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A transverse injection into high-speed freestreams is a significant principle applied to realistic engineering applications, such as drag reduction, fuel service in a scramjet combustor, and fluidic thrust vectoring control. Fluidic thrust vector control is quite popular for micro space launcher propulsion systems due to several advantages, includi...
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... vector control (TVC) is an advanced flow control technique utilized in various air vehicles, such as fighter aircraft, modern rockets, and space platforms (Francis 2018). In addition to providing additional thrust, TVC can change the thrust line and allow for yawing, rolling, and pitching ( Fig. 1). Compared with generalengine aircraft, a fighter aircraft with TVC is dependent on a smaller extent on the aerodynamic control surface to manipulate flexibly, acquiring crucial advantages in air ...
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... best match with existing experimental data. Hence, the SST k-ω turbulence model was considered in the present simulation. Fig. 9 compares normalized static pressure distributions along the nozzle surface on the symmetry plane with experimentally measured data. It is evident that there is a good match on both the upper and lower nozzle surfaces. Fig. 10 compares a density gradient magnitude contour with the experimental shadowgraph. The quantitative and qualitative results indicate that the present numerical simulation with the SST k-ω turbulence model can accurately predict the performance of the rectangular SVC ...
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... to the importance of optimizing the vectoring effect, the SVC performance was studied for different NPR values at a constant IPR level of 2.49. Different operating conditions of the propulsion nozzle were considered, owing to the emergence of various actual engineering applications. Four NPR values (NPR ¼ 3, 3.5, 4.6, and 5) Fig. 11. In all cases, the static pressure variation had a decreasing trend up to X=R ¼ 4.4 on the upper and lower nozzle surfaces. Beyond that, the static pressure underwent a small increase followed by a smooth decrease to the lowest pressure level. Then a steep pressure increase occurred at the location of the boundary layer separation. The ...
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... underwent a small increase followed by a smooth decrease to the lowest pressure level. Then a steep pressure increase occurred at the location of the boundary layer separation. The position of the boundary layer separation moved toward the downstream nozzle exit with increasing NPR. A magnified region of the pressure distribution is shown in Fig. 12 to explain the pressure variation in detail for NPR ¼ 3.5 and IPR ¼ 2.49. In Zone 1, the pressure increased rapidly due to the upper boundary layer separation. Subsequently, a plateau pressure in Zone 2 was affected by the formation of the PUV. A small decrease of the static pressure occurred between the PUV and the IUV, as described ...
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... pressure level was obtained owing to the existence of a PDV and an external vortex (EV). The pressure distribution along the lower nozzle surface on the symmetry plane increased rapidly due to the lower boundary layer separation. Several XOY slices were created along the span direction, and several regions filled with vortexes are depicted in Fig. 13. Because the nozzle sidewall affects the injection penetration height and the separation distance, the vortex scale increased closer to the symmetry plane along the span direction. Either upstream or downstream of the slot injector, the largest PUV, IUV, and PDV regions formed on Plane 1, compared with those on the other two slices. ...
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... injector, the largest PUV, IUV, and PDV regions formed on Plane 1, compared with those on the other two slices. The PDV induced a small secondary separation region, namely EV. On Plane 2, the EV disappeared and the corresponding PUV, IUV, and PDV regions decreased. Plane 3 had only a small PUV region, owing to the effect of the nozzle sidewall. Fig. 14 presents 2D streamlines on the symmetry plane for different values of NPR to clarify the vortex generation and flow separation in the vicinity of the slot injector. For NPR ¼ 5, the IUV, PDV, and EV disappeared, and only a small PUV region occurred because the NPR level was close to the design NPR value of the supersonic nozzle. The reduction of ...
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... to the design NPR value of the supersonic nozzle. The reduction of the NPR value led to more vortexes, such as the IUV and PDV. As the NPR value increased, the area of PUV region diminished, corresponding to a downstream movement of the boundary layer separation. Additionally, the sizes of IUV, PDV, and EV regions decreased with increasing NPR. Fig. 15 depicts the evolution of pitching angle, δ β , and specific impulse amplification coefficient, C AI , as a function of NPR. The pitching angle rapidly decreased with the increase of NPR. Because the IPR was fixed, the thrust of mainstream diminished with overexpansion, which can cause a larger pitching angle ( Sellam et al. ...
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... resultant thrust coefficient, C AF , and thrust efficiency, C AV , are shown in Fig. 16 for different NPR values. The resultant thrust coefficient steeply increased with increasing NPR. Additionally, the relationship between the thrust efficiency and NPR is demonstrated to describe energetic variations. As NPR increased from 3.5 to 5, the thrust efficiency continuously increased. The highest thrust efficiency was at NPR ¼ ...
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... pitching angle decreased with increasing NPR, a more rapid decrease of the mass flow ratio resulted in an increasing thrust efficiency. However, the pitching angle at NPR ¼ 3 was larger than that of NPR ¼ 3.5. To clearly illustrate this variation reason on thrust efficiency, the primary mass flow rate, m 0 , and IMFR, m i =m 0 , are presented in Fig. 17. The primary mass flow rate linearly increased with increasing NPR. The IMFR decreased with the increment of NPR. Although a large IMFR was obtained for NPR ¼ 3, the higher pitching angle of NPR ¼ 3 led to a larger thrust efficiency than that of NPR ¼ ...
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... number contours on the symmetry plane are portrayed in Fig. 18 for different NPR values. The pitching angle increased with decreasing NPR. Furthermore, some variations of the shock structure are shown in the magnified regions. At NPR ¼ 5, there were two oblique shocks downstream of the nozzle exit; one oblique shock formed upstream of the slot injector, and another oblique shock occurred close to ...
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... of the nozzle exit; one oblique shock formed upstream of the slot injector, and another oblique shock occurred close to the lower nozzle exit. The reduction of the NPR value from 5 to 4.6 led to a larger PUV scale, inducing an upstream movement of the upper oblique shock. The NPR affected the IUV region in the vicinity of the slot injector (Fig. 14). The decrease of the NPR caused the shortening of the normal flow recompression process. A further decrease of the NPR value from 4.6 to 3.5 led to the appearance of a Mach disk at the supersonic nozzle exit due to the nozzle overexpansion. The Mach disk and subsonic region behind the normal shock are observed in this figure. As the ...
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... pressure profiles along the upper nozzle surface on the symmetry plane are shown in Fig. 19. In all cases, an overlapping pressure distribution was found up to X=R ¼ 6.2. Beyond that, these static pressures had steep increases at different locations, due to the upper boundary layer separation. The separation point moved upstream as the value of IPR increased. Then, each static pressure increased to a peak value, followed by a ...
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... point of the boundary layer separation. The separation distance, X, and the upstream vortex regions (PUV and IUV) decreased with decreasing IPR. With the decrement of the IPR value, the area of the PUV region diminished, causing The pitching angle, δ β , and specific impulse amplification coefficient, C AI , for different IPR values are shown in Fig. 21. The pitching angle rapidly increased as the value of IPR increased, because the increment of IPR governs the injected ...
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Citations
... For SVC, an axisymmetric conical supersonic nozzle has also been theoretically, experimentally, and numerically studied [39]. The geometric parameters of 3D circular sonic injection into the supersonic region of the nozzle were investigated for NPR of 37.5 with variable SPR. ...
... Increasing Mach would decrease TV efficiency [63] MFR Decreasing MFR of nozzle would result in strong oblique shock wave [39] SPR Increasing SPR improves TV angle, reduce response time, dynamic response, and increases the mass flow rate of secondary flow [30] NPR Decreasing NPR with Mach number results in better TV angle and efficiency. Increasing NPR results in increased dynamic response and mass flow rate of nozzle flow but decreased fluidic injection efficiency [32] Injection angle Decreasing injection angle results in increased dynamic response [64] J Increasing J improves the TV angle and increases deflection angle [25] A graphical representation of these parameters, which includes the effect of NPR, the effect of SPR, injection location, and injection angle, is presented in Figure 5. ...
... An increase in vectoring angle was reported, whereas a decreasing trend for vectoring efficiency and thrust coefficient was observed. At larger SPR, the interaction of shock with the upper wall induced thrust losses and resulted in larger pressure loss [39]. Similarly, Figure 5c reported an increasing trend in the vectoring angle with increasing injection angle and injection location. ...
Thrust vectoring innovations are demonstrated ideas that improve the projection of aerospace power with enhanced maneuverability, control effectiveness, survivability, performance, and stealth. Thrust vector control systems following a variety of concepts have been considered for modern aircraft and missiles to enhance their military performance. Short Take-off and Landing (STOL) and control effectiveness at lower aircraft speeds can be achieved by employing Fluidic Thrust Vectoring Control (FTVC). This paper summarizes a range of ideas for FTVC that have been designed and tested both computationally and experimentally to determine the thrust vectoring performance of supersonic propulsion system nozzles. The conventional method of thrust vectoring involves mechanical means to deflect the direction of flow of the exhaust gases, whereas the most recent method involves fluidic-based thrust vectoring techniques. Fluid-based thrust vectoring has the advantages of simplicity and low weight over mechanical-based thrust vectoring, which has complex geometry and adds extra weight to the aircraft. The fluidic vectoring control nozzles are divided into seven categories: shock vector, bypass shock vector, counterflow, co-flow, throat skewing, dual throat, and bypass dual throat nozzle control. This paper provides a summary of each fluidic thrust vectoring technique with its characteristics, design, classification, and different operational criteria developed to date and compares the intrinsic characteristics of each technique. Based on the present literature, it is concluded that among all the fluidic control techniques, the bypass dual-throat nozzle control can achieve better thrust vectoring performance with large vector angles and low thrust loss.
... The concept of implementing thrust vectoring by injection of secondary fluid into the primary nozzle flow dates back to 1949 and can be credited to A. E. Wetherbee Jr. [20]. The It is defined as the angle between the axial component of thrust, F x and the deflecting force, F y (which may be in the normal direction for the pitch thrust vector angle or in the yaw direction for the yaw thrust vector angle) [16]. ...
... The thrust vectoring efficiency is quantified in terms of the degree of vectoring, d achieved per percentage of secondary flow; the percentage of secondary flow is calculated relative to the primary nozzle flow [16]. ...
... It is defined as the ratio of the vectored thrust to the nonvectored nozzle thrust, F 0 [16]. ...
An efficient propulsion system holds the key for the smooth operation of any aerospace vehicle over different flight regimes. Apart from generating the necessary thrust, emphasis has also been laid on vectoring the direction of thrust. The primitive modes of thrust vectoring chiefly focussed on mechanical means such as the use of gimbals or hinges. The current state of the art technologies demand more efficient methods for thrust vectoring, which minimize the use of mechanical components. These methods, termed as fluidic thrust vector control methods, employ secondary jets for achieving the required attitude and trajectory of the aerospace vehicle. Such methods have greatly helped in reducing aircraft weight, reduction of aircraft maintenance requirements, and enhancement of stealth characteristics of aerospace vehicles. This work presents a review of the various fluidic thrust vectoring systems, starting with a brief overview of traditional thrust vectoring systems, followed by a discussion on the various aspects of fluidic thrust vectoring systems. It also highlights the effect of the various geometrical and operating conditions on the performance parameters of the thrust vectoring system such as the thrust vector angle, system thrust ratio and thrust vectoring efficiency among others. For ensuring the comprehensive character of this work, synthetic jet vectoring techniques have also been included due to its non-mechanical nature and similarities with purely fluidic thrust vectoring techniques.
... FTVN includes counter-flow TVN (Wu et al. 2018, co-flow TVN (Heo and Sung 2012), throat-shifting TVN (TSTVN) (Deere 2003;Deere et al. 2003), dual-throat TVN (DTTVN) (Ferlauto and Marsilio 2016;, bypass DTTVN (BDTTVN) (Wang et al. 2019), shockinduced TVN (SITVN), and bypass SITVN (BSITVN). Waithe and Deere (2003), Wu and Kim (2019a, c), and Wu et al. ( , 2020c experimentally, theoretically, and numerically analyzed the performance of rectangular SITVN using a slot injector, and clarified that nozzle pressure ratio (NPR), injection angle, and position and aspect ratio of the slot affect its performance significantly. Zmijanovic et al. (2012Zmijanovic et al. ( , 2014Zmijanovic et al. ( , 2016, Zou andWang (2011), andSellam et al. (2015) conducted analytical, computational, and experimental research on control effectiveness of the hole injector for conical SITVN, and expounded the impacts of hole location, NPR, and type of gas on the nozzle performance. ...
... In the flow field, shock wave/boundary layer interaction, primary upstream vortex (PUV), and secondary upstream vortex (SUV) occur. The SST k-ω model can better predict the above phenomena (Islam et al. 2018a, b;Wu et al. 2020c). Hence, it is used. ...
This article studies the aerodynamic performance of a novel bypass shock-induced thrust vector nozzle. An arc-shaped bypass is innovatively designed to optimize nozzle performance and equips a variable shrinkage part. The nozzle performance is investigated numerically under diverse shrinkage area ratios. Computational results indicate that both geometry and friction choking have important effects on the nozzle performance. Normally, in the case of without any bypass shrinkage, the flow choking occurs at the bypass outlet. Very small bypass shrinkage is unable to change the flow choking location. The bypass geometry choking comes up at its throat as the shrinkage area ratio of the bypass reaches 0.06. According to computational results, the vectoring angle diminishes with the increasing shrinkage area ratio of the bypass, thrust force ratio, thrust efficiency, specific impulse ratio, and coefficient of discharge increase. As the NPR enlarges, the deflection angle and thrust efficiency decrease, and the thrust force ratio increases.
... However, this is also a great challenge for the current aerodynamic prediction technology [50]. Although many research institutions and universities have carried out wind tunnel experiments, numerical simulations, and theoretical analyses on the aerodynamic characteristics of morphing aircrafts, there is still a long way to go before achieving a mature technology state [51,52]. ...
The high-performance morphing aircraft has become a research focus all over the world. The morphing aircraft, unlike regular unmanned aerial vehicles (UAVs), has more complicated aerodynamic characteristics, making itmore difficultto conduct its design, model analysis, and experimentation. This paper reviews the recent process and the current status of aeroelastic issues, numerical simulations, and wind tunnel test of morphing aircrafts. The evaluation of aerodynamic characteristics, mechanism, and relevant unsteady dynamic aerodynamic modeling throughout the morphing process are the primary technological bottlenecks formorphing aircrafts. The unstable aerodynamic forces have a significant impact on the aircraft handling characteristics, control law design, and flight safety. In the past, the structural analysis of morphing aircrafts, flight dynamics modeling, computational mesh morphing technology, and aerodynamic calculation were performed in promoting the development of next generation UAVs, with nonlinear dynamic challenges includingtransonic aeroelastic problems and high angle of attack aeroelastic problems. At present, many facets of these difficulties, together with the accompanying numerical simulation studies, remain under-explored. In addition, wind tunnel experiments face significant challenges in the dynamic morphing process. Finally, dynamic unsteady aerodynamic characteristics in the continuous morphing process still need to be verified by more related experiments.
... As shown in Figure 1, the vector control technologies commonly have two categories, namely fluidic and mechanical vectoring controls. 2 Fluidic vectoring control techniques usually employ a gas or liquid injection, involving co-flow, 3,4 counter-flow, [5][6][7][8] shock vector, [9][10][11][12] bypass shock vector, 13,14 throat shifting, [15][16][17] dual throat nozzle, 18,19 and bypass dual throat nozzle. 20,21 The above fluidic techniques have some outstanding advantages, for example, fast response, simple mechanical structure, and less thrust loss. ...
... 20,21 The above fluidic techniques have some outstanding advantages, for example, fast response, simple mechanical structure, and less thrust loss. 10,11 However, big storage tanks used to store and offer gas or liquid injectant and other assorted equipment increase system weight remarkably. Moreover, once the gas or liquid injectant is not sufficient, the control effectiveness becomes unstable. ...
... Critical equations in terms of mass, momentum, and energy are given as follows. 11 Mass ...
Mechanical thrust vector control is a classical and important branch in the vectoring control field, offering an extremely reliable control effect. In this article, a simple technology using a cylindrical rod has been numerically investigated to achieve jet controls for three-dimensional conical axisymmetric nozzles. Complex flow phenomena caused by the cylindrical rod on a flat plate and in a converging–diverging nozzle are elucidated with the purpose of a profound understanding of this technique for physical applications. Published experimental data are used to validate the dependability of current CFD results. A grid sensitivity study is carried through and analyzed. The result section discusses the impacts of three factors on performance, involving the rod penetration height, rod location, and nozzle pressure ratio. Significant vectoring performance variations and flow topologies descriptions are illuminated in full detail. When the rod penetration height changes, this technique has an effective control range, namely H/Rt ≤ 0.4. In this effective control range, the vectoring angle and efficiency increase and the thrust coefficient decreases with a deeper rod insertion. As the rod location moves downstream towards the nozzle exit, the vectoring angle increases and the thrust coefficient decays. Moreover, the direction of jet deflection remarkably varies for diverse rod locations. While the nozzle pressure ratio increases, the vectoring angle initially increases to reach the maximum level and then decays slightly. Meanwhile, the thrust coefficient continuously increases.
... In [12], a joint theoretical and numerical analysis was carried out to analyze changes in productivity in a three-dimensional supersonic rectangular nozzle with a slot injector. The calculated static pressure distributions based on the k-ω shear stress transfer turbulence model are in good agreement with the experimentally measured pressure values. ...
The thrust vector control of a rocket engine by disturbing the supersonic flow in its nozzle is used for missile development for various purposes in different countries. Disturbance of the supersonic flow in the jet engine nozzle can be caused by various obstacles on the nozzle wall: solid obstacle, liquid or gas jet, combinations of solid obstacle with injected jets. The simplest and most effective way to create a disturbance is to disturb it by setting a solid cylindrical obstacle on the nozzle wall. The high efficiency is explained by the lack of the working fluid consumption on board the aircraft to create a control force, or its minimum amount necessary to protect the obstacle from the high-temperature oncoming gas flow in the rocket engine nozzle. This paper presents the study results of gas flow simulation with cylindrical obstacle perturbation on the wall of the Laval rocket engine nozzle in its subsonic and supersonic parts. The optimal placement in the nozzle is determined to obtain the maximum lateral control force. As a result of research, it was found that the perturbation of a supersonic flow in a rocket engine nozzle by a cylindrical obstacle has practically the same character when its position changes along the length of the nozzle. In the subsonic part of the nozzle in the median plane, the perturbed pressure on the wall has a positive sign, and on the obstacle wall its sign-alternating. When an obstacle is in the subsonic part of the nozzle, the integral value of the lateral force is negative in comparison with positive for the supersonic part.
... The interaction between a fluid in movement and a solid generates considerable energy losses due to resistance to flow, also called drag. Minimizing drag losses is beneficial for a multitude of industries, such as the naval and aeronautics industries [1][2][3][4][5][6]. Still, in the 1940s, it was discovered that the addition of small amounts of soluble polymers with a high molecular weight was affected by flow resistance without affecting the viscosity or density of the fluid in turbulence [7]. ...
Drag is one of the main energy-dissipating phenomena in engineering applications. Drag-reduction mechanisms have been studied to reduce this cost. Superhydrophobic surfaces (SHS) have high water repellency and have been studied as an alternative mechanism for reducing drag. The high level of repellency is due to the hierarchical structures in the micro- and nano-scales, making these surfaces able to trap air layers that impose the condition of slipping. The present work investigated the phenomenon of drag reduction on surfaces made of Sylgard® 184 elastomer and modified by low-pressure plasma treatments. Atmospheres with 40% Argon and 60% Acetylene, and 20% Argon and 80% Acetylene were used, varying the treatment times from 10 to 15 min of exposure to Acetylene. The surface, morphological and chemical modifications were confirmed by XPS and AFM analyses, showing the impression of a rough structure on the nanometric scale with deposition of chemical elements from the gas plasma. Furthermore, the obtained SHS showed lower resistance to flow, tested by the imposition of flow in channels.
... The F-TVC could achieve identical control effectiveness as M-TVC with a 50% lower cost . Several kinds of concepts have been proposed to control flow deflections, for example, shock-wave TVC (SW-TVC), bypass shock-wave TVC (BSW-TVC), coflowing TVC, counterflowing TVC, throat-skewing TVC (TS-TVC), dual-throat nozzle TVC (DTN-TVC), and bypass dual-throat nozzle TVC (BDTN-TVC), as shown in Fig. 2. Wu and Kim (2019a;2019b;2020b) theoretically and numerically studied the SW-TVC features in a three-dimensional (3-D) rectangular propulsion nozzle with a slot injector and argued some critical parameter effects. Besides, Deng and Kim (2015) and Deng et al. (2016) numerically investigated internal flow characteristics of the BSW-TVC in a conical supersonic nozzle with a cylindrical bypass and argued the influence of the nozzle pressure ratio (NPR). ...
The dual-throat vectoring nozzle is an efficient technique utilizing less high-pressure secondary streams to control mainstream deflections flexibly. In this article, three-dimensional Reynolds-averaged Navier–Stokes simulations were performed using a commercial computational fluid dynamics program, and the numerical methods applied in this study were validated through comparison with the experimental results. Two parameters of the slot injector have been investigated, namely the incident angle of the secondary stream and the slot length-to-width ratio. Critical performance parameters have been quantitatively analyzed, involving the pitching angle, injected mass flow ratio, system resultant thrust ratio, and resultant pitching thrust efficiency. Furthermore, visual flow-field features are expounded using Mach number contours on the center-plane, Mach number contours on various slices, and streaklines. Some meaningful conclusions are drawn herein. The flow field in this three-dimensional dual-throat nozzle is not fully symmetric based on the reference of the center-plane. Consequently, a full domain is essential to capture the flow characteristics accurately, instead of a half domain. Although the pitching angle for the secondary stream incidence angle of 120° is the highest, comprehensive characteristics in terms of resultant pitching thrust efficiency and system resultant thrust ratio for 150° are more outstanding. The pitching angle, system resultant thrust ratio, and resultant pitching thrust efficiency increase with an increase in the slot length-to-width ratio for a constant secondary stream mass flow rate. Under the circumstance of a constant injection pressure ratio, the pitching angle increases with an increase in the slot length, whereas system resultant thrust ratio and resultant pitching thrust efficiency decline with an increasing slot length.Graphic abstract
... A few of fluidic vectoring concepts and principles have been proposed and listed in Fig. 2, e.g., shock wave TVC (SWTVC), bypass shock wave TVC (BSWTVC), counterflowing TVC (COUTVC), coflowing TVC (COTVC), throat shifting TVC (TSTVC), dual throat nozzle TVC (DTNTVC), and bypass dual throat nozzle TVC (BDTNTVC). Wu and Kim (2019a; and Wu et al. (2020c) carried through theoretical and computational fluid dynamics (CFD) work about steady features of the SWTVC in a supersonic rectangular propulsion nozzle and detailedly illuminated the impacts of injection-to-mainstream momentum flux ratio, injector location, and the length-to-width ratio of the slot injection syringe. Deng and Kim (2015) finished some CFD work concerning internal flow characteristics of the BSWTVC and elucidated the influences of nozzle pressure ratio (NPR) and injection-to-mainstream mass flow ratio, separately. ...
Compared to a variety of mechanical vectoring nozzles, fluidic vectoring nozzles possess more research value nowadays. The dual throat nozzle is gradually developing into an outstanding technology to handle supersonic and hypersonic aircraft deflections. Three-dimensional, steady, compressible, and viscous flows in rectangular dual throat nozzles are numerically investigated by resolving Reynolds-averaged Navier-Stokes equations and shear stress transport k-omega turbulence model. Computational fluid dynamics results are verified against the existing experimental data, where a good consistency is gained. The impacts of nozzle pressure ratio, injection-to-mainstream momentum flux ratio, and setup angle of the slot injector on the systemic performance are examined. Useful conclusions are summarized for engineering designers. Firstly, pitching angles decline along with an increasing nozzle pressure ratio, while systemic thrust ratio and thrust efficiency increase. Secondly, thrust vector angles enlarge with an increase of the injection-to-mainstream momentum flux ratio, whereas both systemic thrust ratio and thrust efficiency decay. Finally, the setup angle of the slot injector impacts the systemic performance remarkably. Although the pitching angle for the setup angle of 120° is highest, comprehensive characteristics in terms of systemic thrust efficiency and systemic thrust ratio for the setup angle of 150° are more excellent.
... Advanced vectoring control techniques aim to properly manipulate aircraft flight trajectories by generating side forces (Wu et al. 2020b). Except for offering extra thrust, effective vectoring control systems can deftly implement rolling, pitching, and yawing postures of the aircraft, as indicated in Fig. 1. ...
Currently, the fluidic thrust vectoring technique is a promising method offering an alternative to the classical method of thrust deviation employing mechanical actuators with potential mass gain. In this article, theoretical and computational fluid dynamics investigations of counterflow fluidic thrust vectoring technique of a rectangular nozzle are carried through. A new engineering-type analytical approach based on mass and momentum conservation laws applied to specific control volumes is developed to predict the vectoring performance. Furthermore, the performance of the vectoring technique is computationally clarified for diverse nozzle pressure ratios (NPRs) and secondary pressure ratios (SPRs). Obtained conclusions indicate that the vectoring deflection angle diminishes with an increase in the NPR, whereas the thrust vectoring efficiency coefficient increases. The vectoring deflection angle and the thrust vectoring efficiency coefficient increase with a decrease in the SPR.
