SPECIFIC ENGINE CHARACTERISTICS AND PERFORMANCE

For illustrative purposes, this section will consider the characteristics and performance of specific engines.

Turbojet

The Pratt & Whitney JT4A-3 engine will be used as an example of a turbojet. This engine, installed on the Boeing 707-320 and McDonnell-Douglas DC-8-20, is a two-spool engine. The low-pressure compressor section has eight stages, with seven stages in the high-pressure section. The turbine has two low-pressure stages and one high-pressure stage. Other characteristics of this engine are presented in Table 6.1. This particular model of the JT4 engine has a takeoff thrust-to-dry weight ratio of 3.15. Later versions of this engine, such as the JT4A-12, develop T/W ratios of 3.58.

Table 6.1 Characteristics of the JT4A-3 Engine

Type—turbojet SSL static thrust

The net thrust and fuel consumption curves for this engine are reproduced from the manufacturer’s installation handbook in Figure 6.32a, 6.32b, 6.32c, and 6.32<f. At this point, a definition of net thrust is needed. To do this we first define gross thrust, Fg, as the product of the mass flow rate in the jet exhaust and the velocity attained by the jet after expanding to ambient static pressure.

Fg = rrijVj

The net thrust, F„, is then defined by

Fn = Fg – niiVж

where m, is the inlet mass flow and V^ is the velocity of the ambient air. For static operation, Fg and Fn are equal.

Net thrust for the takeoff rating of this engine is presented in Figure 6.33a, 6.33b, and 6.33c for speeds of 0, 100, and 200 kt and altitudes from sea level to 14,000 ft.

The curves of Figure 6.32 are for standard atmospheric conditions. One rarely finds a standard day, so it is usually necessary to correct engine performance for deviations from the standard. Without delving into the details of compressor design, one can argue that, for the same flow geometry (ratio of rotor speed to axial velocity and M„), the pressure increase across the compressor can be written as

Дp oc pJV2

where N is the rotor angular velocity.

If Дp is expressed as a ratio to the ambient pressure, then

Д p N2

— a —- 7—

Poo Poo/Poo

or

Др N2

—— oc ——–

Poo Too

Thus, if N denotes the rpm of a compressor operating at an ambient temperature of T„, the rpm required to deliver the same pressure ratio at standard sea level conditions is known as the corrected rpm, Nc, given by

(6.79)

9 being the ratio of the absolute temperature to the standard absolute temperature at sea level.

Similarly, one can say that the thrust, F, must be proportional to Др, or

True airspeed, V, knots Figure 6.32a Pratt & Whitney Aircraft JT4A-3 turbojet engine. Estimated thrust, TSFC, and airflow at sea level. Standard atmospheric conditions, 100% ram recovery. (Courtesy, Pratt & Whitney.)

Figure 6.32b Pratt & Whitney Aircraft JT4A-3 turbojet engine. Estimated thrust, TSFC, and airflow at 15,000 ft. Standard atmospheric conditions, 100% ram recovery. (Courtesy, Pratt & Whitney.)

P<X>9 for a constant pressure ratio. Thus, the corrected thrust, Fc, corresponding to the corrected rpm, is defined by

Fc = j (6.80)

where S is the ratio of the ambient pressure to standard sea level pressure. Similarly, corrected values for fuel flow, airflow, and exhaust gas tern-

Net thrust.

Figure 6.32c Pratt & Whitney Aircraft JT4A-3 turbojet engine. Estimated thrust, TSFC, and airflow at 30,000 ft. Standard atmospheric conditions, 100% ram recovery. (Courtesy, Pratt & Whitney.)

3500

»

True airspeed, V, knots

Figure 6.326 Pratt & Whitney Aircraft JT4A-3 turbojet engine. Estimated thrust, and airflow at 45,000 ft. Standard atmospheric conditions, 100% ram recovery. ^Courtesy, Pratt & Whjtney.)

-60 -40 -20 0 20 40 60 80 100 120 Ambient temperature, T.°F Figure 6.33a Pratt & Whitney Aircraft JT4A-3, -5 turbojet engines. Estimated net thrust on runway during takeoff. Zero knots. (Courtesy, Pratt & Whitney.)

perature (EGT) are defined by

c sVe	(6.81)
w waVe "4 s	(6.82)
EGTC =	(6.83)

A more elegant derivation of these corrected parameters, based on Buckingham’s ж theorem of dimensional analysis, can be found in Reference 6.9.

Excluding scale effects, the important point is made that the corrected thrust of a gas turbine engine is a unique function of the corrected values of N, Wa, and Wf. These, in turn, assure a constant value of the pressure ratio. In practice, the pressure ratio used to monitor the corrected thrust is

referred to as the engine pressure ratio (EPR), defined by

EPR = S£L (6.84)

Pt2

The subscript t refers to the total stagnation pressure, the 7 and 2 refer to the engine stations shown in Figure 6.23. Thus EPR is the ratio of the total pressure at the turbine nozzle to the total pressure at the compressor inlet.

в and 5, used to correct the operating parameters, are also based on the total#temperature and pressure, respectively, at the compressor inlet.

(6.85)

ST2 = — (6.86)

P о

where T0 and p0 are the standard sea level values of temperature and pressure. ‘Assuming 100% ram pressure recovery, (i. e., that M = 0 at station

Figure 6.33c Pratt & Whitney Aircraft JT4A-3, -5 turbojet engines. Estimated net thrust on runway during takeoff. Two hundred knots, 100% ram recovery. (Courtesy, Pratt & Whitney.)

2), вт2 and 5T2 can be calculated from

0T2 = в [1 + (-у – 1) МІІ2] (6.87)

ST2 = 8 [1 + (-у – 1) Mil2yh~’ (6.88)

The operating curves for the JT4A-3 turbojet are presented in Figure 6.34a and 6.34b. Turbine discharge temperature, compressor speeds, and fuel flow are presented in Figure 6.34a as a function of EPR. Figure 6.34b shows the net thrust as a function of Mach number for constant values of EPR. All of the curves presented thus far for the JT4A-3 engine assume 100% ram recovery (no inlet duct loss) and a standard nozzle installation prescribed by the manufacturer. They also assume zero power extraction or compressor air bleed. In. an actual airplane installation, corrections must be made for these factors. The details of these corrections are too lengthy to be presented here.

As an example of the use of the performance curves presented thus far for the JT4A-3 engine, consider its operation at an airspeed of 400 kt at an altitude of 30,000 ft. For the maximum continuous thrust rating, a net thrust of

Corrected net thrust, F„/6am — 1000 lb

Mach number, M

Figure 6.34b Net thrust for the JT4A-3 turbojet. One hundred percent ram recovery, standard exhaust nozzle, no airbleed, no power extraction. (Courtesy, Pratt & Whitney.)

53001b is read from Figure 6.32c. Thus, for this altitude and airspeed,

p – = 17,785

^am

Moo = 0.679

From Figure 6.34b,

EPR = 2.56

It follows from Figure 6.34a that

-7= = 6420 rpm

Vel2

-7== = 8850 rpm

Vet2

= 1550°R

W

—Г = 12,700 lb/hr

where Nt = rpm of low-pressure compressor and turbine, N2 = rpm of high – pressure compressor and turbine, and Kc = correction factor yet to be read from Figure 6.34a. At 30,000 ft, 0 = 0.794 and 5 = 0.298. Equations 6.87 and 6.88 give values of

0(2 = 0.867 5,2 = 0.406

From the preceding 0,2, Tt2 = -23 °С, so that Kc = 0.915. The actual values for the operating parameters can now be determined as

AT, = 5978 rpm

N2 = 8240 rpm *

T,7 = 473 °С

W, = 4718 lb/hr

Now consider operation at standard sea level conditions at this same MaAi number and thrust rating. For this case, V equals 448 kt which gives a net thrust of 10,5001b. From Figure 6.32a. Using the same procedure as that followed at 30,000 ft gives, in order,

EPR = 1.92

Ж

КсЬа

Note that the engine rotational speeds and exhaust gas temperature are approximately the same in both cases. Indeed, if other speeds and altitudes at the maximum thrust rating are examined, Nj, N2, and T,7 values ap­proximately equal to those just calculated are found. Thus the thrust available from a turbojet engine at a given speed and altitude depends on the maximum stress and temperature levels that can be tolerated by the engine materials. As

a result, the net thrust of a turbojet will not decrease with altitude in proportion to the density ratio, as with piston engines. As a rough ap­proximation, one can assume Fn to be proportional to a but, in practice, F„ will not decrease with altitude as rapidly as this approximation predicts. For the example just presented, one might predict a net thrust at 30,000 ft at 400 kt based on er and the SSL value of Fn of 3941 lb. This value is 25.6% lower than the rated value previously noted. To illustrate further the accuracy of the approximation, Figure 6.35 presents the rated maximum continuous thrust at 200,400 and 600 kt as a function of altitude and compares this thrust with that obtained by multiplying the sea level values by a. The approximation to Fn is seen to improve for the lower airspeeds and certainly predicts the proper trend. However, at the higher altitudes, the differences between the thrust curves are significant at all airspeeds.