AXIAL FLOW
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`COMPRESSORS
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`Fluid Mechanics and Thermodynamics
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`J. H. HORLOCK
`M.A., Pn.D., A..\I.X.M£cu.E., A.F.R.Az.S.
`Utu'nem'l; Ltcturer in Enginzering
`Cambridge Unirrrrily
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`.2-Q.--QJ,
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`LONDON
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`BUTTERWORTHS SCIENTIFIC PUBLICATIONS
`1953
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`UTC-2018.001
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`GE v. UTC
`Trial IPR2016-00952
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`Butterwonln Publications Limited
`1958
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`Printed and bound in Gun: Britain by
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`UTC-2018.002
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`Chapter 2
`TWO-DIMENSIONAL CASCADES: THEORETICAL
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`2.0
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`Irrmonucnou
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`ANALYSESOFPERFORMANCE
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`In ‘run development of the highly eflicient modern axial flow compressor,
`the study of the two-dimensional flow through cascades of aerofoils has
`played an important part. For compressors in which the ratio of hub radius
`to tip radius is large, the flow through a row of blades may be considered as
`approximately two dimensional, as radial velocities will always be small
`and the cascade is a close model of the flow in the machine. For compressor
`staga of lower hub-tip ratio, blades will be twisted along the length to
`accommodate the radial variations in flow, but
`information from two-
`dimensional cascades is still useful
`to the designer in analysing the flow
`through each section of the blading in such stages.
`Several attempts have been made to analyse the two-dimensional potential
`flaw through cascades of aerofoils. and these are detailed in this chapter.
`Much experimental
`testing of cascades has also been undertaken. and
`several empirical correlations of the tut data have been made. These
`correlations are given in Chapter 3.
`The nomenclature and the basic aerodynamic terminology used in both
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`aspects of this cascade work are tabulated below.
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`2.1.1 Cascade nomenclature and terminology
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`2.1
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`CASCADE Panronuaxca
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`Figure 2.1, which is reproduced from Howell's early paper“ on cascade
`theory and performance, shows the standard nomenclature. related to
`aerofoils in cascade, which is used in both Chapters 2 and 3.
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`In British practice the cascade aerofoil is built up around a basic camber
`line which is usually a circular or parabolic arc. The profiles used in
`British designs are termed the C series of aerofoils” and Table 2.1 gives
`thickness versus length along the chord line for one of these aerofoils {C2 .
`Cascade geometry is then decided completely by the aerofoil specification,
`the stagger (7) and the space-chord ratio (3/1). The aerofoil nomenclature
`is best illustrated by an example.
`l2C-‘l/35 P30 denotes an aerofoil for which the maximum thicltness—chord
`ratio (1/1) is 12 per cent, C4 denotu the base profile, 35 is the camber angle
`in degrees, F denotes a parabolic are camber line. and 30 is the percentage
`of the chord from the leading edge where maximum camber occurs.
`29
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`UTC-2018.003
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`CASCADES: EXPERIMENTAL WORK
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`nearer the ‘negative’ stalling (‘choking’) limit at design operating conditions,
`in order to obtain more flexibility ofl'-design.
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`Solidily - I],
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`Fife: 3.10. Design angles of attack (I, — 7) for NACA65-Ieria.
`(
`J. Herrig, J. C. Emery and J. R. Erwin". Cantu; NACA)
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`3.4 Connaunoxs or THE Errrrzcr or MACH Ntnnnrt
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`As the entry Mach number to a given cascade is increased at a given
`incidence so the pressure rise across the cascade falls off. Figure 3.1] shows
`the beginning of this drop in pressure rise at the critical Mach number 111.,
`(when the maximum local Mach number in the cascade reaches unity).
`At
`the maximum entry Mach number M.__ the cascade is fully choked.
`Howell has attempted to correlate the drops in efficiency and deflection in
`terms of a relation between the operating Mach number M, and the
`critical and maximum Mach numbers
`[(M, — M.,)/(M._, — M.,)]
`(Figure 3.12).
`Using this correlation, curves similar to Figure 3.11 may be drawn for
`each incidence. Figure 3.13 shows how M.‘ and M._, vary with the throat
`-area-inlet area ratio, which may be calculated for a given cascade at each
`incidence.
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`Thus for a given cascade operating lines may be plotted on graphs of
`a,—M,, showing the limit of efficient operation (positive and negative
`stalling) (Figure 3.14). Within the envelope the cascade is unstalled. Such
`graphs are important in the analysis of blade flutter.
`The work of Carter” and Andrews‘ indicates in general that efiicient
`operation at higher Mach numbers can be obtained by moving the maximum
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`UTC-2018.004
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