Nozzle Contour Research Articles

Aerospike nozzle contour design using Angelino’s method and CFD validation

The goal of the present study is to implement an algorithm capable of designing linear aerospike contours and develop a numerical investigation of the altitude adaptive behavior and performance of high enthalpy flow expanded with such contoured nozzle. The contour was designed using Angelino,s rapid method, targeting an exit Mach number of 4.16. An inviscid model and viscous model (employing the realizable k-ϵ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon$$\\end{document} for turbulence) were considered and the results compared, showing that turbulent effects must be taken into account to properly simulate important flowfield aspects such as static pressure, static temperature, entropy and viscous losses. The specific impulse is used as the performance criterion and it was observed that it increased with altitude, with only a 2%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\%$$\\end{document} decrease from an ideal bell nozzle for an underexpanding operation, situation where a nearly axial exhaust plume is obtained. Conversely, when turbulent effects are taken into account, overexpanded conditions have the lowest specific impulse, being lower than a quasi-1D analysis and the inviscid case. The findings summit the advantages of the aerospike nozzle over conventional nozzles. Conventional nozzles not only typically struggle in underexpansion scenarios, but also have high side-loads in overexpansion, due to flow detaching from the nozzle’s wall. A further conclusion is that the realizable k-ϵ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon$$\\end{document} turbulent model proved a reliable and fast tool to evaluate turbulent effects that characterize the aerospike flowfield.

Nozzle Flow Characterization of the SNU Hypersonic Shock Tunnel

AbstractThis paper presents the operational capabilities and the characteristics of the nozzle flow of the Seoul National University Hypersonic Shock Tunnel (SHyST), a recently added impulse facility designed to produce high-enthalpy flows reaching up to 5 MJ/kg through hypersonic contoured nozzles. Within this investigation, emphasis is placed on the design and utilization of a pitot rake, serving as an essential instrument for quantifying pitot pressure and Mach number distributions throughout the test section. The experimental results confirm the presence of axis-symmetric behavior and spatial–temporal uniformity of the freestream Mach number at the nozzle outlet and along the test section. In addition, the study demonstrates a good agreement with the predictions of numerical simulation. Mach number validation is further supported by the measurement of shock standoff distance through schlieren visualization.

Effect of Ramp Geometry on Single Expansion Ramp Nozzle Performance Characteristics

In high-speed flight regimes, the drag plays a significant role in determining the overall performance of the aerospace vehicle. One proposed solution is to integrate a single expansion ramp nozzle (SERN) at the aft of the vehicle to mitigate the drag effects. This work investigates the effects of nozzle geometry on flow and performance characteristics of SERN with a thrust-optimized parabolic and minimum-length nozzle ramp contours, which have not been explored with regard to these aspects. A computational study is carried out on these two ramp contours using compressible Reynolds Averaged Navier–Stokes equations over a range of nozzle pressure ratio (NPR). In the tested range of NPR, the restricted shock separation is found to be the chief mode of flow separation in SERN, along with the change in the size of recirculation zone and separation bubble. At NPR 3, the thrust-optimized parabolic ramp contour shows an increment of thrust coefficient by 29.2% over the minimum-length nozzle; whereas at NPR 3.5, the minimum-length nozzle demonstrates an increment of thrust coefficient by 56.3% over the thrust-optimized parabolic at 0-deg M cowl angle. Further, in the tested range of NPR, the minimum-length nozzle shows an improved lift coefficient at 5 deg cowl angle.

Changes in Primary Nozzle Contours and Ejector Performance- A Numerical Study

Changes in Primary Nozzle Contours and Ejector Performance- A Numerical Study

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.

Computational study of flow separation in truncated ideal contour nozzles under high-altitude conditions

Flow separation in rocket nozzles has been studied mostly under sea-level conditions, which fail to take into account changes in ambient density and ambient pressure during the flight of a rocket. In the present study, numerical analysis is conducted of flow characteristics within a truncated ideal contour (TIC) nozzle to investigate the influence of ambient density and pressure on flow separation. Six different altitudes from a typical flight are considered, from a very low altitude to a high altitude. The flow is analyzed by varying the nozzle pressure ratios corresponding to these altitudes. Both cold flow and hot flow simulations are conducted. The locations of separation positions at various altitude conditions are accurately captured and are found to be in good agreement with experimental results. The results of the study establish that for a given nozzle pressure ratio, the flow separation point is shifted upstream with increasing altitude. This clearly points to a dependence of separation position on the altitude of operation for TIC rocket nozzles.

Development and Numerical validation of an Aerospike nozzle Contour Design

Aerospike nozzle simplified design and analysis, as well as test results, are presented. New techniques in nozzle design have been used to improve the performance of current rocket engines. The use of an aerospike nozzle is one such technique. It outperforms the existing proven bell nozzle in terms of overall performance. This study analyses the development and flow analysis of an aerospike nozzle at sea level, validating their results by taking into account currently used bell nozzles. The flow over the aerospike pump is investigated in higher depth using computational fluid dynamics under an autonomous fire testing condition. This test showed that the approximate design method used to determine an aerospike nozzle shape can lead to extremely effective nozzles. A model of the current 7.45 kN bell nozzle was selected as a specimen to develop an aerospike Nozzle. Gambit and Fluent software were used to model and examine the flow characteristics of building the aerospike nozzle. The developed aerospike nozzle shows a nearly 2% increase in performance over the existing nozzle.

Devising a method to design supersonic nozzles of rocket engines by using numerical analysis methods

The object of research is supersonic nozzles of liquid-propellant rocket engines. The work considers the problem of the lack of an effective method for profiling the supersonic contour of the nozzle, which will generate maximum thrust. For its solution, a method is proposed, the essence of which is approximating the nozzle contour with a power-law polynomial and determining the values of its coefficients by solving a multidimensional minimization problem using numerical modeling methods. The expression for the axial component of the thrust with the opposite sign at the specified values of atmospheric pressure and radius at the nozzle section was chosen as the objective function in this paper. Using the proposed method, contours of optimal nozzles were obtained based on polynomials of powers 2, 3, and 4, which were compared with nozzles obtained by the generally accepted Rao method. The maximum value of the relative deviation modulus calculated during the comparison did not exceed 3 %, which allows us to assert the correctness of the obtained results. The existence of such a discrepancy is explained by the difference in the numerical modeling method used. In contrast to the method of characteristics common in similar problems, the method of finite volumes of the Godunov type was used in the work. This has made it possible to reduce the sensitivity of the calculation to initial and boundary conditions and make decisions regardless of the flow regime of combustion products. In addition, the use of the extended cells method for the integration of finite volumes at the boundary of the calculation domain significantly reduced the total time of solving the problem of profiling the contour of the optimal nozzle

Результати проектування надзвукового сопла з подвійним розширенням для рідинного ракетного двигуна першого ступеня методами обчислювального аналізу

The subject of this study is dual-bell supersonic nozzles of liquid rocket engines. The goal is to design a dual-bell supersonic nozzle that will provide maximum thrust for a liquid rocket engine in the first stage of a launch vehicle by solving an optimization problem using numerical simulation methods. The goal of the study is to choose the exit pressures of each part of the dual-bell nozzle based on the known flight trajectory of the launch vehicle, set and solve the problem of optimizing the dual-bell nozzle contour, and assess the impact of the use of a dual-bell nozzle on the efficiency of a liquid-propellant rocket engine. The methods used are: numerical methods for solving the hyperbolic system of unsteady equations of gas dynamics and multidimensional minimization problems. The following results were obtained. The formulation and solution of the optimization problem of the contour of a dual-bell supersonic nozzle, considering the design limitations in the form of a fixed length of the nozzle, is carried out. By analyzing the flight path of the first stage of the launch vehicle, a first approximation of the nozzle contour was obtained. For further calculations, both sections were approximated by parabolas, the coefficients of which, together with the lengths of the sections, formed a vector of optimized parameters. An expression for the axial component of thrust with the opposite sign was used as the objective function to solve the minimization problem. Because of solving the optimization problem, a dual-bell nozzle contour was designed to provide maximum thrust. An assessment of the effectiveness of his work was also conducted. The calculated value of the average along the trajectory of the specific impulse when using a dual-bell nozzle was higher by 1.6% than when using a standard nozzle. Conclusions. The scientific novelty of the obtained results is as follows: the design of the dual-bell nozzle contour was performed by solving the problem of multidimensional optimization, taking into account the design constraints, and using computational analysis methods

Design and optimization methodology for different 3D processed materials (PLA, ABS and carbon fiber reinforced nylon PA12) subjected to static and dynamic loads

This research presents a methodology for the design and optimization of 3D printed parts with material extrusion (MEX) technology with three different commercial materials: PLA, ABS and N + CF (PA12) subjected to tensile and fatigue stresses, which included three stages: pretreatment, design of experiments and sequential optimization by statistical modeling. In the pretreatment stage, mainly the printing control factors (inner layer and contour height, printing speed, extrusion temperature, nozzle, infill arrangement and printing orientation) were determined; then, factors to optimize tensile strength as a function of printing pattern (linear, 3D, hexagonal), infill percentage (33%, 66%, 100°) and printing orientation (+45°/-45°, 0°/90°) were evaluated. Fatigue analysis was performed as a function of impression orientation using 100% infill, linear impression pattern, 5 Hz and a load range between 90 and 50% UTS. Optimization of tensile strength resulted in parts that exceeded the UTS of their corresponding filament, leading to infinite life relative to fatigue tests. Results were presented for fatigue life prediction based on Weibull analysis, Basquińs model and a multivariate response surface correlation analysis. The best fatigue behavior was related to the optimized tensile strength, the infill pattern applied to the printing orientation and the intrinsic properties of ABS (1 × 107cycles, stress up to 20 MPa). With respect to the other materials, a good fatigue behavior was highlighted at the number of cycles achieved 1 × 106 (stress up to 18 MPa) and 1 × 105 (stress up to 24 MPa) for N + CF and PLA, respectively. This study contributes to a better understanding of how printing parameters correlate with tensile and fatigue properties.

Impinging shear layer instability in over-expanded nozzle dynamics

When rocket engine nozzles operate at a high degree of over-expansion, an internal flow separation occurs with a strong unsteady shock–wave boundary layer interaction. The global dynamics results in a low-frequency mode, which is associated with the shock displacement, and a high-frequency mode, which is correlated with the shear layer–boundary layer interaction. While the mechanism responsible for the low-frequency oscillation is known, the one in charge of the high-frequency unsteadiness is not yet clear. The scope of this paper is to provide a physical explanation for this mechanism. To do that, a delayed detached eddy simulation is used to numerically reproduce the flow in the case of a sub-scale cold-gas truncated ideal contour nozzle. The obtained results are successfully compared to the experiments and confirm the presence of two non-axisymmetric wall pressure signatures at Strouhal numbers St=fDj/Uj≃0.2 and 0.3 with different azimuthal selections. To reveal the origin of such modes, a power spectral density analysis is performed in the separated region. The analysis shows that both modes originate from the external shear layer and behave as “twins” in the separated region. The reason is that both modes are two sides of the same impinging shear layer instability: the acoustic mode propagates with the sound velocity, while the hydrodynamic one propagates with the supersonic shear layer velocity. In this context, the resulting self-sustained dynamics may be due to an acoustic–hydrodynamic feedback loop involving the impinging shear layer instability of the external supersonic shear layer and the separated region.

Propulsion Aerodynamics for a Novel High-Speed Exhaust System

Abstract A key requirement to achieve sustainable high-speed flight and efficiency improvements in space access lies in the advanced performance of future propulsive architectures. Such concepts often feature high-speed nozzles, similar to rocket engines, but employ different configurations tailored to their mission. Additionally, they exhibit complex interaction phenomena between high-speed and separated flow regions at the base, which are not yet well understood. This paper presents a numerical investigation on the aerodynamic performance of a representative, novel exhaust system, which employs a high-speed nozzle and a complex-shaped cavity region at the base. Reynolds-Averaged Navier–Stokes computations are performed for a number of nozzle pressure ratios (NPRs) and freestream Mach numbers in the range of 2.7 < NPR < 24 and 0.7 < M∞ < 1.2, respectively. The corresponding Reynolds number lies within the range of 1.06 × 106 < Red < 1.28 × 106 based on the maximum diameter of the configuration. The impact of the cavity is revealed by direct comparison to an identical noncavity configuration. Results show a consistent trend of increasing base drag with increasing NPR for both configurations, owing to the jet entrainment effect. Cavity is found to have no impact on the incipient separation location of the nozzle flow. At conditions of M∞ = 1.2 and high NPRs, the cavity has a significant effect on the aerodynamic performance, transitioning nozzle operation to underexpanded conditions. This results in approximately 12% higher drag coefficient compared to the noncavity case and shifts the minimum NPR required for positive gross propulsive force to higher values.

Numerical Simulations of Supersonic Exhaust Diffuser At Various Operating Conditions

A numerical study was carried out to determine starting characteristics of a straight cylindrical supersonic exhaust diffuser of a high altitude simulation of high expansion rocket nozzle. The starting conditions of the supersonic exhaust diffuser are numerically simulated for contour nozzle of exit-to-throat area ratio of 21.77, diffuser diameter-to-nozzle throat area ratio of 23.36, and diffuser length-to-diameter ratio of 15. The evacuation performances of supersonic exhaust diffuser at various operating conditions are investigated with help of the Mach contour plots. The Mach variations along the centre line and wall of the diffuser indicate the location of the shock and flow characteristics. Validation of numerical simulation is carried out with experimental data and shows a good agreement between them. Flowfield inside the straight cylinder supersonic exhaust diffuser is presented out for stagnation to ambient pressure ratio of 5.5 - 28. The nozzle is started at the stagnation to ambient pressure ratio of about 17. The straight cylindrical supersonic exhaust diffuser is started at the stagnation pressure to ambient pressure ratio of about 21. The numerical simulations of the flowfield are able to capture the flows filled in the diffuser and the shock system is fully established in the duct.

Design and Development of Conical/Contour Nozzle For Slow Burning Solid Booster Operating In Sub-orbital Mission

In order to optimize the performance of the solid booster operating in sub-orbital altitude the contour of the nozzle needs to be tailored. The conventional convergent/divergent nozzle design is either over or under expanding for the altitude of operation. Therefore, minimizing the flow separation and losses is extremely difficult and cumbersome. In this regard, the divergent portion of nozzle plays vital role to attain the maximum performance with suitable design modification. A novel and promising concept of conical and contour nozzle divergent for slow burning propellant motors operating in sub-orbital altitude is designed and being realized for qualification test. Conical and contour nozzle divergent is a viable solution to avoid flow separation during the lower pressure and lower altitude region of the mission. The design arrived as per the mission requirement, has a conical divergent up to 737 mm from throat plane and third order polynomial profile up to exit, which will give a turn back angle of 5°.The injection point of Secondary Injection Thrust Vector Control System (SITVC) of nozzle is chosen at 45% of total distance from throat plane to exit plane. The present study brings out the theretical estimations of a conical/contour nozzle perfromance with a slowest burning solid booster operating at lower altitude, < 35 km. Theoretical Computational Fluid Dynamics (CFD) simulation study is carried out to assess the effect of nozzle profile on the flow transition. The basic design methodology adopted to avoid flow separation and the governing formulations are presented in this paper.

Design and Computational Analysis of an Axisymmetric Contoured Supersonic Propulsion Nozzle

The design of supersonic axisymmetric nozzles to a required exit Mach number necessitates applying the Method of Characteristics (MoC) that reduces the partial differential equations system of hyperbolic form governing such internal flow-fields to two ordinary differential equations known as the characteristic and the compatibility equations. These relationships are then transformed into finite difference equations and solved using an appropriate predictor-corrector algorithm.The present study applies the MoC to the design of a contoured nozzle that accelerates the combustion gases to supersonic velocities. The selected configuration has a throat constituted of two circular arcs with the one downstream attached to a 2nd-order polynomial profile at the attachment point. The solution, in terms of the static pressure along the centerline and the wall is obtained. It was found that the flow expands gradually without any instability or possibility of shock waves. A gradual expansion represented by a decrease in pressure is noticed immediately downstream of the throat, the flow tending to expand gradually from the throat to the exit. Along the wall, the expansion is important immediately downstream of the throat while it tends to stabilize downstream to reach the ambient pressure at the outlet. In terms of performance, the thrust coefficient developed shows the great expansion process within the divergent supersonic section. The configuration is also found to develop a great specific thrust.

Simulation of parameters effects on fluid flow behavior in the spraying nozzle: A case study of greenhouse cultivation

The study aims to investigate the effect of nozzle diameter size and pressure on the angle and flow rate of the spray nozzle in greenhouse cultivation. The misting system is a new method that is used to provide humidity and reduce the temperature of the greenhouse environment. The study used a factorial experiment in a randomized completely block design (RCBD) to investigate and compare the effect of pressure at three levels of 20, 40, and 60 bar on three types of fog sprayers (nozzle type of 0.05, 0.04, and 0.03) on the quality of spray pattern and particle distribution. The results of the analysis of variance showed that the treatments of spray type, pressure, and interaction of both treatments had a significant difference at the level of 1%. The highest spray angle of 84.93° is related to the pressure of 60 bar, and the lowest spray angle of 71.27° is related to the pressure of 20 bar. The pressure was directly related to the spray angle, and increasing the pressure increased the spray angle in the nozzle. The study also found that the best pressure in the new nozzle for the frequency distribution contour is 40 bar, and the new nozzle contours show that this type of nozzle has increased the uniformity of spraying. Overall, the findings suggest that controlling humidity and temperature in the greenhouse through the use of misting systems and optimized nozzle design can improve the speed and uniformity of plant growth and increase the quality and quantity of plant production in greenhouse cultivation.

Study of fluid-dynamic behavior in a convergent–divergent nozzle by shape optimization using evolutionary strategies algorithms

The performance and thrust of a rocket propulsion system are based mainly on the utilization of the enthalpy of the propellants in the combustion chamber. This accumulated energy is transformed into kinetic energy by the expansion and acceleration of the gases produced by the chemical reaction of combustion, using a device known as a nozzle. This project studies the aerodynamic profile to trace the wall contour of a C-D nozzle based on the technical operating conditions of a rocket engine. The wall contour is traced using different design methods and, for each nozzle section, the behavior of the fluid-thermal properties of the flow field along the flow trajectory of the aerospace nozzle is analyzed. This is necessary because, in each wall contour suggested by the models, the angle of inclination of the curvature is different (the concavity or shape of the curve changes) and, therefore, the physical magnitudes of the properties vary according to the contour. To determine which design complies with the concept that processes occurring within a nozzle are isentropic and reversible, a statistical analysis of data dispersion is performed to choose the design with the lowest energy losses as a function of friction and entropy. An unconstrained optimization is applied to maximize or minimize the cross-sectional area of the nozzle geometric profile through genetic algorithms. To corroborate the nozzle wall contour and the design methodology used, a simulation is performed to evaluate the similarities between the operating characteristics and Mach number with another nozzle of a J-2 rocket engine.

Research on transonic flow of nozzle contractions for providing an asymptotic solution

The effect of a contraction on the flow in a supersonic nozzle is investigated, and improvements are made to provide an accurate asymptotic solution of transonic flow. Owing to the elliptical characteristic of the governing equation, supersonic nozzle contractions are not rigorously designed from aerodynamics theory. The contraction effect is often masked by the design defects of the supersonic nozzle contours and, therefore, is hard to evaluate independently. In this study, the authors use a sufficiently advanced supersonic contour to support numerical and theoretical research on various contractions. The results show that the commonly used contractions lead to abrupt changes in transonic flow field parameters, and the degree does not vary with the nozzle Mach number. Based on the work of Hall, the accurate asymptotic solution of the sonic line in the nozzle is derived. Most practical sonic lines provided by various contractions are inconsistent with the accurate asymptotic solution, which further affects the uniformity of the supersonic flow. By iterating the shift of the Witoszynski contraction, the end point curvature is found to be the core parameter. On this basis, three improved contractions are proposed. These new contractions allow discontinuities in wall curvature and avoid the problem inherent in Sivells' cylindrical-quartic–conical-quartic contraction. Each improved contraction successfully coincides with theoretical transonic flow, helping the supersonic nozzle eliminate waves completely and achieve a high degree of flow uniformity.

Experimental investigation of mini supersonic wind tunnel for flow visualization

The present study proposes to design, fabricate and investigate a miniature supersonic wind tunnel at an affordable cost, safe to operate, and reliable for education purposes. The configuration consists of a high pressure reservoir, and mini tunnel which will be used for providing the supersonic flow over aerodynamic models. To design the mini supersonic wind tunnel, the method of characteristics is used to ensure that any shocks that arise in contact with the surface do not impact the uniformity and velocity of the flow through the duct. To achieve the supersonic flow, the nozzle contour of the supersonic portion of the wind tunnel is built in such a way that the shocks nullify each other and have zero effect on the velocity of the flow. For compressible flow visualization, an affordable Schlieren setup consisting of a torch, mirrors, and a mobile camera is used for flow visualization. Finally, the visualization results of the present study is in good relation with the theoretical calculations. The present facility is also calibrated by measuring the oblique shock angle in the test section, in the range of Mach number 1.6 to 1.8.

The effect of nozzle contour on the vibroacoustic loads that form from high area ratio rocket nozzles during sea level launch

An accurate assessment of the vibro-acoustic loads that form during startup of large area ratio rocket nozzles is important for sea-level launch vehicle design and certification. These loads are driven principally by various flow and shock patterns that form inside the nozzle, which are unique to the nozzle contour. This presentation will review a number of laboratory-scale measurements of different nozzle contours and configurations reported by Baars and Tinney, Exp. Fluids, (2013), Donald et al. AIAA Journal (2014), Canchero etal. AIAA Journal (2016), and Rojo et al. AIAA Journal (2016) as it relates to launch platforms of current interest. In particular are the various sources of noise pertaining to transonic resonance, broadband shock associated noise, and the end-effects-regime (EER). The latter of these is unique to the thrust-optimized parabolic contour nozzle as is used on the current Space Launch System vehicle. This EER event occurs when the annular flow structure is in a partial restricted-shock separated (RSS) flow state and is categorized by an onset of relatively low frequency energy driven by intermittent buffeting between RSS flow and partial free shock separated flow at the nozzle lip.