Abstract
This paper presents an adjoint-based shape optimization framework and its demonstration in a conjugate heat transfer problem in a turbine blading. The gradient of the objective function is computed based on the continuous adjoint method, which also includes the adjoint to the turbulence model. Differences in the gradient resulting from making the frozen turbulence assumption are discussed. The developed software was used to optimize both the blade shape of the internally cooled linear C3X turbine blade and the position of cooling channels aiming at (a) minimum total pressure drop of the hot gas flow and (b) minimum highest temperature within the blade. A two-step optimization procedure was used. A free-form parameterization tool, based on volumetric NURBS, controls the blade airfoil contour, while the cooling channels are free to move following changes in the coordinates of their centers. Geometric and flow constraints are included in the performed optimizations, keeping the cooling channels away from the airfoil sides and retaining the turbine inlet capacity and flow turning.
Highlights
Accepted: 9 June 2021The efficient design of gas turbines with improved performance and longer lifetime, for use in aerospace and marine propulsion, land power plants, and other industrial applications, is of great importance
The pressure, temperature, and heat transfer coefficient distributions at the blade midspan were computed by a 2D conjugate heat transfer (CHT) analysis, in which the average temperature and coolant flow rate per cooling channel were replaced by heat transfer coefficient values
The turbulence model equations are included in the adjoint formulation without making the frozen turbulence assumption, leading to an adjoint model that is consistent, in the continuous sense, to the one used in the CHT analysis
Summary
The efficient design of gas turbines with improved performance and longer lifetime, for use in aerospace and marine propulsion, land power plants, and other industrial applications, is of great importance. Relevant studies account for the interaction of blades and gas flow in gas turbine components This can be done using conjugate heat transfer (CHT) analysis and optimization. The optimization of the cooling system of the C3X blade can be found in [6,7], which both use evolutionary algorithms, and in [8] using the globally convergent method of moving asymptotes In the latter, the objective function derivatives with respect to the design variables needed by the optimization algorithm are computed based on forward finite differences. This optimization is performed in two steps, in which constant heat transfer coefficients are imposed in the cooling holes The latter are based on 3D CHT analysis runs instead of using the empirical expression of [3,9].
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