Development of a dual motion model and its application to investigate the unsteady conjugate heat transfer characteristics of blade tip interacted by casing film cooling

In turbomachinery stator-rotor interactions, the time scales of fluid convection and solid conduction differ by approximately four orders of magnitude, making unsteady conjugate heat transfer (CHT) analysis highly challenging. This paper proposes an innovative method called the Dual Motion Model (DMM) to address this timescale disparity. DMM introduces a displacement variable, mathematically transformed into a degree of freedom in time, allowing the adjustment of rotor-passing time scales arbitrarily while preserving the physical fidelity of flow and heat transfer processes. The method is theoretically derived and validated against conventional simulations and experimental data. It is first applied to a representative stator-rotor case with film cooling holes on the casing, where periodic film injection interacts with the blade tip. A variable timescale coupled aero-thermal simulation is conducted to evaluate unsteady flow and heat transfer characteristics. Results show that as the timescale decreases, the amplitude of the blade tip temperature fluctuation also decreases. At the rated operating speed (timescale of 1 × 10⁻⁶ s), the blade tip temperature remains stable despite significant local flow variations near the tip. Comparisons between DMM, the traditional sliding mesh method, and the frozen rotor approach demonstrate that DMM offers superior flexibility and accuracy in resolving unsteady thermal behavior in stator-rotor interactions. This study confirms that DMM is a promising tool for improving CHT modeling in rotating machinery.