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

: 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.


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 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.

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.

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.

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].

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].

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 threedimensional 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.

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].

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 kε 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.

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].

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].

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].
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.

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].

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].
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.

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 CO 2 , 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.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. 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.

2019
Numerical study on the shock vector control in a rectangular supersonic Nozzle NPR had a positive effect on thrust coefficient, primary MFR and a negative impact on vectoring angle.Vectoring angle increased with increasing SPR. [39]

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.

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].

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 0.19-0.2m, and the slot width varied between 0.017-0.02m [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

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].

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 0.19-0.2m, and the slot width varied between 0.017-0.02m [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.

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.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.
Table 3. Parameters affecting the counter flow control.

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]

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.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.   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.[68]

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.

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

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].
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].

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 nonswept nozzle, thus, causing control problems [86].
A multi-directional TV design based on the rectangular and circular nozzle for coflow 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.A summary of some numerical investigations carried out on co-flow control is presented in Table 6.

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.A summary of some numerical investigations carried out on co-flow control is presented in Table 6.
Table 5. Parameters affecting the co-flow control.

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]  [92]

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.

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.

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 multiaxis 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

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].

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].

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.

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] 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- 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.

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]  TV performance increases with an increase in the secondary mass flow.Both pitch and yaw TV data trends were observed.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]

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.
fluidic nozzle combinations and divergent secondary flow injection obtained efficient TVC.

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.

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

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 0.975-0.980at 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].

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].

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].

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 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].

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.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.

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] Energies 2023, 16, x FOR PEER REVIEW 21 of 33 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.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 9. Parameters affecting the dual throat nozzle control.

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] Figure 13.Effect of NPR and cavity convergence angle on DTN.These data were extracted from the previous investigations [19,109,120] carried out on DTN.To obtain best TV performance the optimal choice for NPR is 4. [105]

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

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 coeffi-

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].

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].

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].

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 .Energies 2023, 16, x FOR PEER REVIEW 24 of 33 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.Effect of NPR on BDTN.These data were extracted from the previous investigations [20,125] carried out on BDTN.
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.

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 shows a comparison matrix for all the seven-candidate systems considered in this study.The evaluation criteria include: negative consequences and potential problems associated with CFTV and Co-flow control, an optimum design is required to obtain optimal TV performance.

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.

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.

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.

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.

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.

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.

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.

Figure 2 .
Figure 2. Schematic of Shock Vector Thrust Vectoring Control causing obliques shock wave by introducing a secondary flow injection in the supersonic portion of the nozzle [21].

Figure 2 .
Figure 2. Schematic of Shock Vector Thrust Vectoring Control causing obliques shock wave by introducing a secondary flow injection in the supersonic portion of the nozzle [21].

Figure 3 .
Figure 3. Schematic of a flow field with slot injection [47].

Figure 3 .
Figure 3. Schematic of a flow field with slot injection [47].

Figure 4 .
Figure 4. Representation of Bypass Shock Vector Thrust Vectoring Control with bypass passage flow [57].

Figure 5 .
Figure 5.Effect of (a) NPR, (b) SPR, (c) Injection angle and injection location on SVC.These data were extracted from the previous investigations [22,39,48] carried out on SVC.

Figure 5 .
Figure 5.Effect of (a) NPR, (b) SPR, (c) Injection angle and injection location on SVC.These data were extracted from the previous investigations [22,39,48] carried out on SVC.

Figure 7 .
Figure 7.Comparison of the effect of SPR and collar length on CFC.These data were extracted from the previous investigations [64,68,71,75] carried out on CFC.

Figure 7 .
Figure 7.Comparison of the effect of SPR and collar length on CFC.These data were extracted from the previous investigations [64,68,71,75] carried out on CFC.

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 Energies 2023, 16, 5721 13 of 33

53 P
Figure 8 signifies the co-flow control schematic for TV.= 17,225,251 Pa T = 300 k length increased, TV angle increased and then started decreasing.

Figure 10 .
Figure 10.Schematic of Throat Skewing Control with secondary flow injection configurations for thrust vectoring [93].

Figure 10 .
Figure 10.Schematic of Throat Skewing Control with secondary flow injection configurations for thrust vectoring [93].

Figure 11 .
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 .
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 8. Summary of recent numerical investigations carried out on TSC.Year Title Model Varying Parameters

Figure 12 .
Figure 12.Schematic of Dual Throat Nozzle Control with secondary flow injection configuration for thrust vectoring [104].

Figure 12 .
Figure 12.Schematic of Dual Throat Nozzle Control with secondary flow injection configuration for thrust vectoring [104].

Figure 13 .
Figure 13.Effect of NPR and cavity convergence angle on DTN.These data were extracted from the previous investigations [19,109,120] carried out on DTN.
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.Energies 2023, 16, x FOR PEER REVIEW 23 of 33 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.

Figure 14 .
Figure 14.Schematic of Bypass Dual Throat Nozzle Control with bypass flow passage configuration for thrust vectoring [20].

Figure 14 .
Figure 14.Schematic of Bypass Dual Throat Nozzle Control with bypass flow passage configuration for thrust vectoring [20].

Figure 15 .
Figure 15.Effect of NPR on BDTN.These data were extracted from the previous investigations [20,125] carried out on BDTN.

Figure 15 .
Figure 15.Effect of NPR on BDTN.These data were extracted from the previous investigations[20,125] carried out on BDTN.

Table 1 .
Parameters affecting the shock vector control.

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

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

Table 4 .
Cont.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.
a = 5000 Pa T a = 300 k Flow field was found symmetrical for case i.Primary flow was deflected in case ii.

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

Table 7 .
Parameters affecting the throat skewing control.

Table 7 .
Parameters affecting the throat skewing control.

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

Table 9 .
Parameters affecting the dual throat nozzle control.

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

Table 11 .
Summary of recent numerical investigations that have been carried out on BDTN.
Fluent/realizable k-ε Model, 44,778 NPR had a negative impact on TV angle.Thrust coefficient was found to decrease

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