The primary requirement for high pressure turbine heat transfer designs is to predict blade metal temperature. There has been a considerable recent effort in developing coupled fluid convection and solid conduction (conjugate) heat transfer prediction methods. They are, however, confined to steady flows. In the present work, a new approach to conjugate analysis for periodic unsteady flows is proposed and demonstrated. First, a simple model analysis is carried out to quantify the huge disparity in time scales between convection and conduction, and the implications of this for steady and unsteady conjugate solutions. To realign the greatly mismatched time scales, a hybrid approach of coupling between the time-domain fluid solution and frequency-domain solid conduction is adopted in conjunction with a continuously updated Fourier transform at the interface. A novel semi-analytical harmonic interface condition is introduced, initially for reducing the truncation error in finite-difference discretization. More interestingly, the semi-analytical interface condition enables the unsteady conjugate coupling to be achieved without simultaneously solving the unsteady temperature field in the solid domain. This unique feature leads to a very efficient and accurate unsteady conjugate solution approach. The fluid and solid solutions are validated against analytical solutions and experimental data. The implemented unsteady conjugate method has been demonstrated for a turbine cascade subject to inlet unsteady hot streaks.

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