Range Of Nozzle Pressure Ratios Research Articles

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.

Evaluation of generalized k-ω turbulence model in strong separated flow estimation of thrust optimized parabolic nozzle

One of the frequently reported defects of RANS-based turbulence models is overestimation of turbulent kinetic energy production in high speed separated flow problems, which causes significant prediction errors. The correct estimation of such flow in thrust optimized parabolic nozzles extremely depends upon the accurate prediction of the onset of flow separation. In this paper, firstly, the significant error of conventional RANS-based turbulence models is shown to predict the onset of flow separation in this type of nozzles. Then, the prediction accuracy is improved through the modification of the essential parameters of the generalized k-ω (GEKO) turbulence model. It was found that modifying the separation and mixing parameters of the GEKO model to realize the turbulent kinetic energy production resulted in the accurate prediction of onset of flow separation at the extensive range of nozzle pressure ratios. Using this modified model with new coefficients reduced the error of about 30% of the k-ω-sst model in estimating the onset of flow separation. Also, the nozzle pressure value at which the transition from free shock separation (FSS) to restricted shock separation (RSS) occurs is well predicted by this approach. After strengthening the turbulence model, the flow physics has been investigated with increasing and decreasing nozzle chamber pressure. The length of the separation shock and reflected shock waves which impose the presence of FSS or RSS patterns and transitional phenomena are discussed. Our new findings show that unlike the transition from FSS to RSS, the inverse transition from RSS to FSS did not depend on the length of the separation and reflective shocks.

Perturbation-based active flow control in overexpanded to underexpanded supersonic rectangular twin jets

The effects of perturbation-based active flow control on supersonic rectangular twin jets (SRTJ) over a wide range of nozzle pressure ratios (NPR = 2.77 to 6.7, corresponding to fully expanded Mach numbers Mj = 1.3 to 1.9) were investigated. The aspect ratio and design Mach number for the bi-conic, converging-diverging nozzles were 2 and 1.5, respectively. The flow and acoustic fields of SRTJ are known to couple, often generating high near-field (NF) pressure fluctuations and elevated far-field (FF) noise levels. Large-scale structures (LSS), or equivalently instability waves or wave packets, are responsible for mixing noise, broadband shock-associated noise, screech and coupling. The primary objective of this research was to manipulate the development of LSS in this complex flow to better understand and mitigate their effects. The organization and passage frequency of the LSS were altered by excitation of instabilities over a wide range of frequencies and modes. Key findings include: (1) the screech mode of each jet was flapping along its minor axis; (2) the jets coupled, out-of-phase primarily in overexpanded cases and in-phase primarily in underexpanded cases, along the minor axis of the SRTJ; (3) coupling has significant effects on the NF pressure fluctuations, but only minor effect on the FF noise; (4) standing waves were observed only on the minor axis plane of the SRTJ; (5) altering or suppressing coupling can significantly reduce NF pressure fluctuations; (6) two high-frequency excitation methods proved effective in reducing the FF noise; and (7) nonlinear interactions between the screech tones and excitation input were observed in controlled cases in which screech was only partially suppressed.

Onset conditions for Mach disk formation in underexpanded jet flows

In this study, the formation conditions of the Mach disk in an underexpanded jet flow were numerically and theoretically investigated under sonic injection conditions and the assumption of an axisymmetric flow. The numerical results demonstrated that the threshold nozzle-pressure ratio (NPR) at which the Mach disk occurred was situated between 3.03 and 3.12, which is lower than those reported in the previous studies. Since the oscillation frequency of the Mach disk was approximately constant over a wide range of NPRs and the amplitude was weak, it was regarded as a steady shock. In addition, the Mach disk was found to form when the total pressure loss reached approximately 40%. To predict the appearance of the Mach disk, we proposed a theoretical model based on a quasi-one-dimensional flow by considering the Mach disk as a normal shock wave on the axis. Based only on injection and ambient conditions, the total-pressure loss ratio derived from the model was in good agreement with that obtained from the numerical simulations, indicating that the proposed model provides useful knowledge for Mach disk occurrence prediction.

Simulation of supersonic gas–particle flows expanding from the nozzle into rarefied atmosphere

The results of numerical simulation of the particle-laden supersonic flows expanding from converging–diverging nozzle into a rarefied atmosphere are presented. To calculate flow quantities in a wide range of nozzle pressure ratios and investigate a possibility of a strong turn of the flow at the nozzle outlet, a marching scheme and finite volume method are applied. The marching calculations of the supersonic jet starts from the nozzle section, in which supersonic flow velocities are realized. The trajectories of motion of solid particles during the flow expansion are provided. The influence of the particle size and coordinates of the particle injection point into the flow on their transport by a supersonic flow is discussed. The results of calculations obtained in the framework of the Stokes approximation for the drag coefficient of an individual particle and with corrections for the inertia of the particle and rarefaction of the gas flow are compared. Conclusions are drawn about the effect of the dispersed phase on the distribution of gas flow quantities. The calculation results are of interest for studying supersonic particle-laden flows around bodies and for calculating oblique shock waves.

Effect of Flap Deflection on Single-Expansion-Ramp Nozzles Performance at Different Pressure Ratios

Experiments have been carried out to investigate the various performance characteristics of single-expansion-ramp nozzle with straight and deflected flap conditions for two different flap lengths. Experiments were performed at different nozzle pressure ratios (NPRs) ranging between 1.5 and 9. Wall static pressure measurements were made to estimate the various performance parameters, such as surface axial force, normal force, overall axial force, pitching moment, and thrust vectoring angles. Schlieren flow visualization technique was adopted to understand the internal shock-induced flow separation and shock patterns inside the nozzle under various NPRs. Flap deflection and NPR control the shock location through area variation, and thus the pressure distribution on the walls. At low NPRs, the internal drag force generated by deflected flap is lesser than that by straight flap, whereas at high NPRs the straight flap produces significantly higher surface axial thrust over the deflected flap. Behavior of normal force and pitching moment was affected by two factors: flap length and shock location. The straight flap shows significantly higher normal force than deflected flap. Hence, the thrust vectoring was better for straight flap nozzles compared to deflected flap nozzles, over the full range of NPRs tested. On the other hand, the gross thrust force performance is better for the straight flap for low NPRs and for the deflected flap for high NPRs. Overall, at high speeds, longer deflected flap appears to give better performance considering all the parameters, but will lead to heavier nozzle.

Numerical study of the separation of a turbulent boundary in rocket engine nozzles with an optimized supersonic part

At present, propulsion systems are being developed for flights of aerospace vehicles both in the Earth’s atmosphere and beyond. At the stage of the propulsion system design, it is necessary to be able to reliably determine the energy and thrust characteristics of rocket engines in regimes with flow separation in the nozzle for a wide range of nozzle pressure ratio (NPR) (1 ≤ m ≤ 30, m = ph /pa , p—pressure, indices h and a refer, respectively, to the parameters of the external environment and at the nozzle exit) characterizing the flow in nozzles and jets. In this case, the nozzle, as a rule, has a thrust optimized contour (TOC) supersonic part. In this regard, we present some results of a numerical study of flows with separation of the turbulent boundary layer in the TOC nozzles of main rocket engines in the above range of the NPR based on the Reynolds Averaged Navier–Stokes (RANS) system of equations.

Aeroacoustic modal analysis of underexpanded pipe jets with and without an upstream cavity

The investigation of the aeroacoustics of an underexpanded pipe-cavity jet is carried out experimentally. Two different aspect ratios of the cavity are tested for a wide range of nozzle pressure ratios. Both internal and externally radiated pipe-cavity acoustics are studied. Linear and higher-order spectral analyses are implemented on the unsteady cavity pressure to comprehend the nature of the cavity acoustics and nonlinear interactions of different acoustic modes of the pipe–cavity system. Results show that an increase in depth leads to an enhancement in the nonlinear interactions. Furthermore, the power spectral and overall sound pressure level analyses of pipe and pipe-cavity jet noise radiation are carried out. High-speed schlieren imaging techniques are used to understand jet dynamics. Highly unsteady motion of the jet initial shear layer is observed due to an upstream disturbance of the cavity. In addition, proper orthogonal and dynamic mode decomposition methods are used to extract the spatial and dynamic modes of the jet structure. These methods are used to segregate the cavity associated jet dynamics and screech dynamics.

Application of Rainbow Schlieren Deflectometry for Jets from Round Laval Nozzles Followed by Cylindrical Ducts

The jet from a round Laval nozzle followed by a cylindrical duct with an inner diameter of 10 mm and a length of 50 mm is investigated experimentally. The Laval nozzle has a design Mach number of 1.5. Quantitative flow visualization of the jet issued from the duct exit is performed over a range of nozzle pressure ratios from 2.0 to 4.5 using the rainbow schlieren deflectometry combined with the computed tomography to investigate the jet three-dimensional structure. The flow features of the near-field shock systems in the jets are displayed with the density contour plot at the cross-section including the jet centerline. Effects of the nozzle pressure ratio on the density profile along the jet centerline are clarified quantitatively. In addition, a comparison between the present experiment and the previous one with a conventional Laval nozzle for jet centerline density profiles is carried out to examine the effect of the cylindrical duct. Furthermore, the three-dimensional structures of overexpanded and underexpanded jets are demonstrated with the isopycnic surfaces to visualize the internal flow features.

Numerical Simulation on Optimization of Pintle Base Shape in Planar Expansion-Deflection Nozzles

Altitude compensating nozzles provide optimum performance over a wide range of altitudes. The planar expansion–deflection nozzle is one such nozzle. It has a rectangular cross-section, and altitude compensation is achieved by incorporating a pintle beyond the throat of a conventional convergent–divergent nozzle. The objective of the present Paper is to investigate the variations in flow caused as a result of a varying pintle base shape in a planar expansion–deflection nozzle. The computational fluid dynamics approach is used for conducting the analysis. Nozzle contour and pintle geometry up to the throat is kept unchanged, and simulations are conducted by altering the geometry of the pintle base profile. For each expansion–deflection nozzle configuration, the flow pattern, base pressure, and coefficient of thrust generated by nozzle are studied over a range of nozzle pressure ratios. The results of the numerical study reveal that the curved pintle with highest base curvature showed better overall performance in terms of contribution of base pressure to thrust output, whereas the pintle with an inclined base indicated the better overall coefficient of thrust when compared to pintles at higher nozzle pressure ratios due to higher contribution from momentum thrust.

Quantitative Flow Visualization by Rainbow Schlieren Deflectometry and Pitot Pressure Measurements for Leek Peeler Nozzle Jets

To optimize the leek peeling performance, a new nozzle has been developed in which the nozzle has a design Mach number of 1.68, an inner diameter of 2.0 mm at the throat, and an inner diameter of 2.3 mm at the exit. Experiments have been conducted over a range of nozzle pressure ratios from 3.0 to 6.0. Flow field issued from the new nozzle is quantitatively visualized by the rainbow schlieren deflectometry and compared with that from a conventional nozzle. Density fields in the free jets are reconstructed by the Abel inversion method for the schlieren images with the horizontal rainbow filter. The density values at the exit of the conventional nozzle obtained by the rainbow schlieren are compared with the analytical results by the flow model proposed in the past. In addition, Pitot probe surveys along the jet centerline were made to obtain the impact pressure distributions. The Mach number and velocity distributions along the jet centerline are obtained from a combination of the density and Pitot pressure data to clarify the fundamental flow structure of leek peeler nozzle jets.

Aerodynamic Analysis of Civil Aeroengine Exhaust Systems Using Computational Fluid Dynamics

As the specific thrust of civil aeroengines reduces, the aerodynamic performance of the exhaust system will become of paramount importance in the drive to reduce engine fuel burn. This paper presents an aerodynamic analysis of civil aeroengine exhaust systems through the use of Reynolds-averaged Navier–Stokes computational fluid dynamics. Two different numerical approaches are implemented, and the numerical predictions are compared to measured data from an experimental high-bypass-ratio separate-jet exhaust system. Over a fan nozzle pressure ratio range from 1.4 to 2.8, a comparison is drawn between values of the thrust coefficient calculated numerically and those obtained from experimental measurements. In addition, the effects of the freestream Mach number and extraction ratio on the aerodynamic behavior of the exhaust system are quantified and correlated to fundamental aerodynamic parameters.

Mixing characterization of highly underexpanded fluid jets with real gas expansion

We report a comprehensive speed of sound database for multi-component mixing of underexpanded fuel jets with real gas expansion. The paper presents several reference test cases with well-defined experimental conditions providing quantitative data for validation of computational simulations. Two injectant fluids, fundamentally different with respect to their critical properties, are brought to supercritical state and discharged into cold nitrogen at different pressures. The database features a wide range of nozzle pressure ratios covering the regimes that are generally classified as highly and extremely highly underexpanded jets. Further variation is introduced by investigating different injection temperatures. Measurements are obtained along the centerline at different axial positions. In addition, an adiabatic mixing model based on non-ideal thermodynamic mixture properties is used to extract mixture compositions from the experimental speed of sound data. The concentration data obtained are complemented by existing experimental data and represented by an empirical fit.

Mixing Characteristics of Elliptical Jet Control with Crosswire

The aerodynamic mixing efficiency of elliptical sonic jet flow with the effect of crosswire is studied computationally and experimentally at different range of nozzle pressure ratio with different orientation along the minor axis of the exit. The cross wire of different orientation is found to reduce the strength of the shock wave formation. Due to the presence of crosswire the pitot pressure oscillation is reduced fast, which weakens the shock cell structure. When the cross wire is placed at center position we see high mixing along the major axis. Similarly, when the cross wire is placed at ¼ and ¾ position we see high mixing promotion along minor axis. It also proves, as the position of the cross wire decreased along minor axis there will be increase in the mixing ratio. In addition to that we also found that, jet spread is high in major axis compared to minor axis due to bifurcation of jet along upstream

Fluidic thrust vector control based on counter-flow concept

Computational studies are conducted on the supersonic nozzle to investigate the possibility of utilizing counter-flow in fluidic thrust vector control. In this work, the design Mach number of the symmetric supersonic nozzle is set to be 2.5. For the validation of methodology, numerical results are compared with experimental data referred from the literature. Two-dimensional numerical simulations are based on well-assessed standard k–ɛ turbulence model with standard wall functions. Second-order accuracy is ensured to reveal more details of flow field. The system thrust ratio, deflection angle, and secondary mass flow ratio were studied for a wide range of nozzle pressure ratios and secondary pressure ratios. The results indicate that deflection angle and secondary mass flow ratio are found to be decreased with increasing nozzle pressure ratio as well as system thrust ratio. The secondary mass flow ratio and deflection angle decrease with the increase of secondary pressure ratio, and system thrust ratio increases with the increasing of secondary pressure ratio. The secondary mass flow rate remains under 2.4% of the primary flow to obtain efficient thrust vector control at high Mach number.

Origin of side-loads in a subscale truncated ideal contour nozzle

An experimental investigation was conducted in a cold flow test facility to identify the origin of various flow conditions that lead to side-load generation in a truncated ideal contour nozzle (of area-ratio 20.66) especially at moderate nozzle pressure ratio range of 20 to 42 during the start-up and shutdown sequences. The major contributors seem to be the transition in flow conditions namely, the change in the circumferential shape of re-circulation region inside the nozzle from a cylindrically dominated regime to a conical one and the end-effect regime that initiate highly unsteady flow conditions in the separation region preceding these transitions. Other flow transitions such as those initiated by the onset of test gas condensation and vice-versa result in a downstream or an upstream jump in separation, respectively, that causes the overall side-load signal to increase. During this flow regime, an increase in the length of the upstream influence region accompanied by a rise in the peak standard deviation value is also observed.

Flow field and acoustic characteristics of elliptical throat CD nozzle

ABSTRACTThe mixing characteristic of circular jet with elliptical throat is studied at different levels of expansion of the nozzle. Two kinds of configurations are studied in this paper, elliptical throat and circular throat jet. At all pressure ratios, the jet with non-circular throat experiences superior mixing than circular throat. The core length of elliptical throat jet is shorter than circular jet. Also, at all pressure ratios, the profile of both configurations looks identical in oscillation; however, the efficiency of the mixing promotion is high in non-circular throat. The promotion of mixing is most efficient at nozzle pressure ratio (NPR) level of 8. As the NPR increases, the core length of the jet reduces nearly 5–10% at each range of NPR. The centreline Pitot pressure profile of non-circular and circular throat shows that the decay of the jet from elliptical throat nozzle is faster than the jet from circular jet. At different levels of expansion, the shock structure shows notable changes with elliptical shape. The amplitude of screech frequency of the jet noise decreases with an increase in NPR. Introduction of elliptical throat to circular throat modifies the shock-cell structures, which significantly change the screech amplitude due to weakening of waves.

Numerical Investigation of the Dynamic Characteristics of a Dual-Throat-Nozzle for Fluidic Thrust-Vectoring

A computational method tailored for the simulation of fluidic thrust-vectoring systems is employed to investigate the dynamic response of a dual-throat nozzle in open- and closed-loop control. Thrust vectoring in fixed, symmetric nozzles is obtained by secondary flow injections that cause local flow separations, asymmetric pressure distributions, and, as a consequence, the vectoring of primary jet flow. The computational technique is based on a well-assessed mathematical model for the compressible unsteady Reynolds-averaged Navier–Stokes equations. A minimal control system governs the unsteady blowing. Nozzle performances and thrust-vector angles have been computed for a wide range of nozzle pressure ratios and secondary flow injection rates. The numerical results are compared with the experimental data available in the open literature. Several computations of the open-loop dynamics of the nozzle under different forcing have been performed to investigate the system response in terms of thrust-vectoring effectiveness and controllability. These computations have been used to extract autoregressive exogenous models of the nozzle dynamics. The effects of including the actuator dynamics are also discussed. Simple strategies of closed-loop control of the nozzle system by proportional–integrative–derivative regulators are investigated numerically. The closed-loop model predictive control of the system, based on the autoregressive exogenous models, is addressed.

A numerical method for the study of fluidic thrust-vectoring

Thrust Vectoring is a dynamic feature that offers many benefits in terms of maneuverability and control effectiveness. Thrust vectoring capabilities make the satisfaction of take-off and landing requirements easier. Moreover, it can be a valuable control effector at low dynamic pressures, where traditional aerodynamic controls are less effective. A numerical investigation of Fluidic Thrust Vectoring (FTV) is completed to evaluate the use of fluidic injection to manipulate flow separation and cause thrust vectoring of the primary jet thrust. The methodology presented is general and can be used to study different techniques of fluidic thrust vectoring like shock-vector control, sonic-plane skewing and counterflow methods. For validation purposes the method will focus on the dual-throat nozzle concept. Internal nozzle performances and thrust vector angles were computed for several range of nozzle pressure ratios and fluidic injection flow rate. The numerical results obtained are compared with the analogues experimental data reported in the scientific literature. The model is integrated using a finite volume discretization of the compressible URANS equations coupled with a Spalart-Allmaras turbulence model. Second order accuracy in space and time is achieved using an ENO scheme.

Numerical Simulation of Fluidic Thrust-Vectoring

The paper focuses on a computational method for the investigation of Fluidic Thrust Vectoring (FTV). Thrust vectoring in symmetric nozzles is obtained by secondary flow injections that cause local flow separations, asymmetric pressure distributions and, therefore, the vectoring of the primary jet thrust. The methodology proposed here can be applied for studying numerically most of the strategies for fluidic thrust vectoring, as shock-vector control, sonic-plane skewing and the counterflow method. The computational technique is based on a well-assessed mathematical model. The flow governing equations are solved according to a finite volume discretization technique of the compressible RANS equations coupled with the Spalart-Allmaras turbulence model. Second order accuracy in space and time is achieved using an Essentially Non Oscillatory scheme. For validation purposes, the proposed numerical tool is used for the simulation of thrust vectoring based on FTV strategies as the shock vector control and the dual-throat nozzle concept, with a special attention to the latter case. Nozzle performances and thrust vector angles are computed for a wide range of nozzle pressure ratios and secondary flow injection rates. The numerical results obtained are compared with the experimental data available in the open literature.