Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

200 Fluid Mechanics, Thermodynamics of Turbomachinery
complex three-dimensional, compressible flows in compressors with varying hub and
tip radii and non-uniform total pressure distributions were found to have become too
unwieldy in practice. In recent years advanced computational methods have been successfully
evolved for predicting the meridional compressible flow in turbomachines
with flared annulus walls.
Through-flow methods
In any of the so-called through-flow methods the equations of motion to be solved are
simplified. First, the flow is taken to be steady in both the absolute and relative frames
of reference. Secondly, outside of the blade rows the flow is assumed to be axisymmetric,
which means that the effects of wakes from an upstream blade row are understood
to have “mixed out” so as to give uniform circumferential conditions. Within the
blade rows the effects of the blades themselves are modelled by using a passage averaging
technique or an equivalent process. Clearly, with these major assumptions, solutions
obtained with these through-flow methods can be only approximations to the real
flow. As a step beyond this Stow (1985) has outlined the ways, supported by equations,
of including the viscous flow effects into the flow calculations.
Three of the most widely used techniques for solving through-flow problems are:
(i) Streamline curvature, which is based on an iterative procedure, is described in some
detail by Macchi (1985) and earlier by Smith (1966). It is the oldest and most
widely used method for solving the through-flow problem in axial-flow turbomachines
and has with the intrinsic capability of being able to handle variously shaped
boundaries with ease. The method is widely used in the gas turbine industry.
(ii) Matrix through-flow or finite difference solutions (Marsh 1968), where computations
of the radial equilibrium flow field are made at a number of axial locations
within each blade row as well as at the leading and trailing edges and outside of
the blade row. An illustration of a typical computing mesh for a single blade row
taken from Macchi (1985) is shown in Figure 6.14.
Radius, r (cm)
20
15
10
L.E.
L.E.
T.E.
T.E.
0 5 10 15
Axial distance, Z (cm)
FIG. 6.14. Typical computational mesh for a single blade row
(adapted from Macchi 1985).