Aerodynamic characteristics of co-flow jet wing with simple high-lift devices

Zhenhao ZHU, Tianhang XIAO, Haolin ZHI, Shuanghou DENG, Yujin LU

College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

KEYWORDS Active flow control;Co-flow jet;Continuous injection;Discrete injection slot;Simple high-lift device

Abstract Numerical investigations are conducted to explore the aerodynamic characteristics of three-dimensional Co-Flow Jet (CFJ) wing with simple high-lift devices during low-speed takeoff and landing. Effects of three crucial parameters of CFJ wing, i.e., angle of attack, jet momentum and swept angle, are comprehensively examined. Additionally, the aerodynamic characteristics of two CFJ configurations, i.e., using open and discrete slots for injection, are compared. The results show that applying CFJ technique to a wing with simple high-lift device is able to generate more lift,reduce drag and enlarge stall margin with lower energy expenditure due to the super-circulation effect. Increasing the jet intensity can reduce the drag significantly, which is mainly contributed by the reaction jet force. The Oswald efficiency factor is, in some circumstances, larger than one,which indicates the potential of CFJ in reducing induced drag. Compared with clean wing configuration, using CFJ technique allows the aerodynamic force variation less sensitive to the swept angle,and such phenomenon is better observed for small swept angle region.Eventually,it is interesting to know that the discrete slotted CFJ configuration demonstrates a promising enhancement in aerodynamic performance in terms of high lift, low drag and efficiency.

1. Introduction

Recently, increasing attentions have been paid to aircraft advanced high-lift system design to meet the raising requirements of short takeoff and landing capability.High-lift system design is one of the essential tasks throughout the entire aircraft design process for the sake of achieving maximum liftto-drag ratio and/or lift coefficient. Advanced high-lift devices1-8and lift enhancement by passive and active flow control means have been put forward during past decades.

Nomenclature AOA Angle of attack, (°)c Wing chord length, m CL Lift coefficient CD Drag coefficient CD0 Zero-lift drag coefficient CD_Baseline Drag coefficient of the baseline configuration CD_CFJ Drag caused by the CFJ reaction force CD_i Induced drag CD_p Pressure drag CD_v Friction drag due to the viscosity CM Pitching moment coefficient Cp Pressure coefficient Cμ Jet momentum coefficient for open slot CFJ wing C′μ Jet momentum coefficient for discrete CFJ wing cp Constant pressure specific heat, kJ/(kg·K)e Oswald efficiency factor FxCFJ, FyCFJ Reaction forces produced by the CFJ in the directions of drag and lift, N MCFJ Pitch moment produced by the CFJ, N·m N Number of grid cells Lj, Ls Length of level arm, m L/D Lift-to-drag ratio(L/D)c Equivalent lift-to-drag ratio corrected by the power consumption of CFJ ˙m Mass flow rate, kg/s pj, ps Static pressure in the injection and suction cavities P Power consumption required by the compressor in the wing Pc Power coefficient Pt Total pressure, Pa R′x, R′y Surface integrals of pressure and shear stress in the drag and lift directions M′ Surface integral of pressure and shear stress in the nose-up pitching direction N Number of grid cells S Area, m2 Tt Total temperature, K V Velocity magnitude, m/s Vinj Velocity magnitude at the injection cavity z/b Spanwise location of the section Γ Total pressure ratio of compressor Λ Swept angle, (°)ρ Density, kg/m3 α Angle of attack β1, β2 Deflection angles of the droop nose and the simple flap, (°)θj, θs Inclined angle, (°)γ Air specific heat ratio η Co-flow jet pumping system efficiency ζ Drag reduction efficiency parameter Abbreviations AFC Active Flow Control ADVINT Adaptive Flow Control Vehicle Integrated Technologies AR Aspect Ratio CFJ Co-Flow Jet OCFJ Open Slot Co-Flow Jet DCFJ Co-Flow Jet Using Discrete Injection Jets FASIP Flow-Acoustic-Structure Interaction Package RANS equation Reynolds-Averaged Navier-Stokes equation TE Trailing Edge LE Leading Edge OF Obstruction Factor SST Suction Surface Translation STOL Short Take-Off and Landing Subscripts j Injection condition s Suction condition∞ In-coming freestream ref Reference

Active Flow Control(AFC) technique has been considered to be one of the most promising ways for developing alternative design or achieving better performance of air vehicles,including boundary ingestion and blowing,9-11circulation control,12-14upper surface blowing flap,15-17plasma flow control,18-21and recently Co-Flow Jet (CFJ) technique.22-33The basic idea of the first three aforementioned flow control techniques is to augment the lift and enlarge the stall margin by means of energizing the boundary layer with the introduction of additional mass flow. However, the air source of the additional mass flow generally comes from the engine,which in practice degrades the thrust and efficiency of the propulsion system. The plasma actuator draws ambient fluid towards the wall and then ejects this fluid tangentially away from the electrode,20so as to achieve zero-net-mass-flux flow control.However,this control strategy has a high demand for the actuator and is still in the experimental stage. Recently, a novel active zero-net-mass-flux flow control strategy called CFJ,proposed by Zha and Paxton,22is able to achieve high efficiency with low energy consumption. The CFJ system is designed to inject the air near the suction peak at the leading edge and to suck the air near the trailing edge where the pressure is high(Fig. 1, where LE represents the Leading Edge, and TE represents the Trailing Edge), and by doing so, low energy consumption and high efficiency can be achieved simultaneously.22Their studies23showed that the CFJ technique is able to achieve great lift enhancement,drag reduction,stall margin enlargement, as well as the moderate pitch down moment for both stationary and pitching airfoils. Most recently, Dano et al.24reported that the aerodynamic performance can be further increased by the CFJ wing using discrete jets instead of a single large open slot. According to their experimental and numerical research,a discrete CFJ with more discrete jets and smaller jet sizes is able to augment lift peak,stall angle, and drag reduction significantly when compared to the open slot CFJ airfoil for the same mass flow rate.24With the gained knowledge of the CFJ concept,Lefebvre and Zha25designed a 4-seat airplane equipped with a rotatable clean CFJ wing.The lift coefficient can reach to 3.9 for the sake of achieving short takeoff/landing capability.

Till now, the existing archived studies associated with CFJ wings are narrowed in its characteristics during level flight or its capability for delaying the flow separation at high incident angles. The only application of CFJ in low-speed takeoff and landing configuration is focused on the trailing edge control surfaces, mainly using a pivot wing to achieve higher angle of attack flight by Lefebvre and Zha.25Therefore, in our previous study,33a comprehensive numerical investigation on the combination of the ‘‘smart wing” concept and CFJ technique has been performed.The results demonstrated that,for the airfoil with simple high-lift devices, the aerodynamic lift generation and the efficiency (indicated by the equivalent lift-todrag ratio defined in Ref. 33) are significantly enhanced compared with clean CFJ airfoil, indicating the potential of this configuration in aerodynamic enhancement during low-speed takeoff and landing. Note that the previous research was mainly focused on two-dimensional airfoils, and when this configuration is extended to the three-dimensional CFJ wings,their three-dimensional effects and the resulting changes in the aerodynamic performance are worthy and necessary to be further discussed. Additionally, for the discrete slot CFJ wing, in view of previous researches24mainly based on quasi threedimensional wings, further insight into its effects on the finite span‘‘smart wing”is also one of the research highlights in the present study.

The present study is dedicated to exploring the effects of several crucial parameters,i.e.,angles of attack,jet momentum coefficients and swept angles on three-dimensional CFJ‘‘smart wings” with the drop nose and the morphing flap. Additionally, the aerodynamic characteristics of two CFJ configurations, i.e., open and discrete slot on CFJ wings are emphasized comprehensively. First, the configurations of the CFJ wings with open and discrete slots and the CFJ parameters are described. Then subsequently describes the numerical methodology employed in the present study along with the validation study. Finally, results and discussion are given, which is followed by the conclusions.

2. Models and CFJ parameters

2.1. CFJ wing configuration with simple high-lift devices

Two CFJ wing configurations, i.e., Open slot CFJ wing(OCFJ) and Discrete slot CFJ wing (DCFJ) will be examined and compared.The information of the two CFJ configurations is shown in Sections 2.1.1 and 2.1.2.

2.1.1. OCFJ wing

A CFJ airfoil with the profile of NASA SC(2)-0712 with simple high-lift devices has been designed, as shown in Fig. 2(a),

where SST is Suction Surface Translation,the bold purple line represents the takeoff and landing configuration with the droop nose and simple flap deflected both at 30°.The injection and suction slots of the CFJ system are located at the leading and trailing edges as rendered in blue and red.The OCFJ wing is obtained by directly stretching the airfoil in the out-plane direction, resulting in a continuous slot, as shown in Fig. 2(b). The aspect ratio of the CFJ wing is set to 10 to illustrate the three-dimensional flow effect. And in order to simplify the computational model, half span wing is applied, which indicates that the wing span is 5 m and the chord is 1 m.

2.1.2. DCFJ wing

The DCFJ wing is built by inserting several tabs in the continuous injection slot of OCFJ as shown in Fig.3.Therefore,with identical mass flow rate, the injection velocity can be controlled by varying the size of the tabs. Here, an Obstruction Factor (OF) is defined as the ratio of the blocked area to the continuous open slot area. According to Dano’s work,24the aerodynamic benefits are augmented when using smaller jet size and more discrete jets with higher injection speed.To narrow the test matrix,74 discrete injection slots(width is 50 mm,i.e.,5%c)are used,resulting in OF=0.75 as shown in Fig.3.

2.2. OCFJ and DCFJ parameters

Section 2.2 is dedicated to introducing several crucial parameters with respect to the aerodynamics of OCFJ and DCFJ wings.

2.2.1. Jet momentum coefficient

The jet momentum coefficient for open slot CFJ wing Cμis defined based on the momentum passing through the injection slot to quantify the jet intensity, which is formulated as.

where ˙mjand Vjare the injection mass flow rate and velocity magnitude,respectively;ρ∞and V∞are the density and velocity of freestream respectively; Srefis the reference area. For DCFJ wings, the decreased jet exit area will result in an increase in the jet momentum coefficient due to the increased jet exit velocity even at a given mass flow rate.For comparison purposes and considering the feasibility of the engineering implementation, the total mass flow rate at the injection slot is kept the same as the OCFJ wings. And in order to make a distinguishment,the jet momentum coefficient for DCFJ wings is written as C′μ.

2.2.2. Power coefficient

The power consumption P required by the compressor in the wing can be determined by the mass flow rate ˙mjand the total pressure ratio of the compressor, Γ = Ptj/Pts(Ptjand Ptsare the total pressure in the injection and suction cavities), which is expressed as

where cpis the constant pressure specific heat;Ttsis the total temperature in the suction cavity; γ is the air specific heat ratio,γ = 1.4; η is the co-flow jet pumping system efficiency, η is set to 100%,which assumes no loss in the pumping system.Here,a non-dimensional parameter denoted as power coefficient, Pc, is used to describe the power consumption,which can be written as

2.2.3. Effective lift and drag coefficients

CFJ technique will produce reaction forces on the wing via a pumping system,which is difficult to calculate in the numerical simulation.As stated by Zha et al.23the reaction forces can be obtained by the momentum and pressure at the injection and suction slots using control volume analysis. They also derived the mathematical formulations to estimate the effective lift and drag in consideration of reaction forces for a single-element CFJ airfoil.Note that for using high-lift devices on CFJ wings,some adjustments have been applied accordingly as

where FxCFJand FyCFJare reaction forces produced by the CFJ in the directions of drag and lift,N;MCFJis pitch moment produced by the CFJ,N·m;the subscripts j and s stand for the injection and suction respectively; pjand psare static pressure in the injection and suction cavities;S is the area,m2;θjand θsare the angles between the injection and suction slot’s surface and a line normal to the airfoil chord;β1and β2are the deflection angle of the droop nose and the simple flap,respectively;α is the angle of attack;L is the length of level arm.As seen,the newly defined Eq. (4) is exactly identical to those defined by Zha et al.23if the deflection angles β1and β2are equal to 0.

The effective drag,lift and pitching moment coefficients can be then expressed as

where Rx′,Ry′and M′are the surface integrals of pressure and shear stress in the drag, lift and nose-up pitching directions.

2.2.4. Equivalent aerodynamic efficiency

The aerodynamic efficiency of the wing is conventionally evaluated by the lift-to-drag ratio.However,it may fail to describe the efficiency of CFJ wings since using CFJ technique could produce thrust rather than drag if applying large jet momentum. CFJ technique consumes extra energy where the power consumption has to be considered to get the equivalent aerodynamic efficiency. The expression of the equivalent aerodynamic efficiency for CFJ wings is formulated as

2.2.5. Components of drag coefficient for CFJ wing

In view of the reaction forces produced by the CFJ technique as mentioned in Section 2.2.3,the total drag coefficient can be divided into

where CD_CFJis drag caused by the CFJ reaction force;CD_iis induced drag; CD_pis pressure drag; CD_vis friction drag due to the viscosity.

2.2.6. Oswald efficiency factor

The Oswald efficiency factor is a correction indicator which represents induced drag effect for 3D wing platform deviated from an elliptic platform. The induced drag coefficient of the CFJ wing can be expressed as

2.2.7. Drag reduction efficiency

In order to characterize even more the performance enhancement of the DCFJ compared with the OCFJ, the drag reduction efficiency parameter ζ is defined as

3. Numerical methodology

3.1. Numerical method

Computations are carried out using an in-house-developed CFD solver,34which solves the 3D compressible Reynolds-Averaged Navier-Stokes (RANS) equations coupled with two-equation k-ω shear stress transport turbulence model by a cell-centered finite volume method on hybrid unstructured meshes. A second-order upwind scheme for the inviscid flux and a central difference scheme for the viscous flux are employed to discretize the governing equations,and the gradients are reconstructed by the least square method. The solution is advanced temporally by the implicit lower-upper symmetric Gauss-Seidel scheme.

3.2. Mesh system and boundary conditions

The mesh system and boundary conditions are plotted in Fig. 4. The computational domain is set to 30 × 10 × 10c,where c is wing chord length, m, and which is filled by hybrid grids in view of its computational efficiency and robust convergence ability.The near-boundary region of the wing is meshed and refined by body-fitted prismatic layers ensuring y+＜1.Additionally, the meshes in the injection and suction cavities

where the flow is complex are also refined to clearly capture the detailed flow topology. The resulting total cell size of the OCFJ and DCFJ wings are around 10 million and 57 million,respectively.

To consider the low-speed takeoff and landing, the incoming freestream velocity is set to 40 m/s resulting in a chord-based Reynolds number at 2.7 × 106. Since the CFJ is a zero-net-mass-flux flow control technique as aforementioned in Section 1, the mass flow rate of the injection slot is set exactly identical to the mass flow withdrawn by the suction slot by adjusting the mass flow rate to a specific Cμwithin a±0.2% disparity.

3.3. Verification and validations

Grid convergence study of the CFJ wing simulation is first conducted followed by two validation cases to examine the computational accuracy of the developed numerical solver,including the Adaptive Flow Control Vehicle Integrated Technologies(ADVINT)scaled AFC model35and the NACA 6415 airfoil with CFJ system archived by Lefebvre et al.26

3.3.1. Verification: Grid convergence study of CFJ wing

To assess the effects of the spatial discretization,a mesh refinement study has been conducted on the tested OCFJ wing with three different resolution meshes as shown in Fig. 5, namely,coarse, medium and fine, with grid cells of 6.04, 10.92 and 15.23 million respectively. Fig. 6 shows the resulted aerodynamic force coefficients, i.e., CLand CD, against N-2/3(N is number of grid cells).The linear variation in lift and drag with N-2/3indicates that the results computed by the current methodology vary monotonically with grid refinement and asymptotic grid convergence is achieved. For trade-off between the accuracy and computational expense,the medium mesh is selected throughout the entire study.

3.3.2. Validation Case 1: ADVINT AFC airfoil

The wind tunnel experiment of ADVINT 5%-scale airfoil is conducted as the first validation case due to its adequate archived experimental data.35The experimental wing lengths at 14 inch (1 inch=2.54 cm) with a tangential blowing slot(width is 0.02 inch) located on the trailing edge flap at 64%c. The computational mesh is shown in Fig. 7 with a total quadrilateral cell size around 0.1 million, where the boundary layer is refined with y+= 1. The freestream velocity is set at 20 m/s in the wind tunnel test,resulting in a chord-based Reynolds number at 5.0×105,and the angle of attack is 11°.Two different Cμ,i.e.,2.40×10-2and 9.61×10-2,are selected.The comparison of chordwise pressure distribution is plotted in Fig. 835and a good agreement between the present computational results and experimental data is revealed.

3.3.3. Validation Case 2: NACA 6415 CFJ airfoil Another code-to-code validation has been carried out to further examine the accuracy of the CFD solver for simulating CFJ applications. The archived data was computed by Flow-Acoustic-Structure Interaction Package (FASIP) CFD code26on a NACA6451 with CFJ system as shown in Fig. 926The injection and suction slot heights are 0.65% c and 1.30% c,which are exactly identical with their setup. Additionally, the angle of attack varies from 0° to 25° with an increment of 5°.Comparison of computed lift and drag between the present developed CFD solver and the data from Lefebvre et al.26is shown in Fig.10.It can be seen that the present solver slightly overestimates the lift and underestimates the drag. However,the largest disparity for both lift and drag is below 8% which can be evidenced as a good agreement.

4. Results and discussion

The present study is dedicated to exploring the threedimensional effects of the CFJ wing with simple high-lift device during low-speed takeoff and landing. Therefore, the content of the results illustration is logically twofold:to examine the effects of pivotal parameters such as angle of attack,jet momentum intensity and swept angle of OCFJ and to compare the aerodynamic performance between OCFJ and DCFJ configurations. To clearly show the aerodynamic benefit from CFJ technique, a finite straight clean wing denoted as the‘baseline’ is also simulated.

4.1. Effects of angle of attack

Fig. 11 plots the aerodynamic characteristics comparison between baseline and OCFJ wings by varying Angle of Attack (AOA), where z/b is the spanwise location of the section. The principle of CFJ is to increase the circulation by means of blowing at the leading edge and suction near the trailing edge, and therefore the accelerated flow on upper wing surface allows a mixture between the jet and main flow to energize the boundary layer. Clearly, the lift is augmented significantly when applying CFJ technique to clean wing and the stall margin is also extended from 10° to 16°. The delayed stall can also be evidenced by the pressure distribution in Fig. 11(f) where a noticeable suction peak is revealed at the aft part of the wing to alleviate the flow separation. In Fig. 11(b), the drag of OCFJ is slightly smaller than the baseline due to the supersuction effect at the leading edge which reduces the pressure drag for small angle of attack, i.e.,AOA = 2°. However, the situation is alternated for large angle of attack that the CFJ increases the drag production.It is easy to imagine that the low-pressure region on the upper surface caused by the injection augments the lift and meanwhile the horizontal component contributes to the drag.Moreover, the contribution in drag increases as the angle of attack increases. In addition, implementing CFJ on aircraft also influences the moment as shown in Fig. 11(c) where a nose-down moment is revealed and decreases with the increase of the incident angle which will in return degrades the stability for high-AOA flight.

For a given Cμ, the power consumption for CFJ wing monotonically decreases before stall occurs at AOA = 16°as denoted in Fig. 11(d). Looking back into Eq. (2), we can see that with the same momentum intensity, the only variable that influences the power consumption is the total pressure ratio between the injection and suction cavities, i.e., Γ = Ptj/Pts.With the increased angle of attack,the low-pressure region around the leading edge keeps decreasing due to the accelerating flow, which allows the injection to be easier, that is,requires less power. However, the low pressure cannot stay when stall happens,which requires more power from the compression system as denoted in Fig.11(d).It is good to find out from Fig. 11(e) that although the overall equivalent aerodynamic efficiency (L/D)cof the OCFJ wing keeps decreasing,but it is still significantly larger than the baseline case, particularly at small angles of attack.

Fig.12 depicts the pressure contours of the baseline and the OCFJ wing along with streamlines rendered by the vorticity magnitude when AOA = 10°. The zoom-in cross-section slice behind the wing tip, which is colored by the pressure coefficient, denotes the strength and size of the tip vortex. Obviously, OCFJ is able to significantly enhance the tip vortex,which has a negative effect on the CFJ controlled flow due to its generated spanwise flow on the suction side.On the other hand,the enhanced tip vortex also plays a positive role in alleviating the flow separation in the CFJ wing case due to the downwash effect.As seen from streamlines at the leading edge,the stagnation point moves backward significantly in the OCFJ wing case, increasing the suction peak and negative pressure area on the suction side. Thus, the mechanism by which CFJ alleviates the flow separation on the flap entirely is the energization of the boundary layer on the flap coupled with downwash effect caused by the enhanced tip vortex.This also explains the great increase in stall margin and lift coefficient as shown in Fig. 11.

4.2. Effects of jet momentum coefficient

The second pivotal parameter of the OCFJ wing is the jet momentum coefficient, denoted by Cμin Eq. (1). Fig. 13 presents the aerodynamic performance for varying jet momentum coefficients when AOA = 10°. In general, the increase of Cμdecreases the drag coefficient greatly while achieving a significant increment in CL. For the sake of evaluating the effect of OCFJ on the drag reduction,the variation of drag components with Cμis plotted in Fig.13(c).It is apparent that the negative drag(or thrust)caused by the reaction jet forces plays a major role in drag reduction. Besides, the decreased pressure drag caused by the CFJ supersuction effect also makes a great contribution.Increasing the lift coefficient is the main approach to improve the Short Take-Off and Landing (STOL) performance.The OCFJ control wing with Cμ=0.35 achieves a significant increment of about 125%. This indicates the great reduction of takeoff and landing field length. Meanwhile, the general aerodynamic efficiency (lift-to-drag ratio L/D) is increased to 19 as shown in Fig.13(e),more than twice higher than that of the baseline. However, in Fig. 13(f), the overall equivalent aerodynamic efficiency, (L/D)c, is decreased due to the more rapid increase of the power coefficient. In other words,the increased lift and reduced drag require more energy.

Fig. 14 depicts the Oswald efficiency factor versus Cμ.Although the OCFJ wing has higher induced drag than the baseline due to the higher lift(as seen in Fig.13(c)),the Oswald efficiency factor of the OCFJ wings is much higher. Note that when Cμis in the range of 0.02 to 0.25, the Oswald efficiency factor is actually greater than 1 for the OCFJ wings,indicating that the Oswald efficiency factor of an OCFJ wing would be greater than that of an elliptic platform. The reason for the high Oswald efficiency factor is that the lift enhancement with the effect of exponential square term outperforms the increase of the induced drag coefficient as indicated by Eq. (9). This result means that the OCFJ wing is penalized less than the baseline wing by the drag due to lift.

The flow structures for Cμ= 0.02, 0.05, 0.15 are shown in Fig. 15. It can be clearly found that the increase of Cμsignificantly augments the suction peak of pressure coefficient Cpat the leading edge, which indicates that the more airflow can be speeded up when passing through the LE, thus energizing the boundary layer. Therefore, coupled with the downwash effect generated by the enhanced tip vortex, the flow separation is diminished effectively.This is also the reason for the significant excitation in lift generation as evidenced in Fig. 13(a). In view of the fact that for the critical jet momentum intensity of Cμ=0.05,herein,the separation on the flap is just completely eliminated (Fig. 15(b)). Further increasing Cμis expected to converge to a certain lift augmentation, which can be seen from the asymptotic lift curve in Fig.13(a).Meanwhile,a local minimum for drag coefficient is formed here (Fig. 13(b)),which also leads to the maximum equivalent aerodynamic efficiency. As a result, in engineering applications, there must exists an optimized jet momentum intensity that balances the lift augmentation and power consumption by the jet mechanism which requires a trade-off study.

4.3. Effects of swept angle

The swept OCFJ wing performance with varying swept angles Λ is explored.The jet momentum coefficient is fixed to the critical value,i.e.,Cμ=0.05,and the angle of attack is still set as 10°.As seen in Fig.16,the increased swept angle decreases not only the lift coefficient, but also the drag coefficient. On the other hand, applying CFJ technique can make the aerodynamic forces less sensitive to the swept angle, and the phenomenon is better observed for small swept angle region,only about 0.2% reduction in CLat Λ = 15° as shown in Fig.16(a).In Fig.16(b)and(c),when increasing to more than 15°, the swept angle effectively reduces the pressure drag and the induced drag due to the decrease in the lift, which leads to a reduction in drag by about 10% at Λ = 30°, while it has slight effect on the negative drag caused by CFJ reaction forces and the friction drag.Compared with the straight OCFJ wing, the overall aerodynamic efficiency (L/D) is slightly reduced as shown in Fig. 16(e). These trends indicate that the wing-tip vortex is enhanced with the increase of swept angles, and thus it is easy to imagine that the suction peak at the leading edge is reduced due to the stronger spanwise flow.As expected, the total pressure loss is increased, causing the rapid increased power consumption as plotted in Fig. 16(d).Thus,the equivalent aerodynamic efficiency is on a downward trend.

Fig.17 presents the static pressure contours of the wing surface along with streamlines for three swept angles of 5°, 15°and 25°. As seen, a slight flow separation is detected at the trailing edge of the inner wing, indicating the increased drag coefficient at small swept angles as shown in Fig. 16(b). And then due to the enhanced downwash effect, the separation is gradually eliminated. However, on the other hand, the enhanced wing-tip vortex leads to a stronger spanwise flow at the flap,and thus the streamlines are no longer well aligned with the freestream direction. It also causes a decrease in the effective local incident angle and freestream velocity. As a result, the suction peak of Cpat the leading edge is reduced,as well as the low-pressure region. This tendency is also observed in Fig. 18 which shows the Cpdistribution at three span locations for various swept angles. With the enhanced wing-tip vortex, the suction peak of Cpdecreases significantly not only at the leading edge,but also at the trailing edge,especially for the outer wing (Fig. 18(b) and (c)). In view of the nearly coincident pressure distribution in Fig. 18(a), it can be suggested that the swept angle almost has no influence on the midspan of the OCFJ wing. Clearly, the higher the swept angle, the smaller the area enclosed by the Cpline. It is therefore the lift coefficient that decreases monotonically as plotted in Fig. 16(a).

4.4. OCFJ versus DCFJ

Table 1 Operating conditions for OCFJ and DCFJ wings.

Compared to OCFJ configuration, i.e., the CFJ slot is performed on the entire wing span, DCFJ is easier from the view of fabrication and flexible to control the flow on the wing surface.For industry applications,it is reasonable to compare the two configurations with identical mass flow rate rather than fixing the momentum jet.The testing matrix of the comparison listed in Table 1 informs the mass flow rate and the derived momentum coefficient as well as the corresponding injection speed,where Vinjis the velocity magnitude at the injection cavity.Note that the angle of attack is also set to 10°which is not changed.

4.4.1. Effects of mass flow rate

Fig.19 illustrates the aerodynamic performance comparison of the OCFJ and DCFJ straight wings along with the baseline case for varying mass flow rates. As seen in Fig. 19(a), the DCFJ wing generates more lift than both the OCFJ (saying increment about 27%) and baseline wings. This indicates that the speedup injection flow due to the blockage can produce a higher bounded circulation. Moving to the drag coefficients in Fig. 19(b), a remarkable low drag production by using DCFJ configuration is revealed. In order to make a thorough inquiry,drag components for both OCFJ and DCFJ wings are shown in Fig. 19(c). Clearly, the pressure drag, induced drag and friction drag are similar in both configurations. The only notable difference is the negative drag due to the reaction jet force, where the contribution of the drag reduction of DCFJ wing is also beneficial from the higher jet speed. With assistance of the augmented injection speed, the increase in lift and the decrease in drag result in a significant drag reduction efficiency of the DCFJ wing as expected,which is nearly twice that for the OCFJ wing as evidenced in Fig.19(d).This observation means that the energy cost to generate injection jet momentum not only benefits the system with a significant lift gain, but also transfers more than 60% of jet momentum to drag reduction. Hence the overall energy expenditure is small compared to the efficiency gain measured as the ratio of lift to drag (L/D). However, for a DCFJ system, the blockage of the injection slot narrows the exit area of the pumping system which requires a higher pressure ratio from the compressor system to guarantee an identical mass flow rate with respect to the OCFJ wing. This is a potential drawback of the DCFJ that the total pressure ratio (i.e., item Γ in Eq. (2)) augmentation sacrifices the power coefficient as evidenced in Fig. 19(e).In Fig. 19(f), the larger power requirement of DCFJ also causes a poor equivalent lift to drag performance. However,the lift production is more promising than the efficiency for low-speed takeoff and landing phase which is the initial goal of prssent study.

The flow topology of the DCFJ wing is plotted in Fig. 20 for the sake of obtaining a better understanding of the aerodynamic performance.As seen,a series of contra-rotating vortex pairs are developed on the airfoil surface and further break down downstream when approaching the trailing edge and the wing tip due to the interference of the tip vortex.These vortex pairs promote the injection jet to expand in the spanwise direction. As a result, the main flow near the leading edge will be induced by the highspeed jet,which in practice creates a better turbulent mixture of the boundary layer.For the flow over the tab,the air is also entrained over the leading edge.Velocity decreases slightly past the tab, but increases once again in the tab flow plane as the jet spreads along the spanwise direction due to the entrainment effect. This observation indicates almost no disparity in velocity magnitude in the LE area,and thus the flow over the entire leading edge can be uniformly accelerated by the adjacent jets. Therefore, the larger lowpressure region and the smaller negative pressure value on the suction side are observed in Fig. 20(a). Compared with the OCFJ wing,DCFJ allows more jet energy transferring into the mainstream and boundary layer,resulting in significant lift enhancement and drag reduction as plotted in Fig. 19.

4.4.2. Effects of swept angle Fig. 21 plots the aerodynamic performance comparison between DCFJ and OCFJ wings when ˙m = 3.04 kg/s and AOA = 10°. As expected, the aerodynamic performance of DCFJ configuration is all the way better than the OCFJ wing.For the tested small swept angles, there is little change in lift coefficient, while a significant increase in drag is observed,especially for the DCFJ wing as shown in Fig. 21(b). For a thorough investigation on this observation, the drag components for both OCFJ and DCFJ wings are plotted in Fig. 21(c). It is apparent that the swept angle has little effect on the friction drag and the negative drag caused by reaction jet forces in both cases. The only significant influence is the increased pressure drag, and that of the DCFJ wing is more sensitive to the increased swept angle.In Fig.21(d),the overall drag reduction efficiency is still more than 40%, which is significantly higher than that of the OCFJ wing. As expected, a poorer equivalent aerodynamic efficiency in the DCFJ case is observed,and becomes worse with the increase of swept angle.

Fig.22 presents the flow structure of the DCFJ swept wing at Λ = 5° and ˙m = 3.04 kg/s. Compared to the straight wing in Fig.20,the leading-edge stagnation point on the swept wing moves backward, further accelerating the flow through the leading edge. Therefore, the suction peak on the leading edge of the swept wing is enhanced. As a result, the flow remains fully attached on the entire DCFJ wing without separation.Besides, the streamlines in the DCFJ swept wing case are very well aligned with the freestream direction with slight deflection toward the tip. When compared with the DCFJ straight wing in Fig.20,the enhanced wing-tip vortex leads to the premature break-down of the contra-rotating vortex pairs, which weakens the mixture of mainstream, high-speed jet and boundary layer, resulting in the performance degradation.

5. Conclusions

The aerodynamic characteristics of three-dimensional CFJ wings with simple high-lift device were studied with the goal to examine the effects of angle of attack, swept angle and jet momentum in the scenario of low-speed takeoff and landing.Additionally, two CFJ configurations, i.e., OCFJ and DCFJ wings, were compared and their aerodynamic gain was revealed. The conclusions are drawn as follows:

(1) Applying CFJ technique to a wing with simple high-lift devices is able to generate more lift and enlarge stall margin,and at the same time has a lower energy expenditure due to the supercirculation effect. The wing-tip vortex is enhanced by the CFJ, which has a negative effect in lift generation;however,the induced downwash can alleviate flow separation on the wing surface.

(2) For both OCFJ and DCFJ cases, increasing the jet intensity can augment the lift production and also contribute to the drag reduction significantly. Moreover,the Oswald efficiency factor is, in some circumstances,larger than the one for CFJ wing which evidences the capability of CFJ technique in alleviating the induced drag.

(3) By applying CFJ technique, sweeping the wing backward less than 15° does not change the aerodynamic forces to a great extent, only about 0.2% for lift coefficient. Additionally, swept angle has slight effect on the negative drag caused by the CFJ reaction forces and the friction drag,while it effectively reduces the pressure drag and the induced drag due to the decrease in the lift,and the phenomenon is better observed for large swept angle region.

(4) A very promising enhancement in aerodynamic performance in terms of high lift, low drag and efficiency is demonstrated by using DCFJ configuration. The vortex pairs generated by the discrete slots affect the flow field on the wing upper surface in both streamwise and spanwise vortex structures, allowing a comprehensive mixture with the mainstream and boundary layer.However, the tip vortex will lead to the premature break-down of the vortex pairs,which weakens the mixture and the DCFJ performance. Thus, for higher efficiency, it is suggested not to arrange the injection jet slots in the vicinity of the wing tip.

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

This study was supported by the National Natural Science Foundation of China (No. 11672133) and the Fundamental Research Funds for the Central Universities, China (No.kfjj20180104). The support from Rotor Aerodynamics Key Laboratory, China (No. RAL20190202-2/RAL20190101-1) is acknowledged as well.