The combustion chamber is that part of a thrust chamber where the combustion or burning of the propellant takes place. The combustion temperature is much higher than the melting points of most chamber wall materials. Therefore it is necessary either to cool these walls (as described in a later section of this chapter) or to stop rocket operation before the critical wall areas become too hot. If the heat transfer is too high and thus the wall temperatures become locally too high, the thrust chamber will fail. Heat transfer to thrust chambers will be described later in this chapter. Section 8.6 gives a sample analysis of a thrust chamber and Ref. 8-2 describes the design and development of one.
Spherical chambers give the least internal surface area and mass per unit chamber volume; they are expensive to build and several have been tried. Today we prefer a cylindrical chamber (or slightly tapered cone frustum) with a flat injector and a converging-diverging nozzle. The chamber volume is defined as the volume up to the nozzle throat section and it includes the cylindrical chamber and the converging cone frustum of the nozzle. Neglecting the effect of the corner radii, the chamber volume Vc is
Here L is the cylinder length, A\/At is the chamber contraction ratio, and Lc is the length of the conical frustum. The approximate surfaces exposed to heat transfer from hot gas comprise the injector face, the inner surface of the cylinder chamber, and the inner surface of the converging cone frustrum. The volume and shape are selected after evaluating these parameters:
1. The volume has to be large enough for adequate mixing, evaporation, and complete combustion of propellants. Chamber volumes vary for different propellants with the time delay necessary to vaporize and activate the propellants and with the speed of reaction of the propellant combination. When the chamber volume is too small, combustion is incomplete and the performance is poor. With higher chamber pressures or with highly reactive propellants, and with injectors that give improved mixing, a smaller chamber volume is usually permissible.
2. The chamber diameter and volume can influence the cooling requirements. If the chamber volume and the chamber diameter are large, the heat transfer rates to the walls will be reduced, the area exposed to heat will be large, and the walls are somewhat thicker. Conversely, if the volume and cross section are small, the inner wall surface area and the inert mass will be smaller, but the chamber gas velocities and the heat transfer rates will be increased. There is an optimum chamber volume and diameter where the total heat absorbed by the walls will be a minimum. This is important when the available cooling capacity of the coolant is limited (for example oxygen-hydrocarbon at high mixture ratios) or if the maximum permissive coolant temperature has to be limited (for safety reasons with hydrazine cooling). The total heat transfer can also be further reduced by going to a rich mixture ratio or by adding film cooling (discussed below).
3. All inert components should have minimum mass. The thrust chamber mass is a function of the chamber dimensions, chamber pressure, and nozzle area ratio, and the method of cooling.
4. Manufacturing considerations favor a simple chamber geometry, such as a cylinder with a double cone bow-tie-shaped nozzle, low cost materials, and simple fabrication processes.
5. In some applications the length of the chamber and the nozzle relate directly to the overall length of the vehicle. A large-diameter but short chamber can allow a somewhat shorter vehicle with a lower structural inert vehicle mass.
6. The gas pressure drop for accelerating the combustion products within the chamber should be a minimum; any pressure reduction at the nozzle inlet reduces the exhaust velocity and the performance of the vehicle. These losses become appreciable when the chamber area is less than three times the throat area.
7. For the same thrust the combustion volume and the nozzle throat area become smaller as the operating chamber pressure is increased. This means that the chamber length and the nozzle length (for the same area ratio) also decrease with increasing chamber pressure. The performance also goes up with chamber pressure.
The preceding chamber considerations conflict with each other. It is, for instance, impossible to have a large chamber that gives complete combustion but has a low mass. Depending on the application, a compromise solution that will satisfy the majority of these considerations is therefore usually selected and verified by experiment.
The characteristic chamber length is defined as the length that a chamber of the same volume would have if it were a straight tube and had no converging nozzle section.
where L* (pronounced el star) is the characteristic chamber length, A, is the nozzle throat area, and Vc is the chamber volume. The chamber includes all the volume up to the throat area. Typical values for L* are between 0.8 and 3.0 meters (2.6 to 10 ft) for several bipropellants and higher for some monopro-pellants. Because this parameter does not consider any variables except the throat area, it is useful only for a particular propellant combination and a narrow range of mixture ratio and chamber pressure. The parameter L* was used about 40 years ago, but today the chamber volume and shape are chosen by using data from successful thrust chambers of prior similar designs and identical propellants.
The stay time ts of the propellant gases is the average value of the time spent by each molecule or atom within the chamber volume. It is defined by ts = Vc/(mV0 (8-10)
where m is the propellant mass flow, V] is the average specific volume or volume per unit mass of propellant gases in the chamber, and Vc is the chamber volume. The minimum stay time at which a good performance is attained defines the chamber volume that gives essentially complete combustion. The stay time varies for different propellants and has to be experimentally determined. It includes the time necessary for vaporization, activation, and complete burning of the propellant. Stay times have values of 0.001 to 0.040 sec for different types of thrust chambers and propellants.
The nozzle dimensions and configuration can be determined from the analyses presented in Chapter 3. The converging section of the supersonic nozzle experiences a much higher internal gas pressure than the diverging section and therefore the design of the converging wall is similar to the design of the cylindrical chamber wall. Most thrust chambers use a shortened bell shape for the diverging nozzle section. Nozzles with area ratios up to 400 have been developed.
In Chapter 3 it was stated that very large nozzle exit area ratios allow a small but significant improvement in specific impulse, particularly at very high altitudes; however, the extra length and extra vehicle mass necessary to house a large nozzle make this unattractive. This disadvantage can be mitigated by a multipiece nozzle, that is stored in annular pieces around the engine during the ascent of the launch vehicle and automatically assembled in space after launch vehicle separation and before firing. This concept, known as extendible nozzle cone, has been successfully employed in solid propellant rocket motors for space applications for about 20 years. The first flight with an extendible nozzle on a liquid propellant engine was performed in 1998 with a modified version of a Pratt & Whitney upper stage engine. Its flight performance is listed in Table 8-1. The engine is shown later in Fig. 8-19 and its carbon-carbon extendible nozzle cone is described in the section on Materials and Fabrication.
Heat is transmitted to all internal hardware surfaces exposed to hot gases, namely the injector face, the chamber and nozzle walls. The heat transfer rate or heat transfer intensity, that is, local wall temperatures and heat transfer per unit wall area, varies within the rocket. A typical heat transfer rate distribution is shown in Fig. 8-8. Only \ to 5% of the total energy generated in the gas is transferred as heat to the chamber walls. For a typical rocket of 44,820 N or 10,000 lbf thrust the heat rejection rate to the wall may be between 0.75 and 3.5 MW, depending on the exact conditions and design. See Section 8.3.
The amount of heat transferred by conduction from the chamber gas to the walls in a rocket thrust chamber is negligible. By far the largest part of the heat is transferred by means of convection. A part (usually 5 to 35%) of the transferred heat is attributable to radiation.
For constant chamber pressure, the chamber wall surface increases less rapidly than the volume as the thrust level is raised. Thus the cooling of chambers is generally easier in large thrust sizes, and the capacity of the wall material or the coolant to absorb all the heat rejected by the hot gas is generally more critical in smaller sizes, because of the volume-surface relationship.
Higher chamber pressure leads to higher vehicle performance (higher Is), but also to higher engine inert mass. However, the resulting increase of heat transfer with chamber pressure often imposes design or material limits on the maximum practical chamber pressure for both liquid and solid propellant rockets.
The heat transfer intensity in chemical rocket propulsion can vary from less than 50 W/cm2 or 0.3 Btu/in.2-sec to over 16 kW/cm2 or 100 Btu/in.2-sec. The
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