Supersonic Nozzle Research Articles

Continuous/smooth transonic solutions to the quasi-one-dimensional steady relativistic Euler equations

This paper establishes the existence and uniqueness of continuous/smooth Meyer type transonic solutions to the quasi-one-dimensional steady isentropic relativistic Euler equations. We use the high-order Taylor’s expansion of the velocity near the sonic point to overcome the difficulties of applying the implicit function theorem caused by the sonic degeneracy. It is verified that the flow in the De Laval nozzle accelerates from subsonic upstream and continuously/smoothly pass through the sonic surface at the throat and then becomes supersonic downstream. Moreover, the flow may have a zero or positive acceleration at the sonic surface, which depends on the geometric property of the nozzle at the throat.

Linking Enceladus’ plume characteristics to the crevasse properties

Supersonic plumes of water vapour and icy particles have been observed by the Cassini spacecraft during several flybys over Enceladus. These plumes originate from the Tiger Stripes located in the South Polar Terrain (SPT), and indicate the presence of a subsurface ocean under the icy crust which is salty and contains complex organic molecules. Other characteristics of the plumes, such as the vent temperature, mass flow rate, velocity and mass fraction of icy particles can be used to determine the conditions in the channel, linking the subsurface ocean to the icy surface. In this paper, we developed a fluid dynamics model that accounts for nucleation, particle growth, wall accretion and sublimation. The channel behaves similarly to a converging–diverging nozzle, which forms supersonic plumes due to a pressure difference between the reservoir where the subsurface ocean is located and the exosphere. The geometry of the channel and its evolution with accretion of gas and sublimation of ice are studied to reproduce the characteristics of the plumes observed by Cassini. We first performed a parameter study on the channel geometry to determine how it influences the plumes’ velocity, solid fraction and exit temperature. Our results show that the size of the icy particles is primarily dependent on the length of the channel, indicating that large particles (∼75μm) must originate from within a kilometer below the surface, while smaller particles (∼3μm) can originate from only hundreds of meters below the surface. We further show that the velocity of the flow, exit temperature and nucleation depend directly on the exit-to-throat size ratio. We find that the channel geometry evolves within a few tens of hours until an equilibrium is reached, when considering the accretion of gas to the walls, or sublimation of ice from the walls. As the channel closes due to accretion, the flow becomes thinner, which in turn reduces accretion. After around 70 h, the accretion is sufficiently slowed such that the geometry does not evolve anymore. This equilibrium geometry produces higher Mach numbers and a larger particle size and solid fraction compared to the initial geometry.

Evaluation of dynamic behaviors in varied swirling flows for high-pressure offshore natural gas supersonic dehydration

The dehydration process involving the supersonic separator (SS) proves advantageous for the high-pressure offshore natural gas industry. By adeptly harnessing energy conversion from pressure to cold energy, the SS efficiently condenses and separates water vapor. In this process, swirl strength is the critical factor. To clarify the influences of different swirl strengths on flow field characteristics, droplet behavior, film formation, separation performance, and energy conversion of the SS in high-pressure offshore natural gas, a computational model was established and validated in this study. The prediction results of three representative thermodynamic models were compared in the Laval nozzle and the SS. The results show that the NIST real gas model possesses the highest prediction accuracy compared to the other two models. The inlet pressure has a significant influence on the separation performance of the SS. The maximum values of water vapor removal rate, dew point depression, optimum droplet diameter, and optimum droplet concentration can increase to 81.75 %, 37.65 K, 3.3 μm, and 0.0026 kg s−1, respectively. The swirl strength significantly influences separation performance and energy conversion. Notably, the normal swirl strength achieves the maximum separation performance, showcasing a water vapor removal rate surpassing that of strong swirl strength by 18.03 %. The temperature drop exhibits maximum deviations of 20.70 % and 12.51 % compared with weak and strong swirl strengths. Moreover, the utilization of supersonic separators in the pre-dehydration process results in a substantial cost reduction of $ 6,691,060 over a 20-year period.

The influence of plug nozzle and Laval nozzle on the flow field and performance of non-premixed rotating detonation combustor

With the rotating detonation engine's (RDE) development to engineering applications, the selection and optimization of nozzle is garnering great concerns, with the aim to maximize the performance benefits of this pressure gain propulsion system. The present study represents the first effort to explore the distinct impacts of two commonly used nozzles in RDE, namely, the plug nozzle and the Laval nozzle, on the internal flow and performance within the combustion chamber. Three-dimensional numerical simulations are conducted on non-premixed annular RDEs with plug nozzles and Laval nozzles. It is found that the Laval nozzle induces a forward-leaning wavefront structure in the combustion chamber. Furthermore, the overall pressure gain of the RDE is divided into the injection pressure loss, the average pressure gain at the chamber bottom, and the flow losses downstream, by combining the wavefront coordinate averaged flow field, which is proposed and applied in this study, and laboratory coordinate averaged flow field. The results show that, for the performance of the combustion chamber, while Laval nozzles enhance pressure gains at the chamber bottom and reduce exit flow non-uniformity, they also increase downstream losses. By comparing the RDE performance with the ideal performance of deflagration-based combustors, it is found that the premixed control group exceeded the deflagration ideal performance by 30%. Despite lower combustion efficiency, non-premixed configurations nearly match the ideal deflagration performance, underscoring the inherent advantages of RDEs.

Influence of emissivity on infrared radiation characteristics of the two-dimensional nozzle

In the case of the same outlet area, the two-dimensional (2-D) nozzle has a large aspect ratio compared to the axisymmetric circline nozzle, which enables it to reduce the visible area of high-temperature components such as the center cone and the flame stabilizer inside the nozzle. It can also strengthen the mixing effect of wake flow and outflow to achieve the effect of cooling. In this work, based on the calculation of the flow field of the 2-D convergent-divergent nozzle, the infrared radiation characteristics of its with different emissivity coatings and the coating under high-temperature coming off are calculated in the 3∼5um waveband. The results show that with the increase of emissivity, the mean value of infrared radiation intensity of the nozzle in the range of detection angle 0°-70° decreases to 68.80%, while the mean value of infrared radiation intensity in the range of detection angle 80°-90° rises to 136.55%. The nozzle coating coming off is caused by excessive temperature and its infrared radiation intensity even exceeds the infrared radiation intensity of the uncoated state when the coating comes off.

Optimizing the design of a supersonic Planar Dual Bell Nozzle (PDBN)

Dual bell nozzles present a promising solution for maximizing propulsion efficiency at high altitudes, while also mitigating dangerous side loads at lower altitudes. Such nozzles are comprised of two distinct contours, with the first optimized for low altitude operation, and the second tailored for high altitude conditions. These contours are interconnected at an inflexion point. The present study focuses on optimizing the contour design of a planar dual bell nozzle. Leveraging the commercial ANSYS-Fluent software, we conducted an investigation into the influence of the inflection angle on the transition between the two operating modes, examined the flow behavior inside the nozzle, and assessed the impact of the inflection angle on the thrust coefficient.

A Systematic Review of Dust Suppression Methods by Experiment Based on Intelligent Technology in the Coal Mines

The mining and its transportation processes generate a substantial quantity of dust, which harms miners' health. The extended inhalation of dust particles could result in pneumoconiosis. There are numerous studies on coal mine dust removal, but only a handful of articles critically comment on it. A systematic coal mine dedusting literature review has been conducted to attempt a comprehensive and reproducible analysis. This article reviews dust suppression methods by experiment in coal mines from three aspects: chemical modification of dust removers, structural improvement of dust removers, and other factors. The review showed that independent experimental research suits dust remover's structural improvement and chemical modification. Compared to non-phytochemical modifications, phytochemical modifications are more efficient and environmentally friendly. The development of dust remover structures concentrates primarily on the nozzle structure, nozzle diameter, the number of holes, and the distance, with the nozzle diameter being of particular significance. Sometimes, tweaking the nozzle structure does not yield significant efficiency improvements. However, supersonic nozzles demonstrate high efficiency and are likely to be a key area of future research. Experiments also investigated other factors' effects on coal mines' dust removal efficacy, including ventilation system, metamorphic degree of coal, and particle diameter. This review provides the latest dust removal technology information for coal mines. Intelligent technology provides the basis for experimental research on dust removal in coal mines. The future trends of experimental research in the coal mine dust control field include intelligent and automated dust control systems, comprehensive control of multiple pollutants, application of new materials and technologies, and interdisciplinary collaboration and cross-disciplinary research.

A shock loss reduction method for the low-pressure rotor of a vaneless counter-rotating turbine using circulation redistribution

This paper proposes the circulation redistribution for the low-pressure (LP) rotor of a highly-loaded vaneless counter-rotating turbine (VCRT) to reduce the LP shock losses. The method is to decrease the mid-span circulation and increase the tip circulation at the exit of the LP rotor with unchanged high-pressure (HP) and LP power output. The LP Blade-to-Blade flow field can be considered as a Laval nozzle model. And the high static pressure drop from the throat to the exit results in strong trailing edge (TE) shocks near the LP mid-span. Also, the suction side TE shock (ST) and the reflected shock of the pressure side TE shock (RPT) near the LP mid-span merge into a relatively strong shock very close to the TE. These two factors result in high shock losses. To reduce the shock losses under the design condition, decreasing the stagger angle and the blade exit angle near the LP mid-span are adopted to reduce the LP mid-span exit circulation. This changes the throat area to exit area ratio near the LP mid-span, prompting the actual static pressure drop from the throat to the exit to be reduced and closer to the theoretical value, so that the TE shock strength is reduced. Besides, the intersection of the RPT and the ST is delayed owing to the improved flow angle distributions near the TE, further contributing to the LP mid-span shock loss reduction. Since the LP power output is decreased and the LP tip-leakage flow (TLF) losses are far lower than the HP TLF losses, increasing the stagger angle and the blade exit angle in LP tip regions are employed to increase the LP exit circulation and decrease the HP exit circulation in tip regions. Then the HP and LP efficiency are both raised with unchanged HP and LP power output after optimizing the blade profiles near the mid-span and in tip regions of the LP rotor. The remarkable thing is that the TE shock strength in LP tip and root regions are both reduced after improved because of the decreased ratio of the exit area to the throat area. And the intersection of the RPT and the ST in LP tip and root regions are also both delayed, leading to reduced shock losses. The reduced TE shock losses along the whole LP span appreciably raise the LP and VCRT efficiency by 0.96% and 0.32% respectively.

Вплив детонаційної хвилі на перерозширений надзвуковий потік газу в со-плі

This paper proposes to use the detonation process to solve the problem of controlling highly maneuverable flying vehicles. The goal of the work is to study a new way of the thrust vector control of a rocket engine using the effect of a detonation shock wave on the gas flow in the nozzle. It is known that the method of thrust vector control by gas injection into the supersonic nozzle area of a rocket engine features one of the lowest losses of specific momentum and a high response speed and produces a significant lateral force. However, for the current level of rocket technology, there is a need to improve these characteristics. Detonation is considered as a method to intensify processes that affect the main gas flow and produce a lateral force. Its features make it possible to develop a system for pulse trajectory correction. In order to study the features of such a system, experimental studies of the detonation wave effect on a supersonic nozzle flow were conducted. A nozzle model and a gas generator for initiating a detonation wave interacting with the main supersonic air flow were developed and made. In the course of experiments, the effect of separation of the main flow from the nozzle wall by the detonation wave during the nozzle operation in the overexpansion mode was revealed. The duration of this effect was much longer than that of the detonation product effect on the main air flow in the nozzle, thus allowing it to be used in the development of a new thrust vector control method. To better understand the experimental results, a numerical simulation of the detonation wave propagation in a supersonic flow was carried out for the test conditions. The simulation was carried out in a non-stationary 2D formulation using the Solid Works software package. The goal of the simulation was to estimate the flow structure and the value of the relative lateral force produced by the change of this structure during detonation product injection into the supersonic nozzle area. The time evolution of the pressure field was obtained. The relative lateral force produced by detonation product injection into the supersonic air flow in the nozzle was determined. The presented features and method of jet engine thrust vector control may be used in unmanned systems operating in a wide range of speeds.

Efforts to Identify the Most Suitable RANS Turbulence Model for Accurate Conjugate Heat Transfer Prediction in Regenerative Cooled Nozzles

Abstract This study presents a two-part numerical study aimed at improving the prediction and understanding of regenerative cooling in supersonic nozzles. The first objective was to identify the most appropriate Reynolds-averaged Navier–Stokes turbulence model for accurately predicting conjugate heat transfer. Three turbulence models, Shear Stress Transport, Reynolds stress model (RSM)-ω, and RSM-ω with shear flow corrections (SFC), were tested through comparative analysis and simulations to evaluate their accuracy in predicting the heat flux rate and temperature on the nozzle wall. The results indicate that the RSM-ω turbulence model with shear flow corrections provides the best thermal prediction, achieving an improvement of 28% compared to the next-best model. The second part assesses the impact of key parameters on cooling efficiency. High coolant pressure proves advantageous for extremely hot-gas flow due to increased saturation temperature. Interestingly, the height of the cooling slot has less significance, suggesting other factors should be prioritized in film-cooling system design. The study also investigates the effectiveness of hydrogen coolant in reducing wall gas temperatures and preventing excessive heat that could melt the nozzle material. Transient results show that the gas-side wall temperature increases more rapidly than the coolant side during start-up and cooling the walls takes longer than reaching a steady-state for the hot-gas flow. The simulation results align well with experimental data, validating the accuracy and reliability of the numerical approach.

Air tab location effect on supersonic jet mixing

Abstract Mixing of Mach 2.1 circular, jet issuing from a straight convergent-divergent circular nozzle, in the presence of sonic air tabs at exit and shifted locations along the jet axis was investigated experimentally at nozzle pressure ratios (NPR) 3–6, insteps of 1. Two constant area tubes of 1 mm diameter positioned diametrically opposite, at 0 D, 0.25 D, 0.5 D and 0.75 D (where D is the nozzle exit diameter), were used for fluidic injection. The injection pressure ratio (IPR) of air tabs was maintained at 6. The Mach 2.1 jet operated at nozzle pressure ratio (NPR) in the range of overexpanded states corresponding to NPR 3–6 was controlled with the sonic air tabs operating at the underexpanded state corresponding to IPR 6. The impact of air tabs on jet mixing was studied from the measured Pitot pressure along the jet centerline. The centerline pressure decay of the jet confirms that the air tab promotes jet mixing with the entrained air mass, and the mixing promotion caused by the air tab is dependent on tab location as well as the NPR. In the presence of air tabs, the jet possesses shorter core and experiences faster decay than the uncontrolled jet. Also, the air tabs were effective in reducing the number of shock cells and rendering the waves weaker in the jet core. Among the tab locations, the mixing promoting effectiveness of air tabs at 0 D is better than the tabs at shifted locations. The jet core length reduction caused by the air tab at 0 D increases from 25.4 % to 77.2 %, with increasing NPR from 3 to 6. The same trend was noticed for tab location 0.75 D, but not for 0.25 D and 0.5 D locations. The core length reduction for 0.75 D tab location is about 61.4 %, at NPR 6, and 62.1 % and 55.8 %, for NPR 5 and 4 for tab locations 0.25 D and 0.5 D, respectively. Shadowgraph images of the waves present in the jet core confirms the findings of centerline pressure decay results.

ДОСЛІДЖЕННЯ РЕГУЛЬОВАНОГО СОПЛА ЛАВАЛЯ

Heat exchangers are the most common and simplest equipment for cooling gas streams, but heat must be removed for their operation. However, by using a Laval nozzle, it is possible to achieve cooling of the gas flow due to a physical phenomenon in which the gas flow velocity is reduced to the speed of sound. The efficiency of such a nozzle depends on the change in the gas flow rate in it. Therefore, to regulate the mode of operation of the Laval nozzle, its design is proposed, which is simpler than the existing ones, cheaper to manufacture and operate. The nozzle is made of an elastic material - silicone, and is located in a special housing, into which a compression nut is inserted, which compresses the nozzle in the axial direction. Due to this achievement, the inner opening of the nozzle is reduced. Conducted simulation studies of the proposed design of the nozzle made it possible to apply its deformed state, developed and printed on a 3D printer of a mold - to make a silicone nozzle and conduct its research. After conducting a study of the silicone nozzle, it was established that the diameter of the hole at the critical section without deformation in the axial direction is 11.8 mm, and at a deformation of 10 mm - 8.6 mm.

КОМП'ЮТЕРНЕ МОДЕЛЮВАННЯ НЕСТАЦІОНАРНОГО ПРОЦЕСУ РОЗВИТКУ НАДЗВУКОВОГО ПЕРЕРОЗШИРЕНОГО СТРУМЕНЮ

Questions of numerical simulation of non-stationary process of the development of a supersonic overexpanded jet are considered. Unsteady Reynolds-averaged Navier-Stokes equations (URANS) of compressible flows, written in an arbitrary coordinate system, along with the Spalart-Allmaras one-equation differential turbulence model are applied. The calculations of non-stationary formation of an air cold supersonic jet during the blowing through a conical Laval nozzle (simulation of engine start-up) were made. The physical features of the shock and acoustic waves generation and propagation are discussed. In the stationary phase an overexpanded free supersonic turbulent jet is formed, which includes a Mach disc in its structure. The obtained results were compared with experimental data and calculations by other authors based on the ANSYS Fluent and FloEFD CFD tools.

Condensation shock topologies in carbon dioxide and a non-condensable gas mixture in supersonic nozzles

Condensation shock waves may occur in many flow expansion devices such as turbomachinery, gas ejectors, micro thrust-nozzles, and supersonic gas flow separators. However, their experimental analysis has been barely addressed as condensation shocks comprise complex phenomena such as compressible flow behavior, a shock-like phase transition, and a two-phase flow expansion. This work characterizes experimentally some condensation shock topologies of a mixture of carbon dioxide and dry air at several compositions in a Laval nozzle. Experiments were carried out in a test-rig instrumented with high-response pressure transducers installed along the Laval nozzle wall along with a Schlieren setup equipped with a high-speed video camera imaging the flow behavior within the nozzle. The nozzle wall profile was built by using the method of characteristics developed from a real equation-of-state suited for the testing mixture. Results revealed the influence of the nozzle wall profile on the condensation shock location and topology. Moreover, there types of flow behavior were captured and named as conventional, transition, and Mach wave condensation shocks. The transition from one topology to another occurred due to the interaction between cancelation waves originated from the nozzle wall and the phase-change phenomenon, giving rise to two distinct regions characterized by certain observable droplet population density. The current investigation presents an in-depth phenomenological discussion of the three types of condensation shock topologies as such assessment has not been previously developed.

Investigation of heterogeneous condensation flow characteristics in the steam turbine based on homogeneous-heterogeneous condensation coupling model using OpenFOAM

Non-equilibrium condensation can result in thermodynamic losses within turbine stages and potentially cause blade erosion. During turbine operation, steam frequently carries foreign particles, which can influence non-equilibrium condensation. However, there is a lack of systematic research on the specific effects of these particles on the condensation processes. This paper firstly utilizes OpenFOAM to establish a homogeneous-heterogeneous condensation coupling model, which is validated for accuracy through experimental data. Secondly, it investigates the effects of NaCl particle concentration and radius on the heterogeneous condensation process in Laval nozzles and Dykas cascades. Finally, it examines the relationship between the kinetic energy ratio, condensation loss ratio, wetness fraction ratio, and particle concentration and radius in turbine cascades to explore the optimal method for reducing the impact of condensation phase change in steam turbines. The results indicate that nucleation rate decreases as particle radius decreases and concentration increases in Laval nozzle. However, the effect of concentration on wetness is non-linear; as concentration increases, wetness initially decreases before increasing. In comparison to homogeneous condensation within Dykas cascades, when the introduced particle radius is 1 × 10−9 m and the concentration is 1014kg−1, the kinetic energy increases by 2.93%, condensation loss decreases by 22.91%, and wetness fraction decreases by 23.64%.

Selected Papers from 4th National Aerospace Propulsion Conference NAPC 2022

The National Aerospace Propulsion Conference (NAPC) is a national conference dedicated to aerospace propulsion technologies. Two erstwhile popular conference series, the National Propulsion Conference (NPC) and the National Conference on Air-Breathing Engines (NCABE) were merged to result in NAPC. This biennial conference is intended to bring together the entire propulsion community spanning the industry, academia and the research labs nationwide. The aerospace propulsion-centred conference is considered an ideal opportunity to showcase one’s research activities with peers and foster future collaborations through networking. The 4th edition of the conference, NAPC-2022, comprised a keynote lecture, several topical invited lectures and presentations of contributed papers in parallel sessions. This special issue contains eight manuscripts selected based on peer-reviews of selected papers presented during the conference. The manuscripts broadly cover several aspects pertaining to aerospace propulsion that includes airbreathing engine components such as intakes, compressors, combustors and nozzles. From the rocket propulsion (non-airbreathing), there are papers that investigate the rocket motor grain port alignment and another paper on the heat transfer characteristics of a supersonic rocket nozzle.

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.

Impact of Laval nozzle structure on the flow characteristics of supersonic gas-solid two-phase flow

This study introduces a mathematical coupling model within the Euler-Lagrange framework to conduct numerical simulations for supersonic gas-particles flow. After validating the model, the gas flow characteristics and particle dynamics within supersonic gas-particle flow under various nozzle configurations are investigated. The findings are as follows: (1) A Laval nozzle with a smoothly connected throat suppresses the generation of fan-shaped Prandtl-Meyer expansion waves and other complex wave systems, effectively mitigating significant changes in gas pressure at the throat and enhancing the stability of supersonic jets. (2) The presence of a particle-free zone in the nozzle divergent segment reduces the collision frequency between particles and the walls, thereby restricting the radial expansion of particles. (3) Utilizing an internally smooth-lined nozzle and expanding the radial divergence angle to 2.5–2.8 times, while ensuring particles maintain consistent axial penetration performance, increases the reflective contact area. This leads to an improvement in the utilization efficiency of particles. These findings provide valuable insights for optimizing nozzle configurations and enhancing the performance of supersonic gas-particle systems.

On the non-existence of real-valued, analytical mass-density solutions corresponding to an expansion or compression of an ideal gas along the streamlines, by considering a steady, isentropic, 2D-flow through a Laval nozzle in orthogonal curvilinear coordinates in the Euclidean 2D-space

On the non-existence of real-valued, analytical mass-density solutions corresponding to an expansion or compression of an ideal gas along the streamlines, by considering a steady, isentropic, 2D-flow through a Laval nozzle in orthogonal curvilinear coordinates in the Euclidean 2D-space

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.