Parametric analyses on dynamic stall control of rotor airfoil via synthetic jet

Qijun ZHAO,Yiyang MA,Guoqing ZHAO

National Key Laboratory of Science and Technology on Rotorcraft Aeromechanics,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China

Parametric analyses on dynamic stall control of rotor airfoil via synthetic jet

Qijun ZHAO*,Yiyang MA,Guoqing ZHAO

National Key Laboratory of Science and Technology on Rotorcraft Aeromechanics,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China

Airfoil; Dynamic stall characteristics; Flow control; Moving-embedded grid methodology; Navier-Stokes equations; Parametric analyses; Rotor; Synthetic jet

The effects of synthetic jet control on unsteady dynamic stall over rotor airfoil are investigated numerically.A moving-embedded grid method and an Unsteady Reynolds Averaged Navier-Stokes(URANS)solver coupled with k-ω Shear Stress Transport(SST)turbulence model are established for predicting the complex flow fields of oscillatory airfoil under jet control.Additionally,a velocity boundary condition modeled by sinusoidal function has been developed to fulfill the perturbation effect of periodic jet.The validity of present CFD method is evaluated by comparisons of the calculated results of baseline dynamic stall case for rotor airfoil and jet control case for VR-7B airfoil with experimental data.Then,parametric analyses are conducted emphatically for an OA212 rotor airfoil to investigate the effects of jet control parameters(jet location,dimensionless frequency,momentum coefficient,jet angle,jet type and dual-jet)on dynamic stall characteristics of rotor airfoil.It is demonstrated by the calculated results that efficiency of jet control could be improved with specific momentum coefficient and jet angle when the jet is located near separation point of rotor airfoil.Furthermore,the dual-jet could improve control efficiency more obviously on dynamic stall of rotor airfoil with respect to the unique jet,and the influence laws of dual-jet’s angles and momentum coefficients on control effects are similar to those of the unique jet.Finally,unsteady aerodynamic characteristics of rotor via synthetic jet which is located on the upper surface of rotor blade in forward flight are calculated,and as a result,the aerodynamic characteristics of rotor are improved compared with the baseline.The results indicate that synthetic jet has the capability in improving aerodynamic characteristics of rotor.

1.Introduction

Due to combination of freestream velocity and rotation velocity of rotor in forward flight,helicopter rotor encounters different flow conditions.The periodic variations of Angle of Attack(AoA)make rotor undergo unsteady dynamic stall on retreating blade,and it induces the loss of lift,and increase of drag and pitching moment of rotor,which significantly impact the stability of rotor and aerodynamic performance of helicopter,resulting in restriction of the speed envelope of helicopter.1,2

In recent years,the rotor technology has tended toward methods of enhancing aerodynamic performance over a wide range of operating conditions.Passive designs involving blade geometry are limited by the conflicting requirements created by advancing blade compressibility and retreating blade stall;hence concepts such as variable droop leading edge airfoils,3trailing edge flaps4and synthetic jet controls5,6have been considered for active flow control.Of these,a novel control strategy by using synthetic jet actuators appears attractive since the synthetic jet is easy to design and implement.Smith and Glezer7investigated the synthetic jet actuator in 1994,and the results showed that the novel control strategy with synthetic jets held wide application prospects.8

Seifert and Park carried out the experiments of flow control on a NACA0015 airfoil with synthetic jet,9and the results showed that jet could control flow separation of airfoil effectively to alter the aerodynamic characteristics with suitably applied jet angles and locations.Kral et al.10investigated numerically the control effects of synthetic jet just according to the experiments of Seifert,and Rehman and Kontis investigated the control effectiveness of the synthetic control with k-ω Shear Stress Transport(SST)turbulent model and predicted the flow events of a stationary and a pitching NACA0015 airfoil successfully.11The results gave us the confidence that the Reynolds Averaged Navier-Stokes(RANS)method with k-ω SST turbulent model could be used to simulate the synthetic jet control.Kim et al.investigated the improvements on performance of tiltrotor airfoils by synthetic jet control12and the results showed that this control method could reduce the download efficiently.Zhao et al.conducted parametric analyses emphatically for an OA213 airfoil to investigate the control effects of jet on the dynamic stall characteristics of airfoil under a developed velocity boundary condition,13and the results indicated that control efficiency could be improved with specific frequencies and jet angles when the jet is located near separation point of rotor airfoil.Regrettably,the airfoil is stationary,which means that the dynamic stall characteristics are not taken into account.Zhao et al.measured the flow field and aerodynamic force of airfoil to investigate the control effects of synthetic jet arrays on dynamic stall.14The results showed that synthetic jet applied on airfoil has the capability in improving the dynamic stall characteristics of airfoil.Lee et al.experimentally investigated the separation control by jet arrays for an inclined flat plate.15However,the dual-jet control effects on dynamic stall of airfoil have not been studied,and in order to understand the control mechanism,Lee also pointed out that the dual-jet should be further investigated.Amitay et al.conducted the experimental investigations on control of flow separation using jet actuators on an unconventional symmetric airfoil.16The results indicated that control effectiveness was distinctly different for low and high actuation frequencies.Alimohammadi et al.investigated the interaction of a pair of synthetic jets by using CFD method and Particle Image Velocimetry(PIV)technology.These investigations led to better physical understanding of the control mechanics of adjacent synthetic jets,and would establish the theoretical basis needed to promote their practical applications.17

Though synthetic jet holds wide application prospects,some problems still need to be solved in the applications of synthetic jets.18For example,numerous controlling parameters make the applications of synthetic jet still theoretic,19such as location,dimensionless frequency,momentum coefficient and jet angle.Also,the separation control mechanisms of dual-jet on airfoil are not very clear yet,and few works have been conducted for parametric analyses of dual-jet now.Furthermore,the parametric analyses of dual-jet control effect on dynamic stall of 2D airfoil and 3D rotor have not been carried out.

In this paper,the control effects of several parameters about Synthetic Jet(SJ)on dynamic stall characteristics over airfoils are investigated numerically.First,solution of the flow field of rotor airfoil is obtained by solving the preconditioned RANS equations with k-ω SST turbulence model,and moving-embedded grid method is employed.Additionally,a dimensionless velocity boundary condition is established to simulate the synthetic jet control effects.As validations,the dynamic stall control case of VR-7B by employing synthetic jet is calculated and compared to the test data.Furthermore,control effects on dynamic stall of OA212 airfoil and rotor in forward flight are parametrically investigated,and a number of valuable conclusions are achieved.

2.Numerical methods

2.1.Governing equations

In order to overcome the stiffness of the solution system when the local Mach number is low,the CFD methods based on unsteady preconditioned Navier-Stokes equations are employed20and used to simulate the unsteady flow field characteristics around an oscillatory airfoil with synthetic jet control.The preconditioned Navier-Stokes equations in a control volume Ω in integral form by using absolute physical quantities as parameters W=[p,u,v,T]T,can be written as

where Fvare the viscous fluxes,F are the convective fluxes including the motion of the dynamic grid system,n is the unit vector normal to the surface element dS,Ω is the volume of grid cell,S is the boundary of grid cell,and Γ is the preconditioning matrix.21

where H is total enthalpy per unit mass,ρTis the derivative of density with respect to temperature at constant pressure.

The parameter Θ is given by

where V is the local velocity,V∞is the velocity of free stream,and a is the speed of sound.The reference velocity,Ur,acts as a cut-off velocity above which preconditioning method is turned off.

The dual time method is used to well simulate the unsteady flow field characteristics of rotor airfoil,and the sub-iteration is fulfilled by the implicit Lower-Upper Symmetric Gauss-Seidel(LU-SGS)method22which can be implemented easily on vector and parallel computers.To accurately predict the dynamic stall characteristics of airfoil with SJ,the third-order Roe scheme23together with Monotone Upwind-centered Scheme for Conservation Laws(MUSCL)approach24is employed for the discretization of convective fluxes.Aimed at well simulating flow separation over the surface of airfoil,the two-equation k-ω SST turbulence model25is employed to calculate turbulent viscosity.

2.2.Boundary conditions

The contribution of synthetic jet to the surrounded fluid is modeled by a suction/blowing type boundary condition.The perturbation of synthetic jet on the unsteady flow field is simulated by specifying the sinusoidal velocity over the orifice of jet actuator as

where ξ, η denote chord wise and normal directions of airfoil respectively,njetis determined by the angle of the jet with the surface,and k denotes the reduced frequency,c and Hjetstand for chord length and the width of the jet orifice respectively,as shown in Fig.1,θjetis jet angle,U is the velocity of the jet and V∞is the free stream velocity.

The spatial variation of the jet is specified by f(ξ)=1.Considering relationship between periodic jet and periodic motion of rotor airfoil,the non-dimensional frequency F+relates the frequency of the jet to the frequency of the oscillatory airfoil,so

where ωjetis the frequency of the jet,and ωairfoilis the frequency of the oscillatory airfoil.

The oscillation momentum coefficient〈Cμ〉determines the amplitude of the synthetic jet,and it is defined as

2.3.Moving-embedded grid method

The quality of grids around rotor airfoil directly influences the solution precision.A moving-embedded grid system is generated for numerical simulation of dynamic stall flow field of airfoil by using synthetic jet control.

Firstly,the orthogonal C-type grids around rotor airfoil are generated by solving Poisson equations

where γ1,γ2,γ3are the coordinate conversion parameters,and φ′,ψ′are the source term used to control the quality of grid.In order to get more details of synthetic jet,clustering grid is adopted near the jet orifice.C-type grids around NACA0012 are generated with a resolution of 356×70 in the chordwise and normal direction of the airfoil respectively.There are 120 and 158 points on the lower and upper surfaces of the airfoil respectively,39 points on each of the wake cuts and 11 points over the jet orifice.The y+at wall grid cell is about 4.The grids around airfoil are depicted in Fig.2.

Then,the moving-embedded grids compose airfoil grids and background grids are generated including two key points:(A)identification for boundary cell of hole;(B)search of donor elements.Based upon the regeneration of airfoil grids,the ‘Top-Map’method26is adopted to accomplish the procedure of embedded grids and the moving-embedded grids are depicted in Fig.3.

3.Validations

3.1.Dynamic stall of rotor airfoil

The effectiveness of the presented CFD method is verified by simulating the unsteady dynamic stall characteristics of airfoil,and OA212 and SC1095 airfoil are taken as numerical examples.The dynamic stall cases 37107 of SC1095 airfoil are numerically simulated.27Fig.4(a)shows the lift coefficient CLand moment coefficient Cmdistributions of the airfoil in one oscillatory period,and the comparisons are undertaken with the experimental data of Ref.27.The OA212 rotor airfoil is operated under a typical condition for retreating blade in forward flight with high speed as Ma∞=0.14 and Re=2.7×106.28Fig.4(b)shows comparisons of aerodynamic forces of SC1095 airfoil.As shown in the figures,the calculated results agree well with the experimental data,and are better than the calculated results in Ref.28(Fig.4(a)).The calculated results indicate that the numerical method can be used to simulate the dynamic stall characteristics of airfoil under dynamic stall and have laid a good foundation for deeply obtaining the effects of several parameters about the control efficiency of synthetic jet on dynamic stall characteristics of airfoil.

3.2.Dynamic stall control via SJ

To verify the efficiency of the synthetic jet applied on dynamic stall control,the VR-7B airfoil is employed for numerical simulations.29The synthetic jet actuator is placed at 50%c of the suction surface of airfoil with a 0.3%c width orifice.The momentum coefficient of the jet is about 〈Cμ〉=0.0004,the jet angle is θjet=25°,and the non-dimensional frequency de fined in this paper is about F+=40.The Mach number of the experimental state is Ma∞=0.1 and the oscillation of the airfoil is α =11°+5°sin(2×0.05×t).

Fig.5 shows lift coefficient of VR-7B airfoil with and without synthetic jet control.As can be seen from the figures,the variation trends of the numerical results correlate well with the experimental data,29and are better than the calculated results in Ref.29.Additionally,the lift coefficient of airfoil could be significantly improved under synthetic jet control,which indicates that synthetic jet could efficiently delay dynamic stall of rotor airfoil.

To further investigate the interactions between the periodic jet and dynamic stall vortex,comparisons of streamlines over airfoil at different AoAs are shown in Fig.6.As can be seen,the jet significantly suppresses the flow separation over the airfoil,resulting in the reduction of drag coefficient CDand moment coefficient Cm,as shown in Fig.7.

4.Parametric analyses

Based on the numerical results of synthetic jet control on airfoil,the synthetic jet control effects on dynamic stall characteristics over OA212 airfoil are analyzed parametrically.The control parameters include jet location,dimensionless frequency,momentum coefficient and angle,jet type and dual-jet.

The C-type grids around OA212 airfoil are generated with a resolution of 367×50,which are depicted in Fig.8.The background grids are Cartesian grids with a resolution of 279×259.The synthetic jet actuators are placed at 10%c and 60%c from the leading edge of airfoil respectively on the upper surface with the width of the jet orifice being 1.0%c.

To obtain the control effects of several parameters on deep dynamic stall characteristics of rotor airfoil,the motion of the airfoil is α =15°+10°sin(2×0.105× t).

4.1.Effects of jet location

The investigations of control effects according to different locations of jet actuators have been carried out with two jet actuators located at different chord wise positions and the dual-jet at the same time.Jet actuator1(A1)is placed at 10%c on the suction surface of airfoil while the other one(A2)is placed at 60%c on the upper surface,and they are under the same jet control condition(F+=30 and θjet=30°).By setting jet momentum coefficient 〈Cμ〉=0.04 and〈Cμ〉=0.09,the control effects of jet location on the dynamic stall characteristics of airfoil are investigated.

Fig.9 shows the comparisons of the lift,drag and moment coefficient of airfoil for the two jet actuators and the dual-jet under different in flow conditions with two momentum coefficients.When 〈Cμ〉=0.04,the control effects of A1 on dynamic stall of airfoil are better than those of A2.Compared with unique jet actuator,the dual-jet could lead to more significant improvements of dynamic stall control of airfoil.When〈Cμ〉=0.09,the gaps among the control effects due to different jet locations become narrow.

To further investigate the control effects between the periodic jet and dynamic stall vortex,comparisons of streamlines over airfoil at different angles of attack are shown in Fig.10.As can be seen in Fig.10,when flow separation occurs near the trailing edge of airfoil,the control effects of A2 on dynamic stall control of airfoil are better than those of A1 and the control effects of the dual-jet are more significant than those of the unique jet control.With the decrease of the angle of attack,the separation point moves towards the leading edge of the airfoil.

The control effects become more significant when the jet is located at 10%c from the leading edge of airfoil.The control effects take the second place when the jet is located at 60%c,while dual-jet can always suppress the flow separation over the airfoil efficiently in the dynamic stall state.

4.2.Effects of dimensionless frequency of jet

The control effects of dimensionless frequency on the dynamic stall characteristics of OA212 airfoil have been investigated under the same jet control condition (θjet=30°,〈Cμ〉=0.0007 and F+=20–50).Two jets,located at 10%c and 60%c respectively,are compared in terms of their effects on aerodynamic force coefficients of airfoil.

Fig.11 presents the comparisons of hysteresis loops of lift,drag and moment coefficient of OA212 airfoil with synthetic jet control at different chord wise positions.As it can be seen,with the increase of dimensionless frequency of the jet,the oscillations of aerodynamic forces of airfoil increase,especially when the synthetic jet is installed at 60%c from the leading edge of airfoil.Non-dimensional frequencies have little effects on the mean aerodynamic forces of airfoil,which are consistent with the conclusions in Ref.30.

4.3.Effects of momentum coefficient

To investigate the influences of momentum coefficient on dynamic stall control and flow separation,some different momentum coefficients are simulated to explore the effect mechanism of momentum coefficient of synthetic jet on improving the aerodynamic characteristics of a dynamic stalled airfoil.As a supplement,all jets are working under the same jet control condition(θjet=30°and F+=30).Fig.12 gives the influences of aerodynamic force coefficients of airfoil under synthetic jet control at two locations with a variety of momentum coefficients.

As can be seen from the Fig.12,with the increase of momentum coefficient,the area of hysteresis loop of aerodynamic forces of rotor airfoil reduces gradually when the jet is located at 10%c from the leading edge of airfoil.Meanwhile,the peak value of lift coefficient increases while the peak values of drag and moment decrease,which indicates that the control effects on airfoil stall are improved with the increase of momentum coefficient.The effects of momentum coefficient on dynamic stall control of airfoil when the jet is located at 60%c from the leading edge are similar to those when the jet actuator is installed at 10%c from the leading edge of airfoil.

It should be noted that when 〈Cμ〉=0.01,for the case of synthetic jet control at 10%c,the peak values of drag and moment of airfoil are increased slightly compared with those of the baseline,and for the case of synthetic jet control at 60%c,the peak values are significantly larger than those of the baseline.To obtain the influences of momentum coefficient on flow field of rotor airfoil in detail,the vorticity contours near airfoil at different AoAs with and without synthetic jet control at 10%c(〈Cμ〉=0.01 and 〈Cμ〉=0.09)are illustrated in Fig.13.As depicted in Fig.13,when 〈Cμ〉=0.01,synthetic jet control promotes the formation of dynamic stall vortex,and the magnitude of dynamic stall vortex is enlarged slightly,which leads to the increase of drag and moment coefficient.When 〈Cμ〉=0.09,formation and shedding of dynamic stall vortex are suppressed and delayed effectively,resulting in sig-nificant improvements of aerodynamic characteristics of airfoil as shown in Fig.12.

4.4.Effects of jet angle

The effects of jet angle on the control effects on dynamic stall and flow separation have been investigated by comparing the aerodynamic forces with different jet angles(5°,25°,45°and 65°)under the jet control condition(F+=30 and 〈Cμ〉=0.04).

Fig.14 shows the aerodynamic forces of controlled airfoils with different jet angles at two jet locations.As shown in the figures,at the jet angle of 25°,the jet control has better improvements in aerodynamic characteristics of OA212 airfoil when the jet is located at 10%c from the leading edge of airfoil,and the area of hysteresis loops is reduced.The peak value of lift coefficient is increased when the peak values of drag and moment are decreased at the same time.When θjet=5°and θjet=45°,the synthetic jet could improve the dynamic stall characteristics of airfoils effectively,but their control efficiencies are weaker than those of controlled case when θjet=25°,which indicates that jet with θjetbeing about 25°has the best control effects on dynamic stall characteristics of airfoil when the jet actuator is placed near the leading edge of airfoil.

When jet actuator locates at 60%c from the leading edge of airfoil,there are good control results at θjetof about 45°and 25°.The control efficiencies of the synthetic jet with θjetbeing about 5°and 65°are slightly inferior,which even aggravate the dynamic stall characteristics of airfoil.It also indicates that when jet is placed far away from the separation point,the medium jet angle could significantly improve the dynamic stall characteristics of airfoil,and the control efficiencies of synthetic jet with larger or smaller angle are weaker.

Table 1 Position of actuators on surface of blade.

4.5.Effects of jet type

Based on the investigations of dynamic stall control via synthetic jet on rotor airfoil,the differences among different types of jet in the dynamic stall control are analyzed.Five types of jet including oscillating blowing jet,oscillating suction jet and synthetic jet are investigated.The instantaneous velocities of these jet types can be expressed as

where Ujetis the velocity of the jet and Ujet，maxis the maximum value of the velocity of the jet,ω is the frequency of the jet.

Fig.15 gives the velocity pro files Ujet/Ujet,maxof different jet types.Fig.16 shows the comparisons of the variety of aerodynamic forces of controlled airfoil with different types of jet under the same jet control condition(〈Cμ〉=0.04，F+=30 and θjet=25°).As can be seen,Jet type 5 has the best control effects on dynamic stall characteristics,and Jet type 3 has secondary control effects only after Jet type 5,which indicates that oscillating suction jet has better control effects compared with oscillating blowing jet.The control effect of Jet type 4 is similar to synthetic jet,while Jet type 2 pulse blowing jet has the worst control effects on dynamic stall characteristics of airfoil.

4.6.Effects of dual-jet

The numerical results in Figs.9 and 10 indicate that the dualjet could lead to better improvements of dynamic stall control of airfoil compared to unique synthetic jet.According to the conclusions above,the control effects of dual-jet on dynamic stall control of OA212 airfoil have been investigated.The influences of dual-jet’s parameters on improvements of unsteady aerodynamic characteristics have been explored.

Firstly,influences of dual-jet momentum coefficient on control efficiency of airfoil under dynamic stall are investigated under the same jet control condition(F+=30 and θjet=20°).The momentum coefficients of jets which are installed at 10%c and 60%c respectively from the leading edge of airfoil are the same value.Fig.17 gives the influences on unsteady aerodynamic forces under dual-jet control with a variety of momentum coefficients.As can be seen from the figure,the control effects of dual-jet on airfoil dynamic stall have better improvements with the increase of momentum coefficient.These conclusions are consistent with those of unique synthetic jet control.

Secondly,the control effects of different combinations of jet angles on the dynamic stall characteristics of airfoil have been investigated under the control condition (F+=30 and〈Cμ〉=0.01).Fig.18 gives the influences on aerodynamic forces under dual-jet control with different combinations of jet angles.The numerical results indicate that a better improvement in the peak value of lift coefficient of OA212 airfoil has been achieved under the dual-jet control when the jet is located at 10%c with jet angle being 20°.Also,the control efficiencies of θjet=40°are better than those of θjet=60°for the jet installed at 60%c.When jet actuators locate at 60%c with jet angle being 20°,the jet near the leading edge of airfoil with small jet angle(40°)has better control effects.Overall,dual-jet has the best control effects when the jet angle is relatively small.

Finally,the influences on the control effects of dual-jet’s phase difference on the dynamic stall of airfoil have been investigated by comparing the aerodynamic forces under the jet control condition(θjet=20°,F+=30 and 〈Cμ〉=0.01).Fig.19 shows the comparisons of the aerodynamic coefficients of airfoil under dual-jet control with different phase differences Δψ.Obviously,the phase difference between dual-jet has a minor effect on dynamic stall control of airfoil.The reason may be the high dimensionless frequency of dual-jet,which makes the effects of phase difference on the interference small between dual-jet.

5.Aerodynamic characteristic of rotor in forward flight under synthetic jet control

There are three steps of grid generation technique for active flow control investigations on rotor.Firstly,the body- fitted and orthogonal C-type grids around rotor airfoils are generated by solving Poisson equations.In order to capture the flow characteristics of synthetic jet in detail,clustering grids over the orifice of jet actuator are generated.Secondly,the C-O type grids around rotor blade are generated automatically by using interpolating and folding of section grids.The ‘top-map’method and ‘PSSDE’method are adopted to accomplish the procedure of embedded grids.23Grids around rotor airfoil and blade with clustering are shown in Fig.20.

The contribution of synthetic jet to the surrounded fluid is modeled by a suction/blowing type boundary condition.Considering relationship between periodic jet and periodic motion of rotor airfoil,the non-dimensional frequency F+and momentum blowing coefficient 〈Cμ〉are defined,which are shown when the unsteady flow field is established by specifying the sinusoidal velocity over the orifice of jet actuator as

where V*is the RMS velocity of the period synthetic jet,h is the width of jet orifice in chord wise direction of airfoil,and ωrotoris the angular velocity of rotation.

The Caradonna-Tung model rotor has two rectangular blades with a conventional NACA0012 airfoil,and the aspect ratio is 7.There are four jet actuators at different chord wise and span wise positions on the surface of rotor blade.The actuators(A1,A3)are placed at 10%c on the suction surface of blade while the other ones(A2,A4)are placed at 50%c on the upper surface,and the width of jet orifices is 1%c,as indicated in Table 1,R is the length of blade.

The grid of blade has a resolution of 343×40×131,and there are 137 points on the lower surface and 137 points on the upper surface of the blade section,as shown in Fig.21,where there are 11 points over the jet orifice.In the calculation,the rotor was operated at different fixed collective pitches.

5.1.Effects of synthetic jet location

Firstly,the control effects of the synthetic jet on aerodynamic performance of rotor with different locations of the actuator are investigated(Matip=0.628 and μ=0.3),and the excitation frequency is F+=10.

The control effects of synthetic jet(the four actuators A1,A2,A3 and A4)on the normal force coefficients Cnof different blade sections are illustrated in Fig.22.The collective pitch is 8°,and the jet control condition of two actuators is the same:momentum coefficient is 〈Cμ〉=0.004,and jet angle is θjet=25°.As shown in the figures,the synthetic jet has significant effects on the sectional normal force coefficients of blades,and the synthetic jet induced by actuator A2(or A4)is more efficient in enhancing normal force coefficients than that by actuator A1(or A3).That is because the control effect of the actuator closer to the middle of chord is better when there is no flow separation on the blade surface(the collective pitch is 8°).At the same time,the relative velocity is smaller in the retreating blade,and the ratio of the jet velocity to the relative velocity is bigger than that in the advancing blade.So there is a better influence of synthetic jet on the normal force coefficients in the retreating blade,and it is useful to control dynamic stall of rotor.

5.2.Effect of momentum coefficient

The control effects of the synthetic jet on aerodynamic performance of blades due to the momentum coefficient of the actuators are investigated.Three typical momentum coefficients(〈Cμ〉=0.001,0.004 and 0.009)are adopted,and the jet angle is constantly equal to 25°.

Fig.23 shows the variation of the sectional normal force coefficient with varied jet momentum coefficient of actuator A1 at 8°collective pitch.As can be seen,the amplitude and average of sectional normal force both increase with the increase of momentum coefficient,and these are more obvious in the retreating blade.

The sectional normal force coefficients with different jet momentum coefficients of actuator A2 and A4 are given in Fig.24.With the increase of the momentum coefficient,the amplitude and average of sectional normal force significantly increase.However,there is still a little difference in the control effect between actuator A2 and A4.For actuator A4 which is much closer to blade tip,the sectional normal force amplitude decreases with the increase of the momentum coefficient.This is largely due to the significant effect on flow separation and the movement of span wise flow near the blade tip.

6.Conclusions

(1)The numerical methods,including the movingembedded grid methodology,the boundary condition of synthetic jet and the preconditioned Navier-Stokes equations,are effective on simulating the unsteady flow field of airfoil and rotor with synthetic jet control under dynamic stall.

(2)Synthetic jet could get the best control effects on dynamic stall when it is located near the flow separation point,and large momentum coefficient could lead to significant improvements of dynamic stall characteristics of rotor airfoil.

(3)To a certain extent,the control effects of adjusting jet angle on the dynamic stall characteristics are similar to those of adjusting momentum coefficients.When the jet actuator is installed near the flow separation point,the jet has the best control effects on aerodynamic forces of airfoil when the jet angle is small.On the other hand,synthetic jet with a medium jet angle is more effective when it locates in the separated flow region.

(4)The control effect of dimensionless frequency on dynamic stall characteristics of airfoil is not obvious.The oscillating suction jet has better control effects than synthetic jet does,while oscillating blowing jet has the worst control effects on unsteady aerodynamic characteristics of airfoils.

(5)Compared to unique jet actuator,the dual-jet could more obviously improve the jet control efficiency on dynamic stall characteristics over rotor airfoil than unique jet.The influence laws of dual-jet’s angles and momentum coefficients are similar to those of unique jet.Moreover,the phase difference between dual-jet has a minor effect on dynamic stall control of airfoil.

(6)Synthetic jet has the capability in improving aerodynamic characteristics of rotor.With the increase of momentum coefficient of the synthetic jet located in the middle of blade along span wise direction,both the oscillation amplitude and average of sectional normal force increase.In addition,the oscillation amplitude will decrease when the synthetic jet is near the blade tip.

This study was co-supported by the National Natural Science Foundation of China(Nos.11272150 and 11572156).

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30 November 2016;revised 13 January 2017;accepted 20 March 2017

Available online 9 September 2017

Ⓒ2017 Production and hosting by Elsevier Ltd.on behalf of Chinese Society of Aeronautics and Astronautics.This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

*Corresponding author.

E-mail address:zhaoqijun@nuaa.edu.cn(Q.ZHAO).

Peer review under responsibility of Editorial Committee of CJA.