Unsteady Flow/Quasi-Steady Heat Transfer Computations on a Turbine Rotor and Comparison With Experiments

The unsteady flow in stator–rotor interactions affects the structural integrity, aerodynamic performance of the stages, and blade-surface heat transfer. Numerous viscous and inviscid computer programs are used for the prediction of unsteady flows in two-dimensional and three-dimensional stator–rotor interactions. The relative effects of the various components of flow unsteadiness on heat transfer are under investigation. In this paper it is shown that for subsonic cases, the reduced frequency parameter for boundary-layer calculations is about two orders of magnitude smaller than the reduced frequency parameter for the core flow. This means that for typical stator–rotor interactions, the unsteady flow terms are needed to resolve the location of disturbances in the core flow, but in many cases the instantaneous disturbances can be input in steady-flow boundary-layer computations to evaluate boundary-layer effects in a quasi-steady approximation. This hypothesis is tested by comparing computations with experimental data on a turbine rotor for which there are extensive experimental heat transfer data available in the open literature. An unsteady compressible inviscid two-dimensional computer program is used to predict the propagation of the upstream stator disturbances into the downstream rotor passages. The viscous wake (velocity defect) and potential flow (pressure fluctuation) perturbations from the upstream stator are modeled at the computational rotor–inlet boundary. The effects of these interactions on the unsteady rotor flow result in computed instantaneous velocity and pressure fields. The period of the rotor unsteadiness is one stator pitch. The instantaneous velocity fields on the rotor surfaces are input in a steady-flow differential boundary-layer program, which is used to compute the instantaneous heat transfer rate on the rotor blades. The results of these quasi-steady heat-transfer computations are compared with the results of unsteady heat transfer experiments and with the results of previous unsteady heat transfer computations. The unsteady flow fields explain the unsteady amplitudes and phases of the increases and decreases in instantaneous heat transfer rate. It is concluded that the present method is accurate for quantitative predictions of unsteady heat transfer in subsonic turbine flows.