Turbojet propulsion

The physical principle of airbreathing propul­sion again derives from Newton’s second law. However, the time rate of change of momentum is now based on the velocity increase of the airflow ma through the turbine. With V the flight velocity and Ve the exhaust velocity the thmst is (neglecting fuel mass and assuming ideal expansion)

F = ma(Ve – V)

The faster the exhaust velocity (turbine output) or the greater the airflow (high bypass), the greater the thrust F. In general, the thmst depends on several parameters:

F = /(Mach, altitude, power setting, angle of attack)

For some of our applications, we neglect the angle-of-attack dependency.

The specific fuel consumption (SFC) bp is an important indicator for the effi­ciency of the turbojet. It is defined by the ratio of fuel flow to thmst

The units of bp are usually given as kilograms/(deka-Newton hour), where dN can be written ION, and rhf is the fuel flow in kilograms/hour. The strange use of dN is justified by the approximate numerical equivalency of metric and English units

1 [kg/(dN h)] = 0.980665 [lbm/(lbf h)]

Typical values of SFC are between 1.0 to 0.3 kg/(dN h), with turbojets being less efficient than high-bypass turbofans.

8.2.4.3 Combine-cycle propulsion. In this section we focus on the high­speed regime of airbreathing engines. It is an area of vigorous research and devel­opment, spurred on by the National Aerospace Plane (NASP), the single-stage-to – orbit (SSTO) requirement, and various X vehicles. We are also motivated to look into high-speed propulsion because the GHAME3 and GHAME6 simulations use turbojet, ramjet, and scramjet engines to ascend through all Mach regimes into the stratosphere.

Turbojets and turbofans are particularly suited for the low-speed portions of the mission and have adequate performance up to Mach 3. The upper limit is imposed by the thermal constraints of their materials. Designs tend to have low overall pressure ratios and low rotor speeds at takeoff. With cryogenic fuels like liquid hydrogen, precooling can increase the maximum Mach-number regime to beyond 4, provided the engine operates above stoichiometric conditions.

Ramjets have no rotating machinery and start to operate above Mach 2. The internal flow remains subsonic, although they may perform up to Mach 6, limited by dissociation and material temperatures. Using hydrogen as a fuel and thus eliminating the need for flameholders can alleviate some of the material constraints.

Turboramjets combine turbojets and ramjets in wraparound or tandem designs. A high efficiency intake is combined with an ejector nozzle. It matches the full intake capture area demanded during transonic flight. The excess capture flow is passed down a duct, concentric with the engine, which also serves to bypass the turbomachinery in the ramjet mode. Turboramjets operate from static conditions at sea level up to Mach 6 at high altitudes.

Turborockets use hydrogen/oxygen combustors to produce the working fluid for the turbine. The combustion is fuel rich so that the turbine entry temperature is kept within the capability of uncooled materials. The excess hydrogen is burned in the fan stream air, with secondary hydrogen injected to produce an overall stoichiometric mixture. Fan materials limit the upper Mach number to about 4.

Scramjets are similar to ramjets, except that their combustion occurs at su­personic speeds. Although they can operate at lower speeds, they become more efficient than ramjets only above Mach 6.

The turboramjet/scramjet is a three-cycle variable inlet geometry design, capa­ble of providing thrust from static sea-level conditions to hypersonic atmospheric exit. NASA uses it for their GHAME concept. The breakpoints for the cycles are 1) turbojet from Mach 0 to Mach 2,2) ramjet until Mach 6, and 3) scramjet beyond.

The authors of the GHAME propulsion package13 apologize for the simplicity of their approach, but I find their model quite lucid. They start with the basic thrust equation (8.24) F = Isvmg0 i. e., thrust equals specific impulse times weight flow rate through the engine. Because we deal with airbreathers, the weight flow rate is essentially the amount of air sucked through the intake area Ac. Therefore, given the speed of the vehicle V =Ma and the air density p, the weight flow rate is

mg о = g0pMaAc

which assumes that the air enters the cowl uniformly. However, the intake flow of a turboramjet/scramjet engine is very intricate, influenced by engine cycle, Mach number, and angle of attack. This complexity is distilled into a capture – area coefficient Ca, which is dependent on Mach number and angle of attack. Subsonically, it starts with values near 1, drops to 0.2 in the transonic region, then rises slightly until the ramjet takes over at Mach 2. Thereafter, it increases beyond 1 and tops out under the scramjet cycle at about 5. As the angle of attack increases, the effective capture area grows, and the Ca value almost doubles at 21 deg. With this correction factor the effective weight flow rate is

mgo – gopMa Ca(M, a)Ac

The pilot controls the fuel flow and the variable intake by the throttle setting thr. Indirectly, the pilot adjusts the fuel/air ratio of the engine to the stoichiometric ratio, which equals 0.029 x thr, by adjusting thr between the values zero and two. The specific impulse /sp is a function of the engine cycle, the throttle setting, and Mach number. It increases with throttle setting and decreases with Mach number.

Now we have assembled all of the elements for the thrust equation (8.24):

F = 0.029 thr /sp(M, thr)g0pMa Ca(M, a)Ac (8.26)

As the vehicle takes off with full throttle, low Mach, and high angle of attack, its thrust is at a near maximum. During the climb-out, in the transonic region with decreasing a the effective capture area is significantly reduced so that the pilot will maintain max throttle until the ramjet regime is reached. Then the pilot begins to throttle back to conserve fuel.

You will be surprised and may be disappointed to learn that this is all I have to say about propulsion. If you have to build a propulsion simulation, you should assemble a team of experts that will model such effects as inlet flow, thermodynamics, combustion efficiency, exhaust, installed drag, and stall. You can then provide the aerodynamics, mass properties, and the simulation environment. Here, I emphasize a general treatment that enables you to build three-, five-, and six-DoF simulations quickly without resorting to specialists.

You will find examples throughout the family of CADAC simulations. ROCKET3 models liquid-fueled, three-stage rockets; GHAME3 and GHAME6 mimic the NASA combined-cycle engine; CRUISE5 and FALCON6 use simple subsonic tur­bojet models; and AIM5, SRAAM5, and SRAAM6 are propelled by solid rocket motors. We will turn now to the description of the two, three-DoF simulations GHAME3 and ROCKET3.