Nozzle Model Research Articles

Modeling condensation of Methane-Water vapor mixtures in the Hedbäck Nozzle: A comparative study of 2D and 3D geometries

This study investigated the condensation behavior of a binary mixture of methane (CH4) and water vapor (H2O) within the Hedbäck nozzle, employing both 2D and 3D modeling approaches. The 2D model was initially developed to analyze the effects of inlet parameters and mixture’s condensation characteristics. However, the inherent limitations of the 2D model in capturing the full complexity of the flow dynamics prompted a transition to a 3D modeling approach. The research explored two distinct 3D geometries: one created by extruding the 2D section and another by rotating the 2D cross-section around its axis. The latter, which more accurately represented real-world nozzle conditions, revealed differences in flow patterns, condensation behavior, and entropy generation, emphasizing the crucial role of 3D effects in the condensation process. The sensitivity of the numerical simulation results to various nucleation theories and droplet growth models was acknowledged, and the most appropriate theory and model were meticulously selected. This approach minimized discrepancies between numerical modeling outcomes and experimental data, enhancing the accuracy and reliability of the findings. The 2D results indicate a 40.5% increase in the inlet partial pressure with a constant temperature and mass fraction, resulting in a 56% rise in maximum liquid mass fraction. Similarly, a 3.6% decrease in inlet temperature under constant pressure and mass fraction increases the average radius of outlet droplets by more than 13%. In addition, entropy generation analysis revealed that less than 1% of entropy generation is attributed to mean flow, whereas 99% is linked to turbulent fluctuations. Moreover, the 3D models demonstrated markedly different entropy generation rates compared to the 2D model, highlighting the importance of 3D approach for a comprehensive understanding of thermodynamic irreversibility within the system.

Enhanced dynamic modeling of regenerative CO2 transcritical power cycles: Comparative analysis of Pham-corrected and conventional turbine models

Turbine modeling plays a critical role in assessing system power output and performance in CO₂ transcritical power cycle (CTPC) systems, particularly under dynamic operating conditions. Conventional turbine models often fail to provide accurate predictions when inlet parameters deviate from the design point, leading to discrepancies in system behavior. This paper introduces a novel methodology by integrating a Pham-based corrected turbine performance map into a regenerative CTPC dynamic system. This approach enhances turbine modeling accuracy compared to traditional models, such as the uncorrected turbine performance map, nozzle model, and empirical model. The proposed Pham-corrected model method improves system response stability, particularly in terms of inlet pressure and CO₂ mass flow rate under heat source temperature reductions, offering more reliable performance predictions. In contrast, the empirical model shows substantial deviations in net power output (32 kW or 4.0 %) and thermal efficiency (1.36 %), leading to longer system stabilization times. The Pham-corrected and uncorrected turbine performance map models exhibit similar responses under cooling water mass flow rate reductions but diverge in turbine inlet pressure trends compared to the nozzle and empirical models. Additionally, the uncorrected turbine performance map model shows significant deviations in net power (25.6 kW or 3.17 %) and thermal efficiency (0.5 %) under a 10 % reduction in pump speed. This study highlights the importance of correcting turbine inlet parameters and addressing prediction deviations in conventional models. The Pham-corrected turbine model improves reliability, performance prediction, and design optimization, especially under fluctuating heat sources. With its potential to enhance system stability and efficiency, this methodology offers significant prospects for future CTPC applications, including waste heat recovery and renewable energy integration.

Modeling and analysis of nonlinear dynamics of axisymmetric vector nozzle based on deep neural network

Abstract The axisymmetric nozzle mechanism is the core part for thrust vectoring of aero engine, which contains complex rigid-flexible coupled multibody system with joints clearance and significantly reduces the efficiency in modeling and calculation, therefore the kinematics and dynamics analysis of axisymmetric vectoring nozzle mechanism based on deep neural network is proposed. The deep neural network model of the axisymmetric vector nozzle is established according to the limited training data from the physical dynamic model and then used to predict the kinematics and dynamics response of the axisymmetric vector nozzle. This study analyses the effects of joint clearance on the kinematics and dynamics of the axisymmetric vector nozzle mechanism by a data-driven model. It is found that the angular acceleration of the expanding blade and the driving force are mostly affected by joint clearance followed by the angle, angular velocity and position of the expanding blade. Larger joint clearance results in more pronounced fluctuations of the dynamic response of the mechanism, which is due to the greater relative velocity and contact force between the bushing and the pin. Since axisymmetric vector nozzles are highly complex nonlinear systems, traditional numerical methods of dynamics are extremely time-consuming. Our work indicates that the data-driven approach greatly reduces the computational cost while maintaining accuracy, and can be used for rapid evaluation and iterative computation of complex multibody dynamics of engine nozzle mechanism.

Movement Characteristics of Droplet Deposition in Flat Spray Nozzle for Agricultural UAVs

At present, research on aerial spraying operations with UAVs mainly focuses on the deposition outcomes of droplets, with insufficient depth in the exploration of the movement process of droplet deposition. The movement characteristics of droplet deposition as the most fundamental factors affecting the effectiveness of pesticide application by UAVs are of great significance for improving droplet deposition. This study takes flat spray nozzles as the research object, uses the Particle Image Velocimetry (PIV) technique to obtain movement data of water droplet deposition under the influence of rotor flow fields, and investigates the variation characteristics of droplet deposition speed under different influencing factors. The results show that the deposition speed and the distribution area of high-speed (>12 m/s) particles increase with the increase of rotor speed, spraying pressure, and nozzle size. When the rotor speed increases from 0 r/min to 1800 r/min, the average increase in maximum droplet deposition speed for nozzle models LU120-02, LU120-03 and LU120-04 is 33.26%, 19.02%, and 7.62%, respectively. The rotor flow field significantly increases the number of high-speed droplets, making the dispersed droplet velocity distribution more concentrated. When the rotor speed is 0, 1000, 1500, and 1800 r/min, the average decay rates of droplet deposition speed are 36.72%, 20.00%, 15.47%, and 13.21%, respectively, indicating that the rotor flow field helps to reduce the decrease in droplet deposition speed, enabling droplets to deposit on the target area at a higher speed, reducing drift risk and evaporation loss. This study’s results are beneficial for revealing the mechanism of droplet deposition movement in aerial spraying by plant protection UAVs, improving the understanding of droplet movement, and providing data support and guidance for precise spraying operations.

Research on Jet Structure and the Virtual Nozzle Model for High-pressure Hydrogen Leakage from Rectangular Nozzles

The shockwave structure generated after high-pressure hydrogen leakage presents a challenge for simulations. To simplify the shockwave structure, virtual nozzle models have been proposed. However, these models are based on circular leak openings, lacking research on rectangular nozzles. This study utilizes OpenFOAM to investigate the characteristics of high-pressure rectangular nozzle hydrogen leakage with pressures up to 90 MPa. A real gas model and a new thermophysical model are adopted to better demonstrate the shock wave structure of the jet under high pressure. The study examines the characteristics of jet structures after leakage from rectangular nozzles with different pressures, aspect ratios, and diameters. The critical conditions for forming Mach disks in rectangular jets are proposed, and an empirical relationship for the position of the central compression wave is summarized. By combining the isentropic expansion equation, mass conservation, momentum conservation, energy conservation, and shock wave relationship before and after, a virtual nozzle model for rectangular nozzles is proposed. Using this model as the boundary condition for calculating large-scale diffusion and comparing the results with previous experimental and simulation data demonstrates its accuracy.

Numerical simulation of condensation of supercritical water gasification products in a supersonic nozzle

The clean and efficient separation of supercritical water gasification products (SCWGP) has emerged as a significant challenge in supercritical water gasification technology. This paper proposes the use of a supersonic nozzle for the condensation and separation of H2 and CO2 from SCWGP, leveraging the high-pressure characteristics of these products. By establishing a flow model and a condensation model for the supersonic nozzle, the effects of inlet pressure and inlet temperature on the condensation process are analyzed. The analysis reveals that the latent heat released during condensation causes an abnormal distribution of pressure and temperature within the nozzle. When the inlet pressure of the nozzle is increased from 7.0 to 9.0 MPa, the liquid phase mass fraction at the outlet rises from 5.3 × 10−3 to 0.056. Similarly, when the inlet temperature is lowered from 300.0 to 290.0 K, the liquid phase mass fraction at the outlet also rises from 5.3 × 10−3 to 0.058. The increase in inlet pressure leads to the condensation location shifting toward the throat by ∼8.5 × 10−3 m⋅MPa−1, while the impact of inlet temperature is approximately −2.3 × 10−3 m⋅K−1. The nucleation rate in the nozzle is always concentrated in a small region.

Computational fluid dynamics modeling of coronary artery blood flow using OpenFOAM: Validation with the food and drug administration benchmark nozzle model.

Cardiovascular disease (CVD), a global health concern, particularly coronary artery disease (CAD), poses a significant threat to well-being. Seeking safer and cost-effective diagnostic alternatives to invasive coronary angiography, noninvasive coronary computed tomography angiography (CCTA) gains prominence. This study employed OpenFOAM, an open-source Computational Fluid Dynamics (CFD) software, to analyze hemodynamic parameters in coronary arteries with serial stenoses. Patient-specific three-dimensional (3D) models from CCTA images offer insights into hemodynamic changes. OpenFOAM breaks away from traditional commercial software, validated against the FDA benchmark nozzle model for reliability. Applying this refined methodology to seventeen coronary arteries across nine patients, the study evaluates parameters like fractional flow reserve computed tomography simulation (FFRCTS), fluid velocity, and wall shear stress (WSS) over time. Findings include FFRCTS values exceeding 0.8 for grade 0 stenosis and falling below 0.5 for grade 5 stenosis. Central velocity remains nearly constant for grade 1 stenosis but increases 3.4-fold for grade 5 stenosis. This research innovates by utilizing OpenFOAM, departing from previous reliance on commercial software. Combining qualitative stenosis grading with quantitative FFRCTS and velocity measurements offers a more comprehensive assessment of coronary artery conditions. The study introduces 3D renderings of wall shear stress distribution across stenosis grades, providing an intuitive visualization of hemodynamic changes for valuable insights into coronary stenosis diagnosis.

Numerical Simulation and Flow Field Analysis of Porous Water Jet Nozzle Based on Fluent

The water jet nozzle is a penetrating drilling tool, which sends the pumped water to the nozzle through a high-pressure hose. It can work in a variety of working environments. When it dredges the blockage in the pipeline, its structural parameters will affect the jet flow field in the pipeline. Taking the self-propelled water jet nozzle as the research object, SolidWorks was used to establish the nozzle model with different parameter structures. Based on Fluent, the k-ε turbulence model was used to simulate the jet of nozzles with different nozzle sizes and arrangements in the pipeline. The distribution of the jet flow field and the change in velocity and displacement of nozzles with different parameters in the pipeline were compared, and then computational fluid dynamics (CFD) were used to process the simulation data for further research. The results show that when the inclination angle of the rear nozzle is 35°, the attenuation of the front jet velocity and the fluctuation of the wall fluid velocity are the smallest. When the nozzle aperture is increased from 2 mm to 3.5 mm, the vortex area inside the pipe is reduced, and the velocity attenuation of the front jet is also reduced, with the velocity attenuation rate decreasing by about 10%. This study provides a reference for the design and parameter optimization of self-propelled water jet nozzles.

Characterization of the Three-Dimensional Flowfield over a Truncated Linear Aerospike

The work focuses on the characterization of the flowfield over a truncated linear aerospike by combining theoretical grounds, numerical simulations and experimental tests. The experimental investigations are carried out on a test rig designed at Politecnico di Torino for advanced nozzle testing. Fully three-dimensional CFD analyses are performed on the actual geometry of the experimental nozzle model. At low nozzle pressure ratios (nprs) the analysis combines numerical simulations and experimental testing, which are also used for validating the CFD results. At higher nprs, the flowfield characterization is performed only by three-dimensional CFD analyses. In addition to the validation of the numerical method, the edge effects at different nprs have been observed.

Genetic algorithm based optimization of nozzle profiles for a hydrogen turbo-expander

Liquid hydrogen plays an important role in the large scale storage and long-distance transportation. The development of hydrogen turbo-expander is the key to increase the efficiency of hydrogen liquefaction, reducing the cost of liquid hydrogen production, storage and transportation. In this paper, a numerical model of hydrogen nozzle is established and validated against experimental data. The performance of four traditional nozzle profiles in hydrogen turbo-expanders is simulated and analyzed. The poor uniformity of outlet flow angle is generally found in these nozzle profiles, leading to nozzle passage and impeller incidence losses in turbo-expanders. A genetic algorithm based method is proposed to optimize the nozzle profiles. The optimization objectives involve the nozzle efficiency, the uniformity of the nozzle outlet angle and the uniformity of the outlet Mach number. The deviations in the outlet angle and Mach number of the optimized nozzle are reduced by 50.26 % and 14.03 %, respectively, while the nozzle efficiency reaches 98.64 %. The matching characteristics of the optimized nozzle with the impeller are obtained via simulation of a hydrogen turbo-expander, and the results indicate the expansion efficiency can be increased by 1.53 %.

PIV And Schlieren Measurements Of A Linear Plug Nozzle Jet Interacting With External Flow

Plug nozzles represent a promising concept as part of a propulsion system for space launchers. The ability to adapt the nozzle jet to the ambient pressure level improves thrust performance in overexpanded operating conditions compared to conventional bell nozzles. In this study, the dynamics of a jet flow of a cold air plug nozzle model are investigated by means of PIV and high-speed schlieren measurements. For a fixed nozzle pressure ratio, the jet flow is studied in an externalouter flow environment with sub-, trans-, and supersonic Mach numbers. The effect of plug truncation is analyzed as well. It is found that the outer Mach number strongly influences the flow pattern, local velocity magnitudes and aerodynamic modes. The frequency and dominance of vortex shedding and jet screeching modes are found to be highly dependent on the Mach number of the surrounding flow. A truncated plug introduces local accelerations in its base wake region, causing an increased shock strength in the jet structure. In addition,it causes severe periodic fluctuations in the flow that are transmitted to the shear layer and induce acoustic wave emissions. The impact of the plug length on the flow dynamics has been seen to decrease with increasing outer Mach number.

A novel semi-flexible coaxial nozzle based on fluid dynamics effects and its self-centering performance study

Coaxial nozzles are widely used to produce fibers with core–shell structures. However, conventional coaxial nozzles cannot adjust the coaxiality of the inner and outer needles in real-time during the fiber production process, resulting in uneven fiber wall thickness and poor quality. Therefore, we proposed an innovative semi-flexible coaxial nozzle with a dynamic self-centering function. This new design addresses the challenge of ensuring the coaxiality of the inner and outer needles of the coaxial nozzle. First, based on the principles of fluid dynamics and fluid–structure interaction, a self-centering model for a coaxial nozzle is established. Second, the influence of external fluid velocity and inner needle elastic modulus on the centering time and coaxiality error is analyzed by finite element simulation. Finally, the self-centering performance of the coaxial nozzle is verified by observing the coaxial extrusion process online and measuring the wall thickness of the formed hollow fiber. The results showed that the coaxiality error increased with the increase of Young’s modulus E and decreased with the increase of flow velocity. The centering time required for the inner needle to achieve force balance decreases with the increase of Young's modulus (E\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E$$\\end{document}) and fluid velocity (vf\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${v}_{f}$$\\end{document}). The nozzle exhibits significant self-centering performance, dynamically reducing the initial coaxiality error from 380 to 60 μm within 26 s. Additionally, it can mitigate the coaxiality error caused by manufacturing and assembly precision, effectively controlling them within 8 μm. Our research provides valuable references and solutions for addressing issues such as uneven fiber wall thickness caused by coaxiality errors.

Simulation and experimental benchmarking of a proton pencil beam scanning nozzle model for development of MR-integrated proton therapy.

MR-integrated proton therapy is under development. It consists of the unique challenge of integrating a proton pencil beam scanning (PBS) beam line nozzle with an magnetic resonance imaging (MRI) scanner. The magnetic interaction between these two components is deemed high risk as the MR images can be degraded if there is cross-talk during beam delivery and imageacquisition. To create and benchmark a self-consistent proton PBS nozzle model for empowering the next stages of MR-integrated proton therapy development, namely exploring and de-risking complete integrated prototype system designs including magnetic shielding of the PBS nozzle. Magnetic field (COMSOL ) and radiation transport (Geant4) models of a proton PBS nozzle located at OncoRay (Dresden, Germany) were developed according to the manufacturers specifications. Geant4 simulations of the PBS process were performed by using magnetic field data generated by the COMSOL simulations. In total 315 spots were simulated which consisted of a scan pattern with 5cm spot spacings and for proton energies of 70, 100, 150, 200, and 220MeV. Analysis of the simulated deflection at the beam isocenter plane was performed to determine the self-consistency of the model. The magnetic fringe field from a sub selection of 24 of the 315 spot simulations were directly compared with high precision magnetometer measurements. These focused on the maximum scanning setting of 20cm beam deflection as generated from the second scanning magnet in the PBS for a proton beam energy of 220MeV. Locations along the beam line central axis (CAX) were measured at beam isocenter and downstream of 22, 47, 72, 97, and 122cm. Horizontal off-axis positions were measured at 22cm downstream of isocenter ( 50, 100, and 150cm from CAX). The proton PBS simulations had good spatial agreement to the theoretical values in all 315 spots examined at the beam line isocenter plane (0-2.9mm differences or within 1.5% of the local spot deflection amount). Careful analysis of the experimental measurements were able to isolate the changes in magnetic fields due solely to the scanning magnet contribution, and showed 1.9 1.2 -9.4 1.2 changes over the range of measurement locations. Direct comparison with the equivalent simulations matched within the measurement apparatus and setup uncertainty in all but one measurementpoint. For the first time a robust, accurate and self-consistent model of a proton PBS nozzle assembly has been created and successfully benchmarked for the purposes of advancing MR-integrated proton therapy research. The model will enable confidence in further simulation based work on fully integrated designs including MRI scanners and PBS nozzle magnetic shielding in order to de-risk and realize the full potential of MR-integrated proton therapy.

A development of a surface frost prediction model for hydrogen fueling nozzle

This study presents a simulation model to predict the nozzle surface freezing phenomenon that causes delays in refueling hydrogen vehicles. Nozzle surface freezing is known to occur when vehicles are refueled consecutively. The developed model allows consecutive refueling of vehicles and incorporates the actual nozzle material to accurately calculate the nozzle surface temperature. The simulation results indicate that, under the applied boundary conditions, the nozzle surface temperature reaches freezing conditions during the third refueling cycle, suggesting the potential suitability of using hot air or nitrogen after the second refueling. Future applications include exploring different boundary conditions in the developed hydrogen refueling model to simulate internal refueling pressure, temperature and nozzle icing conditions. This optimisation could facilitate decision making for the implementation of hot air or nitrogen, which could potentially reduce refueling time and contribute to cost savings at hydrogen refueling stations, depending on specific environmental conditions.

Most appropriate nozzle of six-rotor UAV for prescribed spraying liquid in tea plantation under effects of downwash flow structure in hover

Downwash flow structure development has been an important challenge for Unmanned Aerial Vehicle (UAV) to spray tea although the UAV spray is commonly used in crops, dominantly due to the downwash flow structure development in tea plantations more severe than those in crops. Here the UAV spray for tea cultivation is improved through the relationship between nozzle and spraying liquid, or, by choosing the most appropriate nozzle for the prescribed spraying liquid. As a preliminary step, the UAV spray has been studied under effects of downwash flow structure in hover. The six-rotor UAV with four commonly-used nozzles (VP110-02, XR110-02, FPV110-02, and KZ80-04) is used as the representative. Bifenthrin, widely sprayed for tea cultivation, is used as the prescribed spraying liquid. A three-dimensional model of nozzle & flow fragmentation is developed to estimate the nozzle performances. This study demonstrates that nozzle KZ80-04 is the most suitable for Bifenthrin in tea plantation and provides insight into designing effective UAV spray in crops.

Multiphase flow and nozzle wear with CFD-DEM in high-pressure abrasive water jet

The issue of wear failure in High-Pressure Abrasive Water Jet (HP-AWJ) nozzles is an unavoidable challenge, and studying methods to enhance and predict the effective lifetime of nozzles is worth deep exploration. This paper employs a CFD-DEM coupling numerical approach to investigate wear phenomena inside the HP-AWJ nozzle, aiming to capture the realistic particle wear and erosion failure issues at the focusing tube region, which is a high-wear area of the HP-AWJ nozzle. Furthermore, the study considers realistic particles and nozzle wall constitutive models, incorporating material properties into the physical model, and employs computer-aided design methods to reflect wear failure conditions at different time intervals in the inner wall of the focusing tube at the nozzle. The results demonstrate that the number of realistic particles and initial inlet velocity has no impact on the particle exit kinetic energy. However, the particle-wall restitution coefficient affects the average particle kinetic energy at the outlet in the AWJ nozzle. The equivalent model of the realistic particles reflects the influence of the particle roundness on particle kinetic energy, acceleration, and stress concentration variations in the nozzle. These variations further affect the particle erosion rate on the nozzle wall and the actual wear failure problems on the wall surface. Finally, by combining the proposed erosion and wear model, a representative erosion profile at the AWJ focusing tube location comparable to experimental results is obtained, and the wear depth of the focusing tube changing with time is also studied. The results and methodologies presented in this paper provide valuable guidance for controlling the effective service lifetime of the AWJ nozzle, improving machining efficiency, and extending the lifespan of the AWJ nozzle.

Erosion behaviour of B4C/TiB2/Mo ceramic nozzles

Abstract B4C/TiB2/Mo ceramic nozzles were obtained by uniaxial hot-pressing. The mechanical properties and erosion behaviour of B4C/TiB2/Mo ceramic nozzles were investigated. Volume erosion rate was used to rank the erosion behaviour of the B4C/TiB2/Mo ceramic nozzles. The relationship between mechanical properties and the volume erosion rate of the nozzles was discussed. X-ray diffraction analysis showed that in-situ reaction to form TiB2 happened during sintering. Scanning electron microscopy was employed to observe the fracture surfaces and eroded surfaces of B4C/TiB2/Mo ceramic nozzles. A model of erodent particles and nozzle during the erosion test was established using the JH2 model. The maximum von Mises stresses on the entry, middle and exit surfaces of the nozzle were calculated. The result showed that the hardness played a key role in influencing the erosion behaviour of B4C/TiB2/Mo ceramic nozzles. Erosion mechanisms of B4C/TiB2/Mo ceramic nozzles at the entry, middle and exit bore area were mainly brittle fracture, fracture & plowing and micro-plowing, respectively.

Numerical Simulation and Consequence Analysis of Full-Scale Jet Fires for Pipelines Transporting Pure Hydrogen or Hydrogen Blended with Natural Gas

The use of existing natural gas pipelines for the transport of hydrogen/natural gas mixtures can achieve large-scale, long-distance and low-cost hydrogen transportation. A jet fire induced by the leakage of high-pressure pure hydrogen and hydrogen-blended natural gas pipelines may pose a severe threat to life and property. Based on the Abel–Nobel equation of state and a notional nozzle model, an equivalent pipe leakage model is established to simulate high-pressure pipeline gas leakage jet fire accidents. Large-scale high-pressure hydrogen and natural gas/hydrogen mixture jet fires are simulated, showing the jet impingement process and obtaining an accurate and effective simulation framework. This framework is validated by comparing the simulated and experimental measured results of flame height, flame appearance and thermal radiation. Several combustion models are compared, and the simulated data show that the non-premixed chemical equilibrium combustion model is superior to other combustion models. The influence of the pipe pressure and the hydrogen blending ratio on the consequences of natural gas/hydrogen mixture pipeline leakage jet fire accidents is explored. It is found that when the hydrogen blending ratio is lower than 22%, the increase in the hydrogen blending ratio has little effect on the decrease in the thermal radiation hazard distance.

Analysis of Jet Blast Distance of a Refined Engine Nozzle Model for Departing Aircraft

To evaluate the influence distance and evolution law of the jet blast under the full thrust state of the aircraft engine, we constructed a refined single-engine nozzle model in this study. Using a specific B737-800 engine as an illustrative example, this model takes into account both the internal combustion of the engine and the shearing effect of the tail cone on the airflow; based on a structured grid, the grid and far-field independence of the numerical solution were verified. The numerical simulation results obtained via the Fluent software were compared with the data outlined in the Boeing aircraft characteristics manual for a thorough analysis. Our results indicated that the calculated jet influence distance from the refined nozzle model aligns more closely with the data in the aircraft characteristics manual, albeit with superior accuracy compared to the simplified nozzle model employed in previous studies. The findings of this study can serve as a valuable reference for computing jet influence distances across various aircraft types and engine models, providing data support for the study of safety intervals for aircraft crossing the runway behind the takeoff point.

Updating Nonlinear Stochastic Dynamics of an Uncertain Nozzle Model Using Probabilistic Learning With Partial Observability and Incomplete Dataset

Abstract This article introduces a methodology for updating the nonlinear stochastic dynamics of a nozzle with uncertain computational model. The approach focuses on a high-dimensional nonlinear computational model constrained by a small target dataset. Challenges include the large number of degrees-of-freedom, geometric nonlinearities, material uncertainties, stochastic external loads, underobservability, and high computational costs. A detailed dynamic analysis of the nozzle is presented. An updated statistical surrogate model relating the observations of interest to the control parameters is constructed. Despite small training and target datasets and partial observability, the study successfully applies probabilistic learning on manifolds (PLoM) to address these challenges. PLoM captures geometric nonlinear effects and uncertainty propagation, improving conditional mean statistics compared to training data. The conditional confidence region demonstrates the ability of the methodology to accurately represent both observed and unobserved output variables, contributing to advancements in modeling complex systems.