Assessing Viscous Body Forces for Unsteady Calculations

A strategy has been developed to model the three dimensional unsteady flows through turbomachines subject to non-axisymmetric flow/geometrical conditions such as low order distortions with relatively long length scale unsteadiness, by modelling the viscous effects as local source terms for a coarse computational mesh but not calculating them directly. In general full annulus multirow calculations are required for such flows but currently the computational resources are devoted to resolving detailed viscous flow very close to the walls, which in some cases is not the centre of concern. By avoiding resolving detailed viscous effects the model can accelerate the calculation by at least two orders of magnitude. The method has been illustrated to be able to resolve disturbances down to the blade passing frequency and give good estimates of overall unsteady blade forces due to blade row interactions. Obviously the correct modelling of the viscous body force as source terms in the governing equations is the key for accuracy of such calculations. Different ways of constructing/approximating the viscous body force term are discussed and their adequacy in unsteady flow calculations is assessed. It is found that in general the viscous force is relatively small compared to the total blade force, even smaller the unsteady fluctuation of the viscous force and a simple drag coefficient model is quite adequate to model both time mean and dynamic viscous effects. Whilst for the cases when separations are present variations in the drag coefficient may become large and more detailed modelling may be required.