Nozzle Length Research Articles

Flow and Heat Transfer Behaviors of Impinging Spiral Jet Arrays in a Rectangular Channel Based on Battery Cooling Technique

Impinging spiral jet array cooling, an innovative concept, has been proposed as a way to enhance the thermal management of batteries in electric vehicles. The comprehensive flow and heat transfer behaviors of impinging spiral jet arrays in a rectangular channel with/without crossflow were numerically studied. In this study, the total spiral nozzle length was 290 mm under the helix generated at a slot nozzle thickness of 1.0 mm. The rectangular crossflow channel for the heated zone had length and width ratios of 18 and 12. The jet-to-target spacing was 1.0. The jet Reynolds numbers ranging from 5000 to 20000 were performed via the shear stress transport turbulence model. The results showed that the regional average Nusselt number increased with the increase in jet Reynolds number for all conditions. The average heat transfer rate in the case with crossflow was beyond 7.8% higher than in the case without crossflow due to the cumulative crossflow, the concentration of each impingement jet was deflected and bent downstream.

Simulation-Based Design for Inlet Nozzle of Vortex Tube to Enhance Energy Separation Effect

The vortex tube, also known as the Ranque–Hilsch vortex tube, is a mechanical device that separates compressed gas into hot and cold streams. It offers a reliable and cost-effective solution to a wide range of cooling applications, as it operates without moving parts, electricity, or refrigerants. Research on vortex tubes has primarily focused on understanding the mechanisms of energy separation and optimizing cooling performance by altering geometric operational parameters. In this study, a Computation Fluid Dynamics (CFD) analysis was conducted to enhance the prediction of energy separation performance and improve the overall energy efficiency of the vortex tube. First, the geometry of the experimental device was modeled to closely match its actual shape, unlike the simplified geometries commonly used in previous CFD studies. Simulations were then carried out with variation in grid systems and turbulence models, and the results demonstrated improved agreement with experimental data compared to those reported in previous studies. Finally, simulations with a modified shape of the inlet nozzle shape were performed, revealing that the energy separation effect of the vortex tube could be enhanced by approximately 15% with an increased inlet expansion ratio (ϵ) while maintaining a constant nozzle length.

Flux growth of Cs1-xRbxBF3 (B = Ca, Sr) crystals by the micro-pulling-down method

The possibility of growing Cs1-xRbxBF3 (B = Ca, Sr) crystals by micro-pulling-down was investigated due to their potential for application in ultrafast scintillation detectors. A LiF flux was applied to lower the melting point and therefore suppress evaporation of CsF from the melt. Suitable growth conditions were obtained through careful choice of the hot zone elements. A crucible with minimal nozzle length improved mass transport and an afterheater with four windows provided a steep temperature gradient. Inclusion and crack-free crystals of Cs1-xRbxCaF3 (x = 0, 0.1, 0.25, 0.5, 0.75, 0.9, and 1) and CsCa1-xSrxF3 (x = 0, 0.1, and 0.25) were grown under optimized conditions. Despite the hygroscopic nature of the heavy alkali metal fluorides, all the grown crystals are non-hygroscopic which significantly improves their application potential. Growth of CsCa1-xSrxF3 crystals with higher Sr concentration was complicated by the low solubility of SrF2 in the LiF-CsF melt and the hygroscopic nature of the CsSrF3. The formation of solid solution in the Cs1-xRbxCaF3 and CsCa1-xSrxF3 systems was investigated through the dependence of lattice parameters on nominal composition.

CFD investigation of supersonic two parallel expansions nozzles

This paper aims to validate the design contours and result parameters of the newly developed Dual Expansion Nozzle (DEN) using the Fastran software when it enters the non-adaptation regime with the increase in altitude and variation of the Nozzle Pressure Ratio (NPR). DEN design and Computational Fluid Dynamic (CFD) application utilize the High Temperature (HT) model defined by a calorically imperfect and thermally perfect gas, providing good accuracy compared to PG model. The computational domain is decomposed into subdivisions of structured grids using the algebraic grid generator software CFD-GEOM. The mesh convergence was analyzed using three mesh resolutions: coarse, medium, and fine. A comparison was made between the two conventional nozzles, MLN and the newly developed BPN, as both are currently used in aerospace propulsion to enhance aerodynamic performance. If a rocket engine operates under strongly over-expanded conditions with ambient pressure considerably higher than the nozzle exit pressure, and by increasing NPR value, the flow separates from the wall and can lead to high side loads. These loads are reduced in DEN. The flow separation point is observed close to the exit section for the DEN in comparison with Minimum Length Nozzle (MLN) and Best Performance Nozzle (BPN) for the same NPR, resulting in low flow separation and low side load effects for DEN. This result demonstrates a small loss in the exit Mach number, leading to less loss in the thrust coefficient and a small effect of boundary layer friction for DEN. Enhanced over-expanded aerodynamics is observed in DEN compared to MLN and BPN. The application is made for air with an exit Mach number equal to 3.00.

大型贮罐清理机器人吸尘系统的设计与研究

Taking the large storage tank as the cleaning object, a cleaning robot integrating shoveling, crushing, sweeping and dust-absorbing was developed, and its dust-absorbing system was analyzed and optimized. Firstly, Fluent-EDEM gas-solid coupling was utilized to simulate the dust-absorbing system. By analyzing the fluid distribution and particle trajectory, the internal structure of the dust collection box was optimized to reduce the dust particles entering the fan box. Then, by analyzing the structural parameters of the suction nozzle, the influence of the nozzle shoulder angle, nozzle length, and shoulder height on the dust-absorbing effect was explored, and the parameters were determined, so as to reduce the energy loss and increase the flow rate on both sides of the nozzle. Finally, through the dust suction test, different models of nozzles were tested for dust suction, and the wind speed at the nozzle was measured, and the leakage of dust particles on both sides of the nozzle was significantly reduced after optimization, which verified the reliability of the simulation results and provided a theoretical basis for the design of the sweeping robot.

Kinetic Simulation of Nozzle Flow in a Micronewton-Class Cold Gas Thruster

Many scientific space missions need highly precise attitude and orbit control or ultrafine drag compensation, which relies on the variable-thrust propulsion technology operating at the micronewton level. Cold gas thruster (CGT) is a very promising solution, mainly because of its high reliability. One of the keys to the success of micronewton variable-thrust CGT is to understand the flow in its nozzle, whose configuration is much more complex than traditional CGT nozzles. This paper applies kinetic-based multiscale models to investigate the gas flow in the complex nozzle of a micronewton variable-thrust CGT. The simulations reveal that the flow simultaneously experiences all kinds of regimes from continuum to free molecular. The continuum breakdown is likely to occur near the throat region due to large gradients of flow variables and in the expander due to low gas density. Frictional choking is observed, and the nozzle length can be optimized to improve the thruster performance. Nozzle performance measures such as thrust, discharge coefficient, and thrust efficiency are found to change only with the throat Knudsen number Knt. The performance curves can be divided into two sections at Knt≃0.1, and thereby an empirical piecewise formula for thrust prediction is proposed.

Two parallel expansions for improving supersonic axisymmetric nozzle performance

The aim of this work is to develop a numerical computation program allowing designing new contours of a supersonic axisymmetric nozzle having two expansions at the throat, named by DEN (Dual Expansion Nozzle). This new nozzle gives a uniform and parallel flow at the exit section, to improve considerably the performances compared to the conventional Minimum Length Nozzle (MLN), and the Best Performances Nozzle (BPN). The present nozzle has a two unknowns external and central body curved walls. Each of them is started by an initial expansion angle to give a uniform and horizontal flow at the exit section. Two others transition regions are calculated in parallel with the contours points to give the desired exit Mach number. The walls are determined point by point by the High Temperature Method of Characteristics (HT MOC) model. The resolution of the four compatibility and characteristics equations is done numerically by the finite difference predictor corrector algorithm. The validation of the results is controlled by the convergence of the calculated critical sections ratio to that given by the theory. The design depends on four parameters, where MLN and BPN become special cases of DEN. A comparison is made with MLN, since it is currently used in the aerospace propulsion and with BPN aiming to improve their performances. The comparison is made for the same critical mass flow rate. The results demonstrate a remarkable reduction up of 45 %, and 52 % in the mass of DEN when the exit Mach number ME = 3.00 and the stagnation temperature T0 = 2000 K. The application is made for air and for future aerospace missiles in order to improve their trajectory parameters. The chosen example demonstrates an improvement of 13 % and 16 % on the missile range compared, respectively to MLN, and BPN.

(015) DEVELOPMENT OF A VAGINAL DILATOR DEVICE AND A HOME INSEMINATION DEVICE FOR CIS- AND TRANSGENDER PEOPLE, BASED ON THE ACTUAL ANATOMY OF THE PELVIS

Abstract Introduction Individuals undergoing vaginoplasty with canal creation must undertake life-long self-dilation and douching to maintain canal patency and hygiene. Commercially available dilators and douches are designed for cisgender anatomy, and are either straight, or, have an abrupt upward curve at the tip, inconsistent with neovaginal canal anatomy, which lacks the elasticity of a cisgender woman’s vagina, making it sensitive to dilator shape, and douche nozzle length. In addition, many LGBTQ+ individuals with a uterus seek pregnancy without a male sexual partner, but few devices exist for this population. Objective We assessed the vaginal canal shape in transgender and cisgender women and sought to: 1) Design a vaginal dilator which reflects pelvic and canal anatomy. 2) Create a novel dilator that combines dilation, douching, and depth measurement functions. 3) To create a vaginal dilator that can be irrigated with semen by trans men and by cis women seeking pregnancy without a male sexual partner Methods A floppy radio-opaque catheter was placed into the neovaginal canal from the introitus to the vault apex of 12 transgender women who underwent vaginoplasty with neovaginal canal creation. C-Arm fluoroscopy delineated canal curvature based on the catheter. In addition, gynaecologic texts were reviewed and both current and historical surgical instruments were examined to ascertain the shape of a cisgender woman’s vaginal canal. Based on these findings, a novel dilator was designed using ink-drawings, whereupon a CAD-file was designed and 3-D printed. A sex-toy company made our initial prototypes. Results A smooth “S-shape” was found in the vaginal canal of both cis- and transgender women, consistent with the shape of modern and historical cervical dilators. In cisgender women, the vaginal vault, which is elastic, is located much closer to the introitus than that of transgender women, whose canal is inelastic and fixed. The cervix is typically located on the anterior surface of the canal, and, located between 0.5 to 4cm proximal to the posterior fornix. Our vaginal dilators (Figure 1a) (five, each 8-12 cm circumference) and reflect the smooth S-shaped curvature observed, with depth markings, and, side-wall grooves to allow air and liquid to pass with insertion and withdrawal. The dilator is also hollow with holes at the distal end and can be fitted with a douche-bulb. Our insemination device (Figure 1b-c) is only 9 cm. circumference, is similar in shape but is shorter, is hollow to accommodates a 10cc syringe (for introduction of semen), and has a recessed anterior wall, 0.5-4cm from the tip (where the cervix normally resides) for up to 6cc of semen to pool and bathe the cervix with sperm for conception. Conclusions The design improvements shown should make dilation and douching more comfortable, and should improve hygiene and decrease the incidence of granulation tissue. Our inseminator offers a private, at-home means of achieving fertilization for both cisgender and transgender individuals. (U.S. Patent 11638808; Neovaginal and vaginal health devices) Disclosure No.

Transonic Flow Field Analysis of a Minimum Nozzle Length Rocket Engine

The aim of this paper is to develop a profile of axisymmetric minimum length nozzle giving a uniform and parallel flow at the exit section. The study is done at high temperature, lower than the dissociation threshold of the molecules. The design is made by the method of characteristics (MOC). The variation of the specific heats with the temperature is considered. The numerical results have been validated with CFD simulation Ansys-Fluent software. The second part of this study is to calculate and analyze the transonic flow field of this supersonic nozzle. The computation of the flow field characteristics at the throat is thus essential to the nozzle developed thrust value and therefore to the aircraft or rocket it propels. An investigation was conducted to analyze the effects of parameters on the position of the sonic line. These parameters include stagnation temperature T0, radius of the nozzle, types of gases, and exit Mach number ME.

Numerical modeling of the non-equilibrium condensation in multi-component flows through the high expansion ratio nozzles

Excessive flow expansion in the thruster nozzles reduces the flow temperature and pressure. This provides conditions for the condensation phenomena in the nozzle, which can affect the thrust performance of thrusters. In this paper, the condensation effect of water components in the decomposition products of hydrogen peroxide in a typical thruster nozzle is modeled. To describe the state and properties of the real gas mixture, the Peng-Robinson equation of state is used. Moreover, the effects of H2O2 concentration and nozzle profile on the condensation and nozzle performance parameters are studied. The results show that by more flow expansion and crossing the saturated state of condensable components, the thrust coefficient improves up to 6%. This improvement decreases by increasing the H2O2 concentration in the reaction chamber for a fixed nozzle expansion ratio. Due to the small growth of droplets during the free molecular regime of the droplet growth in the high-speed flow, the non-equilibrium condensation continues until the nozzle outflow. In addition, although all the profiles have the same expansion ratio for nucleation start, increasing the nozzle length results in larger nano-droplets, more liquid mass fraction formation up to 4%, and moving the Wilson point to the further upstream sections in the nozzle.

Beam Position Projection Algorithms in Proton Pencil Beam Scanning.

Beam position uncertainties along the beam trajectory arise from the accelerator, beamline, and scanning magnets (SMs). They can be monitored in real time, e.g., through strip ionization chambers (ICs), and treatments can be paused if needed. Delivery is more reliable and accurate if the beam position is projected from monitored nozzle parameters to the isocenter, allowing for accurate online corrections to be performed. Beam position projection algorithms are also used in post-delivery log file analyses. In this paper, we investigate the four potential algorithms that can be applied to all pencil beam scanning (PBS) nozzles. For some combinations of nozzle configurations and algorithms, however, the projection uses beam properties determined offline (e.g., through beam tuning or technical commissioning). The best algorithm minimizes either the total uncertainty (i.e., offline and online) or the total offline uncertainty in the projection. Four beam position algorithms are analyzed (A1-A4). Two nozzle lengths are used as examples: a large nozzle (1.5 m length) and a small nozzle (0.4 m length). Three nozzle configurations are considered: IC after SM, IC before SM, and ICs on both sides. Default uncertainties are selected for ion chamber measurements, nozzle entrance beam position and angle, and scanning magnet angle. The results for other uncertainties can be determined by scaling these results or repeating the error propagation. We show the propagation of errors from two locations and the SM angle to the isocenter for all the algorithms. The best choice of algorithm depends on the nozzle length and is A1 and A3 for the large and small nozzles, respectively. If the total offline uncertainty is to be minimized (a better choice if the offline uncertainty is not stable), the best choice of algorithm changes to A1 for the small nozzle for some hardware configurations. Reducing the nozzle length can help to reduce the gantry size and make proton therapy more accessible. This work is important for designing smaller nozzles and, consequently, smaller gantries. This work is also important for log file analyses.

Design of Rocket Engine Nozzle Using Method of Characteristics

Abstract: This report focuses on the design of a 2D theoretical layout of a rocket engine nozzle. Convergent and divergent are to be designed separately with the focus on divergent part for a minimum length nozzle. The divergent part is to be designed using method of characteristics with left and right running characteristics using the known (sonic) values at the throat of the convergent-divergent nozzle. These characteristics would be pressure, density, velocity and temperature. A computer code has been designed to calculate the values of these characteristics and the end characteristics at the exit. CFD analysis has also been carried out on the designed nozzle using commercial software ANSYS.

Acoustical analysis and optimization design of the hair dryers

Abstract The sound qualities and wind speeds of the four commercial hair dryers (Panasonic, Confu, Flyco, and Philips) were investigated through experimental methods in the present study. The sound qualities included loudness, sharpness, roughness, and fluctuation strength. The experimental results showed that the maximum sound pressure level (SPL) of all hair dryers occurred at about 200 Hz except Flyco hair dryer, which occurred at about 400 Hz. The highest loudness and highest sharpness were found when the hair dryers were set to hot mode and cold mode, respectively. No consistent relationship was found between the effect of room space and SPLs of the hair dryers. The Box–Behnken design method was used to design 13 pieces of oval and rectangular nozzles, and their sound levels and wind speeds were measured. Thereafter, these experimental results were used to derive correlation coefficients between the hair dryer nozzle area, aspect ratio, nozzle length, loudness, and wind speed using the Anova analysis method. Finally, an oval nozzle and a rectangular nozzle with an area of 0.0005 m 2 {}^{2} , an aspect ratio of 1, and nozzle lengths of 0.052 and 0.055 m, respectively, were designed and were tested. These nozzles managed to reduce the sound loudness by 15 and 9.6%, respectively, while maintaining the same level of wind speed.

Stagnation point heat transfer under a free-surface jet

Laminar free-surface jet impingement is a crucial configuration for heat transfer processes. Focusing on the link between stagnation-point heat transfer and near-axis radial acceleration, its dependence on jet width and profile is studied. Thus, heat transfer depends on: fluid properties, flow rate, nozzle length, nozzle-to-plate spacing, surface tension and gravity (Pr, Re, L/d, H/d, We & Fr, accordingly). As existing theory is limited to specific cases, a new general description is developed from analogy to submerged jets. Validated by two-phase flow simulations, this description captures key jet dynamics evolution (centerline velocity, profile curvature). It reveals significant property changes during jet flight due to relaxation (L dependence) and contraction (Re/Fr dependence). Unlike submerged jets, contraction raises arrival Reynolds number, leading to additional dependencies Nu ∝ L and Nu ∝ H/Fr, and further deviations at low-We and -Re. The theory successfully predicts heat transfer across diverse conditions and converges to negligible gravity (horizontal jet) as expected.

Simulation of Internal Flow Field in Pulse Thruster Unit

Pulse thrusters are widely used in the attitude control and flight trajectory control of rotating ammunition and vertical launching ammunition, which use own pulse impulse to change the attitude and trajectory of the missile. This paper simulates the internal flow field of a double-layer pulse thruster unit (PTU). The internal flow field of the PTU is simulated at various temperatures based on the three-dimensional compressible N-S governing equations and k-ω SST turbulence model. In addition, the influence of nozzle throat length and divergence half-angle on the performance of pulse T-thruster is analyzed. The simulation results demonstrate that the thrust output error of the PTU is minimum, when the nozzle throat length of the internal pulse thruster is 38 mm. Moreover, the stability of the PTU is improved.

The utilization of novel jet extension designs in multi-jet impingement for crossflow mitigation and thermal efficiency enhancement

The aim of this study is to mitigate the distorting effect of crossflow on jet flow and to enhance heat transfer performance in multi-jet impingement heat transfer. To accomplish this objective, novel jet extension designs are proposed: a design with uniform jet extension, a design with linear jet extension in the streamwise direction, a design featuring an initial increase followed by a decrease, a design featuring an initial decrease followed by an increase, and a design where the last five jets exhibit a uniform extension inside the region mostly influenced by crossflow. The effects of various novel jet extension designs on flow and heat transfer are analyzed numerically in this study, focusing on the following: velocity contours, streamlines and velocity vectors, Local Nusselt number variations, variations of the average Nusselt number, friction coefficient, and thermal enhancement factor with Reynolds number. The study findings indicate that the investigated nozzle extension designs yield a notable enhancement of 13.26% in heat transfer. However, it is important to note that these designs may also lead to a substantial rise of 39% in the friction coefficient. In relation to thermohydraulic performance, it is found that all extension designs exhibit better results when compared to the reference state. Notably, the uniform extension design with dimensionless nozzle length of 2 demonstrates a higher degree of thermohydraulic performance.

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.

Modeling of primary breakup considering turbulent nozzle flow, internal turbulence and surface instability of liquid jet using turbulence decay theory

In heat engines utilizing fuel injection, the processes of atomization and spray formation have a significant impact on the combustion process, thereby determining both efficiency and emission characteristics. Accurate prediction and control of spray formation in fuel injection systems play a key role in improving the efficiency and environmental performance of thermal engines, especially with the emergence of carbon-neutral fuels. To achieve accurate prediction of spray mixture formation, it is imperative to refine the atomization model for the liquid jet within numerical simulations. This requires a phenomenological representation of the atomization process that avoids reliance on computational constants obtained from spray experimental results. Consequently, the present study attempts to mathematically model the turbulent nozzle flow and liquid jet atomization process, leading to the development of a novel primary breakup model. The construction of the primary breakup model involves an analysis of the turbulence at the nozzle inlet. By merging this turbulence with the turbulence resulting from wall shear flow within the nozzle, the model provides insight into the internal turbulence and surface instability of the liquid jet, encompassing the turbulence spectrum. Consequently, the influence of nozzle length on the turbulent flow within the nozzle can be understood, and the droplet formation characteristics of the liquid jet can be predicted along with its multi-wavelength dispersion characteristics. The model effectively captures the experimental results in terms of breakup length and droplet dispersion characteristics, thus adding a higher level of accuracy to numerical simulations. Ultimately, the in-depth study of this model, coupled with its comparison with experimental results, enhances the understanding of the liquid jet atomization process.

(038) Development of a Vaginal Dilator and Home Insemination Device for Cis-And Transgender People, Based on Actual Pelvic Anatomy

Abstract Introduction Genital gender-affirming surgery (gGAS) is a rapidly evolving surgical field. Specific to feminizing gGAS, one surgical option pertains to vaginoplasty with creation of a neovaginal canal. Given this canal is commonly lined with skin, peritoneum, or colon, women who undergo these procedures as part of their gender affirmation must commit to life-long self-dilation and douching to maintain canal patency and hygiene. Current commercially available dilators and douches are designed for cisgender anatomy, and are either straight, or, have an abrupt upward curve at the tip, inconsistent with neovaginal canal anatomy, which also lacks the elasticity of a cisgender woman’s vagina, making it sensitive to dilator shape, and douche nozzle length. In addition, many LGBTQ+ individuals with a uterus seek pregnancy without a male sexual partner, but few devices exist which cater to this specific population. Objective 1) To design a vaginal dilator which more accurately reflects pelvic and vaginal canal anatomy, 2) Design a novel dilator which combines dilation, douching, and depth measurement functions, and 3) Modify our new dilator-douche device for use with semen for home insemination by both cis- and transgender women, and, transgender men seeking to become pregnant. Methods A radio-opaque catheter was placed into the neovaginal canal of 12 transgender women who underwent vaginoplasty with canal creation. C-Arm fluoroscopy delineated canal curvature based on the catheter. In addition, gynecologic texts and instruments were examined to ascertain the shape of a cisgender woman’s vaginal canal. Based on these findings, a novel dilator was designed and 3-D printed. Results A smooth “S-shape” was found in the vaginal canal of both cis- and transgender women, consistent with the shape of cervical dilators. In cisgender women, the vaginal vault, which is elastic, is closer to the introitus than that of transgender women. The cervix is typically anteriorly located between 0.5 to 4cm proximal to the posterior fornix. Our vaginal dilators (Figure 1a) (five, each 8–12cm circumference) and insemination device (Figure 1b-c) (9cm circumference) reflect the same smooth S-shaped design. Our dilators have depth markings, side-wall grooves to allow air and liquid to pass, and, can be fitted with a douche-bulb to maintain hygiene. Our insemination device can accommodate a 10cc syringe and has a recessed anterior wall 0.5–4cm from the tip to deposit semen around the cervix for conception. Conclusions The design improvements shown with respect to this dilator-douche device should make dilation and douching more comfortable, improve hygiene, and, decrease the incidence of granulation tissue. Our inseminator offers a private, at-home means of achieving fertilization for both cisgender and transgender individuals. (U.S. Patent 11638808; Neovaginal and vaginal health devices) Disclosure No.

Multi-objective aerodynamic optimization of expansion–deflection nozzle based on B-spline curves

An expansion–deflection nozzle (EDN) is an altitude-compensated nozzle that can accommodate a wide range of nozzle pressure ratio (NPR) variations. An EDN design with good thrust performance under both high- and low-NPR conditions can effectively improve the launch capability of the vehicle. In this study, a multi-objective aerodynamic optimization design is developed considering the performance of the EDN in both open and closed wake modes. The design method of the outer wall and pintle of the EDN is developed using B-spline curves. The design variables are the coordinates of the control points of the curves, and the objective functions are the thrust efficiencies of the EDN at NPRs of 30 and 400. The nozzle thrust is obtained using a Reynolds Averaged Navier–Stokes (RANS) equation solver and validated by experimental results. A radial basis function neural network and a non-dominated sorting genetic algorithm II (NSGA-II) are used to construct the surrogate model and search for the Pareto front, respectively. The relationship between the nozzle contour geometry and the nozzle thrust characteristics of the four optimised individuals on the Pareto front is discussed and analysed. The results demonstrate the effectiveness of the multi-objective optimization design for an EDN. One of the optimized designs improved the thrust efficiency at NPR = 30 by 3.5 % while improving the thrust efficiency at NPR = 400 by 0.6 %. Moreover, to ensure superior performance of the EDN in both operating modes, the nozzle length and pintle ending angle must be designed as a compromise, whereas a larger nozzle exit angle is favoured for both conditions. This study demonstrates the potential of the B-spline method for nozzle optimization design.