Figures & data
Figure 1. The string deformation in a 2-D flow.
Figure 2. Free body diagram of an arbitrary link 'i ’ of the chain, (a) kinematics and (b) forces.
Figure 3. Implementation of the inverse design algorithm.
Table 1. Grid, number of iterations and CPU time for a test case.
Figure 4. Geometry of bumped and straight duct.
Figure 5. Pressure distribution along the bottom surface of bumped and straight duct.
Figure 6. Shape modification process of the string from the bumped wall to the straight wall.
Figure 7. Shape modification process of the string from straight wall to the bumped wall.
Figure 8. (a) Geometries of Michael nozzle and initial guess. (b) Initial and target wall pressure distributions.
Figure 9. Shape modification process from a straight converging nozzle to the Michael nozzle.
Figure 10. Shape modification process from the straight diffuser to the Michael nozzle.
Figure 11. Shape modification process from the straight duct to the Michael nozzle.
Figure 12. Pressure distribution along the lower and upper wall of the S-duct.
Figure 13. Shape modification process from a nozzle to the S-duct nozzle.
Figure 14. (a) S-duct geometry after 350 modifications with the target shape and (b) their corresponding wall pressure distributions.
Figure 15. Convergent–divergent nozzle with its grid.
Figure 16. Wall shape modification from straight convergent duct to the supersonic nozzle with normal shock.
Figure 17. Initial guess and TPD for convergent–divergent nozzle.
Table 2. Effect of ρ decrement on improvement of convergence rate.
Figure 18. The number of shape modifications for the Michael nozzle at four different grids vs. .
Figure 19. Calculated bumped wall after 200 iterations with no filtering operation.
Figure 20. Wall pressure distribution of an ideal nozzle and Michael nozzle.
Figure 21. (a) Michael nozzle as the initial guess and (b) the designed ideal nozzle as the final shape.
