Dfx

Third

FIGURE 13-7. Standard T-burner and its longitudinal mode standing waves (pressure and velocity).

Use of the T-burner for assessing the stability of a full-scale solid rocket presupposes valid theoretical models of the phenomena occurring in both the T-burner and the actual rocket motor; these theories are still not fully validated. In addition to assessing solid rocket motor combustion stability, the T-burner also is used to evaluate new propellant formulations and the importance of seemingly small changes in ingredients, such as a change in aluminum powder particle size and oxidizer grind method.

Once an instability has been observed or predicted in a given motor, the motor design has to fix the problem. There is no sure method for selecting the right remedy, and none of the cures suggested below may work. The usual alternatives are:

1. Changing the grain geometry to shift the frequencies away from the undesirable values. Sometimes, changing fin locations, port cross-section profile, or number of slots has been successful.

First

Second

Third

FIGURE 13-7. Standard T-burner and its longitudinal mode standing waves (pressure and velocity).

2. Changing the propellant composition. Using aluminum as an additive has been most effective in curing transverse instabilities, provided that the particle-size distribution of the aluminum oxide is favorable to optimum damping at the distributed frequency. Changing size distribution and using other particulates (Zr, A1203, or carbon particles) has been effective in some cases. Sometimes changes in the binder have worked.

3. Adding some mechanical device for attenuating the unsteady gas motions or changing the natural frequency of cavities. Various inert resonance rods, baffles, or paddles have been added, mostly as a fix to an existing motor with observed instability. They can change the resonance frequencies of the cavities, introduce additional viscous surface losses, but also cause extra inert mass and potential problems with heat transfer or erosion.

Combustion instability has to be addressed during the design process, usually through a combination of some mathematical simulation, understanding similar problems in other motors, studies of possible changes, and supporting experimental work (e.g., T-burners, measuring particle-size distribution). Most solid propellant rocket companies have in-house two-and three-dimensional computer programs to calculate the likely acoustic modes (axial, tangential, radial, and combinations of these) for a given grain/motor, the initial and intermediate cavity geometries, and the combustion gas properties calculated from thermochemical analysis. Data on combustion response (dynamic burn rate behavior) and damping can be obtained from T-burner tests. Data on particle sizes can be estimated from prior experience or plume measurements (Ref. 13-20). Estimates of nozzle losses, friction, or other damping need to be included. Depending on the balance between gain and damping, it may be possible to arrive at conclusions on the grain's propensity to instability for each specific instability mode that is analyzed. If unfavorable, either the grain geometry or the propellant usually have to be modified. If favorable, full-scale motors have to be built and tested to validate the predicted stable burning characteristics. There is always a trade-off between the amount of work spent on extensive analysis, subscale experiments and computer programs (which will not always guarantee a stable motor), and taking a chance that a retrofit will be needed after full-scale motors have been tested. If the instability is not discovered until after the motor is in production, it is often difficult, time consuming, and expensive to fix the problem.

Vortex-Shedding Instability

This instability is associated with burning on the inner surfaces of slots in the grain. Large segmented rocket motors have slots between segments, and some grain configurations have slots that intersect the centerline of the grain. Figure 13-8 shows that hot gases from the burning slot surfaces enter the main flow in

Streamlines of gas flow

Conical

Conical

Streamlines of gas flow

FIGURE 13-8. Simple sketches of four partial grain sections each with a slot or a step. Heavy lines identify the burning surfaces. The flow patterns cause the formation of vortices. The shedding of these vortices can induce flow oscillations and pressure instabilities.

Streamlines of gas flow

FIGURE 13-8. Simple sketches of four partial grain sections each with a slot or a step. Heavy lines identify the burning surfaces. The flow patterns cause the formation of vortices. The shedding of these vortices can induce flow oscillations and pressure instabilities.

the perforation or central cavity of the grain. The hot gas from the slot is turned into a direction toward the nozzle. The flow from the side stream restricts the flow emanating from the upstream side of the perforation and, in effect, reduces the port area. This restriction causes the upstream port pressure to rise; sometimes there is a substantial pressure rise. The interaction of the two subsonic gas flows causes turbulence. Vortices form and are periodically shed or allowed to flow downstream, thereby causing an unstable flow pattern. The vortex shedding patterns can interact with the acoustic instabilities. Reference 13-21 gives a description and Ref. 13-22 a method for analyzing these vortex-shedding phenomena. The remedy usually is to apply inhibitors to some burning surfaces or to change the grain geometry; for example, by increasing the width of the slot, the local velocities are reduced and the vortices become less pronounced.

1. (a) Calculate the length of a T-burner to give a first natural oscillation of 2000 Hz using a propellant that has a combustion temperature of 2410 K, a specific heat ratio of 1.25, a molecular weight of 25 kg/kg-mol, and a burning rate of 10.0 mm/ sec at a pressure of 68 atm. The T-burner is connected to a large surge tank and prepressurized with nitrogen gas to 68 atm. The propellant disks are 20 mm thick. Make a sketch to indicate the T-burner dimensions, including the disks. (b) If the target frequencies are reached when the propellant is 50% burned, what will be the frequency at propellant burnout? Answers: (a) Length before applying propellant = 0.270 m; (b) frequency at burnout = 1854 Hz.

2. An igniter is needed for a rocket motor similar to one shown in Fig. 11-1. Igniters have been designed by various oversimplified design rules such as Fig. 13-3. The motor has an internal grain cavity volume of 0.055 m3 and an initial burning surface of 0.72 m2. The proposed igniter propellant has these characteristics: combustion temperature 2500 K and an energy release of about 40 J/kg-sec. Calculate the minimum required igniter propellant mass (a) if the cavity has to be pressurized to about 2 atm (ignore heat losses); (b) if only 6% of the igniter gas energy is absorbed at the burning surface, and it requires about 20 cal/cm2-sec to ignite in about 0.13 sec.

3. Using the data from Fig. 13^1, plot the total heat flux absorbed per unit area versus pressure to achieve ignition with the energy needed to ignite being just above the deflagration limit. Then, for 0.75 atm, plot the total energy needed versus ignition time. Give a verbal interpretation of the results and trend for each of the two curves.

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