This two-parts paper addresses the design of a U-bend for serpentine internal cooling channels optimized for minimal pressure loss. The total pressure loss for the flow in a U-bend is a critical design parameter as it augments the pressure required at the inlet of the cooling system, resulting in a lower global efficiency. In this first part of the paper the design methodology of the cooling channel is presented. The minimization of the total pressure loss is achieved by means of a numerical optimization method that uses a metamodel assisted differential evolution algorithm in combination with an incompressible Navier-Stokes solver. The profiles of the internal and external side of the bend are parameterized using piece-wise Bezier curves. This allows for a wide variety of shapes, respecting the manufacturability constraints of the design. The pressure loss is computed by the Navier-Stokes solver, which is based on a two-equation turbulence model and is available from the open source software OpenFOAM. The numerical method predicts an improvement of 36% in total pressure drop with respect to a circular U-bend, mainly due to the reduction of the separated flow region along the internal side of the bend. The resulting design is subjected to experimental validation, presented in Part II of the paper.

This two-part paper addresses the design of a U-bend for serpentine internal cooling channels optimized for minimal pressure loss. The total pressure loss for the flow in a U-bend is a critical design parameter as it augments the pressure required at the inlet of the cooling system, resulting in a lower global efficiency. In the first part of the paper the design methodology of the cooling channel was presented. In this second part the optimized design is validated. The results obtained with the numerical methodology described in Part I are checked against pressure measurements and Particle Image Velocimetry (PIV) measurements. The experimental campaign is carried out on a magnified model of a two-legged cooling channel that reproduces the geometrical and aerodynamical features of its numerical counterpart. Both the original profile and the optimized profile are tested. The latter proves to outperform the original geometry by about 36%, in good agreement with the numerical predictions. Two-dimensional PIV measurements performed in planes parallel to the plane of the bend highlight merits and limits of the computational model. Despite the well-known limits of the employed eddy viscosity model, the overall trends are captured. The study demonstrates that the proposed optimization method based on an evolutionary algorithm, a Navier-Stokes solver and a meta-model of it is a valid design tool to minimize the pressure loss across a U-bend in internal cooling channels.

This two-part paper addresses the design of a U-bend for serpentine internal cooling channels optimized for minimal pressure loss. The total pressure loss for the flow in a U-bend is a critical design parameter, as it augments the pressure required at the inlet of the cooling system, resulting in a lower global efficiency. In this first part of the paper, the design methodology of the cooling channel is presented. The minimization of the total pressure loss is achieved by means of a numerical optimization method that uses a metamodel-assisted differential evolution algorithm in combination with an incompressible Navier–Stokes solver. The profiles of the internal and external side of the bend are parameterized using piece-wise Bezier curves. This allows for a wide variety of shapes, respecting the manufacturability constraints of the design. The pressure loss is computed by the Navier–Stokes solver, which is based on a two-equation turbulence model and is available from the open source software OpenFOAM. The numerical method predicts an improvement of 36% in total pressure drop with respect to a circular U-bend, mainly due to the reduction of the separated flow region along the internal side of the bend. The resulting design is subjected to experimental validation, presented in Part II of the paper.