Underexpanded Jet Research Articles

A Numerical Simulation of the Underwater Supersonic Gas Jet Evolution and Its Induced Noise

To explore the complex flow field and noise characteristics of underwater high-speed gas jets, the mixture multiphase model, large eddy simulation method, and Ffowcs Williams–Hawking (FW–H) acoustic model were used for simulations, and the numerical methods were validated by the gas jet noise experimental results. The results revealed that during the initial stages, the jet collided with the water surface and created low-pressure high-temperature gas bubbles, accompanied by much high-frequency noise. When the jet reached its maximum length, its impact weakened, the bubble broke, the jet transformed into a conical shape, and the jet noise changed from high- to low-frequency. The pressure fluctuation peaked near the position at which the Mach number reached 1, indicating that the jet was the most unstable at the sonic point. Additionally, at low frequencies, the sound pressure levels between jets with different nozzle pressure ratios were similar, whereas above 400 Hz, under-expanded jets had higher sound pressure levels. This paper provides theoretical guidance for the study of underwater jet noise.

Characteristics of dust explosion venting pressure and flame under high activation pressure

A 20 L spherical explosive device with a venting diameter of 110 mm was used to study the vented pressure and flame propagation characteristics of corn dust explosion with an activation pressure of 0.78–2.1 bar and a dust concentration of 400∼900 g/m3. And the formation and prevention of secondary vented flame are analyzed and discussed. The results show that the maximum reduced explosion overpressure increases with the activation pressure, and the vented flame length and propagation speed increase first and then decrease with time. The pressure and flame venting process models are established, and the region where the secondary flame occurs is predicted. Whether there is pressure accompanying or not in the venting process, the flame venting process is divided into two stages: overpressure venting and normal pressure venting. In the overpressure venting stage, the flame shape gradually changes from under-expanded jet flame to turbulent jet flame. In the normal pressure venting stage, the flame form is a turbulent combustion flame, and a secondary flame occurs under certain conditions. The bleed flames within the test range are divided into three regions and four types according to the shape of the flame and whether there is a secondary flame. The analysis found that when the activation pressure is 0.78 bar and the dust concentration is less than 500 g/m3, there will be no secondary flame. Therefore, to prevent secondary flames, it is necessary to reduce the activation pressure and dust concentration. When the dust concentration is greater than 600 g/m3, the critical dust concentration of the secondary flame gradually increases with the increase of the activation pressure. Therefore, when the dust concentration is not controllable, a higher activation pressure can be selected based on comprehensive consideration of the activation pressure and destruction pressure of the device to prevent the occurrence of the secondary flame.

Physical model of non-adiabatic blowdown of cryo-compressed hydrogen storage tanks

This paper describes a model of hydrogen blowdown dynamics for storage tanks needed for hydrogen safety engineering to accurately represent incident scenarios. Heat transfer through a tank and pipe walls affects the temperature and pressure transients inside the storage vessel and at the nozzle exit, and thus the characteristics of the resulting hydrogen jet in the case of loss of containment. Current non-adiabatic blowdown models are validated against experiments performed with hydrogen storage tanks at only ambient temperature. The effect of heat transfer for cryo-compressed hydrogen is more significant due to a larger difference of temperature between the stored hydrogen and the surrounding atmosphere, especially in case of equipment insulation failure during an incident. Our previous work demonstrated that the heat transfer through a discharge pipe wall can significantly affect the mass flow rate of cryogenic hydrogen releases. Thoroughly validated models of non-adiabatic blowdown dynamics for cryo-compressed hydrogen are missing at the moment. This work develops further the non-adiabatic blowdown model at ambient temperature using the under-expanded jet theory developed at Ulster University, to expand it to cryo-compressed hydrogen storage tanks. The non-ideal behaviour of cryo-compressed hydrogen due to low temperatures is taken into account through the high-accuracy Helmholtz energy formulations. The developed model includes effect of heat transfer at both the tank and the discharge pipe walls. The model is thoroughly validated against sixteen tests on blowdown of hydrogen storage tanks with initial pressure 0.6–20 MPa ab and temperature 80–310 K, through release nozzle of diameter in the range 0.5–4.0 mm, performed within the PRESLHY project. The model well reproduces the experimental pressure and temperature recordings in the storage tank during the entire blowdown duration for the whole set of sixteen tests. In conjunction with the volumetric source model, explained in detail, the physical model allows to perform CFD simulations accurately reproducing the temperature distribution in time and space for the cryogenic hydrogen jet experiment.

The source localization and dynamical evolution of axisymmetric screech modes in underexpanded supersonic jets

High order numerical simulations of underexpanded supersonic cold jets issuing from a circular sonic nozzle are conducted to investigate the effective source location of axisymmetric mode screech tones. The frequency and sound pressure level of screech tone agree well with the experimental results in literature. The detailed generation processes of axisymmetric screech modes in a complete cycle are exhibited through investigating the dynamic evolutions of the flow structures and acoustic waves. By implementing spectral proper orthogonal decomposition (SPOD) of jet velocity field and pressure field, the corresponding SPOD modes to the A1 and A2 screech modes are extracted respectively and their evolutions along streamwise direction are analyzed. The source location of A1 mode and A2 mode screech tones were revealed based on the dynamic evolution analysis and the Fourier mode decomposition. It is worth noting that the screech waves of each axisymmetric screech mode radiate from an isolated discrete source rather than the distributed sources at a given jet Mach number. Another interesting finding is that the effective source position of screech A2 mode varies with jet Mach number.

Numerical investigation of the rarefied supersonic underexpanded jet structure using the DSMC method

Numerical investigation of the rarefied supersonic underexpanded jet structure using the DSMC method

The influence of cryogenic temperature on the shock structure of impinging under-expanded flow over a convex surface

This study comprehensively investigates the effect of cryogenic nozzle inlet temperature on the flow structure and interactions of an under-expanded supersonic jet with a spherical solid surface. A combined experimental and numerical approach was employed to achieve this goal, utilizing high-speed Z-type schlieren visualization and Reynolds-averaged Navier–Stokes simulations with a Redlich–Kwong real gas equation of state. This study is significant as it addresses a relatively unexplored area of research on the flow structure of the cryogenic under-expanded supersonic jet. The study examines the shock pattern and interaction region through varying static inlet temperature (Tin = 178–290 K) and nozzle pressure ratio (NPR 5–14). Additionally, parameters including nozzle exit-to-throat area ratio (A/A* = 1.277), the distance between the sphere and the nozzle (1.5 cm), and the diameter of the sphere (d = 1.5 cm) were considered fixed. The results show that the supersonic jet exhibits a change in shock patterns in the first shock cell concerning the location and width of the Mach disk, accompanied by a shift in the location of the last shock crossing point and the shock plate. The simulation provides a more detailed insight into the flow, indicating a temperature drop to 105 K in the case of the cryogenic nozzle inlet. At such a low temperature, the compressibility factor exhibits a 5% reduction from unity, while in the case of the ambient nozzle inlet, the minimum temperature at the nozzle exit reached 170 K, leading to only a 1% drop in the compressibility factor, which is negligible. It triggers different flow structures concerning the nozzle inlet temperature. These findings can contribute to the complex flow structures of supersonic jets seen in different industrial and scientific fields.

Super-resolution of time-resolved three-dimensional density fields of the B mode in an underexpanded screeching jet

The estimation of time-resolved three-dimensional (3D) density fields of an underexpanded jet at the nozzle pressure ratio of 2.42, a so-called “spatiotemporal super-resolution” was conducted using non-time-resolved three-dimensional background-oriented schlieren (3D-BOS) and time-resolved microphone measurements. This approach aims to reconstruct three-dimensional density fields associated with the intermittent and switching behavior of the B mode of a screeching jet from the microphone data by constructing a linear regression model. An azimuthal Fourier decomposition is applied to the 3D-BOS and microphone data, and the proper orthogonal decomposition (POD) is performed for each of their azimuthal Fourier modes. The m=1 azimuthal Fourier mode is dominant in both cases, and the leading two POD modes in the m=1 azimuthal mode of the microphone data are associated with the B mode. The linear regression model is constructed from the POD modes of the m=1 azimuthal 3D-BOS data and the first two microphone POD modes of the m=1 azimuthal mode of the microphone data. The three-dimensional density fields reconstructed from each POD mode of the m=1 azimuthal mode of the microphone data have helical structures with opposite rotation directions. The amplitudes of those POD modes change with time, and the azimuthal structure associated with the B mode is determined depending on those amplitudes. The present result showed that intermittency in the flapping to helical structures and their strength can be interpreted by the temporal changes in the strengths of two rotating helical structures with opposite rotation directions.

Investigation of slanted perforation diameter in tabs for supersonic jet control

PurposeThis study aims to investigate the effect of slanted perforation diameter in tabs for the control of Mach 1.4 underexpanded supersonic jet flow characteristics.Design/methodology/approachNumerical investigation was carried out for NPR 5 to analyze the effect of slanted perforation diameter in tabs to control the Mach 1.4 jet. Four sets of tabs with slanted circular perforation geometries (Φp = 1, 1.5, 2 and 2.5 mm) were considered in this study. The inclination angle of 20° (αP) with reference to the jet axis was maintained constant for all the four tabs considered.FindingsDetermined value indicates there is a 68%, 71%, 73% and 75% drop in supersonic core for the Φp = 1, 1.5, 2.0 and 2.5 mm, respectively. The results show that the tabs with 2.5 mm perforation diameter were found to be efficient in reducing the supersonic jet core in comparison with other tab cases. The reduction in supersonic core length is due to the extent of miniscule vortices exuviating from slanted small and large diameter perforation in the tabs.Practical implicationsThe concept of slanted perforation can be applied in scramjet combustion, which finds its best application in hypersonic vehicles and in noise suppression in fighter aircraft.Originality/valueSlanted perforation and circular shapes with different diameters have not been studied in the supersonic regime. Examining the effect of circular diameter in slanted perforation is an innovation in this research paper.

Spatial mapping of low pressure cluster jets using Rayleigh scattering

In this work, we report evolution of atomic clusters in a highly under-expanded supersonic jet of Argon. A high resolution and sensitive Rayleigh scattering based experimental set-up is designed to overcome the limitations encountered in conventional set-ups. Further, the measurement range could be extended from a few nozzle diameters to 50 nozzle diameters. Simultaneously, we had been able to generate 2D profiles of the distribution of clusters inside the jet. This paves the way to track the growth of clusters along the flow direction experimentally, which until now was limited to few nozzle diameters. The results show that spatial distribution of clusters inside the supersonic core deviates considerably from the prediction of the free expansion model. We exploit this to estimate cluster growth along the expansion direction. Further, it is observed that the growth of the clusters gets saturated after a certain distance from the nozzle. At the jet boundary, we see substantial cluster strengthening immediately upstream of barrel shock while the normal shock exhibits disintegration of clusters. These observations are noticed for the first time, which, we believe will further the understanding of cluster dynamics in a supersonic jet.

Heat transfer investigation on under-expanded supersonic impinging jets

In this study, wall-resolved large-eddy simulations are performed to investigate the underpinning physics of impingement heat transfer in under-expanded supersonic impinging jets. The jet is generated with an infinite-lipped nozzle of diameter D, has a nozzle-to-wall distance of 5D, a nozzle pressure ratio (NPR) of 3.4 and a Reynolds number of 6×104 based on the ideally-expanded jet velocity. Two thermal boundary conditions of a heated isothermal wall and an adiabatic wall for the impingement plate are considered.Both impinging jets in the current study feature a strong stand-off shock, which oscillates periodically in front of the impingement plate at two dominant frequencies. These oscillations result in two local peaks of the mean heat transfer coefficients with the first peak located in the stagnation region but shifted away from the stagnation point (i.e. jet axis), whilst the second peak is located in the wall jet region. The instantaneous fields of pressure, vorticity and Nusselt number are first discussed to study qualitatively the connection between these two peaks of the mean heat transfer coefficient and the near-wall flow structures. The characteristics of these two peaks are then analysed using the near-wall statistics and spectra of the pressure, axial velocity and Nusselt number distribution.It is found that the first peak of the Nusselt number forms as a consequence of the jet impingement of the non-periodic turbulent structures, whilst the second peak is linked to the reattachment of the recirculation bubble in the wall jet. It is shown that the unsteady separation and reattachment processes are strongly related to the oscillatory motion of the stand-off shock at the dominant frequencies. Last but not the least, the first local minimum close to the stagnation point is also found to be associated with the strong oscillatory behaviour of the stand-off shock.

Influences of semi-circular, square, and triangular grooves on mixing behavior of an axisymmetric supersonic jet

The length of the supersonic jet ejected from the military aircraft must be reduced in order to decrease its heat signature and aeroacoustic noise and thereby to enhance its stealth capability. The reduction or manipulation of the supersonic core can be achieved through various passive control techniques. Considering this, the present study explores the mixing characteristics of supersonic jets with and without passive controls. Passive controls in the form of grooves configured at the exit of a Mach 1.73 convergent–divergent nozzle are investigated computationally. Particularly, the supersonic jet decay characteristics and flow development for a plain nozzle and a nozzle with semi-circular, square, and triangular grooves are presented. In addition, the study explores different turbulence models, namely, Spalart–Allmaras, realizable k-ε, std k-ω, shear stress transport (SST) k-ω, and SST transition. The realizable k-ε turbulence model is found to be the most effective one in capturing the supersonic jet structure. It is observed that the grooves produce large distortions in the jet structure, accompanied by significant mass entrainment and lateral spread. Interestingly, semi-circular grooves are proven to be most effective in all cases of expansion level than square and triangular grooves. For the semi-circular grooves, a maximum of 48.5% reduction in the supersonic core length of the correctly expanded jet at nozzle pressure ratio (NPR) of 5 is achieved. The reduction in the supersonic core length for semi-circular grooves is 31% for the overexpanded jet at NPR 4 and 29% for the underexpanded jet at NPR 7.

On the application of gradient based reconstruction for flow simulations on generalized curvilinear and dynamic mesh domains

Accurate high-speed flow simulations of practical interest require numerical methods with high-resolution properties. In this paper, we present an extension and demonstration of the high-accuracy Gradient-based reconstruction and α-damping schemes introduced by Chamarthi (2022) for simulating high-speed flows in generalized curvilinear and dynamic mesh domains with the freestream preservation property. In the first part of this paper, the algorithms are detailed within the generalized curvilinear coordinate framework, with a focus on demonstration through stationary and dynamic mesh test cases. It has been shown both theoretically and through the use of test cases that the conservative metrics, including their interpolation to cell interfaces, must be numerically computed using a central scheme that is consistent with the inviscid flux algorithm to achieve the freestream preservation property. The second part of the paper illustrates the efficacy of the algorithm in simulating supersonic jet screech by displaying its capability to capture the screech tones and accurately characterize the unsteady lateral flapping mode of a Mach 1.35 under-expanded supersonic jet, in contrast to the WENO-Z scheme which fails to do so at the same grid resolution. In the final part of the paper, the parallelizability of the schemes on GPU architectures is demonstrated and performance metrics are evaluated. A significant speedup of over 200× (compared to a single core CPU) and a reduction in simulation completion time to 34.5 h per simulation were achieved for the supersonic jet noise case at a grid resolution of 13 million cells.

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.

Physics model validation of propane and methane for Hydrogen Plus Other Alternative Fuels Risk Assessment Models (HyRAM+)

HyRAM+ is a toolkit that includes fast-running models for the unconstrained (i.e., no wall interactions) dispersion and flames for non-premixed fuels. The models were developed for use with hydrogen, but the toolkit was expanded to include propane and methane in a recent release. In this work we validate the dispersion and flame models for these additional fuels, based on reported literature data. The validation efforts spanned a range of release conditions, from subsonic to underexpanded jets and flames for a range of mass flow rates. In general, the dispersion model works well for both propane and methane although the width of the jet/plume is predicted to be wider than observed in some cases. The flame model tends to over-predict the induced buoyancy for low-momentum flames, while the radiative heat flux agrees with the experimental data reasonably well, for both fuels. The models could be improved but give acceptable predictions for propane and methane behavior for the purposes of risk assessment.

Numerical simulation of ideal and non-ideal under-expanded supersonic jets with adaptive grids

This paper numerically investigates the effect of flow non-ideality on the Mach disk pattern occurring in axisymmetric under-expanded supersonic jets. The explored conditions are found in the non-ideal gas region close to the liquid–vapor saturation curve and the critical point, where involved thermodynamics cannot be accurately described by the ideal gas law. Numerical simulations of steady inviscid compressible flows are carried out by adopting the polytropic ideal gas model and improved Peng–Robinson thermodynamic model, via the open-source computational fluid dynamics code SU2. To properly resolve the Mach disk position and radius, a mesh adaptation procedure is used. An assessment of the most suitable mesh adaptation criteria for the considered ideal and non-ideal flow configurations is carried out, considering isotropic and anisotropic mesh adaptation criteria. The best mesh adaptation criterion for ideal and non-ideal under-expanded jets results to be the anisotropic criterion based on the Hessian of the density and Mach number field. Then, the effects of the flow non-ideality on the Mach disk are investigated by simulating different operating conditions of under-expanded nozzle jets of five different vapors. For nitrogen, oxygen, carbon dioxide, the Mach disk moves downstream and has a smaller radius with a higher level of non-ideality. Conversely, for siloxanes MM and MDM, the Mach disk moves upstream and has a larger radius as the non-ideality of the flows increases.

Numerical study of hydrogen jet in methane / air premixed atmosphere

The work presented a numerical study on the transient characteristics of under-expanded hydrogen jets from a cylindrical nozzle. The finite-volume solution was adopted in the two-dimensional simulation of high-pressure chocked hydrogen jets, by solving the Navier-Stokes equations for gas phase flow. Numerical analyses were respectively performed over the micro level to characterize the fine structures, and over macro levels to explore the key global parameters of the gaseous jets. Parameterization work was conducted in terms of the microscopic characteristics of jets, such as, the length of jet core, the diameter of jet vortex, and the key global parameters, i.e. the penetration and the steady fuel injection rate. The effects of the injection parameters on the micro-structure and macro characteristics were hence quantified.

Experimental study of hydrocarbon aviation fuel jets at high temperatures up to the critical point

An experimental study was conducted to investigate the effects of fuel temperature up to the critical point on the injection and hydrodynamic characteristics of practical hydrocarbon aviation fuel jets. Pressurized heated hydrocarbon, simulating aviation fuel used as coolant in the active cooling system of a hypersonic flight vehicle, was injected through a set of plain orifice nozzles of exit diameters 0.7 and 1.0 mm. The fuel was heated to close to 700 K (427 °C) using an induction heater, and discharged to atmospheric pressure and temperature conditions. Visual observation of the fuel spray and the shock structure near the nozzle exit shows that morphological change is drastic in the temperature range between the boiling point and the critical temperature; this allows delineation of the liquid, flash boiling, and near-critical regimes. An in-depth investigation of the near-critical regime through shadowgraph images reveals that the structure of the hydrocarbon fuel jets near the critical temperature looks very similar to that of typical underexpanded jets. Furthermore, visual observation confirms that the distance hs from the nozzle exit to the shock structures is correlated with the injection pressure ΔP irrespective of the fuel injection temperature Tinj. Hydraulic characterization by measuring ΔP and the resultant discharge coefficient Cd with respect to Tinj under fixed mass flow rates shows that Cd is almost constant in the liquid regime, while it decreases with Tinj in the flash boiling regime, and that a discontinuity near the boiling point occurs where the liquid injection transitions to flash boiling. A simple linear model is proposed to estimate the P-T relation in the flash boiling regime by linearly extending the characteristics of the hydraulic performance.

Acoustic resonance mechanism for axisymmetric screech modes of underexpanded jets impinging on an inclined plate

In this paper, the acoustic resonance mechanism for different axisymmetric screech modes of the underexpanded jets that impinge on an inclined plate is investigated experimentally. The ideally expanded Mach number of jets ( $M_j$ ) ranges from 1.05 to 1.56. The nozzle-to-plate distance at the jet axis and the impingement angle are respectively set as 5.0 $D$ and $30^{\circ }$ , where $D$ is the nozzle exit diameter. The acoustic results show that the $M_j$ range for the A2 screech mode of impinging jets is broader than that of underexpanded free jets, and a new axisymmetric screech mode A3 appears. With the increase of $M_j$ , the effect of the impinging plate on the shock cell structures of jets becomes obvious gradually, and the second suboptimal peaks are evident in the axial wavenumber spectra of mean shock structures. The coherent flow structures at screech frequencies are extracted from time-resolved schlieren images via the spectral proper orthogonal decomposition (SPOD). The axial wavenumber spectra of the selected SPOD modes suggest that the A1, A2 and A3 screech modes are respectively closed by the guided jet modes that are energized by the interactions between the Kelvin–Helmholtz wavepacket and the first three shock wavenumber peaks. The upstream- and downstream-propagating waves that constitute the screech feedback loop are analysed by applying wavenumber filters to the wavenumber spectra of SPOD modes. The frequencies of these three screech modes can be predicted by the phase constraints between the nozzle exit and the rear edge of the third shock cell. For the A3 mode, the inclined plate invades the third shock cell with the increase of $M_j$ , and the phase constraint cannot be satisfied at the lower side of the jets, which leads the A3 mode to fade away. The present results suggest that external boundaries can modulate the frequency and mode of jet screech by changing the axial spacings of shock cells.

Numerical characterization of hydrogen under-expanded jets with a focus on Internal Combustion Engines applications

In the context of reducing carbon dioxide ([Formula: see text]) emissions, hydrogen is gaining momentum as a possible fuel for Internal Combustion Engines (ICEs). In-cylinder direct injections allow for a higher specific power density while enabling different levels of charge stratification. The high-pressure injection leads to the onset of under-expanded jets, characterized by complex patterns of shock waves and expansion fans. In ICEs simulations, such physics needs to be correctly solved to obtain a reliable assessment of the mixture formation. In this paper, the main features of hydrogen under-expanded jets are examined under the conditions typically found in turbocharged engines. Improved correlations are provided for the assessment of the Mach disk height and diameter, up to a Nozzle Pressure Ratio (NPR) equal to 60. The dependency of the hydrogen-air mixing on the cylinder temperature has been analyzed, and the unsteady jet dynamics has been examined by continuously varying the combustion chamber pressure. To the authors’ knowledge, no studies of this kind can be found in the literature for the specific case of hydrogen. Lastly, a preliminary investigation of the jet-jet interaction (a Coanda-like effect) is reported. This phenomenon is observable when multi-hole injectors are employed, and it may have a great impact on the mixture formation.

Numerical Investigation on the Thrust Vectoring Performance of Bypass Dual Throat Nozzle

Modern aircraft and missiles are gradually integrating thrust vector control systems to enhance their military capabilities. Bypass Dual-Throat Nozzle (BDTN) control is a new fluidic thrust vectoring technique capable of achieving superior performance with large vector angles and low thrust loss. In this study, we analyzed the flow characteristics and performance parameters of BDTN by varying the bypass angle, nozzle convergence angle, and bypass width. The flow governing equations are solved according to a finite volume discretization technique of the compressible RANS equations coupled with the Renormalization Group (RNG) k-ϵ turbulence model for Nozzle Pressure Ratio (NPR = 2~10) to capture the significance of under-expanded and over-expanded jets. Results show that by decreasing the bypass angle from 90° to 35°, there is a 6% increase in vectoring angle while the vectoring efficiency is enhanced by 18%. However, a decrease of 3% in the thrust and discharge coefficients is also observed. When the convergence angle was increased from 22° to 37°, vectoring angle, discharge coefficient, and thrust coefficient increased by 2%, 1%, and 0.26%, respectively. Moreover, vectoring efficiency is also enhanced by 8% by reducing the convergence angle from 37° to 22°. Based on the investigated parameters, it is determined that nozzle convergence angle does not significantly influence thrust vectoring performance, however, bypass width and bypass angle have a significant effect on thrust vectoring performance.