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Picture: Courtesy, United Technologies Corporation, Pratt&Whitney GESP.

As a thumb rule, the takeoff maximum thrust available must be around 30% of the gross weight. Here it means that the thrust must be 204,000 lbs. For airliners, takeoff is the most demanding thrust condition, so it drives the selection of the engines.

There are several ways to get the 204,000 lbs. We can't use just one engine: there are none big enough, and we certainly don't want to worry about what happens if it quits. We also don't want to use a large number of engines, because this would greatly increase the complexity, and add all the weight of those parts which must be duplicated for each engine. Modern airliners use 2, 3 or 4 engines, and the trend appears to be towards using just 2 engines if possible.

Some new engines are:

Pratt & Whitney 4084: Rated thrust of 77,200 lbs.

Pratt & Whitney 4090: 90,000 lbs.

http://www.pratt-whitney.com/gesp/gov.html

From P&W, GESP

General Electric GE90: 90,000 lbs.

Rolls-Royce Trent 890: 90,000 lbs.

If we go for any of these, we will have to pich two of them plus a third engine, or face an unhappy prospect of an underpowered airliner.

We will select the UGA-98, rated at 110,000 lbs, and use two of them. This engine is expected to be available by the Year 2007, well in advance of the roll-out date of the GT2010. Now before we go further, lets see how jet engines work.

Jet engines work using the Gas Turbine Cycle, a process which consists of the following 4 steps:

Air enters the engine at pressure P₁, and is compressed to a very high pressure P₂. This is done by doing work on the air using the rotating blades of a fan and a compressor. The temperature also rises as the air is compressed.

For the GT2010, we will assume that this Overall Pressure Ratio is 50.

2) Heat addition:

Heat is aded to this high-pressure air by burning fuel in it. The pressure remains constant, and the temperature rises to a high level (the highest in the engine), called the "Turbine Inlet Temperature". This temperature is controlled by varying the amount of fuel added. If the air temperature stays higher than this for extended periods, the turbine blades will get weakened and may fail. On modern military engines, this temperature may be more than 2000K. For the UGA-98, we are going to assume that the Turbine Inlet Temperature is 2100K at the maximum thrust condition.

3) Expansion and Work Extraction

The hot, high pressure air is allowed to blow out through a turbine, and then a nozzle. The turbine is forced by the air to spin at high speeds, driving the compressor and fan. This takes work out of the air, lowering its pressure and temperature. Some engines have a propeller, instead of a fan. The air then blows out a a jet, with a velocity u_E and static pressure P_Exhaust = P_A.

To complete the cycle, we must consider the cooling of air (constant-temperature heat release) in the atmosphere before the next jet aircraft comes along and gulps it in. However, since we don't directly pay for this step inside the engine, we don't consider it much.

Thrust

Thrust is calculated using Newton's Second Law of motion.

Let's say that the flight speed of the aircraft (and thus the engine) is U_a. So, the engine gulps in

kilograms per second, moving at u_a with respect to the engine. It adds

kilograms of fuel per second. All of this mass blows out of the exhaust at u_E meters per second.

So we see that the function of the jet engine is to increase the momentum of fluid passing through it. There are many ways of doing this. You don't have to pass all of the air through the "core" of the engine where the fuel is burned and the turbine is placed. Enough air must go through the core to add heat and drive the turbine so that it drives the compressor, and the fan or propeller. The air going through the fan or propeller also gets accelerated; this is called the Bypass air.

In the case of rockets, we also have to consider the "pressure thrust" in addition to the "momentum thrust". The exhaust of a rocket comes out highly supersonic, and expands down to the atmospheric pressure, which may be very low or even zero if the rocket is at a high altitude or in outer space. When the exhaust is supersonic, (meaning flowing faster than the speed of sound) there is no way for the "news" to propagate into the nozzle on what the ouside pressure is, so the exhaust jet will not adjust to this pressure before it comes out of the nozzle exit. The pressure thrust is basically the force due to the difference in pressure between the exhaust plane and the outside, acting on the exhaust area. Also, in the case of the rocket, there is no incoming mass flow rate: the mass flow rate going through the nozzle is entirely composed of fluid which originated inside the rocket.

This is a rocket engine from United Technologies Corporation's Chemical Systems Division. As seen below, the rocket engine consists of the pumps to take the fuel and oxidizer from the tanks (see the orange thing in the picture above), a combustion chamber, a section which converges down to a narrow "throat", and then a large expanding nozzle where the flow becomes faster than the speed of sound. The fuel-oxidizer mixture thus starts out at zero velocity with respect to the vehicle (since it is carried on board), and is then accelerated to a high exhaust velocity. There is thrust produced by this change in momentum, and there is also thrust produced when the supersonic exhaust flow encounters the outside environment, where the pressure may be much lower. We can group these two sources of thrust together, divide the total by the mass flow rate of gas exiting the nozzle, and the result has units of velocity. We call this the "effective exhaust velocity", c_E.

Here the air is allowed into the engine through an intake, while the ramjet is flying a a high Mach number (typically above 0.6, mostly supersonic, up to Mach 8.). As the air slows down inside the engine, its pressure goes up, and since the Mach number is so high, the pressure rise is very large. Thus without using a mechanical compressor, a high pressure ratio is achieved. The air is added to the fuel inside the engine and heat is released by burning. The hot high-pressure gases are exhausted through a nozzle. Since the flight speed is supersonic, the exhaust Mach number is also supersonic. Hence, like the rocket engine, the exhaust pressure here too will probably be different from the ambient pressure, so that there is a large pressure thrust term.

Obviously, a pure ramjet engine cannot start from rest and accelerate: at rest there is no compression. Typically, ramjets are used as a second stage of an engine which starts out either as a turbojet (as in the case of the SR-71) or as a rocket, as in the case of some missiles. One interesting type of hybrid engine is one where the vehicle starts out using a solid rocket engine and accelerates to a speed where the ramjet can start operating. As the rocket propellant burns, space is opened up in the combustion chamber, and intake doors are opened to allow air to come in. Liquid fuel may be injected into the combustion chamber to continue the ramjet mode of operation, and to provide better control of thrust.

http://www.pratt-whitney.com/gesp/gov.html

The figure above shows the stations and nomenclature which we will use in the following analysis.

where the pressure thrust term is only active when the engine is operating at high Mach numbers and high altitudes where the exhaust is supersonic.

The aircraft above has Turboprop engines, where the majority of the work extracted from the flow by the turbine is fed to a gearbox (to reduce the rotational speed down to propeller speeds), and then used to run a propeller.

Some Notes on Engine Design

1. Thermodynamics shows that the efficiency in converting heat to work is highest when the heat is added at the highest possible pressure.

. Hence modern engines have high Overall Pressure Ratio P_B/P_A. Even when this ratio is 40, note that the thermal efficiency, as computed above, is only 65%.

2. The Propulsive Efficiency measures the efficiency in converting the kinetic energy of the fluid (air) to thrust.

. This is maximized by driving the exhaust velocity as close as possible to the flight speed u.

Specific fuel consumption of an aircraft (SFC) is the fuel consumed per distance traveled. Obviously, we want SFC and TSFC to be as small as possible.

We see that thrust is produced by gulping in air and accelerating it. Thrust is proportional to the mass flow rate of air, and to the velocity difference produced by the engine. Now, mass flow rate is proportional to the distance traveled per unit time, and to the density of the air, and to the area of the "streamtube", the air inside which is ingested into the engine.

As we go up in the atmosphere, the density decreases. So, for a given flight speed, thrust decreases as altitude increases. This rate of decrease is called the thrust lapse rate.

Specific Fuel Consumption changes mainly with speed for a given aircraft.

From the data given in the text by Shevell (p. 338-339), the following empirical expressions can be developed for large turbofan engines of the type envisaged for the GT2010:

Thrust Lapse Rate:

Thrust at altitude = (Static Thrust at sea-level) *(0.45-0.17*10^-4*(altitude-5000)), altitude in meters.

Below 5000 meters, if you don't have any better data, assume that the thrust varies linearly, as follows:

Calculate the thrust at 5000 meters using the above formula. Then, use the following expression:
Thrust at a given altitude = [thrust at sea-level] - [(thrust at sea-level - thrust at 5000meters)]*[altitude/5000].

The variation of thrust with Mach number is milder than the variation with altitude. The expression is not monotonic (i.e., it does not just keep increasing, or keep decreasing, with increasing Mach number), so it is not attempted here.The variation can be calculated quite easily using the Propulsion course material (click on the Propulsion course from the list at the very beginning of the Introduction Page), but don't try it without learning the thermodynamics and "isentropic flow" material in that course.

Specific Fuel Consumption (sfc) = 0.55 + (0.65 - 0.4)/0.35*(M-0.3) for 0.3< M <0.85

This expression is obtained using the data in Shevell for sfc vs. bypass ratio (which is based on 1970s technology) and then reducing the sfc by 10% to aniticipate technology advances.

DESIGN-CENTERED INTRODUCTION TO AEROSPACE ENGINEERING

8. SELECTING ENGINES: INTRODUCTION TO PROPULSION

HOW JET ENGINES WORK

Thrust