Flows and temperatures in compressor and turbine wheelspaces

This paper sets out principles by which the turbomachine designer can determine the flows and hence the temperatures in the spaces between the rotating and stationary surfaces beneath, or inside, the mainstream annular flow region of axial flow machines. The geometry of these 'wheelspaces' ranges between slender single volumes of low hub-tip ratios to complex segmented regions of lower aspect ratio with large hub-tip ratios. Fluid temperatures in these spaces are determined by the supply of a secondary cooling air stream from near the engine axis, ingress of mainstream fluid from the external annulus, and leakage through the labyrinth glands separating axially adjacent wheelspaces. The paper uses the inviscid form of the momentum equation for rotating flows to determine the pressures in these spaces and simple Bernoulli principles to determine the corresponding flows and, from a heat balance, the fluid temperatures. Such a simplified analysis of what, in practice, are very complicated flow systems inevitably requires an input of empirical coefficients to define the flows, especially coefficients of discharge for the controlling restrictions in the rotating flows. There is a substantial amount of published data from deeper wheelspaces that yield a remarkably self-consistent set of coefficients. These are used to compare the predicted performance of sealing systems with observations, taking account of conditions in the external mainstream, including the effect of pressure perturbations and results from a full turbine stage. Similar predictions are made for stator wells, on which there is little relevant published information, although the critical flow parameters are apparent from the analysis.