Publication Date



Open access

Embargo Period


Degree Type


Degree Name

Master of Science (MS)


Mechanical Engineering (Engineering)

Date of Defense


First Committee Member

GeCheng Zha

Second Committee Member

HongTan Liu

Third Committee Member

Manuel Huerta


The objective of this thesis is to numerically study the power minimization for subsonic Co-Flow Jet (CFJ) active flow control airfoil using fixed geometry for the whole flight envelop. The focus is to answer how to minimize the CFJ power consumption and drag while maximizing the lift coefficient at different cruise Mach numbers and at low speed for takeoff/landing. It is important to maximize the cruise efficiency and the efficiency at takeoff/landing, which includes vertical takeoff/landing (VTOL) and Extremely Short Takeoff/landing (ESTOL). The simulations employ the intensively validated in house FASIP CFD code, which utilizes a 3D RANS solver with Spalart-Allmaras (S-A) turbulence model, 3rd order WENO scheme for the inviscid fluxes, and 2nd order central differencing for the viscous terms. To minimize the CFJ power consumption, the CFJ6421-SST150-SUC133-INJ065 airfoil previously designed by Lefebvre and Zha is redesigned by varying the size of the injection and suction slot. The optimized airfoil has the same suction surface translation (SST), but has an injection slot size of 1.17% of its chord length (C), enlarged by 80%, and a suction slot size of 2.47% C, enlarged by 85%. The optimized airfoil is named CFJ6421-SST150-INJ117-SUC247 to identify its geometry. The Mach number effect on cruise performance for the optimized 2D CFJ airfoil is studied at freestream Mach number of 0.15, 0.30, 0.46 and 0.5. The results show that the best CFJ airfoil corrected aerodynamic efficiency occurs at freestream Mach number of 0.30, which produces a efficiency of 81.04 at jet momentum coefficient of 0.03 and AoA of 6 degree. At the same jet momentum coefficient and AoA, the maximum Mach number on the CFJ airfoil suction surface at freestream Mach number of 0.15, 0.30, 0.46, 0.50 is 0.264, 0.558, 1.025 and 1.289 respectively. For the case of freestream Mach number of 0.50, the flow becomes transonic with the maximum Mach number of 1.289. As the freestream Mach number increases, the lift coefficient is also increased due to the stronger compressibility effect that creates a greater suction effect. The case at freestream Mach number of 0.30 has higher compressibility than that at freestream Mach number of 0.15, but is still far from the sonic speed. The favorable conditions hence provide the optimum aerodynamic efficiency. At freestream Mach number of 0.46, which is the critical Mach number for the airfoil, the corrected aerodynamic efficiency is still very good. But when the freestream Mach number is increased to 0.5, the corrected aerodynamic efficiency is significantly dropped due to the appearance of supersonic flow region and shock wave, which increases wave drag and CFJ power consumption. For the optimum cruise condition with the Mach number varying from 0.15 to 0.5, the injection jet velocity ratio is varied from 1.14 to 1.24, and the total pressure ratio between the injection and suction slot is from 1.02 to 1.24. The low jet velocity is beneficial to reduce the noise and the low total pressure ratio is beneficial to achieve the low power requirement at cruise.The study of the CFJ airfoil power minimization indicates that the power consumption of the CFJ airfoil at cruise can be substantially reduced by using larger slot size with reduced injection velocity and jet total pressure ratio. It is very beneficial if the same fixed geometry with enlarged injection slot size can be also used to generate super-lift coefficient for takeoff/landing. This is particularly important for the same CFJ airfoil with fixed geometry to be used for whole flight envelop. The maximum lift coefficient and its power consumption of the optimized CFJ6421-SST150-INJ117-SUC247 airfoil for cruise is investigated. The high lift CFJ airfoil previously designed by Yang and Zha, CFJ641-SST016-SUC053-INJ009, has substantially smaller size in both the injection and suction slot. Compared with the CFJ6421-SST016-SUC053-INJ009 airfoil, the CFJ6421-SST150-SUC247-INJ117 achieves higher maximum lift coefficient while having a substantially lower power consumption. The reason is that the CFJ power consumption is determined linearly by the mass flow rate, but exponentially by the total pressure ratio. The larger injection slot size yields a higher mass flow rate, but a much smaller flow energy loss and hence substantially lower total pressure ratio. For example, at a maximum lift coefficient of 9, the total pressure ratio is reduced from 4.2 to 1.3 when the injection slot size is increased from 0.09% C to 1.17% C. The power coefficient is reduced by 5 times. Such phenomenon applies to all active flow control using fluidic actuators. With the 2D CFJ airfoil optimized for cruise and takeoff/landing using fixed geometry, the induced drag of 3D Co-Flow Jet (CFJ) wings formed by the optimized 2D CFJ airfoil CFJ6421-SST150-SUC247-INJ117 at cruise conditions with different aspect ratios is studied. The simulated aspect ratios are 20, 10 and 5. The results are also compared with the wings formed by CFJ6421-SST150-SUC133-INJ065 airfoil. The baseline wings with the non-controlled NACA 6421 airfoil are also simulated for comparison at the same aspect ratios. A jet momentum coefficient of 0.03 and 0.04 are used at the cruise condition and generate the optimum aerodynamic efficiency and productivity efficiency. The angle of attack is fixed at 5 degree, which produces the optimum aerodynamic efficiency for the two CFJ wings and the baseline wings. The study indicates that the induced drag coefficient of CFJ wings is increased with the decrease of aspect ratio. However, the Oswald efficiency is also increased. The CFJ wings have higher Oswald efficiency than the baseline wings with the same aspect ratio. In other words, the CFJ wing is less penalized even though the lift coefficient is higher than the baseline wing. The CFJ wing always has substantially higher ratio of lift/drag than the baseline wing since CFJ reduces the pressure drag significantly. For the corrected aerodynamic efficiency that includes the CFJ power consumption, the CFJ6421-SST150-SUC247-INJ117 wing's result is only slightly better than the baseline wing at aspect ratio of 20 and similar at aspect ratio of 10 and 5. However, attributed to the increased cruise lift coefficient, the productivity efficiency of the CFJ6421-SST150-SUC247-INJ117 wing is increased by 32.1% for the wing of AR of 20, by 19.4% for the wing of AR of 10 and by 5.6% for the wing of AR of 5. For the power consumption comparison, the CFJ6421-SST150-SUC247-INJ117 wings at all the aspect ratio have substantially lower CFJ power coefficient benefited from the larger injection and suction slot size. For the same momentum coefficient, the CFJ6421-SST150-SUC247-INJ117 wings with larger slot size have lower injection velocity, lower total pressure ratio between the injection and suction slot, and larger mass flow rate. Hence a decrease of the total pressure ratio has the major impact to reduce the CFJ power consumption. As the result, the productivity efficiency of the CFJ6421-SST150-SUC247-INJ117 wing is increased by 12.9%, 9.8% and 8.7% for AR 20, 10 and 5 respectively compared with the CFJ6421-SST150-SUC133-INJ065 wing. In conclusion, this thesis demonstrates that the CFJ6421-SST150-SUC247-INJ117 airfoil with fixed geometry can achieve both the super lift coefficient for takeoff/landing and ultra-high cruise efficiency for cruise. For 3D CFJ wing, the induced drag penalty is much less than conventional non-controlled wing.


Power Minimization; Co-Flow Jet; Flow Control; Fixed Airfoil Geometry; Active Flow Control