Numerical study of a trapezoidal bypass dual throat nozzle

Shuai HUANG, Jinglei XU,*, Kaikai YU, Yangsheng WANG,Ruifeng PAN, Kuangshi CHEN, Yuqi ZHANG

a State Key Laboratory of Mechanics and Control of Aeronautics and Astronautics Structures, Nanjing 210016, China

b College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

c Jiangsu Province Key Laboratory of Aerospace Power System, Nanjing 210016, China

KEYWORDS Bypass dual throat nozzle;Infrared stealth performance;Mixing performance;Trapezoidal cross-sections;Thrust vectoring

Abstract Bypass Dual Throat Nozzle(BDTN)is a novel type of fluidic thrust vectoring nozzle.To improve the infrared stealth performance of BDTN, a nozzle based on BDTN is proposed and numerically simulated.Each cross-section along the x-axis of the novel nozzle becomes a trapezoid,which is named‘‘BDTN-TRA.”The main numerical simulation results show that BDTN-TRA can produce a thrust vectoring angle when the upper or lower bypass valve is open.The angle difference between the two conditions mentioned above is usually approximately 1°–2°.Even if the two bypasses are closed,BDTN-TRA can produce a small thrust vectoring angle at around 3°–5°.When the sidewall angle increases from 60°to 90°,the thrust coefficient and thrust vectoring angle under each work condition usually decrease.A larger aspect ratio indicates better performance.As the aspect ratio increases over 7.2,the performance of BDTN-TRA is quite close to that of BDTN with rectangular cross-sections at the same aspect ratio.These features will benefit the control and trimming for future aircraft design, especially for the flying wing layout aircraft.Last but not least,BDTN-TRA has a more extraordinary mixing performance compared with BDTN.The distributions of static temperature and axial velocity along the x-axis of BDTN-TRA with sidewall angle of 60° decrease faster than those of BDTN.When the total temperature of the inlet equals 1600 K, the static temperature difference between BDTN-TRA with sidewall angles of 60° and 90°is over 360 K at twice the length of the nozzle downstream of the nozzle exit,which is the reflection for excellent infrared stealth for the fighter.

1.Introduction

High flight maneuverability and stealth are the most critical features for fighters in the future.A fighter with better flight maneuverability has high possibility of winning an air combat.A fighter with great stealth can reduce the likelihood of being detected by radars or decrease the detecting distance of radars.From the point of view of flight maneuverability,the thrust vectoring nozzle plays a critical and influential role.The Russian fighter Su-35 equipped with two axisymmetric mechanical hydraulic thrust vectoring nozzles and the American fighter F-22 utilizing the thrust vectoring nozzles with rectangular exits are powerful representatives of super-maneuverability.Their thrust vectoring nozzles are driven by mechanical hydraulic components,so do other applied thrust vectoring nozzles.This kind of nozzle generates thrust vectoring by making mechanical hydraulic components deflect.However, when designing and manufacturing these nozzles, achieving a smooth movement between the components while maintaining the sealing of the nozzle is challenging.This leads to the complication of structures, which then increases the weight and reliability problems.As a result,the reliability of the mechanical hydraulic thrust vectoring nozzle decreases dramatically.

The Fluidic Thrust Vectoring Nozzle (FTVN) finds a solution from the flow control, which uses a small amount of airflow to manipulate the primary flow and reorganizes the flow field to produce the distinctive thrust vectoring.The potentiality of FTVN has been widely recognized and estimated in the National Aeronautics and Space Administration (NASA) and United States Air Force (USAF) Fluidic Injection Nozzle Technology(FLINT)program.The program shows that more than 37 % of nozzle procurement and life cycle cost can be reduced after FTVN is applied.1After over 30 years of development, FTVNs have evolved into several types: Shock Vectoring Control (SVC),2–4Counter Flow (CF),5Throat Shifting (TS),6,7Dual Throat Nozzle (DTN),8and fluidic oscillators9,10.

DTN has been developed based on the TS method proposed by NASA Langley Research Center in 2003.8The two throats and the cavity between them are the features of DTN’s structure.The separation region occurring in the cavity is the distinctive characteristic of DTN’s flow field.In general,thrust vectoring is produced by injecting the secondary flow with relatively high pressure near the first throat.From the experimental results, each 1 % injection can produce thrust vectoring angle at about 6.1°, and the thrust coefficient is as high as 0.968.11,12Different shapes of DTN cross-sections have been designed, simulated, optimized, and experimented.13–15All the previous studies show that this kind of FTVN can satisfy more comprehensive working conditions and less limitations to the Nozzle Pressure Ratio (NPR).Yet, most of them need a high-pressure secondary flow to disturb the main flow,which is usually drawn from the high-pressure compressors of the aero-engine.12This kind of disturbance method determines huge thrust loss.

The Bypass Dual Throat Nozzle (BDTN) is the evaluation of DTN, and it is created to overcome the disadvantages of DTN.BDTN utilizes the bypasses to connect the inlet with the first throat of the nozzle to produce a stable and apparent thrust vectoring instead of injecting a high-pressure secondary flow, thus decreasing the thrust loss.By controlling the valve of the bypass, BDTN can obtain the exact thrust vectoring angle.The typical performances of BDTN have been obtained through experiments, such as thrust vectoring angle, thrust coefficient, and dynamic vector rates.16Similar studies have been conducted on the axisymmetric divergent DTN with bypass17,18.

Fig.1 Infrared images of F-2221.

Furthermore, stealth is one of the most critical performances affecting survivability on the battlefield.The aircraft attacked and destroyed by infrared-guided missiles are approximately-three times the fighters shot and killed by radar-guided missiles in the local wars that happened in these years.19The nozzle and high-temperature gas exhausting from the nozzle’s exit are undoubtedly the primary resources of the infrared signals in the aircraft’s rear hemisphere.In addition,more than 70 % of the infrared radiation energy of the exhausting jet comes from the core region of the high temperature of the exhausting jet.20Fig.1 shows the infrared images of F-22, which depicts a strong infrared radiation signature from the hot exhausting jet.21Therefore,enhancing the mixing of the exhausting gas with the cold ambient air is one of the most effective methods to reduce the infrared signal.21–23Serpentine nozzles are widely used in stealth bombers and unmanned aerial vehicles,and they have been designed,experimented, and analyzed.The typical optimized serpentine nozzle can achieve a thrust coefficient as large as 0.976,24,25but it cannot produce thrust vectoring to improve flight maneuverability at the same time.The infrared suppressor more suitable for helicopters can also be applied to improve infrared stealth.26Irregular shapes of nozzle exits have been applied for unmanned aerial vehicles to increase radar stealth and infrared stealth.For example, the shape of USAF RQ-170′s nozzle looks like a trapezoid or half a lip, as shown in Fig.227.This shape accelerates the cooling of the hot exhausting gas and makes the sidewalls of the fuselage sloping, thus improving the radar stealth at the same time.In summary,the integrated design of aircraft should consider the low observation design, especially for the nozzle of the aero-engine28.

From the above studies, FTVNs are regarded as a promising,realizable,and effective approach to achieve thrust vectoring in the future.Many relevant studies demonstrate the advantages of FTVNs, such as light weight, low thrust loss,and significant thrust vectoring angle.However, almost all the studies concentrate on how to produce thrust vectoring,analyze the special phenomenon occurring in the internal flow field, or control the airflow to maintain the steadiness of the flow field.To the best knowledge of the authors, few reports are about the design of the thrust vectoring nozzle from the requirement of the integrated aircraft-aero-engine design or the design of the FTVN that enhances the mixing performance downward the exit.This study is an extended investigation and exploration based on BDTN with rectangular cross-sections.A novel kind of BDTN with trapezoidal cross-sections is developed and designed, which changes the shape of each crosssection from the rectangle into the trapezoid.The improvement of BDTN can be called‘‘BDTN-TRA.”First,the sketch of BDTN-TRA is presented based on BDTN.Second, the description of the numerical setup is presented.Third,BDTN-TRAs with different sidewall angles (ω) and aspect ratios (W/H1) are simulated and researched.Finally, the flow field downstream of BDTN-TRA is compared with that of BDTN to obtain the influence of the different angles of the sidewall on the mixing performance.

Fig.2 USAF RQ-17027.

2.Model and methodology

2.1.Principles of BDTN and BDTN-TRA

BDTN can produce thrust vectoring by controlling the opening of the valves of the self-adaptive bypasses instead of bleeding from compressors or other components of the engine29.The concept of BDTN is shown in Fig.3.The bypass of BDTN is the connection between the inlet and the first throat of the nozzle.When the two bypasses are closed,no secondary flow is injected into the main flow,the sonic line is not shifted,and BDTN does not produce any apparent thrust vectoring angle.When a valve of the bypass is opened, a small amount of secondary flow is injected into the main flow,and it then disturbs the main flow, which causes the sonic line to be shifted.The disturbance is amplified in the cavity downstream,and an obvious thrust vectoring angle is produced.By controlling the opening of two bypasses, the thrust vectoring angle can be adjustable.The secondary flow comes from the nozzle inlet instead of the high-pressure compressor, which decreases the influence on the compressor, combustor, and turbine of the aero-engine,thus reducing the thrust loss and enhance the stability of aero-engine operation.Furthermore, compared with other fluidic thrust vectoring nozzles which need air bleeding from compressors, this method overcomes the disadvantage of affecting the efficiency of the compressors and decreases the thrust loss.30–32The secondary flow is injected into the first throat instead of spreading outside of the nozzle,which makes the secondary flow with relatively high pressure continue to expand in the nozzle.In summary, the design of the bypass is a brilliant idea to produce thrust vectoring and reduce the costs at the same time, such as thrust loss and the influence on the stability of aero-engine operation.

In general, two sidewalls of rectangular BDTN are parallel to each other and vertical to the upwall and downwall, as shown in Fig.4(a).If the two sidewalls of BDTN are inclined,each cross-section along the x-axis in BDTN will be changed into a trapezoid (i.e., BDTN-TRA), which is shown in Fig.4(b).From the comparison between the figures, BDTN and BDTN-TRA have similar flow paths except for different shapes of each cross-section.The two bypasses of BDTNTRA have the same function as the ones of BDTN.The sizes and through-flow areas of the two bypasses vary though.Although the area of each cross-section of the main flow remains the same,the performance of BDTN-TRA is different from that of BDTN.The most obvious difference is the thrust vectoring angles in pitching movement.The upwall and downwall of BDTN with rectangular cross-sections are identical in shape and symmetrically arranged.However, the upwall and downwall of BDTN-TRA have different widths.BDTNTRA inherits the advantages of BDTN especially for the bypass.The opening of the two bypasses can be controlled to adjust the thrust vectoring angle continuously.

Fig.3 Sketch of BDTN.

Fig.4 Flow path of BDTN and BDTN-TRA.

2.2.Configuration of computational model

Fig.5 Configuration of BDTN-TRA computational model.

The configuration of the computational model is shown in Fig.5.Each part of BDTN-TRA is quite similar to that of common BDTN, but the shape is different from that of common BDTN.The sketch of the inlet, first throat, and second throat is shown in Fig.5(a).The sidewalls of BDTN-TRA are flat, which means the inlet, first throat, and second throat are all trapezoids with the same sidewall angle (ω).The height of the nozzle inlet (Hin) is 60 mm.The height of the first nozzle throat (H1) is 20 mm.The height of the second throat (H2) (i.e., the exit of the nozzle) is 24 mm.The expansion ratio of the nozzle is 1.2.The width (W) is the distance between the midpoints of the two sidewalls, which is 48 mm.The sketch of BDTN-TRA’s symmetry is shown in Fig.5(b).The divergence angle before the first nozzle throat (α) is 30°.The divergence angle of the cavity (θ1) is 14.79°, and the convergence angle of the cavity (θ2) is 50°.The cavity length (Lc)is 3.34H1, and the total length (L) is 8H1.The rounding radius of the cavity bottom (Rcb) is 0.80 mm.The bypass is the connection between the nozzle inlet and the first throat,which plays a critical role in the high flight maneuverability.The secondary flow injects into the main flow through this bypass.The self-adaptive bypass angle (β) is 44.79°, and the height of the bypass (He) is 3.7 mm.The bypass valve is set at the horizontal part of the bypass, whose opening is adjustable.The original point of the coordinate system is set at the midpoint of the cavity inlet’s height and width unless otherwise stated, as shown in Figs.5(a) and (b), which is downstream of the first throat.

To obtain the influence of the sloping sidewall on the nozzle performance,the symmetry of each nozzle studied is the same.The sidewall angle (ω) and aspect ratio (W/H1) are the main research subjects.The aerodynamic performance and mixing performance downstream the second throat should be concentrated on.When the sidewall angle changes, the shape of each cross-section changes, and the area of each bypass also becomes different.However, the total area of each crosssection remains the same.

Unlike BDTN with rectangular cross-sections with the equivalent area, BDTN-TRA has a more complex internal flow field owing to the asymmetrical shape of the upwall and downwall.However, from the point of view of integrated design of future aircraft,compared with BDTN with rectangular cross-sections and rectangular exit, BDTN-TRA has a more obvious advantage that the sloped sidewalls are easier to be integrated with the fuselage, thus leading to less drag and smaller lateral Radar Cross-Section (RCS).Furthermore,if the two bypasses are closed,the small thrust vectoring angle can be beneficial for aircraft control and trimming.33–35The famous Russian aero-engine AЛ-31Φ equipped with Su-27 has similar design detail.The angle between the centerline of its nozzle and its shafts is 5°,which can produce thrust vectoring to reduce the take-off/landing distance and help with the aircraft control and trimming36.

For ease of description,the narrower wall acts as the upwall of BDTN-TRA.That is, the downwall is wider than the upwall.Furthermore, when the upper bypass is open, a pitching-up moment is produced.On the contrary, when the lower bypass valve is open, a pitching-down moment is produced.When the two bypasses are closed,BDTN-TRA works under the Non-Thrust Vectoring (No-TV) condition.In this study, the cases are simulated and investigated when the bypass valve is fully open or closed.The bypass can be partially opened indeed, which is a separate issue that deserves to be researched separately.

2.3.Computational fluid dynamics method and verification

The Computational Fluid Dynamics (CFD) method is implemented to investigate the physical-flow phenomenon and verify the design method.The Three-Dimensional (3D), steady,compressible Reynolds-averaged Navier-Stokes equations are solved in accordance with the finite volume method.The Realizable k-ε(RKE)model with the standard wall function is utilized, and it has been verified by many former studies.18,37–39The turbulent transport equations are discretized by a second-order upwind scheme.A no-slip boundary condition is imposed on the wall surface.The Sutherland equation is applied to obtain the dynamic viscosity.When the numerical simulation converges, the difference of the mass flow rate between the inlet and the second throat, the mass-weighted average velocity of the second throat, and the integral of the static pressure of nozzle surface should be steady.In addition,the error of them should be less than 0.01 %.

A NASA experiment15is used to verify the effectiveness of the numerical simulation method, which has been applied and validated in the previous work.18,37–39The numerical simulation data are compared with the experimental data15to validate the effectiveness of the simulation method and the turbulence model, as shown in Fig.6.The static pressure distributions along the upwall of the cavity from numerical and experimental results are shown in Fig.7.The results from the NASA experiment15and those from the RKE model agree well.The applied numerical method is effective to obtain the details of the flow field clearly and accurately.Therefore, the RKE model with the standard wall function can be used for the following simulation.

Fig.6 Comparison of experimental results and numerical simulation of flow field.

Fig.7 Comparison of experimental results and numerical simulation of upwall pressure.39

2.4.Grid independence analysis

BDTN-TRA with ω=60°and W/H1=2.4 is chosen to conduct the grid independence study.Structured 3D meshes generated for the numerical simulation are shown in Fig.8.

Fig.9 Static pressure distributions of different grids on cavity’s symmetries.

Fig.10 Mach number contours of different grids.

Three meshes with different node numbers are generated under the same grid topology to analyze the grid independence to determine the grid resolution: there are 1722000 nodes(coarse), 2633000 nodes (medium), and 4056000 nodes (fine).The first grid height in the boundary layer is set as approximately 0.05 mm to meet the requirement of the RKE model with the standard wall function for y+≈20.The static pressure distributions along the cavity’symmetries are shown in Fig.9.An apparent difference is noted between the coarse mesh and the others.The average deviation between the medium one and the fine one is relatively small though,which can be acceptable.Fig.10 shows the Mach number contours obtained from the different grids,which are almost the same.Therefore,the medium resolution is selected for further research as a reasonable and acceptable compromise between computational resources and simulation precision.

3.Definitions of nozzle performance parameters

Certain parameters are used to evaluate the performance of the nozzle.The Nozzle Pressure Ratio (NPR), which has significant effects on the nozzle’s performance, is defined as

where Fxand Fyare the axial force(x-component of force)and normal force(y-component of force),respectively.They can be obtained from the following equations:

where Ainis the area of the nozzle inlet, A2is the area of the nozzle second throat, vxand vyare the axial velocity(x-component of velocity) and normal velocity(y-component of velocity), respectively, Axis the projected area of the surface along the x-axis, Ayis the projected area of the surface along the y-axis, Pbis the ambient static pressure, Fwall-xis the total axial component of resultant force along nozzle walls, and Fwall-yis the total normal component of resultant force along nozzle walls.Given the realistic geometry of the nozzle, the projected areas of the inlet along the y-axis and the projected area of the second throat along the y-axis can be ignored.Thus, Eq.(4) can be simplified as

The pitching moment is also important except for the aircraft equipped with this nozzle.Owing to the layout of the aircraft and the length of the straight section downstream the nozzle inlet, the pitching moment makes a big difference.For this reason, the pitching moment is not taken into consideration.

4.Results and discussion

The influence of sidewall angles (ω) and aspect ratios (W/H1)on the aerodynamic performance is numerically studied.The impact of the sidewall angles on the downstream mixing performance is then investigated using the same method.

In this section, the sidewall angles of BDTN-TRAs range from 60°to 90°.The aspect ratios range from 2.4 to 9.6.When the sidewall angle equals 90°, each cross-section of BDTNTRA becomes a rectangle, which is the most common BDTN and can be regarded as a particular configuration of BDTNTRA.In addition, BDTN-TRA with ω = 90° is the reference to BDTN-TRA with trapezoidal exit.If the sidewall angle is less than 60° and the aspect ratio is not large enough, each cross-section of BDTN-TRA becomes a triangle, and the upwall of BDTN-TRA disappears.Moreover, the sidewall angle of the new generation stealth fighter’s fuselage is usually approximately 60°, such as that of USAF F-2240–43, which is the limitation to the sidewall angle of the nozzle

For ease of description and accurate understanding,BDTN is used to refer specifically to BDTN-TRA with ω = 90°,which has rectangular cross-sections and rectangular exit,and BDTN-TRA is used to refer specifically to BDTN-TRA whose sidewall angle is less than 90°.

4.1.Influence of different sidewall angles (ω) on aerodynamic performance

Fig.11 shows the aerodynamic performance of BDTN-TRAs with different sidewall angles under three different working conditions.In Figs.11(a) and (b), BDTN has a more significant thrust coefficient than BDTN-TRAs with ω = 60° and ω = 75° do.The sloping sidewall has a negative effect on the thrust coefficient of BDTN.As for BDTN-TRA with ω = 60° and ω = 75°, the thrust coefficient of pitching-up and pitching-down is also different,and the deviation between the thrust coefficient under the two conditions is less than 3%.As for the thrust vectoring angle shown in Fig.11(c), BDTNTRA can produce a small pitching-down thrust vectoring angle at nearly 5°, which is an advantage for short take-off and landing and trimming.Under the Thrust-Vectoring (TV)condition, BDTN-TRA has different pitching-up and pitching-down thrust vectoring angles.The value of pitchingup thrust vectoring angle is usually around 1°–2°smaller than the value of pitching-down thrust vectoring angle.This feature can be applied to avoid stalling for the aircraft33–35.Compared with those of BDTN, the sloping sidewalls of BDTN-TRA have a negative effect on the thrust vectoring angle.The tendency is similar to that of the thrust coefficient.

Furthermore, the small thrust vectoring angle under No-TV condition has small effect on the axial force (xcomponent of force).For example, when the thrust vectoring angle is smaller than 5°, the axial force is greater than 99.6%of the resultant thrust.When the thrust vectoring angle is smaller than 10°,the axial force is greater than 98.5%of the resultant thrust.This is one of the reasons why some engines produce a small thrust vectoring during their normal flight,such as AЛ-31Φ36.

Fig.11 Aerodynamic performance of BDTN-TRAs with different sidewall angles.

4.1.1.No-TV condition

Fig.12 Static pressure distributions along cavity’s symmetries of BDTN-TRAs with different sidewall angles when NPR=4 under No-TV condition.

Compared with other kinds of FTVNs and Laval nozzle, the cavity between the first throat and second throat, which enlarges the disturbance caused by the secondary flow, is a unique structure for DTN.Static pressure distribution along the cavity can judge the flow separation and reattachment to analyze the internal flow field44.Fig.12 shows static pressure distributions along the cavity’s symmetries of BDTN-TRA with different sidewall angles when NPR = 4 under the No-TV condition.This distribution reveals the flow mechanics for the existence of the small thrust vectoring angle under the No-TV condition.The static pressure distributions are quite different between the cavity’s upwall and downwall owing to the squeezing of the two sloping sidewalls.Furthermore, the pressure along the cavity’s upwall is usually larger than that along the cavity’s downwall,which leads to the larger value of the normal components of the resultant force of the cavity’s upwall than that of the cavity’s downwall.The direction of the total normal components of the resultant force of the cavity is upward, and BDTN-TRA produces the pitching-down moment.Combined with the Mach number contours shown in Fig.13, the main flow field in the cavity’s symmetry plane is symmetric up and down before the first throat; however, it becomes asymmetric in the cavity, which is more obvious near the second throat.The main flow keeps speeding up after the first throat.As the downwall of the cavity is wider than the upwall of the cavity, the upper part of the cavity limits the main flow to expand further, which forms an oblique shock appearing at the expanding part of the cavity’s upwall.The convergence part of the cavity and the two sloping sidewalls form a relatively narrow space for the main flow, which makes the flow field more complex.Finally, the flow is injected out in a slightly downward direction from the second throat.

The total pressure recovery coefficient (σ) is defined as the ratio of the total pressure of the second throat cross-section to the total pressure of the nozzle’s inlet, as shown in Fig.14.Compared with those of BDTN, the sloping sidewalls of BDTN-TRA produce vortexes along the x-axis.Owing to the compression of the sidewalls, the main flow tends to flow downward to the downwall at the second throat crosssection, which leads to a couple of vortexes at the upwall of the second throat.Although the three BDTN-TRAs have different sidewall angles,the geometric area of their second throat cross-sections is equal.The area where the total pressure recovery coefficient is over 0.90 at the second throat cross-section is defined as the core region of the cross-section, which can be obtained from the simulation results.There are 60.2 %,60.1 %, and 64.0 % area of the core region at the second throat of BDTN-TRA with ω = 60°, 75°, 90°, respectively.

Fig.13 Mach number contours of BDTN-TRA’s symmetries with different sidewall angles when NPR = 4 under No-TV condition.

The trapezoidal cross-section leads to a relatively less core area owing to more giant corner vortexes.The smaller effective flow-through area at the second throat cross-section increases the under expansion of the nozzle.This is one of the reasons why the sloping sidewall leads to the lower thrust coefficient under the No-TV condition.

4.1.2.TV condition of pitching-up

When the bypass valve of the short edge of BDTN-TRA is open, the nozzle produces a pitching-up moment.The secondary flow injects into the first throat form the upper bypass.The SFR of the upper bypass with different sidewall angles is shown in Fig.15.As for a nozzle with a certain sidewall angle,SFR almost remains the same as the NPR increases.While the sidewall angle increases, the area of the cross-section of the upper bypass increases, and SFR increases, as obviously shown in Fig.15.More secondary flow is injected into the first throat to produce thrust vectoring.This is one of the reasons why the larger the sidewall angle,the greater the thrust vectoring angle.Nonetheless, SFR is not the only cause or the decisive factor affecting thrust vectoring angle.

Fig.14 Total pressure recovery coefficient contours of BDTNTRA’s second throats with different sidewall angles when NPR = 4 under No-TV condition.

Fig.15 SFR of upper bypass with different sidewall angles under TV condition of pitching-up.

The pressure distributions along the cavity’s symmetries when NPR = 4 are shown in Fig.16.After flowing through the first throat, the mainstream flows along the downwall of the cavity and finally injects out of the second throat.During flowing along the cavity, separation and reattachment happen near the bottom of the cavity.From this figure,BDTN has the most considerable difference between the upwall and downwall of the cavity, which is evidence of the fact that the BDTN’s cavity has the most significant normal components of the resultant force and the enormous thrust vectoring angle.

The Mach number contours of the symmetries under the TV condition of pitching-up when NPR = 4 are shown in Fig.17.The main flow can flow along the downwall of the cavity in BDTN-TRA with ω=75°and ω=90°,which is closer to the downwall of the cavity.In comparison,the main flow of BDTN-TRA with ω = 60° keeps a certain distance to the downwall.As for the flow field downstream the second throat,the zone with high Mach number of BDTN is more prominent,whereas the one of BDTN-TRA with ω= 60° is the smallest.A detail of the contours should be paid attention to: the main flow downstream of the second throat forms a narrow and curved flow path section because of a series of vortexes produced by mixing the outer flow and the main flow ejecting from the nozzle.

Fig.16 Static pressure distributions along cavity’s symmetries of BDTN-TRAs with different sidewall angles when NPR=4 under TV condition of pitching-up.

Fig.17 Mach number contours of BDTN-TRA’s symmetries with different sidewall angles when NPR=4 under TV condition of pitching-up.

Fig.18 Total pressure recovery coefficient contours of BDTNTRA’s second throats with different sidewall angles when NPR = 4 under TV condition of pitching-up.

Fig.18 shows the total pressure recovery coefficient contours of BDTN-TRA’s second throat with different sidewall angles when NPR = 4 under the TV condition of pitchingup.Under this condition,the main flow is disturbed by the secondary flow injected from the upper bypass,causing it to flow close to the downwall.The vortexes near the two sloping sidewalls and the primary separation vortex near the upwall of the cavity decrease the effective flow area and increase the loss.There are 56.0%,52.9%,and 60.3%area of the core region at the second throat of BDTN-TRA with ω = 60°, 75°, 90°,respectively, which explains the reason why the sloping sidewall leads to a relatively more extensive loss in the main flow and a smaller thrust coefficient.

4.1.3.TV condition of pitching-down

Under the TV condition of pitching-down, the bypass of the longer edge is open, and the secondary flow from this bypass disturbs the main flow near the first throat and hits the main flow upward.Then, the main flow is closer to the upwall of the cavity, and typical flow separation and reattachment happen at the expansion and convergence parts of the cavity,respectively.Under this working condition, as the sidewall angle increases, the area of each cross-section of the lower bypass decreases, thus affecting the secondary mass flow ratio and decreasing SFR.Nevertheless, the thrust vectoring angle becomes greater as the sidewall angle increases,which is shown in Fig.19.SFR is not the only cause or the decisive factor affecting thrust vectoring angle, but the change of the internal flow field happening in the cavity matters.As for a certain nozzle, NPR has quite a small influence on SFR.

Fig.19 SFR of lower bypass with different sidewall angles under TV condition of pitching-down.

From Fig.20, the position of the oblique shock happening at the expansion part and reattachment point happening at the convergence part can be judged quite easily.With the increase of the sidewall angle, the position of the oblique shock keeps moving upstream,so does the reattachment point.The integration of the static pressure and the area along the cavity can be considered as the force on the cavity.The area of the region enclosed by the static pressure distributions can reflect the amount of force qualitatively.In terms of the length or the height, the area of BDTN’s region is the maximum among the three configurations, which is the reason for producing the most significant thrust vectoring angle among the three configurations.

Fig.21 shows the Mach number contours of BDTN-TRA’s symmetries with different sidewall angles when NPR = 4 under the TV condition of pitching-down.From these figures,the main flow is close to the upwall of the cavity obviously.As the geometric area of each cross-section of the flow path is the same,the actual mass flow rate is similar.After being disturbed by the secondary flow, the flow path of the main flow shifts upward,and then the first oblique shock happens at the beginning of the cavity.Regarding the cavity,the upwall is narrower than the downwall.Under the similar mass flow rate, as the sidewall angle decreases, the symmetric cross-section of the main flow path becomes higher.Moreover,due to the geometric characteristics of BDTN-TRA, the bottom of the cavity’s upwall is the narrowest position of the nozzle.For this reason,the sidewall angle affects the second oblique shock.The second oblique shock becomes vertical and weaker with the increase of the sidewall angle.The second oblique shock is too weak to appear in BDTN’s contour.Under the influence of the two sidewalls and the first and second oblique shock waves, the main flow is closer to the cavity’s upwall as the sidewall angle increases,leading to the larger angle of jet exhausting from the nozzle.

Fig.20 Static pressure distributions along cavity’s symmetries of BDTN-TRAs with different sidewall angles when NPR=4 under TV condition of pitching-down.

Fig.21 Mach number contours of BDTN-TRA’s symmetries with different sidewall angles when NPR=4 under TV condition of pitching-down.

In Fig.22, the corner vortex can be observed clearly in the contours of BDTN-TRA with ω = 60° and ω = 75°.As for the position of the core region among the three kinds of nozzles, BDTN has the closest core region to the upwall of the nozzle,thus producing the largest thrust vectoring angle under the same working condition.There are 56.0 %, 58.0 %, and 60.3 % area of the core region at the second throat of BDTN-TRA with ω = 60°, 75°, 90°, respectively.Under this condition,the smaller the sidewall angle is,the smaller the area of the core region is,the larger the loss of the main flow is,and the smaller the thrust coefficient is.

Fig.22 Total pressure recovery coefficient contours of BDTNTRA’s second throats with different sidewall angles when NPR = 4 under TV condition of pitching-down.

4.2.Influence of different aspect ratios(W/H1)on aerodynamic performance

Fig.23 shows the aerodynamic performance of BDTN-TRAs with different aspect ratios under the typical conditions.Figs.23(a) - (c) are the influence of different aspect ratios on the thrust coefficient.Under the No-TV condition and TV condition of pitching-up, the effect of different aspect ratios on the thrust coefficient is less than 1.5 %.When the lower bypass valve is open, different aspect ratios have a positive influence on the thrust coefficient.When the aspect ratio becomes larger, the thrust coefficient becomes greater.Under this condition,the thrust coefficient of the W/H1=9.6 configuration is approximately 2 % larger than the smallest one.Fig.23(d) shows the influence of different aspect ratios on the thrust vectoring angle, which is quite similar to the influence on thrust coefficient.Under the TV condition of pitching-down, the influence is obvious, that is, the larger the aspect ratio is, the larger the thrust vectoring angle is.Especially for BDTN with W/H1=9.6,which is the largest aspect ratio configuration calculated, although the relative width difference between the upwall and the downwall is quite small,the thrust vectoring angles and the thrust coefficients are not equal under different TV conditions.The thrust coefficient under the TV condition of pitching-down is around 1 %–2%larger than that under the TV condition of pitching-up, and the thrust vectoring angle under the TV condition of pitching-down is nearly 7° larger than that under the TV condition of pitching-up only when NPR = 2.Furthermore, the thrust vectoring angle under the TV condition of pitchingdown is quite near to the thrust vectoring angle of BDTN -TRA with ω = 90°, as shown in Fig.11.

4.2.1.No-TV condition

Fig.24 and Fig.25 show the static pressure distributions along the cavity’s symmetries and Mach number contours of BDTNTRA’s symmetry with different aspect ratios when NPR = 4 under the No-TV condition.A difference is noted in the static pressure distributions between the upwall and the downwall of the cavity.With the increase of the aspect ratio, the difference does not change substantially.Under the influence of the sidewall, the main flow forms a clear asymmetric region downstream of the second throat.The expansion near the upwall of the cavity is one of the main phenomena of the asymmetric region.As the aspect ratio increases,the asymmetric expansion downstream the second throat decreases, but the high Mach number region remains below the centerline of the second throat,which leads to a small thrust vectoring angle of approximately 3°, as shown in Fig.25.

As for the total pressure recovery coefficient contours of the second throat cross-sections shown in Fig.26, all of them are under the No-TV condition, but the structures of their flow field are different.The area occupied by the corner vortex is almost the same,but the vortexes near the upwall of the second throat are different.In Figs.26(a) - (c), there is a couple of vortexes along the flow direction near the upwall, which leads to a low total pressure region at the symmetry plane of BDTNTRA.Fig.26(d) presents three low total pressure regions.From another point of view, the area ratios of the core region to the second throat of each configuration can be obtained,which are 60.2%,60.9%,65.2%,and 68.6%when the aspect ratio equals 2.4, 4.8, 7.2, and 9.6, respectively.Enlarging the aspect ratio can increase the area ratio of the core region to the second throat cross-section.

4.2.2.TV condition of pitching-up

Under TV condition of pitching-up, the SFR of the upper bypass can be obtained from numerical simulations, as shown in Fig.27.When the aspect ratio increases from 2.4 to 4.8,SFR also doubles.As the aspect ratio increases from 4.8 to 9.6, SFR keeps rising.SFR is approximately 0.1 at W/H1= 9.6, which approaches the SFR of BDTN with ω = 90°.As the aspect ratio increases, the sloping sidewall has a smaller influence on the aerodynamics.The effect of NPR on SFR is consistent with the results of the previous study.

The static pressure distributions along the cavity’s symmetries with different aspect ratios under the typical working condition of pitching-up are displayed in Fig.28.The static pressure distributions of downwall with W/H1= 4.8, 7.2,and 9.6 are similar, whereas the static pressure distribution of downwall with W/H1=2.4 is relatively low near the second throat and relatively high near the first throat.As for the area of the region enclosed by the static pressure distributions of the downwall and upwall of the cavity,the region of BDTN-TRA with W/H1= 9.6 has the maximum area because the static pressure distribution of its upwall is the lowest one and the static pressure distribution of its downwall is pretty large.As for BDTN-TRA with W/H1= 9.6, the largest difference between the upwall and downwall of the static pressure distribution appears near the cavity’s bottom.Compared with other configurations, the most obvious difference of BDTN-TRA with W/H1= 9.6 is located closest to the second throat, thus producing the largest pitching-up moment.A narrow and curved flow path section appears downstream the second throat, as shown in Fig.29(a),whereas the main flow injecting out of the second throat smoothly is shown in Figs.29(b)-(d).The relatively small aspect ratio has an obvious influence on the mixing performance of BDTN-TRA.

Fig.23 Aerodynamic performance of BDTN-TRAs with different aspect ratios (ω = 60°).

Fig.24 Static pressure distributions along cavity’s symmetries of BDTN-TRAs with different aspect ratios when NPR = 4 under No-TV condition.

Fig.25 Mach number contours of BDTN-TRA’s symmetries with different aspect ratios when NPR = 4 under No-TV condition.

Fig.26 Total pressure recovery coefficient contours of BDTNTRA’s second throats with different aspect ratios when NPR=4 under No-TV condition.

Fig.27 SFR of upper bypass with different aspect ratios under TV condition of pitching-up.

Fig.28 Static pressure distributions along cavity’s symmetries of BDTN-TRA with different aspect ratios when NPR = 4 under TV condition of pitching-up.

Fig.30 shows the total pressure recovery coefficient contours of BDTN-TRA’s second throat with different aspect ratios when NPR = 4 under the TV condition of pitchingup.Under the interaction of the secondary flow from the upper bypass, the core region moves downward, and the separation region near the upwall of the cavity takes up the low total pressure region near the upwall of the second throat.With the increase of the aspect ratio, the small low total pressure near the downwall of the cavity disappears.

Fig.29 Mach number contours of BDTN-TRA’s symmetries with different aspect ratios when NPR=4 under TV condition of pitching-up.

Fig.30 Total pressure recovery coefficient contours of BDTNTRA’s second throats with different aspect ratios when NPR=4 under TV condition of pitching-up.

Fig.31 SFR of lower bypass with different aspect ratios under TV condition of pitching-down.

Fig.32 Static pressure distributions along cavity’s symmetries of BDTN-TRAs with different aspect ratios when NPR = 4 under TV condition of pitching-down.

Fig.33 Mach number contours of BDTN-TRA’s symmetries with different aspect ratios when NPR=4 under TV condition of pitching-down.

4.2.3.TV condition of pitching-down

SFR is obtained from numerical simulations, as shown in Fig.31.The increase of the aspect ratio leads to the increase of the area of the bypass cross-section, while SFR decreases.This outcome verifies that SFR is not the most critical cause of the thrust vectoring angle.The area of the bypass crosssection does not have a certain influence on SFR and the thrust vectoring angle.If the aspect ratio is large enough,the sloping sidewall does not have an obvious influence on the aerodynamic performance.

Fig.32 shows the static pressure distributions along the cavity’s symmetries, and Fig.33 shows their Mach number contours.The static pressure distributions of BDTN-TRAs with W/H1=4.8,7.2,9.6 do not differ much from each other,so their thrust vectoring angles are similar to one another.Furthermore,from the point of view of the flow field structure,the high Mach number regions of BDTN-TRAs with W/H1=4.8,7.2, 9.6 are quite similar both inside the cavities and outside the nozzles, whereas BDTN-TRA with W/H1=2.4 has a larger high Mach number region before the oblique shock and smaller one after exhausting from the second throat.

Fig.34 Total pressure recovery coefficient contours of BDTNTRA’s second throats with different aspect ratios when NPR=4 under TV condition of pitching-down.

Fig.34 shows the total pressure recovery coefficient contours of BDTN-TRA’s second throat with different aspect ratios when NPR = 4 under the TV condition of pitchingdown.Under the interaction of the secondary flow passing through the lower bypass,the main flow moves near the upwall of the cavity.The low total pressure region can be found in each contour whose shape is different.The area of corner vortexes near the downwall and the sidewalls keeps almost the same, whereas the corner vortexes near the upwall and the sidewalls keep changing irregularly.

4.3.Influence of different sidewall angles (ω) on downstream mixing performance

Infrared stealth is the critical requirement for stealthy fighters.Mixing performance affects the static temperature distributions downward the nozzle’s exit, which can be equated to infrared stealth21–23.The better the mixing performance downstream the nozzle exit, that is, the faster the cooling speed of the hot gas exhausting from the nozzle,the greater the infrared stealth.The BDTN-TRA configurations of ω = 60° and ω = 90° in W/H1= 2.4 are chosen to be studied to reveal the influence of different sidewall angles on the mixing performance downstream the nozzles.Considering the realistic conditions of the air combat, the mixing performance of BDTNTRA under No-TV condition is more important.

Fig.35 Static temperature distributions along x-axis of BDTNTRAs with different sidewall angles and different total temperatures of inlet under No-TV condition (NPR = 4).

Fig.36 Distributions of axial velocity along x-axis of BDTNTRAs with different sidewall angles and different total temperatures of inlet under No-TV condition (NPR = 4).

After the main flow is exhausted from the second throat, a large amount of heat exchange occurs between the hot main flow and the relatively cold environment airflow.The vortexes inside the main flow suck the ambient airflow downward,leading the static temperature and the velocity to decay together along the x-axis.The infrared radiation decreases as the static temperature decreases.That is, the static temperature and the axial velocity (i.e., the velocity in the x-direction coordinate)should be paid much attention to38,45.During the numerical simulation, some typical total temperatures ranging from 600 K to 1600 K are imposed on BDTN-TRA’s inlet as boundary conditions.The remaining conditions are set as the ground ones.

For a clearer display of the simulation results in this subsection, the x-axis of the coordinate system is transformed.The position of(x-Lc+L)/L=0 is the nozzle’s inlet.The position of (x - Lc+ L)/L = 1 is the second throat.

Fig.35 shows the static temperature distributions along the x-axis of BDTN-TRAs with different sidewall angles and different total temperatures of inlet under the No-TV condition.Despite the different sidewall angles of each cross-section, the static temperatures of the second throats are quite similar.The trends of similar static temperature distributions along the xaxis do not differ much before (x - Lc+ L)/L = 2.When the main flow passes one time the length of nozzle downstream of the second throat, the static temperature distribution of BDTN-TRA with ω = 60° decreases obviously faster than that of BDTN.The higher the total temperature of the nozzle inlet is,the faster the static temperature distribution decreases.When the total temperature of the nozzle inlet equals 1200 K and 1600 K, the static temperature differences between BDTN-TRA with ω = 60° and ω = 90° are over 360 K at(x - Lc+ L)/L = 3, which means that BDTN-TRA with ω = 60° has more excellent infrared stealth performance owing to the rapidly decreasing static temperature.

Fig.36 shows the distributions of the axial velocity along the x-axis of BDTN-TRAs with different sidewall angles and different total temperatures of inlet under the No-TV condition.When the main flow passes through (x - Lc+ L)/L = 1.5, the axial velocity of BDTN-TRA with ω = 60°decreases faster than that of BDTN.This phenomenon confirms that the mixing of the environment and the exhausting jet causes the velocity to decrease.From this point, BDTNTRA with ω = 60° has better mixing performance than BDTN.

Fig.37 Static temperature contours of horizontal and vertical cross-sections of BDTN-TRA with different sidewall angles when NPR = 4 and = 1600 K under No-TV condition.

Fig.38 Static temperature contours of different cross-sections of BDTN-TRA with different sidewall angles when NPR = 4 and = 1600 K under No-TV condition.

Fig.37 is the static temperature contours of the horizontal and vertical cross-sections of BDTN-TRA with different sidewall angles when NPR = 4 and T*in= 1600 K under the No-TV condition, respectively.Despite a small thrust vectoring angle occurring downward the second throat for configuration of ω = 60°, the static temperature contours of vertical crosssections do not differ much.The contours of the horizontal cross-sections have a noticeable difference.In the contour of BDTN-TRA with ω=60°,the high static temperature region looks like a trident generated by the ejection of ambient air and the mixing of the main flow with the environment airflow.The mixing mentioned above is the reason why the static temperature distribution and velocity distribution decrease faster in the configuration of ω = 60°.

Fig.39 Comparison between areas of high static temperature region of BDTN-TRAs with different sidewall angles.

Fig.38 shows the static temperature contours of the different cross-sections of BDTN-TRA with different angles of sidewall when NPR = 4 and T*in= 1600 K under the No-TV condition.Each cross-section is vertical to the x-axis.Figs.38(a)and(b)show the static temperature contours of the second throats of the two nozzles.Compared with Fig.38(b),the temperature of the two corners near the downwall of BDTN-TRA with ω = 60° is higher.The shape of the cross-sections of the main flow looks like an ellipse or a rhombus downward the BDTN’s second throat.As for BDTN-TRA with ω = 60°,the shape of the main flow cross-section is not typical.Some cold airstream is ejected by the main flow with high temperature and high speed.The vortexes caused by mixing the main flow with the ambient air pull and squeeze the shape of each cross-section downstream the second throat, thus increasing the contact area between the hot main flow and cold environment air.

The area of the high static temperature region(Acore-T)can be obtained by post-processing Fig.38,which is defined as the region where the static temperature is above the 70 % total temperature of the nozzle inlet45,as shown in Fig.39.This figure displays the change of the area of high static temperature region along the x-axis.From(x-Lc+L)/L=1 to approximately(x-Lc+L)/L=1.5,the under-expanded main flow continues to expand downstream the second throat,which can also be inferred from Fig.36.From (x - Lc+ L)/L = 1.5 to nearly (x - Lc+ L)/L = 2.5, the static pressure of the main flow of BDTN-TRA with ω=60°approaches to the environment pressure, so the static temperature and the axial velocity keep decreasing.After roughly(x-Lc+L)/L=2.5,the difference between the static temperature and the axial velocity of the two kinds of BDTN-TRA is quite apparent.The phenomenon can explain the change of the high static temperature region’s area.For this reason, the area of the high static temperature region of BDTN-TRA with ω = 60° is larger at(x - Lc+ L)/L = 1.5 and smaller after (x - Lc+ L)/L=1.75.Furthermore,the area of the high static temperature region of BDTN-TRA with ω = 60° is about 40 % smaller than that of BDTN at (x - Lc+ L)/L = 2, the area of the high static temperature region of BDTN-TRA with ω = 60°is approximately half of the area of BDTN at (x - Lc+ L)/L = 3.It should be noted that the under-expanded main flow continues to expand downstream the second throat, and the distributions of the static temperature and the axial velocity along the x-axis downstream the second throat change drastically and fluctuate obviously.The phenomena are caused by the expansion of the under-expanded main flow accompanied by the strong mixing procession.Even if the data of more cross-sections’high static temperature region are counted,the dimensionless area shown in Fig.39 will still change drastically and fluctuate obviously.

Finally,the contours of the vorticity along the x-axis can be obtained, which are shown in Fig.40.The production and development of the vortexes downstream of the second throat are displayed clearly during the mixing process.The mixing process of BDTN-TRA with ω=60°is stronger in the vortex size and the number of vortex couples.The intense mixing process ejects more cold ambient air into the hot main flow and increases the contact area of the two airstreams, thus decreasing the temperature of the main flow rapidly.It is the nature causing the enhanced mixing performance of BDTN-TRA.

Fig.40 Contours of vorticity along x-axis of BDTN-TRA with different sidewall angles at(x-Lc+L)/L=1.125 when NPR=4 and T*in = 1600 K under No-TV condition.

In Fig.38 and Fig.40, the contour of each cross-section is displayed, which is vertical to the x-axis instead of vertical to the exhausting jet flow direction, but it has quite small influence on the analysis of the mixing performance and flow field downstream the second flow.For example, the exhausting jet of BDTN-TRA deflects, causing the cross-section along the flow direction to have a certain angle with the cross-section along the x-axis.The cross-section along the x-axis can be regarded as the projected surface of the cross-section along the flow direction.Furthermore, the angle between the x-axis and the flow direction is only approximately 5°,which can be speculated from Fig.11.This means that the contours of the two cross-sections are almost the same even if such small angle is taken into consideration.The flow structures and the static temperature distributions of the two cross-sections are similar.Therefore, no matter which cross-section is chosen to analyze the flow field structure,it does not affect the result that BDTNTRA with ω = 60° has better mixing performance.

5.Conclusions

High flight maneuverability and stealth are the most critical features for fighters in the future.The thrust vectoring nozzle can help the aircraft increase the flight maneuverability,which leads to high possibility of winning an air combat.The fluidic thrust vectoring nozzle gains popularity with lightweight,excellent performance, and reliability.The nozzle and its exhausted gas are the primary resources of the infrared signals in the aircraft’s rear hemisphere.Cooing the exhausted gas downstream the nozzle exit as fast as possible can reduce the likelihood of being detected.Thus, a fluidic thrust vectoring nozzle with better mixing performance can be an important research direction.A novel Trapezoidal Bypass Dual Throat Nozzle(BDTN-TRA)has been proposed and analyzed numerically from the viewpoint of the high flight maneuverability,mixing performance, and integrated aircraft-aero-engine design.The mixing performance can be improved obviously simply by changing the sidewall angle, while the ability of thrust vectoring remains excellent.This feature of BDTNTRA is the most attractive.The following conclusions are drawn from the numerical simulation:

(1) BDTN-TRA has the same advantage as the Bypass Dual Throat Nozzle (BDTN), which produces thrust vectoring angle by controlling the opening of the valves at two self-adaptive bypasses.This method can decrease the thrust loss obviously without any secondary flow from the high-pressure parts of the engine.

(2) The typical configurations with different sidewall angles(ω) ranging from 60° to 90° are simulated, which leads to the different shapes of each cross-section.Compared with the configuration with ω=90°,the configurations with ω = 60° and ω = 75° can produce unequal thrust vectoring angles under the Thrust-Vectoring(TV)conditions of pitching-up and pitching-down.The difference between the unequal thrust vectoring angles is usually around 1°–2°.Furthermore, when the two bypasses are closed under the Non-Thrust Vectoring(No-TV) condition, BDTN-TRA with ω = 60° and ω = 75° can also produce approximately 5° thrust vectoring angle.This feature can benefit the aircraft with flying wing layout from their control and trimming after considering how to equip the aircraft with BDTN-TRA.

(3) The typical configurations with different aspect ratios ranging from 2.4 to 9.6 are simulated, and the sidewall angles remain the same.The aspect ratio has a more obvious influence on the thrust coefficient under the TV condition than under the No-TV condition, and the thrust coefficient under the TV condition of pitching-down is around 1%–2%larger than that under the TV condition of pitching-up.With the increase of the aspect ratio, the thrust vectoring angle of BDTNTRA approaches that of BDTN.

(4) The mixing performances of BDTN-TRAs with ω=60°and ω = 90° are obtained.The distributions of static temperature and the axial velocity of BDTN-TRA with ω=60°decrease faster than those of BDTN.Owing to the ejection of ambient gas and the mixing of the main flow with the environment, the area of the high static temperature region of BDTN-TRA with ω = 60° is about 40 % smaller than that of BDTN at the position of the length of BDTN-TRA downstream the second throat along the x-axis.At the position of twice the length of BDTN-TRA downstream the second throat along the x-axis,the static temperature of the exhausted gas of BDTN-TRA with ω = 60° is 360 K lower than that of BDTN at T*in=1600 K,and the area of the high static temperature region of BDTN-TRA with ω = 60°is approximately half of the area of BDTN.Furthermore, the vortexes produced by the ejection mentioned above separate the static temperature contour of BDTN-TRA’s horizontal cross-section into three branches, which looks like a trident.Further analysis shows that the mixing process of BDTN-TRA with ω = 60° is stronger in the vortex size and the number of vortex couples.All these conclusions prove the better mixing performance of BDTN-TRA with ω=60°,leading to more extraordinary infrared stealth performance.

In summary, BDTN-TRA can produce a slight thrust vectoring angle to assist the aircraft control and trim under No-TV condition, while under TV conditions, BDTN-TRA can produce a thrust vectoring angle at over 12°.Furthermore,the exhausted gas spreading out from the exit can be cooled faster, which benefits the infrared stealth.These advantages satisfy the development trend of the aero-engine and the advanced stealthy fighter.In the future application, BDTNTRA needs to be further optimized under the comprehensive consideration of the requirements of the aerodynamic performance, the stealthy performance, and the installation space.The geometric parameters of BDTN-TRA,such as the sidewall angle and the aspect ratio, can be adjusted.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

We would like to acknowledge the continued support of the National Science and Technology Major Project, China (No.2019-II-0007-0027), the Defense Industrial Technology Development Program, China (No.JCKY2019605D001), the Advanced Jet Propulsion Creativity Center, Aero Engine Academy of China(No.HKCX2020-02-011), the Aeronautics Power Foundation, China (No.6141B09050383), the Science and Technology on Complex System Control and Intelligent Agent Cooperation Laboratory of China,the Jiangsu Funding Program for Excellent Postdoctoral Talent, China（No.2022ZB214), and the China Postdoctoral Science Foundation.