Analysis of Stage Matching and Off-Design Performance of Multistage Axial-Flow Compressors Page: 7 of 40
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NACA RM E52D07
used as the basic,stage performance. It is important to note that the
pressure ratio remains essentially constant at low flows. An explana-
tion for this phenomenon is indicated in figure 2 which shows a longi-
tudinal section through the compressor. It is believed that a rotor
tip-stall condition at these low flows sets up a reirculating flow,
such as that described in reference 6, which increases in size as flow
is reduced. Thus the decrease in flow, accomplished by a reduction in
the effective flow area, causes the hub stations to continue to operate
at essentially constant flow angles. As a result, the mass-averaged
pressure ratio remains almost constant.
The single-stage-performance curves presented in figure 1 are not
suitable for the stacking method used in the present paper because the
variables involved are a function of compressor size and speed. These
variables must be independent of size in order to apply equally well to
all stages of the compressor. The desired parameters are obtained from
Euler's turbine equation, the continuity condition, and.the velocity-
diagram geometry presented in figure 5.
The temperature rise across the stage is related to the velocity
diagram by Euler's turbine equation; no change in radius is assumed
cJgT = uAve
If the axial velocity is assumed to be constant across the rotor row:
cpJg4T = Uv (tan aR-tan as) (1)
tan aR U Vz tan
If the expression for_ tan R- is substituted into equation (1) and the
terms are rearranged,
U2 =1 U (tan pR + tancas) (2)
Equation (2) indicates that if cS and R are constant, which
is approximately the case for unstalled blade rows, then the ratio of
temperature rise to mean blade speed squared is constant at a fixed
value of Vz/U. A curve of AT/U2 against V/U obtained from single-
stage data is therefore assumed to be constant regardless of rotor
speed. Although the terms of equation (2) are dimensionless and appear
to be satisfactory for the stacking procedure, the variables involved
must be expressed in terms of the performance parameters of figure 1.
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Finger, Harold B. & Dugan, James F., Jr. Analysis of Stage Matching and Off-Design Performance of Multistage Axial-Flow Compressors, report, June 27, 1952; (https://digital.library.unt.edu/ark:/67531/metadc59396/m1/7/: accessed May 19, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.