Developing Buoyancy-Modified Turbulent Flow in Ducts Rotating in Orthogonal Mode

Abstract

A numerical study of developing flow through a heated duct of square cross section rotating in orthogonal mode is reported. The two main aims are to explore the effects of rotational buoyancy on the flow development and to assess the ability of available turbulence models to predict such flows. Two test cases have been computed corresponding to values of the rotation number, Ro, of 0.12 and 0.24, which are typical of operating conditions in internal cooling passages of gas turbine blades. Computations from three turbulence models are presented: a k–ε eddy viscosity (EVM) model matched to a low-Reynolds-number one-equation EVM in the near-wall region; a low-Re k–ε EVM and a low-Re algebraic stress model (ASM). Additional computations in which the fluid density is assumed to remain constant allow the distinct contributions from buoyancy and Coriolis forces to be separated. It is thus shown that rotational buoyancy can have a substantial influence on the flow development and that, in the case of outward flow, it leads to a considerable increase of the side-averaged heat transfer coefficient. The Coriolis-induced secondary motion leads to an augmentation of the mean heat transfer coefficient on the pressure surface and a reduction on the suction side. The k–ε/one-equation EVM produces a mostly reasonable set of heat transfer predictions, but some deficiencies do emerge at the higher rotation number. In contrast, predictions with the low-Re k–ε EVM return a spectacularly unrealistic behavior while the low-Re ASM thermal predictions are in encouragingly close agreement with available measurements.