Blowing momentum and duty cycle effect on aerodynamic performance of flap by pulsed blowing

Control surface, which is often located in the trailing edge of wings, is important in the attitude control of an aircraft. However, the efficiency of the control surface declines severely under the high deflect angle of the control surface because of the flow separation. To improve the efficiency of control surface, this study discusses a flow-control technique aimed at suppressing the flow separation by pulsed blowing at the leading edge of the control surface. Results indicated that flow separation over the control surface can be suppressed by pulsed blowing, and the maximum average lift coefficient of the control surface can be 95% times higher than that of without blowing when average blowing momentum coefficient is 0.03 relative to that of without blowing. Finally, this study shows that the average blowing momentum coefficient and non-dimensional frequency of pulsed blowing are two of the key parameters of the pulsed blowing control technique. Otherwise, duty cycle also has influence on the effect of pulsed blowing. Numerical simulation is used in this study.


Introduction
In modern aircraft designing, the attitude control of an aircraft is still relies on traditional control surface such as flap, which is often located in the trailing edge of wings. However, the efficiency of the control surface declines severely under the high deflect angle of the control surface because of the flow separation. This condition leads to the penalty of attitude control and limited aerodynamic performance of an aircraft. In order to improve the efficiency of flap, flow control is necessary. In the past decades, scientists have exerted considerable effort to develop flow control techniques. Moreover, various flow control techniques [1] has been used to suppress flow separation such as moving surface control technique [2][3][4] , plasma flow control technique [5][6][7][8] and co-flow jet control technique [9][10][11][12] . Although flow separation on the control surface can be suppressed substantially by these flow control technique, the application of these techniques in engineering are limited because of complicated devices or other reasons. Relatively, the flow control technique by blowing at the leading edge of flap catch people's eyes because of its simple device, rapidly remarkable lift increment and low gas consumption. In order to reduce the gas consumption further, pulsed blowing technique is taken into consideration. Study shows that lift coefficient of flap can be higher with pulsed blowing compared with that of continuous blowing.
This study introduces an flow control technique by pulsed blowing near the leading edge of the flap to suppress the flow separation over the flap that is located on the tailing edge of an airfoil. First, the effect of pulsed blowing on the aerodynamic performance of the flap is investigated thoroughly. Thereafter, the effect of cycle duty of pulsed blowing are discussed. All the results of this study is completed based on the following conditions: the angle of attack of the main wing is 0° and the deflect angle of the flap is 20°.

Numerical Model
The airfoil model used in the study is based on NACA0025 airfoil with a 0.6 m chord length. This model can be divided into two parts (see Figure 1): the main wing and a flap that is as long as 0.206m.

Data Process
Average blowing momentum coefficient is used to represent the gas consumption. The equation is as follows: where Cμ represent average blowing momentum coefficient, T is the cycle time, mj is the mass flow rate of the blowing jet, Vj is the jet velocity from the blowing slot, ∞ is the density of freestream, is the reference area of the flap, ∞ is the velocity of freestream and ∆ is the interval time of two adjacent time step.
The Strouhal number Str is the parameter that represents pulsed frequency. The equation of the Strouhal number is as follows: where Str is the Strouhal number. f is the pulsed frequency and c is the chord length of the flap. Duty cycle dr is defined as the proportion of blowing time in one single cycle time.

Validation of the Numerical Simulation Results
The validation experiment is conducted in the D-4 low-speed wind tunnel of Beihang University.

Effect of Pulsed Blowing on Aerodynamic Performance of Flap
Pulsed blowing at the leading edge of flap can cut the consumption of gas greatly while higher lift increment is get. Figure 7   Strouhal number. CL reaches the maximum value when Str=0.206. With the continuously increase of Str, CL decrease slightly. However, the lift coefficient of pulsed blowing is constantly higher than that of continuous blowing under the same Cμ. When Str=0.206, CL of pulsed blowing is 67% higher than that of continuous blowing under the same Cμ.

Effect of Duty Cycle on Average Lift Coefficient of the Flap
When Cμ keep constant, the duty cycle also has effect on CL. Figure 8 shows the CL changing with Str under different duty cycle and the following conditions: angle of attack α=0°, deflection angle of the flap δe=20°, V∞=20m/s, and Re=0.8×10 6   Based on the study before, the mechanism of improving the lift of the flap by pulsed blowing can be divided into two components. First, blowing jet can be treated as an injector. The flow upstream of the blowing slot is injected by the blowing jet and induces a suction peak, which is the same mechanism as continuous blowing. Second, the vortex generated by the switch of blowing and non-blowing over the blowing slot induces a suction peak. Lift increment is generated by these two components of suction peak. Both the inject effect and vortex need sufficient time to develop. When Str is low, the lift increment supplied by the inject effect can reach its maximum value and stability. The lift increment supplied by the vortex reaches the maximum value and decreases thereafter. A critical value of Str balances the both components of the lift increment and leads their sum into maximum value. When Str is higher than the critical value, the vortex generated by the switch from blowing and non-blowing cannot obtain sufficient time to develop, thereby leading to a lift increment penalty in the non-blowing period. By contrast, the blowing jet cannot induce a high speed-up in the upstream of blowing slot, thereby leading to a lift increment penalty in the blowing period. When Cμ keep instant, the higher the duty cycle is, the lower the blowing momentum coefficient in blowing-period is. Thereby, the lift increment generated by inject effect decreases with the increase of duty cycle. Meanwhile, the time of non-blowing period is decrease with the increase of duty cycle. This leads to a lower lift increment of vortex.

Conclusions
Based the above discussion, the following conclusions can be made: (1) Pulsed blowing can increase the lift coefficient of the flap evidently and improve the control efficiency of the flap.
(2) The lift coefficient of the flap increase with the increase of the Strouhal number rapidly and decrease slightly if Strouhal number continuously increase. When Strouhal number is high enough, the lift coefficient of the flap will keep instant.
(3) The maximum value of average lift coefficient of the flap and the critical Strouhal number increases with the increase of duty cycle when the average blowing momentum coefficient keeps constant.