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Fig. 5. Variation of (a) bump design and (b) normalized C;, Cp during the bump control optimization process. is used with a relative height of 1.2% chord consisting of the arcs located between x = 0.5c and 0.99c with the junction of the arcs at x =0.9c on the Rae5243 airfoil section. 5. Discrete suction-optimization study As in the case of 2D contour bump, the effect of discrete suc- tion on drag has been investigated. The flow control parameters such as mass flow coefficient, Cg, location of actuator, x;, and suction/blowing angle relative to the local surface tangent, 6, are optimized to get the minimum drag. The width of the actuator, Wg, is kept fixed as 0.0035 during the optimization. The angle is defined as the angle between the jet flow direction and the local airfoil surface tangent. The effects of these parameters were ana- lyzed by the authors of this paper in 2009 [22]. Fig. 8 shows the parameters of the control jet. The lift coefficient is constrained to the non-control value, C, = 0.5299, during the optimization process. The objective is to mini- mize the total drag coefficient. The optimization problem is defined in the following form:

Figure 5 Variation of (a) bump design and (b) normalized C;, Cp during the bump control optimization process. is used with a relative height of 1.2% chord consisting of the arcs located between x = 0.5c and 0.99c with the junction of the arcs at x =0.9c on the Rae5243 airfoil section. 5. Discrete suction-optimization study As in the case of 2D contour bump, the effect of discrete suc- tion on drag has been investigated. The flow control parameters such as mass flow coefficient, Cg, location of actuator, x;, and suction/blowing angle relative to the local surface tangent, 6, are optimized to get the minimum drag. The width of the actuator, Wg, is kept fixed as 0.0035 during the optimization. The angle is defined as the angle between the jet flow direction and the local airfoil surface tangent. The effects of these parameters were ana- lyzed by the authors of this paper in 2009 [22]. Fig. 8 shows the parameters of the control jet. The lift coefficient is constrained to the non-control value, C, = 0.5299, during the optimization process. The objective is to mini- mize the total drag coefficient. The optimization problem is defined in the following form:

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Fig. 1. The automated optimization process.
Fig. 1. The automated optimization process.
Fig. 2. The computational grid used in 2D simulation.
Fig. 2. The computational grid used in 2D simulation.
Initial and optimal parameters for bump optimization. Table 2 2D contour bump has been optimized for drag reduction at transonic speed using the gradient-based optimization. The length, Iz, maximum height, hg, and the crest position relative to bump and airfoil, cg, xg, depicted in Fig. 4 are chosen as the key param- eters. For the initial points as given in Table 2, asymmetric bump The Rae5243 airfoil was tested by Fulker and Simmons [7] at different transonic speeds with surface mass injection. The valida- tion case used in this study has a Reynolds number of 18.68 x 10° million based on airfoil chord, Mj. = 0.6799, a = 0.77°, corre-
Initial and optimal parameters for bump optimization. Table 2 2D contour bump has been optimized for drag reduction at transonic speed using the gradient-based optimization. The length, Iz, maximum height, hg, and the crest position relative to bump and airfoil, cg, xg, depicted in Fig. 4 are chosen as the key param- eters. For the initial points as given in Table 2, asymmetric bump The Rae5243 airfoil was tested by Fulker and Simmons [7] at different transonic speeds with surface mass injection. The valida- tion case used in this study has a Reynolds number of 18.68 x 10° million based on airfoil chord, Mj. = 0.6799, a = 0.77°, corre-
Rae5243 airfoil lift and drag coefficient without and with suction. Table 1 of the Rae5243 airfoil. The control devices are stayed in a much refined region. The domain was decomposed into four blocks to make the computations parallel. The cases were run at Old Do- minion University’s teraflop computer cluster.
Rae5243 airfoil lift and drag coefficient without and with suction. Table 1 of the Rae5243 airfoil. The control devices are stayed in a much refined region. The domain was decomposed into four blocks to make the computations parallel. The cases were run at Old Do- minion University’s teraflop computer cluster.
Fig. 6. Bump-optimization study results: (a) comparison of airfoil shapes, (b) Cp distributions, (c) BL comparison.
Fig. 6. Bump-optimization study results: (a) comparison of airfoil shapes, (b) Cp distributions, (c) BL comparison.
Fig. 7. Mach contours: (a) baseline and (b) with bump.
Fig. 7. Mach contours: (a) baseline and (b) with bump.
is reliant on the actuator location. The suction, located at x/c = 0.3944, slightly reduces the BL thickness upstream of the shock location, x,/c = 0.53, after the shock the decrement is considerably increased. The actuator located upstream of the shock, dependent on the suction rate, spreading the top of the shock to three small pieces. The separation can be seen from the Mach contours given in Fig. 11. These small partitions cause reduction in pressure drag with increment in lift value.
is reliant on the actuator location. The suction, located at x/c = 0.3944, slightly reduces the BL thickness upstream of the shock location, x,/c = 0.53, after the shock the decrement is considerably increased. The actuator located upstream of the shock, dependent on the suction rate, spreading the top of the shock to three small pieces. The separation can be seen from the Mach contours given in Fig. 11. These small partitions cause reduction in pressure drag with increment in lift value.
value. The optimization results are given in Table 3. The aerody- namic performance, lift-to-drag ratios is increased 6.5%. Initial and optimal values for actuator optimization. Fig. 10 indicates the comparison of the pressure distributions and the boundary layer thickness normalized by the baseline BL thickness for the cases without flow control and with optimized flow control. The effect of suction on the pressure distributions Table 3
value. The optimization results are given in Table 3. The aerody- namic performance, lift-to-drag ratios is increased 6.5%. Initial and optimal values for actuator optimization. Fig. 10 indicates the comparison of the pressure distributions and the boundary layer thickness normalized by the baseline BL thickness for the cases without flow control and with optimized flow control. The effect of suction on the pressure distributions Table 3
Fig. 9. The variation of (a) Cg and (b) normalized C,, Cp values during the optimization process.
Fig. 9. The variation of (a) Cg and (b) normalized C,, Cp values during the optimization process.
The results of the computations of a contour bump in combi- nation with downstream slot suction is illustrated in Fig. 13 by pressure distributions and boundary layer parameter. The bound- ary layer was only increased at the interaction region. As already seen in the previous sections, the surface suction with appropriate selection of Cg, 6, X-c decreases the drag, 3.13% with an increment in lift value, 3.17% and the optimum bump alone results in a drag reductions of 0.9843% without any penalty in lift. The optimiza- tion of hybrid control raises the drag reduction to 3.94% and lift increment to 5.04%. The corresponding pressure distributions and boundary layer thickness in Fig. 13 show that the hybrid control reduces the wave drag, 32.58%, due to pushing and spreading the shock upstream with increasing viscous drag around 19.15%. As
The results of the computations of a contour bump in combi- nation with downstream slot suction is illustrated in Fig. 13 by pressure distributions and boundary layer parameter. The bound- ary layer was only increased at the interaction region. As already seen in the previous sections, the surface suction with appropriate selection of Cg, 6, X-c decreases the drag, 3.13% with an increment in lift value, 3.17% and the optimum bump alone results in a drag reductions of 0.9843% without any penalty in lift. The optimiza- tion of hybrid control raises the drag reduction to 3.94% and lift increment to 5.04%. The corresponding pressure distributions and boundary layer thickness in Fig. 13 show that the hybrid control reduces the wave drag, 32.58%, due to pushing and spreading the shock upstream with increasing viscous drag around 19.15%. As
Fig. 12. Variation of (a) design variables and (b) normalized C,, Cp during hybrid control optimization process.
Fig. 12. Variation of (a) design variables and (b) normalized C,, Cp during hybrid control optimization process.
Fig. 13. Comparison of (a) airfoil, (b) Cp distributions and (c) BL thickness.
Fig. 13. Comparison of (a) airfoil, (b) Cp distributions and (c) BL thickness.
Fig. 14. Mach contours: (a) baseline and (b) with hybrid control.
Fig. 14. Mach contours: (a) baseline and (b) with hybrid control.
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