Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

68 Fluid Mechanics, Thermodynamics of Turbomachinery
FIG. 3.10. Apparent flow angle variation measured by three different combination
probes traversed across a transverse variation of total pressure (adapted from Bryer
and Pankhurst 1971).
probe instruments are subject to this type of directional error when traversed across a
total pressure variation such as a blade wake.
An extensive bibliography on all types of measurement in fluid flow is given by
Dowden (1972). Figure 3.11 shows a typical cascade test result from a traverse across
two blade pitches taken by Todd (1947) at an inlet Mach number of 0.6. It is observed
that a total pressure deficit occurs across the blade row arising from the fluid friction
on the blades. The fluid deflection is not uniform and is a maximum at each blade trailing
edge on the pressure side of the blades. From such test results, average values of
total pressure loss and fluid outlet angle are found (usually on a mass flow basis). The
use of terms like total pressure loss and fluid outlet angle in the subsequent discussion
will signify these average values.
Similar tests performed for a range of fluid inlet angles, at the same inlet Mach
number M1 and Reynolds number Re, enables the complete performance of the cascade
to be determined (at that M1 and Re). So as to minimise the amount of testing required,
much cascade work is performed at low inlet velocities, but at a Reynolds number
greater than the “critical” value. This critical Reynolds number Rec is approximately 2
¥ 10 5 based on inlet velocity and blade chord. With Re > Rec, total pressure losses and
fluid deflections are only slightly dependent on changes in Re. Mach number effects
are negligible when M 1 < 0.3. Thus, the performance laws, eqn. (3.28), for this flow
simplify to
(3.28a)