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More Components: Inlets, Mixers, and Nozzles

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The integration of a gas turbine engine into a functioning jet propulsion engine for an airplane requires more components: inlets and nozzles. For the inlet, the special care exercised to avoid ingestion of boundary layers air is described. The design features of nozzles are described and extended to include discussion of more extreme configurations such as those found on rocket engines.


  • Inlet
  • Mixer
  • Nozzle
  • Nozzle expansion
  • Nozzle throat
  • Choking
  • Supersonic inlet
  • Mixing
  • Rocket staging
  • Specific impulse
  • Airplane range

13.1 Inlets

We return to vortices to see where they play important roles in the operation of a jet engine. One aspect of an engine installation design is reflective of the comments made on the wing design. Recall that a nice rounded leading edge on the wing is desirable to allow for operation over a wide range of angles of attack. That same thinking also applies to the inlet that has to handle air nicely in flight and on the ground where the airplane is almost stationary. At low speed, the stagnation point (line) on the inlet air flow is located on the outside of the nacelle. Near a nacelle’s maximum width, the curious person will find a red line and words to the effect: “don’t stand forward of this line during engine runups on the ground, or else”! The point is to warn persons not to participate in the suction exercised by the engine when it is running on the ground. The roundedness on the inlet parallels the design of a wing at its leading edge. The inlet must manage inlet flow to be uniform in low-speed flight, specifically at high angle of attack or with a cross wind on the runway. The rounded lip allows the entering air flow entry to be relatively uniform. At cruise speed the stagnation line is almost coincident with the foremost highlight of the nacelle, its leading edge if you will. The two stagnation streamlines are shown in Fig. 13.1.

Fig. 13.1
figure 1

Sketch of the flow pattern in and around a subsonic airplane inlet at low speed on takeoff (green streamlines) and at cruise (red). Dashed lines are the stagnation streamlines. The * denotes the inlet throat area. Under all conditions, the flow Mach number at the engine face is about 0.5

13.1.1 An Old Wives’ Tale About Inlets

Descriptions of how a jet engine works are sometimes said to involve the notion that the engine “sucks” itself along to propel the airplane. The reality for an airplane in flight is that nothing could be further from what actually happens. In flight, the purpose of the inlet is to slow the freestream. In this way, the inlet performs part of the compression process. There is no suction involved in its function in a cruise flight condition. The question really has to be centered on the pressure at the engine inlet face. That, in turn, has to do with the flow speed, i.e., the Mach number in that location.

For the sake of argument, one can say that the flow Mach number at the engine face, be that a fanjet or a turbojet is about 0.5. The airflow around the blades requires that under most conditions. Subsonic flight inlet performance is close to ideal, meaning the effect of total pressure losses are minimal. One can say that the flow from the outside world where the pressure is the static pressure to the engine face always preserves the total pressure associated with the flight speed.

At takeoff conditions, the static pressure at the engine face (local M = 0.5) is about 20% lower than the outside (where the local Mach number is near zero), hence air is indeed sucked in. However, during flight, say at M = 0.8, the conservation of total pressure will increase the static pressure at the engine face because the inlet decreases the flow speed. Under such conditions, the pressure at the engine face is about 30% higher—no suction here! At flight conditions like those of a Concorde (M = 2) or the SR-71 (M = 3.2), the pressures at the engine face are about 7 or 40 (respectively) times the static pressure outside, even though these inlets suffer some (minimized by design) loss in total pressure because of the shock waves in the inlet. Certainly, no suction there either! On a supersonic airplane, the inlet does a significant portion of the engine’s necessary compression. On a ramjet engine that is necessarily flown at supersonic speeds, the inlet does all the air compression and the use of rotating machinery is dispensed with altogether in such an engine.

The proper way to attribute performance contribution by the inlet relative to the engine is to discuss the amount of compression done by the inlet and compare that to the amount done by the compressor. One cannot talk about the relative contributions to thrust because inlet, engine, and nozzle work together as a system. It would be a little like talking about the contribution to a runner’s athletic performance by his liver!

In flight, the higher pressures on the inlet do raise hardware design issues. The associated forces have to be taken into account for the mounting hardware that is used to affix the inlet to the engine. Insufficiently strong bolts will result in a forward departure of the inlet and the likely end of proper engine operation. The same pressure forces also play similar roles at the nozzle. High inside pressure and low outside pressure there also require a strong connection between nozzle and engine. The forces associated with that of the restraining bolts have nothing to say about engine thrust (Fig. 13.2).

Fig. 13.2
figure 2

Forces on ancillary engine components. At the engine faces (front and rear) the pressures are higher than outside, hence the bolts holding the inlet and nozzle onto the engine are in tension

The DC-10 inlet in Fig. 13.3 is of a typical design for commercial airliner. The internal surfaces of the inlet handily serve as a sound absorbing liner to reduce noise emissions. The many small holes and the cavities behind them are designed to absorb the noise frequencies associated with the blading behind the inlet. The figure also illustrates the use of a vortex generator on the shoulders of the nacelle to improve the flow over the wing that might have stall issues due to the nacelle ‘shadowing’ the wing at high angles of attack. This vortex generator (there may be two of them in some applications, humorously referred to as “rabbit ears” but technically called a ‘strake’) is very effective at low speed and aerodynamically close to absent in cruise when the external flow aligns itself closely with that of the ‘ears’. In some instances, the strake may also be made effective at improving the flow in the space on either side of the strut and under the wing.

Fig. 13.3
figure 3

The inlet of a DC-10 airliner wing mounted engine nacelle. One of the two “rabbit ear” vortex generators is located at the 11 o’clock position of the cowling

On a subsonic inlet like that shown in Fig. 13.3, the highest local flow velocity is always close to the location where the flow area is a minimum. This area is called the throat. The flow velocity there is close to sonic but nominally subsonic. During operation at takeoff, the velocities there are high enough that the local static air temperature can drop below the dew point so that condensation takes place, just as it may on the upper surface of the wing. Figure 13.4 shows an airliner taking off under such conditions. There is little performance impact by this condensation!

Fig. 13.4
figure 4

A LAN (Argentina) Boeing 767 taking off from Los Angeles. The white “cloud” just inside the inlet is water vapor condensation at the minimum flow area where static temperatures are lowest and, in this case, below the dew point (Photo courtesy Werner Horvath,

13.2 Inlet Geometry and Diverters

On airplanes capable of supersonic flight, the inlet is more complicated. Total pressure recovery, i.e., minimal loss of the total pressure available, is an important design goal. This is a concern from two aspects: total pressure losses through shock waves and flow uniformity if the inlet is located along the fuselage of the airplane. The inlet to a M = 2.2 airplane (Fig. 13.5, a McDonnell F-4) embodies features that deal with these concerns.

Fig. 13.5
figure 5

A McDonnell F-4 in flight showing the shock generation ramp on the inlet and the boundary layer diverter between the inlet and the fuselage (Picture credit: USAF—, curid = 50920146). At right is the Museum of Flight display showing the diverter head-on. Note the small diverter on the scoop at lower right and the inlet instrument probe

The first order is to minimize the losses associated with shock waves. Total pressure losses are minimized when the flow can be made to slow through a series of oblique shock waves rather than a single normalFootnote 1 shock. The flow entering the engines may or may not have gone through the shock wave generated by the nose of the airplane. Typically, a wave is created by a ramp that reduces the flow Mach number by turning the air flow slightly outward. On each engine, the F-4 has such a flow deflecting ramp adjacent to the fuselage. In general, the inlet compression process is improved when the flow is turned by more than one ramp. This is usually employed for airplanes where operating efficiency is at a premium. The Concorde is an example, Fig. 13.6. In that example, the shock generated on the underside of the wing is the first wave encountered by the airflow to the engines.

Fig. 13.6
figure 6

The two-dimensional inlet of the Concorde supersonic airliner. The wave generating ramps (there are two hinged elements for each inlet) are fully retracted in this picture so that maximum airflow is admitted as, for example, during takeoff. The ramp has the word “DANGER” noted. Note also the diversion of the boundary layer air between the top of the inlet and the wing. The boundary layer is thicker on the inboard side of the inlet, hence a wider gap. The boundary layer air from the underside of the delta wing is dumped to the side of the inlets

In the F-4 image, the ramp is not on the body but offset by a few inches. That offset is to address the second aspect of the design of a supersonic inlet: avoid ingestion of the air slowed by the boundary layer on the airplane’s body.

The inlet of the Concorde supersonic airliner is illustrated in a takeoff configuration (photo) and in cruise flight condition (sketch) of Fig. 13.6. There are three wave generating ramps with two hinged elements for each inlet. In the photograph, these are fully retracted so that maximum airflow is admitted as, for example, during takeoff. The keen observer will note doors on the underside of the inlet to discharge excess air or admit additional air when necessary, notably during takeoff. The sketch shows schematically the array of oblique shocks generated by the three deflection surfaces in a cruise configuration. A normal shock will conclude the diffusion process of the supersonic flow. Further slowing of the air takes place in a diverging duct much like that in a subsonic transport engine.

The geometric variability together with the need to control the shock boundary layer interactions required for an inlet designed for supersonic flight is very complicated and involves a costly part of the design process of the propulsion system. This description of the essential features of such inlets is necessarily quite simplified. The reader may wish to consult more detailed descriptions of such inlets, specifically those for supersonic military bombers.

The inlet on a Lockheed F-104 (M = 2) employs (half) an axisymmetric (conical) shock wave to slow the flow (Fig. 13.7). The boundary layer air is also diverted on that airplane. A good example of a whole axisymmetric inlet is that of the SR-71 (M = 3.2) where a conical shock wave is generated on the sharply pointed cone. From there the air enters the internal portion of the inlet and proceeds to encounter a number of relatively weak shock waves. This inlet is also designed to remove the boundary layer air on the internal inlet surfaces by suction on these surfaces to minimize the deleterious effects of shock/boundary layer interactions. These can cause flow separation from the wall much like those discussed in connection with transonic drag rise for a wing.

Fig. 13.7
figure 7

Axisymmetric inlets for supersonic aircraft, F-104 and SR-71. In the lower right background of the SR-71 is a display of a P&W R4360 with its 28 cylinders (Photos taken by the author at the Museum of Flight in Seattle)

In all cases, inlets will complete the diffusion process with a divergent flow section where the near sonic flow is slowed to near M = 0.5 that the engine’s compressor blades can handle.

13.3 Mixing

Internal flow mixing in an engine was carried out in many turbofan engine configurations of modest bypass. The Pratt & Whitney JT8D shown in Fig. 10.2 is a good example. The mixer can be seen at the rear of the engine where fan air and engine core exhaust are mixed. The idea is to create a single, uniform jet stream for expansion by a common nozzle. This design is a follow-on from the earlier P&W J57 engine-based JT3D low bypass engine where the fan flow was directed out of the engine via a separate exit nozzle. The performance of mixed and separate flow configurations is quite similar, except that the mixed flow engine has lower noise emissions. A view of a mixer for a high bypass engine from the rear is shown in Fig. 13.8. The idea is to create a large contact area between the two flows with a wide vortex sheet between them so that mixing takes place rapidly. The differential speeds of the mixing flows generate the vortex sheet that allows the mixing.

Fig. 13.8
figure 8

An internal mixer for engine core flow emanating from “behind” the round central cone with the fan flow originating in the surrounding darker space (Photo by author at the service education facility of General Electric in Evendale, Ohio)

Modern high-bypass and very-high-bypass engines may or may not sport fan/primary flow mixers as the flow rates are quite disparate. The performance advantage gained has to be balanced against the weight penalty of the associated hardware. An example of a separate flow high-bypass nozzle configuration is shown in Fig. 13.10.

A substantial amount of mixing of very hot and cooler flows also takes place in the combustor to achieve acceptable turbine inlet temperatures as described in Chap. 12.

13.4 The Nozzle

The last element of a jet engine is the nozzle where the high-pressure gas produced by the pump that is the engine, expands to atmospheric pressure and in the process, creates the propulsive jet. In its simplest form, a nozzle is a duct of decreasing flow area (a convergent nozzle). This geometry is universally used for turbofan engines where the flow exits the engine with a pressure that is not sufficient to drive the jet to sonic speed. A ratio of total to static pressure (outside) on the order of 1.9 is required to do that. In engines for commercial airliners, the nozzle pressure ratio, as this number is called, is kept to lower values because of the need to avoid the wave generation by supersonic turbulent parts of the flow. This aspect of the turbulent mixing with the freestream is the source of much jet noise in high-speed jets. In fact, in the early turbojet transports, the supersonic flow noise was so severe that extraordinary means had to the employed to minimize it. The approach used then was to force rapid mixing with the freestream air by external daisy petal mixers (Fig. 13.9) and similar devices. Their use imposed a thrust and fuel consumption penalty that had to be borne. The advent of the turbofan obviated the use of such mixers because the jet total pressure was significantly lower.

Fig. 13.9
figure 9

An early turbofan engine on a Boeing 707 (a Rolls-Royce Conway) with a daisy petal mixer that joins the external and the primary core flow of the engine. In this engine, the fan flow exits through two nozzles on the sides of the nacelle. These nozzles are partially obscured in this view but the visible one exits the nacelle between 2 and 4 o’clock positions (The Boeing Company)

Fig. 13.10
figure 10

The (convergent and scalloped) fan flow nozzle exit lip of a commercial airliner, a Boeing 737 MAX. Both core flow and fan flows are partially expanded against the conical, external nozzles (Photo by author at the Boeing assembly plant in Renton, Washington)

The older reader may remember listening to the roar of a 1970s commercial jet taking off. The crackle in the tonal mix was from the supersonic cells interacting with the environment. Some business jets may still be equipped with engines with the higher nozzle pressure ratio and their noise may be enjoyed by those who wish to do so.

External mixing is also done on modern jet engines as, for example, on the Boeing 737 shown in Fig. 13.10. The goal is also to limit the volume of the region where the mixing takes place that is the source of jet noise. This is done by getting the mixing done quickly. The scallops in the trailing edge of the nozzle could also be properly described as vortex generators.

The core flow of the engine shown in Fig. 13.10 expands the jet by means of an external expansion nozzle that is visible as the central cone of that engine (no scallops on the exit lip). An external expansion nozzle operates pretty much as does the axisymmetric inlet, except in reverse: The nozzle accelerates the flow while the diffuser (or inlet) decelerates it. Both devices handle flows that are fairly close to reversible (free of losses). The fan flow in Fig. 13.10 also expands against an external nozzle wall, but to a lesser degree.

This discussion of the nozzle and that of the inlet allows a revisit to the subject of property variations through the entire engine. Specifically, the sketch of Fig. 9.2 can be revisited to show the variation of temperatures and pressures through the jet engine as a system. Figure 13.11 is the earlier figure augmented with the variation of the gas properties through the inlet and the nozzle. The solid lines are of the total values (in the engine reference frame) with the dashed (red and green) lines are an indication of the static values. The static pressure varies from atmospheric value back to atmospheric value, while the higher static temperature in the jet reflects the need to comply with the Second Law of Thermodynamics that requires a certain amount of heat to be wasted. For purposes of this sketch, we consider a simple turbojet rather than a turbofan where two flows would be involved, making for an overly complicated sketch. The variation of the fan flow can be inferred from that through the core engine, without heat addition and without a turbine. Further, to simplify matters in the sketch, the inlet and nozzle flows are taken to be reversible so that the total pressure losses associated in these components are overlooked. In reality, especially in the inlets of supersonic flight airplanes, some total pressure losses would be experienced.

Fig. 13.11
figure 11

Schematic variation of properties through a turbojet with reversible inlet and nozzle flows. The black dotted line establishes the level of static quantities in the air processed by the engine. The solid lines are total quantities in the engine reference frame. The dashed lines describe the variation of static quantities. The letters I … N refer to inlet, compressor, burner, turbine, and nozzle, respectively

A textbook on propulsion nozzles will state that thrust from a nozzle consists of two parts: the momentum of the moving gas and a force resulting from pressure mismatch between atmospheric pressure and the pressure at the nozzle exit plane. The pressure mismatch contribution to thrust is small in jet engines and absent when the jet flow is subsonic because the pressures in question necessarily equilibrate. Hence, we can speak of thrust being largely the momentum term for such nozzles. For propulsion systems in high performance aircraft, the pressure mismatch term does contribute a correction that can be minimized by proper design, but it is safe to say that the momentum term in thrust dominates the performance so that this aspect of thrust can be relegated to being a detail addressed when performance accuracy is desired. For rocket engines designed to fly into space the matter of pressure mismatch is significant as we shall see. For the present, let us stay with jet engines.

13.5 Choking

For military jets that need large amounts of thrust and fly much faster than transonic commercial transports, the nozzles are often designed and operated with a sonic flow in the throat of the nozzle and further expansion in a divergent cone. Such nozzles are called convergent-divergent. The jet from such nozzles is supersonic with a high speed of sound because the gas is hot and it is consequently noisy. Military operations are not as concerned with noise as flight operations at civilian airports are. Often, the engines of military aircraft are equipped with afterburners. When such an afterburner is in use, the exhaust gas is even hotter and lower in density so that the flow limiting throat has to be enlarged to pass the air volume that the engine provides. For this reason, afterburner engines usually have variable geometry nozzles, specifically the throat opening size than can be altered as conditions require.

When the afterburner is in operation, the Mach number of the hot flow in the duct where combustion takes place tends toward M = 1 as heat is released by the burning fuel. Under such conditions a limitation on flow rate may be imposed by thermal chokingFootnote 2 rather than geometric choking set by the minimum flow area or throat. A geometric throat minimum is hardly discernable in Fig. 13.12 on the B-58 engine nozzle displayed in afterburn mode which means that the process of afterburning drives the flow Mach number quite close to unity.

Fig. 13.12
figure 12

Left: The propulsion nozzle of a supersonic B-58 bomber. Note the throat and the divergent cone that is variable in geometry (in both throat and exit areas) to accommodate afterburning. The flame-holders for this device are visible at the far end of the afterburner cavity with enough flow length to the nozzle throat to allow for more-or-less complete combustion of the fuel added (Photo by author at the National Museum of the USAF). Right: On the Space Shuttle ‘Discovery’ at the Udvar-Hazy Center of the Smithsonian National Air and Space Museum, the nozzle throats are near the bulkhead and are roughly one eighth the nozzle exit skirt diameter

Flow choking is a very important aspect of internal flows, i.e., flows through engines. When a flow is choked, the mass flow rate through the area where M = 1.0 is a maximum that can only be influenced by upstream total pressure and total temperature because these two quantities determine the mass density of the gas and the local speed of sound. Specifically, the mass flow rate cannot be altered by lowering downstream pressure because information about the pressure there cannot be transmitted upstream. In practice, choking is a controlling factor in the ability of internal combustion engine’s ability to process air past the valves. It is also a factor in controlling the flow through the gas turbine engine because the turbine nozzle is always choked whereas the primary propulsion nozzle of a jet engine may or may not be. Finally, choking is a central issue in flow through the rocket nozzle.

13.6 More Extreme Nozzles: The Rocket Engine

The requirement for a nozzle area minimum in an air-breathing engine nozzle parallels that for a convergent-divergent rocket engine where nozzle pressure ratios (chamber to ambient) are much greater and the exit to throat area relation is much more pronounced. The three hydrogen–oxygen rockets engines (‘acronymed’ as the SSME, the Space Shuttle Main Engines) on the Space Shuttle illustrate this (Fig. 13.12). The steady pressure in the combustion chamber of these engines is more than two hundred times atmospheric pressure (about 3000 psi). During its ascent flight, the nozzle pressure ratio varies from about 200 at sea level and rises dramatically during ascent. Such high nozzle pressure ratios require a significant divergent nozzle skirt so that as much of the available thrust can be realized by matching the flow pressure at the nozzle exit to the atmospheric pressure. The actual design increased the throat area by a factor of 69 and forced the flow to a jet Mach number of about 5 at the nozzle exit.

13.6.1 Overexpansion

At launch or as illustrated on a test stand (Fig. 13.13), the nozzle is overexpanded. The nozzle skirt expands the flow too much, i.e., it is too long and should have been taken to only about 15 times the throat area. At this condition, the flow must recompress after leaving the exit to match the high atmospheric pressure. This can be seen in the converging boundary of the jet and in the observation of a normal shock wave to bring the flow closer to the relatively high pressure of the environment. Not visible in the picture (because the jet gas is nearly transparent) is that the first (weak) compression wave is a conical oblique shock wave that connects the exit lip of the nozzle and the perimeter of the central normal shock in the image. The normal shock doing the recompression in the middle of the stream is evidently strong because of the greater luminosity behind the shock resulting from the higher static pressure and static temperature (reconversion of kinetic energy to heat!). These static conditions would be those measured by an unfortunate (theoretical) bug were it to make this trip through the nozzle!!

Fig. 13.13
figure 13

The over-expanded SSME on a test stand running with oxygen and hydrogen. The absence of hydrocarbons makes for a beautiful and clear image of the flow (NASA)

13.6.2 Under-Expansion

As the vehicle ascends in the atmosphere, the atmospheric pressure around the vehicle and engine falls, and the need for recompression is diminished. The normal shock seen in Fig. 13.13 will move to the rear and weaken. There will be an altitude where the expansion is just right and matches the flow pressure at the nozzle exit. The nozzle will be perfectly expanded at this point. For the SSME engines, this is estimated to occur at an altitude of about 15,000 feet. As the vehicle ascends further, the (static) pressure at the exit will stay as it was and the flow will have to expand further outside to match the ever lower atmospheric pressure. The nozzle is now under-expanded. A rocket nozzle design for ascent to space must be optimized for this aspect of performance and the important consideration is the engine weight, specifically the weight of the nozzle skirt.

The nozzle pressure ratios when the engines approach shutoff during flight are very large. Near the end of burn, the expansion after the flow leaves the nozzles is dramatic as shown in Fig. 13.14. The picture is of the Saturn V launch of Apollo 11. Such a nozzle is under-expanded in this picture. Ideally one would have wanted the nozzle skirt to be as large as the expanded jet in the image, but that is evidently not realistic. Here, the jet is made visible because the combustion is of a hydrocarbon fuel rather than hydrogen. In a similar view of the Space Shuttle at high altitude and after solid rocket booster burnout, the large external jet would be hard to see because the water vapor (and a substantial amount of hydrogen) jet produced is almost transparent to visible light.

Fig. 13.14
figure 14

The Saturn V rocket in flight carrying Apollo 11. Note the very large width of the jet from an under-expanded nozzle (NASA)

The conical waves that start at the exit lip (Fig. 13.13), both compression shock or expansion waves, are the beginnings of a train of waves that interact with the free boundary and reflect from it in the opposite sense that they impact the boundary. That is, a compression wave will be reflected as an expansion wave and vice versa ad infinitum. Thus, one can imagine the succession of waves in the jet getting weaker as one proceeds further from the end of the nozzle. While it is hard to see this in the image of the Saturn V flight, it is easily observed in an afterburning turbojet (see Fig. 13.15). The picture is of an afterburning Pratt & Whitney J58 on an SR-71 in flight.

Fig. 13.15
figure 15

Over- and under-expansion waves in an afterburning J58 propelling an SR-71 (NASA)

The alternating nature of reflected waves by the free boundary of a jet contrasts to the reflection of waves in a flow with rigid boundaries. There, waves are reflected in kind, meaning that a compression wave is reflected as another compression wave. To some extent this is exploited in the design of high Mach number supersonic inlets where supersonic flow enters the inlet and the internal shape of the inlet causes a series of reflected compression waves to slow the flow as isentropically as practical. Often, although not necessarily, such inlets use an external cone to reduce the flow Mach number from its flight value to something lower where the internal inlet flow completes the Mach number transition to subsonic values. The inlet on the SR-71 shown in Fig. 13.7 illustrates this design approach.

One might wonder whether the addition of further rocket nozzle hardware to take advantage of the high pressure in the flow could be worthwhile. Indeed, it would, but the mechanical complexity of adding more of a nozzle skirt while the rocket is in flight is a challenge that reality might rule out as a solution.

13.6.3 Staging

In practice, this issue is often resolved by staging, i.e., employing a number of series or parallel stages to build a complete rocket. The nozzles can then be designed to operate in an appropriate range of altitudes with acceptable performance. The staging also addresses the concern that a vehicle may be limited in structural strength to a certain level of acceleration. The level of g-forces acting on the structure increases markedly in any ascent to space because the thrust may or may not be reducible as fuel is burned off and the vehicle becomes ever lighter. Further, there is no point to expending power and fuel to haul excess engine thrust capacity and empty tanks to an altitude where they are not needed. To that end, the (parallel) solid propellant boosters (a stage of sorts) of the Space Shuttle were designed to provide a decreasing amount of thrust as they burn during their 125 s of use when they burn out at about 145,000 feet of altitude. The Apollo rocket system is a set of stages in series, meaning they are fired in a sequence after an earlier stage used up its fuel supply.

13.6.4 Specific Impulse and a Little Chemistry

In order to circle back to the discussion of flow along a streamline, a few comments involving the conservation of total enthalpy, are particularly interesting in connection with the function of a rocket engine like the SSME. Expansion of the rocket’s jet into vacuum leads, ideally, to a complete conversion of the total enthalpy along the streamlines to kinetic energy. The velocity associated with that kinetic energy is the momentum (per unit mass) wanted for thrust. The more the better, because the only other way to increase the thrust is to increase mass flow rate and that is costly in terms of weight that must be launched. Thus, we examine the only quantities that determine a high jet velocity in chemical rocket: a high total temperature and a low molecular weight of the gas. Rocket propulsion people call this velocity by a special name: thrust per unit weight flow rate of propellant, or specific impulse (Isp). It is nothing more than the jet velocity divided by the acceleration of gravity. The definition of Isp means that it is measured in seconds.

Hydrocarbon fuels burning with oxygen produce a gas with Isp =  ~ 350 s. A solid propellant might operate with 280 s. The hydrogen–oxygen combustion in the SSME yields a superior performance with about 450 s (~ 14,500 feet/s!) in the vacuum of space but only about 360 s at takeoff where the over-expansion of the flow reduces the performance. Here is a good place to point out that the airbreathing engines that do not have to carry the air (oxygen) used for combustion can be contrasted to a rocket. The specific impulse of a modern turbofan engine in cruise is about 6500 s!Footnote 3 No wonder we don’t use rockets in airliners!

The hydrogen–oxygen reaction is quite energetic yielding high combustion temperatures. The chemically correct proportion of hydrogen and oxygen is 2 ⋅ H2 + 1 ⋅ O2 to produce two molecules of water vapor. This translates to a ratio of 1:8 by weight. Oxygen is really heavy compared to hydrogen. The resulting jet consisting of pure water vapor has a molecular weight of 18. A maximum total enthalpy per unit mass can be obtained with a reduced temperature and reduced molecular if an excess of hydrogen is processed. Indeed, the SSME burns the reactants fuel-rich in 1:6 (H/O) proportion. The molecular weight of the gas is thereby reduced by about 35%. The lower temperature together with the dearth of (chemically very reactive) oxygen ease the design, construction, and reusability of the engine.

We conclude the discussion of rocket flight to space with a comment on dynamic pressure (q) tackled earlier in our story. Recall this pressure involves only speed and air density. Enthusiasts of flights to space might note that launch operations often involve notation of the point along the ascent where the rocket reaches a point of “max q”. That there is such a maximum should be self-evident as the rocket is flying ever faster into an environment of ever lower atmospheric air density, eventually reaching space with near zero density. The max q point is where the aerodynamic heating and aerodynamic loads are at maxima. Later in the flight, these aspects become an ever-smaller concern.

Rocket propulsion involves a lot of chemistry and the identification of “good” fuels and reactions is a part of the challenge. This is part of the work done by rocket scientists! On top of that is the challenge of getting the engine to fire up and run reliably, all without sudden surprises!

One of the interesting dimensions of liquid fuel rocketry is that it employs the same thermodynamic cycle as did the first successful engine: the steam engine. Central to the cycle is compression of a liquid: water in the old and the chemical propellants in the new. Expansion in the old is against a piston or through a turbine. In the new, expansion is via a nozzle to create a propulsive jet. The SSME is a steam engine!

13.7 Airplane Range

Returning all the way back to the discussion of aerodynamic performance of a wing or airplane, we note the aerodynamicist is largely concerned with maximizing the M L/D to obtain long range and low fuel costs in an airliner or similar transport vehicle. That quantity is also central in the goal of a long-range airplane design. If either of the parameters, M L/D or Isp, has an important influence on the empty weight of an airplane, then some serious optimization will have to be undertaken and there lies the heart of successfully designing an airplane.


  1. 1.

    A normal shock reduces a supersonic flow to subsonic in one (irreversible) step, see the shadowgraph in Fig. 7.5.

  2. 2.

    Choking is the phenomenon where flow rate in a stream tube is governed only by conditions upstream of the location with choked flow, i.e., the total pressure and temperature, and not by the downstream static pressure.

  3. 3.

    Airplane propulsion people use a fuel consumption number called the thrust specific fuel consumption (TSFC) measured in pounds per hour per pound of thrust. TSFC is essentially the inverse of Isp.

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Correspondence to Reiner Decher .

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Decher, R. (2022). More Components: Inlets, Mixers, and Nozzles. In: The Vortex and The Jet. Springer, Singapore.

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-16-8027-4

  • Online ISBN: 978-981-16-8028-1

  • eBook Packages: EngineeringEngineering (R0)