A numerical procedure is presented to simulate conjugate heat transfer in generalized coordinates and used in some typical turbomachinery applications. The discretized equations at the solid-fluid interface are obtained using energy conservation principles and computational nodes are placed exactly on that interface, thus yielding the corresponding temperatures directly, without the need for inter- or extrapolation from neighboring nodes. The temperature field over both the fluid and the solid domains is computed implicitly, i.e., without iterating between the two. The computer code used for the computations is based on the finite-volume method and the SIMPLE algorithm along with various turbulence models. Both a version of the low-Reynolds-number k-ϵ model suitable for recirculating flows with heat transfer and the standard k-ϵ have been used, with suitable modifications.
The successful treatment of the boundary condition at the solid-fluid interface has been verified by comparing against analytical solutions for laminar, conjugate heat transfer over a flat plate of finite thickness. The agreement was found to be quite good, when temperature profiles were compared at various streamwise distances from the leading edge. Further applications have been sought in the field of turbomachinery and as the main test case, the turbulent flow and heat transfer in labyrinth seals has been selected. Two such configurations have been considered, a straight-through and a stepped labyrinth seal. Results were compared with measured data obtained for the same configurations and the agreement was found to be satisfactory. In addition, the applicability of the current method to a film-cooling problem and the merits of it are being demonstrated.