St Radial

FIGURE 9-4. Simplified representation of transverse pressure oscillation modes at two time intervals in a cylindrical combustion chamber. The solid line curves indicate pressures greater than the normal or mean operating pressure and the dashed lines indicate lower pressures. The N-N lines show the node locations for these wave modes.

is usually achieved by redesign of the injector rather than by the application of baffles or absorbers.

Some combustion instabilities can be induced by pulsations in the liquid flow originating in turbopumps. Unsteady liquid flow can be caused by irregular cavitation at the leading edge of the inducer impellers or the main pump impellers. Also, when an impeller's trailing edge passes a rib or stationary vane of the volute, a small pressure perturbation always occurs in the liquid flow that travels downstream to the injector. These two types of pressure fluctuation can be greatly amplified if they coincide with the natural frequency of combustion vibrations in the chamber.

The estimated natural frequencies can be determined from the wavelength /, or the distance traveled per cycle, and the acoustic velocity a (see Eq. 3-10). The frequency, or number of cycles per second, is where k is the specific heat ratio, R' the universal gas constant, 9J? the estimated molecular weight of the hot chamber gases, and T the local average absolute temperature. The length of wave travel depends on the vibrational mode, as shown in Fig. 9-4. Smaller chambers give higher frequencies.

Table 9-3 shows a list of estimated vibration frequencies for the Vulcain HM 60 rocket thrust chamber; it operates with liquid hydrogen and liquid oxygen propellants at a vacuum thrust of 1008 kN, a nominal chamber pressure of 10 MPa, and a nominal mixture ratio of 5.6 (see Ref. 9-13). The data in the table are based on acoustic measurements at ambient conditions with corrections for an appropriate sonic velocity correlation; since the chamber has a shallow conical shape and no discrete converging nozzle section, the purely longitudinal vibration modes would be weak; in fact, no pure longitudinal modes were detected.

Figure 9-5 shows a series of time-sequenced diagrams of frequency-pressure-amplitude measurements taken in the oxygen injector manifold of the Vulcain HM 60 engine during the first 8 sec of a static thrust chamber test while operating at off-nominal design conditions. Chugging can be seen at low

TABLE 9-3. Estimated Acoustic Hot Gas Frequencies for Nominal Chamber Operating Conditions for the Vulcain HM-60 Thrust Chamber frequency = aj I = (1 /l)JkTR'/m

Mode'

Frequency

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