Development a computationally efficient method to solve direct and inverse aerodynamic problems related to turbomachines - Subotovich, Valery; Yudin, Oleksandr; Babaiev, Artem; Barannik, Valentyn; Avdieieva, Olena (Eastern-European Journal of Enterprise Technologies, 2026)
This study investigates aerodynamic processes in interblade, axial annular, and radial-axial channels in turbomachines. The task addressed relates to the need to improve the computational efficiency in solving direct and inverse aerodynamic problems when analyzing and designing flow parts of turbomachines. A computationally efficient method for solving direct and inverse aerodynamic problems has been proposed, which provides acceptable accuracy for engineering practice at significantly lower computational costs compared to conventional CFD approaches. The results include a devised single mathematical formulation based on Euler equations for a compressible fluid, written in terms of the flow function. The proposed method makes it possible to consider direct and inverse problems within a common mathematical structure. The system of equations is reduced to a single differential equation and a set of algebraic relations while the global flow problem is decomposed into a set of independent problems for individual cross-sections. The inverse problem is stated as a nonlinear optimization problem based on the mass flow rate agreement condition derived from the energy equation. The computational complexity is reduced by using the flow function and the decomposition of the computational domain. The method combines the capabilities of direct analysis and reconstruction of the flow channel geometry based on the predefined aerodynamic characteristics. Verification by experimental data and direct calculation results demonstrated good agreement between the velocity distributions and the reconstructed geometry; the maximum deviations did not exceed 0.3%. The results could be practically applied to preliminary design, parametric optimization, as well as inverse design of the flow parts in turbomachines