Abstract
In this study, a new inverse design method is proposed for the full 3-D inverse design of S-ducts using curvature-based dimensionless pressure distribution as a target function. The wall pressure distribution in a 3-D curved duct is a function of the centerline curvature and the cross-sectional profile and area. A dimensionless pressure parameter was obtained as a function of the duct curvature and height of the cross-sections based on the normal pressure gradient equation. The dimensionless pressure parameter was used to eliminate the effect of the cross-sectional area on the wall pressure distribution. Full 3-D inverse design of an S-shaped duct was carried out by substituting the 3-D duct with a large number of 2-D planar ducts. The ball-spine inverse design method with vertical spins was coupled with the dimensionless pressure parameter as a target function for the design of the planar ducts. The inverse design process was performed in two steps. First, the height of each cross-section was considered constant, and only the duct centerline was allowed to be deformed by applying the difference between the dimensionless pressure on the upper and lower lines of symmetry plane. Then, a constant curvature was considered for each centerline in the equation, and the difference between the current and the target dimensionless pressure was applied to each upper and lower line of the planar sections to correct the heights of the 2-D planar sections, separately. The method was validated by choosing a straight duct as an initial guess, which converges to the target S-shaped duct. The results showed that the method is an efficient physical-based residual-correction method with low computational cost and good convergence rate. The 3-D wall pressure distribution of a high-deflected 3-D S-shaped diffuser was modified to eliminate the separation, secondary flow, and outlet distortion. Finally, the geometry corresponding to the modified pressure was obtained by the proposed 3-D inverse design method, which revealed higher pressure recovery, lower total pressure loss, and lower outlet flow distortion and swirl angle.
Highlights
The flow pattern in curved ducts such as S-shaped ducts is quite complex because of the curvature, diffusion, and inflexion in the curvature
The results show that corrections while the optimized S-shaped duct in [18] converged after 1300 iterations
The pressure distribution on the wall of a 3-D duct is influenced by the centerline curvature, area, and cross-sectional shape
Summary
The flow pattern in curved ducts such as S-shaped ducts is quite complex because of the curvature, diffusion, and inflexion in the curvature. In mathematical-based decoupled shape design algorithms, which are commonly called optimization methods, the difference between the target and current pressure distribution is defined as an objective function, and the minimum of this function is sought using ideas rooted in calculus. ZiaeiRad et al [14] developed an efficient algorithm for the design optimization of the compressible fluid flow problem through a flexible structure They coupled a supersonic flow solver, an aeroelastic solver, and genetic algorithm to calculate the optimum shape of a supersonic diffuser with flexible wall for a prescribed pressure distribution. Chiereghin et al [16] coupled the free form deformation method with a multi-objective genetic algorithm to optimize the shape of a diffusing S-duct. The original BSA inverse design method diverges if the wall nodes are corrected based on the difference of the target and current pressures. Numerical Procedure modified so that the pressure loading decreased on the symmetry plane and increased on planar planes to remove the separation and secondary flow
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