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Comprehensive Analysis of Turbine Blade Design Methods for Entropy Production Minimization

This report compares gradient calculations from Euler and N-S methods, presents two inverse design cases of C3X turbine blade, and explores optimal designs to minimize entropy production. Figures and tables illustrate various design parameters and performance metrics for different scenarios. Findings include efficiency improvements and total pressure increases.

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Comprehensive Analysis of Turbine Blade Design Methods for Entropy Production Minimization

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  1. Weekly Report01/02/2009 • Comparison of gradients obtained from both Euler and N-S • calculations; • Two inverse design cases of C3X turbine blade with inviscid • hub and casing; • 3. Optimal design to minimize entropy production by restaggeting • exist blade and directly modifying blade profile.

  2. Gradients with Euler Calculations Fig. 1 Gradients of both finite difference method and adjoint method

  3. Comparison of Gradients with N-S Calculations Fig. 2(a) Gradients with laminar flow (b) Gradients with B-L turbulent flow

  4. Inverse Design Cases of C3X Turbine Blade Fig. 3 Cost function without boundary layer Fig. 4 Cost function with inlet boundary layer

  5. Inverse Design Cases of C3X Turbine Blade (Continued) Fig. 5 Mass and turn without boundary layer Fig. 6 Mass and turn with inlet boundary layer

  6. Inverse Design Cases of C3X Turbine Blade (Continued) Fig. 7 Comparison of designed stagger distributions Fig. 8 Comparison of exit flow angle distributions

  7. Optimal Design to Minimize Entropy ProductionPart I Euler Case Fig. 9 Entropy production vs. design cycles Fig. 10 Variation of stagger angle

  8. Optimal Design to Minimize Entropy ProductionPart I Euler Case (Continued) Fig. 11 Exit total pressure and efficiency vs. design cycles Fig. 12 Flow mass and turning vs. design cycles Total pressure increased by 0.53%; efficiency 0.73%

  9. Optimal Design to Minimize Entropy ProductionPart II N-S Case With Flow Angle Constraint Fig. 13 Entropy production vs. design cycles Fig. 14 Variation of stagger angle

  10. Optimal Design to Minimize Entropy ProductionPart II N-S Case With Flow Angle Constraint (Continued) Fig. 15 Exit total pressure and efficiency vs. design cycles Fig. 16 Flow mass and turning vs. design cycles Total pressure increased by 0.24%; efficiency 0.34%

  11. Optimal Design to Minimize Entropy ProductionPart II N-S Case With Flow Angle Constraint (Continued) Fig. 17 Spanwise distribution of exit total pressure Fig. 18 Spanwise distribution of efficiency

  12. Optimal Design to Minimize Entropy ProductionPart II N-S Case With Flow Angle Constraint (Continued) Fig. 19 Spanwise distribution of exit flow angle Fig. 20 Spanwise distribution of axial velocity

  13. Optimal Design to Minimize Entropy ProductionPart II N-S Case With Flow Angle Constraint (Continued) Table 1 Flow quality of four cases Case 1– Original blade shape and original stagger Case 2– Original blade shape and designed stagger Case 3– Designed blade shape and original stagger Case 4--Designed blade shape and designed stagger

  14. Optimal Design to Minimize Entropy ProductionPart II N-S Case With Flow Angle Constraint (Continued) Fig. 21 Blade profiles of K=17 Fig. 22 Isentropic mach number of K=17

  15. Optimal Design to Minimize Entropy ProductionPart II N-S Case With Flow Angle Constraint (Continued) Fig. 23 Blade profiles of K=25 Fig. 24 Isentropic mach number of K=25

  16. Optimal Design to Minimize Entropy ProductionPart II N-S Case With Flow Angle Constraint (Continued) Fig. 25 Contours of pitch averaged total pressure

  17. Optimal Design to Minimize Entropy ProductionPart II N-S Case With Flow Angle Constraint (Continued) Fig. 26(a) Isentropic mach number contour on suction surface (b) Total pressure contour on suction surface

  18. Optimal Design to Minimize Entropy ProductionPart III N-S Case With Flow Mass Constraint Fig. 27 Entropy production vs. design cycles Fig. 28 Variation of stagger angle

  19. Optimal Design to Minimize Entropy ProductionPart III N-S Case With Flow Mass Constraint (Continued) Fig. 29 Exit total pressure and efficiency vs. design cycles Fig. 30 Flow mass and turning vs. design cycles Total pressure increased by 0.32%; efficiency 0.45%

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