the internal thermal environment and thermochemical ablation process in aluminized solid rocket motor (SRM). However, these two effects were not revealed systematically in previous studies. In this paper, a multiscale methodology combined radiative properties of molten alumina particles at microscale calculated by Mie theory and the two-phase flow and radiative heat transfer at macroscale calculated by Eulerian-Lagrangian method coupling with discrete ordinate method is constructed within aluminized SRM. The convection and radiation are coupled with the chemical kinetics to predict the thermochemical ablation and thermal environment. The influence of two-phase fluid flow and thermal radiation on the internal thermal environment and thermochemical ablation of a SRM nozzle is analyzed quantitatively. Comparisons are made among the methodologies that models the alumina particles as gas species, considers the effect of two-phase flow and considers the effects of two-phase flow and radiative heat transfer. The results show that the erosion rate and total heat flux at the inner wall in the convergent section increase noticeably when considering the effect of two-phase flow. Meanwhile, the erosion rate in the divergent section also increases and the thermal environment is dependent on the particle size and aluminum content. Radiative heat transfer considerably enhances the total heat flux, especially in the convergent section. On the contrary, its impact on the erosion rate is very small except for the inner wall with very low temperature.

A novel in-flight thrust modulation technique for SPRM: proof of concept

Thrust modulation (termination or reduction) is one of the most sophisticated topics in rocket motors. Thrust termination is employed when combustion must be terminated to ensure proper stage separation, to avoid motor explosion, to attain certain range, or for research purposes. While liquid and hybrid propellant rocket motors have the ability to extinguish thrust, thrust termination in solid propellant rocket motors (SPRMs) need the use of specialized technology. In-flight thrust termination of (SPRMs) can be achieved by sudden and sufficient increase in throat area. Increasing throat area causes high depressurization rate which consequently leads to extinguishing the rocket motor. In contrast, in-flight thrust reduction can be theoretically attained either by reducing chamber pressure to a new equilibrium level or by reducing the divergent section length. The objective of the present paper is to prove the concept of using Linear Shaped Charge (LSC) for thrust modulation; a technique novel to SPRM applications. Thrust termination concept is proved via a set of static firing tests on a standard test motor. In addition, a mathematical model is developed to predict the drop in thrust due to cutting the nozzle at any arbitrary location. The model is validated by comparing with published experiments for thrust termination and reduction. A parametric study is conducted based on model results. It is confirmed that by cutting the nozzle along its divergent section, thrust reduction less than 20% can be attained. Further reduction can be achieved by cutting the nozzle along its convergent section.

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.

Relation between the divergent section’s angle and two-phase heat in the condensation flow of wet steam in a supersonic nozzle

Relation between the divergent section’s angle and two-phase heat in the condensation flow of wet steam in a supersonic nozzle