Propellant Grain And Grain Configuration

The grain is the shaped mass of processed solid propellant inside the rocket motor. The propellant material and geometrical configuration of the grain determine the motor performance characteristics. The propellant grain is a cast, molded, or extruded body and its appearance and feel is similar to that of hard rubber or plastic. Once ignited, it will burn on all its exposed surfaces to form hot gases that are then exhausted through a nozzle. A few rocket motors have more than one grain inside a single case or chamber and very few grains have segments made of different propellant composition (e.g., to allow different burning rates). However, most rockets have a single grain.

There are two methods of holding the grain in the case, as seen in Fig. 11-14. Cartridge-loaded or freestanding grains are manufactured separately from the case (by extrusion or by casting into a cylindrical mold or cartridge) and then loaded into or assembled into the case. In case-bonded grains the case is used as a mold and the propellant is cast directly into the case and is bonded to the case or case insulation. Free-standing grains can more easily be replaced

Case with , inner liner

Case with , inner liner

Aft / insulation

Cartridge-loaded grain Case-bonded grain

(free-standing)

FIGURE 11-14. Simplified schematic diagrams of a free-standing (or cartridge-loaded) and a case-bonded grain.

Forward support

Insulation

Nozzle

Cartridge

Grain

Case

Cartridge

Grain

Case

Support Flange

Forward support

Insulation

Nozzle if the propellant grain has aged excessively. Aging is discussed in the next chapter. Cartridge-loaded grains are used in some small tactical missiles and a few medium-sized motors. They often have a lower cost and are easier to inspect. The case-bonded grains give a somewhat better performance, a little less inert mass (no holding device, support pads, and less insulation), a better volumetric loading fraction, are more highly stressed, and often somewhat more difficult and expensive to manufacture. Today almost all larger motors and many tactical missile motors use case bonding. Stresses in these two types of grains are briefly discussed under structural design in the next section.

Definitions and terminology important to grains include:

Configuration-. The shape or geometry of the initial burning surfaces of a grain as it is intended to operate in a motor.

Cylindrical Grain: A grain in which the internal cross section is constant along the axis regardless of perforation shape, (see Fig. 11-3).

Neutral Burning: Motor burn time during which thrust, pressure, and burning surface area remain approximately constant (see Fig. 11-15), typically within about ±15%. Many grains are neutral burning.

Perforation: The central cavity port or flow passage of a propellant grain; its cross section may be a cylinder, a star shape, etc. (see Fig. 11-16).

Progressive Burning: Burn time during which thrust, pressure, and burning surface area increase (see Fig. 11-15).

Regressive Burning: Burn time during which thrust, pressure, and burning surface area decrease (see Fig. 11-15).

Sliver: Unburned propellant remaining (or lost—that is, expelled through the nozzle) at the time of web burnout (see sketch in Problem 11-6).

Grain Configuration
FIGURE 11-15. Classification of grains according to their pressure-time characteristics.

Propellant

Propellant

Bonded insulation Chamber V_ /

End-burner (case bonded), neutral burn

Bonded insulation Chamber V_ /

End-burner (case bonded), neutral burn

Web thickness b

Internal burning tube, progressive

Web thickness b

Internal burning tube, progressive

Slots and tube, neutral burn

Slots and tube, neutral burn

Star (neutral)

Star (neutral)

Radial grooves and tube, neutral burn

Radial grooves and tube, neutral burn

Wagon wheel (neutral)

Multiperforated (progressive-regressive)

Wagon wheel (neutral)

Multiperforated (progressive-regressive)

Dog bone Dendrite

(case bonded)

FIGURE 11-16. Simplified diagrams of several grain configurations.

Burning Time, or Effective Burning Time, tb: Usually, the interval from 10% maximum initial pressure (or thrust) to web burnout, with web burnout usually taken as the aft tangent-bisector point on the pressure-time trace (see Fig. 11-13).

Action Time, ta: The burning time plus most of the time to burn slivers; typically, the interval between the initial and final 10% pressure (or thrust) points on the pressure-time trace (see Fig. 11-13).

Deflagration Limit The minimum pressure at which combustion can still be barely self-sustained and maintained without adding energy. Below this pressure the combustion ceases altogether or may be erratic and unsteady with the plume appearing and disappearing periodically.

Inhibitor. A layer or coating of slow- or nonburning material (usually, a polymeric rubber type with filler materials) applied (glued, painted, dipped, or sprayed) to a part of the grain's propellant surface to prevent burning on that surface. By preventing burning on inhibited surfaces the initial burning area can be controlled and reduced. Also called restrictor.

Liner: A sticky non-self-burning thin layer of polymeric-type material that is applied to the cases prior to casting the propellant in order to promote good bonding between the propellant and the case or the insulator. It also allows some axial motion between the grain periphery and the case.

Internal Insulator: An internal layer between the case and the propellant grain made of an adhesive, thermally insulating material that will not burn readily. Its purpose is to limit the heat transfer to and the temperature rise of the case during rocket operation. Liners and insulators can be seen in Figs. 11-1, 11-2, 11-4, and 11-14, and are described in Chapter 12.

Web Thickness, b: The minimum thickness of the grain from the initial burning surface to the insulated case wall or to the intersection of another burning surface; for an end-burning grain, b equals the length of the grain (see Fig. 11-16).

Web Fraction, bf. For a case-bonded internal burning grain, the ratio of the web thickness b to the outer radius of the grain:

Volumetric Loading Fraction, Vf. The ratio of propellant volume Vb to the chamber volume Vc (excluding nozzle) available for propellant, insulation, and restrictors. Using Eq. 2-4 and Vb = mjp:

where I, is the total impulse, Is the specific impulse, and pb the propellant density.

A grain has to satisfy several interrelated requirements:

1. From the flight mission one can determine the rocket motor requirements. They have to be defined and known before the grain can be designed. They are usually established by the vehicle designers. This can include total impulse, a desired thrust-time curve and a tolerance thereon, motor mass, ambient temperature limits during storage and operation, available vehicle volume or envelope, and vehicle accelerations caused by vehicle forces (vibration, bending, aerodynamic loads, etc.).

2. The grain geometry is selected to fit these requirements; it should be compact and use the available volume efficiently, have an appropriate burn surface versus time profile to match the desired thrust-time curve, and avoid or predictably control possible erosive burning. The remaining unburned propellant slivers, and often also the shift of the center of gravity during burning, should be minimized. This selection of the geometry can be complex, and it is discussed in Refs. 11-1 and 11-7 and also below in this section.

3. The propellant is usually selected on the basis of its performance capability (e.g., characteristic velocity), mechanical properties (e.g., strength), ballistic properties (e.g., burning rate), manufacturing characteristics, exhaust plume characteristics, and aging properties. If necessary, the propellant formulation may be slightly altered or "tailored" to fit exactly the required burning time or grain geometry. Propellant selection is discussed in Chapter 12 and in Ref. 11-7.

4. The structural integrity of the grain, including its liner and/or insulator, must be analyzed to assure that the grain will not fail in stress or strain under all conditions of loading, acceleration, or thermal stress. The grain geometry can be changed to reduce excessive stresses. This is discussed in the next section of this chapter.

5. The complex internal cavity volume of perforations, slots, ports, and fins increases with burning time. These cavities need to be checked for resonance, damping, and combustion stability. This is discussed in Chapter 13.

6. The processing of the grain and the fabrication of the propellant should be simple and low cost (see Chapter 12).

The grain configuration is designed to satisfy most requirements, but sometimes some of these six catégories are satisfied only partially. The geometry is crucial in grain design. For a neutral burning grain (approximately constant thrust), for example, the burning surface Ab has to stay approximately constant, and for a regressive burning grain the burning area will diminish during the burning time. From Eqs. 11-3 and 11-14 the trade-off between burning rate and the burning surface area is evident, and the change of burning surface with time has a strong influence on chamber pressure and thrust. Since the density of most modern propellants falls within a narrow range (about 0.066 lbm/in.3 or 1830 kg/m3 +2 to -15%), it has little influence on the grain design.

As a result of motor developments of the past three decades, many grain configurations are available to motor designers. As methods evolved for increasing the propellant burning rate, the number of configurations needed decreased. Current designs concentrate on relatively few configurations, since the needs of a wide variety of solid rocket applications can be fulfilled by combining known configurations or by slightly altering a classical configuration. The trend has been to discontinue configurations that give weak grains which can form cracks, produce high sliver losses, have a low volumetric loading fraction, or are expensive to manufacture.

The effect of propellant burning on surface area is readily apparent for simple geometric shapes such as rods, tubes, wedges, and slots, as shown in the top four configurations of Fig. 11-16. Certain other basic surface shapes burn as follows: external burning rod—regressive; external burning wedge— regressive. Most propellant grains combine two or more of these basic surfaces to obtain the desired burning characteristic. The star perforation, for example, combines the wedge and the internal burning tube. Figure 11-17 indicates typical single grains with combinations of two basic shapes. The term conocyl is a contraction of the words cone and cylinder.

Configurations that combine both radial and longitudinal burning, as does the internal-external burning tube without restricted ends, are frequently referred to as "three-dimensional grains" even though all grains are geometrically three-dimensional. Correspondingly, grains that burn only longitudinally

FIGURE 11-17. Typical common grain configurations using combinations of two basic shapes for the grain cavity.

Composite Rocket Motor Case

Stress-relieving insulation

FIGURE 11-17. Typical common grain configurations using combinations of two basic shapes for the grain cavity.

Spherical (case-bonded) with slots and cylinder

Stress-relieving insulation

Spherical (case-bonded) with slots and cylinder or only radially are "two-dimensional grains." Grain configurations can be classified according to their web fraction bf, their length-to-diameter ratio L/D, and their volumetric loading fraction Vf. These three dependent variables are often used in selecting a grain configuration in the preliminary design of a motor for a specific application. Obvious overlap of characteristics exists with some of the configurations, as given in Table 11-4 and shown by simple sketches in Fig. 11-16. The configurations listed above the line in the table are common in recent designs. The bottom three were used in earlier designs and usually are more difficult to manufacture or to support in a case. The end burner has the highest volumetric loading fraction, the lowest grain cavity volume for a given total impulse, and a relatively low burning area or thrust with a long duration. The internal burning tube is relatively easy to manufacture and is neutral burning with unrestricted ends of L/D ~ 2. By adding fins or cones (see Fig. 11-17) this configuration works for 2 < L/D < 4. The star configuration is ideal for web fractions of 0.3 to 0.4; it is progressive above 0.4, but can be neutralized with fins or slots. The wagon wheel is structurally superior to the star shape around 0.3 and is necessary at a web fraction of 0.2 (high thrust and short burn time). Dendrites are used in the lowest web fraction when a relatively large burning area is needed (high thrust and short duration), but stresses may be high. Although the limited number of configurations given in this table may not encompass all the practical possibilities for fulfilling a nearly constant thrust-time performance requirement, combinations of these features should be considered to achieve a neutral pressure-time trace and high volumetric loading before a relatively unproven configuration is accepted. The capabilities of basic configurations listed in these tables can be

TABLE 11-4. Characteristics of Several Grain Configurations
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Responses

  • Isa
    How to calculate burn area of a propellant in star shape configuration?
    26 days ago

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