https://orcid.org/0000-0002-3145-4182
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ABSTRACT
Achieving a unique solution for the 3D inverse design of a curved duct is a challenging problem in aerodynamic design. The centre-line curvature, and cross-sections’ area and shape of a 3D curved duct influence the wall pressure distribution. All the previous developments on the ball-spine method were limited to 2D and quasi-3D ducts, in which only the upper and lower lines of the symmetry plane were modified based on the target pressure distribution. In the present work, the ball-spine method was three-dimensionally developed for the design of curved ducts while considering the effects of cross-sectional shape and area. To validate the method, all the nodes of a 3D duct wall were iteratively corrected under the modified ball-spine method to reach the target geometry. The effects of the ball movement directions (spines) and the grid generation scheme in achieving the unique solution in inverse design were evaluated. The results showed that the new method converges to a unique solution only if the streamline-based grids are applied for the flow numerical solution, and the horizontal spines are considered as the directions for the displacement of the nodes. Finally, the wall pressure distribution of a high-deflected 3D S-shaped diffuser was three-dimensionally modified to reduce the separation, secondary flow, and flow distortion.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Nomenclature
| a | = | Linear acceleration (m s−2) |
| a | = | Half the cross-section height (m) |
| A | = | Area (m2) |
| b | = | Half the cross-section width (m) |
| C | = | Geometry correction coefficient (m2 s2 kg−1) |
| E | = | Inviscid flux vectors in x-direction |
| = | Total internal energy (J kg−1) | |
| F | = | Force vector (N), Inviscid flux vectors in y-direction |
| G | = | Inviscid flux vectors in z-direction |
| H | = | Total enthalpy (J kg−1) |
| L | = | Duct length (m) |
| n | = | Index of cross-sectional profile |
| = | Number of nodes in axial direction | |
| = | Number of nodes in radial direction | |
| = | Number of nodes in azimuthal direction | |
| = | Mass flow rate (kg s−1) | |
| P | = | Static pressure (Pa) |
| Q | = | Conservative vector in physical domain |
| t | = | Time (s) |
| TPD | = | Target Pressure Distribution |
| U | = | Velocity component in x-direction (m s−1) |
| V | = | Velocity component in y-direction (m s−1) |
| V | = | Flow velocity (m s−1) |
| W | = | Velocity component in z-direction (m s−1) |
| W | = | Width of duct (m) |
| X | = | x coordinate |
| Y | = | y coordinate |
| Z | = | z coordinate |
| Δt | = | Time step (s) |
| ΔP | = | Target and computed pressure difference (Pa) |
| θ | = | Angle between force vector and spine (rad) |
| = | Circumferential location (deg) | |
| = | Density (kg m−3) |
Subscripts
| Comp | = | Computed conditions |
| Target | = | Target conditions |
| (e) | = | Exit or outlet node |