Page 74 - Fluid Mechanics and Thermodynamics of Turbomachinery

CHAPTER 3

Two-dimensional Cascades

Let us first understand the facts and then we may seek the causes. (ARISTOTLE.)

Introduction

The operation of any turbomachine is directly dependent upon changes in the
working fluid’s angular momentum as it crosses individual blade rows. A deeper
insight of turbomachinery mechanics may be gained from consideration of the flow
changes and forces exerted within these individual blade rows. In this chapter the
flow past two-dimensional blade cascades is examined.
A review of the many different types of cascade tunnel, which includes low-speed,
high-speed, intermittent blowdown and suction tunnels, etc. is given by Sieverding
(1985). The range of Mach number in axial-flow turbomachines can be considered
to extend from M D 0.2 to 2.5 (of course, if we also include fans then the lower
end of the range is very low). Two main types of cascade tunnel are:

(1) low-speed, operating in the range 20 60 m/s; and
(2) high-speed, for the compressible flow range of testing.

A typical low-speed, continuous running, cascade tunnel is shown in Figure 3.1(a).
The linear cascade of blades comprises a number of identical blades, equally spaced
and parallel to one another. A suction slot is situated on the ceiling of the tunnel
just before the cascade to allow the controlled removal of the tunnel boundary layer.
Carefully controlled suction is usually provided on the tunnel sidewalls immediately
upstream of the cascade so that two-dimensional, constant axial velocity flow can
be achieved.
Figure 3.1b shows the test section of a cascade facility for transonic and moderate
supersonic inlet velocities. The upper wall is slotted and equipped for suction,
allowing operation in the transonic regime. The flexible section of the upper wall
allows for a change of geometry so that a convergent divergent nozzle is formed,
thus allowing the flow to expand supersonically upstream of the cascade.
To obtain truly two-dimensional flow would require a cascade of infinite extent.
Of necessity cascades must be limited in size, and careful design is needed to ensure
that at least the central regions (where flow measurements are made) operate with
approximately two-dimensional flow.
For axial flow machines of high hub-tip ratio, radial velocities are negligible and,
to a close approximation, the flow may be described as two-dimensional. The flow in
a cascade is then a reasonable model of the flow in the machine. With lower hub-tip
radius ratios, the blades of a turbomachine will normally have an appreciable amount
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