Some problems in viscous gas flow in turbomachinery - Viscous and heat-transfer terms, and methods for solution of basic equations

The incorporation of viscous and heat-transfer terms in the equations of 3D flow in turbomachines is analyzed. The viscous terms of the momentum and energy equations are introduced, including viscous stress tensor, strain tensor, stress-strain relation, viscous forces, the rates of work done by viscous stresses and dissipation function, and the heat-transfer term. The simplifications of these terms corresponding to the 3D problem, S1 and S2 stream-surface flow, an annulus wall boundary layer, and a 3D boundary layer on a rotating blade surface are presented; the tensor, differential, and integral forms of the 3D aerothermodynamical equations of viscous flow are obtained; and solution techniques are indicated.