Equilibrium Operating Performance of Axial-Flow Turbojet Engines by Means of Idealized Analysis Page: 3 of 12
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EQUILIBRIUM OPERATING PERFORMANCE OF AXIAL-FLOW TURBOJET ENGINES BY MEANS OF IDEALIZED ANALYSIS 675
.U .n .16 .2o .24 .2
Tur-bine- -total- o-stao c -pressure - rotio pa rnefer
k I4 I' - '-r _ 4 + Va
1.-ReIation between turbine-total-pressure-ratio parameter and total-to-static-
pressure-ratio parameter. Turbojet engine A.
The areas A, and A, in equations (3) and (5), respectively,
are effective flow areas rather than actual passage areas.
These areas were calculated using equations (3) and (5) and
observed engine data. Experimental variation from average
values of A,/A, for two engines is plotted against engine
speed N in figure 2.
In the development of equation (5), the turbine-outlet
temperature T4 was determined assuming the turbine
temperature drop to be isentropic. Thus, the turbine-outlet
temperature us&d in the theoretical calculations is somewhat
lower than the actual temperature. The error involved in
making this assumption, however, is small and can be
neglected. (See reference 3.)
Equilibrium.-In order to establish equilibrium operation
of a turbojet engine, two general conditions must be satisfied.
The compressor air flow plus fuel flow must equal the gas
flow through the turbine and the exhaust nozzle, and the
power delivered by the turbine must equal the power neces-
sary to drive the compressor. In this analysis, no air is
assumed to leave the system and no mechanical losses are
assumed to be incurred. From these relations and the five
equations developed from the component-model analysis,
equations may be developed that define equilibrium perform-
ance of the complete turbojet engine.
Equating the two expressions for mass flow (equations (1)
and (3)) and the power expressions (equations (2) and (4))
provides two separate expressions for the compressor pressure
ratio r,. The equation for equilibrium operation can be
determined by setting the two equations for r, equal to each
With the assumption of constant values for r,, -,, and r
and with r, held constant for any one series of calculation
equation (6) expresses the speed parameter -tfKl ,MK,
as a function of the temperature parameter f(T/To)q,'
The turbine pressure ratio r, can be combined with r, an
the quantity rjr, plotted against functions of engine speed
and temperature to indicate the pumping capacity of an
In this analysis, however, it is of more interest to develop
a correlation of nozzle-to-turbine minimum-passage-arE
ratio A,/A, as a function of engine speed and temperatur
C 7' ( 7']3 t
L A (r,) 2 2Y
Hence, by combination of equations (3) and (5), the following
expression for A,/A, can be developed in terms of r,:
A (r,) ",1
2%Y - 2
A '+1__ 2
7-'= F +t
After the equilibrium operating conditions have been
established, the analysis can be expanded to provide specific
performance figures. As an example, an expression for engine
net thrust per unit turbine area F/PA, is developed in the
appendix. The final expression for this quantity is given in
the following equation:
F (V 2cf I yt 3
lye 'yfy- T0
7rt-1 7 -
GENERALIZED EQUILIBRIUM CHARTS
ture parameter f T ,ll for three values of A/A, and two
Equilibrium operating lines.-The general solution of the tauesthA
equilibrium equations is shown in figure 3 in which the speed values of r,.
E-perimental data indicated that the pressure loss in the
parameter KL, is plotted against the tempera- burner had to be accounted for in establishing correct equi-
As \c 1)/ librium performance. The average value of pressure ratio
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Sanders, John C. & Chapin, Edward C. Equilibrium Operating Performance of Axial-Flow Turbojet Engines by Means of Idealized Analysis, report, February 25, 1949; (digital.library.unt.edu/ark:/67531/metadc60326/m1/3/: accessed December 16, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.