The expression is simplest in the case of a rocket operating outside the atmosphere. In this case, the thrust is simply given by:
where Ve is the exit velocity of the exhaust flow. The exhaust gases may be the by-products of the rocket fuel combustion, or just unburned expanded gas, or any other mass. In the case of electric rocket propulsion, small droplets of Mercury or other heavy material are accelerated in an electric field to produce thrust. The fuel (or other mass) flow for a given thrust is minimized by achieving high exit velocities. Typical values of exit velocity are 3000 to 4000 m/s (10000-13000 ft/sec) for liquid propellant rockets.
There is a large advantage to be gained if one does not have to carry all of the mass used to generate thrust. This can be seen by examining the total energy required to produce the change in momentum. The rate of change of energy is given by:
Thus, to produce the most thrust with the least energy consumption, it is best to do so with a large value of dm/dt and a small change in U. This is because the energy required varies with U2 while the momentum change is linear in U. This basic principal applies to many systems. It is why helicopters have large diameter rotors, wings need large spans, and propellers are more efficient than jets at low speeds. This concept serves to distinguish the several types of propulsion systems, as discussed in the following sections.
Ambient air can be used, not only to provide oxidizer for burning fuel, but also as a source of mass. This is done most simply in the ramjet engine.
The ramjet has no moving parts. High speed air enters the inlet, is compressed as it is slowed down, is mixed with fuel and burned in the combustion chamber, and is finally expanded and ejected through the nozzle. For the combustion process to be efficient, the air most be compressed sufficiently. This is possible only when the freestream Mach number exceeds about 3, and so ramjets have been practical for only a few missile applications. A hybrid engine, part turbojet, part ramjet, was also used on the SR-71 high speed reconnaissance aircraft and is a topic of current research interest for several possible hypersonic applications.
When additional compression is required of the intake air, a separate compressor may be added to the ramjet as shown in the figure below. A single-stage centrifugal compressor was used until about 1953. Such a compressor could produce an increase in total pressure of about 4. More modern axial compressors can produce overall pressure ratios (OPR) of about 8.5 with a single stage and by including several stages of compression, pressure ratios of 13 have been achieved on turbojet engines. For the turbofan designs discussed in the next section, the multi-stage compressors achieve pressure ratios of 25-30, enabling efficient operation at subsonic speeds.
In order to power the compressor, a windmill is placed in the engine exhaust-in principal that is what the turbine stage does. The turbine is located downstream of the combustor and is connected to the compressor blades with a shaft. It extracts power from the flow in the same way that a windmill extracts power.
Increased efficiency at low speeds requires that the mass of air affected by the engine be increased. However, for a given rate of fuel burned, there is a corresponding mass of air that should be mixed with the fuel and one cannot simply force more air through the combustor. Instead, one may route some of the air around the combustor and turbine, and so bypass the engine core. Engines are characterized by their bypass ratio (BPR), the ratio of mass flux bypassing the combustor and turbine to the mass flux through the core. Engines with bypass ratios of 0 are called straight jets or sometimes turbojets. Engines with bypass ratios of 1 to 2 are generally termed low bypass ratio turbofans. High bypass turbofans found on most current transport aircraft have BPR's of 5-8. It is sometimes necessary to drive the first few stages of the compressor (fan) at a slower speed than the high pressure stages, so twin-spool engines or even triple spool engines (three separate shafts from turbine to compressor stages) are common. Gearing between the turbine and fan stages is also possible to provide more optimal fan performance. More detail is shown in the figures on the following pages.
The figure below shows a Pratt and Whitney 4084 engine used on the 777. The diameter of this 84,000 lb thrust engine with nacelle is only somewhat smaller than the diameter of a 717.
When the bypass ratio is increased to 10-20 for very efficient low speed performance, the weight and wetted area of the fan shroud (inlet) become large, and at some point it makes sense to eliminate it altogether. The fan then becomes a propeller and the engine is called a turboprop. Turboprop engines provide efficient power from low speeds up to as high as M=0.8 with bypass ratios of 50-100.
One can increase the efficiency of turbofans from their current values of 35% - 40% to values close to 45% by further increasing the bypass ratio. Advanced designs with bypass ratios of 12-25 are sometimes termed advanced ducted propellers or ADP's. Although the propulsive efficiency of such designs is very high, they are often less desirable than the engines with more moderate bypass ratios. This is due to the difficulties of installing these very large diameter engines, especially on low-wing configurations, and on the weight and drag penalties associated with the large duct.
An unusual ADP with the fan located aft and attached directly to the turbine. Note the stator vanes in both turbine and fan sections to reduce swirl losses.
A counter-rotating prop-fan. At some value of bypass ratio, the advantages associated with the duct are overwhelmed by the weight and drag of the duct itself. Bypass ratio 50, ductless propfans such as the one shown here have been proposed for aircraft that fly up to Mach 0.8.
It is possible, of course, to power the propeller by any available means, from turbine to piston engine, electric motor to rotary engine, rubber bands to human muscle. In many of these cases, the bypass ratio is infinite. Very high efficiency especially at low speeds is possible, although as the propeller diameter is increased, installation issues become more severe.
The following discussion from Boeing describes the recent thrust of engine development work for the high speed civil transport (HSCT).
Some additional information on current supersonic engine development efforts from NASA Lewis follows:
Data on several specific engines is provided in the section on engine performance. Links to manufacturers' sites are provided in that section as well.
One of the questions to be answered early in the conceptual design stage is how many engines will be desirable. The recent trend is definitely toward fewer engines, with twin engine aircraft becoming the most popular design. This has become possible for larger aircraft as the thrust of engines has climbed to levels that were nearly unimaginable not long ago. 100,000+ lb sea level static thrust engines are now available.
The interest in large twin engine aircraft come from the greater economy afforded by using fewer engines. Current engine prices are such that it is less expensive to obtain a specified sea level static thrust level with two large engines than with three or four smaller ones.
However, when more engines are used, the system is more reliable. And it is not just the propulsion system that is more reliable. When additional electrical generators or hydraulic pumps are available, overall system reliability is improved. However, it is more likely that at least one engine will fail.
These considerations limited the use of twin engine aircraft for long flights. The U.S. operating rules limited two and three engine aircraft to routes over which the airplane could not be more than 60 minutes from an alternate airport after an engine had failed. In 1964, three-engine turbine-powered aircraft were exempted from this rule. More recently, the FAA approved extended range operations for twin engine aircraft requiring that the aircraft stay within 120 minutes (with engine failure) of an appropriate airport and 180 minute ETOPS are becoming more common.
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