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In the GA Toolbox, ga- Genetic Algorithm is set as a solver. The objective function is called in the GA Toolbox as @objfun and the number of variables is set to 8.

Figure 6 In the GA Toolbox, ga- Genetic Algorithm is set as a solver. The objective function is called in the GA Toolbox as @objfun and the number of variables is set to 8.

Related Figures (20)

Shen M. et al [2] have defined a two dimensional multiple-peak contour using Genetic Algorithm to search for maximun value of the problem. With two different Mach numbers, the optimization method was used to modify the blade mentione« before at the cases of design condition: Mach | = 0.828 and a transonic condition: Mach 2 = 1.06. Comparisons betwee original and modified blade shapes are given in Figure 2 (a) and (b). The loss coefficient was decreased from 0.0359 tc 0.0275 at the case of Mach=0.828, and decreased from 0.515 to 0.231 at the case of Mach = 1.06.
Shen M. et al [2] have defined a two dimensional multiple-peak contour using Genetic Algorithm to search for maximun value of the problem. With two different Mach numbers, the optimization method was used to modify the blade mentione« before at the cases of design condition: Mach | = 0.828 and a transonic condition: Mach 2 = 1.06. Comparisons betwee original and modified blade shapes are given in Figure 2 (a) and (b). The loss coefficient was decreased from 0.0359 tc 0.0275 at the case of Mach=0.828, and decreased from 0.515 to 0.231 at the case of Mach = 1.06.
Figure 2 Blade shape comparison, design (a) and transonic condition (b) [2]
Figure 2 Blade shape comparison, design (a) and transonic condition (b) [2]
Figure 3 Model of initial aerofoil (a) and optimized aerofoil (b) [4]
Figure 3 Model of initial aerofoil (a) and optimized aerofoil (b) [4]
Table 1 CURVE PROFILE COORDINATES Picked six clouds of points with t division are:
Table 1 CURVE PROFILE COORDINATES Picked six clouds of points with t division are:
Table 2 PICKED UPPER SIDE POINTS Table 3 PICKED LOWER SIDE POINTS
Table 2 PICKED UPPER SIDE POINTS Table 3 PICKED LOWER SIDE POINTS
By now, all input data are created for our fifth order Bezier curve formula. In Bezier, the control points are the driving points to create a curve [14]. We need control points of the upper and lower aerofoil profile to create an aerofoil in CATIA which later will be used as design parameters in the optimization process.
By now, all input data are created for our fifth order Bezier curve formula. In Bezier, the control points are the driving points to create a curve [14]. We need control points of the upper and lower aerofoil profile to create an aerofoil in CATIA which later will be used as design parameters in the optimization process.
The corrected aerofoil coordinate values of upper and lower curve are presented below on Table 4and 5, respectively. Table 5 CORRECTED CONTROL POINTS FOR LOWER PROFILE
The corrected aerofoil coordinate values of upper and lower curve are presented below on Table 4and 5, respectively. Table 5 CORRECTED CONTROL POINTS FOR LOWER PROFILE
Where, c = 5(1-u)**u*P, + 10(1-u)**u?*P,+ 10(1-u)’*u**P3 + 5(1-u)*u**P,
Where, c = 5(1-u)**u*P, + 10(1-u)**u?*P,+ 10(1-u)’*u**P3 + 5(1-u)*u**P,
B. Aerodynamic Performance Analysis The parameterization of ‘the aerofoil ‘was carried out using Bezier control points. The y-ordinates of the control points 2 through 5 and 8 through 11 form the vector of design variables.
B. Aerodynamic Performance Analysis The parameterization of ‘the aerofoil ‘was carried out using Bezier control points. The y-ordinates of the control points 2 through 5 and 8 through 11 form the vector of design variables.
Figure 4 Range of Bezier control points (Design variables)
Figure 4 Range of Bezier control points (Design variables)
As the GA will let us find the optimal design parameters 27 experiments are run with varying control point values as an input and lift coefficient, drag coefficient and drag-to-lift ratio as a response. The experimental plan is presented on Table 7. The baseline, the upper and lower limit values of the design variables are as follows:
As the GA will let us find the optimal design parameters 27 experiments are run with varying control point values as an input and lift coefficient, drag coefficient and drag-to-lift ratio as a response. The experimental plan is presented on Table 7. The baseline, the upper and lower limit values of the design variables are as follows:
The minimum C,/C; values in each run are recorded and presented as follows: From the aerodynamic shape optimization perspective with 8 design variables, the number of coefficients are n; = 45. For ease of comparison and data modeling, the 27 aerofoils are analyzed with AoA of zero. Using MINITAB 16, surface response was analyzed for the DOE presented in Table 7.
The minimum C,/C; values in each run are recorded and presented as follows: From the aerodynamic shape optimization perspective with 8 design variables, the number of coefficients are n; = 45. For ease of comparison and data modeling, the 27 aerofoils are analyzed with AoA of zero. Using MINITAB 16, surface response was analyzed for the DOE presented in Table 7.
The minimum C,/C, value is 0.0022982 and attained at 51 generation which is roughly less than the least C,/C, valu recorded in the analyses. The objective function value and final design points are shown in Figure 7 below.
The minimum C,/C, value is 0.0022982 and attained at 51 generation which is roughly less than the least C,/C, valu recorded in the analyses. The objective function value and final design points are shown in Figure 7 below.
Figure 8 Convergence of objective function value
Figure 8 Convergence of objective function value
Using Fluent’s various capabilities; the following plots were generated at AoA of 0.1° Figure 9 Contours of Pressure Coefficient (in Pascal) over the entire aerofoil
Using Fluent’s various capabilities; the following plots were generated at AoA of 0.1° Figure 9 Contours of Pressure Coefficient (in Pascal) over the entire aerofoil
Figure 10 Velocity vectors over aerofoil colored by velocity magnitude (in m/s) Figure 9 shows that there is a region of high pressure at the LE (stagnation point) and region of low pressure on the uppe and lower surfaces of the aerofoil (relatively lower pressure on upper surface). This is what was expected from analysis of th velocity vector plot. From the Bernoulli equation, it is known that whenever there is high velocity, there is low pressure, an vice versa (See Figure 10).
Figure 10 Velocity vectors over aerofoil colored by velocity magnitude (in m/s) Figure 9 shows that there is a region of high pressure at the LE (stagnation point) and region of low pressure on the uppe and lower surfaces of the aerofoil (relatively lower pressure on upper surface). This is what was expected from analysis of th velocity vector plot. From the Bernoulli equation, it is known that whenever there is high velocity, there is low pressure, an vice versa (See Figure 10).
Table 10 NACA64A410 AND OPTIMIZED COMPARISON n Figure 11, the pressure coefficients of the two aerofoils are compared. The lower side of the curve in the figure depicts the ressure coefficient value of the upper aerofoil profiles the upper side of the curve in the figure depicts the pressure oefficient value of the lower aerofoil profile for both aerofoils.
Table 10 NACA64A410 AND OPTIMIZED COMPARISON n Figure 11, the pressure coefficients of the two aerofoils are compared. The lower side of the curve in the figure depicts the ressure coefficient value of the upper aerofoil profiles the upper side of the curve in the figure depicts the pressure oefficient value of the lower aerofoil profile for both aerofoils.
Figure 11 Comparison of pressure coefficient The lower curves have a negative pressure coefficient as the pressure is lower than the reference pressure. And the value of pressure coefficient of the optimized aerofoil is relatively lower than NACA64A410 aerofoil. On the other hand, the upper curves, in the figure, have mostly positive pressure coefficient as the pressure is higher than the reference pressure. The value of pressure coefficient of the optimized aerofoil on the lower side of the aerofoil is relatively higher than NACA64A410 aerofoil.
Figure 11 Comparison of pressure coefficient The lower curves have a negative pressure coefficient as the pressure is lower than the reference pressure. And the value of pressure coefficient of the optimized aerofoil is relatively lower than NACA64A410 aerofoil. On the other hand, the upper curves, in the figure, have mostly positive pressure coefficient as the pressure is higher than the reference pressure. The value of pressure coefficient of the optimized aerofoil on the lower side of the aerofoil is relatively higher than NACA64A410 aerofoil.
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