Power Efficiency Guide

As the speed increases, the engine performance becomes characterized by energy conservation rather than by combustion: energy conservation is far more important than chemistry [Ahern, 1992]. The result is a spectrum of operation over the speed regime developed by Czysz and Murthy [1991] and shown in Figure 4.7. This figure illustrates the extent to which the kinetic energy of free stream air entering the vehicle inlet capture area and the fuel mass and internal energy become gradually more significant and critical as the flight speed increases. Thus the operating limits of the airbreather can be clearly identified.

Figure 4.7 shows flight altitude versus flight speed, in kft/s. The corridor, labeled "acceleration", that begins at zero speed and extends across the figure to nearly orbital speed (20 kft/s) is the flight corridor for airbreathing vehicles to reach orbital speed. This corridor is based on the dynamic pressure limits of accelerating airbreathing vehicles. The lower limit is based on structural weight and skin temperatures. The upper limit is based on having sufficient thrust to accelerate efficiently to orbital speed. The narrow corridor cutting across the acceleration corridor, labeled "cruise", is the corridor for hypersonic cruise vehicles to achieve maximum range. The vertical shaded area identifies the flight speeds at which a subsonic through-flow engine (ramjet) should transition to a supersonic through-

Figure 4.7. Operating boundaries of Brayton cycle engines based on enthalpy and entropy analyses.

Flight Speed (kft/sec)

Figure 4.7. Operating boundaries of Brayton cycle engines based on enthalpy and entropy analyses.

flow engine (scramjet). The shaded area between 5 and 7 kft/s is the transition region defined by Builder for hydrogen and hydrocarbon fuels as the region where kinetic compression to subsonic speeds ahead of the combustor alone yields optimum enthalpy compression ratio [Builder, 1964]. To the left of this area mechanical compression is required to reach the optimum enthalpy compression ratio. In this area engines are generally limited to the practical compression ratios achievable, and do not achieve the optimum enthalpy compression ratio. To the right of this area the kinetic enthalpy compression ratio exceeds the value of the optimum enthalpy compression ratio. So diffusion of the air stream has to be limited in order to limit the enthalpy compression ratio (the engine through-flow speed is greater than subsonic speed). This means that engine through-flow needs to remain supersonic and increase in through-flow speed as the flight speed increases. The goal in limiting flow diffusion is to maintain a constant value for the optimum enthalpy compression ratio. Analysis of the Second Law of Thermodynamics by Builder documented that the engine design enthalpy compression ratio (rather than the design pressure ratio) and the fuel define the cycle efficiency. Hydrocarbon fuels are to the left side of the shaded area and hydrogen is to the right side of the area. The vertical lines identified with the numbers 0.5, 1, 2, 4, and 7 represent the ratio of flight kinetic energy to the available fuel energy accounting for Carnot losses. As indicated by the arrows, to the left of the vertical shaded area engines are subsonic through-flow, and to the right of the vertical shaded area engines are supersonic through-flow. As pointed out in equation (4.5d), the kinetic energy of the injected, hot, gaseous fuel is a source of energy very useful to overcome the internal drag and mixing losses. As indicated by the arrows and text adjacent to the vertical lines, this energy addition becomes more critical to engine operation as the speed increases.

The speed regime to the right of the 4 energy ratio line is questionable for an operational vehicle. It is totally possible for a research vehicle to investigate this area but, as we shall see, at the 4 energy ratio boundary the airbreathing vehicle has achieved a significant fraction of the benefits from incorporating airbreathing in terms of the propellant required to achieve a given speed increment. As the energy ratio increases, the scramjet-powered vehicle thrust-to-drag ratio decreases. As the thrust-to-drag ratio decreases the acceleration (effective) Isp = 7spe decreases to the point where the high thrust-to-drag rocket uses less propellant for a given speed increment than the scramjet. At that point the rocket engine is clearly a better accelerator than the airbreathing engine. So, from an energy viewpoint, a practical maximum airbreathing speed is about 14,200 ft/s (4.33 km/s). To the right of this line the payoff achieved compared to the resources required reaches diminishing returns. That is, the velocity increment produced per unit propellant mass and volume flow is less for the airbreather: beyond this point a hydrogen/oxygen rocket requires less propellant mass flow per velocity increment and less vehicle storage volume than the airbreathing engine. So, in terms of available energy and of the propellant required to produce a given velocity increment, the airbreather is outperformed by a hydrogen/oxygen rocket. This is a result of the fact that the thrust-to-drag ratio of the airbreather is diminishing as speed and altitude are increased, while the thrust-to-

drag ratio for the rocket is increasing. So the acceleration (effective) 7spe of the airbreather falls below that of the rocket.

Returning to the consideration of entropy and applying the criteria from equation (4.7), the loss of exhaust velocity begins at about 120,000 ft (36,576 m), shown as a horizontal dashed line. The altitude regime above 120,000 ft altitude produces a degradation of thrust because the increasing entropy levels limit the internal molecular energy that can be converted into kinetic energy and exhaust gas velocity. Dr Frederick Billig of APL/JHU advocated the introduction of excess hydrogen in the flow to act as a molecular collision third body. In equation (4.5d) excess hydrogen means the equivalence ratio (0) is greater than 1. For a phi of 1 the fuel burns all of the oxygen available in the air. Excess hydrogen provides abundant third bodies for the dissociated air molecules to recombine [Billig, 1989; Czysz and Murthy, 1991]. The hydrogen molecule dissociates into two hydrogen atoms, but unlike the other diatomic gases, atomic hydrogen has about 90% of the velocity potential as molecular hydrogen. And being a low-molecular-weight gas, it is a better working fluid than air, and pound per pound produces more thrust. However, again due to entropy, this only works up to a point. In terms of altitude, that point is about 170,000 ft (51,816 m). Between 120,000 and 170,000 ft the excess hydrogen ameliorates the energy "frozen" in the non-equilibrium gas chemistry. Above that altitude, the entropy levels are such that, even with the third body collisions provided by the hydrogen, the irreversible energy cannot be recovered and it is improbable that a Brayton cycle engine can produce sufficient thrust. If excess hydrogen fuel is used in Brayton cycle engines below 150,000 feet and at less than 14,500 ft/s, it can convert a fraction of the aerodynamic heating into net thrust via injection of the heated hydrogen into the engine at velocity corresponding to flight speed. Note that cruise engines operate at greater cycle entropy levels than acceleration engines and thus may require a larger excess hydrogen flow than the acceleration engines.

Up to this point, we have used first principles to determine that the vehicle will be stout, and not too small if it is to be built from available industrial capability, see Figures 3.22 to 3.24. We have also established it is not practicable for an operational vehicle to exceed 14,200 ft/s in airbreathing mode, and apparently 12,700 ft/s would be less challenging while retaining the benefits of airbreather operation.

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