Extended Solid Rocket Nozzles

Po'Pa

Figure 4.9 Performance comparison of comparable bell, aerospike, and ideal nozzles in the earth's atmosphere (the ideal nozzle as in Figs. 4.6 and 4.8).

stagnation pressure po to the ambient pressure pa. The data are for the same values of the effective ratio of the specific heats, y = 1.25, and of the area ratio Aex/A* = 50 that were used to construct Figs. 4.6 and 4.8. The curve labeled "ideal nozzle" represents the case of one-dimensional flow of an ideal gas without losses.

4.6.1 Comparison of Different Types of Nozzles

Including all losses, typical thrust ratios of aerospike and of bell nozzles are shown in Fig. 4.9 for comparison with the ideal nozzle. The improved performance in the atmosphere of the aerospike (and, similarly, of the expansion-deflection nozzle) in comparison with the bell nozzle is evident.

Also indicated in Fig. 4.9 is the performance at sea level. In this case, an upstream stagnation pressure of 2200 N/cm2 (the combustion chamber pressure of the U.S. Space Shuttle main engines) is assumed. It may be noted for comparison that if the same rocket motor and nozzle were operated in the atmosphere of Mars (ambient atmospheric pressure at Mars mean radius = 4.9 mbar = 490 N/m2, hence about 0.5% of the pressure at earth sea level), the thrust of a bell nozzle would be close to 99% of the vacuum thrust.

When bell nozzles are used in launch vehicles, the throat-to-exit-plane area ratio needs to be chosen as a compromise between what would be optimal for performance in the lower atmosphere and optimal for the higher atmosphere or in vacuum.

At the earth's sea level, for the ideal bell nozzle of Figs. 4.6 and 4.8 and a combustion chamber stagnation pressure of 2200 N/cm2, the thrust would

Annular throat

Nozzle base

Inner free-jet boundary

Outer free-jet boundary ~~

Toroidal Aerospike

Figure 4.10 Flow field of an aerospike nozzle in the atmosphere. From Ref. 2, Huzel, D. K. et al., "Modern Engineering for the Design of Liquid Propel-lant Rocket Engines." Courtesy Rocketdyne Division of Rockwell International. Copyright © 1992, AIAA—reprinted with permission.

Annular throat

Nozzle base

Inner free-jet boundary

\ Secondary flow

Primary flow

Outer free-jet boundary ~~

Subsonic recirculating flow

Trailing shock —

Figure 4.10 Flow field of an aerospike nozzle in the atmosphere. From Ref. 2, Huzel, D. K. et al., "Modern Engineering for the Design of Liquid Propel-lant Rocket Engines." Courtesy Rocketdyne Division of Rockwell International. Copyright © 1992, AIAA—reprinted with permission.

be 86% of the vacuum thrust. At the density scale height of the atmosphere (i.e., at 9290 m altitude), the thrust would already be 96% of the vacuum thrust.

Again taking as an example the Space Shuttle main engines, their nozzle exit pressure is about 0.08 atm. They do not approach the ideal expansion condition until an altitude of 18 km is reached. The loss of thrust at sea level compared with vacuum is about 20%. This loss of thrust of the main engines is tolerable because the solid-propellant boosters (which are designed for low-altitude performance) provide 80% of the liftoff thrust.

Aerospike nozzles have a more complex flow pattern, as indicated schematically in Fig. 4.10 for the case of an axially symmetric configuration. The combustion gas exits from the annular combustion chamber and throat to form a jet that is bounded partially by the surface of the spike and partially by the separation surface formed with the atmospheric air. The deflection of the combustion gas by the spike produces Mach compression cones that then coalesce into an oblique shock cone. The pressure of the gas on the spike contributes substantially to the total thrust.

Depending on altitude and vehicle velocity, the flow pattern changes and adapts to the variable air pressure. Because the combustion chamber and the throat have a large diameter, the aerospike nozzle tends to be somewhat heavier than a corresponding bell nozzle with its smaller throat diameter. Nevertheless, the aerospike nozzle is often preferred because of its superior adaptability to different atmospheric pressures. Truncation of the aerospike saves weight but produces a wake region with some attendant losses. With proper design, this loss can be kept small.

Expansion-deflection nozzles (Fig. 4.7) have configurations that are intermediate between those of bell and aerospike nozzles. The flow tends to close quickly behind the plug, creating a low-pressure wake. This reduces the thrust significantly, unless either gas from the turbo-pump system or air is bled into the wake.

Solid-Propellant

Solid-Propellant

Nozzle Shape Rocket
Figure 4.11 Solid-propellant rocket motor with extendable exit cone. (Courtesy of United Technologies Chemical Systems Division, U.S.A.)

Extendable exit cones (Fig. 4.11) have already been mentioned. They are suitable for ablatively or radiatively cooled nozzles; regenerative cooling as illustrated in Fig. 4.2 is evidently not practical.

Engines that are designed exclusively for operating in space in principle would require testing in a vacuum chamber. Because of the practical impossibility of providing ground test facilities with the required pumping rates, large space engines therefore must be tested at atmospheric conditions. If the nozzles designed for space operations were used in such tests, the nozzles might operate in a strongly overexpanded mode with internal shocks and flow separation. It may then be necessary to ground test the engines with nozzles that have an exit-plane-to-throat area ratio smaller than the design value and to rely on analytical methods to predict the thrust that will be obtained in space.

4.7 Two- and Three-Dimensional Effects

4.7.1 Nozzle Internal Shocks

The occurrence of internal shocks in the nozzle at high overexpansion was already mentioned in Sect. 4.4.4. The discussion there, however, was only qualitative. In fact, rather than a normal shock, there tends to be flow separation, coupled to one or more oblique shocks. Wakes at approximately ambient pressure will be formed downstream of the line of separation so that the nozzle will no longer flow full (Fig. 4.12). The flow will be unsteady, with a separation line that oscillates and with shocks and wakes that often rotate. The engines cannot be operated in this range of overexpansion,

Under Expanded Nozzle
Figure 4.12 Schematic of strongly overexpanded bell nozzle with flow separation and oblique shock.

not only because of the drastic loss in thrust but also because of the often destructive engine vibrations that are induced by the nonsteady flow.

An empirical relation, applicable to bell nozzles, states that flow separation in the nozzle is likely to occur when

where a varies from about 0.25 to 0.35. This condition is known as the Summerfield criterion. The range for which it applies at typical operating conditions is indicated in Fig. 4.8.

Of lesser practical significance are the two- and three-dimensional flow patterns downstream of the nozzle exit plane. If the flow is underexpanded, the plume will contain a series of Mach cones (the characteristics of the hyperbolic equation that governs the flow) that interact with each other and reflect at the gas-air boundary. In the overexpanded case, oblique shocks, combined with expansion and compression Mach cones, occur that interact with each other and reflect at the jet boundary, forming an approximately diamond-shaped pattern. The gas in the plume may have cooled to the point where, because of partial condensation of the combustion gas, the shocks become visible.

4.7.2 Plume Deflection

At or near the vacuum condition, parts of the plume near the nozzle exit may be so strongly deflected that they impinge on nearby surfaces of the spacecraft. The resulting contamination by the combustion gas can increase the absorption of solar radiation, thereby raising the temperature of the spacecraft. Often more critical is the contamination by the plume of the surfaces of optical scientific instruments and of spacecraft components such as earth sensors.

An estimate of the effect can be obtained by using well-known results from the continuum, supersonic flow of the turning of a gas at the edge of a boundary. Figure 4.13 illustrates this case for an assumed nozzle exit plane Mach number of 2.00 and a ratio of the specific heats of 1.25. When

- Stream Lines N

Mach Lines ^

.V Nozzle

Exit Plane

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