Erosive burning

The two-dimensional nature of the process initially forced semiempiricism upon theoretical descriptions of erosive burning. The first proposed empirical burning-rate formulas were of the form 

FIGURE 7.5. Schematic diagram of a laterally burning charge in a solid propellant rocket motor. 

Equations (45) and (46) are only two of many formulas that have been used to describe erosive burning [8]. Most of the formulas that have been suggested are based on physical concepts of influences of crossflow on propellant burning. Among these concepts is the idea that high external velocities produce a turbulent boundary layer (see Chapter 12) on the propellant surface and thereby effectively increase the thermal diffusivity of the gas, which in turn increases the rate of heat transfer to the propellant and hence the burning rate [99]. The idea that turbulent convective heat transfer from the hot combustion products outside the boundary layer provides an additive contribution to the heat flux reaching the propellant surface and, 

Although the most recent studies of erosive burning [102]-[110] have helped greatly to improve our understanding of the process, the theoretical problems remain difficult. Even in laminar boundary-layer flows, erosive burning of solid propellants presents one of the more challenging problems because simplifications achievable for nonpremixed combustion (Chapter 

Sutton, Rocket Propulsion Elements, New York Wiley, 1949 3d ed., 1963, Chapters 10-12, 310-387. 

Huggett, Combustion of Solid Propellants, in Combustion Processes, vol. II of High Speed Aerodynamics and Jet Propulsion, B. Lewis, R. N. Pease, and H. S. Taylor, eds. Princeton Princeton University Press, 1956, 514-574. 

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A. Jankowski, Mechanism of Erosive Burning of Solid Rocket Propellants , ArchProcesowSpalonia 3 (3), 249-77 (1972)... 

A discussion of the theory of erosion burning (wherein the flow of combustion products increases the rate of proplnt burning) confirms the role of the Pobednostev criteria relative to such burnings... 

Green (G3) has proposed an alternate approach based on the concept of a critical mass-velocity required to produce a Mach number of 1 in a constant-area channel. Green showed this approach was able to correlate the erosive-burning data he obtained for both a double-base propellant and a composite propellant. 

Generally speaking, these studies of erosive burning have been able to correlate the observed effects. Until the structure of the combustion zone is defined and quantitatively characterized in detail, it would appear that the currently available bases for correlating erosive-burning data are adequate. 

Fig. 13.6 Erosive ratio and threshold velocity of erosive burning for high-energy, reference, and low-energy double-base propellants, showing that the low-energy propellant is most sensitive to the convective heat flux.

Though erosive burning is highly dependent on the cross-flow velocity, the physical structure of the propellant also plays a dominant role in determining the erosive... 

Fig.13.8 Erosive burning model calculation and experimental data for erosive ratio as a function of gas flow velocity or mass flow velocity.

Fig. 13.21 shows another example of oscillatory burning of an RDX-AP composite propellant containing 0.40% A1 particles. The combustion pressure chosen for the burning was 4.5 MPa. The DC component trace indicates that the onset of the instability is 0.31 s after ignition, and that the instability lasts for 0.67 s. The pressure instability then suddenly ceases and the pressure returns to the designed pressure of 4.5 MPa. Close examination of the anomalous bandpass-filtered pressure traces reveals that the excited frequencies in the circular port are between 10 kHz and 30 kHz. The AC components below 10 kHz and above 30 kHz are not excited, as shown in Fig. 13.21. The frequency spectrum of the observed combustion instability is shown in Fig. 13.22. Here, the calculated frequency of the standing waves in the rocket motor is shown as a function of the inner diameter of the port and frequency. The sonic speed is assumed to be 1000 m s and I = 0.25 m. The most excited frequency is 25 kHz, followed by 18 kHz and 32 kHz. When the observed frequencies are compared with the calculated acoustic frequencies shown in Fig. 13.23, the dominant frequency is seen to be that of the first radial mode, with possible inclusion of the second and third tangential modes. The increased DC pressure between 0.31 s and 0.67 s is considered to be caused by a velocity-coupled oscillatory combustion. Such a velocity-coupled oscillation tends to induce erosive burning along the port surface. The maximum amplitude of the AC component pressure is 3.67 MPa between 20 kHz and 30 kHz. - ...

Razdan, M. K., and Kuo, K. K., Erosive Burning of Solid Propellants, Eundamen-tals of Solid-Propellant Combustion, Chapter 10, Vol. 90, Progress in Astronautics and Aeronautics, AlAA (Eds. ... 

Ishihara, A., and Kubota, N., Erosive Burning Mechanism of Double-Base Propellants, 21 St Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, PA (1986), pp. 1975-1981. 

Table 14.3 Parameter values of an erosive-burning test motor.

It is evident that erosive burning occurs only in the inihal stage of combustion and diminishes about 0.5 s after ignition in each of the cases shown in Fig. 14.19 the burning pressure then returns to the designed pressure, For example, the head-end pressure reaches more than 3.5 times the designed pressure of = 5 M Pa just after ignition at L/D =16, but the pressure decreases rapidly thereafter and the propellant continues to burn at constant pressure, p,.. ... 

The pressure peaks observed in the combustion tests shown in Fig. 14.19 are computed as a function of L/D as shown in Fig. 14.20. The peak pressures computed by means of the Lenoir-Robillard empirical equation are confirmed by the measured pressure at the head-end of the motor. It is evident thatp values predicted without erosive burning are significantly lower than the measured maximum pressures. Fig. 14.21 shows the erosive ratio, 8 = r/to, as a function of the mass flow rate per unit cross-sectional area in the port, G. The erosive ratio increases with increasing Mach number in the port at constant L/D. 

In order to understand the erosive burning effect in a motor, an overall erosive burning ratio, 8, is defined as... 

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