# Equilibrium operating performance of axial-flow turbojet engines by means of idealized analysis Page: 2 of 12

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REPORT 987--NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

V velocity, feet per second f

V, compressor-blade-tip velocity, feet per second

'W mass flow, slugs per second

7 ratio of specific heat at constant pressure to specific

heat at constant volume

8 ratio of compressor-inlet absolute total pressure to

NACA standard sea-level absolute pressure

? efficiency

0 ratio of compressor-inlet absolute total temperature

to NACA standard sea-level absolute temperature

p mass density, slugs per cubic foot

0b pressure coefficient

Subscripts:

b burner

c compressor

j jet

n nozzle

r ram

t turbine

0 ambient

1 compressor inlet

2 compressor outlet

3 turbine inlet

4 turbine outlet

5 nozzle outlet

ANALYSIS

DESCRIPTION OF COMPONENT MODELS

In order to establish theoretical equilibrium operating con-

ditions, the performance of each engine component must be

described. The descriptive equations for each component

and the development of the analysis are given in the appen-

dix. The principal equations of the analysis are described

in the following paragraphs.

. . . . . . ... ... . . .=.Compressor.-The development of the analysis requires

that a simple expression for compressor mass flow be known.

The ratio of inlet-air velocity to compressor-blade-tip veloc-

ity K, for axial-flow compressors has been found to be

approximately constant, particularly at or near design speed.

Hence, with the use of this relation, the following expression

for compressor air flow WT' can be developed:Po c =KMc(rr) ly

PO WT(1)

The power to drive the compressor may be expressed as

550 C"' --) -70-

(2)

Turbine.-In order to obtain a simplified expression for

the gas flow through the turbine W,, the turbine and the

turbine nozzle were considered similar to a simple channel of

varying cross section. The expression for It is then written

as .

P0 o -'jiAtT r

(3)The turbine power may be expressed as

.lhp,=- 5 - q RT3, 1(4)

(Herein,- A is the turbine minimum-passage area.)

Exhaust nozzle.-The exhaust nozzle is described in the

same manner as the turbine and the equation for the flow

through the exhaust nozzle becomes2,

Po- (.--1)R-~.L' . rKr

(r,) 2,EQUILIBRIUM PERFORMANCE

The assumptions are now stated and all descriptive equa-

tions are combined to define equilibrium operating perform-

ance of the complete engine.

Assumptions.-Equation (3) is used as an approximation

for W, in order to avoid complications in the equilibrium

analysis. For low-reaction turbines and turbines operating

at or near choking conditions, the approximation is of suffi-

cient accuracy. A further assumption made using equation

(3) is that the turbine pressure ratio used in calculating

equilibrium performance is considered to be the total-

pressure ratio from the inlet to the outlet of the turbine. The

turbine pressure ratio in equation (3) should be the total-to-

static pressure ratio across the turbine; however, the error

in this assumption is small. Figure 1 shows the magnitudeof error in using r, as the total-to-total pressure ratio in the

expression

rather than the total-to-static pressure. The error reaches

a maximum of about 5 percent at low values of r,. If a

more accurate solution is required, a factor Ccan be included

in equation (3), as shown, to correct the erior.

The burner pressure ratio rb appearing in equations (3)

and (5) represents a measure of the pressure drop in the

burner. In order to make the equations as simple as pos-

sible, this pressure ratio was included rather than a more

complicated equation for the loss.(5)

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Sanders, John C & Chapin, Edward C. Equilibrium operating performance of axial-flow turbojet engines by means of idealized analysis, report, January 1, 1950; (digital.library.unt.edu/ark:/67531/metadc60326/m1/2/: accessed September 26, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.