Fuel injection energy gain c / vehicle i§L=f f )2

In equation (4.5d) ^ is the equivalence ratio.

The only positive term that adds to the available energy is the kinetic energy of the injected fuel. If the temperature of the fuel (in this case hydrogen) is scheduled so that the injected fuel velocity is equal to the flight speed, and the fuel injection angle is in the 6° to 10° range, then the injected fuel energy to air stream kinetic energy ratio is 0.0292^. For an equivalence ratio of six, this provides an energy addition of 17.5% of the air stream kinetic energy. So recovering normally discarded energy as thrust is as critical as burning fuel in the engine. This will be discussed further on in this chapter, when identifying the operational zone for Brayton cycle propulsion systems.

The principal culprit in the drag energy loss inside the combustion chamber (equation (4.5a)) is the wetted area of the engine referenced to the engine module cowl cross-sectional area, and the shock and wake losses from struts and injectors in the combustor flow. To keep the wetted area, and therefore skin friction loss, to a minimum, the combustor cross-sectional shape and length are critical. Cross-sectional shape is generally driven by integration consideration with the aircraft, and have only limited variability. The combustor length used is based on both experimental data [Swithenbank, 1966, 1969] and Computational Fluid Dynamics (CFD) analyses with Second Law (available energy) losses considered [Riggins, 1996]. From both sources, the combustor length for maximum energy efficiency is 0.40 meters (15.7 inches). Swithenbank's measurements in a shock tube combustor test facility verified that for methane, atomized hydrocarbons, and hydrogen the

Figure 4.4. Four representative ram/scramjet module configurations. For clarity the aircraft is compression side up, with the airflow from right to left.

combustion time was 35 microseconds ±5 microseconds over the combustor gas speed range of 6,000 to 12,000 ft/s (1,828 to 3,658 m/s) [Swithenbank, 1984].

With the wetted area minimized, the remaining task is to identify the shock wave and wake losses. This was done for four combustor configurations in Figure 4.4 [Czysz and Murthy, 1991]. The total internal drag area for four internal combustor geometries are shown in Figure 4.5. In addition to the work by Murthy and Czysz, these were analyzed by students in the Parks College Hypersonic Propulsion and Integration class with the same results. Case 2 is a set of five vertical struts with fuel or rocket injectors in the strut base to produce wake turbulence mixing that is characteristic of many ram/scramjet designs. Case 1 is from Professor James Swithenbank of Sheffield University and is a single horizontal strut with a line of trailing-edge triangles inclined a few degrees to the flow to form a lifting surface that creates a trailing vortex for mixing. The fuel injection is in from the strut base and at the base of each triangular "finger". The trailing-edge angle is sufficient to produce a subsonic trailing edge in the Mach 4 to 5 combustor flow. The trailing-edge vortex mixing is that produced by a subsonic trailing edge on a lifting surface and was developed via experiments in the late 1960s. Case 0 is an adaptation of the Swithen-bank vortex mixing concept to a wall injector configured as a surface inclined to the wall with a subsonic trailing-edge angle [Swithenbank et al. 1966, 1969; Swithenbank, 1984]. The subsonic trailing edge produces the mixing vortex. The author (PC) was shown these injectors by Professor Swithenbank in 1988. The concept of a trailing-edge vortex on a lifting surface was also proposed by Leonard Townend [Townend, 1986]. Case 3 is a shock-confined combustion zone formed between the body and the low-angle body shock wave when the engine module is retracted. With Mach numbers on the order of 10 or greater the resistance

Figure 4.5. Four very different internal drags for the four module configurations.

of the shock system to normal flow is as great as a physical wall. This concept was successfully tested in an RAE facility by Leonard Townend in 1966, and offers the lowest losses of any configuration. It was also a configuration developed at McDonnell Aircraft under the leadership of H.D. Altis [Czysz, 1999, Figure 15]. For each of these cases the internal drag area based on skin friction and shock wave drag (CDS) was determined and referenced to the engine module cowl area (CDS/Aj)eng for each of the four engine module combustor configurations in Figure 4.4 as a function of flight Mach number. Note that as the supersonic combustor through-flow begins (that is, scramjet operation begins) there is a sharp increase in the internal drag. The stronger the shock waves and shock interference associated with the internal geometry, the sharper the drag rise.

With this information the magnitude of the internal engine drag can be compared to the external aircraft drag. The ratio of engine drag to aircraft drag can determined using the relationship in equation set (4.6). The value for the aircraft drag area referenced to the geometric capture area (CDS/A0)air is essentially a constant for the supersonic through-flow operation of the engine above Mach 6 and has a value of approximately 0.090. The engine airflow contraction ratio (A0/A2) depends on whether the engine is operating in supersonic through-flow mode or subsonic through-flow mode. Table 4.2 compares the combustor entrance conditions for the flight speed of 14,361 ft/s (4,377 m/s). Once supersonic through-flow is established, the combustor static pressure and temperature remain essentially constant, as determined by Builder's thermodynamic analysis

Table 4.2. Combustor entrance geometry and conditions for 14,361 ft/s flight speed. V0 = 14,361 ft/s Z0 = 124,000 ft q0 = 1,122 lb/ft2 V0 = 4,377 m/s Z0 = 37,795m q0 = 57.72kPa

Combustor conditions




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