Techniques of Fluidic Thrust Vectoring in Jet Engine Nozzles: A Review

Abstract

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.

1. Introduction

Every time, new technologies emerge that are innovative enough to dramatically change the nature of military operations. For high-performance aircraft, thrust vectoring technology has emerged so profoundly that it has redefined traditional aircraft design methods and the use of the aircraft itself. Thrust vectoring technology offers many advantages in terms of maneuverability, control effectiveness, survivability, performance, and stealth characteristics of the aircraft. It is a technique that can provide effective forces and moments, making take-off and landing requirements easier, even at low dynamic pressure. Thrust vectoring provides additional thrust and allows pitching, yawing, and rolling movements by changing the line of thrust.

Thrust vectoring (TV) technology works on the principle of deflecting the thrust direction of the aircraft. It relies on a working fluid, or a source mounted on the aircraft, and an engine exhaust nozzle providing a passage for the fluids. For providing the maximum thrust possible to the aircraft, the nozzle designs must ensure the requirement of thrust, cost, mission profile, and weight of the aircraft. Until now, nozzles for thrust vectoring have been technologically advanced from single-axis to multi-axis systems. Single-axis convergent-divergent nozzles deflect the thrust in the pitch direction, whereas multi-axis convergent-divergent nozzles are capable of deflecting thrust around all three-body axis. These nozzles actively complement or even eliminate the use of control surfaces [1]. To date, TV is achieved in an aircraft using two methods. The traditional method involves mechanical means to deflect the direction of flow of the exhaust gases, whereas the most recent method involves fluidic-based thrust vectoring techniques.

Mechanical thrust vectoring (MTV) is a technique achieved mechanically by deflecting the engine nozzle to alter the direction of thrust with the use of actuators and gimbaling mechanisms. Although it produces effective TV, the thrust vectoring configurations become heavy, complex, and expensive. To overcome the complexity and integration inefficiency of MTV, fluidic thrust vectoring (FTV) techniques were developed and investigated. FTV is a technique that uses a secondary flow source for controlling the exhaust flow of the engine nozzle. Fluidic-based methods provide the advantage of reduced weight, higher reliability, and engine airframe integration [2,3,4]. Fluidic injection for throttling and vectoring was explored in the 1950s for application to rocket nozzle systems. It actively controlled the primary flow deflection by penetrating the secondary fluid into the divergent section of the rocket nozzle [5,6,7]. However, its interest was lost. It was in the 1990s when researchers were again attracted to FTV due to its fascinating thrust vectoring performance characteristics. The research concluded that FTV was capable of achieving the same vectoring control as MTV but with 50% reduced weight and cost. Several FTV controls were investigated to deflect the primary flow. It was observed experimentally that a small variation in the nozzle area could result in an entire flow modification of the nozzle [8,9,10]. FTV provides aircraft with several advantages. Firstly, it requires no moving part, which leads to reduced weight and complexity of the system. Secondly, for high-temperature conditions, an optimal nozzle can be designed, which can reduce drag and radar cross-section. FTV is more desirable due to its quick integration into existing systems [11,12]. In dry and afterburner cruise operating conditions, fixed exhaust nozzles demonstrated significant thrust vectoring capabilities [13,14]. These benefits have led to a vast investigation and development of FTV techniques. To date, depending upon investigations, FTV controls are divided into seven control systems. These control systems are Shock Vector Control, Bypass Shock Vector Control, Counter Flow Control, Co-Flow Control, Throat Skewing control, Dual Throat Nozzle Control, and Bypass Dual Throat Nozzle Control. Among all these vectoring controls, counter-flow control works on the principle of suction to control the primary flow deflection. However, the rest of the control techniques depend upon the principle of blowing to control the primary flow deflection. Different methods of fluidic thrust vectoring control are represented in Figure 1.

The motivation behind this work was to provide a summary of current knowledge about Fluidic Thrust Vectoring Controls (FTVC) developed to date. This study sought to determine which technique appears to be the most promising for achieving the best TV performance. The belief behind this review was that the bypass dual throat nozzle is the optimal technique for generating fluidic thrust vectoring. In order to arrive at this conclusion, we must compare the intrinsic characteristics, effects, advantages, and disadvantages of each technique, as well as the potential problems associated with integrating these systems. Therefore, by discussing the findings presented in recent research papers, we aim to create an understanding of different fluidic thrust vectoring techniques for the readers. As far as the authors are aware, there has been no recent comparative review of all control systems. In this paper, Section 2 introduces the concept of shock vector control (SVC). SVC involves secondary flow penetrated in the divergent part of the nozzle. To overcome the thrust losses generated by SVC, a bypass SVC has also been investigated. Bypass SVC involves a bypass passage flow for vectoring the primary flow. Section 3 presents the counter flow thrust vectoring technique. This method uses momentum removal to control the primary flow. Section 4 refers to co-flow thrust vectoring control. It involves momentum injection to control the primary flow. Section 5 introduces throat skewing thrust vectoring control. It involves a secondary flow injection in the throat area of the nozzle for vectoring the flow. Section 6 presents the concept of dual throat nozzle control. It consists of two minimum areas with a secondary flow injected in the upstream minimum area of a CDC nozzle. These FTV controls consume an inevitably high-pressure secondary injection, which introduces thrust losses due to bleeding air from the engine compressor or fan. To overcome these losses, a new kind of bypass dual throat nozzle was developed, which is presented in Section 7. Section 8 compares all the seven-candidate control systems under certain evaluation criteria. The evaluation criteria include design, impact on the system, implementation, thrust vectoring angle, thrust coefficient, thrust efficiency, thrust losses, negative consequences, and potential problems. The conclusions are drawn in Section 9.

Figure 1. History of fluidic thrust vectoring controls techniques [15,16,17,18,19,20].

Figure 1. History of fluidic thrust vectoring controls techniques [15,16,17,18,19,20].

2. Shock Vector Control (SVC)

Shock vector control is an FTV technique that introduces a secondary fluidic flow injection in the divergent portion of the convergent-divergent nozzle. The disturbance caused by this injected flow generates an oblique shock wave due to the low-pressure region downstream of the injection port. The interaction of the oblique shock wave with primary flow deflects the flow supersonically, thus resulting in thrust vectoring. A schematic of SVC is shown in Figure 2.

2.1. Effect of NPR and SPR

A series of experiments were performed for a nozzle pressure ratio (NPR) of 10–30, along with different secondary pressure ratios (SPR) for a supersonic nozzle [22]. The maximum vectoring angle reported was 5°, significantly less than previous investigations carried out on the SVC technique. A thrust ratio of 0.88 was observed in both cases (NPR = 20–30). It was believed that the over-expanded nature of nozzle flow might have resulted in such a low value [23]. The effects of secondary injection on SVC performance were investigated for a range of NPR up to 10 with an SPR value from 0.4 to 1. For NPR = 4.6 and SPR = 0.7 and 1, the thrust vectoring angle achieved was 7.5°. NPR values of 2.5 and above showed a good agreement between numerical and experimental data, but NPR values less than 2.5 (highly over-expanded flows) showed a disagreement [24]. TV angle of 4.4° at NPR = 3 and thrust coefficient of 0.891 was achieved as the best TV efficiency. The thrust coefficient relates to the ratio of resultant thrust to ideal thrust. It determines the amplification of thrust during flow expansion. Injection parameters such as location, angle, length-to-width ratio, and momentum flux ratio (J) were investigated for NPR = 4.6. It was observed that increasing momentum flux and length-to-width ratio caused an increase in TV angle [25]. For NPR = 3 and 4.6, the largest TV angle achieved was 17.2° and 17.6°. The largest deflection angle was achieved when the injection location moved upstream and decreased when it moved downstream. The injection angle also played a vital role in the deflection angle [26]. The effect of secondary flow for an NPR = 4–10 with SPR = 1–2 at two different injection locations was investigated. The result indicated that SPR had a positive impact on TV moments [27]. Two different nozzle models were compared to evaluate the performance of FTV for different NPR = 3–10 and SPR = 1–3 with two injection locations [28]. The internal performance of a 2D nozzle was investigated for NPR up to 10 and SPR up to 2.7. Two shock waves were generated, a weak shock at the upstream of injection and a stronger wave at the injection interface. The primary flow was deflected twice, but the stronger shock resulted in deflecting the flow [29].

2.2. Transverse Injection

The SVC technique has the ability to provide large TV angles by generating a shock system. However, due to operating in over-expanded conditions, SVC also suffered from over-expansion losses in order to achieve high TV angles [30,31]. SVC-induced problems related to thrust losses due to the penetration of secondary flow and the formation and interaction of oblique shock with the primary flow. For achieving maximum thrust vectoring angle with minimum thrust losses, an optimized secondary injection design based on transverse injection flow was conceived [32]. Some researchers [33,34] investigated the transverse injection cases; the result indicated that separation and shock interaction occur along the deflected jets. Due to the secondary injected flow, unbalanced forces act in the divergent section [35]. An experimental study was carried out to investigate yaw thrust vectoring for a low subsonic flow regime with varying secondary injection momentum ratios. The study found that the vectoring angle increases with increasing the momentum ratio of the secondary flow [36]. A study conducted compared the Reynolds stress and k-ε turbulence model with experimental data. The Reynolds stress model predicted the experimental result accurately compared to k-ε. As pressure ratios increased, Reynolds stress model results became less consistent [37]. To evaluate the performance, two- and three-dimensional cases were proposed, investigated, and numerically modeled. These models were experimentally complemented and improved numerically [38]. Until now, there have been many optimal strategies developed for SVC. However, an optimal application for transverse injection is still under investigation.

2.3. Slot Injection

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. The results indicated that TV through secondary flow was dominantly affected by the inclination and position of injection in the nozzle [40]. A circular injector port was used for penetrating the secondary flow in the divergent part of the nozzle and could generate a strong shock to deflect the primary flow. Figure 3 signifies the schematic of the flow field with slot injection. When a secondary flow was injected into the primary flow, the flow encountered a bow shock wave with various viscous and boundary layer interactions. Due to an adverse pressure gradient, weak shock waves appeared at the initial separation point [41,42]. However, as the boundary layer got close to the secondary fluidic injection port, the separation deepened and allowed the formation of a strong bow shock wave. This strong bow shock wave was caused due to the compression fan interaction. The region of recirculating bubbles was observed both upstream and downstream of the nozzle, as well as the injected upstream region [43,44]. The primary flow, when crossing from the separation point, attached the bow shock to itself and continued its motion forward. Sometimes, the interaction between the primary and secondary flow caused the formation of a more complex reflection of the shock wave, including surface effects [45,46].

2.4. Injection Configurations

A 2D SVC nozzle with secondary injection located at 68.8% of the divergent section of the nozzle was analyzed. The parameters considered were NPR = 6–16, SPR = 0.6, 0.8, 1, 1.2, secondary angle of 90° and 130°, along with 7, 9, and 13 orifice injection configurations. The result indicated that the TV angle for the 19 orifices injection configuration was greater compared to the 7 and 13 orifices. It was concluded that the thrust coefficient decreased with decreasing the number of injection orifices for different SPRs. Although the 19 orifices had a better vectoring angle than the 13 and 7 orifices, it was still less than the vectoring angle obtained from a single injection slot. For obtaining a larger vectoring angle in SVC, single-slot injection was a better option [48]. The effects of multiple port injections for a 2D non-axisymmetric nozzle were investigated both experimentally and computationally. The results demonstrated the benefits of using multiple injection ports. For NPR less than 4 and higher SPR, increasing the injection port from one to two resulted in improved TV performance. At the same time, no benefits were recorded for NPR values greater than 4 [49]. A 3D study using an orifice injector demonstrated that the deviation angle increases from 5.49° to 9.23° with increasing SPR from 0.667 to 1.167 [50].

2.5. Effect of Hot and Cold States

A plenum above the span-wise slot for a 2D nozzle was investigated. The plenum was used for facilitating the secondary flow injection [51]. The effect of cold and hot states on the thrust was investigated. The operation included five states: no nozzle, fixed nozzle, secondary injection in the throat area, secondary injection in the divergent area, and secondary injection in both the throat and divergent area. At secondary pressure of 0.5 MPa, the thrust obtained for the five states ranged between 27.3 N to 50.9 N. The result demonstrated that cold injection through secondary injection not only enhanced the thrust performance but was also capable of reducing the over-expansion and under-expansion losses [52].

2.6. Bypass Flow Injection

A bypass flow injection has been investigated to control the deflection angle [53,54,55,56]. To minimize the influence of secondary injection and to maximize the thrust vectoring angle with minimal thrust loss, a bypass passage flow SVC was conceived. A control valve was used to control the bypass flow rate. It was observed that with increasing the bypass flow rate, there was an increase in thrust vectoring angle as well. With a bypass flow of less than 10%, 10° thrust vectoring was achieved [57]. Figure 4 signifies the bypass SVC schematic for TV.

2.7. Injectors

The asymmetric two-dimensional nozzle was investigated for different kinds of injectors. Two adjacent sonic injections were examined by NASA [49]. A single injector for the SVC configuration was observed for NPR = 4.6 and 8.78, along with SPR values of 0, 0.7, and 1. The best TV angle achieved was about 6.9°, providing an efficiency of 1.7 with a 4% injection mass flow rate and 0.96 thrust coefficient [58]. Aerodynamic effects on FTV were also examined. Results were computed for free stream and static flow conditions. Compared to static flow conditions, TV performance and efficiency decreased for free stream flow [22]. The effect of secondary injection reaction heat on TVC was also explored computationally and experimentally. For primary and secondary flow, methane and air reaction were used for the reaction process [59]. The effect of the different gas injectors on the main nozzle was investigated. The gases included CO₂, argon, and helium for SPR = 1 and MFR = 0.076. Helium gas was indicated to produce large TV angles of 16.2° and 15.15° [60].

FTV performance for a 2D single expansion ram nozzle was numerically calculated. The impact of the suction tunnel position, angle, and width was also analyzed [61]. Different models and designs were investigated and proposed for the axisymmetric nozzle to achieve better performance for the vectoring control system [62]. In summary, many parameters have been examined for fluidic SVC. A few parameters and their effects on TV for different configurations are compiled in

Table 1. Parameters affecting the shock vector control.

Parameters	Effects	Ref
Mach	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. All the trends observed for these parameters were obtained from the data available in the literature. The trend for vectoring angle and vectoring coefficient at different NPR were observed in Figure 5a. Vectoring angle showed a decreasing trend with increasing NPR, whereas the thrust coefficient was observed to increase for NPR < 6.5 and decrease for NPR > 6.5. It was reported that increasing NPR resulted in eliminating the shock and improving the separation in the nozzle, which improved the thrust but degraded the vectoring angle [22,48]. Figure 5b refers to the trend of vectoring angle, vectoring efficiency, and thrust coefficient at different SPRs. 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. Increasing the injection angle and injection location had a negative impact on vectoring efficiency and thrust coefficient [39,48].

SVC has widely investigated thrust vectoring control until now. It was reported that SVC achieves a higher vectoring angle, but the shock formation degrades the performance of the nozzle. Multiple turbulence models were investigated for SVC. It was reported that SST k-ω was able to predict the separation position and pressure rise in agreement with the experimental values. The potential downside of using SVC is the creation of shock which introduces performance losses and structural damage due to the shock boundary layer interaction in the nozzle. A summary of some numerical investigations carried out on SVC is presented in

Table 2. Summary of recent numerical investigations carried out on SVC.

Year	Title	Model	Varying Parameters	Computational Setup and Details	Conclusions	Ref
2014	A study on the thrust vector control using a bypass flow passage	2D nozzle with bypass flow injection	NPR = 5–20 BFR = 2.1–12.2	Fluent/SST k-ω Model $0.3\times {10}^6$ grid cells ${\mathrm{P}}_{\mathrm{a}}$ = 101,325 Pa ${\mathrm{T}}_{\mathrm{a}}$ = 300 k	BFR has a positive impact on TV angle.	[57]
2016	Investigation on Flow field Characteristics and Performance of Shock Vector Control Nozzle Based on Confined Transverse Injection	2D nozzle	Orifice = 7–19 NPR = 6–16 SPR = 0.6–1.5	Fluent/SST k-ω Model $2.0\times {10}^6$ grid cells ${\mathrm{T}}_{\mathrm{a}}$ = 800 k	TV coefficient decreased with decreasing the number of injections orifices for different SPR.	[48]
2017	Numerical Investigation of Optimization of Injection Angle Effects on Fluidic Thrust Vectoring	2D rectangular nozzle	NPR = 3–4.6 SPR = 0.7–1.3 Injection angle = 60°–120°	Fluent/Spalart-Allmaras Model $1.04\times {10}^6$ grid cells ${\mathrm{P}}_{\mathrm{a}}$ = 101,325 Pa ${\mathrm{T}}_{\mathrm{a}}$ = 293.1 k	Increasing SPR with optimized injection angle had a positive impact on TV angle but a negative impact on thrust efficiency.	[65]
2017	Influence of Secondary Injection Parameters on Performance of Shock Vector Control Nozzle	Circular to rectangular nozzle	SPR = 0.4–1.5	Fluent/SST k-ω Model $3.0\times {10}^6$ grid cells ${\mathrm{P}}_{\mathrm{a}}$ = 101,325 Pa ${\mathrm{T}}_{\mathrm{a}}$ = 300 k	Stronger shock waves at higher SPR. With increasing SPR, TV angle increased and then started to decrease.	[66]
2019	Fluidic Thrust Vector Control Using Shock Wave Concept	2D transverse slot injection	J = 0.1–0.9	Fluent/SST k-ω Model $2.0\times {10}^6$ grid cells ${\mathrm{P}}_{\mathrm{a}}$ = $4.0\times {10}^6$ Pa ${\mathrm{T}}_{\mathrm{a}}$ = 300 k	As J increased, the TV angle increased whereas TV coefficient decreased.	[64]
2019	Numerical study on the shock vector control in a rectangular supersonic Nozzle	3D rectangular nozzle	J = 0.1–0.89 X/L = 0.73–0.85 Λ = 45°–135°	Fluent/SST k-ω Model $1.0\times {10}^6$ grid cells ${\mathrm{P}}_{\mathrm{a}}$ = 4.6 atm ${\mathrm{T}}_{\mathrm{a}}$ = 300 k	Increasing J and X/L ratio caused an increase in TV angle. The largest deflection angle was achieved when the injection location moved upstream and decreased when it moved downstream.	[25]
2020	Theoretical and Numerical Analyses of Aerodynamic Characteristics on Shock Vector Control	3D rectangular nozzle	NPR = 3–5 SPR = 2.49	Fluent/SST k-ω Model ${\mathrm{P}}_{\mathrm{a}}$ = 101,325 Pa ${\mathrm{T}}_{\mathrm{a}}$ = 300 k	NPR had a positive effect on thrust coefficient, primary MFR and a negative impact on vectoring angle. Vectoring angle increased with increasing SPR.	[39]

.

3. Counter Flow Control (CFC)

The counter-flow thrust vectoring technique involves a secondary fluidic flow penetrated in the opposite direction of the primary flow. Usually, in the counterflow technique, the application of suction creates a secondary fluidic flow stream and produces an asymmetric flow in the primary fluid. The difference between co-flow and counter-flow thrust vectoring control is that the former involves momentum injection, while the latter uses momentum removal for controlling the primary flow. CFTV can achieve large TV angles by using suctions between the nozzle’s trailing edge and an aft collar. Figure 6 details the CFTV schematic for the TV.

3.1. Shear Layer CFTV

Several theoretical and numerical investigations on CFTV control have been carried out. A new calculation on a 3D rectangular nozzle current CFTV shear layer system for different mainstream temperatures was examined. It was found that by increasing the mainstream temperature, the Mach number increased, and the TV angle gradually declined. However, this experiment reported that the mainstream temperature doesn’t significantly affect the thrust coefficient [68]. Several other parameters were studied for CFTV, which included collar length, collar radius, and the gap height between the primary and secondary flow. The results for the shear layer CFTV technique provided a more controllable region than the co-flow FTV technique [16,17]. A multi-axis diamond-shaped nozzle CFTV was investigated for achieving TV for a Mach number of 2. The maximum deflection achieved was 15°. A comparison of a multi-axis and a single-axis was also inspected. It was found that a single-axis CFTV system was more efficient in producing TV and had reasonably linear behavior [69]. In CFTV, for steering the jet, no moving parts and surfaces were in contact with the moving fluids. However, the drawback of the use of the CFTV application was restricted due to engine integration, hysteresis, and additional equipment for suction [70].

3.2. Collar Geometry

By increasing the gap height, the suction MFR also increased. A proper range of collar length was required for side forces to act adequately on the primary flow. Different experiments on collar geometry indicated that without a proper collar, control flow was not efficient [71]. Being said, the collar played a vital role in ensuring the optimal efficiency of the counterflow TV system. The collar allowed a path for secondary fluid to flow, which created a mixing layer across the collar area. By disrupting the continuity of the operation, the collar was found to be responsible for creating hysteresis and bi-stability problems. For a certain condition at the nozzle, the jet attached to the wall due to a bi-stability problem reached a stable equilibrium [64]. Effects of geometric parameters (slot width, length of the collar) on the Laval nozzle were numerically studied. A critical length of collar was obtained between 0.19–0.2 m, and the slot width varied between 0.017–0.02 m [72]. For implementing CFTV in the aircraft propulsion system, a well-established rectangular jet for a Mach number of 1.4 was investigated [73]. For CFTV, a TV angle of 16° was achieved for a supersonic rectangular jet [74]. By designing the collar geometry properly, the Coanda effect could be avoided. A proper collar design must consider the stability of the aircraft, TV efficiency, and continuous performance at a high TV angle. CFTV was able to produce a maximum vector angle of 15° at NPR = 5. The thrust coefficient at NPR of 5 was 0.2. At NPR = 8, CFTV was able to achieve a vector angle of 12° with a 0.945 thrust coefficient [75]. It was concluded that adding a large collar to the CFTV control technology made it more efficient compared to other FTV techniques.

3.3. Effect of NPR

At different NPRs, the effects of various characteristics for a Mach number of 2.5 on TV performance for CFTV were investigated. For NPR = 15–17 and 18–20 values, at a constant SPR of 0.8, it was observed that with increasing the NPR, the primary MFR increased, and thus, the MFR of secondary flow decreased. For SPR of 0.9–0.6, a low value of secondary mass ratio (0.6%–2.3%) was reported. It was found that with a decreased value of SPR, an increased value of thrust loss was achieved. The deflection angle achieved for the SPR value of 0.6 was 5.5°. For an SPR value of 0.8, the MFR of secondary flow was obtained between 0.9% and 2.4% [64]. A study was conducted at an NPR range of 3.5–10 values for a collar length of 8 inches (100% and 50%) with different suction slot heights. When comparing 50% and 100% collars, the latter was found to produce the largest TV angle. Upon decreasing the slot height, the decreasing behavior of the resultant thrust ratio was obtained [67]. Several parameters have been examined for fluidic counterflow control. A few parameters and their effects on TV for different configurations are compiled in

Table 3. Parameters affecting the counter flow control.

Parameters	Effects	Ref
Collar radius	Collar radius directly affected the pitching angle and suction MFR whereas it inversely affected the thrust coefficient	[68]
Collar length	The length of the collar affected how side forces would act on the mainstream. The proper range affected the system’s performance. An excessively long collar would lead to hysteresis length occurrence and unnecessary weight	[72]
Gap height	It had a direct effect on pitching angle and an inverse effect on thrust coefficient, as well as suction MFR	[76]
NPR	The mass flow rate of primary flow increased whereas the mass flow rate of secondary flow decreased with increasing NPR. Additionally, NPR had a negative effect on the system thrust ratio (STR)	[77]

. A graphical representation of the effect of SPR and collar length is presented in Figure 7. All the trends observed for these parameters were obtained from the data available in the literature. Vectoring angle showed a decreasing trend with increasing SPR, whereas the thrust coefficient was observed to increase with increasing SPR. At constant NPR = 17, the performance of vectoring angle and thrust coefficient reported was better for high Mach conditions. Another important parameter affecting the performance of CFC was collar length. A decreasing trend for vectoring angle and an increasing trend for thrust coefficient at varying collar lengths were observed [64,68]. A summary of some numerical investigations carried out on CFTV is presented in

Table 4. Summary of recent numerical investigations carried out on CFTV.

Year	Title	Model	Varying Parameters	Computational Setup and Details	Conclusions	Ref
2017	Numerical simulation of fluidic thrust vectoring in an axisymmetric supersonic nozzle	2D nozzle	Collar length = 0.17–0.23 Slot width = 0.014–0.026	Fluent/k-ε Model ${\mathrm{P}}_{\mathrm{a}}$ = 0.1–0.6 atm ${\mathrm{T}}_{\mathrm{a}}$ = 300 k	For larger collar length, the flow attached to upper collar wall.	[72]
2017	Investigation on Flow field Characteristics and Performance of Shock Vector Control Nozzle Based on Confined Transverse Injection	3D nozzle	Coanda surface = 0.5–1.75, Gap height = 0.02–0.05	Fluent/k-ε Model	Secondary gap height had a negative impact on TV angle. The dead zone appeared at low secondary MFR where TV angle was small.	[78]
2017	Numerical Investigation of Optimization of Injection Angle Effects on Fluidic Thrust Vectoring	2D nozzle	NPR = 15–20 SPR = 0.6–0.9	Fluent/k-ε Model 153,136 grid cells ${\mathrm{P}}_{\mathrm{a}}$ = 0.1–0.6 atm ${\mathrm{T}}_{\mathrm{a}}$ = 300 k	With constant SPR, NPR directly affected the primary MFR and inversely affected secondary MFR.	[64]
2018	Influence of Secondary Injection Parameters on Performance of Shock Vector Control Nozzle	2D nozzle	Mach no = 0.1–0.8	Fluent/k-ε Model 153,760 grid cells ${\mathrm{P}}_{\mathrm{a}}$ = 7.824 atm ${\mathrm{T}}_{\mathrm{a}}$ = 300 k	TV angle did not have a much influence under large Mach number.	[79]
2019	Fluidic Thrust Vector Control Using Shock Wave Concept	2D nozzle	NPR = 15–20 SPR = 0.6–0.9	Fluent/k-ε Model 153,136 grid cells ${\mathrm{T}}_{\mathrm{a}}$ = 300 k	When increasing or decreasing NPR and SPR, hysteresis phenomena occurred. For SPR = 0.8, the TV angle and secondary MFR increased with decreasing NPR. Additionally, for NPR = 17, the TV angle and the secondary MFR decreased with an increasing SPR	[80]
2019	Numerical study on the shock vector control in a rectangular supersonic nozzle	3D nozzle	Gas source Case i. Both sides control joint closed Case ii. One side control joint open	${\mathrm{P}}_{\mathrm{a}}$ = 5000 Pa ${\mathrm{T}}_{\mathrm{a}}$ = 300 k	Flow field was found symmetrical for case i. Primary flow was deflected in case ii.	[81]
2020	Theoretical and Numerical Analyses of Aerodynamic Characteristics on Shock Vector Control	3D nozzle	NPR = 17 SPR = 0.8 Gap height = 0.28–0.53	Fluent/k-ε Model ${\mathrm{P}}_{\mathrm{a}}$ = 17,225,251 Pa ${\mathrm{T}}_{\mathrm{a}}$ = 300 k	Collar radius had a positive impact on TV angle. As collar length increased, TV angle increased and then started decreasing.	[68]

.

4. Co-Flow Control (Co-Flow TVC)

Like the CFTV technique, the co-flow TV concept involves a secondary fluidic flow source with the Coanda effect for TV facilitation. The co-flow method involves a tangential injection to control the primary flow vectoring. For this phenomenon, a separate air stream is introduced in the primary flow that follows the principle of the Coanda effect and turns the main flow into a curved path. The secondary flow that is introduced can be observed on the side nearest to the surface. This entrained air then introduces a pressure difference that is perpendicular to the axis of the centerline of the jet flow. This creates a localized low-pressure region that causes an increment in the rate of entrainment on the side of the secondary jet that is not bounded by the Coanda surface. Thus, TV takes place as there is a change in the field of the flow of the primary jet centerline. This process of co-flow TV can be further aided with the introduction of another curved surface to the rear side of the nozzle and then introducing a secondary jet flow parallel to the Coanda surface. Figure 8 signifies the co-flow control schematic for TV.

4.1. Three Significant Zones

Different configurations for co-flow were investigated numerically and experimentally by researchers. The effects of multiple jet geometries on the effectiveness of TV were examined, and a new model was designed for low-speed aircraft. It was found that the effectiveness of TV depended upon the secondary flow height and the diameter of the Coanda surface. The control response curve for co-flow consisted of three significant zones during the investigation. The primary zone, known as the dead zone, had a nearly steady magnitude for thrust vectoring angle. This zone occurred when the secondary flow separated from the Coanda surface at a low speed. The second zone was known as the linear zone. The vectoring angle increased by expanding the blowing proportion. Since the vectoring angle could not surpass the mathematical point of the collar, flow proportions past the cut-off value had a slight impact on the thrust vector angle. This zone was called the saturation zone that existed because of physical impediments [83]. The three significant zones of a control response curve are presented in Figure 9. The investigation of a 2D exhaust nozzle with a small gas turbine demonstrated a maximum angle of 23° achieved during the experiment on a 57 mm radius collar and 1.4 mm height of secondary flow. The result demonstrated that the TV angle increased with increasing the primary and secondary flow rates [84]. Varying secondary flow height for a constant diameter of Coanda surface on TV effectiveness for a 3D rectangular duct was investigated. The observed trend data indicated that for a secondary flow height of 0.0294, the vectoring angle obtained was 28.7° for a constant diameter of 3.35 mm. Increasing the secondary flow height resulted in a decreased TV angle. A dead zone appeared for a low secondary flow blowing rate which resulted in no flow control and a low thrust vector angle. The length of the dead zone depended upon the diameter of Coanda surfaces. The large diameter resulted in a short period of the dead zone. Once overcoming the dead zone, the thrust vectoring increased with an increase in mass flow ratio [85].

4.2. Swept and Non-Swept Nozzle

An investigation on swept and non-swept nozzles using co-flow FTVC was carried out. The experiment indicated that the swept nozzle could achieve better results in terms of performance when compared to the non-swept nozzle. It was due to the fact that the swept nozzle depicted an almost entirely linear response for a range of secondary flow blowing coefficients. On the other hand, a non-linear response was indicated by the non-swept nozzle, thus, causing control problems [86].

A multi-directional TV design based on the rectangular and circular nozzle for co-flow has also been proposed, investigated, and complemented [87,88]. The Co-flow method was effective and efficient and provided moderate TV performance at subsonic primary flow [86,89]. Co-flow had the potential benefit of increasing the thrust efficiency with the tangential injection involved in deflecting the primary flow. These systems were lightweight, with simple integration of fixed geometry. The secondary flow could be penetrated by the engine compressor. The main drawback associated with the use of co-flow involved inefficient control effectiveness for supersonic primary flow. A few parameters and their effects on TV for co-flow are compiled in

Table 5. Parameters affecting the co-flow control.

Parameters	Effects	Ref
Secondary Flow blowing rate	Increasing the secondary flow blowing rate results in an increased vectoring angle	[90]
Secondary flow height	With an increase in secondary flow height, the value of thrust vectoring angle decreases	[85]
MFR	It affects the TV angle once overcoming the dead zone	[87]
Coanda surface diameter	The prolongation period of the dead zone depends upon the diameter of the Coanda surface. Large diameter results in a short dead zone range and vice versa	[83]

. A summary of some numerical investigations carried out on co-flow control is presented in

Table 6. Summary of recent numerical investigations carried out on Co-flow TVC.

Year	Title	Model	Varying Parameters	Computational Setup and Details	Conclusions	Ref
2007	Experimental and computational investigation into the use of co-flow fluidic thrust vectoring on a small gas turbine	3D nozzle	Gap height = 1–2 mm RPM = 78,000–110,000	Fluent/k-ε Model 471,700 grid cells ${\mathrm{P}}_{\mathrm{a}}$ = 0.1–0.6 atm ${\mathrm{T}}_{\mathrm{a}}$ = 300 k	Increasing the gap height for a constant secondary air mass flow rate reduces the TV angle. For a fixed geometry, enhanced shaft speed had a negative impact on TV angles.	[84]
2007	Multi-Directional Co-Flow Fluidic Thrust Vectoring Intended for a Small Gas Turbine	3D nozzle	Single section = 0% and 6.8% Two sections = 20.96% secondary MFR	Fluent/k-ε Model 684,400 grid cells	For yaw control a single secondary section can be used, however, for pitch control a two secondary section provided an efficient TV angle.	[87]
2016	An investigation of empirical formulation and design optimization of co-flow fluidic thrust vectoring nozzles	3D nozzle	RPM = 58,000–98,000	Fluent/k-ε Model 520,000–690,000 grid cells	The optimized nozzle design provided 32% improved TV angle over conventional nozzles.	[88]
2017	Fluidics Thrust Vectoring Using Co-Flow Method	3D nozzle	Gap height = 0.0296–0.1176, Coanda diameter = 1.176–3.529	Fluent/k-ε Model	TV angle increased with decreasing gap height. Dead zone length depended upon Coanda diameter.	[85]
2018	Bidirectional Thrust Vectoring Control of a Rectangular Sonic Jet	3D nozzle	NPR = 2–4	On–off operation of two control valves connected to two secondary chambers. ${\mathrm{T}}_{\mathrm{a}}$ = 288 k	It achieved a TV angle greater than 60° at limited NPR range of 2.3 to 2.6. The TV angle then decreases for NPR > 2.7. Thrust losses can be minimized by opening both valves to atmospheric pressure which eliminates the shock structure within the nozzle.	[91]
2018	Directional Control of a Jet Using the Coanda Effect	2D nozzle	Secondary jet speed = 0–70 m/s	${\mathrm{P}}_{\mathrm{a}}$ = 5000 Pa ${\mathrm{T}}_{\mathrm{a}}$ = 300 k	TV angles were unaffected for jet speed over 60 m/s. Increasing the secondary jet velocity increased the jet deflection and changed the jet velocity profile shape.	[90]
2018	Computational and experimental investigation of fluidic thrust vectoring actuator	3D nozzle	Exit height = 0.026–0.080, Coanda radius = 0.33–0.5	CFX/k-ε Model 0–0.13	TV did not occur at dead zone (msec/mpri < 0.04). For msec/mpri > 0.118 in saturation region, no increase in vectoring angle occurs. Between 0.04 < msec/mpri > 0.118, increasing secondary flow enhanced TV angles in control region.	[92]

.

5. Throat Skewing Control (TSC)

The throat skewing control hypothesis is related to the penetration of a secondary fluidic flow resulting in TV by throat shifting. Asymmetric pumping at the throat produces the turning effect in the primary flow. At all operating conditions, the TSC nozzle can achieve thrust vectoring by controlling the secondary fluidic flow injection at the throat and flap of the nozzle [18,92]. TSC is more efficient than SVC, as the latter shuns the shock formation in the divergent part of the convergent-divergent nozzle. Under a vectored state, no new skewed minimum area is created, and the throat occurs on the minimum area of the nozzle. However, a new minimum area is created under a non-vectored state, thus in a subsonic regime. Figure 10 signifies the TS schematic for TV. Different design parameters, such as vectoring angle, thrust coefficient, thrust losses, injector geometry, and flow properties, were investigated for the TS nozzle. The throttle performance for jet area control was studied, making sure that jet area control was not compromised by the throttle performance.

5.1. Single and Multi-Axis Nozzle

A single-axis pitch vectoring 2D nozzle was developed and inspected, followed by a 3D multi-axis pitch and yaw vectoring nozzle. It was reported that flap length affected the vectoring effectiveness. For a long flap length, oblique shock occurred in the divergent portion of the nozzle, thus reducing vectoring effectiveness. Similarly, for a very short flap, the secondary flow detaches from the flap, which results in poor vectoring effectiveness. Thus, an optimum flap length should be obtained. The maximized performance of the TV was achieved when the flap injector was located at the exit [94]. Similarly, the effect of flap injector angle, expansion ratio, and NPR on TV performance was investigated [93]. Keeping both the nozzle expansion ratio and the length of the flaps small could result in a better performance in terms of deflecting the primary flow. A single-axis 2D and a multi-axis 3D investigation were carried out. It was found that nozzles having a low expansion ratio and short divergent flaps of the nozzle had a better performance in vectoring the primary flow. Results for yaw vectoring for a single yaw slot indicated that increasing the secondary mass flow increased the vectoring performance. For NPR = 5.5, a vectoring angle of 7.23° with a thrust efficiency of 2.6% was achieved. For NPR values lower than 5.5, the vectoring angle achieved was as high as 13.66°. Similarly, the data trend for pitch vectoring at NPR = 5.5 resulted in an 8.5° vectoring angle along with a thrust efficiency of 2.6%. The multi-axis data trend for yaw and pitch vectoring angles observed was up to 8.5° and 9°. Comparing the single and multi-axis data trends, it was concluded that the multi-axis TS nozzle achieved better thrust vectoring performance without having a large impact on thrust efficiency [95].

5.2. Pitch and Yaw Thrust Vectoring

A multifunction non-axisymmetric nozzle for TV has been investigated. Pitch thrust vectoring was achieved by rotating the divergent flaps of the nozzle, whereas yaw thrust vectoring could be achieved by deflecting the yaw flaps, which were attached to the sidewalls at the exit of the nozzle. The concept of producing pitch thrust vectoring by rotating divergent flaps was found to be efficient, but the concept of producing yaw thrust vectoring through deflecting yaw flaps was inefficient statically and had a large resultant thrust ratio with a lower TV angle. The need for a new concept to produce yaw thrust vectoring was conducted. The deflection of yaw flaps hinges was examined for 4 different locations located downstream of the nozzle, as well as the throat plane along with the flap length [96].

5.3. Slot Configuration

Different fixed nozzle configurations were refined to achieve TS vectoring. Including baseline and high SPR single slot, asymmetric and multi-hole injection, and dual slot configuration for SPR 6 and NPR 7. All the nozzle geometries tested had a similar trend with a change in magnitude only. For higher values of NPR, the primary discharge coefficient ranged from 0.93 to 0.65. Dual slots were investigated, where the multiple slots still had the same total area (or injected mass flow) as the single slot configurations. Among all the injections, as the dual-slot injection was located downstream of the nozzle throat, it was found to have less effect on reducing the discharge coefficient [97]. A modified 3D-shaped nozzle with an expansion ratio of 1.17 for secondary injection was tested at NPR = 4. The nozzle achieved a vectoring angle of 20° with low thrust losses. Different configurations of injection slots were selected [98]. A conformal fluidic nozzle model having a non-axisymmetric exit was tested for NPR up to 5.5. For a single yaw slot, the data trend indicated that with increasing the secondary MFR, the vectoring performance was increased. For NPR = 5.5 and lower values, a yaw TV angle of 7.23° and 13.66° was achieved. Increasing the injected mass flow had a negative impact on the gross thrust coefficient. For NPR = 5.5, a pitch thrust vectoring angle of 8.5° was obtained [95]. Several performance parameters for the multi-axis nozzle concept were tested for a range of NPR = 2–11.5. A pitch and yaw vectoring angle of 35°and 31° were obtained [99].

Several parameters have been examined for fluidic TS control. Some parameters and their effects on TV for different configurations of the TS technique are compiled in Table 7. A graphical representation of the trend observed for vectoring effectiveness at different NPR and divergent flap lengths is presented in Figure 11. All the trends observed for these parameters were obtained from the data available in the literature. NPR was reported to have a small impact on vectoring effectiveness. A small increase in vectoring effectiveness was recorded for decreasing NPR below the intended design. The vectoring effectiveness was reported to increase with increasing flap length. A much longer flap introduced a strong oblique shock wave in the nozzle, which degraded the vectoring performance. However, for a very short flap length, the secondary flow was detached from the flap, which degraded the vectoring performance. Therefore, an ideal length of the flap should be selected for optimal performance [93].

TSC technique was reported to operate effectively and generate efficient vectoring performance at different Mach numbers. Using various turbulence models for TSC vectoring analysis, it can be concluded that SST k-ω was able to precisely predict the turbulence effect of the separation zone and near the nozzle wall with the experimental results. Although TSC produces effective vectoring performance, no higher vectoring angles are achieved using this technique. A summary of a few numerical investigations carried out on the TS technique is presented in Table 8.

Figure 11. Effect of Divergent flap length and NPR on TSC. These data were extracted from the previous investigations [93,95,96] carried out on TSC.

Figure 11. Effect of Divergent flap length and NPR on TSC. These data were extracted from the previous investigations [93,95,96] carried out on TSC.

Table 7. Parameters affecting the throat skewing control.

Parameters	Effects	Ref
Divergent flap length	Flap length affected the vectoring effectiveness. For a long flap length, oblique shock occurred in the divergent portion of the nozzle, thus reducing vectoring effectiveness. Similarly, for a very short flap, the secondary flow detached from the flap, which resulted in poor vectoring effectiveness	[96]
Expansion area ratio	Increasing the expansion ratio provided an increased pitch vectoring angle. It also moderately affected the vectoring effectiveness	[93]
Injector angle	Injector angle strongly and inversely affected the vectoring effectiveness. For a smaller injector angle, the vectoring effectiveness increased	[100]
NPR	NPR had a small effect on the vectoring effectiveness. TS was suggested to be robust to variation in flight condition	[95]

Table 7. Parameters affecting the throat skewing control.

Parameters	Effects	Ref
Divergent flap length	Flap length affected the vectoring effectiveness. For a long flap length, oblique shock occurred in the divergent portion of the nozzle, thus reducing vectoring effectiveness. Similarly, for a very short flap, the secondary flow detached from the flap, which resulted in poor vectoring effectiveness	[96]
Expansion area ratio	Increasing the expansion ratio provided an increased pitch vectoring angle. It also moderately affected the vectoring effectiveness	[93]
Injector angle	Injector angle strongly and inversely affected the vectoring effectiveness. For a smaller injector angle, the vectoring effectiveness increased	[100]
NPR	NPR had a small effect on the vectoring effectiveness. TS was suggested to be robust to variation in flight condition	[95]

Table 8. Summary of recent numerical investigations carried out on TSC.

Year	Title	Model	Varying Parameters	Computational Setup and Details	Conclusions	Ref
2001	Demonstration of Fluidic Throat Skewing for Thrust Vectoring in Structurally Fixed Nozzles	3D conformal nozzle	NPR = 2.0–5.5	Design of experiments for single and multi-axis TV concept. Cold-flow test.	TV performance increases with an increase in the secondary mass flow. Both pitch and yaw TV data trends were observed.	[95]
2002	Fluidic Thrust Vectoring and Throat Control Exhaust Nozzle	3D FAVE nozzle	Mass flow Ratio = 0–0.3	NPARC code /Spalart Allmaras Model	NPR impact was reduced on the TV angle due to the secondary flow at the nozzle throat.	[98]
2012	Combination of Fluidic Thrust Modulation and Vectoring in a 2D Nozzle	2D nozzle	Area ratio = 0.1–0.2 Injection angle = 30°–90° NPR = 30–40	Fluent/k-ω Model	Area ratio, injection angle, and NPR had a significant effect on thrust modulation.	[100]
2017	Thrust Control by Fluidic Injection in Solid Rocket Motors	Combination of TS and SVC nozzle	Mass flow Ratio = 0–0.6	Cold thermal flow test	The combination can achieve better TV performance for solid rocket motors.	[101]
2019	Secondary Flow TVC for Fluidic-Throat Nozzles	6 types of axisymmetric nozzle	Injector location = 0.12–0.5	Cold test flow	Better TV performance can be achieved for different injection schemes.	[102]
2020	Experimental research on vector control features of a pulse detonation tube with fluidic nozzle	3D nozzle	Injection location = 30–60 mm, 10 injection combinations	Valveless operation mode	For adjusting the direction of exhaust gases, asymmetric injections were found to be effective. Additionally, the combination of throat and divergent secondary flow injection obtained efficient TVC.	[103]

Table 8. Summary of recent numerical investigations carried out on TSC.

Year	Title	Model	Varying Parameters	Computational Setup and Details	Conclusions	Ref
2001	Demonstration of Fluidic Throat Skewing for Thrust Vectoring in Structurally Fixed Nozzles	3D conformal nozzle	NPR = 2.0–5.5	Design of experiments for single and multi-axis TV concept. Cold-flow test.	TV performance increases with an increase in the secondary mass flow. Both pitch and yaw TV data trends were observed.	[95]
2002	Fluidic Thrust Vectoring and Throat Control Exhaust Nozzle	3D FAVE nozzle	Mass flow Ratio = 0–0.3	NPARC code /Spalart Allmaras Model	NPR impact was reduced on the TV angle due to the secondary flow at the nozzle throat.	[98]
2012	Combination of Fluidic Thrust Modulation and Vectoring in a 2D Nozzle	2D nozzle	Area ratio = 0.1–0.2 Injection angle = 30°–90° NPR = 30–40	Fluent/k-ω Model	Area ratio, injection angle, and NPR had a significant effect on thrust modulation.	[100]
2017	Thrust Control by Fluidic Injection in Solid Rocket Motors	Combination of TS and SVC nozzle	Mass flow Ratio = 0–0.6	Cold thermal flow test	The combination can achieve better TV performance for solid rocket motors.	[101]
2019	Secondary Flow TVC for Fluidic-Throat Nozzles	6 types of axisymmetric nozzle	Injector location = 0.12–0.5	Cold test flow	Better TV performance can be achieved for different injection schemes.	[102]
2020	Experimental research on vector control features of a pulse detonation tube with fluidic nozzle	3D nozzle	Injection location = 30–60 mm, 10 injection combinations	Valveless operation mode	For adjusting the direction of exhaust gases, asymmetric injections were found to be effective. Additionally, the combination of throat and divergent secondary flow injection obtained efficient TVC.	[103]

6. Dual Throat Nozzle (DTN)

A dual throat nozzle is developed as an extension to improve the Fluidic Throat skewing thrust vectoring system. It is based on the throat-shifting nozzle concept using separation control. A DTN consists of two minimum areas (upstream and downstream) and a recessed cavity located between the convergent-divergent-convergent nozzle. A secondary fluidic flow is injected in the upstream minimum area, which creates a new area downstream of the flow. The creation of a new area downstream skews the sonic plane, which separates the flow in the cavity near the injection. Figure 12 signifies the DTN schematic for TV.

6.1. Effect of NPR and SPR

Different geometries of DTN were investigated both computationally and experimentally. A study on 3D rectangular DTN for a range of NPR = 2–5, along with an SPR of 7.6, was carried out. The impact of multiple parameters, such as NPR, slot injection angle, and injection-to-primary momentum flux ratio, were observed for DTN. Increasing the NPR resulted in an increased thrust ratio and thrust efficiency along with a decrease in TV angle. The injection to primary momentum flux had a direct effect on vectoring angle [105]. A 2D DTN with a nozzle area ratio of 1 was studied for NPR = 2–10. For NPR = 2, vectoring angle of 16.8° was achieved. However, an angle of 12° and 11.2° were obtained at NPR 7 and 10. A decrease in the behavior of the thrust coefficient was observed after reaching a value of 0.96 at NPR = 5. With increasing the SPR, a decrease in discharge coefficient trends was reported [106]. Another study on the 2D computational domain was conducted to analyze the thrust performance parameters on DTN at NPR = 4 and SPR = 7.6. From this study, it was concluded that for SPR = 7.6, increasing NPR resulted in increased thrust efficiency and thrust ratio, while decreasing NPR resulted in increased deflection angle [107]. An experimental study on 2D DTN indicated that convergent cavity angle had a direct effect on vectoring angle and vectoring efficiency. No secondary injection caused a decrease in vectoring angle and thrust ratio [108]. A 2D analysis on DTN at freestream Mach no of 0.05 and NPR = 3.858 was investigated. The TV efficiency increased from 0.84°/% to 2.15°/% by increasing the injection angle from 50° to 150°. TV efficiency was also reported to improve with decreasing the cavity length [109]. Another experiment implemented for NPR = 2 indicated a thrust efficiency of 7.7% with a thrust ratio of 0.963 for the DTN system. A thrust ratio of 0.962 with a thrust efficiency of 5.8% was observed at NPR= 5 [104]. The results for a DTN tested in NASA Langley Research Center Jet Exit Test Facility indicated that the nozzle could achieve a thrust ratio of 0.975–0.980 at NPR = 3 with no secondary injection. The maximum thrust efficiency was observed at a secondary injection angle of 150°. A vectoring angle of 15° was obtained for NPR = 4 [19].

6.2. Unsteady Simulation

For unsteady simulation, two types of nozzle, an open-loop and a closed-loop control, have been developed and numerically investigated. The characterization of the DTN flow field depended upon the boundary layer, moving shocks, and separation zone interactions, which caused a complex and dynamic response [110]. Effects of a cavity on unsteady simulation of two models for DTN were performed to observe the cavity effects during the starting process [111].

6.3. DTN-Starting Problem

An asymmetric divergent dual throat nozzle for improved thrust performance under certain Mach number and NPR conditions was presented. The effects of cavity geometry (convergence angle, divergence angle, length) along with expansion ratio and radius at the nozzle throat were considered. The results indicated that due to the presence of a normal shock wave, there was no increase in the efficiency of the nozzle. The normal shock wave moved downstream of the divergent part but remained inside the recessed cavity. Further increasing the NPR did not affect the shock wave structure. This type of problem was called the DTN-starting problem. This problem was solved by penetrating a secondary fluidic flow in the throat or the divergent part of the nozzle [112,113,114].

6.4. Fixed and Variable Geometry

A 2D axisymmetric DTN for supersonic aircraft was investigated for a nozzle exit ratio of 1. 3 curves for fixed DTN geometry were presented for different expansion ratios, and a single curve for variable DTN geometry. It was concluded that fixed geometry DTN provided an enhanced thrust vectoring performance than variable geometry DTN. Comparing the data with the previous analysis, a decreased vectoring angle and vectoring efficiency trend were observed for decreasing cavity length. A better trend for the discharge coefficient of primary flow was reported for variable geometry DTN than fixed geometry DTN [115,116].

6.5. Secondary Injection

Along with a steady secondary injection, a pulsed secondary injection was also investigated [117,118,119]. The study revealed that steady secondary injection was more effective in vectoring the primary flow than pulsed secondary injection [104]. The investigation of 2D and axisymmetric DTN optimal design and performance both computationally and experimentally at NASA Langley Research Center was conducted. Until now, the investigation of steady-state DTN performance has been studied for different secondary injection geometries [120]. However, dynamic DTN performance testing is still in the research phase [121].

Several parameters have been examined for DTN. A few parameters and their effects on TV for different configurations are compiled in

Table 9. Parameters affecting the dual throat nozzle control.

Parameters	Effects	Ref
Cavity length	Cavity length had a negative impact on thrust ratio and discharge coefficient but had a positive effect on TV angle and efficiency	[108]
Convergence angle of the cavity	Increased Cavity convergence angle would increase TV angle and decrease thrust ratio and discharge coefficient	[19]
Expansion ratio	Increasing expansion ratio and NPR resulted in an increased cavity length	[116]
NPR	Increasing NPR would decrease TV angle with increase thrust ratio and thrust efficiency	[120]
Flap length	Decreasing flap length resulted in an increased expansion ratio and NPR	[110]

. A graphical representation of the effect of NPR and cavity convergence angle is presented in Figure 13. All the trends observed for these parameters were obtained from the data available in the literature. The trend reported for vectoring angle and vectoring efficiency for different NPR was observed. Vectoring angle showed a decreasing trend with increasing NPR, whereas the vectoring efficiency was observed to increase with increasing NPR. However, vectoring angle and vectoring efficiency were reported to increase with increasing cavity convergence angle. It was reported that increasing the cavity convergence angle improved the vectoring angle at the cost of thrust performance [109].

So far, among the investigated nozzles, DTN achieved the highest vectoring performance. This method can be desirable for its great performance characteristics, but the requirement of secondary injection induces thrust losses and can reduce the maximum possible thrust that can be achieved by the engine. A summary of some numerical investigations carried out on DTN is presented in Table 10.

Table 10. Summary of recent numerical investigations that have been carried out on DTN.

Year	Title	Model	Varying Parameters	Computational Setup and Details	Conclusions	Ref
2009	Preliminary Analysis and Design Enhancements of a Dual Throat FTV Nozzle Concept	2D nozzle	NPR = 2–10	Fluent/k-ε Model	For the designed geometry the MFR and TV angle was found to be 5.47 kg/s and 24.5°.	[122]
2013	Effects of Cavity on the Performance of Dual Throat Nozzle During the Thrust-Vectoring Starting Transient Process	2D nozzle with 3 cases	NPR = 1–4	Fluent/k-ε Model 21,600 nodes, ${\mathrm{P}}_{\mathrm{a}}$ = 101,325 Pa ${\mathrm{T}}_{\mathrm{a}}$ = 300 k	Negative TV angle appeared before the nozzle produced an efficient TV angle.	[111]
2015	Numerical Simulation of Fluidic Thrust vectoring	2D nozzle	NPR = 2–10	Fluent/Spalart- Allmaras Model	Increasing the secondary MFR resulted in increased TV angles.	[123]
2016	Experimental and Computational Investigation of a Dual-Throat Fluidic Thrust-Vectoring Nozzle	2D nozzle with 3 different secondary injection geometries	NPR = 1–4 Air and nitrogen	Fluent/k-ε Model 560,000 grid cells, ${\mathrm{P}}_{\mathrm{a}}$ = 101,325 Pa ${\mathrm{T}}_{\mathrm{a}}$ = 300 k	NPR of 2 had the most impact on TV angle. Whereas the influence of secondary injection was reduced at NPR of 4.	[120]
2016	Study of Starting Problem of Axisymmetric Divergent Dual Throat Nozzle	2D nozzle	Expansion ratio = 1.1025–1.96 Radius ratio = 1.05–1.4	Fluent/k-ε Model 21,600 nodes, ${\mathrm{P}}_{\mathrm{a}}$ = 101,325 Pa ${\mathrm{T}}_{\mathrm{a}}$ = 300 k	Higher expansion ratios created shock oscillations in the cavity.	[112]
2019	Performance Analyses of Fluidic Thrust Vector Control System Using Dual Throat Nozzle	2D nozzle	Nozzle A with identical first and second throat and Nozzle B with second throat of 1.5 times the first throat	Direct simulation Monte Carlo method	Nozzle achieved 19° of TV angle, however, a TV angle of 15° was achieved for another configuration of nozzle.	[124]
2020	Numerical Study of Fluidic Thrust Vector Control Using Dual Throat Nozzle	3D rectangular nozzle	NPR = 2–5 X/L = 0.25–0.67 J = 0.43–2.76	Fluent/k-ω Model 2,078,000 grid cells, ${\mathrm{P}}_{\mathrm{a}}$ = 101,325 Pa ${\mathrm{T}}_{\mathrm{a}}$ = 300 k	To obtain best TV performance the optimal choice for NPR is 4.	[105]

Table 10. Summary of recent numerical investigations that have been carried out on DTN.

Year	Title	Model	Varying Parameters	Computational Setup and Details	Conclusions	Ref
2009	Preliminary Analysis and Design Enhancements of a Dual Throat FTV Nozzle Concept	2D nozzle	NPR = 2–10	Fluent/k-ε Model	For the designed geometry the MFR and TV angle was found to be 5.47 kg/s and 24.5°.	[122]
2013	Effects of Cavity on the Performance of Dual Throat Nozzle During the Thrust-Vectoring Starting Transient Process	2D nozzle with 3 cases	NPR = 1–4	Fluent/k-ε Model 21,600 nodes, ${\mathrm{P}}_{\mathrm{a}}$ = 101,325 Pa ${\mathrm{T}}_{\mathrm{a}}$ = 300 k	Negative TV angle appeared before the nozzle produced an efficient TV angle.	[111]
2015	Numerical Simulation of Fluidic Thrust vectoring	2D nozzle	NPR = 2–10	Fluent/Spalart- Allmaras Model	Increasing the secondary MFR resulted in increased TV angles.	[123]
2016	Experimental and Computational Investigation of a Dual-Throat Fluidic Thrust-Vectoring Nozzle	2D nozzle with 3 different secondary injection geometries	NPR = 1–4 Air and nitrogen	Fluent/k-ε Model 560,000 grid cells, ${\mathrm{P}}_{\mathrm{a}}$ = 101,325 Pa ${\mathrm{T}}_{\mathrm{a}}$ = 300 k	NPR of 2 had the most impact on TV angle. Whereas the influence of secondary injection was reduced at NPR of 4.	[120]
2016	Study of Starting Problem of Axisymmetric Divergent Dual Throat Nozzle	2D nozzle	Expansion ratio = 1.1025–1.96 Radius ratio = 1.05–1.4	Fluent/k-ε Model 21,600 nodes, ${\mathrm{P}}_{\mathrm{a}}$ = 101,325 Pa ${\mathrm{T}}_{\mathrm{a}}$ = 300 k	Higher expansion ratios created shock oscillations in the cavity.	[112]
2019	Performance Analyses of Fluidic Thrust Vector Control System Using Dual Throat Nozzle	2D nozzle	Nozzle A with identical first and second throat and Nozzle B with second throat of 1.5 times the first throat	Direct simulation Monte Carlo method	Nozzle achieved 19° of TV angle, however, a TV angle of 15° was achieved for another configuration of nozzle.	[124]
2020	Numerical Study of Fluidic Thrust Vector Control Using Dual Throat Nozzle	3D rectangular nozzle	NPR = 2–5 X/L = 0.25–0.67 J = 0.43–2.76	Fluent/k-ω Model 2,078,000 grid cells, ${\mathrm{P}}_{\mathrm{a}}$ = 101,325 Pa ${\mathrm{T}}_{\mathrm{a}}$ = 300 k	To obtain best TV performance the optimal choice for NPR is 4.	[105]

7. Bypass Dual Throat Nozzle (BDTN)

All the FTV techniques studied so far consume an inevitably high-pressure secondary injection, which introduces thrust losses due to bleeding air from the engine compressor or fan. Under the vectored and non-vectored state, thriving for better performance, a new kind of FTV bypass dual throat nozzle has been developed and investigated [20,121]. Based on the conventional DTN, having high thrust vectoring efficiency with low thrust loss and less analytical modeling, BDTN was introduced. BDTN did not consume a secondary fluid from the engine compressor or fan, so usually, it had minimal or no impact on thrust loss. The TV performance was similar to conventional DTN. Figure 14 represents the BDTN schematic for TV. The figure shows a 2D BDTN. The bypass is introduced at the upstream throat of the convergent-divergent-convergent nozzle. The secondary flow flowing through the bypass induces flow separation in the cavity, thus deflecting the primary flow of the nozzle. BDTN is capable of achieving a high thrust deflection angle without compromising the thrust coefficient, thrust efficiency, and discharge coefficient. This made BDTN more desirable for obtaining large vectoring angles and minimal loss of thrust.

7.1. Effect of NPR

An experimental investigation of 2D and 3D BDTN was carried out for NPR = 3, 5, and 10 [20,125]. This actively demonstrated that an increased value of NPR resulted in decreased vectoring angle. For 2D analysis, the angles obtained were 27.24°, 23.12°, and 20.27°, however, vectoring angle of 26.95°, 21.08°, and 20.27° were obtained for 3D, respectively, for NPR = 3, 5, and 10. For NPR = 4, the maximum value of the thrust coefficient obtained was 0.96 [20]. Different thrust vectoring parameters were investigated for different NPR on 3D BDTN. Increasing NPR from 1 to 4 resulted in an increase in thrust coefficient from 0.76 to 0.93 [125]. Optimization of the bypass dual throat nozzle has been carried out by analyzing three aspects of the nozzle parameters. It was found that bypass angle and bypass width have a significant impact on the thrust vectoring performance of the nozzle [126].

7.2. Secondary Mass Flow Modulation

The effects of secondary mass flow modulation were investigated for different NPR and bypass settings. A vectoring angle of 23°, with a thrust coefficient of 0.86 along with a discharge coefficient of 0.92, was obtained for NPR = 2 [127].

7.3. Axisymmetric Divergent BDTN

Two improved configurations of axisymmetric divergent BDTN were investigated. The highest thrust coefficient of 0.94, along with the vectoring angle of 19.52°, was obtained for NPR = 4. The improved configuration was able to achieve the best thrust vectoring performance along with a 50% increase in throat area [128,129].

7.4. Comparison of DTN and BDTN

A comparison of DTN and BDTN was carried out. For DTN, at NPR values of 2 and 10, the thrust vectoring angles of 20° and 16° were achieved. Whereas, for BDTN, at NPR = 2 and 10, the values of vectoring angle of 32° and 21.30° were obtained. Thus, BDTN was found to be well suited FTV nozzle [20].

A graphical representation of the effect of NPR on vectoring angle and thrust coefficient is presented in Figure 15. All the trends observed for these parameters were obtained from the data available in the literature. The decreasing trend was reported for vectoring angle with increasing NPR. Higher vectoring angles were reported for NPR < 6 because the squeezing effect of the vortex achieved was highest at lower NPR. With increasing NPR, the squeezing effect decreased, which resulted in lower angles. The thrust coefficient was reported to increase for NPR < 5 and then decrease for NPR > 5. A 2D and 3D comparison of vectoring angle and thrust coefficient is also reported in the same figure.

BDTN was reported to achieve the highest vectoring performance among all the FTVCs developed until now. The vectoring mechanism is similar to DTN, but the requirement of no secondary injection makes this FTVC desirable for its use in supersonic applications. Although it is a newly investigated technique, different parameters are yet to be investigated for this nozzle. A Summary of some numerical investigations carried out on BDTN is presented in

Table 11. Summary of recent numerical investigations that have been carried out on BDTN.

Year	Title	Model	Varying Parameters	Computational Setup and Details	Conclusions	Ref
2014	Experimental and Numerical Investigations of a Bypass Dual Throat Nozzle	2–3D nozzle	NPR = 1–16	Fluent/realizable k-ε Model, 44,778 grid cells Pa = 101,325 Pa, Ta= 300 k	NPR had a negative impact on TV angle. Thrust coefficient was found to decrease with increasing NPR. Best performance was recorded at NPR = 4	[20]
2015	Dynamic Experimental Investigations of a Bypass Dual Throat Nozzle	3D nozzle	NPR = 3–10	Cold blowdown wind tunnel facility	At NPR = 3, 5, and 10, BDTN was able to achieve 50 deg/s, 40 deg/s, and 34 deg/s dynamic vector rate.	[121]
2019	Computational study of axisymmetric divergent bypass dual throat nozzle	2–3D nozzle	Expansion ratio = 1.1025–1.5625 Radius ratio = 1.05–1.25	Fluent/Spalart Allmaras Model 2.3 × 106 nodes Ppri = 405,300 Pa, Psec = 607,950 Pa Pa = 101,325 Pa, Ta= 300 k	The effect of radius of throat on TV performance was relatively small. Increasing the bypass width enhanced the thrust and discharge coefficients.	[128]
2020	Design and Preliminary Analysis of the Variable Axisymmetric Divergent Bypass Dual Throat Nozzle	3D nozzle	NPR = 4.47 i. After burning state ii. Non-afterburning state	Fluent/Spalart Allmaras Model 2.3 × 106 nodes Paf = 453,138 Pa, Pin = 453,138 Pa Pa = 101,325 Pa, Taf = 2000 k, Tin = 904 k	Non-after burner state reported increased TV angles than afterburning states for both improve geometry scheme. Discharge and thrust coefficients were approximately equal for both nozzle states.	[129]
2020	Experimental evaluation and numerical simulation of performance of the bypass dual throat nozzle	3D nozzle	NPR = 2–16 Bypass position = 0–0.17	Fluent/RNG k-ε Model 855,000 grid cells Pa = 101,325 Pa, Ta = 300 k	Increasing bypass position leads to increased TV efficiency. The thrust coefficient was reported in range of 0.85–0.93 with increasing NPR from 2 to 4.	[125]
2023	Numerical Investigation on the Thrust Vectoring Performance of Bypass Dual Throat Nozzle	3D nozzle	NPR = 2–10 Bypass angle = 35°–90° Convergence angle = 22°–37° Bypass width = 2.6–5 mm	Fluent/RNG k-ε Model, Pa = 101,325 Pa, Ta = 300 k	Increasing the bypass angle has a positive impact on vectoring angle and efficiency. Convergence angle has no significant impact on vectoring performance.	[130]

.

8. Comparison of FTVCs

The TV systems must be carefully integrated into the flight control and engine control unit. Control problems relate to the integrity of this integration and vector control system. The use of the TV significantly affects the requirements for the control system. The application of a thrust vector to the aircraft increases maneuverability and mobility. This is especially effective for controlling flight attitudes, such as low speed and high angle of attack, where the aircraft’s control surface is less effective. This may also include preventing or correcting “stall” and “take-off” maneuvers [131].

Table 12. A comparison matrix of all FTVC systems.

Evaluation Criteria	SVC	BSVC	CFC	Co flow	TSC	DTN	BDTN
Design	Secondary flow injection in the supersonic region	A bypass flow injection in the divergent section	Secondary flow penetrated in the opposite direction of primary flow	Secondary flow penetrated along with the primary flow	Asymmetrical injection in the throat	Secondary flow is injected in the upstream minimum area	Bypass is introduced at the upstream throat
Impact on system	Reduces the maximum resultant thrust	No secondary injection requirement	No moveable parts for flow vectoring	Minimal momentum loss	No shock losses	Enhanced performance due to the cavity regions	No thrust losses
Implementation	Readily integrated into existing systems	Readily integrated into existing systems	Critical design Required for optimum performance	Critical design Required for optimum performance	Readily integrated into existing systems	Readily integrated into existing systems	Readily integrated into existing systems
TV angle	Large	Small	Large	Small	Small	Large	Large
Thrust coefficient	Lower	Higher	Higher	Lower	Higher	Higher	Higher
Thrust efficiency	Higher	Lower	Higher	Lower	Higher	Higher	Higher
Thrust losses	Higher	Higher	Higher	Lower	Lower	Lower	Lower
Negative consequences	Large thrust losses	Complex flow field	Hysteresis, suction source and integration problems	Limitation on TV angle	Low performance	High-pressure secondary injection	No negative consequences predicted until now
Potential problem	High differential pressure losses. In fully expanded conditions, the oblique shock wave is less effective in deflecting the primary flow	Shock waves induced at a higher SPR are insufficient for vector operation because they interact with the opposite wall at a higher bypass injection angle	Connection of the main jet to the suction collar	Connection of the main jet to the suction collar	Vectoring and jet area control are possible simultaneously, but it can be difficult to separate them	TV operation adversely affects discharge coefficient	So far, no potential problems were listed in the literature

shows a comparison matrix for all the seven-candidate systems considered in this study. The evaluation criteria include:

8.1. Design

The design feature is a comparative rating of the evaluation criteria. The complexities in integrating the control system with the engine airframe and the risks included with these integrations are evaluated. FTV nozzles are simply fixed geometries and weigh less than MTV. Among these seven candidate systems, counterflow works on the principle of suction to deflect the primary flow. At the same time, the rest of FTVC works on the blowing principle to control primary flow deflection.

8.2. Impact on System

Impact on system evaluation criteria is compared on a relative basis. This impact includes the effects of each candidate control system on the airframe and engine configurations. SVC offers substantial TV angle control but often at the expense of system thrust ratio. The bypass SVC requires no secondary injection for deflecting the main flow. CFTV is able to provide large TV angles with small secondary flow requirements. Co-flow provides minimal momentum loss because the direction of primary and secondary flow is the same. No shock formations are observed in the TS system as the flow turning is achieved sub-sonically. DTN, an extension of the TS technique, provides better TV performance among all the candidate systems. The drawback of these six candidate systems is the consumption of high-pressure secondary injection from the engine, which induces thrust losses. BDTN is reported to provide the best TV performance without compromising on thrust losses, as no secondary injection is required.

8.3. Implementation

Implementation criteria are comparatively analyzed. All these candidate systems can be readily integrated into the existing systems as it requires no moveable parts. Due to the negative consequences and potential problems associated with CFTV and Co-flow control, an optimum design is required to obtain optimal TV performance.

8.4. Thrust Vectoring Angle

TV angle is the ratio of the nozzle axial and normal force components acting on the nozzle exit. The study made a comparison of TV angles among all the control systems. Larger TV angles are achieved for SVC, CF control, DTN, and BDTN control systems. Small angles are recorded for bypass SVC as separation flow reattaches in the downstream region. Additionally, Co-flow and TS control systems are able to produce small TV angles.

8.5. Thrust Coefficient

The thrust coefficient relates to the ratio of resultant thrust to ideal thrust. It determines the amplification of thrust during flow expansion and is a core parameter in defining the thrust performance. The comparative rating of the thrust coefficient is evaluated for all control systems. For SVC, as the momentum flux ratio increases, the thrust coefficient decreases. Bypass SVC, along with secondary injection flow, produces a higher thrust coefficient. An optimal CFTV design can obtain a higher thrust coefficient. However, increasing the gap height of the secondary flow has a negative impact on the thrust coefficient. Lower thrust coefficients are recorded for co-flow control. TS, DTN, and BDTN control systems obtain higher thrust coefficients.

8.6. Thrust Efficiency

Thrust efficiency defines the relation between the TV angle and the secondary MFR of the injection. The study compares the thrust efficiency of all the control systems. It is a core parameter in demonstrating the performance of the control systems. SVC, CFTV, TS, DTN, and BDTN control systems are capable of providing higher thrust efficiency. Whereas lower thrust efficiencies are reported for bypassing SVC and co-flow control systems.

8.7. Thrust Losses

Thrust losses relate to the loss of thrust from the engine and the reliability of the control systems. Any control system that improves the thrust losses can achieve better TV performance. Thrust losses in SVC are higher due to oblique shock formation in the nozzle, which reduces the maximum resultant thrust. The bypass SVC system achieves higher thrust losses due to the presence of a reverse shock structure in the flow field. Lower thrust losses are recorded for co-flow, TS, DTN, and BDTN control systems.

8.8. Negative Consequences

The negative consequences criteria for control systems are evaluated. This criterion compares the performance of each candidate system. It includes parameters such as thrust losses, complex flow field, limited TV angle, and consumption of high-pressure secondary injection from the engine. SVC achieves TV with no variation in the primary nozzle throat area. It may be effective in vectoring the primary flow but at the expense of the system thrust ratio as the flow is turned through oblique shocks in the nozzle. In bypass SVC, the flow field gets complex with complicated vortices formation. It also experiences five different flow losses on the exit plane. The CFTV system is an appealing TV method, but it involves hysteresis, suction source, and airframe integration problems. In the co-flow control system, shocks appear at the nozzle exit and divergent wall as the control-flow pressure increases, which limits the TV angle. Design complexity included in both CFTV and co-flow technique makes it difficult to be implemented in current-day nozzle designs. TSC suffers from low performance. Along with DTN, these control systems inevitably consume high-pressure secondary injection. However, the ongoing research on BDTN suggests that no negative consequences have been reported until now.

8.9. Potential Problems

The potential problems are comparatively analyzed. To obtain better TV performance, these problems and their complexities should be eliminated. At off-design conditions in SVC, the oblique shock wave can eliminate the flow separation. At over-expanded conditions, TV performance losses are often high. At fully expanded conditions, the oblique shock is less effective in deflecting the flow. In bypass SVC, at a higher bypass injection angle, the shock wave interacts with the opposite wall. That’s why the bypass injection angle should be coupled with SPR. Jet attachment to the suction collar at certain operating conditions and geometric configuration occurs to be the most potential drawback of both CFTV and co-flow control systems. This problem is hysterical and not easy to control. In the TS control system, area control is maintained while vectoring the primary flow. However, it can be challenging to completely decouple them. DTN control systems adversely affect the discharge coefficient, which can cause problems in engine operation. This, however, needs to be compensated, or additional developments are required. The research conducted on BDTN so far suggests no potential problems.

9. Conclusions

The purpose of this study was to provide a concise overview of recent developments in fluidic thrust vectoring techniques. By analyzing the intrinsic characteristics of each candidate system, a coherent argument is developed that identifies which FTVC technique is more capable of generating thrust vectoring. The paper focuses on seven techniques that have been analyzed for high thrust vectoring performance. Existing literature indicates that shock vector control performs well in terms of thrust vectoring angle and thrust efficiency. The only drawback that makes the embracement of SVC difficult is the shock impingement on the opposite wall of the nozzle. Although counter and co-flow controls are practically attainable, the Coanda effect makes these techniques undesirable due to causing instability in certain operating flow regimes. The throat skewing method is found to be an effective fluidic thrust vectoring system with a relevantly simple structure and a high thrust efficiency; however, the aircraft maneuvering ability is limited due to the small vectoring angles. The dual throat nozzle improves TV performance because it has cavity regions downstream, but it requires a high-pressure secondary injection that adversely affects the discharge coefficient. Based on the evaluation criteria, it was found that the bypass dual throat technique was the most effective, had higher thrust vectoring performance, and could overcome thrust losses, as it did not require secondary injection. The BDTN configurations reach the highest value according to the proposed research criteria in this article. Moreover, it is considered to be a good balance between safety, complexity, and performance. Due to its minimal impact on thrust losses, BDTN could be the right choice for thrust vectoring control in the future.