Determination of local internal heat transfer in the cooling channels of turbine blades with a validated calculation method considering special boundary layer phenomena

In the present publication, a validation by means of the dimensionless ratios between the calculation of heat transfer coefficients and the experiment on an isothermally rotating device is performed. The investigations provide important insights into the design of internal cooling channels of turbine blades. It is shown that forced convection is dominant. For this reason, an isothermally rotating tube is chosen for the validation. This leads to further precision of the validation, since the buoyancy effect (described by the Archimedes-Number of rotations, Ar≈0) in the axial direction is eliminated. The variation to determine the dimensionless heat transfer Nu-Number takes place in the ratio range Reynolds (Re)-Numbers=8,500 to 52,000, Rotational (Ro)-Numbers=0 to 0,2 and at a Prandtl (Pr)-Number of 2.5. In order to keep the isothermal conditions and to get an extremely high local resolution of the Nu-Numbers, experimental investigations were carried out with the Heat- and Mass-Transfer-Analogy. This is possible because the differential equations (energy / concentration) are the same at small Mach-Numbers (Ma ≈0) and the Stefan-current is negligible. By analogy with the Nu-Number, a dimensionless mass transfer Sh-Number could be chosen. The dimensionless Pr-Number then corresponds to the dimensionless Schmidt (Sc) -Number. Local Sh-Numbers (and thus the Nu-Numbers) could be determined with high resolution via the layer thickness loss of the sublimate (naphthalene /air system, Sc =2.5). The local Sh-Number and thus the Nu-Number are known. The Nu, Sh results are determined as a function of the Re-and Ro-Number (related to the pipe diameter), in the pipe circumferential direction φ and dimensionless length x/d (with and without hydraulic flow) for the Pr, Sc-number and compared with the numerical calculations and the correlation. It could be shown that the use of a sublimate results in the following advantages for the validation: no vagrant heat flows in the wall, exact compliance with the boundary condition, pipe wall temperature=const (since wall concentration is constant) and Ar≈0. Thus, for the numerical investigation (with Pr, Sc=2.5), the boundary conditions could be accurately reproduced and compared with the experimental results and correlation. The numerical flow problem was solved using the steady-state Reynolds-averaged Navier-Stokes (RANS) equations. For the closure problem, the Boussinesq approximation was used. The turbulent eddy viscosity of th